Subgroups — C₃×#85841 #11903466

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5824	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5580	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5578	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5556	C₂	1	2	yes	maximal, complemented
9	C₃×#5554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5547	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5540	C₂	1	2	yes	maximal, complemented
13	C₃×#5539	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5538	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5531	C₂	1	2	yes	maximal, complemented
18	C₃×#5529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5527	C₂	1	2	yes	maximal, complemented
20	C₃×#5479	C₂	1	2	yes	maximal, complemented
21	C₃×#5479	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#872	C₂	1	2	yes	maximal, complemented
24	C₃×#3475	—	3	1	no	maximal
25	#85841	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
27	C₂×C₃×#237	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×#235	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
31	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
36	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
37	C₃²×#117	C₂²	1	2	yes	complemented
38	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
40	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
41	C₃×#947	C₂²	1	1	yes	characteristic
42	C₃×#946	C₂²	1	1	yes	characteristic
43	C₃×#946	C₂²	1	1	yes	characteristic, complemented
44	C₃×#944	C₂²	1	1	yes	characteristic, complemented
45	C₃×#939	C₂²	1	2	yes	—
46	C₃×#939	C₂²	1	2	yes	complemented
47	C₃×#937	C₂²	1	2	yes	—
48	C₃×#935	C₂²	1	2	yes	complemented
49	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
50	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
51	C₃×#930	C₂²	1	1	yes	characteristic
52	C₃×#930	C₂²	1	2	yes	—
53	C₃×#929	C₂²	1	2	yes	—
54	C₃×#929	C₂²	1	2	yes	complemented
55	C₃×#929	C₂²	1	2	yes	complemented
56	C₃×C₄×#67	C₂²	1	1	yes	characteristic
57	C₃×C₄×#67	C₂²	1	2	yes	—
58	C₃×C₄×#67	C₂²	1	1	yes	characteristic
59	C₃×C₄×#67	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×#67	C₂²	1	2	yes	complemented
61	C₃×C₄×#67	C₂²	1	2	yes	complemented
62	C₃×C₄×#67	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
64	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
65	C₃×#926	C₂²	1	1	yes	characteristic, complemented
66	C₃×#924	C₂²	1	1	yes	characteristic, complemented
67	C₃×#924	C₂²	1	2	yes	complemented
68	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
70	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
71	C₃×#898	C₂²	1	2	yes	complemented
72	C₃×#898	C₂²	1	2	yes	complemented
73	C₃×#897	C₂²	1	1	yes	characteristic
74	C₃×#896	C₂²	1	2	yes	—
75	C₃×#896	C₂²	1	2	yes	complemented
76	C₃×#895	C₂²	1	1	yes	characteristic
77	C₃×#894	C₂²	1	2	yes	—
78	C₃×#894	C₂²	1	2	yes	complemented
79	C₃×#893	C₂²	1	1	yes	characteristic
80	C₃×#892	C₂²	1	1	yes	characteristic, complemented
81	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	C₃×#890	C₂²	1	1	yes	characteristic, complemented
83	C₃×#889	C₂²	1	2	yes	complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#888	C₂²	1	1	yes	characteristic, complemented
86	C₃×#887	C₂²	1	1	yes	characteristic, complemented
87	C₃×#886	C₂²	1	2	yes	—
88	C₃×#885	C₂²	1	2	yes	complemented
89	C₃×#884	C₂²	1	2	yes	complemented
90	C₃×#883	C₂²	1	2	yes	—
91	C₃×#882	C₂²	1	2	yes	—
92	C₃×#67⋊C₄	C₂²	1	2	yes	—
93	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
94	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
95	C₃×#879	C₂²	1	2	yes	complemented
96	C₃×#878	C₂²	1	2	yes	complemented
97	C₃×#878	C₂²	1	2	yes	complemented
98	C₃×#877	C₂²	1	2	yes	complemented
99	C₃×#876	C₂²	1	2	yes	complemented
100	C₃×#876	C₂²	1	2	yes	complemented
101	C₃×#876	C₂²	1	2	yes	complemented
102	C₃×#875	C₂²	1	1	yes	characteristic
103	C₃×#875	C₂²	1	2	yes	complemented
104	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
105	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
106	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
107	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
108	C₃×#872	C₂²	1	2	yes	—
109	C₃×#872	C₂²	1	2	yes	—
110	C₃×#872	C₂²	1	2	yes	—
111	C₃×#872	C₂²	1	1	yes	characteristic
112	C₃×#872	C₂²	1	2	yes	complemented
113	C₃×#872	C₂²	1	2	yes	complemented
114	C₃×#872	C₂²	1	2	yes	complemented
115	C₃×#872	C₂²	1	2	yes	complemented
116	C₃×#872	C₂²	1	1	yes	characteristic, complemented
117	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
118	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
119	C₃×#870	C₂²	1	2	yes	complemented
120	C₃×#870	C₂²	1	1	yes	characteristic, complemented
121	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#556	—	3	1	no	—
126	C₃×#555	—	3	1	no	—
127	C₃×#554	—	3	1	no	—
128	C₃×#553	—	3	2	no	—
129	C₃×#552	—	3	1	no	—
130	C₃×#552	—	3	1	no	—
131	C₃×#552	—	3	2	no	—
132	C₃×#551	—	3	2	no	—
133	C₃×#551	—	3	2	no	—
134	C₃×#547	—	3	1	no	—
135	C₃×#546	—	3	1	no	—
136	C₃×#546	—	3	1	no	—
137	C₃×#533	—	3	1	no	—
138	C₃×#529	—	3	1	no	—
139	C₃×#529	—	3	2	no	—
140	C₃×#529	—	3	2	no	—
141	C₃×#529	—	3	1	no	—
142	C₃×#525	—	3	2	no	—
143	C₃×C₄×#41	—	2	1	no	—
144	C₃×C₄×#41	—	3	1	no	—
145	C₃×C₄×#41	—	3	1	no	—
146	C₃×C₄×#41	D₃	1	1	yes	characteristic, complemented
147	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×C₃×C₄×D₄	—	3	1	no	—
149	C₂×C₃×#117	—	3	2	no	—
150	#5829	C₂×C₃	1	1	yes	characteristic, complemented
151	#5824	C₂×C₃	1	1	yes	characteristic, complemented
152	#5581	C₂×C₃	1	1	yes	characteristic, complemented
153	#5580	C₂×C₃	1	1	yes	characteristic, complemented
154	#5578	C₂×C₃	1	1	yes	characteristic, complemented
155	#5568	C₂×C₃	1	1	yes	characteristic, complemented
156	#5556	C₂×C₃	1	2	yes	complemented
157	#5554	C₂×C₃	1	1	yes	characteristic, complemented
158	#5547	C₂×C₃	1	2	yes	complemented
159	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
160	#5540	C₂×C₃	1	2	yes	complemented
161	#5539	C₂×C₃	1	1	yes	characteristic, complemented
162	#5538	C₂×C₃	1	2	yes	complemented
163	C₄×#237	C₂×C₃	1	1	yes	characteristic, complemented
164	#5532	C₂×C₃	1	1	yes	characteristic, complemented
165	#5531	C₂×C₃	1	2	yes	complemented
166	#5529	C₂×C₃	1	1	yes	characteristic, complemented
167	#5527	C₂×C₃	1	2	yes	complemented
168	#5479	C₂×C₃	1	1	yes	characteristic, complemented
169	#5479	C₂×C₃	1	2	yes	complemented
170	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
171	C₂×#872	C₂×C₃	1	2	yes	complemented
172	C₂³×C₃×D₃	C₂³	1	2	yes	—
173	C₃²×#41	—	2	4	no	—
174	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
175	C₂×C₃²×D₄	C₂³	1	2	yes	—
