Subgroups — #27096295

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	#20257265	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256202	C₂	1	2	yes	maximal, complemented
3	#20256180	C₂	1	2	yes	maximal, complemented
4	#20256117	C₂	1	2	yes	maximal, complemented
5	#20256095	C₂	1	2	yes	maximal, complemented
6	#20256084	C₂	1	2	yes	maximal, complemented
7	#20256059	C₂	1	2	yes	maximal, complemented
8	#20256048	C₂	1	2	yes	maximal, complemented
9	#20256023	C₂	1	2	yes	maximal, complemented
10	#20253747	C₂	1	2	yes	maximal, complemented
11	C₂×#15689471	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253213	C₂	1	2	yes	maximal, complemented
13	#20253197	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252927	C₂	1	2	yes	maximal, complemented
15	#20252868	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252216	C₂	1	2	yes	maximal, complemented
18	C₄×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13094049	C₂²	1	2	yes	—
21	C₂×#13094044	C₂²	1	1	yes	characteristic
22	#15689858	C₂²	1	2	yes	—
23	#15689858	C₂²	1	2	yes	—
24	#15689795	C₂²	1	2	yes	—
25	#15689795	C₂²	1	2	yes	—
26	#15689764	—	2	2	no	—
27	#15689764	—	2	2	no	—
28	#15689729	—	2	2	no	—
29	#15689692	C₂²	1	2	yes	—
30	#15689674	—	2	1	no	—
31	#15689674	—	2	1	no	—
32	C₂×#13094021	C₂²	1	1	yes	characteristic
33	#15689597	C₂²	1	2	yes	—
34	C₄×#10625350	C₂²	1	1	yes	characteristic
35	#15689489	C₂²	1	4	yes	complemented
36	#15689485	C₂²	1	4	yes	complemented
37	#15689480	C₂²	1	4	yes	complemented
38	#15689471	C₂²	1	2	yes	—
39	#15689471	C₂²	1	2	yes	—
40	#15689471	C₂²	1	2	yes	—
41	#15689471	C₂²	1	2	yes	—
42	#15689471	C₂²	1	4	yes	complemented
43	#15689420	C₂²	1	4	yes	complemented
44	#15689420	C₂²	1	4	yes	complemented
45	#15689415	C₂²	1	2	yes	complemented
46	#15689410	C₂²	1	2	yes	complemented
47	#15689410	C₂²	1	4	yes	complemented
48	#15689405	C₂²	1	2	yes	complemented
49	#15689400	C₂²	1	2	yes	complemented
50	#15689400	C₂²	1	4	yes	complemented
51	#15689345	C₂²	1	4	yes	complemented
52	#15689338	C₂²	1	4	yes	complemented
53	#15689323	C₂²	1	2	yes	—
54	#15689323	C₂²	1	2	yes	—
55	#15689323	C₂²	1	4	yes	complemented
56	#15689318	C₂²	1	2	yes	—
57	#15689318	C₂²	1	2	yes	—
58	#15689318	C₂²	1	4	yes	complemented
59	#15689254	C₂²	1	2	yes	complemented
60	#15689254	C₂²	1	2	yes	complemented
61	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
62	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
63	#15689233	C₂²	1	4	yes	complemented
64	#15689221	C₂²	1	4	yes	complemented
65	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
66	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
67	C₄×#10625336	C₂²	1	4	yes	complemented
68	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
69	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
70	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
71	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
72	C₄×#10625334	C₂²	1	1	yes	characteristic, complemented
73	C₄×#10625334	C₂²	1	4	yes	complemented
74	C₄×#10625334	C₂²	1	1	yes	characteristic, complemented
75	#15689163	C₂²	1	2	yes	—
76	#15689159	C₂²	1	1	yes	characteristic
77	#15689150	C₂²	1	2	yes	—
78	#15689147	C₂²	1	1	yes	characteristic
