Subgroups — #27096293

Order 12032.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257264	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257207	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256200	C₂	1	2	yes	maximal, complemented
4	#20256178	C₂	1	2	yes	maximal, complemented
5	#20256115	C₂	1	2	yes	maximal, complemented
6	#20256093	C₂	1	2	yes	maximal, complemented
7	#20256082	C₂	1	2	yes	maximal, complemented
8	#20256057	C₂	1	2	yes	maximal, complemented
9	#20256046	C₂	1	2	yes	maximal, complemented
10	#20256021	C₂	1	2	yes	maximal, complemented
11	#20253746	C₂	1	2	yes	maximal, complemented
12	C₂×#15689470	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253222	C₂	1	2	yes	maximal, complemented
14	#20253203	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252925	C₂	1	2	yes	maximal, complemented
16	#20252868	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252322	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252223	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13094049	C₂²	1	2	yes	—
21	#15689858	C₂²	1	2	yes	—
22	#15689858	C₂²	1	2	yes	—
23	Q₈×Dic₉₄	C₂²	1	2	yes	complemented
24	#15689852	C₂²	1	2	yes	complemented
25	#15689830	—	2	2	no	—
26	#15689830	C₂²	1	2	yes	complemented
27	#15689794	C₂²	1	2	yes	—
28	#15689794	C₂²	1	2	yes	—
29	D₄×Dic₉₄	—	2	2	no	—
30	D₄×Dic₉₄	C₂²	1	2	yes	complemented
31	#15689769	—	2	2	no	—
32	#15689769	—	2	2	no	—
33	#15689751	—	2	2	no	—
34	#15689751	C₂²	1	2	yes	—
35	#15689728	—	2	2	no	—
36	#15689687	C₂²	1	2	yes	—
37	#15689680	—	2	1	no	—
38	#15689680	C₂²	1	1	yes	characteristic
39	#15689673	—	2	1	no	—
40	#15689673	—	2	1	no	—
41	C₂×#13094024	—	2	1	no	—
42	C₂×#13094024	C₂²	1	1	yes	characteristic
43	C₂×#13094021	C₂²	1	1	yes	characteristic
44	#15689606	C₂²	1	2	yes	—
45	#15689597	C₂²	1	2	yes	—
46	#15689486	C₂²	1	4	yes	complemented
47	#15689484	C₂²	1	4	yes	complemented
48	#15689479	C₂²	1	4	yes	complemented
49	#15689470	C₂²	1	2	yes	—
50	#15689470	C₂²	1	2	yes	—
51	#15689470	C₂²	1	2	yes	—
52	#15689470	C₂²	1	2	yes	—
53	#15689468	C₂²	1	4	yes	complemented
54	#15689426	C₂²	1	4	yes	complemented
55	#15689422	C₂²	1	4	yes	complemented
56	#15689418	C₂²	1	2	yes	complemented
57	#15689413	C₂²	1	2	yes	complemented
58	#15689412	C₂²	1	4	yes	complemented
59	#15689408	C₂²	1	2	yes	complemented
60	#15689403	C₂²	1	2	yes	complemented
61	#15689402	C₂²	1	4	yes	complemented
62	#15689347	C₂²	1	4	yes	complemented
63	#15689340	C₂²	1	4	yes	complemented
64	#15689323	C₂²	1	2	yes	—
65	#15689323	C₂²	1	2	yes	—
66	#15689321	C₂²	1	4	yes	complemented
67	#15689318	C₂²	1	2	yes	—
68	#15689318	C₂²	1	2	yes	—
69	#15689316	C₂²	1	4	yes	complemented
70	#15689253	C₂²	1	2	yes	complemented
71	#15689253	C₂²	1	2	yes	complemented
72	C₈×Dic₉₄	C₂²	1	2	yes	complemented
73	C₈×Dic₉₄	C₂²	1	2	yes	complemented
74	#15689232	C₂²	1	4	yes	complemented
75	#15689226	C₂²	1	4	yes	complemented
76	#15689208	C₂²	1	4	yes	complemented
77	#15689203	C₂²	1	4	yes	complemented
78	#15689166	C₂²	1	2	yes	—
79	#15689149	C₂²	1	2	yes	—
80	#15689147	C₂²	1	1	yes	characteristic
81	#15689127	C₂²	1	2	yes	—
82	#15689124	C₂²	1	2	yes	—
83	C₂×#13093946	C₂²	1	2	yes	—
84	C₂×#13093946	C₂²	1	2	yes	—
85	#15689078	C₂²	1	2	yes	—
86	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
87	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
88	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