176	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃²×C₄	C₂³	1	2	yes	—
178	C₂²×C₃²×C₄	C₂³	1	2	yes	—
179	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
180	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
181	C₂²×C₃²×C₄	C₂³	1	2	yes	—
182	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×#67	C₂³	1	2	yes	—
184	C₂×C₃×#67	C₂³	1	2	yes	—
185	C₂×C₃×#67	C₂³	1	1	yes	characteristic
186	C₂×C₃×#67	C₂³	1	1	yes	characteristic
187	C₂×C₃×#67	C₂³	1	2	yes	—
188	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
189	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
190	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
191	C₃×#237	—	2	4	no	—
192	C₃×D₃×D₄	—	2	4	no	—
193	C₃×#235	—	2	4	no	—
194	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
195	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
196	C₂×C₃×D₁₂	C₂³	1	2	yes	—
197	C₂×C₃×C₄×D₃	—	2	8	no	—
198	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
199	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
200	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
203	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
207	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
208	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
209	C₂×C₃×Dic₆	C₂³	1	2	yes	—
210	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
213	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
214	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃²×C₄²	C₂³	1	1	yes	characteristic
218	C₃²×C₄²	C₂³	1	1	yes	characteristic
219	C₃²×C₄²	C₂³	1	2	yes	—
220	C₃²×C₄²	C₂³	1	1	yes	characteristic
221	C₃²×C₄²	C₂³	1	1	yes	characteristic
222	C₃²×C₄²	C₂³	1	2	yes	—
223	C₃²×C₄²	C₂³	1	2	yes	—
224	C₃×#217	C₂³	1	2	yes	—
225	C₃×#217	C₂³	1	2	yes	—
226	C₃×#217	C₂³	1	1	yes	characteristic
227	C₃×#217	C₂³	1	2	yes	—
228	C₃×#217	C₂³	1	1	yes	characteristic
229	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
231	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
233	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
235	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
236	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
237	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
241	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
242	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
243	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
244	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
245	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
246	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
247	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
248	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
249	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
250	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
251	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
252	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
253	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
255	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
256	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
257	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
258	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
260	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
261	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
263	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
264	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
265	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
266	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
267	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
268	C₃×C₄×Dic₃	C₂³	1	2	yes	—
269	C₃×C₄×Dic₃	C₂³	1	2	yes	—
270	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
271	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
272	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
273	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
274	C₃×C₄×Dic₃	C₂³	1	2	yes	—
275	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
276	#3475	—	3	1	no	Sylow
277	C₂×C₃×#41	—	2	1	no	—
278	C₂×C₃×#41	—	3	1	no	—
279	C₂×C₃×#41	—	3	1	no	—
280	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
281	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
282	C₂²×C₃×D₄	—	3	1	no	—
283	C₂³×C₃×C₄	—	3	2	no	—
284	C₂×#237	C₂²×C₃	1	1	yes	characteristic
285	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
286	C₂×#235	C₂²×C₃	1	1	yes	characteristic
287	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
288	C₃×C₄⋊Q₈	—	3	1	no	—
289	C₃×C₄⋊Q₈	—	3	1	no	—
290	C₃×#126	—	3	2	no	—
291	C₃×#126	—	3	2	no	—
292	C₃×#126	—	3	2	no	—
293	C₃×#126	—	3	2	no	—
294	C₃×#126	—	3	2	no	—
295	C₃×#126	—	3	2	no	—
296	C₃×#125	—	3	2	no	—
297	C₃×#125	—	3	2	no	—
298	C₃×#125	—	3	1	no	—
299	C₃×#125	—	3	2	no	—
300	C₃×#125	—	3	1	no	—
301	C₃×#124	—	3	1	no	—
302	C₃×#124	—	3	2	no	—
303	C₃×#124	—	3	1	no	—
304	C₃×#124	—	3	2	no	—
305	C₃×#123	—	3	2	no	—
306	C₃×#123	—	3	2	no	—
307	C₃×#123	—	3	2	no	—
308	C₃×#123	—	3	2	no	—
309	C₃×#123	—	3	2	no	—
310	C₃×#123	—	3	2	no	—
311	C₃×#123	—	3	2	no	—
312	C₃×#123	—	3	2	no	—
313	C₃×C₂²⋊Q₈	—	3	1	no	—
314	C₃×C₂²⋊Q₈	—	3	1	no	—
315	C₃×C₂²⋊Q₈	—	3	1	no	—
316	C₃×C₂²⋊Q₈	—	3	2	no	—
317	C₃×C₂²⋊Q₈	—	3	2	no	—
318	C₃×C₂²⋊Q₈	—	3	2	no	—
319	C₃×C₂²⋊Q₈	—	3	1	no	—
320	C₃×C₂²⋊Q₈	—	3	2	no	—
321	C₃×C₂²⋊Q₈	—	3	2	no	—
322	C₃×#121	—	3	2	no	—
323	C₃×#121	—	3	2	no	—
324	C₃×#121	—	3	2	no	—
325	C₃×#121	—	3	1	no	—
326	C₃×#121	—	3	1	no	—
327	C₃×#121	—	3	2	no	—
328	C₃×#120	—	3	2	no	—
329	C₃×#120	—	3	2	no	—
330	C₃×C₄×Q₈	—	2	1	no	—
331	C₃×C₄×Q₈	—	2	1	no	—
332	C₃×C₄×Q₈	—	3	1	no	—
333	C₃×C₄×Q₈	—	3	1	no	—
334	C₃×C₄×Q₈	—	3	1	no	—
335	C₃×C₄×Q₈	—	3	1	no	—
336	C₃×C₄×Q₈	—	3	2	no	—
337	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
338	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
339	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
340	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
341	C₃×C₄×D₄	—	2	1	no	—
342	C₃×C₄×D₄	—	2	1	no	—
343	C₃×C₄×D₄	—	2	2	no	—
344	C₃×C₄×D₄	—	2	2	no	—
345	C₃×C₄×D₄	—	3	1	no	—
346	C₃×C₄×D₄	—	3	1	no	—
347	C₃×C₄×D₄	—	3	2	no	—
348	C₃×C₄×D₄	—	3	1	no	—
349	C₃×C₄×D₄	—	3	1	no	—
350	C₃×C₄×D₄	—	3	2	no	—
351	C₃×C₄×D₄	—	3	1	no	—
352	C₃×C₄×D₄	—	3	1	no	—
353	C₃×C₄×D₄	—	3	2	no	—
354	C₃×C₄×D₄	—	3	1	no	—
355	C₃×C₄×D₄	—	3	2	no	—
356	C₃×C₄×D₄	—	3	2	no	—
357	C₃×C₄×D₄	—	3	1	no	—
358	C₃×C₄×D₄	—	3	1	no	—
359	C₃×C₄×D₄	—	3	1	no	—
360	C₃×C₄×D₄	—	3	2	no	—
361	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
362	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
363	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
