Subgroups — C₃×#86761 #11906154

Order 1152.

2340 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#946	C₂	1	2	yes	maximal, complemented
4	C₃×#5730	C₂	1	2	yes	maximal, complemented
5	C₃×#5729	C₂	1	2	yes	maximal, complemented
6	C₃×#5728	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5727	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5636	C₂	1	4	yes	maximal, complemented
9	C₃×#5635	C₂	1	2	yes	maximal, complemented
10	C₃×#5634	C₂	1	4	yes	maximal, complemented
11	C₃×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
12	C₃×#5579	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5578	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5545	C₂	1	2	yes	maximal
15	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
16	C₃×#5543	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5539	C₂	1	2	yes	maximal, complemented
18	C₃×#3501	—	3	1	no	maximal
19	#86761	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂²×C₃²×Q₈	C₂²	1	2	yes	complemented
21	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
22	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄×D₄	C₂²	1	2	yes	—
30	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₃×#946	C₂²	1	1	yes	characteristic
32	C₃×#946	C₂²	1	2	yes	—
33	C₃×#946	C₂²	1	4	yes	—
34	C₃×#946	C₂²	1	2	yes	complemented
35	C₃×#946	C₂²	1	2	yes	complemented
36	C₃×#946	C₂²	1	4	yes	complemented
37	C₃×#946	C₂²	1	4	yes	complemented
38	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
39	C₃×#944	C₂²	1	1	yes	characteristic, complemented
40	C₃×#944	C₂²	1	4	yes	complemented
41	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
42	C₃×D₄×Dic₃	C₂²	1	2	yes	—
43	C₃×C₄×#67	C₂²	1	2	yes	—
44	C₃×C₄×#67	C₂²	1	4	yes	—
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
46	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
47	C₃×#924	C₂²	1	4	yes	complemented
48	C₃×#924	C₂²	1	2	yes	complemented
49	C₂×C₃×Dic₃⋊C₄	C₂²	1	4	yes	complemented
50	C₃×#897	C₂²	1	1	yes	characteristic
51	C₃×#897	C₂²	1	2	yes	—
52	C₃×#897	C₂²	1	4	yes	complemented
53	C₃×#896	C₂²	1	2	yes	—
54	C₃×#896	C₂²	1	4	yes	—
55	C₃×#896	C₂²	1	4	yes	complemented
56	C₃×#896	C₂²	1	4	yes	complemented
57	C₃×#893	C₂²	1	1	yes	characteristic
58	C₃×#893	C₂²	1	2	yes	—
59	C₃×#892	C₂²	1	2	yes	—
60	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
61	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
62	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
63	C₃×#890	C₂²	1	2	yes	complemented
64	C₃×#890	C₂²	1	2	yes	complemented
65	C₃×#889	C₂²	1	2	yes	complemented
66	C₃×#889	C₂²	1	4	yes	complemented
67	C₃×#888	C₂²	1	2	yes	complemented
68	C₃×#888	C₂²	1	1	yes	characteristic, complemented
69	C₃×#887	C₂²	1	2	yes	complemented
70	C₃×#67⋊C₄	C₂²	1	2	yes	—
71	C₃×#67⋊C₄	C₂²	1	4	yes	—
72	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₃×#878	C₂²	1	4	yes	complemented
75	C₃×#878	C₂²	1	4	yes	complemented
76	C₃×#878	C₂²	1	4	yes	complemented
77	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
78	C₃×C₄×D₁₂	C₂²	1	2	yes	—
79	C₃×#872	C₂²	1	2	yes	—
80	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
81	C₃×#870	C₂²	1	2	yes	complemented
82	C₃×#869	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
84	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
85	C₃×#554	—	3	2	no	—
86	C₃×#554	—	3	2	no	—
87	C₃×#554	—	3	4	no	—
88	C₃×#554	—	3	1	no	—
89	C₃×#554	—	3	2	no	—
90	C₃×#554	—	3	1	no	—
91	C₃×D₄×Q₈	—	2	1	no	—
92	C₃×D₄×Q₈	—	3	2	no	—
93	C₃×D₄×Q₈	—	3	1	no	—
94	C₃×D₄×Q₈	D₃	1	1	yes	characteristic, complemented
95	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
96	C₃×#544	—	3	2	no	—
97	C₃×#543	—	3	4	no	—
98	C₃×#533	—	3	1	no	—
99	C₃×#533	—	3	1	no	—
100	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
101	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
102	C₃×#518	—	3	2	no	—
103	C₂×C₃×C₄×D₄	—	3	1	no	—
104	Q₈×#67	C₂×C₃	1	2	yes	complemented
105	C₂×#946	C₂×C₃	1	2	yes	complemented
106	#5730	C₂×C₃	1	2	yes	complemented
107	#5729	C₂×C₃	1	2	yes	complemented
108	#5728	C₂×C₃	1	1	yes	characteristic, complemented
109	#5727	C₂×C₃	1	1	yes	characteristic, complemented
110	#5636	C₂×C₃	1	4	yes	complemented
111	#5635	C₂×C₃	1	2	yes	complemented
112	#5634	C₂×C₃	1	4	yes	complemented
113	D₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
114	#5579	C₂×C₃	1	1	yes	characteristic, complemented
115	#5578	C₂×C₃	1	1	yes	characteristic, complemented
116	#5545	C₂×C₃	1	2	yes	—
117	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
118	#5543	C₂×C₃	1	1	yes	characteristic, complemented
119	#5539	C₂×C₃	1	2	yes	complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₂×C₃²×Q₈	—	4	4	no	—
