Subgroups — #27094370

Order 12032.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257255	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257181	C₂	1	1	yes	maximal, characteristic
3	#20255653	C₂	1	2	yes	maximal, complemented
4	#20255601	C₂	1	2	yes	maximal, complemented
5	#20255496	C₂	1	2	yes	maximal, complemented
6	#20255466	C₂	1	2	yes	maximal, complemented
7	#20255451	C₂	1	2	yes	maximal, complemented
8	#20255421	C₂	1	2	yes	maximal, complemented
9	#20255272	C₂	1	2	yes	maximal, complemented
10	#20255220	C₂	1	2	yes	maximal, complemented
11	#20253777	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253360	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253349	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253044	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253028	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689346	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252686	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252668	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13094054	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252131	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251917	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251910	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094071	C₂²	1	1	yes	characteristic
25	C₂×#13094070	C₂²	1	1	yes	characteristic
26	C₂×#13094054	C₂²	1	1	yes	characteristic
27	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#10625325	C₂²	1	1	yes	characteristic
29	C₂×#13094030	C₂²	1	1	yes	characteristic
30	C₂×#13094030	C₂²	1	1	yes	characteristic, complemented
31	#15689858	—	2	1	no	—
32	#15689852	—	2	1	no	—
33	#15689847	C₂²	1	2	yes	complemented
34	#15689846	—	2	1	no	—
35	#15689846	—	2	1	no	—
36	#15689834	C₂²	1	2	yes	complemented
37	#15689811	C₂²	1	2	yes	complemented
38	#15689811	C₂²	1	2	yes	complemented
39	#15689785	C₂²	1	2	yes	—
40	#15689785	C₂²	1	2	yes	—
41	#15689768	—	2	2	no	—
42	#15689768	—	2	2	no	—
43	#15689768	C₂²	1	2	yes	—
44	#15689768	C₂²	1	2	yes	—
45	#15689722	—	2	2	no	—
46	#15689699	—	2	1	no	—
47	#15689699	C₂²	1	1	yes	characteristic
48	#15689699	C₂²	1	1	yes	characteristic
49	#15689699	C₂²	1	1	yes	characteristic, complemented
50	#15689692	—	2	1	no	—
51	#15689692	C₂²	1	1	yes	characteristic
52	#15689673	—	2	1	no	—
53	#15689673	C₂²	1	1	yes	characteristic
54	#15689659	—	2	2	no	—
55	C₂×#13094012	—	2	1	no	—
56	C₂×#13094012	C₂²	1	1	yes	characteristic
57	#15689603	C₂²	1	1	yes	characteristic
58	#15689603	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
60	#15689485	C₂²	1	2	yes	complemented
61	#15689485	C₂²	1	2	yes	complemented
62	#15689480	C₂²	1	2	yes	complemented
63	#15689480	C₂²	1	2	yes	complemented
64	#15689467	C₂²	1	2	yes	complemented
65	#15689466	C₂²	1	2	yes	complemented
66	#15689460	C₂²	1	2	yes	complemented
67	#15689455	C₂²	1	2	yes	complemented
68	#15689450	C₂²	1	2	yes	complemented
69	#15689449	C₂²	1	2	yes	complemented
70	#15689443	C₂²	1	2	yes	complemented
71	#15689438	C₂²	1	2	yes	complemented
72	#15689382	C₂²	1	2	yes	complemented
73	#15689382	C₂²	1	2	yes	complemented
74	#15689370	C₂²	1	2	yes	complemented
75	#15689370	C₂²	1	2	yes	complemented
76	#15689365	C₂²	1	2	yes	complemented
77	#15689365	C₂²	1	2	yes	complemented
78	#15689353	C₂²	1	2	yes	complemented
79	#15689353	C₂²	1	2	yes	complemented
80	#15689346	C₂²	1	2	yes	complemented
81	#15689346	C₂²	1	2	yes	complemented
82	#15689346	C₂²	1	2	yes	complemented
83	#15689346	C₂²	1	2	yes	complemented
84	#15689288	C₂²	1	2	yes	—
85	#15689288	C₂²	1	2	yes	—
86	#15689286	C₂²	1	2	yes	complemented
87	#15689286	C₂²	1	2	yes	complemented
88	#15689280	C₂²	1	2	yes	complemented
89	#15689280	C₂²	1	2	yes	complemented
90	#15689275	C₂²	1	2	yes	—
91	#15689275	C₂²	1	2	yes	—
92	#15689228	C₂²	1	2	yes	complemented
93	#15689223	C₂²	1	2	yes	complemented
94	C₄×#10625337	C₂²	1	2	yes	complemented
95	C₄×#10625335	C₂²	1	2	yes	complemented
96	#15689200	C₂²	1	2	yes	complemented
97	#15689193	C₂²	1	2	yes	complemented
98	#15689193	C₂²	1	2	yes	complemented
99	#15689188	C₂²	1	2	yes	complemented
100	#15689166	C₂²	1	1	yes	characteristic, complemented
101	#15689131	C₂²	1	1	yes	characteristic, complemented
102	#15689131	C₂²	1	1	yes	characteristic, complemented
103	#15689131	C₂²	1	1	yes	characteristic, complemented
104	#15689130	C₂²	1	2	yes	complemented
105	#15689127	C₂²	1	1	yes	characteristic
106	#15689127	C₂²	1	1	yes	characteristic
107	#15689126	C₂²	1	2	yes	—
108	#15689124	C₂²	1	1	yes	characteristic
109	#15689123	C₂²	1	2	yes	—
110	#15689121	C₂²	1	2	yes	complemented
111	#15689118	C₂²	1	2	yes	—
112	#15689116	C₂²	1	2	yes	complemented