79	#15689127	C₂²	1	2	yes	—
80	#15689122	C₂²	1	2	yes	—
81	#15689119	C₂²	1	1	yes	characteristic
82	#15689117	C₂²	1	1	yes	characteristic
83	C₂×#13093944	C₂²	1	2	yes	—
84	C₂×#13093944	C₂²	1	2	yes	—
85	#15689079	C₂²	1	2	yes	—
86	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
87	Q₈²×C₄₇	C₂²	1	2	yes	complemented
88	C₄₇×#557	C₂²	1	2	yes	complemented
89	C₄₇×#554	—	2	2	no	—
90	C₄₇×#554	C₂²	1	2	yes	complemented
91	D₄×Q₈×C₄₇	—	2	2	no	—
92	D₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
93	C₄₇×#544	—	2	2	no	—
94	C₄₇×#544	C₂²	1	2	yes	—
95	C₄₇×#533	—	2	1	no	—
96	C₄₇×#533	C₂²	1	1	yes	characteristic
97	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
98	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
99	C₄₇×#520	C₂²	1	2	yes	—
100	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
101	C₂×#10625354	—	2	2	no	—
102	C₂×#10625354	—	2	2	no	—
103	C₂×#10625350	C₂³	1	1	yes	characteristic
104	C₂²×D₁₈₈	—	2	1	no	—
105	C₂²×D₁₈₈	—	2	1	no	—
106	C₂²×D₁₈₈	C₂³	1	2	yes	—
107	#13094049	—	2	8	no	—
108	#13094044	—	2	4	no	—
109	C₂×#10625337	C₂³	1	1	yes	characteristic
110	C₂×#10625335	C₂³	1	1	yes	characteristic
111	C₂×#10625336	C₂³	1	4	yes	—
112	C₂×#10625336	C₂³	1	1	yes	characteristic
113	C₂×#10625334	C₂³	1	4	yes	—
114	C₂×#10625334	C₂³	1	1	yes	characteristic
115	C₂×#10625329	C₂³	1	2	yes	—
116	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
118	#13094021	—	2	1	no	—
119	#13094021	—	2	1	no	—
120	#13094021	C₂³	1	4	yes	—
121	#13094021	C₂³	1	2	yes	—
122	#13094021	C₂³	1	2	yes	—
123	#13094013	—	2	2	no	—
124	#13094013	—	2	2	no	—
125	#13094012	C₂³	1	4	yes	—
126	#13094009	—	2	4	no	—
127	#13094009	—	2	4	no	—
128	#13093999	—	2	4	no	—
129	#13093999	—	2	4	no	—
130	#13093999	—	2	2	no	—
131	#13093999	—	2	2	no	—
132	#13093999	—	2	2	no	—
133	#13093999	—	2	2	no	—
134	#13093994	—	2	4	no	—
135	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
136	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
137	C₄×D₁₈₈	C₂³	1	4	yes	—
138	C₄×D₁₈₈	C₂³	1	4	yes	—
139	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
140	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
141	#13093986	—	2	2	no	—
142	#13093986	—	2	2	no	—
143	#13093986	—	2	2	no	—
144	#13093986	—	2	2	no	—
145	C₄×C₂²⋊D₄₇	—	2	1	no	—
146	C₄×C₂²⋊D₄₇	—	2	1	no	—
147	#13093983	C₂³	1	1	yes	characteristic
148	#13093981	—	2	1	no	—
149	C₂²⋊C₄×D₄₇	—	2	4	no	—
150	C₄²×D₄₇	—	2	1	no	—
151	#13093957	C₂³	1	1	yes	characteristic
152	#13093957	C₂³	1	1	yes	characteristic
153	#13093957	C₂³	1	4	yes	—
154	#13093955	C₂³	1	4	yes	—
155	#13093955	C₂³	1	1	yes	characteristic
156	#13093955	C₂³	1	1	yes	characteristic
157	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
158	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
159	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
160	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
161	#13093948	C₂³	1	1	yes	characteristic
162	#13093948	C₂³	1	1	yes	characteristic
163	#13093947	C₂³	1	1	yes	characteristic
164	#13093947	C₂³	1	1	yes	characteristic
165	#13093947	C₂³	1	4	yes	—
166	#13093945	C₂³	1	1	yes	characteristic
167	#13093945	C₂³	1	1	yes	characteristic
168	#13093944	C₂³	1	4	yes	—