364	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
365	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
366	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
367	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
368	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
369	C₃×#117	—	2	2	no	—
370	C₃×#117	—	2	1	no	—
371	C₃×#117	—	3	1	no	—
372	C₃×#117	—	3	1	no	—
373	C₃×#117	—	3	2	no	—
374	C₃×#117	—	3	1	no	—
375	C₃×#117	—	3	2	no	—
376	C₃×#117	—	3	2	no	—
377	C₃×#117	—	3	2	no	—
378	C₃×#117	—	3	2	no	—
379	C₃×#117	—	3	2	no	—
380	C₃×#117	—	3	2	no	—
381	C₃×#117	—	3	2	no	—
382	C₃×#117	—	3	1	no	—
383	C₃×#117	C₂×D₃	1	2	yes	complemented
384	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
385	C₃×#117	C₂²×C₃	1	2	yes	complemented
386	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
387	C₂×C₃×C₄⋊C₄	—	3	2	no	—
388	C₂×C₃×C₄⋊C₄	—	3	2	no	—
389	C₂×C₃×C₄⋊C₄	—	3	1	no	—
390	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
391	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
392	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
393	C₂×C₃×C₄²	—	2	2	no	—
394	C₂×C₃×C₄²	—	2	1	no	—
395	C₂×C₃×C₄²	—	3	2	no	—
396	C₂×C₃×C₄²	—	3	1	no	—
397	C₂×C₃×C₄²	—	3	1	no	—
398	C₂×C₃×C₄²	C₂×D₃	1	2	yes	complemented
399	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
400	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	complemented
401	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
402	#947	C₂²×C₃	1	1	yes	characteristic
403	#946	C₂²×C₃	1	1	yes	characteristic
404	#946	C₂²×C₃	1	1	yes	characteristic, complemented
405	#944	C₂²×C₃	1	1	yes	characteristic, complemented
406	#939	C₂²×C₃	1	2	yes	—
407	#939	C₂²×C₃	1	2	yes	complemented
408	#937	C₂²×C₃	1	2	yes	—
409	#935	C₂²×C₃	1	2	yes	complemented
410	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
411	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
412	#930	C₂²×C₃	1	1	yes	characteristic
413	#930	C₂²×C₃	1	2	yes	—
414	#929	C₂²×C₃	1	2	yes	—
415	#929	C₂²×C₃	1	2	yes	complemented
416	#929	C₂²×C₃	1	2	yes	complemented
417	C₄×#67	C₂²×C₃	1	1	yes	characteristic
418	C₄×#67	C₂²×C₃	1	1	yes	characteristic
419	C₄×#67	C₂²×C₃	1	2	yes	—
420	C₄×#67	C₂²×C₃	1	1	yes	characteristic, complemented
421	C₄×#67	C₂²×C₃	1	1	yes	characteristic, complemented
422	C₄×#67	C₂²×C₃	1	2	yes	complemented
423	C₄×#67	C₂²×C₃	1	2	yes	complemented
424	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
425	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
426	#926	C₂²×C₃	1	1	yes	characteristic, complemented
427	#924	C₂²×C₃	1	1	yes	characteristic, complemented
428	#924	C₂²×C₃	1	2	yes	complemented
429	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
430	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
431	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
432	#898	C₂²×C₃	1	2	yes	complemented
433	#898	C₂²×C₃	1	2	yes	complemented
434	#897	C₂²×C₃	1	1	yes	characteristic
435	#896	C₂²×C₃	1	2	yes	—
436	#896	C₂²×C₃	1	2	yes	complemented
437	#895	C₂²×C₃	1	1	yes	characteristic
438	#894	C₂²×C₃	1	2	yes	—
439	#894	C₂²×C₃	1	2	yes	complemented
440	#893	C₂²×C₃	1	1	yes	characteristic
441	#892	C₂²×C₃	1	1	yes	characteristic, complemented
442	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
443	#890	C₂²×C₃	1	1	yes	characteristic, complemented
444	#889	C₂²×C₃	1	2	yes	complemented
445	#889	C₂²×C₃	1	2	yes	complemented
446	#888	C₂²×C₃	1	1	yes	characteristic, complemented
447	#887	C₂²×C₃	1	1	yes	characteristic, complemented
448	#886	C₂²×C₃	1	2	yes	—
449	#885	C₂²×C₃	1	2	yes	complemented
450	#884	C₂²×C₃	1	2	yes	complemented
451	#883	C₂²×C₃	1	2	yes	—
452	#882	C₂²×C₃	1	2	yes	—
453	#67⋊C₄	C₂²×C₃	1	2	yes	—
454	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
455	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
456	#879	C₂²×C₃	1	2	yes	complemented
457	#878	C₂²×C₃	1	2	yes	complemented
458	#878	C₂²×C₃	1	2	yes	complemented
459	#877	C₂²×C₃	1	2	yes	complemented
460	#876	C₂²×C₃	1	2	yes	complemented
461	#876	C₂²×C₃	1	2	yes	complemented
462	#876	C₂²×C₃	1	2	yes	complemented
463	#875	C₂²×C₃	1	1	yes	characteristic
464	#875	C₂²×C₃	1	2	yes	complemented
465	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
466	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
467	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
468	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
469	#872	C₂²×C₃	1	1	yes	characteristic
470	#872	C₂²×C₃	1	2	yes	—
471	#872	C₂²×C₃	1	2	yes	—
472	#872	C₂²×C₃	1	2	yes	—
473	#872	C₂²×C₃	1	2	yes	complemented
474	#872	C₂²×C₃	1	2	yes	complemented
475	#872	C₂²×C₃	1	2	yes	complemented
476	#872	C₂²×C₃	1	2	yes	complemented
477	#872	C₂²×C₃	1	1	yes	characteristic, complemented
478	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
479	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
480	#870	C₂²×C₃	1	2	yes	complemented
481	#870	C₂²×C₃	1	1	yes	characteristic, complemented
482	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
483	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
484	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
485	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
486	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
487	C₂³×C₃²	C₂⁴	1	2	yes	—
488	C₂²×C₃×D₃	—	2	4	no	—
489	C₂²×C₃×D₃	—	2	4	no	—
490	C₂²×C₃×D₃	—	4	2	no	—
491	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
492	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
493	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
494	C₃²×Q₈	—	2	2	no	—
495	C₃²×D₄	—	2	4	no	—
496	C₃²×D₄	#41	1	4	yes	complemented
497	C₂×C₃²×C₄	—	2	4	no	—
498	C₂×C₃²×C₄	—	2	2	no	—
499	C₂×C₃²×C₄	—	2	4	no	—
500	C₂×C₃²×C₄	—	2	2	no	—
501	C₂×C₃²×C₄	—	4	2	no	—
502	C₂×C₃²×C₄	—	4	1	no	—
503	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
504	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
507	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
508	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
509	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
510	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
512	C₃×#67	—	2	4	no	—
513	C₃×#67	—	2	4	no	—
514	C₃×#67	—	2	2	no	—
515	C₃×#67	—	2	2	no	—
516	C₃×#67	—	4	2	no	—
517	C₂×C₃×Dic₃	—	2	4	no	—
518	C₂×C₃×Dic₃	—	2	4	no	—
519	C₂×C₃×Dic₃	—	4	2	no	—
520	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
521	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
522	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
523	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
524	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
525	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
