Subgroups — #27112896

Order 12032.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256952	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256259	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256251	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256073	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256037	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256014	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255983	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255957	C₂	1	2	yes	maximal, complemented
9	#20255942	C₂	1	2	yes	maximal, complemented
10	#20255698	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255687	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255598	C₂	1	2	yes	maximal, complemented
13	#20255583	C₂	1	2	yes	maximal, complemented
14	#20254784	C₂	1	2	yes	maximal, complemented
15	#20254761	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254556	C₂	1	2	yes	maximal, complemented
17	#20254547	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253431	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253400	C₂	1	2	yes	maximal, complemented
20	#20253206	C₂	1	2	yes	maximal, complemented
21	#20253181	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252520	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3515	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689846	C₂²	1	1	yes	characteristic
25	#15689838	C₂²	1	1	yes	characteristic
26	#15689833	C₂²	1	1	yes	characteristic
27	#15689823	—	2	1	no	—
28	#15689814	—	2	1	no	—
29	#15689813	C₂²	1	2	yes	—
30	#15689802	—	2	2	no	—
31	#15689778	C₂²	1	1	yes	characteristic
32	#15689769	C₂²	1	2	yes	—
33	#15689680	C₂²	1	1	yes	characteristic
34	#15689657	C₂²	1	2	yes	—
35	#15689651	—	2	2	no	—
36	#15689630	—	2	1	no	—
37	C₄×#10625350	C₂²	1	2	yes	—
38	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
39	#117×D₄₇	—	2	1	no	—
40	#15689526	C₂²	1	1	yes	characteristic, complemented
41	#15689522	C₂²	1	2	yes	complemented
42	#15689522	C₂²	1	2	yes	complemented
43	#15689519	C₂²	1	1	yes	characteristic, complemented
44	#15689480	C₂²	1	2	yes	—
45	#15689480	C₂²	1	2	yes	—
46	#15689475	C₂²	1	1	yes	characteristic, complemented
47	#15689475	C₂²	1	1	yes	characteristic, complemented
48	#15689464	C₂²	1	2	yes	—
49	#15689464	C₂²	1	2	yes	—
50	#15689461	C₂²	1	2	yes	complemented
51	#15689458	C₂²	1	2	yes	complemented
52	#15689456	C₂²	1	1	yes	characteristic
53	#15689453	C₂²	1	2	yes	complemented
54	#15689444	C₂²	1	2	yes	complemented
55	#15689441	C₂²	1	2	yes	—
56	#15689439	C₂²	1	1	yes	characteristic
57	#15689436	C₂²	1	2	yes	—
58	#15689430	C₂²	1	2	yes	complemented
59	#15689427	C₂²	1	2	yes	complemented
60	#15689427	C₂²	1	2	yes	complemented
61	#15689427	C₂²	1	2	yes	complemented
62	#15689427	C₂²	1	2	yes	complemented
63	#15689427	C₂²	1	2	yes	complemented
64	#15689423	C₂²	1	2	yes	complemented
65	#15689420	C₂²	1	2	yes	—
