Subgroups — C₃×#85837 #11901739

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 869 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×#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5828	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5583	C₂	1	2	yes	maximal, complemented
5	C₃×#5582	C₂	1	2	yes	maximal, complemented
6	C₃×#5564	C₂	1	4	yes	maximal, complemented
7	C₃×#5562	C₂	1	2	yes	maximal, complemented
8	C₃×#5561	C₂	1	2	yes	maximal, complemented
9	C₃×#5560	C₂	1	4	yes	maximal, complemented
10	C₃×#5528	C₂	1	4	yes	maximal, complemented
11	C₃×#5524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5517	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5479	C₂	1	4	yes	maximal, complemented
14	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3455	—	3	1	no	maximal
17	#85837	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×#235	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
21	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
22	C₃²×C₄×D₄	C₂²	1	4	yes	—
23	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
24	C₃²×#117	C₂²	1	1	yes	characteristic
25	C₃²×#117	C₂²	1	2	yes	complemented
26	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
28	C₃×#947	C₂²	1	1	yes	characteristic, complemented
29	C₃×#946	C₂²	1	2	yes	—
30	C₃×#944	C₂²	1	1	yes	characteristic, complemented
31	C₃×#940	C₂²	1	1	yes	characteristic, complemented
32	C₃×#939	C₂²	1	4	yes	—
33	C₃×#938	C₂²	1	2	yes	—
34	C₃×#937	C₂²	1	2	yes	—
35	C₃×#936	C₂²	1	1	yes	characteristic, complemented
36	C₃×#935	C₂²	1	2	yes	—
37	C₃×#930	C₂²	1	4	yes	—
38	C₃×#929	C₂²	1	4	yes	—
39	C₃×#929	C₂²	1	4	yes	complemented
40	C₃×C₄×#67	C₂²	1	4	yes	—
41	C₃×C₄×#67	C₂²	1	4	yes	—
42	C₃×C₄×#67	C₂²	1	4	yes	complemented
43	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
44	C₃×#926	C₂²	1	1	yes	characteristic
45	C₃×#924	C₂²	1	4	yes	complemented
46	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
47	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
48	C₃×#898	C₂²	1	4	yes	—
49	C₃×#897	C₂²	1	2	yes	—
50	C₃×#896	C₂²	1	4	yes	complemented
51	C₃×#895	C₂²	1	2	yes	—
52	C₃×#894	C₂²	1	4	yes	—
53	C₃×#890	C₂²	1	2	yes	complemented
54	C₃×#889	C₂²	1	4	yes	complemented
55	C₃×#888	C₂²	1	2	yes	complemented
56	C₃×#886	C₂²	1	2	yes	—
57	C₃×#885	C₂²	1	4	yes	—
58	C₃×#884	C₂²	1	4	yes	—
59	C₃×#883	C₂²	1	4	yes	complemented
60	C₃×#882	C₂²	1	2	yes	—
61	C₃×#879	C₂²	1	4	yes	complemented
62	C₃×#878	C₂²	1	4	yes	—
63	C₃×#876	C₂²	1	4	yes	—
64	C₃×#876	C₂²	1	4	yes	complemented
65	C₃×#875	C₂²	1	4	yes	—
66	C₃×C₄×D₁₂	C₂²	1	4	yes	—
67	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
68	C₃×#872	C₂²	1	2	yes	—
69	C₃×#872	C₂²	1	2	yes	—
70	C₃×#872	C₂²	1	2	yes	—
71	C₃×#872	C₂²	1	2	yes	—
72	C₃×#872	C₂²	1	2	yes	complemented
73	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
74	C₃×#870	C₂²	1	4	yes	complemented
75	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
76	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
77	C₃×#542	—	3	2	no	—
78	C₃×#542	—	3	2	no	—
79	C₃×#541	—	3	2	no	—
80	C₃×#540	—	3	2	no	—
81	C₃×#539	—	3	4	no	—
82	C₃×#538	—	3	4	no	—
83	C₃×#533	—	3	1	no	—
84	C₃×#532	—	3	1	no	—
85	C₃×#529	—	3	4	no	—
86	C₃×#529	—	3	4	no	—
87	C₃×#525	—	3	1	no	—
88	C₃×#525	—	3	1	no	—
89	C₃×C₄×#41	—	2	1	no	—
90	C₃×C₄×#41	—	3	1	no	—
91	C₃×C₄×#41	D₃	1	1	yes	characteristic, complemented
92	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×C₃×#117	—	3	1	no	—
94	#5832	C₂×C₃	1	1	yes	characteristic, complemented
95	#5828	C₂×C₃	1	1	yes	characteristic, complemented
96	#5583	C₂×C₃	1	2	yes	complemented
97	#5582	C₂×C₃	1	2	yes	complemented
98	#5564	C₂×C₃	1	4	yes	complemented
99	#5562	C₂×C₃	1	2	yes	complemented
100	#5561	C₂×C₃	1	2	yes	complemented
101	#5560	C₂×C₃	1	4	yes	complemented
102	#5528	C₂×C₃	1	4	yes	complemented
103	#5524	C₂×C₃	1	1	yes	characteristic, complemented
104	#5517	C₂×C₃	1	1	yes	characteristic, complemented