526	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
527	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
528	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
529	C₃×D₁₂	—	2	2	no	—
530	C₃×D₁₂	—	2	2	no	—
531	C₃×D₁₂	—	4	2	no	—
532	C₃×C₄×D₃	—	2	4	no	—
533	C₃×C₄×D₃	—	2	4	no	—
534	C₃×C₄×D₃	—	2	2	no	—
535	C₃×C₄×D₃	—	2	2	no	—
536	C₃×C₄×D₃	—	2	2	no	—
537	C₃×C₄×D₃	—	2	4	no	—
538	C₃×C₄×D₃	—	4	1	no	—
539	C₃×C₄×D₃	—	4	1	no	—
540	C₃×C₄×D₃	#41	1	4	yes	complemented
541	C₃×Dic₆	—	2	2	no	—
542	C₃×Dic₆	—	2	2	no	—
543	C₃×Dic₆	—	4	2	no	—
544	#556	—	3	1	no	—
545	#555	—	3	1	no	—
546	#554	—	3	1	no	—
547	#553	—	3	2	no	—
548	#552	—	3	1	no	—
549	#552	—	3	1	no	—
550	#552	—	3	2	no	—
551	#551	—	3	2	no	—
552	#551	—	3	2	no	—
553	#547	—	3	1	no	—
554	#546	—	3	1	no	—
555	#546	—	3	1	no	—
556	#533	—	3	1	no	—
557	#529	—	3	1	no	—
558	#529	—	3	2	no	—
559	#529	—	3	2	no	—
560	#529	—	3	1	no	—
561	#525	—	3	2	no	—
562	C₄×#41	—	3	1	no	—
563	C₄×#41	—	3	1	no	—
564	C₄×#41	C₃×D₃	1	1	yes	characteristic, complemented
565	C₂×C₄×D₄	—	3	1	no	—
566	C₂×#117	—	3	2	no	—
567	C₂⁴×C₃	—	3	2	no	—
568	C₂³×D₃	C₂³×C₃	1	2	yes	—
569	C₃×#41	—	2	8	no	—
570	C₃×#41	—	2	4	no	—
571	C₃×#41	—	2	4	no	—
572	C₃×#41	—	6	4	no	—
573	C₃×#41	—	6	4	no	—
574	C₂×C₃×Q₈	—	2	1	no	—
575	C₂×C₃×Q₈	—	3	1	no	—
576	C₂×C₃×Q₈	—	3	1	no	—
577	C₂×C₃×Q₈	—	3	2	no	—
578	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
579	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
580	C₂×C₃×D₄	—	2	2	no	—
581	C₂×C₃×D₄	—	2	1	no	—
582	C₂×C₃×D₄	—	3	1	no	—
583	C₂×C₃×D₄	—	3	2	no	—
584	C₂×C₃×D₄	—	3	1	no	—
585	C₂×C₃×D₄	—	3	2	no	—
586	C₂×C₃×D₄	—	3	2	no	—
587	C₂×C₃×D₄	—	3	1	no	—
588	C₂×C₃×D₄	—	3	1	no	—
589	C₂×C₃×D₄	—	3	2	no	—
590	C₂×C₃×D₄	—	6	4	no	—
591	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
592	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
593	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
594	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
595	C₂²×C₃×C₄	—	2	2	no	—
596	C₂²×C₃×C₄	—	2	1	no	—
597	C₂²×C₃×C₄	—	2	2	no	—
598	C₂²×C₃×C₄	—	2	1	no	—
599	C₂²×C₃×C₄	—	2	2	no	—
600	C₂²×C₃×C₄	—	2	1	no	—
601	C₂²×C₃×C₄	—	3	1	no	—
602	C₂²×C₃×C₄	—	3	2	no	—
603	C₂²×C₃×C₄	—	3	2	no	—
604	C₂²×C₃×C₄	—	3	2	no	—
605	C₂²×C₃×C₄	—	3	1	no	—
606	C₂²×C₃×C₄	—	3	1	no	—
607	C₂²×C₃×C₄	—	3	2	no	—
608	C₂²×C₃×C₄	—	3	2	no	—
609	C₂²×C₃×C₄	—	3	1	no	—
610	C₂²×C₃×C₄	—	3	2	no	—
611	C₂²×C₃×C₄	—	3	1	no	—
612	C₂²×C₃×C₄	—	3	1	no	—
613	C₂²×C₃×C₄	—	6	8	no	—
614	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
615	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
616	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
617	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
618	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
619	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
620	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
621	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
622	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
623	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
625	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
626	C₂×#67	C₂³×C₃	1	2	yes	—
627	C₂×#67	C₂³×C₃	1	2	yes	—
628	C₂×#67	C₂³×C₃	1	1	yes	characteristic
629	C₂×#67	C₂³×C₃	1	1	yes	characteristic
630	C₂×#67	C₂³×C₃	1	2	yes	—
631	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
632	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
633	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
634	#237	—	2	4	no	—
635	D₃×D₄	—	2	4	no	—
636	#235	—	2	4	no	—
637	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
638	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
639	C₂×D₁₂	C₂³×C₃	1	2	yes	—
640	C₂×C₄×D₃	—	2	8	no	—
641	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
642	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
643	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
644	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
645	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
646	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
647	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
648	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
649	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
650	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
651	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
652	C₂×Dic₆	C₂³×C₃	1	2	yes	—
653	C₃×C₄⋊C₄	—	2	1	no	—
654	C₃×C₄⋊C₄	—	2	1	no	—
655	C₃×C₄⋊C₄	—	2	2	no	—
656	C₃×C₄⋊C₄	—	2	2	no	—
657	C₃×C₄⋊C₄	—	3	1	no	—
658	C₃×C₄⋊C₄	—	3	1	no	—
659	C₃×C₄⋊C₄	—	3	2	no	—
660	C₃×C₄⋊C₄	—	3	2	no	—
661	C₃×C₄⋊C₄	—	3	2	no	—
662	C₃×C₄⋊C₄	—	3	2	no	—
663	C₃×C₄⋊C₄	—	3	2	no	—
664	C₃×C₄⋊C₄	—	3	2	no	—
665	C₃×C₄⋊C₄	—	3	2	no	—
666	C₃×C₄⋊C₄	—	3	1	no	—
667	C₃×C₄⋊C₄	—	3	2	no	—
668	C₃×C₄⋊C₄	—	3	2	no	—
669	C₃×C₄⋊C₄	—	3	1	no	—
670	C₃×C₄⋊C₄	—	3	2	no	—
671	C₃×C₄⋊C₄	—	3	2	no	—
672	C₃×C₄⋊C₄	—	3	2	no	—
673	C₃×C₄⋊C₄	—	3	1	no	—
674	C₃×C₄⋊C₄	—	3	1	no	—
675	C₃×C₄⋊C₄	—	3	1	no	—
676	C₃×C₄⋊C₄	—	3	1	no	—
677	C₃×C₄⋊C₄	—	3	2	no	—
678	C₃×C₄⋊C₄	—	3	2	no	—
679	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
680	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
681	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
682	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
683	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
684	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
685	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
686	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
687	C₃×C₂²⋊C₄	—	2	2	no	—
688	C₃×C₂²⋊C₄	—	2	2	no	—
689	C₃×C₂²⋊C₄	—	2	2	no	—
690	C₃×C₂²⋊C₄	—	3	2	no	—
691	C₃×C₂²⋊C₄	—	3	2	no	—
692	C₃×C₂²⋊C₄	—	3	1	no	—
693	C₃×C₂²⋊C₄	—	3	1	no	—
694	C₃×C₂²⋊C₄	—	3	2	no	—
695	C₃×C₂²⋊C₄	—	3	1	no	—
696	C₃×C₂²⋊C₄	—	3	1	no	—
697	C₃×C₂²⋊C₄	—	3	2	no	—
698	C₃×C₂²⋊C₄	—	3	2	no	—
699	C₃×C₂²⋊C₄	—	3	2	no	—
700	C₃×C₂²⋊C₄	—	3	2	no	—
701	C₃×C₂²⋊C₄	—	3	2	no	—
702	C₃×C₂²⋊C₄	—	3	2	no	—
703	C₃×C₂²⋊C₄	—	3	2	no	—
704	C₃×C₂²⋊C₄	—	3	2	no	—
705	C₃×C₂²⋊C₄	—	3	1	no	—
706	C₃×C₂²⋊C₄	—	3	2	no	—
707	C₃×C₂²⋊C₄	—	3	1	no	—
708	C₃×C₂²⋊C₄	—	3	2	no	—
709	C₃×C₂²⋊C₄	—	3	2	no	—
710	C₃×C₂²⋊C₄	—	3	2	no	—
711	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
712	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
713	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
714	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
715	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
716	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
717	C₃×C₄²	—	2	1	no	—
718	C₃×C₄²	—	2	2	no	—
719	C₃×C₄²	—	2	1	no	—
720	C₃×C₄²	—	2	1	no	—
721	C₃×C₄²	—	2	2	no	—
722	C₃×C₄²	—	2	2	no	—
723	C₃×C₄²	—	2	1	no	—
724	C₃×C₄²	—	3	2	no	—