66	#15689420	C₂²	1	1	yes	characteristic
67	#15689420	C₂²	1	2	yes	—
68	#15689420	C₂²	1	2	yes	—
69	#15689420	C₂²	1	2	yes	—
70	#15689420	C₂²	1	1	yes	characteristic
71	#15689418	C₂²	1	1	yes	characteristic, complemented
72	#15689413	C₂²	1	1	yes	characteristic, complemented
73	#15689410	C₂²	1	1	yes	characteristic
74	#15689410	C₂²	1	1	yes	characteristic
75	#15689400	C₂²	1	1	yes	characteristic
76	#15689400	C₂²	1	1	yes	characteristic
77	#15689379	C₂²	1	2	yes	—
78	#15689379	C₂²	1	2	yes	complemented
79	#15689374	C₂²	1	2	yes	—
80	#15689371	C₂²	1	2	yes	—
81	#15689367	C₂²	1	2	yes	—
82	#15689367	C₂²	1	2	yes	complemented
83	#15689345	C₂²	1	2	yes	—
84	#15689342	C₂²	1	2	yes	complemented
85	#15689338	C₂²	1	2	yes	—
86	#15689335	C₂²	1	1	yes	characteristic
87	#15689335	C₂²	1	1	yes	characteristic
88	#15689333	C₂²	1	1	yes	characteristic, complemented
89	#15689328	C₂²	1	1	yes	characteristic, complemented
90	#15689283	C₂²	1	2	yes	—
91	#15689273	C₂²	1	1	yes	characteristic
92	#15689266	C₂²	1	2	yes	—
93	#15689256	C₂²	1	1	yes	characteristic
94	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
95	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10625337	C₂²	1	2	yes	complemented
97	C₄×#10625336	C₂²	1	2	yes	—
98	C₄×#10625336	C₂²	1	1	yes	characteristic
99	C₄×#10625336	C₂²	1	1	yes	characteristic
100	C₄×#10625335	C₂²	1	2	yes	complemented
101	C₄×#10625334	C₂²	1	1	yes	characteristic
102	C₄×#10625334	C₂²	1	2	yes	—
103	C₄×#10625334	C₂²	1	1	yes	characteristic
104	#15689201	C₂²	1	2	yes	—
105	#15689201	C₂²	1	2	yes	—
106	#15689201	C₂²	1	1	yes	characteristic, complemented
107	#15689201	C₂²	1	1	yes	characteristic, complemented
108	#15689176	C₂²	1	1	yes	characteristic
109	#15689176	C₂²	1	2	yes	complemented
110	#15689166	C₂²	1	2	yes	—
111	#15689163	C₂²	1	2	yes	complemented
112	#15689163	C₂²	1	2	yes	complemented
113	#15689147	C₂²	1	1	yes	characteristic
114	#15689147	C₂²	1	2	yes	complemented
115	#15689127	C₂²	1	2	yes	—
116	#15689122	C₂²	1	2	yes	—
117	#15689122	C₂²	1	2	yes	—
118	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
119	C₄₇×#554	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#554	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#553	C₂²	1	2	yes	—
122	C₄₇×#552	—	2	2	no	—
123	C₄₇×#552	—	2	1	no	—
124	C₄₇×#552	C₂²	1	2	yes	—
125	C₄₇×#547	—	2	1	no	—
126	C₄₇×#547	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#541	—	2	1	no	—
128	C₄₇×#539	—	2	2	no	—
129	C₄₇×#533	C₂²	1	1	yes	characteristic
130	C₄₇×#529	C₂²	1	1	yes	characteristic
131	C₄₇×#529	C₂²	1	2	yes	complemented
132	C₂×#125×C₄₇	C₂²	1	2	yes	complemented
133	C₄₇×#520	—	2	1	no	—
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	2	yes	—
136	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₄₇	—	2	1	no	—
138	C₂×#10625337	C₂³	1	2	yes	—
139	C₂×#10625335	C₂³	1	2	yes	—
140	C₂×#10625336	C₂³	1	1	yes	characteristic
141	C₂×#10625336	C₂³	1	1	yes	characteristic