89	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
90	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
93	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
97	C₄₇×#427	C₂²	1	1	yes	characteristic
98	C₄₇×#416	C₂²	1	1	yes	characteristic
99	C₄₇×#416	C₂²	1	1	yes	characteristic
100	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
101	C₂×#10625350	—	2	2	no	—
102	C₂×#10625350	—	2	2	no	—
103	C₂²×Dic₉₄	—	2	1	no	—
104	C₂²×Dic₉₄	—	2	2	no	—
105	C₂²×D₁₈₈	—	2	1	no	—
106	C₂²×D₁₈₈	—	2	1	no	—
107	C₂²×D₁₈₈	C₂³	1	2	yes	—
108	#13094049	—	2	8	no	—
109	C₂×#10625336	C₂³	1	4	yes	—
110	C₂×#10625334	C₂³	1	4	yes	—
111	C₂×#10625329	C₂³	1	2	yes	—
112	#13094024	—	2	2	no	—
113	#13094024	—	2	1	no	—
114	#13094024	—	2	1	no	—
115	#13094024	—	2	2	no	—
116	#13094024	—	2	2	no	—
117	#13094024	D₄	1	1	yes	characteristic
118	#13094024	D₄	1	1	yes	characteristic
119	#13094024	C₂³	1	2	yes	—
120	#13094024	C₂³	1	2	yes	—
121	#13094023	—	2	4	no	—
122	#13094023	C₂³	1	4	yes	—
123	#13094021	—	2	1	no	—
124	#13094021	—	2	1	no	—
125	#13094021	C₂³	1	2	yes	—
126	#13094021	C₂³	1	2	yes	—
127	#13094020	C₂³	1	4	yes	—
128	#13094016	—	2	2	no	—
129	#13094016	D₄	1	2	yes	—
130	#13094015	—	2	4	no	—
131	#13094015	C₂³	1	4	yes	—
132	#13094013	C₂³	1	4	yes	—
133	#13094012	—	2	2	no	—
134	#13094012	—	2	2	no	—
135	#13094009	—	2	4	no	—
136	#13094009	—	2	4	no	—
137	#13094003	—	2	2	no	—
138	#13094003	—	2	2	no	—
139	#13094003	D₄	1	2	yes	—
140	#13094003	D₄	1	2	yes	—
141	#13094001	—	2	4	no	—
142	#13094001	—	2	4	no	—
143	#13094001	—	2	4	no	—
144	#13093998	—	2	2	no	—
145	#13093998	—	2	2	no	—
146	#13093998	—	2	2	no	—
147	#13093998	—	2	2	no	—
148	#13093997	—	2	4	no	—
149	#13093997	—	2	4	no	—
150	#13093992	—	2	4	no	—
151	Q₈×Dic₄₇	C₂³	1	4	yes	—
152	C₄×Dic₉₄	—	2	2	no	—
153	C₄×Dic₉₄	—	2	2	no	—
154	C₄×Dic₉₄	C₂³	1	2	yes	—
155	C₄×Dic₉₄	C₂³	1	2	yes	—
156	C₄×D₁₈₈	—	2	2	no	—
157	C₄×D₁₈₈	—	2	2	no	—
158	C₄×D₁₈₈	—	2	2	no	—
159	C₄×D₁₈₈	—	2	2	no	—
160	D₄×Dic₄₇	—	2	4	no	—
161	D₄×Dic₄₇	C₂³	1	4	yes	—
162	#13093986	C₂³	1	4	yes	—
163	#13093986	C₂³	1	4	yes	—
164	#13093983	—	2	2	no	—
165	#13093983	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₄₇	—	2	1	no	—
167	C₂×C₄⋊Dic₄₇	—	2	2	no	—
168	C₂×C₄⋊Dic₄₇	—	2	2	no	—
169	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
170	C₂²⋊C₄×D₄₇	—	2	4	no	—
171	#13093957	C₂³	1	4	yes	—
172	#13093955	C₂³	1	4	yes	—
173	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
174	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
175	Dic₄₇⋊C₈	C₂³	1	4	yes	—
176	Dic₄₇⋊C₈	C₂³	1	4	yes	—
177	#13093948	C₂³	1	4	yes	—
178	#13093946	C₂³	1	4	yes	—
179	#13093946	C₂³	1	4	yes	—
180	#13093946	C₂³	1	4	yes	—
181	#13093946	C₂³	1	4	yes	—
182	#13093945	C₂³	1	4	yes	—
183	#13093944	C₂³	1	4	yes	—
184	#13093944	C₂³	1	4	yes	—
185	#13093934	C₂³	1	4	yes	—
186	C₈×Dic₄₇	C₂³	1	4	yes	—
187	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
188	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
189	#135×C₄₇	—	2	4	no	—
190	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
191	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
192	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
193	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
194	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
195	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