105	#5479	C₂×C₃	1	4	yes	complemented
106	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
107	C₂×#872	C₂×C₃	1	1	yes	characteristic, complemented
108	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
109	C₃²×#41	—	2	4	no	—
110	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
111	C₂×C₃²×D₄	C₂³	1	2	yes	—
112	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₃²×C₄	C₂³	1	2	yes	—
114	C₂²×C₃²×C₄	C₂³	1	2	yes	—
115	C₂²×C₃²×C₄	C₂³	1	4	yes	—
116	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
117	C₂×C₃×#67	C₂³	1	2	yes	—
118	C₂×C₃×#67	C₂³	1	4	yes	—
119	C₂×C₃×#67	C₂³	1	4	yes	—
120	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
121	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
122	C₃×#235	—	2	4	no	—
123	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
124	C₂×C₃×D₁₂	C₂³	1	4	yes	—
125	C₂×C₃×C₄×D₃	—	2	4	no	—
126	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
127	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
128	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
129	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
130	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
131	C₂×C₃×Dic₆	C₂³	1	4	yes	—
132	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₃²×C₄²	C₂³	1	1	yes	characteristic
137	C₃²×C₄²	C₂³	1	1	yes	characteristic
138	C₃²×C₄²	C₂³	1	2	yes	—
139	C₃²×C₄²	C₂³	1	2	yes	—
140	C₃²×C₄²	C₂³	1	4	yes	—
141	C₃×#217	C₂³	1	2	yes	—
142	C₃×#217	C₂³	1	4	yes	—
143	C₃×#217	C₂³	1	4	yes	—
144	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
145	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
146	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
147	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
148	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
149	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
150	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
151	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
152	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
154	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
155	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
156	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
157	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
158	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
159	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
160	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
161	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
162	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
163	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
164	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
165	C₃×C₄×Dic₃	C₂³	1	4	yes	—
166	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
167	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
168	C₃×C₄×Dic₃	C₂³	1	2	yes	—
169	C₃×C₄×Dic₃	C₂³	1	2	yes	—
170	#3455	—	3	1	no	Sylow
171	C₂×C₃×#41	—	2	1	no	—
172	C₂×C₃×#41	—	3	1	no	—
173	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
174	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
175	C₂³×C₃×C₄	—	3	1	no	—
176	C₂×#235	C₂²×C₃	1	1	yes	characteristic
177	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
178	C₃×C₄⋊Q₈	—	3	1	no	—
179	C₃×C₄⋊Q₈	—	3	2	no	—
180	C₃×#127	—	3	1	no	—
181	C₃×#126	—	3	4	no	—
182	C₃×#126	—	3	4	no	—
183	C₃×#126	—	3	4	no	—
184	C₃×#126	—	3	4	no	—
185	C₃×#125	—	3	4	no	—
186	C₃×#125	—	3	2	no	—
187	C₃×#125	—	3	4	no	—
188	C₃×#124	—	3	1	no	—
189	C₃×#124	—	3	1	no	—
190	C₃×#124	—	3	4	no	—
191	C₃×#124	—	3	4	no	—
192	C₃×#123	—	3	2	no	—
193	C₃×#123	—	3	4	no	—
194	C₃×#123	—	3	4	no	—
195	C₃×#123	—	3	4	no	—
196	C₃×#123	—	3	4	no	—
197	C₃×#123	—	3	2	no	—
198	C₃×C₂²⋊Q₈	—	3	2	no	—
199	C₃×C₂²⋊Q₈	—	3	4	no	—
200	C₃×C₂²⋊Q₈	—	3	4	no	—
201	C₃×C₂²⋊Q₈	—	3	2	no	—
202	C₃×C₂²⋊Q₈	—	3	4	no	—
203	C₃×#121	—	3	2	no	—
204	C₃×#121	—	3	4	no	—
205	C₃×#121	—	3	4	no	—
206	C₃×#121	—	3	2	no	—
207	C₃×#121	—	3	4	no	—