142	C₂×#10625334	C₂³	1	1	yes	characteristic
143	C₂×#10625334	C₂³	1	1	yes	characteristic
144	C₂×#10625329	C₂³	1	2	yes	—
145	C₂×#10625329	C₂³	1	2	yes	—
146	C₂×#10625329	C₂³	1	2	yes	—
147	#13094024	C₂³	1	1	yes	characteristic
148	#13094024	C₂³	1	1	yes	characteristic
149	#13094019	—	2	2	no	—
150	#13094018	—	2	2	no	—
151	#13094017	—	2	2	no	—
152	#13094016	—	2	1	no	—
153	#13094016	C₂³	1	2	yes	—
154	#13094014	—	2	2	no	—
155	#13094012	C₂³	1	2	yes	—
156	#13094010	—	2	2	no	—
157	#13094009	—	2	2	no	—
158	#13094007	—	2	2	no	—
159	#13094006	—	2	2	no	—
160	#13094005	—	2	2	no	—
161	#13094003	—	2	1	no	—
162	#13094003	C₂³	1	2	yes	—
163	#13094003	C₂³	1	2	yes	—
164	#13094002	—	2	2	no	—
165	#13094000	—	2	1	no	—
166	#13094000	—	2	1	no	—
167	#13093998	C₂³	1	2	yes	—
168	#13093997	—	2	2	no	—
169	#13093995	—	2	1	no	—
170	#13093995	—	2	1	no	—
171	#13093992	—	2	2	no	—
172	C₄×Dic₉₄	—	2	1	no	—
173	C₄×Dic₉₄	C₂³	1	2	yes	—
174	C₄×Dic₉₄	C₂³	1	2	yes	—
175	C₄×D₁₈₈	—	2	1	no	—
176	C₄×D₁₈₈	—	2	1	no	—
177	C₄×D₁₈₈	C₂³	1	2	yes	—
178	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
179	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
180	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
181	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
182	C₄×C₂²⋊D₄₇	—	2	2	no	—
183	C₄×C₂²⋊D₄₇	—	2	2	no	—
184	C₄×C₂²⋊D₄₇	—	2	2	no	—
185	#13093983	—	2	1	no	—
186	#13093983	C₂³	1	2	yes	—
187	#13093982	—	2	1	no	—
188	#13093982	—	2	1	no	—
189	#13093981	—	2	2	no	—
190	#13093981	—	2	2	no	—
191	#13093980	—	2	2	no	—
192	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₄×D₄₇	—	2	1	no	—
194	C₄⋊C₄×D₄₇	—	2	1	no	—
195	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
196	C₂²⋊C₄×D₄₇	—	2	2	no	—
197	C₄²×D₄₇	—	2	2	no	—
198	#13093957	C₂³	1	2	yes	—
199	#13093957	C₂³	1	1	yes	characteristic
200	#13093957	C₂³	1	2	yes	—
201	#13093957	C₂³	1	2	yes	—
202	#13093957	C₂³	1	2	yes	—
203	#13093957	C₂³	1	2	yes	—
204	#13093957	C₂³	1	1	yes	characteristic
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	2	yes	—
207	#13093955	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	1	yes	characteristic
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
222	#13093947	C₂³	1	2	yes	—
223	#13093947	C₂³	1	2	yes	—
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	2	yes	—
226	#13093947	C₂³	1	2	yes	—
227	#13093947	C₂³	1	2	yes	—
228	#13093945	C₂³	1	1	yes	characteristic
229	#13093945	C₂³	1	1	yes	characteristic
230	#13093945	C₂³	1	2	yes	—
231	#13093944	C₂³	1	1	yes	characteristic
232	#13093944	C₂³	1	1	yes	characteristic
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	2	yes	—
235	#13093944	C₂³	1	1	yes	characteristic
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	1	yes	characteristic
238	#13093944	C₂³	1	2	yes	—
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
242	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
