Subgroups — C₃×#86687 #11909412

Order 1152.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5829	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5827	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5732	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5731	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5665	C₂	1	2	yes	maximal, complemented
9	C₃×#5658	C₂	1	2	yes	maximal, complemented
10	C₃×#5658	C₂	1	2	yes	maximal, complemented
11	C₃×#5649	C₂	1	2	yes	maximal, complemented
12	C₃×#5643	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5642	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5641	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#5624	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5617	C₂	1	2	yes	maximal, complemented
17	C₃×#5601	C₂	1	2	yes	maximal, complemented
18	C₃×#5565	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5545	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5539	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#5538	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#5513	C₂	1	2	yes	maximal, complemented
23	C₂×C₃×#898	C₂	1	2	yes	maximal, complemented
24	C₃×#3521	—	3	1	no	maximal
25	#86687	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
27	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#123	C₂²	1	2	yes	complemented
31	C₃²×#123	C₂²	1	2	yes	complemented
32	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#121	C₂²	1	2	yes	complemented
35	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
38	C₃×#947	C₂²	1	1	yes	characteristic
39	C₃×#947	C₂²	1	1	yes	characteristic
40	C₃×#946	C₂²	1	1	yes	characteristic
41	C₃×#946	C₂²	1	1	yes	characteristic
42	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₃×#939	C₂²	1	1	yes	characteristic
47	C₃×#939	C₂²	1	2	yes	—
48	C₃×#939	C₂²	1	2	yes	—
49	C₃×#939	C₂²	1	2	yes	complemented
50	C₃×#937	C₂²	1	2	yes	—
51	C₃×#937	C₂²	1	2	yes	—
52	C₃×#935	C₂²	1	1	yes	characteristic, complemented
53	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
54	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
55	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
56	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
57	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
58	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
59	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
60	C₃×#930	C₂²	1	1	yes	characteristic
61	C₃×#930	C₂²	1	1	yes	characteristic
62	C₃×#929	C₂²	1	2	yes	—
63	C₃×#929	C₂²	1	2	yes	—
64	C₃×C₄×#67	C₂²	1	2	yes	—
65	C₃×C₄×#67	C₂²	1	1	yes	characteristic
66	C₃×C₄×#67	C₂²	1	1	yes	characteristic
67	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
68	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
69	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
70	C₃×#926	C₂²	1	2	yes	complemented
71	C₃×#926	C₂²	1	2	yes	complemented
72	C₃×#926	C₂²	1	1	yes	characteristic, complemented
73	C₃×#926	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
75	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
76	C₃×#924	C₂²	1	2	yes	complemented
77	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
79	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
80	C₃×#898	C₂²	1	1	yes	characteristic
81	C₃×#898	C₂²	1	2	yes	—
82	C₃×#898	C₂²	1	2	yes	—
83	C₃×#898	C₂²	1	2	yes	—
84	C₃×#898	C₂²	1	2	yes	—
85	C₃×#898	C₂²	1	2	yes	complemented
86	C₃×#898	C₂²	1	2	yes	complemented
87	C₃×#898	C₂²	1	2	yes	complemented
88	C₃×#898	C₂²	1	2	yes	complemented
89	C₃×#898	C₂²	1	2	yes	complemented
90	C₃×#897	C₂²	1	2	yes	complemented
91	C₃×#897	C₂²	1	2	yes	complemented
92	C₃×#893	C₂²	1	1	yes	characteristic
93	C₃×#892	C₂²	1	1	yes	characteristic
94	C₃×#892	C₂²	1	2	yes	complemented
95	C₃×#892	C₂²	1	2	yes	complemented
96	C₃×#890	C₂²	1	2	yes	complemented
97	C₃×#890	C₂²	1	1	yes	characteristic, complemented
98	C₃×#889	C₂²	1	1	yes	characteristic, complemented
99	C₃×#889	C₂²	1	2	yes	complemented
100	C₃×#889	C₂²	1	2	yes	complemented
101	C₃×#888	C₂²	1	1	yes	characteristic, complemented
102	C₃×#887	C₂²	1	2	yes	complemented
103	C₃×#886	C₂²	1	1	yes	characteristic
104	C₃×#886	C₂²	1	2	yes	—
105	C₃×#886	C₂²	1	2	yes	complemented
106	C₃×#885	C₂²	1	1	yes	characteristic
107	C₃×#885	C₂²	1	2	yes	—
108	C₃×#885	C₂²	1	2	yes	complemented
109	C₃×#883	C₂²	1	2	yes	complemented
110	C₃×#883	C₂²	1	2	yes	complemented
111	C₃×#67⋊C₄	C₂²	1	2	yes	—
112	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
113	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
114	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₃×#879	C₂²	1	1	yes	characteristic, complemented
116	C₃×#879	C₂²	1	2	yes	complemented
117	C₃×#878	C₂²	1	1	yes	characteristic, complemented
118	C₃×#878	C₂²	1	2	yes	complemented
119	C₃×#878	C₂²	1	2	yes	complemented
120	C₃×#877	C₂²	1	2	yes	complemented
121	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
122	C₃×#872	C₂²	1	1	yes	characteristic
123	C₃×#870	C₂²	1	1	yes	characteristic, complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#556	—	3	1	no	—
126	C₃×#556	—	3	1	no	—
127	C₃×#554	—	3	1	no	—
128	C₃×#553	—	3	2	no	—
129	C₃×#553	—	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	—	2	1	no	—
135	C₃×#547	D₃	1	1	yes	characteristic, complemented
136	C₃×#547	C₂×C₃	1	1	yes	characteristic, complemented
137	C₃×#546	—	3	1	no	—
138	C₃×#546	—	3	1	no	—
139	C₃×#542	—	3	1	no	—
140	C₃×#541	—	3	1	no	—
141	C₃×#539	—	3	2	no	—
142	C₃×#538	—	3	2	no	—
143	C₃×#529	—	3	2	no	—
144	C₃×#529	—	3	1	no	—
145	C₃×#529	—	3	1	no	—
146	C₂×C₃×#126	—	3	2	no	—
147	C₃×#520	—	3	1	no	—
148	C₃×#518	—	3	1	no	—
149	C₃×C₄×#41	—	3	1	no	—
150	#5829	C₂×C₃	1	1	yes	characteristic, complemented
151	#5829	C₂×C₃	1	1	yes	characteristic, complemented
152	#5827	C₂×C₃	1	1	yes	characteristic, complemented
153	Dic₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
154	#5732	C₂×C₃	1	1	yes	characteristic, complemented
155	#5731	C₂×C₃	1	1	yes	characteristic, complemented
156	#5665	C₂×C₃	1	2	yes	complemented
157	#5658	C₂×C₃	1	2	yes	complemented
158	#5658	C₂×C₃	1	2	yes	complemented
159	#5649	C₂×C₃	1	2	yes	complemented
160	#5643	C₂×C₃	1	1	yes	characteristic, complemented
161	#5642	C₂×C₃	1	1	yes	characteristic, complemented
162	#5641	C₂×C₃	1	1	yes	characteristic, complemented
163	#5624	C₂×C₃	1	1	yes	characteristic, complemented
164	#5617	C₂×C₃	1	2	yes	complemented
165	#5601	C₂×C₃	1	2	yes	complemented
166	#5565	C₂×C₃	1	1	yes	characteristic, complemented