113	C₂×#13093949	C₂²	1	1	yes	characteristic, complemented
114	#103×D₄₇	C₂²	1	2	yes	complemented
115	C₂×#13093946	C₂²	1	1	yes	characteristic
116	#102×D₄₇	C₂²	1	2	yes	—
117	#15689089	C₂²	1	1	yes	characteristic
118	#15689089	C₂²	1	1	yes	characteristic, complemented
119	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#477	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#476	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#475	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#474	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
133	C₄₇×#416	C₂²	1	1	yes	characteristic
134	C₄₇×#416	C₂²	1	1	yes	characteristic
135	#13094071	—	2	4	no	—
136	#13094071	—	4	2	no	—
137	#13094070	—	2	4	no	—
138	#13094070	—	4	2	no	—
139	C₂×#10625354	C₂³	1	2	yes	—
140	C₂×#10625350	—	2	1	no	—
141	C₂×#10625350	—	2	1	no	—
142	C₂×#10625350	C₂³	1	1	yes	characteristic
143	C₂×#10625350	C₂³	1	1	yes	characteristic
144	C₂×#10625352	—	2	2	no	—
145	C₂×#10625352	C₂³	1	2	yes	—
146	C₂²×Dic₉₄	—	2	1	no	—
147	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
148	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
149	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
150	C₂²×D₁₈₈	—	2	1	no	—
151	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
152	C₂×D₄×D₄₇	—	2	2	no	—
153	C₂×D₄×D₄₇	C₂³	1	2	yes	—
154	#13094054	—	2	4	no	—
155	C₂×Dic₁₈₈	—	4	2	no	—
156	C₂×Dic₁₈₈	C₂³	1	2	yes	—
157	C₂×Dic₁₈₈	C₂³	1	2	yes	—
158	C₂×#10625337	C₂³	1	2	yes	—
159	C₂×#10625325	—	4	2	no	—
160	C₂×#10625325	C₂³	1	2	yes	—
161	C₂×#10625325	C₂³	1	2	yes	—
162	C₂×#10625335	C₂³	1	2	yes	—
163	#13094030	—	4	2	no	—
164	#13094030	—	4	2	no	—
165	C₂×#10625329	C₂³	1	1	yes	characteristic
166	C₂×#10625329	C₂³	1	1	yes	characteristic
167	C₂×#10625324	C₂³	1	2	yes	—
168	C₂×#10625324	C₂³	1	2	yes	—
169	C₂×C₈×D₄₇	C₂³	1	2	yes	—
170	C₂×C₈×D₄₇	C₂³	1	2	yes	—
171	#13094024	—	2	1	no	—
172	#13094024	—	2	1	no	—
173	#13094024	—	2	1	no	—
174	#13094024	D₄	1	1	yes	characteristic
175	#13094021	—	2	1	no	—
176	#13094021	D₄	1	1	yes	characteristic
177	#13094019	—	2	2	no	—
178	#13094019	—	2	2	no	—
179	#13094019	—	2	2	no	—
180	#13094019	—	2	2	no	—
181	#13094015	—	2	2	no	—
182	#13094015	—	2	2	no	—
183	#13094015	—	2	2	no	—
184	#13094013	—	2	2	no	—
185	#13094012	—	2	1	no	—
186	#13094012	—	2	1	no	—
187	#13094012	—	2	1	no	—
188	#13094012	—	2	1	no	—
189	#13094012	—	2	1	no	—
190	#13094012	—	2	1	no	—
191	#13094012	—	2	2	no	—
192	#13094012	—	2	2	no	—
193	#13094012	D₄	1	1	yes	characteristic
194	#13094012	D₄	1	1	yes	characteristic
195	#13094012	C₂³	1	2	yes	—
196	#13094012	C₂³	1	2	yes	—
197	#13094009	—	2	2	no	—
198	#13094009	—	2	2	no	—
199	#13094008	—	2	2	no	—
200	#13094008	—	2	2	no	—
201	#13094008	—	2	2	no	—
202	#13094008	—	2	2	no	—
203	#13094008	—	2	2	no	—
204	#13094004	—	2	2	no	—
205	#13094004	—	2	2	no	—
206	#13094004	C₂³	1	2	yes	—
207	#13094004	C₂³	1	2	yes	—
208	#13094004	C₂³	1	2	yes	—
209	#13094004	C₂³	1	2	yes	—
210	#13094004	C₂³	1	2	yes	—
211	#13094004	C₂³	1	2	yes	—
212	#13094000	—	2	2	no	—
213	#13094000	—	2	2	no	—
214	#13093999	—	2	2	no	—
215	#13093999	—	2	2	no	—
216	#13093999	C₂³	1	2	yes	—
217	#13093999	C₂³	1	2	yes	—
218	#13093998	—	2	2	no	—
219	#13093998	—	2	2	no	—
220	#13093998	D₄	1	2	yes	—
221	#13093998	D₄	1	2	yes	—
222	#13093994	—	2	2	no	—
223	#13093994	—	2	2	no	—
224	#13093994	—	2	2	no	—
225	Q₈×Dic₄₇	—	2	2	no	—
226	C₄×Dic₉₄	—	2	1	no	—
227	C₄×Dic₉₄	—	2	1	no	—
228	C₄×Dic₉₄	—	2	1	no	—
229	C₄×Dic₉₄	—	2	1	no	—
230	C₄×Dic₉₄	C₂³	1	2	yes	—
231	C₄×Dic₉₄	C₂³	1	2	yes	—
232	C₄×D₁₈₈	—	2	1	no	—
233	C₄×D₁₈₈	—	2	1	no	—
234	C₄×D₁₈₈	—	2	2	no	—
235	C₄×D₁₈₈	—	2	2	no	—
236	C₄×D₁₈₈	C₂³	1	2	yes	—
237	C₄×D₁₈₈	C₂³	1	2	yes	—
238	#13093986	—	2	2	no	—
239	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
240	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
241	#13093982	—	2	2	no	—
242	#13093982	—	2	2	no	—
243	#13093982	C₂³	1	2	yes	—
244	#13093982	C₂³	1	2	yes	—
245	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
246	C₂×Dic₄₇⋊C₄	—	2	1	no	—
247	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
248	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
249	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
250	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
251	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
252	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
253	C₂×C₄×Dic₄₇	—	2	1	no	—
254	#13093957	C₂³	1	2	yes	—
255	#13093955	C₂³	1	2	yes	—
256	#13093949	C₂³	1	2	yes	—
257	#13093949	C₂³	1	2	yes	—
258	#13093948	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093947	C₂³	1	2	yes	—
262	#13093947	C₂³	1	2	yes	—
263	#13093947	C₂³	1	2	yes	—
264	#13093947	C₂³	1	2	yes	—