122	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
123	C₂×C₃²×Q₈	C₂³	1	2	yes	—
124	C₂×C₃²×Q₈	C₂³	1	4	yes	—
125	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₃²×C₄	C₂³	1	2	yes	—
127	C₂²×C₃²×C₄	C₂³	1	4	yes	—
128	C₂×C₃×#67	C₂³	1	2	yes	—
129	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
130	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
131	C₃×D₃×Q₈	—	4	4	no	—
132	C₃×D₃×D₄	Q₈	1	8	yes	complemented
133	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄×D₃	—	4	4	no	—
135	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
136	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
139	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
140	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
141	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
142	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
143	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
144	C₂×C₃×Dic₆	C₂³	1	2	yes	—
145	C₂×C₃×Dic₆	C₂³	1	2	yes	—
146	C₂×C₃×Dic₆	C₂³	1	4	yes	—
147	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
151	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₄²	C₂³	1	1	yes	characteristic
156	C₃²×C₄²	C₂³	1	2	yes	—
157	C₃×#217	C₂³	1	2	yes	—
158	C₃×#217	C₂³	1	4	yes	—
159	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
160	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
161	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
162	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
164	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
166	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
167	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
168	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
169	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
170	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
171	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
172	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
173	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
174	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
175	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
180	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
182	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
183	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
184	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
185	C₃×C₄×Dic₃	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	2	yes	—
187	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
188	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
189	#3501	—	3	1	no	Sylow
190	C₂²×C₃×Q₈	—	2	2	no	—
191	C₂²×C₃×Q₈	—	3	2	no	—
192	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	complemented
193	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	complemented
194	C₂²×C₃×D₄	—	3	1	no	—
195	C₂³×C₃×C₄	—	3	2	no	—
196	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
197	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
198	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
199	C₃×C₄⋊Q₈	—	2	1	no	—
200	C₃×C₄⋊Q₈	—	2	2	no	—
201	C₃×C₄⋊Q₈	—	3	1	no	—
202	C₃×C₄⋊Q₈	—	3	4	no	—
203	C₃×C₄⋊Q₈	—	3	1	no	—
204	C₃×C₄⋊Q₈	—	3	2	no	—
205	C₃×C₄⋊Q₈	—	3	1	no	—
206	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
207	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
208	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
209	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
210	C₃×#125	—	3	2	no	—
211	C₃×#125	—	3	4	no	—
212	C₃×#125	—	3	2	no	—
213	C₃×#125	—	3	2	no	—
214	C₃×#125	—	3	2	no	—
215	C₃×C₂²⋊Q₈	—	2	2	no	—
216	C₃×C₂²⋊Q₈	—	2	4	no	—
217	C₃×C₂²⋊Q₈	—	3	2	no	—
218	C₃×C₂²⋊Q₈	—	3	1	no	—
219	C₃×C₂²⋊Q₈	—	3	4	no	—
220	C₃×C₂²⋊Q₈	—	3	2	no	—
221	C₃×C₂²⋊Q₈	—	3	2	no	—
222	C₃×C₂²⋊Q₈	—	3	4	no	—
223	C₃×C₂²⋊Q₈	—	3	4	no	—
224	C₃×C₂²⋊Q₈	—	3	2	no	—
225	C₃×C₂²⋊Q₈	—	3	4	no	—
226	C₃×C₂²⋊Q₈	—	3	4	no	—
227	C₃×C₂²⋊Q₈	—	3	2	no	—
228	C₃×C₂²⋊Q₈	—	3	4	no	—
229	C₃×C₂²⋊Q₈	—	3	4	no	—
230	C₃×C₂²⋊Q₈	—	3	1	no	—
231	C₃×C₂²⋊Q₈	—	3	2	no	—
232	C₃×C₂²⋊Q₈	—	3	4	no	—
233	C₃×C₂²⋊Q₈	—	3	4	no	—
234	C₃×C₂²⋊Q₈	—	3	4	no	—
235	C₃×C₂²⋊Q₈	—	3	4	no	—
236	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
237	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
238	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
239	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
240	C₃×C₄×Q₈	—	2	1	no	—
241	C₃×C₄×Q₈	—	3	2	no	—
242	C₃×C₄×Q₈	—	3	2	no	—
243	C₃×C₄×Q₈	—	3	1	no	—
244	C₃×C₄×Q₈	—	3	2	no	—
245	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
246	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