167	#5545	C₂×C₃	1	1	yes	characteristic, complemented
168	#5539	C₂×C₃	1	1	yes	characteristic, complemented
169	#5538	C₂×C₃	1	1	yes	characteristic, complemented
170	#5513	C₂×C₃	1	2	yes	complemented
171	C₂×#898	C₂×C₃	1	2	yes	complemented
172	C₂³×C₃×D₃	C₂³	1	2	yes	—
173	C₃²×#41	—	2	4	no	—
174	C₃²×#41	—	2	4	no	—
175	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
176	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
177	C₂×C₃²×D₄	C₂³	1	2	yes	—
178	C₂×C₃²×D₄	C₂³	1	2	yes	—
179	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
180	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
181	C₂²×C₃²×C₄	C₂³	1	2	yes	—
182	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
183	C₂²×C₃²×C₄	C₂³	1	2	yes	—
184	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
185	C₂²×C₃²×C₄	C₂³	1	2	yes	—
186	C₂×C₃×#67	C₂³	1	2	yes	—
187	C₂×C₃×#67	C₂³	1	2	yes	—
188	C₂×C₃×#67	C₂³	1	2	yes	—
189	C₂×C₃×#67	C₂³	1	1	yes	characteristic
190	C₂×C₃×#67	C₂³	1	1	yes	characteristic
191	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
192	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
193	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
194	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
195	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
196	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
197	C₃×D₃×D₄	—	2	4	no	—
198	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
201	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
202	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
203	C₂×C₃×Dic₆	C₂³	1	2	yes	—
204	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
205	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
209	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
210	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₄²	C₂³	1	1	yes	characteristic
216	C₃×#217	C₂³	1	1	yes	characteristic
217	C₃×#217	C₂³	1	1	yes	characteristic
218	C₃×#217	C₂³	1	2	yes	—
219	C₃×#217	C₂³	1	2	yes	—
220	C₃×#217	C₂³	1	2	yes	—
221	C₃×#217	C₂³	1	1	yes	characteristic
222	C₃×#217	C₂³	1	2	yes	—
223	C₃×#217	C₂³	1	1	yes	characteristic
224	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
240	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
241	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
242	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
243	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
244	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
255	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
256	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
257	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
258	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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×C₄×Dic₃	C₂³	1	2	yes	—
264	C₃×C₄×Dic₃	C₂³	1	2	yes	—
265	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
266	C₃×C₄×Dic₃	C₂³	1	2	yes	—
267	C₃×C₄×Dic₃	C₂³	1	2	yes	—
268	C₃×C₄×Dic₃	C₂³	1	2	yes	—
269	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
270	C₃×C₄×Dic₃	C₂³	1	2	yes	—
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	#3521	—	3	1	no	Sylow
275	C₂×C₃×#41	—	2	1	no	—
276	C₂×C₃×#41	—	2	1	no	—
277	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
278	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
279	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
281	C₂²×C₃×D₄	—	3	1	no	—
282	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
283	C₃×C₄⋊Q₈	—	2	1	no	—
284	C₃×C₄⋊Q₈	—	3	1	no	—
285	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
286	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₃×#126	—	3	1	no	—
288	C₃×#126	—	3	2	no	—
289	C₃×#126	—	3	2	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×#126	—	3	2	no	—
297	C₃×#126	—	3	1	no	—
298	C₃×#126	—	3	2	no	—
299	C₃×#125	—	3	2	no	—
300	C₃×#125	—	3	1	no	—
301	C₃×#125	—	3	2	no	—
302	C₃×#125	—	3	1	no	—
303	C₃×#125	—	3	2	no	—
304	C₃×#125	—	3	1	no	—
305	C₃×#124	—	3	1	no	—
306	C₃×#124	—	3	1	no	—
307	C₃×#124	—	3	1	no	—
308	C₃×#124	—	3	2	no	—
309	C₃×#124	—	3	2	no	—
310	C₃×#123	—	2	2	no	—
311	C₃×#123	—	2	2	no	—
312	C₃×#123	—	3	1	no	—
313	C₃×#123	—	3	2	no	—
314	C₃×#123	—	3	2	no	—
315	C₃×#123	—	3	2	no	—
316	C₃×#123	—	3	2	no	—
317	C₃×#123	—	3	1	no	—
318	C₃×#123	—	3	2	no	—
319	C₃×#123	—	3	2	no	—
320	C₃×#123	C₂×D₃	1	2	yes	complemented
321	C₃×#123	C₂×D₃	1	2	yes	complemented
322	C₃×#123	C₂²×C₃	1	2	yes	complemented
323	C₃×#123	C₂²×C₃	1	2	yes	complemented
324	C₃×C₂²⋊Q₈	—	2	1	no	—
325	C₃×C₂²⋊Q₈	—	2	1	no	—
326	C₃×C₂²⋊Q₈	—	3	1	no	—
327	C₃×C₂²⋊Q₈	—	3	1	no	—
328	C₃×C₂²⋊Q₈	—	3	2	no	—
329	C₃×C₂²⋊Q₈	—	3	2	no	—
330	C₃×C₂²⋊Q₈	—	3	2	no	—
331	C₃×C₂²⋊Q₈	—	3	1	no	—
332	C₃×C₂²⋊Q₈	—	3	2	no	—
333	C₃×C₂²⋊Q₈	—	3	2	no	—
334	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
335	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
336	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
337	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
338	C₃×#121	—	2	2	no	—
339	C₃×#121	—	3	1	no	—
340	C₃×#121	—	3	2	no	—
341	C₃×#121	—	3	2	no	—
342	C₃×#121	—	3	2	no	—
343	C₃×#121	—	3	1	no	—
344	C₃×#121	—	3	1	no	—
345	C₃×#121	C₂×D₃	1	2	yes	complemented
346	C₃×#121	C₂²×C₃	1	2	yes	complemented
347	C₃×#120	—	3	2	no	—
348	C₃×#120	—	3	2	no	—
349	C₃×C₄×Q₈	—	3	1	no	—
350	C₃×C₄×Q₈	—	3	1	no	—
351	C₃×C₄×Q₈	—	3	1	no	—
352	C₃×C₄×Q₈	—	3	1	no	—
353	C₃×C₄×Q₈	—	3	2	no	—
354	C₃×C₄×Q₈	—	3	1	no	—
355	C₃×C₄×D₄	—	2	1	no	—
356	C₃×C₄×D₄	—	2	1	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	—	3	2	no	—
362	C₃×C₄×D₄	—	3	2	no	—
363	C₃×C₄×D₄	—	3	2	no	—
364	C₃×C₄×D₄	—	3	2	no	—
365	C₃×C₄×D₄	—	3	1	no	—
366	C₃×C₄×D₄	—	3	1	no	—
367	C₃×C₄×D₄	—	3	1	no	—
368	C₃×C₄×D₄	—	3	2	no	—
369	C₃×C₄×D₄	—	3	2	no	—
370	C₃×C₄×D₄	—	3	2	no	—
371	C₃×C₄×D₄	—	3	1	no	—
372	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
373	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
374	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
375	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₃×#117	—	3	2	no	—
377	C₃×#117	—	3	1	no	—
378	C₃×#117	—	3	1	no	—
379	C₃×#117	—	3	2	no	—
380	C₃×#117	—	3	1	no	—
381	C₃×#117	—	3	2	no	—
382	C₃×#117	—	3	2	no	—
383	C₃×#117	—	3	2	no	—
384	C₃×#117	—	3	1	no	—
385	C₂×C₃×C₄⋊C₄	—	2	2	no	—
386	C₂×C₃×C₄⋊C₄	—	3	2	no	—
387	C₂×C₃×C₄⋊C₄	—	3	2	no	—
388	C₂×C₃×C₄⋊C₄	—	3	1	no	—
389	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
390	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