265	#13093946	C₂³	1	2	yes	—
266	#13093946	C₂³	1	2	yes	—
267	#13093945	C₂³	1	2	yes	—
268	#13093944	C₂³	1	2	yes	—
269	#13093944	C₂³	1	2	yes	—
270	#13093944	C₂³	1	2	yes	—
271	#13093944	C₂³	1	2	yes	—
272	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
273	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
274	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
275	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
276	#13093935	C₂³	1	2	yes	—
277	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
278	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
281	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	#125×C₄₇	C₂³	1	1	yes	characteristic
284	#125×C₄₇	C₂³	1	1	yes	characteristic
285	C₂²⋊Q₈×C₄₇	—	2	1	no	—
286	C₂²⋊Q₈×C₄₇	—	2	1	no	—
287	C₄×Q₈×C₄₇	—	2	1	no	—
288	C₄×Q₈×C₄₇	—	2	1	no	—
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
295	#117×C₄₇	—	2	1	no	—
296	#117×C₄₇	C₂³	1	1	yes	characteristic
297	#117×C₄₇	C₂³	1	1	yes	characteristic
298	#117×C₄₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₄₇	—	2	1	no	—
300	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
301	#107×C₄₇	C₂³	1	1	yes	characteristic
302	#107×C₄₇	C₂³	1	1	yes	characteristic
303	#107×C₄₇	C₂³	1	1	yes	characteristic
304	#107×C₄₇	C₂³	1	1	yes	characteristic
305	#106×C₄₇	C₂³	1	1	yes	characteristic
306	#106×C₄₇	C₂³	1	1	yes	characteristic
307	#106×C₄₇	C₂³	1	1	yes	characteristic
308	#106×C₄₇	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
310	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
313	#103×C₄₇	C₂³	1	1	yes	characteristic
314	#103×C₄₇	C₂³	1	1	yes	characteristic
315	#103×C₄₇	C₂³	1	1	yes	characteristic
316	#103×C₄₇	C₂³	1	1	yes	characteristic
317	#102×C₄₇	C₂³	1	1	yes	characteristic
318	#102×C₄₇	C₂³	1	1	yes	characteristic
319	#102×C₄₇	C₂³	1	1	yes	characteristic
320	#102×C₄₇	C₂³	1	1	yes	characteristic
321	C₂³×D₄₇	—	2	1	no	—
322	C₂³×D₄₇	—	2	2	no	—
323	#41×C₄₇	—	2	2	no	—
324	#41×C₄₇	#41	1	4	yes	—
325	C₂×Q₈×C₄₇	—	2	1	no	—
326	C₂×Q₈×C₄₇	—	2	1	no	—
327	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₇	—	2	1	no	—
329	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
336	C₂×C₂²⋊D₄₇	—	2	2	no	—
337	C₂×C₂²⋊D₄₇	—	2	2	no	—
338	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
339	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
340	C₂²×Dic₄₇	—	2	1	no	—
341	C₂²×Dic₄₇	—	2	1	no	—
342	C₂²×Dic₄₇	—	2	1	no	—
343	C₂²×Dic₄₇	—	2	2	no	—
344	#10625354	—	2	4	no	—
345	#10625354	—	4	2	no	—
346	Q₈×D₄₇	—	2	4	no	—
347	Q₈×D₄₇	—	4	2	no	—
348	#10625352	—	2	4	no	—
349	#10625352	—	4	2	no	—
350	#10625352	—	4	8	no	—
351	D₄×D₄₇	—	2	4	no	—
352	D₄×D₄₇	—	4	2	no	—
353	D₄×D₄₇	—	4	8	no	—
354	#10625350	—	2	2	no	—
355	#10625350	—	2	2	no	—
356	#10625350	—	2	2	no	—
357	#10625350	—	2	2	no	—
358	#10625350	—	4	4	no	—
359	#10625350	—	4	4	no	—
360	C₂×D₁₈₈	—	2	2	no	—
361	C₂×D₁₈₈	—	2	2	no	—
362	C₂×D₁₈₈	—	2	2	no	—
363	C₂×D₁₈₈	—	2	1	no	—
364	C₂×D₁₈₈	—	2	2	no	—
365	C₂×D₁₈₈	—	2	2	no	—
366	C₂×D₁₈₈	—	4	4	no	—
367	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
368	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
369	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
370	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
371	C₂×D₁₈₈	C₂⁴	1	2	yes	—
372	C₂×C₄×D₄₇	—	2	2	no	—
373	C₂×C₄×D₄₇	—	2	2	no	—
374	C₂×C₄×D₄₇	—	2	2	no	—
375	C₂×C₄×D₄₇	—	2	2	no	—
376	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
377	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
378	C₂×Dic₉₄	—	2	2	no	—
379	C₂×Dic₉₄	—	2	2	no	—
380	C₂×Dic₉₄	—	2	2	no	—
381	C₂×Dic₉₄	—	2	2	no	—
382	C₂×Dic₉₄	—	2	1	no	—
383	C₂×Dic₉₄	—	2	1	no	—
384	C₂×Dic₉₄	—	2	2	no	—
385	C₂×Dic₉₄	—	4	4	no	—
386	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
387	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
388	C₂×Dic₉₄	C₂⁴	1	2	yes	—
389	C₂×Dic₉₄	C₂⁴	1	2	yes	—
390	C₂×C₈×C₄₇	—	2	2	no	—
391	C₂×C₈×C₄₇	—	2	2	no	—
392	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₇	—	2	1	no	—
397	C₄⋊C₄×C₄₇	—	2	1	no	—
398	C₄⋊C₄×C₄₇	—	2	1	no	—
399	C₄⋊C₄×C₄₇	—	2	1	no	—
400	C₄⋊C₄×C₄₇	—	2	1	no	—
401	C₄⋊C₄×C₄₇	—	2	1	no	—
402	C₄⋊C₄×C₄₇	—	2	1	no	—
403	C₄⋊C₄×C₄₇	—	2	1	no	—
404	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₄₇	—	2	1	no	—
411	C₂²⋊C₄×C₄₇	—	2	1	no	—
412	C₂²⋊C₄×C₄₇	—	2	1	no	—
413	C₂²⋊C₄×C₄₇	—	2	1	no	—
414	C₂²⋊C₄×C₄₇	—	2	1	no	—
415	C₄²×C₄₇	—	2	1	no	—
416	C₄²×C₄₇	—	2	1	no	—
417	C₄²×C₄₇	—	2	1	no	—
418	C₄²×C₄₇	—	2	1	no	—
419	C₄²×C₄₇	—	2	1	no	—
420	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
423	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
424	#10625337	—	2	4	no	—
425	#10625335	—	2	4	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	2	no	—