243	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₂×#41×C₄₇	—	2	1	no	—
248	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
249	C₄⋊Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
252	#126×C₄₇	—	2	2	no	—
253	#126×C₄₇	—	2	2	no	—
254	#126×C₄₇	—	2	1	no	—
255	#126×C₄₇	—	2	2	no	—
256	#125×C₄₇	—	2	2	no	—
257	#125×C₄₇	—	2	2	no	—
258	#125×C₄₇	—	2	1	no	—
259	#125×C₄₇	—	2	2	no	—
260	#125×C₄₇	—	2	2	no	—
261	#125×C₄₇	C₂³	1	2	yes	—
262	#125×C₄₇	C₂³	1	2	yes	—
263	#125×C₄₇	C₂³	1	1	yes	characteristic
264	#125×C₄₇	C₂³	1	2	yes	—
265	#124×C₄₇	C₂³	1	1	yes	characteristic
266	#123×C₄₇	—	2	2	no	—
267	#123×C₄₇	—	2	1	no	—
268	#123×C₄₇	—	2	2	no	—
269	#123×C₄₇	—	2	2	no	—
270	#123×C₄₇	—	2	2	no	—
271	C₂²⋊Q₈×C₄₇	—	2	1	no	—
272	C₂²⋊Q₈×C₄₇	—	2	1	no	—
273	C₂²⋊Q₈×C₄₇	—	2	1	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	1	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
279	#121×C₄₇	—	2	2	no	—
280	#121×C₄₇	C₂³	1	1	yes	characteristic
281	#121×C₄₇	C₂³	1	2	yes	—
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	—	2	1	no	—
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₇	—	2	1	no	—
290	C₄×D₄×C₄₇	—	2	2	no	—
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	2	no	—
293	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
294	C₄×D₄×C₄₇	D₄	1	2	yes	—
295	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₇	C₂³	1	2	yes	—
297	C₄×D₄×C₄₇	C₂³	1	2	yes	—
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	#117×C₄₇	—	2	2	no	—
300	#117×C₄₇	—	2	1	no	—
301	#117×C₄₇	—	2	2	no	—
302	#117×C₄₇	D₄	1	1	yes	characteristic
303	#117×C₄₇	D₄	1	2	yes	—
304	#117×C₄₇	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
306	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
307	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
309	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂³×D₄₇	—	2	1	no	—
313	#41×C₄₇	—	4	2	no	—
314	#41×C₄₇	—	4	4	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₇	—	2	2	no	—
320	C₂×D₄×C₄₇	—	2	1	no	—
321	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	—	2	2	no	—
325	C₂²×C₄×C₄₇	—	2	2	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	2	no	—
328	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
330	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
331	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
334	C₂×C₂²⋊D₄₇	—	2	2	no	—
335	C₂×C₂²⋊D₄₇	—	2	2	no	—
336	C₂²×Dic₄₇	—	2	1	no	—
337	#10625350	—	2	4	no	—
338	#10625350	—	4	2	no	—
339	C₂×D₁₈₈	—	2	2	no	—
340	C₂×D₁₈₈	—	2	1	no	—
341	C₂×D₁₈₈	—	4	1	no	—
342	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
343	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₄×D₄₇	—	2	1	no	—
345	C₂×C₄×D₄₇	—	2	2	no	—
346	C₂×C₄×D₄₇	—	2	1	no	—
347	C₂×C₄×D₄₇	—	2	1	no	—
348	C₂×C₄×D₄₇	—	2	1	no	—
349	C₂×C₄×D₄₇	—	2	2	no	—
350	C₂×C₄×D₄₇	—	4	4	no	—
351	C₂×Dic₉₄	—	2	1	no	—
352	C₂×Dic₉₄	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₄₇	—	2	2	no	—