725	C₃×C₄²	—	3	1	no	—
726	C₃×C₄²	—	3	2	no	—
727	C₃×C₄²	—	3	1	no	—
728	C₃×C₄²	—	3	1	no	—
729	C₃×C₄²	—	3	1	no	—
730	C₃×C₄²	—	3	1	no	—
731	C₃×C₄²	—	3	1	no	—
732	C₃×C₄²	—	3	2	no	—
733	C₃×C₄²	C₂²×D₃	1	2	yes	—
734	C₃×C₄²	C₂²×D₃	1	2	yes	—
735	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
736	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
737	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
738	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
739	C₃×C₄²	C₂²×D₃	1	2	yes	—
740	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
741	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
742	C₃×C₄²	C₂³×C₃	1	2	yes	—
743	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
744	C₃×C₄²	C₂³×C₃	1	2	yes	—
745	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
746	C₃×C₄²	C₂³×C₃	1	2	yes	—
747	#217	C₂³×C₃	1	2	yes	—
748	#217	C₂³×C₃	1	2	yes	—
749	#217	C₂³×C₃	1	1	yes	characteristic
750	#217	C₂³×C₃	1	2	yes	—
751	#217	C₂³×C₃	1	1	yes	characteristic
752	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
753	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
754	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
755	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
756	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
757	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
758	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
759	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
760	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
761	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
762	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
763	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
764	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
765	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
766	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
767	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
768	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
769	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
770	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
771	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
772	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
773	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
775	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
776	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
777	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
778	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
781	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
784	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
785	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
787	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
788	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
789	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
790	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
791	C₄×Dic₃	C₂³×C₃	1	2	yes	—
792	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
793	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
794	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
795	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
796	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
797	C₄×Dic₃	C₂³×C₃	1	2	yes	—
798	C₄×Dic₃	C₂³×C₃	1	2	yes	—
799	C₂²×C₃²	—	2	1	no	—
800	C₂²×C₃²	—	2	2	no	—
801	C₂²×C₃²	—	2	2	no	—
802	C₂²×C₃²	—	2	1	no	—
803	C₂²×C₃²	—	2	1	no	—
804	C₂²×C₃²	C₂×#41	1	4	yes	—
805	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
806	C₂×C₃×D₃	—	2	1	no	—
807	C₂×C₃×D₃	—	2	1	no	—
808	C₂×C₃×D₃	—	2	2	no	—
809	C₂×C₃×D₃	—	2	1	no	—
810	C₂×C₃×D₃	—	2	1	no	—
811	C₂×C₃×D₃	—	2	2	no	—
812	C₂×C₃×D₃	—	2	1	no	—
813	C₂×C₃×D₃	—	2	2	no	—
814	C₂×C₃×D₃	—	4	8	no	—
815	C₂×C₃×D₃	C₂×#41	1	2	yes	—
816	C₃²×C₄	—	2	1	no	—
817	C₃²×C₄	—	2	2	no	—
818	C₃²×C₄	—	2	1	no	—
819	C₃²×C₄	—	2	1	no	—
820	C₃²×C₄	—	2	2	no	—
821	C₃²×C₄	—	2	2	no	—
822	C₃²×C₄	—	2	1	no	—
823	C₃²×C₄	C₂×#41	1	2	yes	—
824	C₃²×C₄	C₂×#41	1	2	yes	—
825	C₃×Dic₃	—	2	1	no	—
826	C₃×Dic₃	—	2	2	no	—
827	C₃×Dic₃	—	2	2	no	—
828	C₃×Dic₃	—	2	1	no	—
829	C₃×Dic₃	—	2	1	no	—
830	C₃×Dic₃	—	2	1	no	—
831	C₃×Dic₃	—	2	2	no	—
832	C₃×Dic₃	—	2	1	no	—
833	C₃×Dic₃	C₂×#41	1	2	yes	—
834	C₂×#41	—	3	1	no	—
835	C₂×#41	—	3	1	no	—
836	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
837	C₂²×D₄	—	3	1	no	—
838	C₂³×C₄	—	3	2	no	—
839	C₄⋊Q₈	—	3	1	no	—
840	C₄⋊Q₈	—	3	1	no	—
841	#126	—	3	2	no	—
842	#126	—	3	2	no	—
843	#126	—	3	2	no	—
844	#126	—	3	2	no	—
845	#126	—	3	2	no	—
846	#126	—	3	2	no	—
847	#125	—	3	2	no	—
848	#125	—	3	1	no	—
849	#125	—	3	2	no	—
850	#125	—	3	2	no	—
851	#125	—	3	1	no	—
852	#124	—	3	1	no	—
853	#124	—	3	2	no	—
854	#124	—	3	1	no	—
855	#124	—	3	2	no	—
856	#123	—	3	2	no	—
857	#123	—	3	2	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	—	3	2	no	—
861	#123	—	3	2	no	—
862	#123	—	3	2	no	—
863	#123	—	3	2	no	—
864	C₂²⋊Q₈	—	3	1	no	—
865	C₂²⋊Q₈	—	3	1	no	—
866	C₂²⋊Q₈	—	3	1	no	—
867	C₂²⋊Q₈	—	3	2	no	—
868	C₂²⋊Q₈	—	3	2	no	—
869	C₂²⋊Q₈	—	3	1	no	—
870	C₂²⋊Q₈	—	3	2	no	—
871	C₂²⋊Q₈	—	3	2	no	—
872	C₂²⋊Q₈	—	3	2	no	—
873	#121	—	3	2	no	—
874	#121	—	3	2	no	—
875	#121	—	3	2	no	—
876	#121	—	3	1	no	—
877	#121	—	3	1	no	—
878	#121	—	3	2	no	—
879	#120	—	3	2	no	—
880	#120	—	3	2	no	—
881	C₄×Q₈	—	3	1	no	—
882	C₄×Q₈	—	3	1	no	—
883	C₄×Q₈	—	3	1	no	—
884	C₄×Q₈	—	3	1	no	—
885	C₄×Q₈	—	3	2	no	—
886	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
887	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
888	C₄×D₄	—	3	1	no	—
889	C₄×D₄	—	3	1	no	—
890	C₄×D₄	—	3	2	no	—
891	C₄×D₄	—	3	2	no	—
892	C₄×D₄	—	3	1	no	—
893	C₄×D₄	—	3	1	no	—
894	C₄×D₄	—	3	1	no	—
895	C₄×D₄	—	3	1	no	—
896	C₄×D₄	—	3	2	no	—
897	C₄×D₄	—	3	1	no	—
898	C₄×D₄	—	3	2	no	—
899	C₄×D₄	—	3	2	no	—
900	C₄×D₄	—	3	1	no	—
901	C₄×D₄	—	3	1	no	—
902	C₄×D₄	—	3	1	no	—
903	C₄×D₄	—	3	2	no	—
904	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
905	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
906	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
907	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
908	#117	—	3	1	no	—
909	#117	—	3	1	no	—
910	#117	—	3	2	no	—
911	#117	—	3	1	no	—
912	#117	—	3	2	no	—
913	#117	—	3	2	no	—
914	#117	—	3	2	no	—
915	#117	—	3	2	no	—
916	#117	—	3	2	no	—
917	#117	—	3	2	no	—
918	#117	—	3	2	no	—
919	#117	—	3	1	no	—
920	#117	C₂×C₃×D₃	1	2	yes	complemented
921	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
922	C₂×C₄⋊C₄	—	3	2	no	—
923	C₂×C₄⋊C₄	—	3	2	no	—
924	C₂×C₄⋊C₄	—	3	1	no	—
925	C₂×C₂²⋊C₄	—	3	2	no	—
926	C₂×C₂²⋊C₄	—	3	2	no	—
927	C₂×C₂²⋊C₄	—	3	2	no	—
928	C₂×C₄²	—	3	2	no	—
929	C₂×C₄²	—	3	1	no	—