247	C₃×C₄×D₄	—	2	1	no	—
248	C₃×C₄×D₄	—	2	2	no	—
249	C₃×C₄×D₄	—	3	1	no	—
250	C₃×C₄×D₄	—	3	2	no	—
251	C₃×C₄×D₄	—	3	2	no	—
252	C₃×C₄×D₄	—	3	4	no	—
253	C₃×C₄×D₄	—	3	1	no	—
254	C₃×C₄×D₄	—	3	2	no	—
255	C₃×C₄×D₄	—	3	2	no	—
256	C₃×C₄×D₄	—	3	4	no	—
257	C₃×C₄×D₄	—	3	1	no	—
258	C₃×C₄×D₄	—	3	2	no	—
259	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
260	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
261	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
262	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
263	C₃×#117	—	3	2	no	—
264	C₃×#117	—	3	2	no	—
265	C₂×C₃×C₄⋊C₄	—	3	4	no	—
266	C₂×C₃×C₄⋊C₄	—	3	2	no	—
267	C₂×C₃×C₄⋊C₄	—	3	1	no	—
268	C₂×C₃×C₄⋊C₄	—	3	4	no	—
269	C₂×C₃×C₄⋊C₄	—	3	2	no	—
270	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
271	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
272	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
273	C₂×C₃×C₄²	—	3	1	no	—
274	#946	C₂²×C₃	1	4	yes	—
275	#946	C₂²×C₃	1	2	yes	—
276	#946	C₂²×C₃	1	1	yes	characteristic
277	#946	C₂²×C₃	1	4	yes	complemented
278	#946	C₂²×C₃	1	2	yes	complemented
279	#946	C₂²×C₃	1	4	yes	complemented
280	#946	C₂²×C₃	1	2	yes	complemented
281	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
282	#944	C₂²×C₃	1	4	yes	complemented
283	#944	C₂²×C₃	1	1	yes	characteristic, complemented
284	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
285	D₄×Dic₃	C₂²×C₃	1	2	yes	—
286	C₄×#67	C₂²×C₃	1	2	yes	—
287	C₄×#67	C₂²×C₃	1	4	yes	—
288	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
289	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
290	#924	C₂²×C₃	1	4	yes	complemented
291	#924	C₂²×C₃	1	2	yes	complemented
292	C₂×Dic₃⋊C₄	C₂²×C₃	1	4	yes	complemented
293	#897	C₂²×C₃	1	2	yes	—
294	#897	C₂²×C₃	1	1	yes	characteristic
295	#897	C₂²×C₃	1	4	yes	complemented
296	#896	C₂²×C₃	1	2	yes	—
297	#896	C₂²×C₃	1	4	yes	—
298	#896	C₂²×C₃	1	4	yes	complemented
299	#896	C₂²×C₃	1	4	yes	complemented
300	#893	C₂²×C₃	1	2	yes	—
301	#893	C₂²×C₃	1	1	yes	characteristic
302	#892	C₂²×C₃	1	2	yes	—
303	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
304	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
305	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
306	#890	C₂²×C₃	1	2	yes	complemented
307	#890	C₂²×C₃	1	2	yes	complemented
308	#889	C₂²×C₃	1	4	yes	complemented
309	#889	C₂²×C₃	1	2	yes	complemented
310	#888	C₂²×C₃	1	1	yes	characteristic, complemented
311	#888	C₂²×C₃	1	2	yes	complemented
312	#887	C₂²×C₃	1	2	yes	complemented
313	#67⋊C₄	C₂²×C₃	1	4	yes	—
314	#67⋊C₄	C₂²×C₃	1	2	yes	—
315	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
316	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
317	#878	C₂²×C₃	1	4	yes	complemented
318	#878	C₂²×C₃	1	4	yes	complemented
319	#878	C₂²×C₃	1	4	yes	complemented
320	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
321	C₄×D₁₂	C₂²×C₃	1	2	yes	—
322	#872	C₂²×C₃	1	2	yes	—
323	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
324	#870	C₂²×C₃	1	2	yes	complemented
325	#869	C₂²×C₃	1	1	yes	characteristic, complemented
326	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
328	C₂³×C₃²	C₂⁴	1	2	yes	—
329	C₂²×C₃×D₃	—	4	2	no	—
330	C₂²×C₃×D₃	—	4	2	no	—
331	C₂²×C₃×D₃	C₂×Q₈	1	8	yes	complemented
332	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
334	C₃²×Q₈	—	2	2	no	—
335	C₃²×Q₈	—	2	4	no	—
336	C₃²×Q₈	—	4	4	no	—
337	C₃²×D₄	C₂×Q₈	1	4	yes	complemented
338	C₂×C₃²×C₄	—	2	4	no	—
339	C₂×C₃²×C₄	—	4	4	no	—
340	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
341	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
342	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
343	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
344	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
345	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
346	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
347	C₃×#67	C₂×Q₈	1	8	yes	complemented
348	C₂×C₃×Dic₃	—	4	2	no	—
349	C₂×C₃×Dic₃	—	4	4	no	—
350	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
353	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
354	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
355	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
356	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
357	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
358	C₃×C₄×D₃	—	2	2	no	—
359	C₃×C₄×D₃	—	2	4	no	—
360	C₃×C₄×D₃	—	4	2	no	—
361	C₃×C₄×D₃	—	4	2	no	—
362	C₃×C₄×D₃	—	4	1	no	—
363	C₃×C₄×D₃	—	4	4	no	—
364	C₃×C₄×D₃	—	4	4	no	—
365	C₃×C₄×D₃	C₂×Q₈	1	4	yes	complemented
366	C₃×Dic₆	—	2	2	no	—
367	C₃×Dic₆	—	4	2	no	—
368	C₃×Dic₆	—	4	2	no	—
369	C₃×Dic₆	—	4	4	no	—