391	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
392	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
393	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
394	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
395	C₂×C₃×C₄²	—	3	2	no	—
396	C₂×C₃×C₄²	—	3	1	no	—
397	#947	C₂²×C₃	1	1	yes	characteristic
398	#947	C₂²×C₃	1	1	yes	characteristic
399	#946	C₂²×C₃	1	1	yes	characteristic
400	#946	C₂²×C₃	1	1	yes	characteristic
401	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
402	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
403	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
404	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
405	#939	C₂²×C₃	1	2	yes	—
406	#939	C₂²×C₃	1	2	yes	—
407	#939	C₂²×C₃	1	1	yes	characteristic
408	#939	C₂²×C₃	1	2	yes	complemented
409	#937	C₂²×C₃	1	2	yes	—
410	#937	C₂²×C₃	1	2	yes	—
411	#935	C₂²×C₃	1	1	yes	characteristic, complemented
412	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
413	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
414	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
415	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
416	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
417	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
418	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
419	#930	C₂²×C₃	1	1	yes	characteristic
420	#930	C₂²×C₃	1	1	yes	characteristic
421	#929	C₂²×C₃	1	2	yes	—
422	#929	C₂²×C₃	1	2	yes	—
423	C₄×#67	C₂²×C₃	1	1	yes	characteristic
424	C₄×#67	C₂²×C₃	1	1	yes	characteristic
425	C₄×#67	C₂²×C₃	1	2	yes	—
426	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
427	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
428	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
429	#926	C₂²×C₃	1	1	yes	characteristic, complemented
430	#926	C₂²×C₃	1	1	yes	characteristic, complemented
431	#926	C₂²×C₃	1	2	yes	complemented
432	#926	C₂²×C₃	1	2	yes	complemented
433	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
434	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
435	#924	C₂²×C₃	1	2	yes	complemented
436	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
437	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
438	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
439	#898	C₂²×C₃	1	2	yes	—
440	#898	C₂²×C₃	1	2	yes	—
441	#898	C₂²×C₃	1	2	yes	—
442	#898	C₂²×C₃	1	2	yes	—
443	#898	C₂²×C₃	1	1	yes	characteristic
444	#898	C₂²×C₃	1	2	yes	complemented
445	#898	C₂²×C₃	1	2	yes	complemented
446	#898	C₂²×C₃	1	2	yes	complemented
447	#898	C₂²×C₃	1	2	yes	complemented
448	#898	C₂²×C₃	1	2	yes	complemented
449	#897	C₂²×C₃	1	2	yes	complemented
450	#897	C₂²×C₃	1	2	yes	complemented
451	#893	C₂²×C₃	1	1	yes	characteristic
452	#892	C₂²×C₃	1	1	yes	characteristic
453	#892	C₂²×C₃	1	2	yes	complemented
454	#892	C₂²×C₃	1	2	yes	complemented
455	#890	C₂²×C₃	1	2	yes	complemented
456	#890	C₂²×C₃	1	1	yes	characteristic, complemented
457	#889	C₂²×C₃	1	2	yes	complemented
458	#889	C₂²×C₃	1	2	yes	complemented
459	#889	C₂²×C₃	1	1	yes	characteristic, complemented
460	#888	C₂²×C₃	1	1	yes	characteristic, complemented
461	#887	C₂²×C₃	1	2	yes	complemented
462	#886	C₂²×C₃	1	2	yes	—
463	#886	C₂²×C₃	1	1	yes	characteristic
464	#886	C₂²×C₃	1	2	yes	complemented
465	#885	C₂²×C₃	1	2	yes	—
466	#885	C₂²×C₃	1	1	yes	characteristic
467	#885	C₂²×C₃	1	2	yes	complemented
468	#883	C₂²×C₃	1	2	yes	complemented
469	#883	C₂²×C₃	1	2	yes	complemented
470	#67⋊C₄	C₂²×C₃	1	2	yes	—
471	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
472	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
473	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
474	#879	C₂²×C₃	1	2	yes	complemented
475	#879	C₂²×C₃	1	1	yes	characteristic, complemented
476	#878	C₂²×C₃	1	2	yes	complemented
477	#878	C₂²×C₃	1	2	yes	complemented
478	#878	C₂²×C₃	1	1	yes	characteristic, complemented
479	#877	C₂²×C₃	1	2	yes	complemented
480	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
481	#872	C₂²×C₃	1	1	yes	characteristic
482	#870	C₂²×C₃	1	1	yes	characteristic, complemented
483	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
484	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
485	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
486	C₂³×C₃²	C₂⁴	1	2	yes	—
487	C₂²×C₃×D₃	—	2	4	no	—
488	C₂²×C₃×D₃	—	4	2	no	—
489	C₂²×C₃×D₃	—	4	2	no	—
490	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
491	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
492	C₃²×Q₈	—	2	2	no	—
493	C₃²×Q₈	—	2	2	no	—
494	C₃²×D₄	—	2	4	no	—
495	C₃²×D₄	—	2	4	no	—
496	C₃²×D₄	—	4	1	no	—
497	C₃²×D₄	#41	1	4	yes	—
498	C₂×C₃²×C₄	—	2	4	no	—
499	C₂×C₃²×C₄	—	2	4	no	—
500	C₂×C₃²×C₄	—	2	2	no	—
501	C₂×C₃²×C₄	—	2	2	no	—
502	C₂×C₃²×C₄	—	4	2	no	—
503	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
504	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
505	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
506	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
507	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
508	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
509	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
510	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
511	C₃×#67	—	2	4	no	—
512	C₃×#67	—	4	1	no	—
513	C₃×#67	—	4	2	no	—
514	C₃×#67	—	4	1	no	—
515	C₃×#67	—	4	2	no	—
516	C₂×C₃×Dic₃	—	4	2	no	—
517	C₂×C₃×Dic₃	—	4	2	no	—
518	C₂×C₃×Dic₃	—	4	1	no	—
519	C₂×C₃×Dic₃	—	4	1	no	—
520	C₂×C₃×Dic₃	—	4	2	no	—
521	C₂×C₃×Dic₃	—	4	2	no	—
522	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
523	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
524	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
525	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
526	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
527	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
528	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
529	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
530	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
531	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
532	C₃×D₁₂	—	2	2	no	—
533	C₃×C₄×D₃	—	2	2	no	—
534	C₃×C₄×D₃	—	4	2	no	—
535	C₃×C₄×D₃	—	4	2	no	—
536	C₃×Dic₆	—	4	2	no	—
537	C₃×Dic₆	—	4	1	no	—
538	#556	—	3	1	no	—
539	#556	—	3	1	no	—
540	#554	—	3	1	no	—
541	#553	—	3	2	no	—
542	#553	—	3	1	no	—
543	#552	—	3	1	no	—
544	#552	—	3	2	no	—
545	#551	—	3	2	no	—
546	#551	—	3	2	no	—