196	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
197	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
198	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
199	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₄₇	—	2	1	no	—
201	C₄×D₄×C₄₇	—	2	1	no	—
202	C₄×D₄×C₄₇	—	2	1	no	—
203	C₄×D₄×C₄₇	—	2	1	no	—
204	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
205	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
206	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
208	#117×C₄₇	—	2	1	no	—
209	#117×C₄₇	—	2	1	no	—
210	#117×C₄₇	C₂³	1	1	yes	characteristic
211	#117×C₄₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₄₇	—	2	1	no	—
213	C₂×C₄²×C₄₇	—	2	1	no	—
214	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
215	#107×C₄₇	C₂³	1	1	yes	characteristic
216	#107×C₄₇	C₂³	1	1	yes	characteristic
217	#106×C₄₇	C₂³	1	1	yes	characteristic
218	#106×C₄₇	C₂³	1	1	yes	characteristic
219	#103×C₄₇	C₂³	1	1	yes	characteristic
220	#103×C₄₇	C₂³	1	1	yes	characteristic
221	#103×C₄₇	C₂³	1	1	yes	characteristic
222	#103×C₄₇	C₂³	1	1	yes	characteristic
223	#102×C₄₇	C₂³	1	1	yes	characteristic
224	#102×C₄₇	C₂³	1	1	yes	characteristic
225	#102×C₄₇	C₂³	1	1	yes	characteristic
226	#102×C₄₇	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
231	C₂³×D₄₇	—	2	2	no	—
232	#41×C₄₇	—	2	2	no	—
233	#41×C₄₇	—	2	2	no	—
234	#41×C₄₇	—	2	2	no	—
235	#41×C₄₇	#41	1	4	yes	complemented
236	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₄₇	—	2	1	no	—
239	C₂×D₄×C₄₇	—	2	1	no	—
240	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₄₇	—	2	1	no	—
243	C₂²×C₄×C₄₇	—	2	1	no	—
244	C₂²×C₄×C₄₇	—	2	1	no	—
245	C₂²×C₄×C₄₇	—	2	1	no	—
246	C₂²×C₄×C₄₇	—	2	1	no	—
247	C₂²×C₄×C₄₇	—	2	1	no	—
248	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₂²⋊D₄₇	—	2	4	no	—
252	C₂×C₂²⋊D₄₇	—	2	4	no	—
253	C₂²×Dic₄₇	—	2	2	no	—
254	C₂²×Dic₄₇	—	2	4	no	—
255	#10625350	—	8	4	no	—
256	#10625350	—	8	4	no	—
257	C₂×D₁₈₈	—	2	4	no	—
258	C₂×D₁₈₈	—	2	4	no	—
259	C₂×D₁₈₈	—	2	2	no	—
260	C₂×D₁₈₈	—	2	2	no	—
261	C₂×D₁₈₈	—	2	2	no	—
262	C₂×D₁₈₈	—	2	2	no	—
263	C₂×D₁₈₈	—	2	2	no	—
264	C₂×D₁₈₈	—	8	2	no	—
265	C₂×D₁₈₈	—	8	2	no	—
266	C₂×D₁₈₈	C₂⁴	1	4	yes	—
267	C₂×C₄×D₄₇	—	2	4	no	—
268	C₂×C₄×D₄₇	—	2	4	no	—
269	C₂×Dic₉₄	—	2	2	no	—
270	C₂×Dic₉₄	—	2	2	no	—
271	C₂×Dic₉₄	—	2	4	no	—
272	C₂×Dic₉₄	—	8	4	no	—
273	C₂×Dic₉₄	—	8	2	no	—
274	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
275	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
276	Q₁₆×C₄₇	—	2	2	no	—
277	SD₁₆×C₄₇	—	2	2	no	—
278	SD₁₆×C₄₇	—	2	2	no	—
279	D₈×C₄₇	—	2	2	no	—
280	C₂×C₈×C₄₇	—	2	2	no	—
281	C₂×C₈×C₄₇	—	2	2	no	—
282	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
283	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
284	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
285	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₄₇	—	2	1	no	—
287	C₄⋊C₄×C₄₇	—	2	1	no	—
288	C₄⋊C₄×C₄₇	—	2	1	no	—
289	C₄⋊C₄×C₄₇	—	2	1	no	—
290	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
294	C₂²⋊C₄×C₄₇	—	2	1	no	—
295	C₂²⋊C₄×C₄₇	—	2	1	no	—
296	C₂²⋊C₄×C₄₇	—	2	1	no	—
297	C₂²⋊C₄×C₄₇	—	2	1	no	—
298	C₂²⋊C₄×C₄₇	—	2	1	no	—
299	C₂²⋊C₄×C₄₇	—	2	1	no	—
300	C₄²×C₄₇	—	2	1	no	—
301	C₄²×C₄₇	—	2	1	no	—
302	C₄²×C₄₇	—	2	1	no	—
303	C₄²×C₄₇	—	2	1	no	—
304	C₄²×C₄₇	—	2	1	no	—
305	C₄²×C₄₇	—	2	1	no	—
306	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