169	#13093944	C₂³	1	4	yes	—
170	#13093944	C₂³	1	4	yes	—
171	#13093944	C₂³	1	4	yes	—
172	#13093944	C₂³	1	1	yes	characteristic
173	#13093944	C₂³	1	4	yes	—
174	#13093944	C₂³	1	4	yes	—
175	#13093944	C₂³	1	4	yes	—
176	#13093944	C₂³	1	1	yes	characteristic
177	#13093935	C₂³	1	4	yes	—
178	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
179	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
180	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
181	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
182	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
183	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
184	C₂²×Q₈×C₄₇	—	2	2	no	—
185	C₂²×Q₈×C₄₇	—	2	1	no	—
186	C₄⋊Q₈×C₄₇	—	2	2	no	—
187	C₄⋊Q₈×C₄₇	—	2	2	no	—
188	C₄⋊Q₈×C₄₇	—	2	2	no	—
189	C₄⋊Q₈×C₄₇	—	2	4	no	—
190	C₄⋊Q₈×C₄₇	—	2	1	no	—
191	C₄⋊Q₈×C₄₇	—	2	1	no	—
192	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
193	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
194	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
195	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
196	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
197	#125×C₄₇	—	2	2	no	—
198	#125×C₄₇	—	2	4	no	—
199	#125×C₄₇	D₄	1	2	yes	—
200	#125×C₄₇	C₂³	1	4	yes	—
201	C₂²⋊Q₈×C₄₇	—	2	2	no	—
202	C₂²⋊Q₈×C₄₇	—	2	2	no	—
203	C₂²⋊Q₈×C₄₇	—	2	4	no	—
204	C₂²⋊Q₈×C₄₇	—	2	4	no	—
205	C₂²⋊Q₈×C₄₇	—	2	4	no	—
206	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
207	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
208	C₄×Q₈×C₄₇	—	2	2	no	—
209	C₄×Q₈×C₄₇	—	2	2	no	—
210	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
213	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
214	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
215	C₄×D₄×C₄₇	—	2	1	no	—
216	C₄×D₄×C₄₇	—	2	1	no	—
217	C₄×D₄×C₄₇	—	2	4	no	—
218	C₄×D₄×C₄₇	C₂³	1	4	yes	—
219	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
221	#117×C₄₇	—	2	2	no	—
222	#117×C₄₇	—	2	1	no	—
223	#117×C₄₇	C₂³	1	1	yes	characteristic
224	#117×C₄₇	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
226	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
227	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₄₇	—	2	1	no	—
230	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
231	C₂³×D₄₇	—	2	2	no	—
232	#41×C₄₇	—	2	2	no	—
233	#41×C₄₇	#41	1	4	yes	complemented
234	C₂×Q₈×C₄₇	—	2	2	no	—
235	C₂×Q₈×C₄₇	—	2	4	no	—
236	C₂×Q₈×C₄₇	—	2	2	no	—
237	C₂×Q₈×C₄₇	—	8	2	no	—
238	C₂×Q₈×C₄₇	—	8	4	no	—
239	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
241	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₄₇	—	2	1	no	—
243	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₇	—	2	1	no	—
245	C₂²×C₄×C₄₇	—	2	2	no	—
246	C₂²×C₄×C₄₇	—	2	1	no	—
247	C₂²×C₄×C₄₇	—	2	1	no	—
248	C₂²×C₄×C₄₇	—	2	4	no	—
249	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₂²⋊D₄₇	—	2	1	no	—
253	#10625354	—	8	4	no	—
254	#10625354	—	8	4	no	—
255	#10625350	—	2	2	no	—
256	#10625350	—	2	2	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	4	no	—
263	C₂×D₁₈₈	—	2	4	no	—
264	C₂×D₁₈₈	—	2	2	no	—
265	C₂×D₁₈₈	—	2	2	no	—
266	C₂×D₁₈₈	—	8	2	no	—
267	C₂×D₁₈₈	—	8	2	no	—
268	C₂×D₁₈₈	C₂⁴	1	4	yes	—