547	#547	C₃×D₃	1	1	yes	characteristic, complemented
548	#546	—	3	1	no	—
549	#546	—	3	1	no	—
550	#542	—	3	1	no	—
551	#541	—	3	1	no	—
552	#539	—	3	2	no	—
553	#538	—	3	2	no	—
554	#529	—	3	2	no	—
555	#529	—	3	1	no	—
556	#529	—	3	1	no	—
557	C₂×#126	—	3	2	no	—
558	#520	—	3	1	no	—
559	#518	—	3	1	no	—
560	C₄×#41	—	3	1	no	—
561	C₂⁴×C₃	—	3	2	no	—
562	C₂³×D₃	C₂³×C₃	1	2	yes	—
563	C₃×#41	—	2	4	no	—
564	C₃×#41	—	2	4	no	—
565	C₃×#41	—	2	4	no	—
566	C₃×#41	—	2	4	no	—
567	C₃×#41	—	4	4	no	—
568	C₃×#41	—	4	4	no	—
569	C₂×C₃×Q₈	—	2	1	no	—
570	C₂×C₃×Q₈	—	2	1	no	—
571	C₂×C₃×Q₈	—	3	1	no	—
572	C₂×C₃×Q₈	—	3	2	no	—
573	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
574	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
575	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₃×D₄	—	2	1	no	—
578	C₂×C₃×D₄	—	2	1	no	—
579	C₂×C₃×D₄	—	2	2	no	—
580	C₂×C₃×D₄	—	2	2	no	—
581	C₂×C₃×D₄	—	3	2	no	—
582	C₂×C₃×D₄	—	3	1	no	—
583	C₂×C₃×D₄	—	3	1	no	—
584	C₂×C₃×D₄	—	3	2	no	—
585	C₂×C₃×D₄	—	3	2	no	—
586	C₂×C₃×D₄	—	3	1	no	—
587	C₂×C₃×D₄	—	6	4	no	—
588	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
589	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
590	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
591	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
592	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
593	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
594	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
596	C₂²×C₃×C₄	—	2	2	no	—
597	C₂²×C₃×C₄	—	2	2	no	—
598	C₂²×C₃×C₄	—	2	2	no	—
599	C₂²×C₃×C₄	—	2	1	no	—
600	C₂²×C₃×C₄	—	2	1	no	—
601	C₂²×C₃×C₄	—	3	2	no	—
602	C₂²×C₃×C₄	—	3	2	no	—
603	C₂²×C₃×C₄	—	3	1	no	—
604	C₂²×C₃×C₄	—	3	1	no	—
605	C₂²×C₃×C₄	—	3	2	no	—
606	C₂²×C₃×C₄	—	3	2	no	—
607	C₂²×C₃×C₄	—	3	1	no	—
608	C₂²×C₃×C₄	—	3	2	no	—
609	C₂²×C₃×C₄	—	3	2	no	—
610	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
611	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
612	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
613	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
614	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
615	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
616	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
617	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
618	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
619	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
620	C₂×#67	C₂³×C₃	1	2	yes	—
621	C₂×#67	C₂³×C₃	1	2	yes	—
622	C₂×#67	C₂³×C₃	1	2	yes	—
623	C₂×#67	C₂³×C₃	1	1	yes	characteristic
624	C₂×#67	C₂³×C₃	1	1	yes	characteristic
625	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
626	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
627	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
628	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
629	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
630	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
631	D₃×D₄	—	2	4	no	—
632	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
633	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
634	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
635	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
636	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
637	C₂×Dic₆	C₂³×C₃	1	2	yes	—
638	C₃×C₄⋊C₄	—	2	1	no	—
639	C₃×C₄⋊C₄	—	2	2	no	—
640	C₃×C₄⋊C₄	—	2	2	no	—
641	C₃×C₄⋊C₄	—	2	2	no	—
642	C₃×C₄⋊C₄	—	2	1	no	—
643	C₃×C₄⋊C₄	—	2	2	no	—
644	C₃×C₄⋊C₄	—	3	1	no	—
645	C₃×C₄⋊C₄	—	3	2	no	—
646	C₃×C₄⋊C₄	—	3	2	no	—
647	C₃×C₄⋊C₄	—	3	2	no	—
648	C₃×C₄⋊C₄	—	3	1	no	—
649	C₃×C₄⋊C₄	—	3	1	no	—
650	C₃×C₄⋊C₄	—	3	2	no	—
651	C₃×C₄⋊C₄	—	3	1	no	—
652	C₃×C₄⋊C₄	—	3	2	no	—
653	C₃×C₄⋊C₄	—	3	1	no	—
654	C₃×C₄⋊C₄	—	3	1	no	—
655	C₃×C₄⋊C₄	—	3	2	no	—
656	C₃×C₄⋊C₄	—	3	1	no	—
657	C₃×C₄⋊C₄	—	3	2	no	—
658	C₃×C₄⋊C₄	—	3	1	no	—
659	C₃×C₄⋊C₄	—	3	1	no	—
660	C₃×C₄⋊C₄	—	3	2	no	—
661	C₃×C₄⋊C₄	—	3	2	no	—
662	C₃×C₄⋊C₄	—	3	1	no	—
663	C₃×C₄⋊C₄	—	3	1	no	—
664	C₃×C₄⋊C₄	—	3	1	no	—
665	C₃×C₄⋊C₄	—	3	2	no	—
666	C₃×C₄⋊C₄	—	3	2	no	—
667	C₃×C₄⋊C₄	—	3	2	no	—
668	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
669	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
670	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
671	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
672	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
673	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
674	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
675	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
676	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
677	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
678	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
679	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
680	C₃×C₂²⋊C₄	—	2	2	no	—
681	C₃×C₂²⋊C₄	—	2	1	no	—
682	C₃×C₂²⋊C₄	—	2	1	no	—
683	C₃×C₂²⋊C₄	—	2	2	no	—
684	C₃×C₂²⋊C₄	—	2	2	no	—
685	C₃×C₂²⋊C₄	—	3	2	no	—
686	C₃×C₂²⋊C₄	—	3	1	no	—
687	C₃×C₂²⋊C₄	—	3	2	no	—
688	C₃×C₂²⋊C₄	—	3	2	no	—
689	C₃×C₂²⋊C₄	—	3	2	no	—
690	C₃×C₂²⋊C₄	—	3	1	no	—
691	C₃×C₂²⋊C₄	—	3	1	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	1	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	2	no	—
706	C₃×C₂²⋊C₄	—	3	2	no	—
707	C₃×C₂²⋊C₄	—	3	2	no	—
708	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
709	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
710	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
711	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
712	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
713	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
714	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
715	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
716	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
717	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
718	C₃×C₄²	—	2	1	no	—
719	C₃×C₄²	—	3	1	no	—
720	C₃×C₄²	—	3	1	no	—
721	C₃×C₄²	—	3	1	no	—
722	C₃×C₄²	—	3	2	no	—
723	C₃×C₄²	—	3	2	no	—
724	C₃×C₄²	—	3	1	no	—
725	C₃×C₄²	—	3	2	no	—
726	C₃×C₄²	—	3	2	no	—
727	C₃×C₄²	—	3	2	no	—
728	C₃×C₄²	—	3	2	no	—
729	C₃×C₄²	—	3	1	no	—
730	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
731	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
732	#217	C₂³×C₃	1	1	yes	characteristic
733	#217	C₂³×C₃	1	1	yes	characteristic
734	#217	C₂³×C₃	1	2	yes	—
735	#217	C₂³×C₃	1	2	yes	—
736	#217	C₂³×C₃	1	2	yes	—
737	#217	C₂³×C₃	1	1	yes	characteristic