309	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
310	C₂²⋊Dic₄₇	—	2	4	no	—
311	C₂²⋊Dic₄₇	C₂×D₄	1	4	yes	—
312	#10625336	—	2	8	no	—
313	#10625334	—	2	8	no	—
314	(C₂×D₄₇)⋊C₄	—	2	4	no	—
315	(C₂×D₄₇)⋊C₄	—	2	4	no	—
316	(C₂×D₄₇)⋊C₄	—	2	4	no	—
317	(C₂×D₄₇)⋊C₄	—	2	4	no	—
318	C₄⋊Dic₄₇	—	2	2	no	—
319	C₄⋊Dic₄₇	—	2	2	no	—
320	C₄⋊Dic₄₇	—	2	2	no	—
321	C₄⋊Dic₄₇	—	2	4	no	—
322	C₄⋊Dic₄₇	—	2	4	no	—
323	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
324	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
325	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
326	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
327	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
328	Dic₄₇⋊C₄	—	2	4	no	—
329	Dic₄₇⋊C₄	—	2	4	no	—
330	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
331	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
332	C₄×Dic₄₇	—	2	4	no	—
333	C₄×Dic₄₇	C₂⁴	1	4	yes	—
334	#10625329	—	2	4	no	—
335	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
336	C₂³×C₄₇	—	2	1	no	—
337	C₂³×C₄₇	—	2	1	no	—
338	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
339	C₂²×D₄₇	—	2	4	no	—
340	C₂²×D₄₇	—	4	4	no	—
341	C₂²×D₄₇	—	8	2	no	—
342	C₂²×D₄₇	—	8	2	no	—
343	Q₈×C₄₇	—	2	1	no	—
344	Q₈×C₄₇	—	2	1	no	—
345	Q₈×C₄₇	—	2	1	no	—
346	Q₈×C₄₇	C₂×#41	1	2	yes	—
347	D₄×C₄₇	—	2	4	no	—
348	D₄×C₄₇	—	2	1	no	—
349	D₄×C₄₇	—	2	1	no	—
350	D₄×C₄₇	—	2	1	no	—
351	D₄×C₄₇	—	4	2	no	—
352	D₄×C₄₇	C₂×#41	1	2	yes	—
353	C₂×C₄×C₄₇	—	2	1	no	—
354	C₂×C₄×C₄₇	—	2	4	no	—
355	C₂×C₄×C₄₇	—	2	2	no	—
356	C₂×C₄×C₄₇	—	2	2	no	—
357	C₂×C₄×C₄₇	—	2	1	no	—
358	C₂×C₄×C₄₇	—	2	1	no	—
359	C₂×C₄×C₄₇	—	2	1	no	—
360	C₂×C₄×C₄₇	—	2	1	no	—
361	C₂×C₄×C₄₇	—	2	1	no	—
362	C₂×C₄×C₄₇	—	4	2	no	—
363	C₂×C₄×C₄₇	—	4	2	no	—
364	C₂×C₄×C₄₇	—	4	2	no	—
365	C₂×C₄×C₄₇	—	4	2	no	—
366	C₂×C₄×C₄₇	—	4	2	no	—
367	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
373	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
374	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
375	C₂²⋊D₄₇	—	8	4	no	—
376	C₂²⋊D₄₇	—	8	4	no	—
377	C₂×Dic₄₇	—	2	4	no	—
378	C₂×Dic₄₇	—	8	4	no	—
379	C₂×Dic₄₇	—	8	2	no	—
380	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
381	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
382	D₁₈₈	—	2	4	no	—
383	D₁₈₈	—	2	4	no	—
384	D₁₈₈	—	4	4	no	—
385	D₁₈₈	—	4	4	no	—
386	D₁₈₈	—	4	4	no	—
387	D₁₈₈	—	8	2	no	—
388	D₁₈₈	—	8	2	no	—
389	C₄×D₄₇	—	8	4	no	—
390	C₄×D₄₇	—	8	4	no	—
391	Dic₉₄	—	2	4	no	—
392	Dic₉₄	—	2	4	no	—
393	Dic₉₄	—	4	4	no	—
394	Dic₉₄	—	8	4	no	—
395	Dic₉₄	—	8	2	no	—
396	C₈×C₄₇	—	2	1	no	—
397	C₈×C₄₇	—	2	1	no	—
398	C₈×C₄₇	—	2	1	no	—
399	C₈×C₄₇	—	2	1	no	—
400	C₄₇⋊C₈	—	2	4	no	—
401	#61329	—	47	1	no	maximal, Sylow
402	C₂²×C₄₇	—	2	1	no	—
403	C₂²×C₄₇	—	2	1	no	—
404	C₂²×C₄₇	—	2	2	no	—
405	C₂²×C₄₇	—	4	1	no	—
406	C₂²×C₄₇	—	4	1	no	—
407	C₂²×C₄₇	—	4	1	no	—
408	C₂²×C₄₇	—	4	1	no	—
409	C₂²×C₄₇	—	4	1	no	—
410	C₂²×C₄₇	#548	1	2	yes	—
411	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
412	C₂×D₄₇	—	4	4	no	—
413	C₂×D₄₇	—	4	4	no	—
414	C₂×D₄₇	—	4	4	no	—
415	C₂×D₄₇	—	16	4	no	—
416	C₄×C₄₇	—	2	2	no	—
417	C₄×C₄₇	—	2	1	no	—
418	C₄×C₄₇	—	2	1	no	—
419	C₄×C₄₇	—	4	1	no	—
420	C₄×C₄₇	—	4	1	no	—
421	C₄×C₄₇	—	4	1	no	—
422	C₄×C₄₇	—	4	1	no	—
423	C₄×C₄₇	—	4	1	no	—
424	C₄×C₄₇	#548	1	2	yes	—
425	C₄×C₄₇	#576	1	2	yes	—
426	C₄×C₄₇	#577	1	2	yes	—
427	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
428	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