370	#554	—	3	2	no	—
371	#554	—	3	2	no	—
372	#554	—	3	4	no	—
373	#554	—	3	1	no	—
374	#554	—	3	2	no	—
375	#554	—	3	1	no	—
376	D₄×Q₈	—	3	2	no	—
377	D₄×Q₈	—	3	1	no	—
378	D₄×Q₈	C₃×D₃	1	1	yes	characteristic, complemented
379	#544	—	3	2	no	—
380	#543	—	3	4	no	—
381	#533	—	3	1	no	—
382	#533	—	3	1	no	—
383	C₂×C₂²⋊Q₈	—	3	2	no	—
384	C₂×C₂²⋊Q₈	—	3	2	no	—
385	#518	—	3	2	no	—
386	C₂×C₄×D₄	—	3	1	no	—
387	C₂⁴×C₃	—	3	2	no	—
388	C₂³×D₃	C₂³×C₃	1	2	yes	—
389	C₂×C₃×Q₈	—	2	1	no	—
390	C₂×C₃×Q₈	—	2	2	no	—
391	C₂×C₃×Q₈	—	2	4	no	—
392	C₂×C₃×Q₈	—	3	1	no	—
393	C₂×C₃×Q₈	—	3	2	no	—
394	C₂×C₃×Q₈	—	3	2	no	—
395	C₂×C₃×Q₈	—	3	4	no	—
396	C₂×C₃×Q₈	—	4	4	no	—
397	C₂×C₃×Q₈	—	4	4	no	—
398	C₂×C₃×Q₈	—	4	8	no	—
399	C₂×C₃×Q₈	—	12	4	no	—
400	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
401	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
402	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
403	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
405	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
406	C₂×C₃×D₄	—	2	1	no	—
407	C₂×C₃×D₄	—	3	2	no	—
408	C₂×C₃×D₄	—	3	8	no	—
409	C₂×C₃×D₄	—	3	1	no	—
410	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
411	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
412	C₂²×C₃×C₄	—	2	2	no	—
413	C₂²×C₃×C₄	—	2	4	no	—
414	C₂²×C₃×C₄	—	3	1	no	—
415	C₂²×C₃×C₄	—	3	4	no	—
416	C₂²×C₃×C₄	—	3	2	no	—
417	C₂²×C₃×C₄	—	3	1	no	—
418	C₂²×C₃×C₄	—	3	2	no	—
419	C₂²×C₃×C₄	—	3	1	no	—
420	C₂²×C₃×C₄	—	3	4	no	—
421	C₂²×C₃×C₄	—	3	4	no	—
422	C₂²×C₃×C₄	—	3	2	no	—
423	C₂²×C₃×C₄	—	3	2	no	—
424	C₂²×C₃×C₄	—	12	4	no	—
425	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
426	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
427	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
428	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
429	C₂×#67	C₂³×C₃	1	2	yes	—
430	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
431	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
432	D₃×Q₈	—	4	4	no	—
433	D₃×D₄	C₃×Q₈	1	8	yes	complemented
434	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄×D₃	—	4	4	no	—
436	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
438	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
440	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
441	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
442	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
443	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
444	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
445	C₂×Dic₆	C₂³×C₃	1	2	yes	—
446	C₂×Dic₆	C₂³×C₃	1	2	yes	—
447	C₂×Dic₆	C₂³×C₃	1	4	yes	—
448	C₃×C₄⋊C₄	—	2	1	no	—
449	C₃×C₄⋊C₄	—	2	2	no	—
450	C₃×C₄⋊C₄	—	2	1	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	4	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	3	4	no	—
455	C₃×C₄⋊C₄	—	3	2	no	—
456	C₃×C₄⋊C₄	—	3	2	no	—
457	C₃×C₄⋊C₄	—	3	4	no	—
458	C₃×C₄⋊C₄	—	3	4	no	—
459	C₃×C₄⋊C₄	—	3	4	no	—
460	C₃×C₄⋊C₄	—	3	4	no	—
461	C₃×C₄⋊C₄	—	3	2	no	—
462	C₃×C₄⋊C₄	—	3	2	no	—
463	C₃×C₄⋊C₄	—	3	2	no	—
464	C₃×C₄⋊C₄	—	3	2	no	—
465	C₃×C₄⋊C₄	—	3	2	no	—
466	C₃×C₄⋊C₄	—	3	1	no	—
467	C₃×C₄⋊C₄	—	3	2	no	—
468	C₃×C₄⋊C₄	—	3	1	no	—
469	C₃×C₄⋊C₄	—	3	4	no	—
470	C₃×C₄⋊C₄	—	3	2	no	—
471	C₃×C₄⋊C₄	—	3	4	no	—
472	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
473	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
474	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
475	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
476	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
477	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
482	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₃×C₂²⋊C₄	—	2	2	no	—
485	C₃×C₂²⋊C₄	—	2	4	no	—
486	C₃×C₂²⋊C₄	—	3	2	no	—
487	C₃×C₂²⋊C₄	—	3	4	no	—
488	C₃×C₂²⋊C₄	—	3	4	no	—
489	C₃×C₂²⋊C₄	—	3	2	no	—
490	C₃×C₂²⋊C₄	—	3	2	no	—
491	C₃×C₂²⋊C₄	—	3	2	no	—
492	C₃×C₂²⋊C₄	—	3	4	no	—
493	C₃×C₂²⋊C₄	—	3	4	no	—
494	C₃×C₂²⋊C₄	—	3	2	no	—
495	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
496	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₃×C₄²	—	2	1	no	—
500	C₃×C₄²	—	2	2	no	—
501	C₃×C₄²	—	3	1	no	—
502	C₃×C₄²	—	3	1	no	—
503	C₃×C₄²	—	3	1	no	—
504	C₃×C₄²	—	3	4	no	—
505	C₃×C₄²	—	3	2	no	—
506	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
507	C₃×C₄²	C₂²×D₃	1	2	yes	—
508	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
509	C₃×C₄²	C₂³×C₃	1	2	yes	—
510	#217	C₂³×C₃	1	2	yes	—
511	#217	C₂³×C₃	1	4	yes	—
512	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
513	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
514	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