208	C₃×#120	—	3	2	no	—
209	C₃×#120	—	3	2	no	—
210	C₃×C₄×Q₈	—	2	2	no	—
211	C₃×C₄×Q₈	—	3	2	no	—
212	C₃×C₄×Q₈	—	3	4	no	—
213	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
214	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
215	C₃×C₄×D₄	—	2	4	no	—
216	C₃×C₄×D₄	—	2	2	no	—
217	C₃×C₄×D₄	—	3	4	no	—
218	C₃×C₄×D₄	—	3	4	no	—
219	C₃×C₄×D₄	—	3	4	no	—
220	C₃×C₄×D₄	—	3	2	no	—
221	C₃×C₄×D₄	—	3	4	no	—
222	C₃×C₄×D₄	C₂×D₃	1	4	yes	—
223	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
224	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
225	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
226	C₃×#117	—	2	1	no	—
227	C₃×#117	—	2	2	no	—
228	C₃×#117	—	3	1	no	—
229	C₃×#117	—	3	2	no	—
230	C₃×#117	—	3	2	no	—
231	C₃×#117	—	3	2	no	—
232	C₃×#117	—	3	2	no	—
233	C₃×#117	—	3	2	no	—
234	C₃×#117	C₂×D₃	1	1	yes	characteristic
235	C₃×#117	C₂×D₃	1	2	yes	complemented
236	C₃×#117	C₂²×C₃	1	1	yes	characteristic
237	C₃×#117	C₂²×C₃	1	2	yes	complemented
238	C₂×C₃×C₄⋊C₄	—	3	2	no	—
239	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
240	C₂×C₃×C₄²	—	2	1	no	—
241	C₂×C₃×C₄²	—	2	2	no	—
242	C₂×C₃×C₄²	—	3	1	no	—
243	C₂×C₃×C₄²	—	3	2	no	—
244	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂×D₃	1	2	yes	complemented
246	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	complemented
248	#947	C₂²×C₃	1	1	yes	characteristic, complemented
249	#946	C₂²×C₃	1	2	yes	—
250	#944	C₂²×C₃	1	1	yes	characteristic, complemented
251	#940	C₂²×C₃	1	1	yes	characteristic, complemented
252	#939	C₂²×C₃	1	4	yes	—
253	#938	C₂²×C₃	1	2	yes	—
254	#937	C₂²×C₃	1	2	yes	—
255	#936	C₂²×C₃	1	1	yes	characteristic, complemented
256	#935	C₂²×C₃	1	2	yes	—
257	#930	C₂²×C₃	1	4	yes	—
258	#929	C₂²×C₃	1	4	yes	—
259	#929	C₂²×C₃	1	4	yes	complemented
260	C₄×#67	C₂²×C₃	1	4	yes	—
261	C₄×#67	C₂²×C₃	1	4	yes	—
262	C₄×#67	C₂²×C₃	1	4	yes	complemented
263	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
264	#926	C₂²×C₃	1	1	yes	characteristic
265	#924	C₂²×C₃	1	4	yes	complemented
266	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
267	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
268	#898	C₂²×C₃	1	4	yes	—
269	#897	C₂²×C₃	1	2	yes	—
270	#896	C₂²×C₃	1	4	yes	complemented
271	#895	C₂²×C₃	1	2	yes	—
272	#894	C₂²×C₃	1	4	yes	—
273	#890	C₂²×C₃	1	2	yes	complemented
274	#889	C₂²×C₃	1	4	yes	complemented
275	#888	C₂²×C₃	1	2	yes	complemented
276	#886	C₂²×C₃	1	2	yes	—
277	#885	C₂²×C₃	1	4	yes	—
278	#884	C₂²×C₃	1	4	yes	—
279	#883	C₂²×C₃	1	4	yes	complemented
280	#882	C₂²×C₃	1	2	yes	—
281	#879	C₂²×C₃	1	4	yes	complemented
282	#878	C₂²×C₃	1	4	yes	—
283	#876	C₂²×C₃	1	4	yes	—
284	#876	C₂²×C₃	1	4	yes	complemented
285	#875	C₂²×C₃	1	4	yes	—
286	C₄×D₁₂	C₂²×C₃	1	4	yes	—
287	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
288	#872	C₂²×C₃	1	2	yes	—
289	#872	C₂²×C₃	1	2	yes	—
290	#872	C₂²×C₃	1	2	yes	—
291	#872	C₂²×C₃	1	2	yes	—
292	#872	C₂²×C₃	1	2	yes	complemented
293	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
294	#870	C₂²×C₃	1	4	yes	complemented
295	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
296	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
297	C₂³×C₃²	C₂⁴	1	2	yes	—
298	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
299	C₂²×C₃×D₃	—	2	2	no	—
300	C₂²×C₃×D₃	—	4	2	no	—
301	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
302	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
303	C₃²×Q₈	—	2	2	no	—
304	C₃²×D₄	—	2	4	no	—
305	C₃²×D₄	—	2	2	no	—
306	C₂×C₃²×C₄	—	2	4	no	—
307	C₂×C₃²×C₄	—	4	4	no	—
308	C₂×C₃²×C₄	—	4	2	no	—
309	C₂×C₃²×C₄	#41	1	4	yes	—
310	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
311	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
312	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
313	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
314	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
315	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
316	C₃×#67	—	2	4	no	—