429	Dic₄₇	—	2	4	no	—
430	Dic₄₇	—	2	4	no	—
431	Dic₄₇	—	4	4	no	—
432	#3508	—	47	1	no	—
433	#3503	—	47	1	no	—
434	#3375	—	47	2	no	—
435	#3373	—	47	2	no	—
436	#3368	—	47	2	no	—
437	#3366	—	47	2	no	—
438	#3365	—	47	2	no	—
439	#3362	—	47	2	no	—
440	#3361	—	47	2	no	—
441	#3358	—	47	2	no	—
442	#3136	—	47	2	no	—
443	C₂×#486	—	47	1	no	—
444	#3081	—	47	2	no	—
445	#3079	—	47	1	no	—
446	#3045	—	47	2	no	—
447	#3038	—	47	1	no	—
448	#2960	—	47	1	no	—
449	#2946	—	47	2	no	—
450	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
451	C₂×C₄₇	—	2	2	no	—
452	C₂×C₄₇	—	4	2	no	—
453	C₂×C₄₇	—	8	1	no	—
454	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
455	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
456	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
457	D₄₇	—	8	4	no	—
458	C₂×AGL(1,ℤ/8)	—	47	2	no	—
459	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
460	#559	—	47	2	no	—
461	#559	—	47	2	no	—
462	Q₈²	—	47	2	no	—
463	#557	—	47	2	no	—
464	#554	—	47	2	no	—
465	#554	—	94	2	no	—
466	#550	—	47	2	no	—
467	#550	—	47	2	no	—
468	D₄×Q₈	—	47	2	no	—
469	D₄×Q₈	—	94	2	no	—
470	#546	—	94	2	no	—
471	#546	—	94	2	no	—
472	#544	—	47	2	no	—
473	#544	—	94	2	no	—
474	#540	—	94	2	no	—
475	#535	—	47	2	no	—
476	#533	—	47	1	no	—
477	#533	—	94	1	no	—
478	#532	—	94	1	no	—
479	#532	—	94	1	no	—
480	C₂×C₄⋊Q₈	—	47	1	no	—
481	C₂×C₄⋊Q₈	—	94	1	no	—
482	C₂×#127	—	47	1	no	—
483	#520	—	47	2	no	—
484	#518	—	47	2	no	—
485	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
486	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
487	#490	—	47	4	no	—
488	#489	—	47	4	no	—
489	#488	—	47	4	no	—
490	#486	—	47	4	no	—
491	#486	—	47	2	no	—
492	#486	—	47	2	no	—
493	#486	—	47	2	no	—
494	#486	—	47	2	no	—
495	#478	—	47	4	no	—
496	#478	—	47	4	no	—
497	#477	—	47	2	no	—
498	#476	—	47	2	no	—
499	#476	—	47	4	no	—
500	#475	—	47	2	no	—
501	#474	—	47	2	no	—
502	#474	—	47	4	no	—
503	#464	—	47	4	no	—
504	#463	—	47	4	no	—
505	#460	—	47	4	no	—
506	#460	—	47	2	no	—
507	#460	—	47	2	no	—
508	#459	—	47	4	no	—
509	#459	—	47	2	no	—
510	#459	—	47	2	no	—
511	#446	—	47	2	no	—
512	#446	—	47	2	no	—
513	C₈×Q₈	—	47	2	no	—
514	C₈×Q₈	—	47	2	no	—
515	#442	—	47	4	no	—
516	#440	—	47	4	no	—
517	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
518	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
519	C₄×SD₁₆	—	47	4	no	—
520	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
521	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
522	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
523	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
524	C₄×D₈	—	47	4	no	—
525	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
526	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
527	#428	—	47	2	no	—
528	#427	C₂×D₄₇	1	1	yes	characteristic
529	#424	—	47	2	no	—
530	#423	—	47	1	no	—
531	#418	—	47	2	no	—
532	#417	—	47	2	no	—
533	#416	C₂×D₄₇	1	1	yes	characteristic
534	#416	C₂×D₄₇	1	1	yes	characteristic
535	C₂×#102	—	47	2	no	—
536	C₂×#102	—	47	2	no	—
537	#405	—	47	2	no	—
538	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
539	C₄₇	#61329	1	1	yes	characteristic, complemented, Sylow
540	C₂×#41	—	94	2	no	—
541	C₂×#41	—	94	2	no	—
542	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
543	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
544	C₂²×Q₈	—	94	2	no	—