516	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
517	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
518	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
519	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
520	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
521	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
522	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
523	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
524	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
525	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
526	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
527	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
528	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
529	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
530	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
531	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
532	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
533	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
534	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
535	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
536	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
537	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
538	C₄×Dic₃	C₂³×C₃	1	2	yes	—
539	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
540	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
541	C₄×Dic₃	C₂³×C₃	1	4	yes	—
542	C₂²×C₃²	—	2	2	no	—
543	C₂²×C₃²	—	2	2	no	—
544	C₂²×C₃²	C₂²×Q₈	1	4	yes	—
545	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
546	C₂×C₃×D₃	—	2	2	no	—
547	C₂×C₃×D₃	—	2	1	no	—
548	C₂×C₃×D₃	—	2	2	no	—
549	C₂×C₃×D₃	—	2	1	no	—
550	C₂×C₃×D₃	—	4	8	no	—
551	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
552	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	—
553	C₃²×C₄	—	2	2	no	—
554	C₃²×C₄	—	2	4	no	—
555	C₃²×C₄	—	2	2	no	—
556	C₃²×C₄	—	2	1	no	—
557	C₃²×C₄	—	2	2	no	—
558	C₃²×C₄	C₂²×Q₈	1	2	yes	—
559	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
560	C₃×Dic₃	—	2	2	no	—
561	C₃×Dic₃	—	2	2	no	—
562	C₃×Dic₃	—	2	1	no	—
563	C₃×Dic₃	—	2	1	no	—
564	C₃×Dic₃	—	2	4	no	—
565	C₃×Dic₃	—	2	2	no	—
566	C₃×Dic₃	C₂²×Q₈	1	2	yes	—
567	C₂²×Q₈	—	3	2	no	—
568	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	complemented
569	C₂²×D₄	—	3	1	no	—
570	C₂³×C₄	—	3	2	no	—
571	C₄⋊Q₈	—	3	1	no	—
572	C₄⋊Q₈	—	3	4	no	—
573	C₄⋊Q₈	—	3	1	no	—
574	C₄⋊Q₈	—	3	2	no	—
575	C₄⋊Q₈	—	3	1	no	—
576	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
577	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
578	#125	—	3	2	no	—
579	#125	—	3	2	no	—
580	#125	—	3	4	no	—
581	#125	—	3	2	no	—
582	#125	—	3	2	no	—
583	C₂²⋊Q₈	—	3	2	no	—
584	C₂²⋊Q₈	—	3	1	no	—
585	C₂²⋊Q₈	—	3	4	no	—
586	C₂²⋊Q₈	—	3	2	no	—
587	C₂²⋊Q₈	—	3	2	no	—
588	C₂²⋊Q₈	—	3	4	no	—
589	C₂²⋊Q₈	—	3	4	no	—
590	C₂²⋊Q₈	—	3	2	no	—
591	C₂²⋊Q₈	—	3	4	no	—
592	C₂²⋊Q₈	—	3	1	no	—
593	C₂²⋊Q₈	—	3	4	no	—
594	C₂²⋊Q₈	—	3	2	no	—
595	C₂²⋊Q₈	—	3	2	no	—
596	C₂²⋊Q₈	—	3	4	no	—
597	C₂²⋊Q₈	—	3	4	no	—
598	C₂²⋊Q₈	—	3	4	no	—
599	C₂²⋊Q₈	—	3	4	no	—
600	C₂²⋊Q₈	—	3	4	no	—
601	C₂²⋊Q₈	—	3	4	no	—
602	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
603	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
604	C₄×Q₈	—	3	2	no	—
605	C₄×Q₈	—	3	2	no	—
606	C₄×Q₈	—	3	1	no	—
607	C₄×Q₈	—	3	2	no	—
608	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
609	C₄×D₄	—	3	1	no	—
610	C₄×D₄	—	3	2	no	—
611	C₄×D₄	—	3	2	no	—
612	C₄×D₄	—	3	4	no	—
613	C₄×D₄	—	3	1	no	—
614	C₄×D₄	—	3	2	no	—
615	C₄×D₄	—	3	2	no	—
616	C₄×D₄	—	3	4	no	—
617	C₄×D₄	—	3	1	no	—
618	C₄×D₄	—	3	2	no	—
619	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
620	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
621	#117	—	3	2	no	—
622	#117	—	3	2	no	—
623	C₂×C₄⋊C₄	—	3	4	no	—
624	C₂×C₄⋊C₄	—	3	2	no	—
625	C₂×C₄⋊C₄	—	3	1	no	—
626	C₂×C₄⋊C₄	—	3	4	no	—
627	C₂×C₄⋊C₄	—	3	2	no	—
628	C₂×C₂²⋊C₄	—	3	4	no	—
629	C₂×C₂²⋊C₄	—	3	2	no	—
630	C₂×C₂²⋊C₄	—	3	4	no	—
631	C₂×C₄²	—	3	1	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	3	1	no	—
634	C₂³×C₃	—	3	2	no	—
635	C₂³×C₃	—	3	8	no	—
636	C₂³×C₃	—	12	2	no	—
637	C₂³×C₃	—	12	2	no	—
638	C₂³×C₃	C₂³×D₃	1	2	yes	—
639	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
640	C₂²×D₃	—	4	2	no	—
641	C₂²×D₃	—	4	2	no	—
642	C₂²×D₃	C₂×C₃×Q₈	1	8	yes	complemented
643	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
644	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
645	C₃×Q₈	—	2	4	no	—
646	C₃×Q₈	—	2	2	no	—
647	C₃×Q₈	—	2	4	no	—
648	C₃×Q₈	—	2	4	no	—
649	C₃×Q₈	—	2	2	no	—
650	C₃×Q₈	—	4	4	no	—
651	C₃×Q₈	—	4	4	no	—
652	C₃×Q₈	—	4	4	no	—