930	C₂×C₄²	—	3	1	no	—
931	C₂×C₄²	C₂×C₃×D₃	1	2	yes	complemented
932	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
933	C₂³×C₃	—	2	1	no	—
934	C₂³×C₃	—	2	2	no	—
935	C₂³×C₃	—	3	1	no	—
936	C₂³×C₃	—	3	2	no	—
937	C₂³×C₃	—	3	1	no	—
938	C₂³×C₃	—	6	4	no	—
939	C₂³×C₃	—	6	4	no	—
940	C₂³×C₃	—	12	2	no	—
941	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
942	C₂³×C₃	C₂³×D₃	1	2	yes	—
943	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
944	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
945	C₂²×D₃	—	2	4	no	—
946	C₂²×D₃	—	2	4	no	—
947	C₂²×D₃	—	4	2	no	—
948	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
949	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
950	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
951	C₃×Q₈	—	2	4	no	—
952	C₃×Q₈	—	2	2	no	—
953	C₃×Q₈	—	2	2	no	—
954	C₃×Q₈	—	6	2	no	—
955	C₃×Q₈	—	6	2	no	—
956	C₃×Q₈	—	12	2	no	—
957	C₃×D₄	—	2	8	no	—
958	C₃×D₄	—	2	4	no	—
959	C₃×D₄	—	2	4	no	—
960	C₃×D₄	—	2	4	no	—
961	C₃×D₄	—	6	2	no	—
962	C₃×D₄	—	6	2	no	—
963	C₃×D₄	—	6	2	no	—
964	C₃×D₄	—	6	4	no	—
965	C₃×D₄	—	6	4	no	—
966	C₃×D₄	—	6	2	no	—
967	C₃×D₄	—	12	2	no	—
968	C₃×D₄	—	12	2	no	—
969	C₃×D₄	#235	1	4	yes	complemented
970	C₃×D₄	C₃×#41	1	4	yes	complemented
971	C₂×C₃×C₄	—	2	8	no	—
972	C₂×C₃×C₄	—	2	4	no	—
973	C₂×C₃×C₄	—	2	4	no	—
974	C₂×C₃×C₄	—	2	4	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	2	4	no	—
977	C₂×C₃×C₄	—	2	2	no	—
978	C₂×C₃×C₄	—	2	4	no	—
979	C₂×C₃×C₄	—	2	2	no	—
980	C₂×C₃×C₄	—	2	2	no	—
981	C₂×C₃×C₄	—	2	1	no	—
982	C₂×C₃×C₄	—	2	1	no	—
983	C₂×C₃×C₄	—	2	1	no	—
984	C₂×C₃×C₄	—	2	2	no	—
985	C₂×C₃×C₄	—	2	1	no	—
986	C₂×C₃×C₄	—	2	2	no	—
987	C₂×C₃×C₄	—	2	1	no	—
988	C₂×C₃×C₄	—	2	1	no	—
989	C₂×C₃×C₄	—	2	2	no	—
990	C₂×C₃×C₄	—	3	1	no	—
991	C₂×C₃×C₄	—	3	4	no	—
992	C₂×C₃×C₄	—	3	1	no	—
993	C₂×C₃×C₄	—	3	1	no	—
994	C₂×C₃×C₄	—	3	1	no	—
995	C₂×C₃×C₄	—	3	2	no	—
996	C₂×C₃×C₄	—	3	1	no	—
997	C₂×C₃×C₄	—	3	2	no	—
998	C₂×C₃×C₄	—	3	1	no	—
999	C₂×C₃×C₄	—	3	2	no	—
1000	C₂×C₃×C₄	—	4	4	no	—
1001	C₂×C₃×C₄	—	4	2	no	—
1002	C₂×C₃×C₄	—	4	1	no	—
1003	C₂×C₃×C₄	—	4	2	no	—
1004	C₂×C₃×C₄	—	4	2	no	—
1005	C₂×C₃×C₄	—	4	1	no	—
1006	C₂×C₃×C₄	—	4	2	no	—
1007	C₂×C₃×C₄	—	4	4	no	—
1008	C₂×C₃×C₄	—	6	4	no	—
1009	C₂×C₃×C₄	—	6	4	no	—
1010	C₂×C₃×C₄	—	6	4	no	—
1011	C₂×C₃×C₄	—	6	4	no	—
1012	C₂×C₃×C₄	—	6	2	no	—
1013	C₂×C₃×C₄	—	6	2	no	—
1014	C₂×C₃×C₄	—	6	4	no	—
1015	C₂×C₃×C₄	—	6	2	no	—
1016	C₂×C₃×C₄	—	12	1	no	—
1017	C₂×C₃×C₄	—	12	1	no	—
1018	C₂×C₃×C₄	—	12	2	no	—
1019	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1020	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1021	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1022	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1023	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1024	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1025	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1026	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1027	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1028	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1029	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1030	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1031	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1032	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1033	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1034	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1035	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1036	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1037	#67	—	2	4	no	—
1038	#67	—	2	4	no	—
1039	#67	—	2	2	no	—
1040	#67	—	2	2	no	—
1041	#67	—	4	2	no	—
1042	C₂×Dic₃	—	2	4	no	—
1043	C₂×Dic₃	—	2	4	no	—
1044	C₂×Dic₃	—	4	2	no	—
1045	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1046	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1047	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1048	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1049	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1050	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1051	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1052	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1053	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1054	D₁₂	—	2	2	no	—
1055	D₁₂	—	2	2	no	—
1056	D₁₂	—	4	2	no	—
1057	C₄×D₃	—	2	4	no	—
1058	C₄×D₃	—	2	4	no	—
1059	C₄×D₃	—	2	2	no	—
1060	C₄×D₃	—	2	2	no	—
1061	C₄×D₃	—	2	2	no	—
1062	C₄×D₃	—	2	4	no	—
1063	C₄×D₃	—	4	1	no	—
1064	C₄×D₃	—	4	1	no	—
1065	C₄×D₃	C₃×#41	1	4	yes	complemented
1066	Dic₆	—	2	2	no	—
1067	Dic₆	—	2	2	no	—
1068	Dic₆	—	4	2	no	—
1069	C₂×C₃²	—	2	4	no	—
1070	C₂×C₃²	—	4	1	no	—
1071	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1072	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1073	C₂×C₃²	#585	1	1	yes	characteristic
1074	C₃×D₃	—	2	2	no	—
1075	C₃×D₃	—	4	1	no	—
1076	C₃×D₃	—	4	2	no	—
1077	C₂⁴	—	3	2	no	—
1078	#41	—	2	4	no	—
1079	#41	—	6	4	no	—
1080	#41	—	6	4	no	—
1081	C₂×Q₈	—	3	1	no	—
1082	C₂×Q₈	—	3	1	no	—
1083	C₂×Q₈	—	3	2	no	—
1084	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1085	C₂×D₄	—	3	1	no	—
1086	C₂×D₄	—	3	2	no	—
1087	C₂×D₄	—	3	1	no	—
1088	C₂×D₄	—	3	2	no	—
1089	C₂×D₄	—	3	2	no	—
1090	C₂×D₄	—	3	1	no	—
1091	C₂×D₄	—	3	1	no	—
1092	C₂×D₄	—	3	2	no	—
1093	C₂×D₄	—	6	4	no	—
1094	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1095	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1096	C₂²×C₄	—	3	1	no	—
1097	C₂²×C₄	—	3	2	no	—
1098	C₂²×C₄	—	3	2	no	—
1099	C₂²×C₄	—	3	2	no	—
1100	C₂²×C₄	—	3	1	no	—
1101	C₂²×C₄	—	3	1	no	—
1102	C₂²×C₄	—	3	1	no	—
1103	C₂²×C₄	—	3	2	no	—
1104	C₂²×C₄	—	3	2	no	—
1105	C₂²×C₄	—	3	2	no	—
1106	C₂²×C₄	—	3	1	no	—
1107	C₂²×C₄	—	3	1	no	—
1108	C₂²×C₄	—	6	8	no	—
1109	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1110	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1111	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1113	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1114	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1115	C₄⋊C₄	—	3	1	no	—
1116	C₄⋊C₄	—	3	1	no	—
1117	C₄⋊C₄	—	3	2	no	—
1118	C₄⋊C₄	—	3	2	no	—
1119	C₄⋊C₄	—	3	2	no	—
1120	C₄⋊C₄	—	3	2	no	—
1121	C₄⋊C₄	—	3	2	no	—
1122	C₄⋊C₄	—	3	2	no	—
1123	C₄⋊C₄	—	3	1	no	—
1124	C₄⋊C₄	—	3	2	no	—
1125	C₄⋊C₄	—	3	1	no	—
1126	C₄⋊C₄	—	3	1	no	—
1127	C₄⋊C₄	—	3	1	no	—
1128	C₄⋊C₄	—	3	2	no	—
1129	C₄⋊C₄	—	3	2	no	—
1130	C₄⋊C₄	—	3	1	no	—
1131	C₄⋊C₄	—	3	1	no	—
1132	C₄⋊C₄	—	3	2	no	—
1133	C₄⋊C₄	—	3	2	no	—
1134	C₄⋊C₄	—	3	2	no	—
1135	C₄⋊C₄	—	3	2	no	—
1136	C₄⋊C₄	—	3	2	no	—
1137	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1138	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1139	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1140	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1141	C₂²⋊C₄	—	3	2	no	—