431	(C₂×D₄₇)⋊C₄	—	2	2	no	—
432	(C₂×D₄₇)⋊C₄	—	2	2	no	—
433	(C₂×D₄₇)⋊C₄	—	2	2	no	—
434	(C₂×D₄₇)⋊C₄	—	2	2	no	—
435	(C₂×D₄₇)⋊C₄	—	2	2	no	—
436	(C₂×D₄₇)⋊C₄	—	2	2	no	—
437	(C₂×D₄₇)⋊C₄	—	2	2	no	—
438	(C₂×D₄₇)⋊C₄	—	2	2	no	—
439	(C₂×D₄₇)⋊C₄	—	2	2	no	—
440	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
441	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
442	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
443	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
444	C₄⋊Dic₄₇	—	2	1	no	—
445	C₄⋊Dic₄₇	—	2	2	no	—
446	C₄⋊Dic₄₇	—	2	2	no	—
447	C₄⋊Dic₄₇	—	2	2	no	—
448	C₄⋊Dic₄₇	—	2	2	no	—
449	C₄⋊Dic₄₇	—	2	2	no	—
450	C₄⋊Dic₄₇	—	2	2	no	—
451	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
452	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
453	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
454	Dic₄₇⋊C₄	—	2	2	no	—
455	Dic₄₇⋊C₄	—	2	2	no	—
456	Dic₄₇⋊C₄	—	2	2	no	—
457	Dic₄₇⋊C₄	—	2	2	no	—
458	C₄×Dic₄₇	—	2	2	no	—
459	C₄×Dic₄₇	—	2	2	no	—
460	C₄×Dic₄₇	—	2	2	no	—
461	C₄×Dic₄₇	—	2	2	no	—
462	#10625329	—	2	2	no	—
463	#10625329	—	2	2	no	—
464	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
465	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
466	Dic₁₈₈	—	4	2	no	—
467	Dic₁₈₈	—	4	2	no	—
468	#10625325	—	4	2	no	—
469	#10625325	—	4	2	no	—
470	#10625324	—	4	2	no	—
471	#10625324	—	4	2	no	—
472	C₈×D₄₇	—	4	2	no	—
473	C₈×D₄₇	—	4	2	no	—
474	C₂³×C₄₇	—	2	1	no	—
475	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
476	C₂²×D₄₇	—	2	2	no	—
477	C₂²×D₄₇	—	4	4	no	—
478	C₂²×D₄₇	—	4	2	no	—
479	C₂²×D₄₇	—	8	2	no	—
480	C₂²×D₄₇	—	8	2	no	—
481	C₂²×D₄₇	—	8	1	no	—
482	C₂²×D₄₇	—	8	1	no	—
483	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
484	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
485	Q₈×C₄₇	—	2	1	no	—
486	Q₈×C₄₇	—	4	2	no	—
487	Q₈×C₄₇	—	8	1	no	—
488	Q₈×C₄₇	C₂×#41	1	2	yes	—
489	D₄×C₄₇	—	2	4	no	—
490	D₄×C₄₇	—	2	1	no	—
491	D₄×C₄₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₄₇	—	2	1	no	—
493	C₂×C₄×C₄₇	—	2	4	no	—
494	C₂×C₄×C₄₇	—	2	1	no	—
495	C₂×C₄×C₄₇	—	2	1	no	—
496	C₂×C₄×C₄₇	—	2	1	no	—
497	C₂×C₄×C₄₇	—	2	1	no	—
498	C₂×C₄×C₄₇	—	2	1	no	—
499	C₂×C₄×C₄₇	—	2	1	no	—
500	C₂×C₄×C₄₇	—	4	1	no	—
501	C₂×C₄×C₄₇	—	4	1	no	—
502	C₂×C₄×C₄₇	—	8	1	no	—
503	C₂×C₄×C₄₇	—	8	1	no	—
504	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
510	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
511	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
512	C₂²⋊D₄₇	—	2	4	no	—
513	C₂²⋊D₄₇	—	2	4	no	—
514	C₂²⋊D₄₇	—	4	4	no	—
515	C₂²⋊D₄₇	—	4	4	no	—
516	C₂×Dic₄₇	—	2	2	no	—
517	C₂×Dic₄₇	—	2	2	no	—
518	C₂×Dic₄₇	—	2	2	no	—
519	C₂×Dic₄₇	—	4	4	no	—
520	C₂×Dic₄₇	—	4	2	no	—
521	C₂×Dic₄₇	—	4	2	no	—
522	C₂×Dic₄₇	—	8	1	no	—
523	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
524	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
525	D₁₈₈	—	2	2	no	—
526	D₁₈₈	—	2	2	no	—
527	D₁₈₈	—	2	2	no	—
528	D₁₈₈	—	2	2	no	—
529	D₁₈₈	—	4	2	no	—
530	D₁₈₈	—	4	2	no	—
531	D₁₈₈	—	4	4	no	—
532	D₁₈₈	—	4	2	no	—
533	D₁₈₈	—	8	2	no	—
534	D₁₈₈	—	8	2	no	—
535	C₄×D₄₇	—	2	2	no	—
536	C₄×D₄₇	—	2	2	no	—
537	C₄×D₄₇	—	2	2	no	—
538	C₄×D₄₇	—	2	2	no	—
539	C₄×D₄₇	—	4	4	no	—
540	C₄×D₄₇	—	4	4	no	—
541	C₄×D₄₇	—	8	2	no	—
542	C₄×D₄₇	—	8	2	no	—
543	Dic₉₄	—	2	2	no	—
544	Dic₉₄	—	2	2	no	—
545	Dic₉₄	—	2	2	no	—
546	Dic₉₄	—	2	2	no	—
547	Dic₉₄	—	2	2	no	—
548	Dic₉₄	—	2	2	no	—
549	Dic₉₄	—	4	4	no	—
550	Dic₉₄	—	4	2	no	—
551	Dic₉₄	—	4	2	no	—
552	C₈×C₄₇	—	2	1	no	—
553	C₈×C₄₇	—	2	1	no	—
554	C₈×C₄₇	—	2	1	no	—
555	C₈×C₄₇	—	2	1	no	—
556	C₄₇⋊C₈	—	2	2	no	—
557	C₄₇⋊C₈	—	2	2	no	—
558	#61207	—	47	1	no	maximal, Sylow
559	C₂²×C₄₇	—	2	1	no	—
560	C₂²×C₄₇	—	2	1	no	—
561	C₂²×C₄₇	—	2	2	no	—
562	C₂²×C₄₇	—	4	1	no	—
563	C₂²×C₄₇	—	4	1	no	—
564	C₂²×C₄₇	#546	1	2	yes	—
565	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
566	C₂×D₄₇	—	2	2	no	—
567	C₂×D₄₇	—	2	2	no	—
568	C₂×D₄₇	—	2	2	no	—
569	C₂×D₄₇	—	2	2	no	—
570	C₂×D₄₇	—	2	2	no	—
571	C₂×D₄₇	—	2	2	no	—
572	C₂×D₄₇	—	4	2	no	—
573	C₂×D₄₇	—	4	2	no	—
574	C₂×D₄₇	—	4	2	no	—
575	C₂×D₄₇	—	16	4	no	—
576	C₂×D₄₇	—	16	2	no	—
577	C₄×C₄₇	—	2	1	no	—
578	C₄×C₄₇	—	2	1	no	—
579	C₄×C₄₇	—	2	1	no	—
580	C₄×C₄₇	—	2	1	no	—
581	C₄×C₄₇	—	2	2	no	—
582	C₄×C₄₇	—	4	1	no	—
583	C₄×C₄₇	—	4	1	no	—
584	C₄×C₄₇	—	4	1	no	—
585	C₄×C₄₇	—	4	1	no	—
586	C₄×C₄₇	—	4	1	no	—
587	C₄×C₄₇	—	4	1	no	—
588	C₄×C₄₇	#546	1	2	yes	—
589	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
590	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	Dic₄₇	—	2	2	no	—
592	Dic₄₇	—	2	2	no	—
593	Dic₄₇	—	4	2	no	—
594	Dic₄₇	—	4	2	no	—
595	Dic₄₇	—	4	2	no	—
596	#3507	—	47	1	no	—
597	#3500	—	47	1	no	—
598	#3327	—	47	2	no	—
599	#3323	—	47	2	no	—
600	#3316	—	47	2	no	—
601	#3314	—	47	2	no	—