545	C₂²×Q₈	—	94	1	no	—
546	C₂²×D₄	—	47	2	no	—
547	C₂²×D₄	—	94	1	no	—
548	C₂²×D₄	—	94	1	no	—
549	AGL(1,ℤ/8)	—	94	8	no	—
550	#135	—	2	4	no	—
551	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
552	C₂×SD₁₆	—	47	4	no	—
553	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
554	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
555	C₂×D₈	—	47	4	no	—
556	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
557	C₂×M₁₆	—	47	2	no	—
558	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
559	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
560	C₄⋊Q₈	—	47	4	no	—
561	C₄⋊Q₈	—	47	1	no	—
562	C₄⋊Q₈	—	47	1	no	—
563	C₄⋊Q₈	—	47	2	no	—
564	C₄⋊Q₈	—	47	2	no	—
565	C₄⋊Q₈	—	94	2	no	—
566	C₄⋊Q₈	—	94	2	no	—
567	C₄⋊Q₈	—	94	2	no	—
568	C₄⋊Q₈	—	94	4	no	—
569	C₄⋊Q₈	—	94	1	no	—
570	C₄⋊Q₈	—	94	1	no	—
571	#127	—	47	4	no	—
572	#127	—	47	2	no	—
573	#127	—	47	2	no	—
574	#127	—	94	1	no	—
575	#127	—	94	1	no	—
576	#125	—	47	4	no	—
577	#125	—	47	2	no	—
578	#125	—	94	2	no	—
579	#125	—	94	4	no	—
580	#124	—	47	4	no	—
581	#124	—	94	2	no	—
582	#124	—	94	2	no	—
583	#123	—	94	4	no	—
584	#123	—	94	4	no	—
585	C₂²⋊Q₈	—	47	2	no	—
586	C₂²⋊Q₈	—	47	2	no	—
587	C₂²⋊Q₈	—	94	4	no	—
588	C₂²⋊Q₈	—	94	4	no	—
589	C₂²⋊Q₈	—	94	4	no	—
590	C₂²⋊Q₈	—	94	2	no	—
591	C₂²⋊Q₈	—	94	2	no	—
592	#121	—	94	4	no	—
593	#121	—	94	4	no	—
594	#121	—	94	2	no	—
595	#121	—	94	2	no	—
596	#121	—	94	2	no	—
597	#121	—	94	2	no	—
598	#120	—	94	4	no	—
599	C₄×Q₈	—	47	2	no	—
600	C₄×Q₈	—	47	2	no	—
601	C₄×Q₈	—	47	4	no	—
602	C₄×Q₈	—	94	2	no	—
603	C₄×Q₈	—	94	2	no	—
604	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
605	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
606	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
607	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	47	4	no	—
613	C₄×D₄	—	47	4	no	—
614	C₄×D₄	—	47	4	no	—
615	C₄×D₄	—	94	2	no	—
616	C₄×D₄	—	94	2	no	—
617	C₄×D₄	—	94	2	no	—
618	C₄×D₄	—	94	2	no	—
619	C₄×D₄	—	94	4	no	—
620	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
621	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
622	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
623	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	47	2	no	—
627	#117	—	94	2	no	—
628	#117	C₂²×D₄₇	1	1	yes	characteristic
629	#117	C₂²×D₄₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	—	47	2	no	—
631	C₂×C₄⋊C₄	—	94	2	no	—
632	C₂×C₄⋊C₄	—	94	2	no	—
633	C₂×C₄⋊C₄	—	94	1	no	—
634	C₂×C₂²⋊C₄	—	94	4	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
638	#107	—	47	4	no	—
639	#107	C₂²×D₄₇	1	1	yes	characteristic
640	#107	C₂²×D₄₇	1	1	yes	characteristic
641	#106	—	47	4	no	—
642	#106	C₂²×D₄₇	1	1	yes	characteristic
643	#106	C₂²×D₄₇	1	1	yes	characteristic
644	C₄⋊C₈	—	47	4	no	—
645	C₄⋊C₈	—	47	4	no	—
646	C₄⋊C₈	—	47	2	no	—
647	C₄⋊C₈	—	47	2	no	—
648	#103	—	47	4	no	—
649	#103	C₂²×D₄₇	1	1	yes	characteristic
650	#103	C₂²×D₄₇	1	1	yes	characteristic
651	#103	C₂²×D₄₇	1	1	yes	characteristic
652	#103	C₂²×D₄₇	1	1	yes	characteristic
653	#102	—	47	4	no	—
654	#102	—	47	4	no	—
655	#102	—	47	4	no	—
656	#102	—	47	4	no	—
657	#102	—	47	4	no	—
658	#102	—	47	4	no	—
659	#102	—	47	4	no	—
660	#102	C₂²×D₄₇	1	1	yes	characteristic
661	#102	C₂²×D₄₇	1	1	yes	characteristic
662	#102	C₂²×D₄₇	1	1	yes	characteristic
663	#102	C₂²×D₄₇	1	1	yes	characteristic
664	#97	—	47	4	no	—
665	C₄×C₈	—	47	4	no	—
666	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