738	#217	C₂³×C₃	1	2	yes	—
739	#217	C₂³×C₃	1	1	yes	characteristic
740	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
741	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
742	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
743	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
744	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
745	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
746	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
747	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
748	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
749	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
750	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
751	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
752	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
753	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
754	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
755	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
756	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
757	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
758	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
759	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
760	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
761	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
762	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
763	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
764	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
765	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
766	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
767	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
768	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
769	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
770	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
771	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
772	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
773	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
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	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
780	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
781	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
782	C₄×Dic₃	C₂³×C₃	1	2	yes	—
783	C₄×Dic₃	C₂³×C₃	1	2	yes	—
784	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
785	C₄×Dic₃	C₂³×C₃	1	2	yes	—
786	C₄×Dic₃	C₂³×C₃	1	2	yes	—
787	C₄×Dic₃	C₂³×C₃	1	2	yes	—
788	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
789	C₄×Dic₃	C₂³×C₃	1	2	yes	—
790	C₂²×C₃²	—	2	2	no	—
791	C₂²×C₃²	—	2	2	no	—
792	C₂²×C₃²	—	2	1	no	—
793	C₂²×C₃²	—	2	1	no	—
794	C₂²×C₃²	—	2	1	no	—
795	C₂²×C₃²	—	2	1	no	—
796	C₂²×C₃²	—	2	1	no	—
797	C₂²×C₃²	—	2	1	no	—
798	C₂²×C₃²	C₂×#41	1	4	yes	—
799	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
800	C₂×C₃×D₃	—	2	1	no	—
801	C₂×C₃×D₃	—	2	2	no	—
802	C₂×C₃×D₃	—	2	2	no	—
803	C₂×C₃×D₃	—	2	2	no	—
804	C₂×C₃×D₃	—	2	1	no	—
805	C₂×C₃×D₃	—	2	1	no	—
806	C₂×C₃×D₃	—	8	4	no	—
807	C₃²×C₄	—	2	1	no	—
808	C₃²×C₄	—	2	1	no	—
809	C₃²×C₄	—	2	1	no	—
810	C₃²×C₄	—	2	2	no	—
811	C₃²×C₄	—	2	2	no	—
812	C₃²×C₄	—	2	1	no	—
813	C₃²×C₄	—	2	2	no	—
814	C₃²×C₄	C₂×#41	1	2	yes	—
815	C₃×Dic₃	—	2	1	no	—
816	C₃×Dic₃	—	2	1	no	—
817	C₃×Dic₃	—	2	1	no	—
818	C₃×Dic₃	—	2	2	no	—
819	C₃×Dic₃	—	2	1	no	—
820	C₃×Dic₃	—	2	1	no	—
821	C₃×Dic₃	—	2	2	no	—
822	C₃×Dic₃	—	2	1	no	—
823	C₃×Dic₃	—	2	1	no	—
824	C₃×Dic₃	—	2	2	no	—
825	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
826	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
827	C₂²×D₄	—	3	1	no	—
828	C₄⋊Q₈	—	3	1	no	—
829	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
830	#126	—	3	1	no	—
831	#126	—	3	2	no	—
832	#126	—	3	2	no	—
833	#126	—	3	2	no	—
834	#126	—	3	2	no	—
835	#126	—	3	2	no	—
836	#126	—	3	2	no	—
837	#126	—	3	2	no	—
838	#126	—	3	2	no	—
839	#126	—	3	2	no	—
840	#126	—	3	1	no	—
841	#126	—	3	2	no	—
842	#125	—	3	2	no	—
843	#125	—	3	1	no	—
844	#125	—	3	1	no	—
845	#125	—	3	2	no	—
846	#125	—	3	2	no	—
847	#125	—	3	1	no	—
848	#124	—	3	1	no	—
849	#124	—	3	1	no	—
850	#124	—	3	2	no	—
851	#124	—	3	1	no	—
852	#124	—	3	2	no	—
853	#123	—	3	1	no	—
854	#123	—	3	2	no	—
855	#123	—	3	2	no	—
856	#123	—	3	2	no	—
857	#123	—	3	1	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	—	3	2	no	—
861	#123	C₂×C₃×D₃	1	2	yes	complemented
862	#123	C₂×C₃×D₃	1	2	yes	complemented
863	C₂²⋊Q₈	—	3	1	no	—
864	C₂²⋊Q₈	—	3	1	no	—
865	C₂²⋊Q₈	—	3	2	no	—
866	C₂²⋊Q₈	—	3	2	no	—
867	C₂²⋊Q₈	—	3	2	no	—
868	C₂²⋊Q₈	—	3	1	no	—
869	C₂²⋊Q₈	—	3	2	no	—
870	C₂²⋊Q₈	—	3	2	no	—
871	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
872	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
873	#121	—	3	1	no	—
874	#121	—	3	2	no	—
875	#121	—	3	2	no	—
876	#121	—	3	2	no	—
877	#121	—	3	1	no	—
878	#121	—	3	1	no	—
879	#121	C₂×C₃×D₃	1	2	yes	complemented
880	#120	—	3	2	no	—
881	#120	—	3	2	no	—
882	C₄×Q₈	—	3	1	no	—
883	C₄×Q₈	—	3	1	no	—
884	C₄×Q₈	—	3	1	no	—
885	C₄×Q₈	—	3	1	no	—
886	C₄×Q₈	—	3	2	no	—
887	C₄×Q₈	—	3	1	no	—
888	C₄×D₄	—	3	1	no	—
889	C₄×D₄	—	3	2	no	—
890	C₄×D₄	—	3	1	no	—
891	C₄×D₄	—	3	2	no	—
892	C₄×D₄	—	3	2	no	—
893	C₄×D₄	—	3	1	no	—
894	C₄×D₄	—	3	2	no	—
895	C₄×D₄	—	3	2	no	—
896	C₄×D₄	—	3	1	no	—
897	C₄×D₄	—	3	1	no	—
898	C₄×D₄	—	3	1	no	—
899	C₄×D₄	—	3	2	no	—
900	C₄×D₄	—	3	2	no	—
901	C₄×D₄	—	3	2	no	—
902	C₄×D₄	—	3	1	no	—
903	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
904	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
905	#117	—	3	2	no	—
906	#117	—	3	1	no	—
907	#117	—	3	1	no	—
908	#117	—	3	2	no	—
909	#117	—	3	1	no	—
910	#117	—	3	2	no	—
911	#117	—	3	2	no	—
912	#117	—	3	2	no	—
913	#117	—	3	1	no	—
914	C₂×C₄⋊C₄	—	3	2	no	—
915	C₂×C₄⋊C₄	—	3	1	no	—
916	C₂×C₄⋊C₄	—	3	2	no	—
917	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
918	C₂×C₂²⋊C₄	—	3	2	no	—
919	C₂×C₂²⋊C₄	—	3	2	no	—
920	C₂×C₂²⋊C₄	—	3	2	no	—
921	C₂×C₂²⋊C₄	—	3	2	no	—
922	C₂×C₄²	—	3	2	no	—
923	C₂×C₄²	—	3	1	no	—
924	C₂³×C₃	—	2	2	no	—
925	C₂³×C₃	—	2	1	no	—
926	C₂³×C₃	—	2	1	no	—
927	C₂³×C₃	—	3	1	no	—
928	C₂³×C₃	—	3	2	no	—
929	C₂³×C₃	—	6	4	no	—
930	C₂³×C₃	—	12	2	no	—
931	C₂³×C₃	—	12	2	no	—
932	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
933	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
934	C₂³×C₃	C₂³×D₃	1	2	yes	—
935	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
936	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