602	#3313	—	47	2	no	—
603	#3311	—	47	2	no	—
604	#3300	—	47	2	no	—
605	#3296	—	47	2	no	—
606	#3140	—	47	1	no	—
607	#3097	—	47	1	no	—
608	#3096	—	47	1	no	—
609	#3076	D₄₇	1	1	yes	characteristic, complemented
610	#3059	—	47	1	no	—
611	#3057	—	47	1	no	—
612	C₂×#464	—	47	1	no	—
613	#3011	—	47	1	no	—
614	#3009	—	47	1	no	—
615	C₄×#137	—	47	1	no	—
616	#2935	—	47	1	no	—
617	#2898	—	47	1	no	—
618	#2897	—	47	1	no	—
619	C₂×C₄₇	—	2	2	no	—
620	C₂×C₄₇	—	4	2	no	—
621	C₂×C₄₇	C₂×#546	1	1	yes	characteristic
622	C₂×C₄₇	#3584	1	1	yes	characteristic
623	C₂×C₄₇	#3586	1	1	yes	characteristic
624	D₄₇	—	4	2	no	—
625	D₄₇	—	4	2	no	—
626	D₄₇	—	8	2	no	—
627	C₂×2₋¹⁺⁴	—	47	1	no	—
628	C₂×H(5,𝔽₂)	—	47	1	no	—
629	C₂×#137	—	47	1	no	—
630	C₂²×Q₁₆	—	47	1	no	—
631	C₂²×SD₁₆	—	47	1	no	—
632	C₂×#131	—	47	1	no	—
633	C₂×#131	—	47	1	no	—
634	#559	—	94	1	no	—
635	#557	—	94	1	no	—
636	#556	—	47	2	no	—
637	#556	—	94	1	no	—
638	#556	—	94	1	no	—
639	#554	—	47	2	no	—
640	#552	—	47	2	no	—
641	#552	—	47	2	no	—
642	#548	—	47	2	no	—
643	#548	—	47	2	no	—
644	#546	—	47	2	no	—
645	#546	—	47	2	no	—
646	#546	—	94	2	no	—
647	#546	—	94	2	no	—
648	#539	—	94	2	no	—
649	#536	—	47	1	no	—
650	#536	—	47	1	no	—
651	#536	—	47	1	no	—
652	#536	—	94	1	no	—
653	#535	—	47	1	no	—
654	#535	—	94	1	no	—
655	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
656	#532	—	47	1	no	—
657	#532	—	94	1	no	—
658	#529	—	94	2	no	—
659	C₂×#124	—	47	1	no	—
660	C₂×#124	—	94	1	no	—
661	#520	—	47	1	no	—
662	#520	—	47	1	no	—
663	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
664	C₂×C₄×Q₈	—	47	1	no	—
665	#489	—	47	2	no	—
666	#489	—	47	2	no	—
667	#488	—	47	2	no	—
668	#488	—	47	2	no	—
669	#485	—	47	2	no	—
670	#485	—	47	2	no	—
671	#484	—	47	2	no	—
672	#483	—	47	2	no	—
673	#482	—	47	2	no	—
674	#482	—	47	2	no	—
675	#481	—	47	2	no	—
676	#480	—	47	2	no	—
677	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
678	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
679	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
680	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
681	#477	C₂×D₄₇	1	1	yes	characteristic, complemented
682	#476	C₂×D₄₇	1	1	yes	characteristic, complemented
683	#475	C₂×D₄₇	1	1	yes	characteristic, complemented
684	#474	C₂×D₄₇	1	1	yes	characteristic, complemented
685	#470	—	47	2	no	—
686	#470	—	47	2	no	—
687	#468	—	47	2	no	—
688	#468	—	47	2	no	—
689	#467	—	47	2	no	—
690	#467	—	47	2	no	—
691	#465	—	47	2	no	—
692	#465	—	47	2	no	—
693	#464	—	47	2	no	—
694	#464	—	47	2	no	—
695	#464	—	47	2	no	—
696	#464	—	47	2	no	—
697	#452	—	47	2	no	—
698	#452	—	47	2	no	—
699	#452	—	47	2	no	—
700	#452	—	47	2	no	—
701	#451	—	47	2	no	—
702	#451	—	47	2	no	—
703	#450	—	47	2	no	—
704	#450	—	47	2	no	—
705	#441	—	47	2	no	—
706	#440	—	47	2	no	—
707	C₄×Q₁₆	—	47	2	no	—
708	C₄×SD₁₆	—	47	2	no	—
709	#436	—	47	2	no	—
710	#435	—	47	2	no	—
711	#435	—	47	2	no	—
712	C₈×D₄	—	47	2	no	—
713	#428	—	47	1	no	—
714	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
715	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
716	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
717	#419	—	47	1	no	—
718	#419	—	47	1	no	—
719	#419	—	47	1	no	—
720	#419	—	47	2	no	—
721	#418	—	47	1	no	—
722	#418	—	47	1	no	—
723	#418	—	47	2	no	—
724	#417	—	47	1	no	—
725	#417	—	47	2	no	—
726	#417	—	47	2	no	—
727	#416	—	47	2	no	—
728	#416	—	47	2	no	—
729	#416	C₂×D₄₇	1	1	yes	characteristic
730	#416	C₂×D₄₇	1	1	yes	characteristic
731	C₂×#103	—	47	1	no	—
732	C₂×#103	—	47	2	no	—
733	C₂×#102	—	47	1	no	—
734	C₂×#102	—	47	2	no	—
735	#408	—	47	1	no	—
736	#408	—	47	1	no	—
737	C₄×M₁₆	—	47	1	no	—
738	C₄₇	#61207	1	1	yes	characteristic, complemented, Sylow
739	2₋¹⁺⁴	—	94	4	no	—
740	2₋¹⁺⁴	—	188	2	no	—
741	H(5,𝔽₂)	—	94	4	no	—
742	H(5,𝔽₂)	—	188	2	no	—
743	C₂×#41	—	47	1	no	—
744	C₂×#41	—	47	1	no	—
745	C₂×#41	—	47	2	no	—
746	C₂×#41	—	47	2	no	—
747	C₂×#41	—	94	1	no	—
748	C₂×#41	—	94	1	no	—
749	C₂×#41	—	94	2	no	—
750	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
751	C₂²×Q₈	—	47	2	no	—
752	C₂²×Q₈	—	47	1	no	—
753	C₂²×Q₈	—	47	1	no	—
754	C₂²×Q₈	—	94	1	no	—
755	C₂²×D₄	—	47	2	no	—
756	C₂²×D₄	—	47	1	no	—
757	C₂²×D₄	—	94	1	no	—
758	C₂²×D₄	—	94	2	no	—
759	#137	—	94	4	no	—
760	C₂×Q₁₆	—	47	2	no	—
761	C₂×Q₁₆	—	47	2	no	—
762	C₂×Q₁₆	—	47	2	no	—
763	C₂×Q₁₆	—	188	2	no	—
764	C₂×SD₁₆	—	47	2	no	—
765	C₂×SD₁₆	—	47	2	no	—
766	C₂×SD₁₆	—	47	2	no	—
767	C₂×SD₁₆	—	188	2	no	—
768	#131	—	188	2	no	—
769	#131	—	188	2	no	—
770	C₂×M₁₆	—	47	1	no	—
771	C₂×M₁₆	—	47	1	no	—
772	C₂×M₁₆	—	47	2	no	—
773	C₂×M₁₆	—	47	2	no	—
774	C₂²×C₈	—	47	2	no	—
775	C₂²×C₈	—	47	2	no	—
776	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
777	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