317	C₃×#67	—	4	4	no	—
318	C₃×#67	—	4	4	no	—
319	C₂×C₃×Dic₃	—	2	2	no	—
320	C₂×C₃×Dic₃	—	4	2	no	—
321	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
322	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
323	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
324	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
325	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
326	C₃×D₁₂	—	2	2	no	—
327	C₃×D₁₂	—	4	4	no	—
328	C₃×C₄×D₃	—	2	4	no	—
329	C₃×C₄×D₃	—	2	4	no	—
330	C₃×C₄×D₃	—	2	4	no	—
331	C₃×C₄×D₃	—	4	4	no	—
332	C₃×Dic₆	—	2	2	no	—
333	C₃×Dic₆	—	4	4	no	—
334	#542	—	3	2	no	—
335	#542	—	3	2	no	—
336	#541	—	3	2	no	—
337	#540	—	3	2	no	—
338	#539	—	3	4	no	—
339	#538	—	3	4	no	—
340	#533	—	3	1	no	—
341	#532	—	3	1	no	—
342	#529	—	3	4	no	—
343	#529	—	3	4	no	—
344	#525	—	3	1	no	—
345	#525	—	3	1	no	—
346	C₄×#41	—	3	1	no	—
347	C₄×#41	C₃×D₃	1	1	yes	characteristic, complemented
348	C₂×#117	—	3	1	no	—
349	C₂⁴×C₃	—	3	1	no	—
350	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
351	C₃×#41	—	2	8	no	—
352	C₃×#41	—	2	4	no	—
353	C₃×#41	—	2	4	no	—
354	C₃×#41	—	6	4	no	—
355	C₂×C₃×Q₈	—	2	1	no	—
356	C₂×C₃×Q₈	—	3	1	no	—
357	C₂×C₃×Q₈	—	3	4	no	—
358	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
359	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	—	2	1	no	—
362	C₂×C₃×D₄	—	3	2	no	—
363	C₂×C₃×D₄	—	3	4	no	—
364	C₂×C₃×D₄	—	3	4	no	—
365	C₂×C₃×D₄	—	3	1	no	—
366	C₂×C₃×D₄	—	3	4	no	—
367	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
368	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
369	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
370	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	1	no	—
373	C₂²×C₃×C₄	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	4	no	—
375	C₂²×C₃×C₄	—	3	1	no	—
376	C₂²×C₃×C₄	—	3	2	no	—
377	C₂²×C₃×C₄	—	3	2	no	—
378	C₂²×C₃×C₄	—	3	2	no	—
379	C₂²×C₃×C₄	—	3	2	no	—
380	C₂²×C₃×C₄	—	3	4	no	—
381	C₂²×C₃×C₄	—	6	4	no	—
382	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
383	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
384	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
385	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
387	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
388	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
389	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
390	C₂×#67	C₂³×C₃	1	2	yes	—
391	C₂×#67	C₂³×C₃	1	4	yes	—
392	C₂×#67	C₂³×C₃	1	4	yes	—
393	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
394	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
395	#235	—	2	4	no	—
396	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
397	C₂×D₁₂	C₂³×C₃	1	4	yes	—
398	C₂×C₄×D₃	—	2	4	no	—
399	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
400	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
401	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
402	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
403	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
404	C₂×Dic₆	C₂³×C₃	1	4	yes	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	4	no	—
407	C₃×C₄⋊C₄	—	3	2	no	—
408	C₃×C₄⋊C₄	—	3	2	no	—
409	C₃×C₄⋊C₄	—	3	2	no	—
410	C₃×C₄⋊C₄	—	3	2	no	—
411	C₃×C₄⋊C₄	—	3	4	no	—
412	C₃×C₄⋊C₄	—	3	4	no	—
413	C₃×C₄⋊C₄	—	3	4	no	—
414	C₃×C₄⋊C₄	—	3	4	no	—
415	C₃×C₄⋊C₄	—	3	4	no	—
416	C₃×C₄⋊C₄	—	3	2	no	—
417	C₃×C₄⋊C₄	—	3	4	no	—
418	C₃×C₄⋊C₄	—	3	4	no	—
419	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
420	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
421	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
423	C₃×C₂²⋊C₄	—	2	2	no	—
424	C₃×C₂²⋊C₄	—	2	4	no	—
425	C₃×C₂²⋊C₄	—	3	2	no	—
426	C₃×C₂²⋊C₄	—	3	4	no	—
427	C₃×C₂²⋊C₄	—	3	4	no	—
428	C₃×C₂²⋊C₄	—	3	2	no	—
429	C₃×C₂²⋊C₄	—	3	2	no	—
430	C₃×C₂²⋊C₄	—	3	2	no	—
431	C₃×C₂²⋊C₄	—	3	2	no	—
432	C₃×C₂²⋊C₄	—	3	4	no	—
433	C₃×C₂²⋊C₄	—	3	4	no	—
434	C₃×C₂²⋊C₄	—	3	4	no	—
435	C₃×C₂²⋊C₄	—	3	4	no	—
436	C₃×C₂²⋊C₄	—	3	4	no	—