667	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
668	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
669	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
670	C₂⁴	—	94	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	2	2	no	—
674	#41	—	376	4	no	—
675	#41	—	376	4	no	—
676	#41	#10625350	1	4	yes	complemented
677	C₂×Q₈	—	47	2	no	—
678	C₂×Q₈	—	47	2	no	—
679	C₂×Q₈	—	94	4	no	—
680	C₂×Q₈	—	94	2	no	—
681	C₂×Q₈	—	94	2	no	—
682	C₂×Q₈	—	376	2	no	—
683	C₂×Q₈	—	376	4	no	—
684	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
685	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	47	4	no	—
689	C₂×D₄	—	94	4	no	—
690	C₂×D₄	—	94	4	no	—
691	C₂×D₄	—	94	2	no	—
692	C₂×D₄	—	94	2	no	—
693	C₂×D₄	—	94	2	no	—
694	C₂×D₄	—	94	2	no	—
695	C₂×D₄	—	94	2	no	—
696	C₂×D₄	—	94	4	no	—
697	C₂×D₄	—	94	4	no	—
698	C₂×D₄	—	376	2	no	—
699	C₂×D₄	—	376	2	no	—
700	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
701	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	94	4	no	—
709	C₂²×C₄	—	94	4	no	—
710	C₂²×C₄	—	94	4	no	—
711	C₂²×C₄	—	94	2	no	—
712	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
713	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
714	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
715	Q₁₆	—	2	2	no	—
716	SD₁₆	—	2	2	no	—
717	SD₁₆	—	2	2	no	—
718	SD₁₆	—	94	8	no	—
719	D₈	—	2	2	no	—
720	D₈	—	94	8	no	—
721	M₁₆	—	94	4	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	—	2	2	no	—
724	C₂×C₈	—	47	4	no	—
725	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
726	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
727	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
728	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	47	4	no	—
734	C₄⋊C₄	—	47	4	no	—
735	C₄⋊C₄	—	47	2	no	—
736	C₄⋊C₄	—	47	2	no	—
737	C₄⋊C₄	—	47	2	no	—
738	C₄⋊C₄	—	47	2	no	—
739	C₄⋊C₄	—	47	4	no	—
740	C₄⋊C₄	—	94	4	no	—
741	C₄⋊C₄	—	94	4	no	—
742	C₄⋊C₄	—	94	4	no	—
743	C₄⋊C₄	—	94	4	no	—
744	C₄⋊C₄	—	94	2	no	—
745	C₄⋊C₄	—	94	2	no	—
746	C₄⋊C₄	—	94	2	no	—
747	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	47	4	no	—
758	C₂²⋊C₄	—	94	4	no	—
759	C₂²⋊C₄	—	94	4	no	—
760	C₂²⋊C₄	—	94	4	no	—
761	C₂²⋊C₄	—	94	4	no	—
762	C₂²⋊C₄	—	94	4	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	47	4	no	—
770	C₄²	—	94	4	no	—
771	C₄²	D₄×D₄₇	1	1	yes	characteristic
772	C₄²	D₄×D₄₇	1	1	yes	characteristic
773	C₄²	C₂³×D₄₇	1	1	yes	characteristic
774	C₄²	C₂³×D₄₇	1	1	yes	characteristic
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	94	4	no	—
778	C₂³	—	376	2	no	—
779	C₂³	—	376	2	no	—
780	C₂³	—	188	4	no	—
781	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
782	Q₈	—	2	1	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	94	4	no	—
786	Q₈	—	94	4	no	—
787	Q₈	—	376	2	no	—
788	Q₈	—	376	4	no	—
789	Q₈	—	188	4	no	—
790	Q₈	C₂×#10625350	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	4	2	no	—
796	D₄	—	94	4	no	—
797	D₄	—	94	4	no	—
798	D₄	—	376	2	no	—
799	D₄	—	376	2	no	—
800	D₄	—	376	4	no	—
801	D₄	—	376	4	no	—
802	D₄	—	188	4	no	—
803	D₄	—	188	4	no	—
804	D₄	—	188	4	no	—
805	D₄	C₂×#10625350	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	47	4	no	—
821	C₂×C₄	—	47	4	no	—
822	C₂×C₄	—	94	4	no	—
823	C₂×C₄	—	376	4	no	—
824	C₂×C₄	—	376	4	no	—
825	C₂×C₄	—	376	4	no	—
826	C₂×C₄	—	376	2	no	—
827	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