653	C₃×Q₈	—	4	8	no	—
654	C₃×Q₈	—	6	2	no	—
655	C₃×Q₈	—	12	2	no	—
656	C₃×Q₈	—	12	2	no	—
657	C₃×Q₈	—	12	4	no	—
658	C₃×D₄	—	2	4	no	—
659	C₃×D₄	—	3	8	no	—
660	C₃×D₄	—	3	4	no	—
661	C₃×D₄	D₃×Q₈	1	4	yes	complemented
662	C₃×D₄	C₂×C₃×Q₈	1	4	yes	complemented
663	C₂×C₃×C₄	—	2	4	no	—
664	C₂×C₃×C₄	—	2	4	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	4	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	3	1	no	—
673	C₂×C₃×C₄	—	3	4	no	—
674	C₂×C₃×C₄	—	3	1	no	—
675	C₂×C₃×C₄	—	3	1	no	—
676	C₂×C₃×C₄	—	3	2	no	—
677	C₂×C₃×C₄	—	3	4	no	—
678	C₂×C₃×C₄	—	3	2	no	—
679	C₂×C₃×C₄	—	3	2	no	—
680	C₂×C₃×C₄	—	4	4	no	—
681	C₂×C₃×C₄	—	4	4	no	—
682	C₂×C₃×C₄	—	4	4	no	—
683	C₂×C₃×C₄	—	4	8	no	—
684	C₂×C₃×C₄	—	6	2	no	—
685	C₂×C₃×C₄	—	6	4	no	—
686	C₂×C₃×C₄	—	12	4	no	—
687	C₂×C₃×C₄	—	12	1	no	—
688	C₂×C₃×C₄	—	12	2	no	—
689	C₂×C₃×C₄	—	12	2	no	—
690	C₂×C₃×C₄	—	12	4	no	—
691	C₂×C₃×C₄	—	12	4	no	—
692	C₂×C₃×C₄	—	12	2	no	—
693	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
694	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
695	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
696	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
697	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
698	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
699	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
700	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
701	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
702	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
705	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	#67	C₂×C₃×Q₈	1	8	yes	complemented
708	C₂×Dic₃	—	4	2	no	—
709	C₂×Dic₃	—	4	4	no	—
710	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
711	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
712	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
713	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
714	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
715	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
716	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
717	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
718	C₄×D₃	—	2	2	no	—
719	C₄×D₃	—	2	4	no	—
720	C₄×D₃	—	4	2	no	—
721	C₄×D₃	—	4	2	no	—
722	C₄×D₃	—	4	1	no	—
723	C₄×D₃	—	4	4	no	—
724	C₄×D₃	—	4	4	no	—
725	C₄×D₃	C₂×C₃×Q₈	1	4	yes	complemented
726	Dic₆	—	2	2	no	—
727	Dic₆	—	4	2	no	—
728	Dic₆	—	4	2	no	—
729	Dic₆	—	4	4	no	—
730	C₂×C₃²	—	2	4	no	—
731	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
732	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂×C₃²	#585	1	1	yes	characteristic
734	C₃×D₃	—	2	2	no	—
735	C₃×D₃	—	2	4	no	—
736	C₂⁴	—	3	2	no	—
737	C₂×Q₈	—	3	1	no	—
738	C₂×Q₈	—	3	2	no	—
739	C₂×Q₈	—	3	2	no	—
740	C₂×Q₈	—	3	4	no	—
741	C₂×Q₈	—	4	4	no	—
742	C₂×Q₈	—	12	4	no	—
743	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
744	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
745	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
746	C₂×D₄	—	3	2	no	—
747	C₂×D₄	—	3	8	no	—
748	C₂×D₄	—	3	1	no	—
749	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
750	C₂²×C₄	—	3	1	no	—
751	C₂²×C₄	—	3	4	no	—
752	C₂²×C₄	—	3	2	no	—
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	3	2	no	—
755	C₂²×C₄	—	3	1	no	—
756	C₂²×C₄	—	3	4	no	—
757	C₂²×C₄	—	3	4	no	—
758	C₂²×C₄	—	3	2	no	—
759	C₂²×C₄	—	3	2	no	—
760	C₂²×C₄	—	12	4	no	—
761	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
762	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
763	C₄⋊C₄	—	3	4	no	—
764	C₄⋊C₄	—	3	2	no	—
765	C₄⋊C₄	—	3	2	no	—
766	C₄⋊C₄	—	3	1	no	—
767	C₄⋊C₄	—	3	2	no	—
768	C₄⋊C₄	—	3	2	no	—
769	C₄⋊C₄	—	3	1	no	—
770	C₄⋊C₄	—	3	4	no	—
771	C₄⋊C₄	—	3	4	no	—
772	C₄⋊C₄	—	3	4	no	—
773	C₄⋊C₄	—	3	4	no	—
774	C₄⋊C₄	—	3	4	no	—
775	C₄⋊C₄	—	3	2	no	—
776	C₄⋊C₄	—	3	2	no	—
777	C₄⋊C₄	—	3	2	no	—
778	C₄⋊C₄	—	3	2	no	—
779	C₄⋊C₄	—	3	4	no	—
780	C₄⋊C₄	—	3	2	no	—
781	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
784	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
785	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
786	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
787	C₂²⋊C₄	—	3	2	no	—
788	C₂²⋊C₄	—	3	4	no	—
789	C₂²⋊C₄	—	3	4	no	—
790	C₂²⋊C₄	—	3	2	no	—
791	C₂²⋊C₄	—	3	2	no	—
792	C₂²⋊C₄	—	3	2	no	—
793	C₂²⋊C₄	—	3	4	no	—
794	C₂²⋊C₄	—	3	4	no	—
795	C₂²⋊C₄	—	3	2	no	—
796	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
797	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
798	C₄²	—	3	1	no	—
799	C₄²	—	3	1	no	—
800	C₄²	—	3	1	no	—
801	C₄²	—	3	4	no	—
802	C₄²	—	3	2	no	—
803	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