437	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
438	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
439	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
441	C₃×C₄²	—	2	1	no	—
442	C₃×C₄²	—	2	1	no	—
443	C₃×C₄²	—	2	2	no	—
444	C₃×C₄²	—	2	2	no	—
445	C₃×C₄²	—	2	4	no	—
446	C₃×C₄²	—	3	1	no	—
447	C₃×C₄²	—	3	1	no	—
448	C₃×C₄²	—	3	4	no	—
449	C₃×C₄²	—	3	2	no	—
450	C₃×C₄²	—	3	2	no	—
451	C₃×C₄²	C₂²×D₃	1	2	yes	—
452	C₃×C₄²	C₂²×D₃	1	4	yes	—
453	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
454	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
455	C₃×C₄²	C₂²×D₃	1	2	yes	—
456	C₃×C₄²	C₂³×C₃	1	2	yes	—
457	C₃×C₄²	C₂³×C₃	1	2	yes	—
458	C₃×C₄²	C₂³×C₃	1	4	yes	—
459	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
460	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
461	#217	C₂³×C₃	1	2	yes	—
462	#217	C₂³×C₃	1	4	yes	—
463	#217	C₂³×C₃	1	4	yes	—
464	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
465	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
466	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
467	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
468	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
469	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
470	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
471	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
472	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
473	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
474	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
475	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
476	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
477	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
478	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
479	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
480	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
481	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
482	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
483	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
484	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
485	C₄×Dic₃	C₂³×C₃	1	2	yes	—
486	C₄×Dic₃	C₂³×C₃	1	2	yes	—
487	C₄×Dic₃	C₂³×C₃	1	4	yes	—
488	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
489	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
490	C₂²×C₃²	—	2	2	no	—
491	C₂²×C₃²	—	2	2	no	—
492	C₂²×C₃²	—	2	4	no	—
493	C₂²×C₃²	C₂×#41	1	2	yes	—
494	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
495	C₂×C₃×D₃	—	2	2	no	—
496	C₂×C₃×D₃	—	2	2	no	—
497	C₂×C₃×D₃	—	2	4	no	—
498	C₂×C₃×D₃	—	2	2	no	—
499	C₂×C₃×D₃	—	2	2	no	—
500	C₂×C₃×D₃	—	4	4	no	—
501	C₃²×C₄	—	2	2	no	—
502	C₃²×C₄	—	2	2	no	—
503	C₃²×C₄	—	2	4	no	—
504	C₃²×C₄	—	2	2	no	—
505	C₃²×C₄	C₂×#41	1	2	yes	—
506	C₃²×C₄	C₂×#41	1	2	yes	—
507	C₃×Dic₃	—	2	2	no	—
508	C₃×Dic₃	—	2	2	no	—
509	C₃×Dic₃	—	2	2	no	—
510	C₃×Dic₃	—	2	4	no	—
511	C₃×Dic₃	—	2	2	no	—
512	C₂×#41	—	3	1	no	—
513	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
514	C₂³×C₄	—	3	1	no	—
515	C₄⋊Q₈	—	3	1	no	—
516	C₄⋊Q₈	—	3	2	no	—
517	#127	—	3	1	no	—
518	#126	—	3	4	no	—
519	#126	—	3	4	no	—
520	#126	—	3	4	no	—
521	#126	—	3	4	no	—
522	#125	—	3	4	no	—
523	#125	—	3	2	no	—
524	#125	—	3	4	no	—
525	#124	—	3	1	no	—
526	#124	—	3	1	no	—
527	#124	—	3	4	no	—
528	#124	—	3	4	no	—
529	#123	—	3	2	no	—
530	#123	—	3	4	no	—
531	#123	—	3	4	no	—
532	#123	—	3	4	no	—
533	#123	—	3	2	no	—
534	#123	—	3	4	no	—
535	C₂²⋊Q₈	—	3	2	no	—
536	C₂²⋊Q₈	—	3	4	no	—
537	C₂²⋊Q₈	—	3	2	no	—
538	C₂²⋊Q₈	—	3	4	no	—
539	C₂²⋊Q₈	—	3	4	no	—
540	#121	—	3	2	no	—
541	#121	—	3	4	no	—
542	#121	—	3	4	no	—
543	#121	—	3	2	no	—
544	#121	—	3	4	no	—
545	#120	—	3	2	no	—
546	#120	—	3	2	no	—
547	C₄×Q₈	—	3	2	no	—
548	C₄×Q₈	—	3	4	no	—
549	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
550	C₄×D₄	—	3	4	no	—
551	C₄×D₄	—	3	4	no	—
552	C₄×D₄	—	3	4	no	—
553	C₄×D₄	—	3	2	no	—
554	C₄×D₄	—	3	4	no	—
555	C₄×D₄	C₂×C₃×D₃	1	4	yes	—