937	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
938	C₂²×D₃	—	2	4	no	—
939	C₂²×D₃	—	4	2	no	—
940	C₂²×D₃	—	4	2	no	—
941	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
942	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
943	C₃×Q₈	—	2	2	no	—
944	C₃×Q₈	—	2	2	no	—
945	C₃×Q₈	—	2	2	no	—
946	C₃×Q₈	—	2	2	no	—
947	C₃×Q₈	—	4	2	no	—
948	C₃×Q₈	—	4	2	no	—
949	C₃×Q₈	—	12	2	no	—
950	C₃×Q₈	—	12	1	no	—
951	C₃×D₄	—	2	4	no	—
952	C₃×D₄	—	2	4	no	—
953	C₃×D₄	—	2	4	no	—
954	C₃×D₄	—	2	4	no	—
955	C₃×D₄	—	2	4	no	—
956	C₃×D₄	—	4	4	no	—
957	C₃×D₄	—	4	4	no	—
958	C₃×D₄	—	4	1	no	—
959	C₃×D₄	—	4	1	no	—
960	C₃×D₄	—	4	2	no	—
961	C₃×D₄	—	6	4	no	—
962	C₃×D₄	—	6	2	no	—
963	C₃×D₄	—	12	2	no	—
964	C₃×D₄	—	12	1	no	—
965	C₃×D₄	—	12	2	no	—
966	C₃×D₄	—	12	1	no	—
967	C₃×D₄	#237	1	4	yes	—
968	C₃×D₄	C₃×#41	1	4	yes	—
969	C₂×C₃×C₄	—	2	4	no	—
970	C₂×C₃×C₄	—	2	4	no	—
971	C₂×C₃×C₄	—	2	4	no	—
972	C₂×C₃×C₄	—	2	4	no	—
973	C₂×C₃×C₄	—	2	2	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	2	2	no	—
977	C₂×C₃×C₄	—	2	1	no	—
978	C₂×C₃×C₄	—	2	1	no	—
979	C₂×C₃×C₄	—	2	1	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	2	no	—
984	C₂×C₃×C₄	—	2	2	no	—
985	C₂×C₃×C₄	—	3	1	no	—
986	C₂×C₃×C₄	—	3	1	no	—
987	C₂×C₃×C₄	—	3	1	no	—
988	C₂×C₃×C₄	—	3	2	no	—
989	C₂×C₃×C₄	—	3	1	no	—
990	C₂×C₃×C₄	—	3	2	no	—
991	C₂×C₃×C₄	—	3	1	no	—
992	C₂×C₃×C₄	—	3	1	no	—
993	C₂×C₃×C₄	—	3	1	no	—
994	C₂×C₃×C₄	—	3	2	no	—
995	C₂×C₃×C₄	—	4	2	no	—
996	C₂×C₃×C₄	—	4	2	no	—
997	C₂×C₃×C₄	—	4	4	no	—
998	C₂×C₃×C₄	—	4	4	no	—
999	C₂×C₃×C₄	—	4	2	no	—
1000	C₂×C₃×C₄	—	4	2	no	—
1001	C₂×C₃×C₄	—	4	4	no	—
1002	C₂×C₃×C₄	—	6	2	no	—
1003	C₂×C₃×C₄	—	12	2	no	—
1004	C₂×C₃×C₄	—	12	2	no	—
1005	C₂×C₃×C₄	—	12	1	no	—
1006	C₂×C₃×C₄	—	12	2	no	—
1007	C₂×C₃×C₄	—	12	2	no	—
1008	C₂×C₃×C₄	—	12	2	no	—
1009	C₂×C₃×C₄	—	12	1	no	—
1010	C₂×C₃×C₄	—	12	2	no	—
1011	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1012	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1013	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1014	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1015	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1016	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1017	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1019	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1020	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1021	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1022	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1023	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1024	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1025	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1026	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1027	#67	—	2	4	no	—
1028	#67	—	4	1	no	—
1029	#67	—	4	2	no	—
1030	#67	—	4	1	no	—
1031	#67	—	4	2	no	—
1032	C₂×Dic₃	—	4	2	no	—
1033	C₂×Dic₃	—	4	2	no	—
1034	C₂×Dic₃	—	4	1	no	—
1035	C₂×Dic₃	—	4	1	no	—
1036	C₂×Dic₃	—	4	2	no	—
1037	C₂×Dic₃	—	4	2	no	—
1038	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1039	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1040	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1041	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1042	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1043	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1044	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1045	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1046	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1047	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1048	D₁₂	—	2	2	no	—
1049	C₄×D₃	—	2	2	no	—
1050	C₄×D₃	—	4	2	no	—
1051	C₄×D₃	—	4	2	no	—
1052	Dic₆	—	4	2	no	—
1053	Dic₆	—	4	1	no	—
1054	C₂×C₃²	—	2	4	no	—
1055	C₂×C₃²	—	4	1	no	—
1056	C₂×C₃²	—	4	1	no	—
1057	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1058	C₂×C₃²	#585	1	1	yes	characteristic
1059	C₂×C₃²	#585	1	1	yes	characteristic
1060	C₃×D₃	—	4	2	no	—
1061	C₃×D₃	—	4	1	no	—
1062	C₂⁴	—	3	2	no	—
1063	#41	—	2	4	no	—
1064	#41	—	2	4	no	—
1065	C₂×Q₈	—	3	1	no	—
1066	C₂×Q₈	—	3	2	no	—
1067	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1068	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1069	C₂×D₄	—	3	2	no	—
1070	C₂×D₄	—	3	1	no	—
1071	C₂×D₄	—	3	1	no	—
1072	C₂×D₄	—	3	2	no	—
1073	C₂×D₄	—	3	2	no	—
1074	C₂×D₄	—	3	1	no	—
1075	C₂×D₄	—	6	4	no	—
1076	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1077	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1078	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1079	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1080	C₂²×C₄	—	3	2	no	—
1081	C₂²×C₄	—	3	2	no	—
1082	C₂²×C₄	—	3	1	no	—
1083	C₂²×C₄	—	3	1	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	—	3	2	no	—
1086	C₂²×C₄	—	3	1	no	—
1087	C₂²×C₄	—	3	2	no	—
1088	C₂²×C₄	—	3	2	no	—
1089	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1090	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1091	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1092	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1093	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1094	C₄⋊C₄	—	3	1	no	—
1095	C₄⋊C₄	—	3	2	no	—
1096	C₄⋊C₄	—	3	1	no	—
1097	C₄⋊C₄	—	3	1	no	—
1098	C₄⋊C₄	—	3	2	no	—
1099	C₄⋊C₄	—	3	1	no	—
1100	C₄⋊C₄	—	3	2	no	—
1101	C₄⋊C₄	—	3	2	no	—
1102	C₄⋊C₄	—	3	2	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	1	no	—
1105	C₄⋊C₄	—	3	1	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	1	no	—
1108	C₄⋊C₄	—	3	1	no	—
1109	C₄⋊C₄	—	3	2	no	—
1110	C₄⋊C₄	—	3	2	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	—	3	2	no	—
1113	C₄⋊C₄	—	3	1	no	—
1114	C₄⋊C₄	—	3	2	no	—
1115	C₄⋊C₄	—	3	1	no	—
1116	C₄⋊C₄	—	3	1	no	—
1117	C₄⋊C₄	—	3	2	no	—
1118	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1119	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1120	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1121	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1122	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1123	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	—	3	1	no	—
1126	C₂²⋊C₄	—	3	2	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	2	no	—
1129	C₂²⋊C₄	—	3	1	no	—
1130	C₂²⋊C₄	—	3	1	no	—
1131	C₂²⋊C₄	—	3	1	no	—
1132	C₂²⋊C₄	—	3	1	no	—
1133	C₂²⋊C₄	—	3	2	no	—
1134	C₂²⋊C₄	—	3	1	no	—
1135	C₂²⋊C₄	—	3	1	no	—
1136	C₂²⋊C₄	—	3	1	no	—
1137	C₂²⋊C₄	—	3	2	no	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	—	3	2	no	—
1140	C₂²⋊C₄	—	3	2	no	—
1141	C₂²⋊C₄	—	3	2	no	—