804	C₄²	C₂²×C₃×D₃	1	2	yes	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	2	2	no	—
807	C₂²×C₃	—	2	2	no	—
808	C₂²×C₃	—	2	2	no	—
809	C₂²×C₃	—	2	4	no	—
810	C₂²×C₃	—	2	1	no	—
811	C₂²×C₃	—	3	2	no	—
812	C₂²×C₃	—	3	4	no	—
813	C₂²×C₃	—	4	2	no	—
814	C₂²×C₃	—	4	2	no	—
815	C₂²×C₃	—	6	2	no	—
816	C₂²×C₃	—	6	1	no	—
817	C₂²×C₃	—	6	2	no	—
818	C₂²×C₃	—	6	1	no	—
819	C₂²×C₃	—	12	8	no	—
820	C₂²×C₃	C₂×D₃×Q₈	1	4	yes	—
821	C₂²×C₃	C₂²×C₃×Q₈	1	4	yes	—
822	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
823	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
824	C₂×D₃	—	2	2	no	—
825	C₂×D₃	—	2	1	no	—
826	C₂×D₃	—	2	2	no	—
827	C₂×D₃	—	2	1	no	—
828	C₂×D₃	—	4	8	no	—
829	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
830	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	—
831	C₃×C₄	—	2	4	no	—
832	C₃×C₄	—	2	2	no	—
833	C₃×C₄	—	2	2	no	—
834	C₃×C₄	—	2	4	no	—
835	C₃×C₄	—	2	2	no	—
836	C₃×C₄	—	2	1	no	—
837	C₃×C₄	—	2	4	no	—
838	C₃×C₄	—	2	2	no	—
839	C₃×C₄	—	2	2	no	—
840	C₃×C₄	—	2	1	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	2	2	no	—
843	C₃×C₄	—	2	2	no	—
844	C₃×C₄	—	3	2	no	—
845	C₃×C₄	—	4	2	no	—
846	C₃×C₄	—	4	4	no	—
847	C₃×C₄	—	4	2	no	—
848	C₃×C₄	—	4	1	no	—
849	C₃×C₄	—	6	1	no	—
850	C₃×C₄	—	6	2	no	—
851	C₃×C₄	—	6	2	no	—
852	C₃×C₄	—	6	4	no	—
853	C₃×C₄	—	6	2	no	—
854	C₃×C₄	—	6	1	no	—
855	C₃×C₄	#1004	1	2	yes	—
856	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
857	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
858	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
859	Dic₃	—	2	2	no	—
860	Dic₃	—	2	2	no	—
861	Dic₃	—	2	1	no	—
862	Dic₃	—	2	1	no	—
863	Dic₃	—	2	4	no	—
864	Dic₃	—	2	2	no	—
865	Dic₃	C₂²×C₃×Q₈	1	2	yes	—
866	C₃²	#3501	1	1	yes	characteristic, complemented, Sylow
867	C₂³	—	3	1	no	—
868	C₂³	—	3	2	no	—
869	C₂³	—	3	8	no	—
870	C₂³	—	12	2	no	—
871	C₂³	—	12	2	no	—
872	C₂³	C₂³×C₃×D₃	1	2	yes	—
873	Q₈	—	2	2	no	—
874	Q₈	—	2	4	no	—
875	Q₈	—	4	4	no	—
876	Q₈	—	6	2	no	—
877	Q₈	—	12	4	no	—
878	Q₈	—	12	2	no	—
879	Q₈	—	12	2	no	—
880	D₄	—	3	8	no	—
881	D₄	—	3	4	no	—
882	D₄	C₃×D₃×Q₈	1	4	yes	complemented
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	3	1	no	—
885	C₂×C₄	—	3	4	no	—
886	C₂×C₄	—	3	1	no	—
887	C₂×C₄	—	3	1	no	—
888	C₂×C₄	—	3	4	no	—
889	C₂×C₄	—	3	2	no	—
890	C₂×C₄	—	3	2	no	—
891	C₂×C₄	—	3	2	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	6	2	no	—
894	C₂×C₄	—	6	4	no	—
895	C₂×C₄	—	12	2	no	—
896	C₂×C₄	—	12	2	no	—
897	C₂×C₄	—	12	4	no	—
898	C₂×C₄	—	12	4	no	—
899	C₂×C₄	—	12	1	no	—
900	C₂×C₄	—	12	2	no	—
901	C₂×C₄	—	12	4	no	—
902	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
903	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
904	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
905	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
906	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
907	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
908	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
909	C₂×C₃	—	2	4	no	—
910	C₂×C₃	—	2	4	no	—
911	C₂×C₃	—	2	1	no	—
912	C₂×C₃	—	2	1	no	—
913	C₂×C₃	—	2	1	no	—
914	C₂×C₃	—	4	4	no	—
915	C₂×C₃	—	6	2	no	—
916	C₂×C₃	—	6	4	no	—
917	C₂×C₃	C₂×#1004	1	1	yes	characteristic
918	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
919	C₂×C₃	#5968	1	1	yes	characteristic
920	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
921	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
922	C₂×C₃	C₃×#585	1	1	yes	characteristic
923	D₃	—	2	2	no	—
924	D₃	—	2	4	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	3	2	no	—
928	C₂²	—	3	4	no	—
929	C₂²	—	6	2	no	—
930	C₂²	—	6	1	no	—
931	C₂²	—	6	2	no	—
932	C₂²	—	6	1	no	—
933	C₂²	—	12	8	no	—
934	C₂²	C₂×C₃×D₃×Q₈	1	4	yes	—
935	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	1	no	—
941	C₄	—	3	2	no	—
942	C₄	—	6	1	no	—
943	C₄	—	6	2	no	—
944	C₄	—	6	2	no	—
945	C₄	—	6	4	no	—
946	C₄	—	6	2	no	—
947	C₄	—	6	1	no	—
948	C₄	C₃×#1004	1	2	yes	—
949	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
950	C₃	—	2	1	no	—
951	C₃	#86761	1	1	yes	characteristic, direct product factor
952	C₃	C₃×#3501	1	1	yes	characteristic, complemented
953	C₂	—	2	4	no	—
954	C₂	—	6	2	no	—
955	C₂	—	6	4	no	—
956	C₂	C₂×C₃×#1004	1	1	yes	characteristic
957	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
958	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×D₄×Q₈	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×D₄×Q₈	D₃
hypocenter	C₃	C₃×#3501
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃²×D₄×Q₈	C₂	semidirect
2. C₃×Q₈×#67	C₂	semidirect
3. C₂×C₃×#946	C₂	semidirect
4. C₃×#5730	C₂	semidirect
5. C₃×#5729	C₂	semidirect
6. C₃×#5728	C₂	semidirect
7. C₃×#5727	C₂	semidirect