556	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
557	#117	—	3	1	no	—
558	#117	—	3	2	no	—
559	#117	—	3	2	no	—
560	#117	—	3	2	no	—
561	#117	—	3	2	no	—
562	#117	—	3	2	no	—
563	#117	C₂×C₃×D₃	1	1	yes	characteristic
564	#117	C₂×C₃×D₃	1	2	yes	complemented
565	C₂×C₄⋊C₄	—	3	2	no	—
566	C₂×C₂²⋊C₄	—	3	2	no	—
567	C₂×C₄²	—	3	1	no	—
568	C₂×C₄²	—	3	2	no	—
569	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
570	C₂×C₄²	C₂×C₃×D₃	1	2	yes	complemented
571	C₂³×C₃	—	2	2	no	—
572	C₂³×C₃	—	2	1	no	—
573	C₂³×C₃	—	3	2	no	—
574	C₂³×C₃	—	3	2	no	—
575	C₂³×C₃	—	6	2	no	—
576	C₂³×C₃	—	12	2	no	—
577	C₂³×C₃	C₂³×D₃	1	2	yes	—
578	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
579	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
580	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
581	C₂²×D₃	—	2	2	no	—
582	C₂²×D₃	—	4	2	no	—
583	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
584	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
585	C₃×Q₈	—	2	4	no	—
586	C₃×Q₈	—	2	2	no	—
587	C₃×Q₈	—	2	2	no	—
588	C₃×Q₈	—	6	2	no	—
589	C₃×Q₈	—	12	4	no	—
590	C₃×D₄	—	2	8	no	—
591	C₃×D₄	—	2	4	no	—
592	C₃×D₄	—	2	4	no	—
593	C₃×D₄	—	2	4	no	—
594	C₃×D₄	—	2	2	no	—
595	C₃×D₄	—	2	2	no	—
596	C₃×D₄	—	6	4	no	—
597	C₃×D₄	—	6	2	no	—
598	C₃×D₄	—	12	4	no	—
599	C₃×D₄	—	12	4	no	—
600	C₃×D₄	—	12	4	no	—
601	C₂×C₃×C₄	—	2	8	no	—
602	C₂×C₃×C₄	—	2	4	no	—
603	C₂×C₃×C₄	—	2	4	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	4	no	—
610	C₂×C₃×C₄	—	2	4	no	—
611	C₂×C₃×C₄	—	3	2	no	—
612	C₂×C₃×C₄	—	3	2	no	—
613	C₂×C₃×C₄	—	3	4	no	—
614	C₂×C₃×C₄	—	3	2	no	—
615	C₂×C₃×C₄	—	3	2	no	—
616	C₂×C₃×C₄	—	4	2	no	—
617	C₂×C₃×C₄	—	4	4	no	—
618	C₂×C₃×C₄	—	4	4	no	—
619	C₂×C₃×C₄	—	4	2	no	—
620	C₂×C₃×C₄	—	4	4	no	—
621	C₂×C₃×C₄	—	4	8	no	—
622	C₂×C₃×C₄	—	6	2	no	—
623	C₂×C₃×C₄	—	6	4	no	—
624	C₂×C₃×C₄	—	6	4	no	—
625	C₂×C₃×C₄	—	6	4	no	—
626	C₂×C₃×C₄	—	12	4	no	—
627	C₂×C₃×C₄	—	12	2	no	—
628	C₂×C₃×C₄	#235	1	4	yes	—
629	C₂×C₃×C₄	C₃×#41	1	4	yes	—
630	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
631	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
632	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
633	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
634	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
635	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
636	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
637	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
640	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
642	#67	—	2	4	no	—
643	#67	—	4	4	no	—
644	#67	—	4	4	no	—
645	C₂×Dic₃	—	2	2	no	—
646	C₂×Dic₃	—	4	2	no	—
647	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
648	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
649	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
650	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
651	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
652	D₁₂	—	2	2	no	—
653	D₁₂	—	4	4	no	—
654	C₄×D₃	—	2	4	no	—
655	C₄×D₃	—	2	4	no	—
656	C₄×D₃	—	2	4	no	—
657	C₄×D₃	—	4	4	no	—
658	Dic₆	—	2	2	no	—
659	Dic₆	—	4	4	no	—
660	C₂×C₃²	—	2	2	no	—
661	C₂×C₃²	—	4	2	no	—
662	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
663	C₂×C₃²	#585	1	2	yes	—
664	C₃×D₃	—	4	2	no	—
665	C₃×D₃	—	4	2	no	—
666	C₂⁴	—	3	1	no	—
667	#41	—	2	4	no	—
668	#41	—	6	4	no	—
669	C₂×Q₈	—	3	1	no	—
670	C₂×Q₈	—	3	4	no	—
671	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
672	C₂×D₄	—	3	2	no	—
673	C₂×D₄	—	3	4	no	—
674	C₂×D₄	—	3	4	no	—
675	C₂×D₄	—	3	1	no	—
676	C₂×D₄	—	3	4	no	—
677	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
678	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
679	C₂²×C₄	—	3	1	no	—
680	C₂²×C₄	—	3	2	no	—
681	C₂²×C₄	—	3	2	no	—
682	C₂²×C₄	—	3	2	no	—
683	C₂²×C₄	—	3	2	no	—
684	C₂²×C₄	—	3	4	no	—
685	C₂²×C₄	—	6	4	no	—
686	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
687	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