1142	C₂²⋊C₄	—	3	2	no	—
1143	C₂²⋊C₄	—	3	2	no	—
1144	C₂²⋊C₄	—	3	2	no	—
1145	C₂²⋊C₄	—	3	2	no	—
1146	C₂²⋊C₄	—	3	2	no	—
1147	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1148	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1149	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1150	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1151	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1152	C₄²	—	3	1	no	—
1153	C₄²	—	3	1	no	—
1154	C₄²	—	3	1	no	—
1155	C₄²	—	3	2	no	—
1156	C₄²	—	3	2	no	—
1157	C₄²	—	3	1	no	—
1158	C₄²	—	3	2	no	—
1159	C₄²	—	3	2	no	—
1160	C₄²	—	3	2	no	—
1161	C₄²	—	3	2	no	—
1162	C₄²	—	3	1	no	—
1163	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1164	C₂²×C₃	—	2	2	no	—
1165	C₂²×C₃	—	2	2	no	—
1166	C₂²×C₃	—	2	2	no	—
1167	C₂²×C₃	—	2	2	no	—
1168	C₂²×C₃	—	2	1	no	—
1169	C₂²×C₃	—	2	1	no	—
1170	C₂²×C₃	—	2	1	no	—
1171	C₂²×C₃	—	2	1	no	—
1172	C₂²×C₃	—	2	1	no	—
1173	C₂²×C₃	—	2	1	no	—
1174	C₂²×C₃	—	2	1	no	—
1175	C₂²×C₃	—	2	1	no	—
1176	C₂²×C₃	—	2	1	no	—
1177	C₂²×C₃	—	2	1	no	—
1178	C₂²×C₃	—	2	1	no	—
1179	C₂²×C₃	—	2	1	no	—
1180	C₂²×C₃	—	2	4	no	—
1181	C₂²×C₃	—	2	1	no	—
1182	C₂²×C₃	—	4	2	no	—
1183	C₂²×C₃	—	4	2	no	—
1184	C₂²×C₃	—	4	1	no	—
1185	C₂²×C₃	—	4	1	no	—
1186	C₂²×C₃	—	4	1	no	—
1187	C₂²×C₃	—	4	1	no	—
1188	C₂²×C₃	—	4	1	no	—
1189	C₂²×C₃	—	4	1	no	—
1190	C₂²×C₃	—	6	1	no	—
1191	C₂²×C₃	—	6	2	no	—
1192	C₂²×C₃	—	6	2	no	—
1193	C₂²×C₃	—	6	1	no	—
1194	C₂²×C₃	—	6	2	no	—
1195	C₂²×C₃	—	6	1	no	—
1196	C₂²×C₃	—	24	4	no	—
1197	C₂²×C₃	C₂×#237	1	4	yes	—
1198	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
1199	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1200	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1201	C₂×D₃	—	2	1	no	—
1202	C₂×D₃	—	2	2	no	—
1203	C₂×D₃	—	2	2	no	—
1204	C₂×D₃	—	2	2	no	—
1205	C₂×D₃	—	2	1	no	—
1206	C₂×D₃	—	2	1	no	—
1207	C₂×D₃	—	8	4	no	—
1208	C₃×C₄	—	2	2	no	—
1209	C₃×C₄	—	2	1	no	—
1210	C₃×C₄	—	2	1	no	—
1211	C₃×C₄	—	2	2	no	—
1212	C₃×C₄	—	2	2	no	—
1213	C₃×C₄	—	2	1	no	—
1214	C₃×C₄	—	2	2	no	—
1215	C₃×C₄	—	2	1	no	—
1216	C₃×C₄	—	2	1	no	—
1217	C₃×C₄	—	2	1	no	—
1218	C₃×C₄	—	2	2	no	—
1219	C₃×C₄	—	2	2	no	—
1220	C₃×C₄	—	2	1	no	—
1221	C₃×C₄	—	2	2	no	—
1222	C₃×C₄	—	2	1	no	—
1223	C₃×C₄	—	2	2	no	—
1224	C₃×C₄	—	4	1	no	—
1225	C₃×C₄	—	4	1	no	—
1226	C₃×C₄	—	4	2	no	—
1227	C₃×C₄	—	4	2	no	—
1228	C₃×C₄	—	4	2	no	—
1229	C₃×C₄	—	4	1	no	—
1230	C₃×C₄	—	6	1	no	—
1231	C₃×C₄	—	6	1	no	—
1232	C₃×C₄	—	6	1	no	—
1233	C₃×C₄	—	6	2	no	—
1234	C₃×C₄	—	6	1	no	—
1235	C₃×C₄	—	6	2	no	—
1236	C₃×C₄	—	6	1	no	—
1237	C₃×C₄	—	6	2	no	—
1238	C₃×C₄	—	6	1	no	—
1239	C₃×C₄	—	6	1	no	—
1240	C₃×C₄	C₂×#237	1	2	yes	—
1241	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1242	Dic₃	—	2	1	no	—
1243	Dic₃	—	2	1	no	—
1244	Dic₃	—	2	1	no	—
1245	Dic₃	—	2	2	no	—
1246	Dic₃	—	2	1	no	—
1247	Dic₃	—	2	1	no	—
1248	Dic₃	—	2	2	no	—
1249	Dic₃	—	2	1	no	—
1250	Dic₃	—	2	1	no	—
1251	Dic₃	—	2	2	no	—
1252	C₃²	#3521	1	1	yes	characteristic, complemented, Sylow
1253	C₂³	—	3	1	no	—
1254	C₂³	—	3	2	no	—
1255	C₂³	—	6	4	no	—
1256	C₂³	—	12	2	no	—
1257	C₂³	—	12	2	no	—
1258	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1259	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1260	C₂³	C₂³×C₃×D₃	1	2	yes	—
1261	Q₈	—	2	2	no	—
1262	Q₈	—	2	2	no	—
1263	Q₈	—	12	2	no	—
1264	Q₈	—	12	1	no	—
1265	D₄	—	2	4	no	—
1266	D₄	—	2	4	no	—
1267	D₄	—	4	1	no	—
1268	D₄	—	6	4	no	—
1269	D₄	—	6	2	no	—
1270	D₄	—	12	2	no	—
1271	D₄	—	12	1	no	—
1272	D₄	—	12	2	no	—
1273	D₄	—	12	1	no	—
1274	D₄	C₃×#237	1	4	yes	—
1275	C₂×C₄	—	2	4	no	—
1276	C₂×C₄	—	2	4	no	—
1277	C₂×C₄	—	2	2	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	3	1	no	—
1280	C₂×C₄	—	3	1	no	—
1281	C₂×C₄	—	3	1	no	—
1282	C₂×C₄	—	3	2	no	—
1283	C₂×C₄	—	3	1	no	—
1284	C₂×C₄	—	3	2	no	—
1285	C₂×C₄	—	3	1	no	—
1286	C₂×C₄	—	3	1	no	—
1287	C₂×C₄	—	3	1	no	—
1288	C₂×C₄	—	3	2	no	—
1289	C₂×C₄	—	4	2	no	—
1290	C₂×C₄	—	6	2	no	—
1291	C₂×C₄	—	12	2	no	—
1292	C₂×C₄	—	12	2	no	—
1293	C₂×C₄	—	12	1	no	—
1294	C₂×C₄	—	12	2	no	—
1295	C₂×C₄	—	12	2	no	—
1296	C₂×C₄	—	12	2	no	—
1297	C₂×C₄	—	12	1	no	—
1298	C₂×C₄	—	12	2	no	—
1299	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1300	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1301	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1302	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1303	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1304	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1305	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1306	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1307	C₂×C₃	—	2	4	no	—
1308	C₂×C₃	—	2	4	no	—
1309	C₂×C₃	—	2	1	no	—
1310	C₂×C₃	—	2	1	no	—
1311	C₂×C₃	—	2	1	no	—
1312	C₂×C₃	—	4	4	no	—
1313	C₂×C₃	—	4	1	no	—
1314	C₂×C₃	—	4	1	no	—
1315	C₂×C₃	—	4	1	no	—
1316	C₂×C₃	—	4	1	no	—
1317	C₂×C₃	—	8	1	no	—
1318	C₂×C₃	—	8	1	no	—
1319	C₂×C₃	—	12	1	no	—
1320	C₂×C₃	—	12	2	no	—
1321	C₂×C₃	C₂²×#237	1	1	yes	characteristic
1322	C₂×C₃	#5964	1	1	yes	characteristic
1323	C₂×C₃	#5968	1	1	yes	characteristic
1324	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1325	C₂×C₃	C₃×#585	1	1	yes	characteristic
1326	C₂×C₃	C₃×#585	1	1	yes	characteristic
1327	D₃	—	4	1	no	—
1328	D₃	—	4	2	no	—
1329	C₂²	—	2	2	no	—
1330	C₂²	—	2	2	no	—
1331	C₂²	—	2	1	no	—
1332	C₂²	—	2	1	no	—
1333	C₂²	—	2	1	no	—
1334	C₂²	—	2	1	no	—
1335	C₂²	—	2	1	no	—
1336	C₂²	—	2	1	no	—
1337	C₂²	—	6	1	no	—
1338	C₂²	—	6	2	no	—
1339	C₂²	—	6	2	no	—
1340	C₂²	—	6	1	no	—
1341	C₂²	—	6	2	no	—
1342	C₂²	—	6	1	no	—
1343	C₂²	—	24	4	no	—
1344	C₂²	C₂×C₃×#237	1	4	yes	—
1345	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1346	C₄	—	2	1	no	—
1347	C₄	—	2	1	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	2	no	—
1350	C₄	—	2	1	no	—
1351	C₄	—	2	2	no	—
1352	C₄	—	2	1	no	—
1353	C₄	—	6	1	no	—
1354	C₄	—	6	1	no	—
1355	C₄	—	6	1	no	—
1356	C₄	—	6	2	no	—
1357	C₄	—	6	1	no	—
1358	C₄	—	6	2	no	—
1359	C₄	—	6	1	no	—
1360	C₄	—	6	2	no	—
1361	C₄	—	6	1	no	—
1362	C₄	—	6	1	no	—
1363	C₄	C₂×C₃×#237	1	2	yes	—
1364	C₃	—	2	1	no	—
1365	C₃	#86687	1	1	yes	characteristic, direct product factor
1366	C₃	C₃×#3521	1	1	yes	characteristic, complemented
1367	C₂	—	2	4	no	—
1368	C₂	—	4	1	no	—
1369	C₂	—	4	1	no	—
1370	C₂	—	12	1	no	—
1371	C₂	—	12	2	no	—
1372	C₂	C₂²×C₃×#237	1	1	yes	characteristic
1373	C₂	C₃×#5964	1	1	yes	characteristic
1374	C₂	C₃×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#547	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#547	D₃
hypocenter	C₃	C₃×#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#547