269	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×D₄₇	—	2	1	no	—
271	C₂×C₄×D₄₇	—	2	1	no	—
272	C₂×C₄×D₄₇	—	2	1	no	—
273	C₂×C₄×D₄₇	—	2	4	no	—
274	C₂×C₄×D₄₇	—	2	4	no	—
275	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₄₇	—	2	2	no	—
277	C₄⋊C₄×C₄₇	—	2	2	no	—
278	C₄⋊C₄×C₄₇	—	2	4	no	—
279	C₄⋊C₄×C₄₇	—	2	2	no	—
280	C₄⋊C₄×C₄₇	—	2	4	no	—
281	C₄⋊C₄×C₄₇	—	2	1	no	—
282	C₄⋊C₄×C₄₇	—	2	1	no	—
283	C₄⋊C₄×C₄₇	—	2	4	no	—
284	C₄⋊C₄×C₄₇	—	2	4	no	—
285	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
288	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
290	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
291	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
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	4	no	—
298	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
299	C₄²×C₄₇	—	2	1	no	—
300	C₄²×C₄₇	—	2	1	no	—
301	C₄²×C₄₇	—	2	1	no	—
302	C₄²×C₄₇	—	2	4	no	—
303	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
306	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
307	C₄²×C₄₇	C₂⁴	1	4	yes	—
308	C₂²⋊Dic₄₇	—	2	1	no	—
309	#10625337	—	2	2	no	—
310	#10625336	—	2	2	no	—
311	#10625336	—	2	8	no	—
312	#10625335	—	2	2	no	—
313	#10625334	—	2	2	no	—
314	#10625334	—	2	8	no	—
315	(C₂×D₄₇)⋊C₄	—	2	4	no	—
316	(C₂×D₄₇)⋊C₄	—	2	4	no	—
317	(C₂×D₄₇)⋊C₄	—	2	1	no	—
318	(C₂×D₄₇)⋊C₄	—	2	1	no	—
319	(C₂×D₄₇)⋊C₄	—	2	4	no	—
320	(C₂×D₄₇)⋊C₄	—	2	4	no	—
321	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
323	Dic₄₇⋊C₄	—	2	1	no	—
324	Dic₄₇⋊C₄	—	2	1	no	—
325	C₄×Dic₄₇	—	2	1	no	—
326	C₄×Dic₄₇	—	2	1	no	—
327	C₄×Dic₄₇	—	2	1	no	—
328	#10625329	—	2	4	no	—
329	C₂×C₄₇⋊C₈	—	2	2	no	—
330	C₂×C₄₇⋊C₈	—	2	2	no	—
331	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
332	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
333	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
334	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
335	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
336	C₂³×C₄₇	—	2	1	no	—
337	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
338	C₂²×D₄₇	—	2	4	no	—
339	C₂²×D₄₇	—	2	1	no	—
340	C₂²×D₄₇	—	4	4	no	—
341	C₂²×D₄₇	—	8	2	no	—
342	C₂²×D₄₇	—	8	2	no	—
343	Q₈×C₄₇	—	2	4	no	—
344	Q₈×C₄₇	—	2	4	no	—
345	Q₈×C₄₇	—	2	1	no	—
346	Q₈×C₄₇	—	4	4	no	—
347	Q₈×C₄₇	—	8	4	no	—
348	Q₈×C₄₇	—	8	2	no	—
349	Q₈×C₄₇	C₂×#41	1	2	yes	—
350	D₄×C₄₇	—	2	4	no	—
351	D₄×C₄₇	—	2	1	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	4	no	—
360	C₂×C₄×C₄₇	—	4	2	no	—
361	C₂×C₄×C₄₇	—	4	2	no	—
362	C₂×C₄×C₄₇	—	8	4	no	—
363	C₂×C₄×C₄₇	—	8	2	no	—
364	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
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	C₂×#41	1	2	yes	—
372	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
373	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
374	C₂²⋊D₄₇	—	4	2	no	—
375	C₂×Dic₄₇	—	2	1	no	—
376	C₂×Dic₄₇	—	2	1	no	—
377	C₂×Dic₄₇	—	2	1	no	—
378	D₁₈₈	—	2	4	no	—
379	D₁₈₈	—	2	1	no	—
380	D₁₈₈	—	2	4	no	—
381	D₁₈₈	—	2	1	no	—
382	D₁₈₈	—	4	4	no	—
383	D₁₈₈	—	4	4	no	—
384	D₁₈₈	—	4	4	no	—
385	D₁₈₈	—	8	2	no	—
386	D₁₈₈	—	8	2	no	—
387	D₁₈₈	—	8	4	no	—
388	D₁₈₈	—	8	4	no	—
389	C₄×D₄₇	—	4	2	no	—
390	C₄×D₄₇	—	4	2	no	—
391	C₄×D₄₇	—	4	2	no	—
392	C₄×D₄₇	—	8	4	no	—
393	C₄×D₄₇	—	8	4	no	—