8. C₃×#5636	C₂	semidirect
9. C₃×#5635	C₂	semidirect
10. C₃×#5634	C₂	semidirect
11. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
12. C₃×#5579	C₂	semidirect
13. C₃×#5578	C₂	semidirect
16. C₃×#5543	C₂	semidirect
17. C₃×#5539	C₂	semidirect
19. #86761	C₃	direct (N × H)
20. C₂²×C₃²×Q₈	C₂²	semidirect
21. C₂×C₃×D₃×Q₈	C₂²	semidirect
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×C₄⋊Q₈	C₂²	semidirect
26. C₃²×C₂²⋊Q₈	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₃²×C₄×Q₈	C₂²	semidirect
34. C₃×#946	C₂²	semidirect
35. C₃×#946	C₂²	semidirect
36. C₃×#946	C₂²	semidirect
37. C₃×#946	C₂²	semidirect
38. C₃×Q₈×Dic₃	C₂²	semidirect
39. C₃×#944	C₂²	semidirect
40. C₃×#944	C₂²	semidirect
46. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
47. C₃×#924	C₂²	semidirect
48. C₃×#924	C₂²	semidirect
49. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
52. C₃×#897	C₂²	semidirect
55. C₃×#896	C₂²	semidirect
56. C₃×#896	C₂²	semidirect
61. C₃×D₃×C₄⋊C₄	C₂²	semidirect
62. C₃×D₃×C₄⋊C₄	C₂²	semidirect
63. C₃×#890	C₂²	semidirect
64. C₃×#890	C₂²	semidirect
65. C₃×#889	C₂²	semidirect
66. C₃×#889	C₂²	semidirect
67. C₃×#888	C₂²	semidirect
68. C₃×#888	C₂²	semidirect
69. C₃×#887	C₂²	semidirect
74. C₃×#878	C₂²	semidirect
75. C₃×#878	C₂²	semidirect
76. C₃×#878	C₂²	semidirect
81. C₃×#870	C₂²	semidirect
82. C₃×#869	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
94. C₃×D₄×Q₈	D₃	semidirect
95. C₃×D₄×Q₈	C₂×C₃	semidirect
104. Q₈×#67	C₂×C₃	semidirect
105. C₂×#946	C₂×C₃	semidirect
106. #5730	C₂×C₃	semidirect
107. #5729	C₂×C₃	semidirect
108. #5728	C₂×C₃	semidirect
109. #5727	C₂×C₃	semidirect
110. #5636	C₂×C₃	semidirect
111. #5635	C₂×C₃	semidirect
112. #5634	C₂×C₃	semidirect
113. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
114. #5579	C₂×C₃	semidirect
115. #5578	C₂×C₃	semidirect
118. #5543	C₂×C₃	semidirect
119. #5539	C₂×C₃	semidirect
132. C₃×D₃×D₄	Q₈	semidirect
192. C₂²×C₃×Q₈	C₂×D₃	semidirect
193. C₂²×C₃×Q₈	C₂²×C₃	semidirect
196. C₂×D₃×Q₈	C₂²×C₃	semidirect
206. C₃×C₄⋊Q₈	C₂×D₃	semidirect
207. C₃×C₄⋊Q₈	C₂×D₃	semidirect
208. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
209. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
236. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
237. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
238. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
239. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
245. C₃×C₄×Q₈	C₂×D₃	semidirect
246. C₃×C₄×Q₈	C₂²×C₃	semidirect
277. #946	C₂²×C₃	semidirect
278. #946	C₂²×C₃	semidirect
279. #946	C₂²×C₃	semidirect
280. #946	C₂²×C₃	semidirect
281. Q₈×Dic₃	C₂²×C₃	semidirect
282. #944	C₂²×C₃	semidirect
283. #944	C₂²×C₃	semidirect
289. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
290. #924	C₂²×C₃	semidirect
291. #924	C₂²×C₃	semidirect
292. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
295. #897	C₂²×C₃	semidirect
298. #896	C₂²×C₃	semidirect
299. #896	C₂²×C₃	semidirect
304. D₃×C₄⋊C₄	C₂²×C₃	semidirect
305. D₃×C₄⋊C₄	C₂²×C₃	semidirect
306. #890	C₂²×C₃	semidirect
307. #890	C₂²×C₃	semidirect
308. #889	C₂²×C₃	semidirect
309. #889	C₂²×C₃	semidirect
310. #888	C₂²×C₃	semidirect
311. #888	C₂²×C₃	semidirect
312. #887	C₂²×C₃	semidirect
317. #878	C₂²×C₃	semidirect
318. #878	C₂²×C₃	semidirect
319. #878	C₂²×C₃	semidirect
324. #870	C₂²×C₃	semidirect
325. #869	C₂²×C₃	semidirect
326. C₄×Dic₆	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
331. C₂²×C₃×D₃	C₂×Q₈	semidirect
337. C₃²×D₄	C₂×Q₈	semidirect
347. C₃×#67	C₂×Q₈	semidirect
357. C₃×D₁₂	C₂×Q₈	semidirect
365. C₃×C₄×D₃	C₂×Q₈	semidirect
378. D₄×Q₈	C₃×D₃	semidirect
433. D₃×D₄	C₃×Q₈	semidirect
568. C₂²×Q₈	C₂×C₃×D₃	semidirect
576. C₄⋊Q₈	C₂×C₃×D₃	semidirect
577. C₄⋊Q₈	C₂×C₃×D₃	semidirect
602. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
603. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
608. C₄×Q₈	C₂×C₃×D₃	semidirect
642. C₂²×D₃	C₂×C₃×Q₈	semidirect
661. C₃×D₄	D₃×Q₈	semidirect
662. C₃×D₄	C₂×C₃×Q₈	semidirect
707. #67	C₂×C₃×Q₈	semidirect
717. D₁₂	C₂×C₃×Q₈	semidirect
725. C₄×D₃	C₂×C₃×Q₈	semidirect
866. C₃²	#3501	semidirect
882. D₄	C₃×D₃×Q₈	semidirect
951. C₃	#86761	direct (N × H)
952. C₃	C₃×#3501	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₄×Q₈	2
C₃×Q₈×#67	2
C₂×C₃×#946	2
C₃×#5730	2
C₃×#5729	2
C₃×#5728	2
C₃×#5727	2
C₃×#5636	2
C₃×#5635	2
C₃×#5634	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5579	2
C₃×#5578	2
C₃×#5545	2
C₃×C₄×D₃×D₄	2
C₃×#5543	2
C₃×#5539	2
C₃×#3501	3
#86761	3

Subgroups — C3×#86761 #11906154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86761 #11906154