688	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
689	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
690	C₄⋊C₄	—	3	2	no	—
691	C₄⋊C₄	—	3	2	no	—
692	C₄⋊C₄	—	3	2	no	—
693	C₄⋊C₄	—	3	2	no	—
694	C₄⋊C₄	—	3	2	no	—
695	C₄⋊C₄	—	3	4	no	—
696	C₄⋊C₄	—	3	4	no	—
697	C₄⋊C₄	—	3	4	no	—
698	C₄⋊C₄	—	3	4	no	—
699	C₄⋊C₄	—	3	4	no	—
700	C₄⋊C₄	—	3	4	no	—
701	C₄⋊C₄	—	3	4	no	—
702	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
703	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
704	C₂²⋊C₄	—	3	2	no	—
705	C₂²⋊C₄	—	3	4	no	—
706	C₂²⋊C₄	—	3	4	no	—
707	C₂²⋊C₄	—	3	2	no	—
708	C₂²⋊C₄	—	3	2	no	—
709	C₂²⋊C₄	—	3	2	no	—
710	C₂²⋊C₄	—	3	2	no	—
711	C₂²⋊C₄	—	3	4	no	—
712	C₂²⋊C₄	—	3	4	no	—
713	C₂²⋊C₄	—	3	4	no	—
714	C₂²⋊C₄	—	3	4	no	—
715	C₂²⋊C₄	—	3	4	no	—
716	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
717	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
718	C₄²	—	3	2	no	—
719	C₄²	—	3	2	no	—
720	C₄²	—	3	1	no	—
721	C₄²	—	3	1	no	—
722	C₄²	—	3	4	no	—
723	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
724	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
725	C₄²	C₂²×C₃×D₃	1	2	yes	—
726	C₄²	C₂²×C₃×D₃	1	2	yes	—
727	C₄²	C₂²×C₃×D₃	1	4	yes	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	2	2	no	—
730	C₂²×C₃	—	2	4	no	—
731	C₂²×C₃	—	2	2	no	—
732	C₂²×C₃	—	2	4	no	—
733	C₂²×C₃	—	2	2	no	—
734	C₂²×C₃	—	2	4	no	—
735	C₂²×C₃	—	2	2	no	—
736	C₂²×C₃	—	2	1	no	—
737	C₂²×C₃	—	4	2	no	—
738	C₂²×C₃	—	4	4	no	—
739	C₂²×C₃	—	6	2	no	—
740	C₂²×C₃	—	6	2	no	—
741	C₂²×C₃	—	6	4	no	—
742	C₂²×C₃	—	6	2	no	—
743	C₂²×C₃	—	6	2	no	—
744	C₂²×C₃	—	12	4	no	—
745	C₂²×C₃	C₂×#235	1	2	yes	—
746	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
747	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
748	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
749	C₂×D₃	—	2	2	no	—
750	C₂×D₃	—	2	2	no	—
751	C₂×D₃	—	2	4	no	—
752	C₂×D₃	—	2	2	no	—
753	C₂×D₃	—	2	2	no	—
754	C₂×D₃	—	4	4	no	—
755	C₃×C₄	—	2	4	no	—
756	C₃×C₄	—	2	4	no	—
757	C₃×C₄	—	2	2	no	—
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	2	2	no	—
760	C₃×C₄	—	2	4	no	—
761	C₃×C₄	—	2	2	no	—
762	C₃×C₄	—	2	4	no	—
763	C₃×C₄	—	2	2	no	—
764	C₃×C₄	—	2	2	no	—
765	C₃×C₄	—	2	2	no	—
766	C₃×C₄	—	2	2	no	—
767	C₃×C₄	—	4	2	no	—
768	C₃×C₄	—	4	4	no	—
769	C₃×C₄	—	6	2	no	—
770	C₃×C₄	—	6	2	no	—
771	C₃×C₄	—	6	2	no	—
772	C₃×C₄	—	6	4	no	—
773	C₃×C₄	—	6	2	no	—
774	C₃×C₄	C₂×#235	1	2	yes	—
775	C₃×C₄	C₂×#235	1	2	yes	—
776	C₃×C₄	C₂×C₃×#41	1	2	yes	—
777	C₃×C₄	C₂×C₃×#41	1	2	yes	—
778	Dic₃	—	2	2	no	—
779	Dic₃	—	2	2	no	—
780	Dic₃	—	2	2	no	—
781	Dic₃	—	2	4	no	—
782	Dic₃	—	2	2	no	—
783	C₃²	#3455	1	1	yes	characteristic, complemented, Sylow
784	C₂³	—	3	2	no	—
785	C₂³	—	3	2	no	—
786	C₂³	—	6	2	no	—
787	C₂³	—	12	2	no	—
788	C₂³	C₂³×C₃×D₃	1	2	yes	—
789	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
790	Q₈	—	2	2	no	—
791	Q₈	—	6	2	no	—
792	Q₈	—	12	4	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	6	4	no	—
796	D₄	—	6	2	no	—
797	D₄	—	12	4	no	—
798	D₄	—	12	4	no	—
799	D₄	—	12	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	3	2	no	—
802	C₂×C₄	—	3	2	no	—
803	C₂×C₄	—	3	4	no	—
804	C₂×C₄	—	3	2	no	—
805	C₂×C₄	—	3	2	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	6	2	no	—
809	C₂×C₄	—	6	4	no	—
810	C₂×C₄	—	6	4	no	—
811	C₂×C₄	—	6	4	no	—
812	C₂×C₄	—	12	4	no	—
813	C₂×C₄	—	12	2	no	—
814	C₂×C₄	C₃×#235	1	4	yes	—
815	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
816	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
817	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
818	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
819	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
820	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
821	C₂×C₃	—	2	2	no	—
822	C₂×C₃	—	2	2	no	—
823	C₂×C₃	—	2	1	no	—
824	C₂×C₃	—	2	2	no	—
825	C₂×C₃	—	4	2	no	—
826	C₂×C₃	—	4	4	no	—
827	C₂×C₃	—	4	2	no	—
828	C₂×C₃	—	4	2	no	—
829	C₂×C₃	—	12	2	no	—
830	C₂×C₃	—	12	2	no	—
831	C₂×C₃	C₂²×#235	1	1	yes	characteristic