394	Dic₉₄	—	2	1	no	—
395	Dic₉₄	—	2	1	no	—
396	C₄₇⋊C₈	—	2	1	no	—
397	C₄₇⋊C₈	—	2	1	no	—
398	C₄₇⋊C₈	—	2	4	no	—
399	C₄₇⋊C₈	—	2	1	no	—
400	C₄₇⋊C₈	—	2	1	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	#548	1	2	yes	—
408	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
409	C₂×D₄₇	—	4	1	no	—
410	C₂×D₄₇	—	4	4	no	—
411	C₂×D₄₇	—	4	1	no	—
412	C₂×D₄₇	—	4	4	no	—
413	C₂×D₄₇	—	4	1	no	—
414	C₂×D₄₇	—	4	4	no	—
415	C₂×D₄₇	—	16	4	no	—
416	C₄×C₄₇	—	2	2	no	—
417	C₄×C₄₇	—	2	4	no	—
418	C₄×C₄₇	—	2	1	no	—
419	C₄×C₄₇	—	2	4	no	—
420	C₄×C₄₇	—	2	1	no	—
421	C₄×C₄₇	—	4	1	no	—
422	C₄×C₄₇	—	4	4	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	—	4	1	no	—
430	Dic₄₇	—	4	1	no	—
431	Dic₄₇	—	4	1	no	—
432	#3508	—	47	1	no	—
433	#3503	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
451	C₂×C₄₇	—	2	2	no	—
452	C₂×C₄₇	—	4	2	no	—
453	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
454	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
455	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
456	D₄₇	—	8	1	no	—
457	D₄₇	—	8	4	no	—
458	C₂×AGL(1,ℤ/8)	—	47	2	no	—
459	C₂×#135	—	47	1	no	—
460	#559	—	47	2	no	—
461	#559	—	47	2	no	—
462	Q₈²	C₂×D₄₇	1	2	yes	complemented
463	#557	C₂×D₄₇	1	2	yes	complemented
464	#554	—	2	2	no	—
465	#554	C₂×D₄₇	1	2	yes	complemented
466	#550	—	47	2	no	—
467	#550	—	47	2	no	—
468	D₄×Q₈	—	2	2	no	—
469	D₄×Q₈	C₂×D₄₇	1	2	yes	complemented
470	#546	—	94	2	no	—
471	#546	—	94	2	no	—
472	#544	—	2	2	no	—
473	#544	C₂×D₄₇	1	2	yes	—
474	#540	—	94	2	no	—
475	#535	—	47	2	no	—
476	#533	—	2	1	no	—
477	#533	C₂×D₄₇	1	1	yes	characteristic
478	#532	—	94	1	no	—
479	#532	—	94	1	no	—
480	C₂×C₄⋊Q₈	—	2	1	no	—
481	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
482	C₂×#127	—	47	1	no	—
483	#520	C₂×D₄₇	1	2	yes	—
484	#518	—	47	2	no	—
485	C₄×#41	—	47	1	no	—
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	—	47	1	no	—
518	C₄×Q₁₆	—	47	1	no	—
519	C₄×SD₁₆	—	47	1	no	—
520	C₄×SD₁₆	—	47	4	no	—
521	C₄×SD₁₆	—	47	1	no	—
522	C₄×SD₁₆	—	47	1	no	—
523	C₄×SD₁₆	—	47	1	no	—
524	C₄×D₈	—	47	1	no	—
525	C₄×D₈	—	47	4	no	—
526	C₄×D₈	—	47	1	no	—
527	#428	—	47	2	no	—
528	#427	—	47	1	no	—
529	#424	—	47	2	no	—
530	#423	—	47	1	no	—
531	#418	—	47	2	no	—
532	#417	—	47	2	no	—
533	#416	—	47	1	no	—
534	#416	—	47	1	no	—
535	C₂×#102	—	47	2	no	—
536	C₂×#102	—	47	2	no	—
537	#405	—	47	2	no	—
538	C₂×C₄×C₈	—	47	1	no	—
539	C₄₇	#61329	1	1	yes	characteristic, complemented, Sylow
540	C₂×#41	—	47	1	no	—
541	C₂×#41	—	94	2	no	—
542	C₂×#41	—	94	2	no	—
543	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
544	C₂²×Q₈	—	2	2	no	—
545	C₂²×Q₈	—	2	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	—	94	4	no	—
551	C₂×Q₁₆	—	47	1	no	—
552	C₂×SD₁₆	—	47	1	no	—
553	C₂×SD₁₆	—	47	4	no	—
554	C₂×SD₁₆	—	47	1	no	—
555	C₂×D₈	—	47	1	no	—
556	C₂×D₈	—	47	4	no	—
557	C₂×M₁₆	—	47	2	no	—
558	C₂²×C₈	—	47	1	no	—
559	C₂²×C₈	—	47	1	no	—
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	—	2	4	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
567	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
568	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
569	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