1142	C₂²⋊C₄	—	3	2	no	—
1143	C₂²⋊C₄	—	3	1	no	—
1144	C₂²⋊C₄	—	3	1	no	—
1145	C₂²⋊C₄	—	3	2	no	—
1146	C₂²⋊C₄	—	3	1	no	—
1147	C₂²⋊C₄	—	3	1	no	—
1148	C₂²⋊C₄	—	3	2	no	—
1149	C₂²⋊C₄	—	3	2	no	—
1150	C₂²⋊C₄	—	3	2	no	—
1151	C₂²⋊C₄	—	3	2	no	—
1152	C₂²⋊C₄	—	3	2	no	—
1153	C₂²⋊C₄	—	3	2	no	—
1154	C₂²⋊C₄	—	3	2	no	—
1155	C₂²⋊C₄	—	3	2	no	—
1156	C₂²⋊C₄	—	3	1	no	—
1157	C₂²⋊C₄	—	3	2	no	—
1158	C₂²⋊C₄	—	3	1	no	—
1159	C₂²⋊C₄	—	3	2	no	—
1160	C₂²⋊C₄	—	3	2	no	—
1161	C₂²⋊C₄	—	3	2	no	—
1162	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1163	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1164	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1165	C₄²	—	3	1	no	—
1166	C₄²	—	3	2	no	—
1167	C₄²	—	3	1	no	—
1168	C₄²	—	3	2	no	—
1169	C₄²	—	3	2	no	—
1170	C₄²	—	3	1	no	—
1171	C₄²	—	3	1	no	—
1172	C₄²	—	3	1	no	—
1173	C₄²	—	3	1	no	—
1174	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1175	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1176	C₄²	C₂²×C₃×D₃	1	2	yes	—
1177	C₄²	C₂²×C₃×D₃	1	2	yes	—
1178	C₄²	C₂²×C₃×D₃	1	2	yes	—
1179	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1180	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1181	C₂²×C₃	—	2	2	no	—
1182	C₂²×C₃	—	2	2	no	—
1183	C₂²×C₃	—	2	2	no	—
1184	C₂²×C₃	—	2	2	no	—
1185	C₂²×C₃	—	2	2	no	—
1186	C₂²×C₃	—	2	1	no	—
1187	C₂²×C₃	—	2	1	no	—
1188	C₂²×C₃	—	2	1	no	—
1189	C₂²×C₃	—	2	1	no	—
1190	C₂²×C₃	—	2	1	no	—
1191	C₂²×C₃	—	2	1	no	—
1192	C₂²×C₃	—	2	4	no	—
1193	C₂²×C₃	—	2	1	no	—
1194	C₂²×C₃	—	3	2	no	—
1195	C₂²×C₃	—	4	2	no	—
1196	C₂²×C₃	—	4	2	no	—
1197	C₂²×C₃	—	4	1	no	—
1198	C₂²×C₃	—	4	1	no	—
1199	C₂²×C₃	—	6	1	no	—
1200	C₂²×C₃	—	6	1	no	—
1201	C₂²×C₃	—	6	1	no	—
1202	C₂²×C₃	—	6	2	no	—
1203	C₂²×C₃	—	6	2	no	—
1204	C₂²×C₃	—	6	1	no	—
1205	C₂²×C₃	—	6	1	no	—
1206	C₂²×C₃	—	6	2	no	—
1207	C₂²×C₃	—	12	8	no	—
1208	C₂²×C₃	C₂×#235	1	4	yes	—
1209	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
1210	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1211	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1212	C₂×D₃	—	2	1	no	—
1213	C₂×D₃	—	2	1	no	—
1214	C₂×D₃	—	2	2	no	—
1215	C₂×D₃	—	2	1	no	—
1216	C₂×D₃	—	2	1	no	—
1217	C₂×D₃	—	2	2	no	—
1218	C₂×D₃	—	2	1	no	—
1219	C₂×D₃	—	2	2	no	—
1220	C₂×D₃	—	4	8	no	—
1221	C₂×D₃	C₂×C₃×#41	1	2	yes	—
1222	C₃×C₄	—	2	2	no	—
1223	C₃×C₄	—	2	4	no	—
1224	C₃×C₄	—	2	2	no	—
1225	C₃×C₄	—	2	1	no	—
1226	C₃×C₄	—	2	2	no	—
1227	C₃×C₄	—	2	2	no	—
1228	C₃×C₄	—	2	1	no	—
1229	C₃×C₄	—	2	1	no	—
1230	C₃×C₄	—	2	1	no	—
1231	C₃×C₄	—	2	2	no	—
1232	C₃×C₄	—	2	1	no	—
1233	C₃×C₄	—	2	2	no	—
1234	C₃×C₄	—	2	1	no	—
1235	C₃×C₄	—	2	2	no	—
1236	C₃×C₄	—	2	2	no	—
1237	C₃×C₄	—	2	1	no	—
1238	C₃×C₄	—	2	1	no	—
1239	C₃×C₄	—	2	2	no	—
1240	C₃×C₄	—	2	2	no	—
1241	C₃×C₄	—	3	2	no	—
1242	C₃×C₄	—	4	2	no	—
1243	C₃×C₄	—	4	1	no	—
1244	C₃×C₄	—	4	1	no	—
1245	C₃×C₄	—	4	2	no	—
1246	C₃×C₄	—	6	1	no	—
1247	C₃×C₄	—	6	1	no	—
1248	C₃×C₄	—	6	2	no	—
1249	C₃×C₄	—	6	2	no	—
1250	C₃×C₄	—	6	1	no	—
1251	C₃×C₄	—	6	1	no	—
1252	C₃×C₄	—	6	2	no	—
1253	C₃×C₄	—	6	1	no	—
1254	C₃×C₄	C₂×#235	1	2	yes	—
1255	C₃×C₄	D₃×#41	1	2	yes	—
1256	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1257	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1258	Dic₃	—	2	1	no	—
1259	Dic₃	—	2	2	no	—
1260	Dic₃	—	2	2	no	—
1261	Dic₃	—	2	1	no	—
1262	Dic₃	—	2	1	no	—
1263	Dic₃	—	2	1	no	—
1264	Dic₃	—	2	2	no	—
1265	Dic₃	—	2	1	no	—
1266	Dic₃	C₂×C₃×#41	1	2	yes	—
1267	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
1268	C₂³	—	3	1	no	—
1269	C₂³	—	3	2	no	—
1270	C₂³	—	3	1	no	—
1271	C₂³	—	6	4	no	—
1272	C₂³	—	6	4	no	—
1273	C₂³	—	12	2	no	—
1274	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1275	C₂³	C₂³×C₃×D₃	1	2	yes	—
1276	Q₈	—	2	2	no	—
1277	Q₈	—	6	2	no	—
1278	Q₈	—	6	2	no	—
1279	Q₈	—	12	2	no	—
1280	D₄	—	2	4	no	—
1281	D₄	—	6	2	no	—
1282	D₄	—	6	2	no	—
1283	D₄	—	6	2	no	—
1284	D₄	—	6	4	no	—
1285	D₄	—	6	4	no	—
1286	D₄	—	6	2	no	—
1287	D₄	—	12	2	no	—
1288	D₄	—	12	2	no	—
1289	D₄	C₃×#235	1	4	yes	complemented
1290	C₂×C₄	—	2	4	no	—
1291	C₂×C₄	—	2	2	no	—
1292	C₂×C₄	—	2	4	no	—
1293	C₂×C₄	—	2	2	no	—
1294	C₂×C₄	—	3	1	no	—
1295	C₂×C₄	—	3	4	no	—
1296	C₂×C₄	—	3	1	no	—
1297	C₂×C₄	—	3	1	no	—
1298	C₂×C₄	—	3	1	no	—
1299	C₂×C₄	—	3	2	no	—
1300	C₂×C₄	—	3	1	no	—
1301	C₂×C₄	—	3	2	no	—
1302	C₂×C₄	—	3	1	no	—
1303	C₂×C₄	—	3	2	no	—
1304	C₂×C₄	—	4	1	no	—
1305	C₂×C₄	—	4	2	no	—
1306	C₂×C₄	—	6	4	no	—
1307	C₂×C₄	—	6	4	no	—
1308	C₂×C₄	—	6	4	no	—
1309	C₂×C₄	—	6	4	no	—
1310	C₂×C₄	—	6	2	no	—
1311	C₂×C₄	—	6	2	no	—
1312	C₂×C₄	—	6	4	no	—
1313	C₂×C₄	—	6	2	no	—
1314	C₂×C₄	—	12	1	no	—
1315	C₂×C₄	—	12	1	no	—
1316	C₂×C₄	—	12	2	no	—
1317	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1318	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1319	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1320	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1321	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1322	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1323	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1324	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1325	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1326	C₂×C₃	—	2	4	no	—
1327	C₂×C₃	—	2	4	no	—
1328	C₂×C₃	—	2	1	no	—
1329	C₂×C₃	—	2	1	no	—
1330	C₂×C₃	—	2	1	no	—
1331	C₂×C₃	—	4	4	no	—
1332	C₂×C₃	—	4	2	no	—
1333	C₂×C₃	—	4	1	no	—
1334	C₂×C₃	—	4	1	no	—
1335	C₂×C₃	—	6	2	no	—
1336	C₂×C₃	—	12	2	no	—
1337	C₂×C₃	—	12	1	no	—
1338	C₂×C₃	C₂²×#235	1	1	yes	characteristic
1339	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1340	C₂×C₃	#5964	1	1	yes	characteristic
1341	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1342	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1343	C₂×C₃	C₃×#585	1	1	yes	characteristic
1344	D₃	—	2	2	no	—
1345	D₃	—	4	2	no	—
1346	D₃	—	4	1	no	—
1347	C₂²	—	2	2	no	—
1348	C₂²	—	2	2	no	—
1349	C₂²	—	2	1	no	—
1350	C₂²	—	2	1	no	—
1351	C₂²	—	2	1	no	—
1352	C₂²	—	3	2	no	—
1353	C₂²	—	6	1	no	—
1354	C₂²	—	6	1	no	—
1355	C₂²	—	6	1	no	—
1356	C₂²	—	6	2	no	—
1357	C₂²	—	6	2	no	—
1358	C₂²	—	6	1	no	—
1359	C₂²	—	6	1	no	—
1360	C₂²	—	6	2	no	—
1361	C₂²	—	12	8	no	—
1362	C₂²	C₂×C₃×#235	1	4	yes	—
1363	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1364	C₄	—	2	1	no	—
1365	C₄	—	2	2	no	—
1366	C₄	—	2	2	no	—
1367	C₄	—	2	1	no	—
1368	C₄	—	2	1	no	—
1369	C₄	—	2	1	no	—
1370	C₄	—	2	2	no	—
1371	C₄	—	3	2	no	—
1372	C₄	—	6	1	no	—
1373	C₄	—	6	1	no	—
1374	C₄	—	6	2	no	—
1375	C₄	—	6	2	no	—
1376	C₄	—	6	1	no	—
1377	C₄	—	6	1	no	—
1378	C₄	—	6	2	no	—
1379	C₄	—	6	1	no	—
1380	C₄	C₂×C₃×#235	1	2	yes	—
1381	C₄	C₃×D₃×#41	1	2	yes	—
1382	C₃	—	2	1	no	—