832	C₂×C₃	#5964	1	2	yes	—
833	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
834	C₂×C₃	C₃×#585	1	2	yes	—
835	D₃	—	4	2	no	—
836	D₃	—	4	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	6	2	no	—
841	C₂²	—	6	2	no	—
842	C₂²	—	6	4	no	—
843	C₂²	—	6	2	no	—
844	C₂²	—	6	2	no	—
845	C₂²	—	12	4	no	—
846	C₂²	C₂×C₃×#235	1	2	yes	—
847	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	4	no	—
852	C₄	—	6	2	no	—
853	C₄	—	6	2	no	—
854	C₄	—	6	2	no	—
855	C₄	—	6	4	no	—
856	C₄	—	6	2	no	—
857	C₄	C₂×C₃×#235	1	2	yes	—
858	C₄	C₂×C₃×#235	1	2	yes	—
859	C₃	—	2	1	no	—
860	C₃	#85837	1	1	yes	characteristic, direct product factor
861	C₃	C₃×#3455	1	1	yes	characteristic, complemented
862	C₂	—	2	2	no	—
863	C₂	—	4	2	no	—
864	C₂	—	12	2	no	—
865	C₂	—	12	2	no	—
866	C₂	C₂²×C₃×#235	1	1	yes	characteristic
867	C₂	C₃×#5964	1	2	yes	—

	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×#3455
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×#5832	C₂	semidirect
3. C₃×#5828	C₂	semidirect
4. C₃×#5583	C₂	semidirect
5. C₃×#5582	C₂	semidirect
6. C₃×#5564	C₂	semidirect
7. C₃×#5562	C₂	semidirect
8. C₃×#5561	C₂	semidirect
9. C₃×#5560	C₂	semidirect
10. C₃×#5528	C₂	semidirect
11. C₃×#5524	C₂	semidirect
12. C₃×#5517	C₂	semidirect
13. C₃×#5479	C₂	semidirect
14. C₃×C₄×#235	C₂	semidirect
15. C₂×C₃×#872	C₂	semidirect
17. #85837	C₃	direct (N × H)
21. C₃²×C₄×Q₈	C₂²	semidirect
23. C₃²×C₄×D₄	C₂²	semidirect
25. C₃²×#117	C₂²	semidirect
27. C₂×C₃²×C₄²	C₂²	semidirect
28. C₃×#947	C₂²	semidirect
30. C₃×#944	C₂²	semidirect
31. C₃×#940	C₂²	semidirect
35. C₃×#936	C₂²	semidirect
39. C₃×#929	C₂²	semidirect
42. C₃×C₄×#67	C₂²	semidirect
45. C₃×#924	C₂²	semidirect
50. C₃×#896	C₂²	semidirect
53. C₃×#890	C₂²	semidirect
54. C₃×#889	C₂²	semidirect
55. C₃×#888	C₂²	semidirect
59. C₃×#883	C₂²	semidirect
61. C₃×#879	C₂²	semidirect
64. C₃×#876	C₂²	semidirect
67. C₃×C₄×D₁₂	C₂²	semidirect
72. C₃×#872	C₂²	semidirect
73. C₃×C₄²×D₃	C₂²	semidirect
74. C₃×#870	C₂²	semidirect
75. C₃×C₄×Dic₆	C₂²	semidirect
76. C₃×C₄×Dic₆	C₂²	semidirect
91. C₃×C₄×#41	D₃	semidirect
92. C₃×C₄×#41	C₂×C₃	semidirect
94. #5832	C₂×C₃	semidirect
95. #5828	C₂×C₃	semidirect
96. #5583	C₂×C₃	semidirect
97. #5582	C₂×C₃	semidirect
98. #5564	C₂×C₃	semidirect
99. #5562	C₂×C₃	semidirect
100. #5561	C₂×C₃	semidirect
101. #5560	C₂×C₃	semidirect
102. #5528	C₂×C₃	semidirect
103. #5524	C₂×C₃	semidirect
104. #5517	C₂×C₃	semidirect
105. #5479	C₂×C₃	semidirect
106. C₄×#235	C₂×C₃	semidirect
107. C₂×#872	C₂×C₃	semidirect
213. C₃×C₄×Q₈	C₂×D₃	semidirect
214. C₃×C₄×Q₈	C₂²×C₃	semidirect
223. C₃×C₄×D₄	C₂×D₃	semidirect
225. C₃×C₄×D₄	C₂²×C₃	semidirect
235. C₃×#117	C₂×D₃	semidirect
237. C₃×#117	C₂²×C₃	semidirect
245. C₂×C₃×C₄²	C₂×D₃	semidirect
247. C₂×C₃×C₄²	C₂²×C₃	semidirect
248. #947	C₂²×C₃	semidirect
250. #944	C₂²×C₃	semidirect
251. #940	C₂²×C₃	semidirect
255. #936	C₂²×C₃	semidirect
259. #929	C₂²×C₃	semidirect
262. C₄×#67	C₂²×C₃	semidirect
265. #924	C₂²×C₃	semidirect
270. #896	C₂²×C₃	semidirect
273. #890	C₂²×C₃	semidirect
274. #889	C₂²×C₃	semidirect
275. #888	C₂²×C₃	semidirect
279. #883	C₂²×C₃	semidirect
281. #879	C₂²×C₃	semidirect
284. #876	C₂²×C₃	semidirect
287. C₄×D₁₂	C₂²×C₃	semidirect
292. #872	C₂²×C₃	semidirect
293. C₄²×D₃	C₂²×C₃	semidirect
294. #870	C₂²×C₃	semidirect
295. C₄×Dic₆	C₂²×C₃	semidirect
296. C₄×Dic₆	C₂²×C₃	semidirect
347. C₄×#41	C₃×D₃	semidirect
549. C₄×Q₈	C₂×C₃×D₃	semidirect
556. C₄×D₄	C₂×C₃×D₃	semidirect
564. #117	C₂×C₃×D₃	semidirect
570. C₂×C₄²	C₂×C₃×D₃	semidirect
783. C₃²	#3455	semidirect
860. C₃	#85837	direct (N × H)
861. C₃	C₃×#3455	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×#5832	2
C₃×#5828	2
C₃×#5583	2
C₃×#5582	2
C₃×#5564	2
C₃×#5562	2
C₃×#5561	2
C₃×#5560	2
C₃×#5528	2
C₃×#5524	2
C₃×#5517	2
C₃×#5479	2
C₃×C₄×#235	2
C₂×C₃×#872	2
C₃×#3455	3
#85837	3

Subgroups — C3×#85837 #11901739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85837 #11901739