778	C₄⋊Q₈	—	47	1	no	—
779	C₄⋊Q₈	—	94	1	no	—
780	C₄⋊Q₈	—	94	1	no	—
781	C₄⋊Q₈	—	94	1	no	—
782	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
783	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
784	#127	—	47	1	no	—
785	#127	—	94	1	no	—
786	#126	—	94	2	no	—
787	#126	—	94	2	no	—
788	#126	—	94	2	no	—
789	#126	—	94	2	no	—
790	#125	—	94	2	no	—
791	#125	—	94	2	no	—
792	#125	—	94	2	no	—
793	#125	C₂²×D₄₇	1	1	yes	characteristic
794	#125	C₂²×D₄₇	1	1	yes	characteristic
795	#124	—	47	1	no	—
796	#124	—	47	1	no	—
797	#124	—	47	2	no	—
798	#124	—	47	2	no	—
799	#124	—	94	2	no	—
800	#124	—	94	2	no	—
801	#124	—	94	1	no	—
802	#124	—	94	1	no	—
803	#124	—	94	1	no	—
804	#124	—	94	1	no	—
805	#124	—	94	2	no	—
806	#124	—	94	1	no	—
807	#124	—	94	1	no	—
808	#123	—	94	2	no	—
809	#123	—	94	2	no	—
810	#123	—	94	2	no	—
811	#123	—	94	2	no	—
812	#123	—	94	2	no	—
813	#123	—	94	2	no	—
814	#123	—	94	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	47	2	no	—
818	C₂²⋊Q₈	—	47	2	no	—
819	C₂²⋊Q₈	—	47	2	no	—
820	C₂²⋊Q₈	—	47	2	no	—
821	C₂²⋊Q₈	—	47	2	no	—
822	C₂²⋊Q₈	—	47	2	no	—
823	C₂²⋊Q₈	—	94	2	no	—
824	C₂²⋊Q₈	—	94	2	no	—
825	C₂²⋊Q₈	—	94	2	no	—
826	C₂²⋊Q₈	—	94	2	no	—
827	#121	—	47	2	no	—
828	#121	—	47	2	no	—
829	#121	—	47	2	no	—
830	#121	—	47	2	no	—
831	#121	—	94	2	no	—
832	#121	—	94	2	no	—
833	#121	—	94	2	no	—
834	#121	—	94	2	no	—
835	#120	—	94	2	no	—
836	#120	—	94	2	no	—
837	#120	—	94	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	47	2	no	—
841	C₄×Q₈	—	47	2	no	—
842	C₄×Q₈	—	94	1	no	—
843	C₄×Q₈	—	94	1	no	—
844	C₄×Q₈	—	94	2	no	—
845	C₄×Q₈	—	94	1	no	—
846	C₄×Q₈	—	94	1	no	—
847	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
848	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	47	2	no	—
852	C₄×D₄	—	47	2	no	—
853	C₄×D₄	—	94	2	no	—
854	C₄×D₄	—	94	2	no	—
855	C₄×D₄	—	94	1	no	—
856	C₄×D₄	—	94	1	no	—
857	C₄×D₄	—	94	2	no	—
858	C₄×D₄	—	94	2	no	—
859	C₄×D₄	—	94	2	no	—
860	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
861	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
862	#117	—	2	1	no	—
863	#117	—	47	2	no	—
864	#117	—	47	2	no	—
865	#117	—	94	2	no	—
866	#117	—	94	2	no	—
867	#117	C₂²×D₄₇	1	1	yes	characteristic
868	#117	C₂²×D₄₇	1	1	yes	characteristic
869	#117	C₂²×D₄₇	1	1	yes	characteristic
870	C₂×C₄⋊C₄	—	47	1	no	—
871	C₂×C₄⋊C₄	—	47	2	no	—
872	C₂×C₄⋊C₄	—	47	2	no	—
873	C₂×C₄⋊C₄	—	94	1	no	—
874	C₂×C₂²⋊C₄	—	94	2	no	—
875	C₂×C₂²⋊C₄	—	94	2	no	—
876	C₂×C₂²⋊C₄	—	94	1	no	—
877	C₂×C₂²⋊C₄	—	94	1	no	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	—	94	1	no	—
880	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
881	#107	—	47	2	no	—
882	#107	C₂²×D₄₇	1	1	yes	characteristic
883	#107	C₂²×D₄₇	1	1	yes	characteristic
884	#107	C₂²×D₄₇	1	1	yes	characteristic
885	#107	C₂²×D₄₇	1	1	yes	characteristic
886	#106	—	47	2	no	—
887	#106	C₂²×D₄₇	1	1	yes	characteristic
888	#106	C₂²×D₄₇	1	1	yes	characteristic
889	#106	C₂²×D₄₇	1	1	yes	characteristic
890	#106	C₂²×D₄₇	1	1	yes	characteristic
891	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
892	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
893	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
894	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
895	#103	—	47	2	no	—
896	#103	—	47	2	no	—
897	#103	—	47	2	no	—
898	#103	—	47	2	no	—
899	#103	—	47	2	no	—
900	#103	—	47	2	no	—
901	#103	—	47	2	no	—
902	#103	—	47	2	no	—
903	#103	—	47	2	no	—
904	#103	C₂²×D₄₇	1	1	yes	characteristic
905	#103	C₂²×D₄₇	1	1	yes	characteristic
906	#103	C₂²×D₄₇	1	1	yes	characteristic
907	#103	C₂²×D₄₇	1	1	yes	characteristic
908	#102	—	47	2	no	—
909	#102	—	47	2	no	—
910	#102	—	47	2	no	—
911	#102	—	47	2	no	—
912	#102	—	47	2	no	—
913	#102	—	47	2	no	—
914	#102	—	47	2	no	—
915	#102	C₂²×D₄₇	1	1	yes	characteristic
916	#102	C₂²×D₄₇	1	1	yes	characteristic
917	#102	C₂²×D₄₇	1	1	yes	characteristic
918	#102	C₂²×D₄₇	1	1	yes	characteristic
919	C₂²⋊C₈	—	47	2	no	—
920	C₂²⋊C₈	—	47	2	no	—
921	C₂²⋊C₈	—	47	2	no	—
922	C₂²⋊C₈	—	47	2	no	—
923	#97	—	47	2	no	—
924	C₄×C₈	—	47	2	no	—
925	C₂⁴	—	94	2	no	—
926	C₂⁴	—	94	1	no	—
927	#41	—	2	2	no	—
928	#41	—	94	2	no	—
929	#41	—	94	2	no	—
930	#41	—	94	2	no	—
931	#41	—	94	2	no	—
932	#41	—	94	4	no	—
933	#41	—	94	4	no	—
934	#41	—	188	4	no	—
935	#41	—	188	4	no	—
936	#41	—	188	2	no	—
937	#41	—	188	2	no	—
938	#41	—	188	8	no	—
939	#41	#10625354	1	4	yes	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	47	1	no	—
943	C₂×Q₈	—	47	1	no	—
944	C₂×Q₈	—	47	2	no	—
945	C₂×Q₈	—	47	2	no	—
946	C₂×Q₈	—	94	2	no	—
947	C₂×Q₈	—	94	1	no	—
948	C₂×Q₈	—	94	1	no	—
949	C₂×Q₈	—	94	4	no	—
950	C₂×Q₈	—	94	2	no	—
951	C₂×Q₈	—	94	2	no	—
952	C₂×Q₈	—	94	2	no	—