1383	C₃	#85841	1	1	yes	characteristic, direct product factor
1384	C₃	C₃×#3475	1	1	yes	characteristic, complemented
1385	C₂	—	2	4	no	—
1386	C₂	—	4	1	no	—
1387	C₂	—	6	2	no	—
1388	C₂	—	12	2	no	—
1389	C₂	—	12	1	no	—
1390	C₂	C₂²×C₃×#235	1	1	yes	characteristic
1391	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1392	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×C₄×#41	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×C₄×#41	D₃
hypocenter	C₃	C₃×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₄×#41	C₂	semidirect
2. C₃×#5829	C₂	semidirect
3. C₃×#5824	C₂	semidirect
4. C₃×#5581	C₂	semidirect
5. C₃×#5580	C₂	semidirect
6. C₃×#5578	C₂	semidirect
7. C₃×#5568	C₂	semidirect
8. C₃×#5556	C₂	semidirect
9. C₃×#5554	C₂	semidirect
10. C₃×#5547	C₂	semidirect
11. C₃×C₄×D₃×D₄	C₂	semidirect
12. C₃×#5540	C₂	semidirect
13. C₃×#5539	C₂	semidirect
14. C₃×#5538	C₂	semidirect
15. C₃×C₄×#237	C₂	semidirect
16. C₃×#5532	C₂	semidirect
17. C₃×#5531	C₂	semidirect
18. C₃×#5529	C₂	semidirect
19. C₃×#5527	C₂	semidirect
20. C₃×#5479	C₂	semidirect
21. C₃×#5479	C₂	semidirect
22. C₃×C₄×#235	C₂	semidirect
23. C₂×C₃×#872	C₂	semidirect
25. #85841	C₃	direct (N × H)
31. C₃²×C₄×Q₈	C₂²	semidirect
32. C₃²×C₄×Q₈	C₂²	semidirect
35. C₃²×C₄×D₄	C₂²	semidirect
36. C₃²×C₄×D₄	C₂²	semidirect
37. C₃²×#117	C₂²	semidirect
38. C₃²×#117	C₂²	semidirect
39. C₂×C₃²×C₄²	C₂²	semidirect
40. C₂×C₃²×C₄²	C₂²	semidirect
43. C₃×#946	C₂²	semidirect
44. C₃×#944	C₂²	semidirect
46. C₃×#939	C₂²	semidirect
48. C₃×#935	C₂²	semidirect
54. C₃×#929	C₂²	semidirect
55. C₃×#929	C₂²	semidirect
59. C₃×C₄×#67	C₂²	semidirect
60. C₃×C₄×#67	C₂²	semidirect
61. C₃×C₄×#67	C₂²	semidirect
62. C₃×C₄×#67	C₂²	semidirect
65. C₃×#926	C₂²	semidirect
66. C₃×#924	C₂²	semidirect
67. C₃×#924	C₂²	semidirect
68. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
69. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
70. C₂×C₃×C₄×Dic₃	C₂²	semidirect
71. C₃×#898	C₂²	semidirect
72. C₃×#898	C₂²	semidirect
75. C₃×#896	C₂²	semidirect
78. C₃×#894	C₂²	semidirect
80. C₃×#892	C₂²	semidirect
82. C₃×#890	C₂²	semidirect
83. C₃×#889	C₂²	semidirect
84. C₃×#889	C₂²	semidirect
85. C₃×#888	C₂²	semidirect
86. C₃×#887	C₂²	semidirect
88. C₃×#885	C₂²	semidirect
89. C₃×#884	C₂²	semidirect
93. C₃×#67⋊C₄	C₂²	semidirect
95. C₃×#879	C₂²	semidirect
96. C₃×#878	C₂²	semidirect
97. C₃×#878	C₂²	semidirect
98. C₃×#877	C₂²	semidirect
99. C₃×#876	C₂²	semidirect
100. C₃×#876	C₂²	semidirect
101. C₃×#876	C₂²	semidirect
103. C₃×#875	C₂²	semidirect
107. C₃×C₄×D₁₂	C₂²	semidirect
112. C₃×#872	C₂²	semidirect
113. C₃×#872	C₂²	semidirect
114. C₃×#872	C₂²	semidirect
115. C₃×#872	C₂²	semidirect
116. C₃×#872	C₂²	semidirect
118. C₃×C₄²×D₃	C₂²	semidirect
119. C₃×#870	C₂²	semidirect
120. C₃×#870	C₂²	semidirect
121. C₃×C₄×Dic₆	C₂²	semidirect
122. C₃×C₄×Dic₆	C₂²	semidirect
123. C₃×C₄×Dic₆	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
146. C₃×C₄×#41	D₃	semidirect
147. C₃×C₄×#41	C₂×C₃	semidirect
150. #5829	C₂×C₃	semidirect
151. #5824	C₂×C₃	semidirect
152. #5581	C₂×C₃	semidirect
153. #5580	C₂×C₃	semidirect
154. #5578	C₂×C₃	semidirect
155. #5568	C₂×C₃	semidirect
156. #5556	C₂×C₃	semidirect
157. #5554	C₂×C₃	semidirect
158. #5547	C₂×C₃	semidirect
159. C₄×D₃×D₄	C₂×C₃	semidirect
160. #5540	C₂×C₃	semidirect
161. #5539	C₂×C₃	semidirect
162. #5538	C₂×C₃	semidirect
163. C₄×#237	C₂×C₃	semidirect
164. #5532	C₂×C₃	semidirect
165. #5531	C₂×C₃	semidirect
166. #5529	C₂×C₃	semidirect
167. #5527	C₂×C₃	semidirect
168. #5479	C₂×C₃	semidirect
169. #5479	C₂×C₃	semidirect
170. C₄×#235	C₂×C₃	semidirect
171. C₂×#872	C₂×C₃	semidirect
337. C₃×C₄×Q₈	C₂×D₃	semidirect
338. C₃×C₄×Q₈	C₂×D₃	semidirect
339. C₃×C₄×Q₈	C₂²×C₃	semidirect
340. C₃×C₄×Q₈	C₂²×C₃	semidirect
363. C₃×C₄×D₄	C₂×D₃	semidirect
364. C₃×C₄×D₄	C₂×D₃	semidirect
367. C₃×C₄×D₄	C₂²×C₃	semidirect
368. C₃×C₄×D₄	C₂²×C₃	semidirect
383. C₃×#117	C₂×D₃	semidirect
384. C₃×#117	C₂×D₃	semidirect
385. C₃×#117	C₂²×C₃	semidirect
386. C₃×#117	C₂²×C₃	semidirect
398. C₂×C₃×C₄²	C₂×D₃	semidirect
399. C₂×C₃×C₄²	C₂×D₃	semidirect
400. C₂×C₃×C₄²	C₂²×C₃	semidirect
401. C₂×C₃×C₄²	C₂²×C₃	semidirect
404. #946	C₂²×C₃	semidirect
405. #944	C₂²×C₃	semidirect
407. #939	C₂²×C₃	semidirect
409. #935	C₂²×C₃	semidirect
415. #929	C₂²×C₃	semidirect
416. #929	C₂²×C₃	semidirect
420. C₄×#67	C₂²×C₃	semidirect
421. C₄×#67	C₂²×C₃	semidirect
422. C₄×#67	C₂²×C₃	semidirect
423. C₄×#67	C₂²×C₃	semidirect
426. #926	C₂²×C₃	semidirect
427. #924	C₂²×C₃	semidirect
428. #924	C₂²×C₃	semidirect
429. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
430. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
431. C₂×C₄×Dic₃	C₂²×C₃	semidirect
432. #898	C₂²×C₃	semidirect
433. #898	C₂²×C₃	semidirect
436. #896	C₂²×C₃	semidirect
439. #894	C₂²×C₃	semidirect
441. #892	C₂²×C₃	semidirect
443. #890	C₂²×C₃	semidirect
444. #889	C₂²×C₃	semidirect
445. #889	C₂²×C₃	semidirect
446. #888	C₂²×C₃	semidirect
447. #887	C₂²×C₃	semidirect
449. #885	C₂²×C₃	semidirect
450. #884	C₂²×C₃	semidirect
454. #67⋊C₄	C₂²×C₃	semidirect
456. #879	C₂²×C₃	semidirect
457. #878	C₂²×C₃	semidirect
458. #878	C₂²×C₃	semidirect
459. #877	C₂²×C₃	semidirect
460. #876	C₂²×C₃	semidirect
461. #876	C₂²×C₃	semidirect
462. #876	C₂²×C₃	semidirect
464. #875	C₂²×C₃	semidirect
468. C₄×D₁₂	C₂²×C₃	semidirect
473. #872	C₂²×C₃	semidirect
474. #872	C₂²×C₃	semidirect
475. #872	C₂²×C₃	semidirect
476. #872	C₂²×C₃	semidirect
477. #872	C₂²×C₃	semidirect
479. C₄²×D₃	C₂²×C₃	semidirect
480. #870	C₂²×C₃	semidirect
481. #870	C₂²×C₃	semidirect
482. C₄×Dic₆	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
484. C₄×Dic₆	C₂²×C₃	semidirect
485. C₄×Dic₆	C₂²×C₃	semidirect
496. C₃²×D₄	#41	semidirect
540. C₃×C₄×D₃	#41	semidirect
564. C₄×#41	C₃×D₃	semidirect
886. C₄×Q₈	C₂×C₃×D₃	semidirect
887. C₄×Q₈	C₂×C₃×D₃	semidirect
906. C₄×D₄	C₂×C₃×D₃	semidirect
907. C₄×D₄	C₂×C₃×D₃	semidirect
920. #117	C₂×C₃×D₃	semidirect
921. #117	C₂×C₃×D₃	semidirect
931. C₂×C₄²	C₂×C₃×D₃	semidirect
932. C₂×C₄²	C₂×C₃×D₃	semidirect
969. C₃×D₄	#235	semidirect
970. C₃×D₄	C₃×#41	semidirect
1065. C₄×D₃	C₃×#41	semidirect
1267. C₃²	#3475	semidirect
1289. D₄	C₃×#235	semidirect
1383. C₃	#85841	direct (N × H)
1384. C₃	C₃×#3475	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₄×#41	2
C₃×#5829	2
C₃×#5824	2
C₃×#5581	2
C₃×#5580	2
C₃×#5578	2
C₃×#5568	2
C₃×#5556	2
C₃×#5554	2
C₃×#5547	2
C₃×C₄×D₃×D₄	2
C₃×#5540	2
C₃×#5539	2
C₃×#5538	2
C₃×C₄×#237	2
C₃×#5532	2
C₃×#5531	2
C₃×#5529	2
C₃×#5527	2
C₃×#5479	2
C₃×C₄×#235	2
C₂×C₃×#872	2
C₃×#3475	3
#85841	3

Subgroups — C3×#85841 #11903466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85841 #11903466