570	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
571	#127	—	47	2	no	—
572	#127	—	47	2	no	—
573	#127	—	47	4	no	—
574	#127	—	94	1	no	—
575	#127	—	94	1	no	—
576	#125	—	2	2	no	—
577	#125	—	2	4	no	—
578	#125	C₂²⋊D₄₇	1	2	yes	—
579	#125	C₂²×D₄₇	1	4	yes	—
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	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
591	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
592	#121	—	94	2	no	—
593	#121	—	94	2	no	—
594	#121	—	94	2	no	—
595	#121	—	94	2	no	—
596	#121	—	94	4	no	—
597	#121	—	94	4	no	—
598	#120	—	94	4	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	47	1	no	—
602	C₄×Q₈	—	47	1	no	—
603	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
604	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
605	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
606	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
607	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	—	47	1	no	—
612	C₄×D₄	—	47	1	no	—
613	C₄×D₄	—	47	4	no	—
614	C₄×D₄	—	47	4	no	—
615	C₄×D₄	—	94	1	no	—
616	C₄×D₄	—	94	1	no	—
617	C₄×D₄	—	94	2	no	—
618	C₄×D₄	—	94	2	no	—
619	C₄×D₄	—	94	2	no	—
620	C₄×D₄	—	94	2	no	—
621	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
622	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
623	C₄×D₄	C₂²×D₄₇	1	4	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	1	no	—
626	#117	—	47	1	no	—
627	#117	—	94	1	no	—
628	#117	C₂²×D₄₇	1	1	yes	characteristic
629	#117	C₂²×D₄₇	1	2	yes	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
634	C₂×C₂²⋊C₄	—	94	4	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	94	1	no	—
637	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
638	#107	—	47	1	no	—
639	#107	—	47	1	no	—
640	#107	—	47	4	no	—
641	#106	—	47	1	no	—
642	#106	—	47	1	no	—
643	#106	—	47	4	no	—
644	C₄⋊C₈	—	47	2	no	—
645	C₄⋊C₈	—	47	2	no	—
646	C₄⋊C₈	—	47	4	no	—
647	C₄⋊C₈	—	47	4	no	—
648	#103	—	47	1	no	—
649	#103	—	47	1	no	—
650	#103	—	47	1	no	—
651	#103	—	47	1	no	—
652	#103	—	47	4	no	—
653	#102	—	47	1	no	—
654	#102	—	47	1	no	—
655	#102	—	47	4	no	—
656	#102	—	47	4	no	—
657	#102	—	47	4	no	—
658	#102	—	47	4	no	—
659	#102	—	47	1	no	—
660	#102	—	47	1	no	—
661	#102	—	47	4	no	—
662	#102	—	47	4	no	—
663	#102	—	47	4	no	—
664	#97	—	47	4	no	—
665	C₄×C₈	—	47	1	no	—
666	C₄×C₈	—	47	1	no	—
667	C₄×C₈	—	47	1	no	—
668	C₄×C₈	—	47	1	no	—
669	C₄×C₈	—	47	4	no	—
670	C₂⁴	—	94	2	no	—
671	#41	—	2	2	no	—
672	#41	—	94	2	no	—
673	#41	—	94	2	no	—
674	#41	—	376	4	no	—
675	#41	—	376	4	no	—
676	#41	#10625354	1	4	yes	complemented
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	8	2	no	—
681	C₂×Q₈	—	8	4	no	—
682	C₂×Q₈	—	47	1	no	—
683	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
684	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
685	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	47	4	no	—
688	C₂×D₄	—	47	1	no	—
689	C₂×D₄	—	94	1	no	—
690	C₂×D₄	—	94	4	no	—
691	C₂×D₄	—	94	4	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	2	no	—
697	C₂×D₄	—	94	4	no	—
698	C₂×D₄	—	94	4	no	—
699	C₂×D₄	—	376	2	no	—
700	C₂×D₄	—	376	2	no	—
701	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	94	4	no	—
708	C₂²×C₄	—	94	4	no	—
709	C₂²×C₄	—	94	1	no	—