953	C₂×Q₈	—	94	2	no	—
954	C₂×Q₈	—	188	4	no	—
955	C₂×Q₈	—	188	2	no	—
956	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	47	2	no	—
959	C₂×D₄	—	47	2	no	—
960	C₂×D₄	—	47	1	no	—
961	C₂×D₄	—	47	1	no	—
962	C₂×D₄	—	47	2	no	—
963	C₂×D₄	—	47	2	no	—
964	C₂×D₄	—	47	2	no	—
965	C₂×D₄	—	94	2	no	—
966	C₂×D₄	—	94	2	no	—
967	C₂×D₄	—	94	2	no	—
968	C₂×D₄	—	94	2	no	—
969	C₂×D₄	—	94	4	no	—
970	C₂×D₄	—	94	2	no	—
971	C₂×D₄	—	94	1	no	—
972	C₂×D₄	—	94	2	no	—
973	C₂×D₄	—	94	2	no	—
974	C₂×D₄	—	188	4	no	—
975	C₂×D₄	—	188	2	no	—
976	C₂×D₄	—	188	8	no	—
977	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	47	2	no	—
982	C₂²×C₄	—	47	2	no	—
983	C₂²×C₄	—	94	2	no	—
984	C₂²×C₄	—	94	2	no	—
985	C₂²×C₄	—	94	2	no	—
986	C₂²×C₄	—	94	2	no	—
987	C₂²×C₄	—	94	2	no	—
988	C₂²×C₄	—	94	1	no	—
989	C₂²×C₄	—	94	1	no	—
990	C₂²×C₄	—	94	1	no	—
991	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
992	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
993	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
994	Q₁₆	—	94	4	no	—
995	Q₁₆	—	188	2	no	—
996	Q₁₆	—	188	2	no	—
997	SD₁₆	—	94	4	no	—
998	SD₁₆	—	188	2	no	—
999	SD₁₆	—	188	2	no	—
1000	M₁₆	—	94	2	no	—
1001	M₁₆	—	94	2	no	—
1002	M₁₆	—	188	2	no	—
1003	M₁₆	—	188	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	47	2	no	—
1007	C₂×C₈	—	47	2	no	—
1008	C₂×C₈	—	188	2	no	—
1009	C₂×C₈	—	188	2	no	—
1010	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1011	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1012	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1013	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	47	2	no	—
1023	C₄⋊C₄	—	47	2	no	—
1024	C₄⋊C₄	—	47	2	no	—
1025	C₄⋊C₄	—	94	2	no	—
1026	C₄⋊C₄	—	94	2	no	—
1027	C₄⋊C₄	—	94	2	no	—
1028	C₄⋊C₄	—	94	2	no	—
1029	C₄⋊C₄	—	94	2	no	—
1030	C₄⋊C₄	—	94	2	no	—
1031	C₄⋊C₄	—	94	2	no	—
1032	C₄⋊C₄	—	94	2	no	—
1033	C₄⋊C₄	—	94	2	no	—
1034	C₄⋊C₄	—	94	2	no	—
1035	C₄⋊C₄	—	94	1	no	—
1036	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1037	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1038	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1039	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1040	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1041	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	47	2	no	—
1048	C₂²⋊C₄	—	47	2	no	—
1049	C₂²⋊C₄	—	47	2	no	—
1050	C₂²⋊C₄	—	47	2	no	—
1051	C₂²⋊C₄	—	94	2	no	—
1052	C₂²⋊C₄	—	94	2	no	—
1053	C₂²⋊C₄	—	94	2	no	—
1054	C₂²⋊C₄	—	94	2	no	—
1055	C₂²⋊C₄	—	94	2	no	—
1056	C₂²⋊C₄	—	94	2	no	—
1057	C₂²⋊C₄	—	94	2	no	—
1058	C₂²⋊C₄	—	94	2	no	—
1059	C₂²⋊C₄	—	94	2	no	—
1060	C₂²⋊C₄	—	94	2	no	—
1061	C₂²⋊C₄	—	94	2	no	—
1062	C₂²⋊C₄	—	94	2	no	—
1063	C₂²⋊C₄	—	94	2	no	—
1064	C₂²⋊C₄	—	94	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	1	no	—
1070	C₄²	—	94	2	no	—
1071	C₄²	—	94	2	no	—
1072	C₄²	—	94	2	no	—
1073	C₄²	—	94	2	no	—
1074	C₄²	D₄×D₄₇	1	1	yes	characteristic
1075	C₄²	D₄×D₄₇	1	1	yes	characteristic
1076	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1077	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	47	2	no	—
1080	C₂³	—	47	2	no	—
1081	C₂³	—	94	2	no	—
1082	C₂³	—	376	1	no	—
1083	C₂³	—	376	1	no	—
1084	C₂³	—	376	2	no	—
1085	C₂³	—	376	2	no	—
1086	C₂³	—	188	4	no	—
1087	C₂³	—	188	2	no	—
1088	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1089	Q₈	—	2	1	no	—
1090	Q₈	—	4	2	no	—
1091	Q₈	—	8	1	no	—
1092	Q₈	—	94	2	no	—
1093	Q₈	—	94	2	no	—
1094	Q₈	—	94	2	no	—
1095	Q₈	—	94	2	no	—
1096	Q₈	—	94	2	no	—
1097	Q₈	—	94	2	no	—
1098	Q₈	—	188	4	no	—
1099	Q₈	—	188	2	no	—
1100	Q₈	—	188	2	no	—
1101	Q₈	C₂×#10625354	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	94	4	no	—
1105	D₄	—	94	4	no	—
1106	D₄	—	94	2	no	—
1107	D₄	—	94	2	no	—
1108	D₄	—	94	2	no	—
1109	D₄	—	94	2	no	—
1110	D₄	—	376	2	no	—
1111	D₄	—	376	2	no	—
1112	D₄	—	188	2	no	—
1113	D₄	—	188	2	no	—
1114	D₄	—	188	4	no	—
1115	D₄	—	188	4	no	—
1116	D₄	—	188	4	no	—
1117	D₄	—	188	2	no	—
1118	D₄	C₂×#10625354	1	2	yes	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	47	2	no	—
1132	C₂×C₄	—	47	2	no	—
1133	C₂×C₄	—	94	2	no	—
1134	C₂×C₄	—	94	2	no	—
1135	C₂×C₄	—	94	2	no	—
1136	C₂×C₄	—	94	2	no	—
1137	C₂×C₄	—	94	2	no	—
1138	C₂×C₄	—	94	2	no	—
1139	C₂×C₄	—	94	2	no	—
1140	C₂×C₄	—	376	2	no	—
1141	C₂×C₄	—	376	2	no	—
1142	C₂×C₄	—	376	1	no	—
1143	C₂×C₄	—	188	4	no	—
1144	C₂×C₄	—	188	4	no	—
1145	C₂×C₄	—	188	4	no	—
1146	C₂×C₄	—	188	2	no	—
1147	C₂×C₄	—	188	2	no	—
1148	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1149	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1150	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1151	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1152	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1153	C₂×C₄	C₂×#10625354	1	2	yes	—