Complements

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

N	H ≅ G/N	type
1. C₃²×#547	C₂	semidirect
2. C₃×#5829	C₂	semidirect
3. C₃×#5829	C₂	semidirect
4. C₃×#5827	C₂	semidirect
5. C₃×Dic₃×#41	C₂	semidirect
6. C₃×#5732	C₂	semidirect
7. C₃×#5731	C₂	semidirect
8. C₃×#5665	C₂	semidirect
9. C₃×#5658	C₂	semidirect
10. C₃×#5658	C₂	semidirect
11. C₃×#5649	C₂	semidirect
12. C₃×#5643	C₂	semidirect
13. C₃×#5642	C₂	semidirect
14. C₃×#5641	C₂	semidirect
15. C₃×#5624	C₂	semidirect
16. C₃×#5617	C₂	semidirect
17. C₃×#5601	C₂	semidirect
18. C₃×#5565	C₂	semidirect
19. C₃×#5545	C₂	semidirect
20. C₃×#5539	C₂	semidirect
21. C₃×#5538	C₂	semidirect
22. C₃×#5513	C₂	semidirect
23. C₂×C₃×#898	C₂	semidirect
25. #86687	C₃	direct (N × H)
29. C₃²×C₄⋊Q₈	C₂²	semidirect
30. C₃²×#123	C₂²	semidirect
31. C₃²×#123	C₂²	semidirect
32. C₃²×C₂²⋊Q₈	C₂²	semidirect
33. C₃²×C₂²⋊Q₈	C₂²	semidirect
34. C₃²×#121	C₂²	semidirect
36. C₃²×C₄×D₄	C₂²	semidirect
37. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
42. C₃×Q₈×Dic₃	C₂²	semidirect
43. C₃×Q₈×Dic₃	C₂²	semidirect
44. C₃×Q₈×Dic₃	C₂²	semidirect
45. C₃×Q₈×Dic₃	C₂²	semidirect
49. C₃×#939	C₂²	semidirect
52. C₃×#935	C₂²	semidirect
56. C₃×D₄×Dic₃	C₂²	semidirect
57. C₃×D₄×Dic₃	C₂²	semidirect
58. C₃×D₄×Dic₃	C₂²	semidirect
59. C₃×D₄×Dic₃	C₂²	semidirect
70. C₃×#926	C₂²	semidirect
71. C₃×#926	C₂²	semidirect
72. C₃×#926	C₂²	semidirect
73. C₃×#926	C₂²	semidirect
74. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
75. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
76. C₃×#924	C₂²	semidirect
77. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
78. C₂×C₃×C₄×Dic₃	C₂²	semidirect
79. C₂×C₃×C₄×Dic₃	C₂²	semidirect
85. C₃×#898	C₂²	semidirect
86. C₃×#898	C₂²	semidirect
87. C₃×#898	C₂²	semidirect
88. C₃×#898	C₂²	semidirect
89. C₃×#898	C₂²	semidirect
90. C₃×#897	C₂²	semidirect
91. C₃×#897	C₂²	semidirect
94. C₃×#892	C₂²	semidirect
95. C₃×#892	C₂²	semidirect
96. C₃×#890	C₂²	semidirect
97. C₃×#890	C₂²	semidirect
98. C₃×#889	C₂²	semidirect
99. C₃×#889	C₂²	semidirect
100. C₃×#889	C₂²	semidirect
101. C₃×#888	C₂²	semidirect
102. C₃×#887	C₂²	semidirect
105. C₃×#886	C₂²	semidirect
108. C₃×#885	C₂²	semidirect
109. C₃×#883	C₂²	semidirect
110. C₃×#883	C₂²	semidirect
112. C₃×#67⋊C₄	C₂²	semidirect
113. C₃×#67⋊C₄	C₂²	semidirect
115. C₃×#879	C₂²	semidirect
116. C₃×#879	C₂²	semidirect
117. C₃×#878	C₂²	semidirect
118. C₃×#878	C₂²	semidirect
119. C₃×#878	C₂²	semidirect
120. C₃×#877	C₂²	semidirect
123. C₃×#870	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
135. C₃×#547	D₃	semidirect
136. C₃×#547	C₂×C₃	semidirect
150. #5829	C₂×C₃	semidirect
151. #5829	C₂×C₃	semidirect
152. #5827	C₂×C₃	semidirect
153. Dic₃×#41	C₂×C₃	semidirect
154. #5732	C₂×C₃	semidirect
155. #5731	C₂×C₃	semidirect
156. #5665	C₂×C₃	semidirect
157. #5658	C₂×C₃	semidirect
158. #5658	C₂×C₃	semidirect
159. #5649	C₂×C₃	semidirect
160. #5643	C₂×C₃	semidirect
161. #5642	C₂×C₃	semidirect
162. #5641	C₂×C₃	semidirect
163. #5624	C₂×C₃	semidirect
164. #5617	C₂×C₃	semidirect
165. #5601	C₂×C₃	semidirect
166. #5565	C₂×C₃	semidirect
167. #5545	C₂×C₃	semidirect
168. #5539	C₂×C₃	semidirect
169. #5538	C₂×C₃	semidirect
170. #5513	C₂×C₃	semidirect
171. C₂×#898	C₂×C₃	semidirect
285. C₃×C₄⋊Q₈	C₂×D₃	semidirect
286. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
320. C₃×#123	C₂×D₃	semidirect
321. C₃×#123	C₂×D₃	semidirect
322. C₃×#123	C₂²×C₃	semidirect
323. C₃×#123	C₂²×C₃	semidirect
334. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
335. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
336. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
337. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
345. C₃×#121	C₂×D₃	semidirect
346. C₃×#121	C₂²×C₃	semidirect
373. C₃×C₄×D₄	C₂×D₃	semidirect
375. C₃×C₄×D₄	C₂²×C₃	semidirect
389. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
390. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
401. Q₈×Dic₃	C₂²×C₃	semidirect
402. Q₈×Dic₃	C₂²×C₃	semidirect
403. Q₈×Dic₃	C₂²×C₃	semidirect
404. Q₈×Dic₃	C₂²×C₃	semidirect
408. #939	C₂²×C₃	semidirect
411. #935	C₂²×C₃	semidirect
415. D₄×Dic₃	C₂²×C₃	semidirect
416. D₄×Dic₃	C₂²×C₃	semidirect
417. D₄×Dic₃	C₂²×C₃	semidirect
418. D₄×Dic₃	C₂²×C₃	semidirect
429. #926	C₂²×C₃	semidirect
430. #926	C₂²×C₃	semidirect
431. #926	C₂²×C₃	semidirect
432. #926	C₂²×C₃	semidirect
433. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
434. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
435. #924	C₂²×C₃	semidirect
436. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
437. C₂×C₄×Dic₃	C₂²×C₃	semidirect
438. C₂×C₄×Dic₃	C₂²×C₃	semidirect
444. #898	C₂²×C₃	semidirect
445. #898	C₂²×C₃	semidirect
446. #898	C₂²×C₃	semidirect
447. #898	C₂²×C₃	semidirect
448. #898	C₂²×C₃	semidirect
449. #897	C₂²×C₃	semidirect
450. #897	C₂²×C₃	semidirect
453. #892	C₂²×C₃	semidirect
454. #892	C₂²×C₃	semidirect
455. #890	C₂²×C₃	semidirect
456. #890	C₂²×C₃	semidirect
457. #889	C₂²×C₃	semidirect
458. #889	C₂²×C₃	semidirect
459. #889	C₂²×C₃	semidirect
460. #888	C₂²×C₃	semidirect
461. #887	C₂²×C₃	semidirect
464. #886	C₂²×C₃	semidirect
467. #885	C₂²×C₃	semidirect
468. #883	C₂²×C₃	semidirect
469. #883	C₂²×C₃	semidirect
471. #67⋊C₄	C₂²×C₃	semidirect
472. #67⋊C₄	C₂²×C₃	semidirect
474. #879	C₂²×C₃	semidirect
475. #879	C₂²×C₃	semidirect
476. #878	C₂²×C₃	semidirect
477. #878	C₂²×C₃	semidirect
478. #878	C₂²×C₃	semidirect
479. #877	C₂²×C₃	semidirect
482. #870	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
547. #547	C₃×D₃	semidirect
829. C₄⋊Q₈	C₂×C₃×D₃	semidirect
861. #123	C₂×C₃×D₃	semidirect
862. #123	C₂×C₃×D₃	semidirect
871. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
872. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
879. #121	C₂×C₃×D₃	semidirect
904. C₄×D₄	C₂×C₃×D₃	semidirect
917. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
1252. C₃²	#3521	semidirect
1365. C₃	#86687	direct (N × H)
1366. C₃	C₃×#3521	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#547	2
C₃×#5829	2
C₃×#5827	2
C₃×Dic₃×#41	2
C₃×#5732	2
C₃×#5731	2
C₃×#5665	2
C₃×#5658	2
C₃×#5649	2
C₃×#5643	2
C₃×#5642	2
C₃×#5641	2
C₃×#5624	2
C₃×#5617	2
C₃×#5601	2
C₃×#5565	2
C₃×#5545	2
C₃×#5539	2
C₃×#5538	2
C₃×#5513	2
C₂×C₃×#898	2
C₃×#3521	3
#86687	3

Subgroups — C3×#86687 #11909412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86687 #11909412