710	C₂²×C₄	—	94	1	no	—
711	C₂²×C₄	—	94	1	no	—
712	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
713	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
714	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
715	Q₁₆	—	94	2	no	—
716	SD₁₆	—	94	2	no	—
717	SD₁₆	—	94	8	no	—
718	SD₁₆	—	94	2	no	—
719	D₈	—	94	2	no	—
720	D₈	—	94	8	no	—
721	M₁₆	—	94	4	no	—
722	C₂×C₈	—	47	1	no	—
723	C₂×C₈	—	47	1	no	—
724	C₂×C₈	—	47	1	no	—
725	C₂×C₈	—	47	1	no	—
726	C₂×C₈	—	47	4	no	—
727	C₂×C₈	—	94	2	no	—
728	C₂×C₈	—	94	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	47	1	no	—
739	C₄⋊C₄	—	47	1	no	—
740	C₄⋊C₄	—	94	1	no	—
741	C₄⋊C₄	—	94	1	no	—
742	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
743	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
744	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
745	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
746	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
747	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
748	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
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	4	no	—
755	C₂²⋊C₄	—	94	1	no	—
756	C₂²⋊C₄	—	94	4	no	—
757	C₂²⋊C₄	—	94	4	no	—
758	C₂²⋊C₄	—	94	1	no	—
759	C₂²⋊C₄	—	94	1	no	—
760	C₂²⋊C₄	—	94	4	no	—
761	C₂²⋊C₄	—	94	4	no	—
762	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	94	1	no	—
768	C₄²	—	94	1	no	—
769	C₄²	—	94	1	no	—
770	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
771	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
772	C₄²	C₂³×D₄₇	1	1	yes	characteristic
773	C₄²	C₂³×D₄₇	1	1	yes	characteristic
774	C₄²	C₂³×D₄₇	1	4	yes	—
775	C₂³	—	2	1	no	—
776	C₂³	—	94	4	no	—
777	C₂³	—	94	1	no	—
778	C₂³	—	376	2	no	—
779	C₂³	—	376	2	no	—
780	C₂³	—	188	4	no	—
781	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	8	2	no	—
787	Q₈	—	8	4	no	—
788	Q₈	—	94	1	no	—
789	Q₈	—	94	1	no	—
790	Q₈	C₂×#10625354	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	1	no	—
793	D₄	—	94	4	no	—
794	D₄	—	94	1	no	—
795	D₄	—	94	4	no	—
796	D₄	—	94	1	no	—
797	D₄	—	376	2	no	—
798	D₄	—	376	2	no	—
799	D₄	—	376	4	no	—
800	D₄	—	376	4	no	—
801	D₄	—	188	2	no	—
802	D₄	—	188	4	no	—
803	D₄	—	188	4	no	—
804	D₄	—	188	4	no	—
805	D₄	C₂×#10625354	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	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	94	1	no	—
818	C₂×C₄	—	94	1	no	—
819	C₂×C₄	—	94	1	no	—
820	C₂×C₄	—	376	4	no	—
821	C₂×C₄	—	376	4	no	—
822	C₂×C₄	—	188	2	no	—
823	C₂×C₄	—	188	2	no	—
824	C₂×C₄	—	188	2	no	—
825	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
826	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
827	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
828	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
829	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
830	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
832	C₂×C₄	C₂×#10625354	1	2	yes	—
833	C₂×C₄	#13094072	1	2	yes	—
834	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
835	C₈	—	94	1	no	—
836	C₈	—	94	1	no	—
837	C₈	—	94	4	no	—
838	C₈	—	94	1	no	—
839	C₈	—	94	1	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	—	188	1	no	—
846	C₂²	—	188	4	no	—