1154	C₂×C₄	#13094070	1	2	yes	—
1155	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	94	2	no	—
1161	C₈	—	94	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	94	2	no	—
1168	C₂²	—	94	2	no	—
1169	C₂²	—	94	2	no	—
1170	C₂²	—	94	2	no	—
1171	C₂²	—	94	2	no	—
1172	C₂²	—	94	2	no	—
1173	C₂²	—	188	2	no	—
1174	C₂²	—	188	2	no	—
1175	C₂²	—	188	2	no	—
1176	C₂²	—	752	2	no	—
1177	C₂²	—	752	4	no	—
1178	C₂²	#15689764	1	2	yes	—
1179	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	94	2	no	—
1192	C₄	—	94	2	no	—
1193	C₄	—	188	2	no	—
1194	C₄	—	188	2	no	—
1195	C₄	—	188	2	no	—
1196	C₄	#15689764	1	2	yes	—
1197	C₄	C₂²×#10625354	1	1	yes	characteristic
1198	C₄	C₂×#13094070	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	376	2	no	—
1202	C₂	—	188	2	no	—
1203	C₂	—	188	2	no	—
1204	C₂	C₂×#15689764	1	1	yes	characteristic
1205	C₂	#20258157	1	1	yes	characteristic
1206	C₂	#20258172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3076	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257181	C₂
hypercenter	#3076	D₄₇
hypocenter	C₄₇	#61207
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #20257255	C₂	semidirect
3. #20255653	C₂	semidirect
4. #20255601	C₂	semidirect
5. #20255496	C₂	semidirect
6. #20255466	C₂	semidirect
7. #20255451	C₂	semidirect
8. #20255421	C₂	semidirect
9. #20255272	C₂	semidirect
10. #20255220	C₂	semidirect
11. #20253777	C₂	semidirect
12. #20253360	C₂	semidirect
13. #20253349	C₂	semidirect
14. #20253044	C₂	semidirect
15. #20253028	C₂	semidirect
16. C₂×#15689346	C₂	semidirect
17. #20252686	C₂	semidirect
18. #20252668	C₂	semidirect
19. C₄×#13094054	C₂	semidirect
20. #20252131	C₂	semidirect
21. #20251917	C₂	semidirect
22. #20251910	C₂	semidirect
23. C₄₇×#3076	C₂	semidirect
27. C₂²×Dic₁₈₈	C₂²	semidirect
30. C₂×#13094030	C₂²	semidirect
33. #15689847	C₂²	semidirect
36. #15689834	C₂²	semidirect
37. #15689811	C₂²	semidirect
38. #15689811	C₂²	semidirect
49. #15689699	C₂²	semidirect
58. #15689603	C₂²	semidirect
59. C₂×C₄×Dic₉₄	C₂²	semidirect
60. #15689485	C₂²	semidirect
61. #15689485	C₂²	semidirect
62. #15689480	C₂²	semidirect
63. #15689480	C₂²	semidirect
64. #15689467	C₂²	semidirect
65. #15689466	C₂²	semidirect
66. #15689460	C₂²	semidirect
67. #15689455	C₂²	semidirect
68. #15689450	C₂²	semidirect
69. #15689449	C₂²	semidirect
70. #15689443	C₂²	semidirect
71. #15689438	C₂²	semidirect
72. #15689382	C₂²	semidirect
73. #15689382	C₂²	semidirect
74. #15689370	C₂²	semidirect
75. #15689370	C₂²	semidirect
76. #15689365	C₂²	semidirect
77. #15689365	C₂²	semidirect
78. #15689353	C₂²	semidirect
79. #15689353	C₂²	semidirect
80. #15689346	C₂²	semidirect
81. #15689346	C₂²	semidirect
82. #15689346	C₂²	semidirect
83. #15689346	C₂²	semidirect
86. #15689286	C₂²	semidirect
87. #15689286	C₂²	semidirect
88. #15689280	C₂²	semidirect
89. #15689280	C₂²	semidirect
92. #15689228	C₂²	semidirect
93. #15689223	C₂²	semidirect
94. C₄×#10625337	C₂²	semidirect
95. C₄×#10625335	C₂²	semidirect
96. #15689200	C₂²	semidirect
97. #15689193	C₂²	semidirect
98. #15689193	C₂²	semidirect
99. #15689188	C₂²	semidirect
100. #15689166	C₂²	semidirect
101. #15689131	C₂²	semidirect
102. #15689131	C₂²	semidirect
103. #15689131	C₂²	semidirect
104. #15689130	C₂²	semidirect
110. #15689121	C₂²	semidirect
112. #15689116	C₂²	semidirect
113. C₂×#13093949	C₂²	semidirect
114. #103×D₄₇	C₂²	semidirect
118. #15689089	C₂²	semidirect
119. C₄×#10625329	C₂²	semidirect
120. C₄₇×#533	C₂²	semidirect
122. C₄₇×#479	C₂²	semidirect
123. C₄₇×#479	C₂²	semidirect
124. C₄₇×#478	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
126. C₄₇×#477	C₂²	semidirect
127. C₄₇×#476	C₂²	semidirect
128. C₄₇×#475	C₂²	semidirect
129. C₄₇×#474	C₂²	semidirect
130. C₄₇×#427	C₂²	semidirect
131. C₄₇×#427	C₂²	semidirect
132. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
609. #3076	D₄₇	semidirect
655. #533	C₂×D₄₇	semidirect
677. #479	C₂×D₄₇	semidirect
678. #479	C₂×D₄₇	semidirect
679. #478	C₂×D₄₇	semidirect
680. #478	C₂×D₄₇	semidirect
681. #477	C₂×D₄₇	semidirect
682. #476	C₂×D₄₇	semidirect
683. #475	C₂×D₄₇	semidirect
684. #474	C₂×D₄₇	semidirect
714. #427	C₂×D₄₇	semidirect
715. #427	C₂×D₄₇	semidirect
716. C₂×C₄⋊C₈	C₂×D₄₇	semidirect
738. C₄₇	#61207	semidirect

Maximal subgroups

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

subgroup	index
#20257255	2
#20257181	2
#20255653	2
#20255601	2
#20255496	2
#20255466	2
#20255451	2
#20255421	2
#20255272	2
#20255220	2
#20253777	2
#20253360	2
#20253349	2
#20253044	2
#20253028	2
C₂×#15689346	2
#20252686	2
#20252668	2
C₄×#13094054	2
#20252131	2
#20251917	2
#20251910	2
C₄₇×#3076	2
#61207	47