828	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
829	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
830	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
831	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
832	C₂×C₄	C₂×#10625350	1	2	yes	—
833	C₂×C₄	#13094071	1	2	yes	—
834	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	94	4	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	188	4	no	—
849	C₂²	—	188	4	no	—
850	C₂²	—	188	4	no	—
851	C₂²	—	752	4	no	—
852	C₂²	#15689782	1	2	yes	—
853	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	94	4	no	—
863	C₄	—	94	4	no	—
864	C₄	—	188	4	no	—
865	C₄	#15689782	1	2	yes	—
866	C₄	#15689925	1	2	yes	—
867	C₄	#15689930	1	2	yes	—
868	C₄	C₂²×#10625350	1	1	yes	characteristic
869	C₄	C₂×#13094071	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	1	no	—
873	C₂	—	376	4	no	—
874	C₂	C₂×#15689782	1	1	yes	characteristic
875	C₂	C₂×#15689925	1	1	yes	characteristic
876	C₂	C₂×#15689930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	#61329
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20257264	C₂	semidirect
2. #20257207	C₂	semidirect
3. #20256200	C₂	semidirect
4. #20256178	C₂	semidirect
5. #20256115	C₂	semidirect
6. #20256093	C₂	semidirect
7. #20256082	C₂	semidirect
8. #20256057	C₂	semidirect
9. #20256046	C₂	semidirect
10. #20256021	C₂	semidirect
11. #20253746	C₂	semidirect
12. C₂×#15689470	C₂	semidirect
13. #20253222	C₂	semidirect
14. #20253203	C₂	semidirect
15. #20252925	C₂	semidirect
16. #20252868	C₂	semidirect
17. #20252322	C₂	semidirect
18. #20252223	C₂	semidirect
19. C₄×#135×C₄₇	C₂	semidirect
23. Q₈×Dic₉₄	C₂²	semidirect
24. #15689852	C₂²	semidirect
26. #15689830	C₂²	semidirect
30. D₄×Dic₉₄	C₂²	semidirect
46. #15689486	C₂²	semidirect
47. #15689484	C₂²	semidirect
48. #15689479	C₂²	semidirect
53. #15689468	C₂²	semidirect
54. #15689426	C₂²	semidirect
55. #15689422	C₂²	semidirect
56. #15689418	C₂²	semidirect
57. #15689413	C₂²	semidirect
58. #15689412	C₂²	semidirect
59. #15689408	C₂²	semidirect
60. #15689403	C₂²	semidirect
61. #15689402	C₂²	semidirect
62. #15689347	C₂²	semidirect
63. #15689340	C₂²	semidirect
66. #15689321	C₂²	semidirect
69. #15689316	C₂²	semidirect
70. #15689253	C₂²	semidirect
71. #15689253	C₂²	semidirect
72. C₈×Dic₉₄	C₂²	semidirect
73. C₈×Dic₉₄	C₂²	semidirect
74. #15689232	C₂²	semidirect
75. #15689226	C₂²	semidirect
76. #15689208	C₂²	semidirect
77. #15689203	C₂²	semidirect
89. C₄×Q₁₆×C₄₇	C₂²	semidirect
90. C₄×Q₁₆×C₄₇	C₂²	semidirect
91. C₄×SD₁₆×C₄₇	C₂²	semidirect
92. C₄×SD₁₆×C₄₇	C₂²	semidirect
93. C₄×SD₁₆×C₄₇	C₂²	semidirect
94. C₄×SD₁₆×C₄₇	C₂²	semidirect
95. C₄×D₈×C₄₇	C₂²	semidirect
96. C₄×D₈×C₄₇	C₂²	semidirect
235. #41×C₄₇	#41	semidirect
450. C₄×#135	D₄₇	semidirect
517. C₄×Q₁₆	C₂×D₄₇	semidirect
518. C₄×Q₁₆	C₂×D₄₇	semidirect
520. C₄×SD₁₆	C₂×D₄₇	semidirect
521. C₄×SD₁₆	C₂×D₄₇	semidirect
522. C₄×SD₁₆	C₂×D₄₇	semidirect
523. C₄×SD₁₆	C₂×D₄₇	semidirect
525. C₄×D₈	C₂×D₄₇	semidirect
526. C₄×D₈	C₂×D₄₇	semidirect
539. C₄₇	#61329	semidirect
676. #41	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257264	2
#20257207	2
#20256200	2
#20256178	2
#20256115	2
#20256093	2
#20256082	2
#20256057	2
#20256046	2
#20256021	2
#20253746	2
C₂×#15689470	2
#20253222	2
#20253203	2
#20252925	2
#20252868	2
#20252322	2
#20252223	2
C₄×#135×C₄₇	2
#61329	47