847	C₂²	—	188	4	no	—
848	C₂²	—	188	1	no	—
849	C₂²	—	188	4	no	—
850	C₂²	—	188	1	no	—
851	C₂²	—	752	4	no	—
852	C₂²	#15689784	1	2	yes	—
853	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	4	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	4	no	—
861	C₄	—	4	1	no	—
862	C₄	—	188	1	no	—
863	C₄	—	188	1	no	—
864	C₄	—	188	1	no	—
865	C₄	#15689784	1	2	yes	—
866	C₄	#15689926	1	2	yes	—
867	C₄	#15689931	1	2	yes	—
868	C₄	C₂²×#10625354	1	1	yes	characteristic
869	C₄	C₂×#13094072	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	376	4	no	—
873	C₂	—	376	1	no	—
874	C₂	C₂×#15689784	1	1	yes	characteristic
875	C₂	C₂×#15689926	1	1	yes	characteristic
876	C₂	C₂×#15689931	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3503	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3503	D₄₇
hypocenter	C₄₇	#61329
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3503

Complements

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

N	H ≅ G/N	type
1. #20257265	C₂	semidirect
2. #20256202	C₂	semidirect
3. #20256180	C₂	semidirect
4. #20256117	C₂	semidirect
5. #20256095	C₂	semidirect
6. #20256084	C₂	semidirect
7. #20256059	C₂	semidirect
8. #20256048	C₂	semidirect
9. #20256023	C₂	semidirect
10. #20253747	C₂	semidirect
11. C₂×#15689471	C₂	semidirect
12. #20253213	C₂	semidirect
13. #20253197	C₂	semidirect
14. #20252927	C₂	semidirect
15. #20252868	C₂	semidirect
16. #20252323	C₂	semidirect
17. #20252216	C₂	semidirect
18. C₄×#13094044	C₂	semidirect
19. C₄₇×#3503	C₂	semidirect
35. #15689489	C₂²	semidirect
36. #15689485	C₂²	semidirect
37. #15689480	C₂²	semidirect
42. #15689471	C₂²	semidirect
43. #15689420	C₂²	semidirect
44. #15689420	C₂²	semidirect
45. #15689415	C₂²	semidirect
46. #15689410	C₂²	semidirect
47. #15689410	C₂²	semidirect
48. #15689405	C₂²	semidirect
49. #15689400	C₂²	semidirect
50. #15689400	C₂²	semidirect
51. #15689345	C₂²	semidirect
52. #15689338	C₂²	semidirect
55. #15689323	C₂²	semidirect
58. #15689318	C₂²	semidirect
59. #15689254	C₂²	semidirect
60. #15689254	C₂²	semidirect
61. Q₈×C₄₇⋊C₈	C₂²	semidirect
62. Q₈×C₄₇⋊C₈	C₂²	semidirect
63. #15689233	C₂²	semidirect
64. #15689221	C₂²	semidirect
65. C₄×#10625337	C₂²	semidirect
66. C₄×#10625337	C₂²	semidirect
67. C₄×#10625336	C₂²	semidirect
68. C₄×#10625336	C₂²	semidirect
69. C₄×#10625336	C₂²	semidirect
70. C₄×#10625335	C₂²	semidirect
71. C₄×#10625335	C₂²	semidirect
72. C₄×#10625334	C₂²	semidirect
73. C₄×#10625334	C₂²	semidirect
74. C₄×#10625334	C₂²	semidirect
87. Q₈²×C₄₇	C₂²	semidirect
88. C₄₇×#557	C₂²	semidirect
90. C₄₇×#554	C₂²	semidirect
92. D₄×Q₈×C₄₇	C₂²	semidirect
233. #41×C₄₇	#41	semidirect
433. #3503	D₄₇	semidirect
462. Q₈²	C₂×D₄₇	semidirect
463. #557	C₂×D₄₇	semidirect
465. #554	C₂×D₄₇	semidirect
469. D₄×Q₈	C₂×D₄₇	semidirect
539. C₄₇	#61329	semidirect
676. #41	#10625354	semidirect

Maximal subgroups

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

subgroup	index
#20257265	2
#20256202	2
#20256180	2
#20256117	2
#20256095	2
#20256084	2
#20256059	2
#20256048	2
#20256023	2
#20253747	2
C₂×#15689471	2
#20253213	2
#20253197	2
#20252927	2
#20252868	2
#20252323	2
#20252216	2
C₄×#13094044	2
C₄₇×#3503	2
#61329	47