354	C₄⋊C₄×C₄₇	—	2	1	no	—
355	C₄⋊C₄×C₄₇	—	2	1	no	—
356	C₄⋊C₄×C₄₇	—	2	2	no	—
357	C₄⋊C₄×C₄₇	—	2	1	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	2	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	1	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	—	2	1	no	—
367	C₄⋊C₄×C₄₇	—	2	1	no	—
368	C₄⋊C₄×C₄₇	—	2	2	no	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
372	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
377	C₂²⋊C₄×C₄₇	—	2	2	no	—
378	C₂²⋊C₄×C₄₇	—	2	2	no	—
379	C₂²⋊C₄×C₄₇	—	2	1	no	—
380	C₂²⋊C₄×C₄₇	—	2	1	no	—
381	C₂²⋊C₄×C₄₇	—	2	1	no	—
382	C₂²⋊C₄×C₄₇	—	2	1	no	—
383	C₂²⋊C₄×C₄₇	—	2	2	no	—
384	C₂²⋊C₄×C₄₇	—	2	2	no	—
385	C₂²⋊C₄×C₄₇	—	2	1	no	—
386	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
389	C₄²×C₄₇	—	2	2	no	—
390	C₄²×C₄₇	—	2	2	no	—
391	C₄²×C₄₇	—	2	1	no	—
392	C₄²×C₄₇	C₂×D₄	1	2	yes	—
393	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₄₇	C₂×D₄	1	2	yes	—
396	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄²×C₄₇	C₂⁴	1	2	yes	—
398	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	C₂²⋊Dic₄₇	—	2	2	no	—
401	C₂²⋊Dic₄₇	—	2	2	no	—
402	#10625337	—	4	2	no	—
403	#10625336	—	2	2	no	—
404	#10625336	—	4	1	no	—
405	#10625335	—	4	2	no	—
406	#10625334	—	2	2	no	—
407	#10625334	—	4	1	no	—
408	(C₂×D₄₇)⋊C₄	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	1	no	—
411	(C₂×D₄₇)⋊C₄	—	2	1	no	—
412	(C₂×D₄₇)⋊C₄	—	2	1	no	—
413	(C₂×D₄₇)⋊C₄	—	2	1	no	—
414	(C₂×D₄₇)⋊C₄	—	2	2	no	—
415	(C₂×D₄₇)⋊C₄	—	2	2	no	—
416	C₄⋊Dic₄₇	—	2	1	no	—
417	C₄⋊Dic₄₇	—	2	1	no	—
418	C₄⋊Dic₄₇	—	2	1	no	—
419	C₄⋊Dic₄₇	—	2	1	no	—
420	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	C₄×Dic₄₇	—	2	2	no	—
430	C₄×Dic₄₇	—	2	2	no	—
431	C₄×Dic₄₇	—	2	2	no	—
432	#10625329	—	4	2	no	—
433	#10625329	—	4	2	no	—
434	#10625329	—	4	2	no	—
435	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
438	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
439	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
441	C₂³×C₄₇	—	2	1	no	—
442	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
443	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
444	C₂²×D₄₇	—	2	1	no	—
445	C₂²×D₄₇	—	2	1	no	—
446	C₂²×D₄₇	—	4	2	no	—
447	C₂²×D₄₇	—	4	2	no	—
448	C₂²×D₄₇	—	8	1	no	—
449	Q₈×C₄₇	—	2	2	no	—
450	Q₈×C₄₇	—	2	1	no	—
451	Q₈×C₄₇	—	2	1	no	—
452	Q₈×C₄₇	—	4	2	no	—
453	Q₈×C₄₇	—	8	1	no	—
454	D₄×C₄₇	—	2	2	no	—
455	D₄×C₄₇	—	2	1	no	—
456	D₄×C₄₇	—	2	1	no	—
457	D₄×C₄₇	—	4	2	no	—
458	D₄×C₄₇	—	4	4	no	—
459	D₄×C₄₇	—	8	1	no	—
460	C₂×C₄×C₄₇	—	2	2	no	—
461	C₂×C₄×C₄₇	—	2	1	no	—
462	C₂×C₄×C₄₇	—	2	2	no	—
463	C₂×C₄×C₄₇	—	2	1	no	—
464	C₂×C₄×C₄₇	—	2	2	no	—
465	C₂×C₄×C₄₇	—	2	1	no	—
466	C₂×C₄×C₄₇	—	2	2	no	—
467	C₂×C₄×C₄₇	—	2	2	no	—
468	C₂×C₄×C₄₇	—	2	1	no	—
469	C₂×C₄×C₄₇	—	2	1	no	—
470	C₂×C₄×C₄₇	—	4	1	no	—
471	C₂×C₄×C₄₇	—	4	2	no	—
472	C₂×C₄×C₄₇	—	4	2	no	—
473	C₂×C₄×C₄₇	—	4	4	no	—
474	C₂×C₄×C₄₇	—	4	2	no	—
475	C₂×C₄×C₄₇	—	8	2	no	—
476	C₂×C₄×C₄₇	—	8	2	no	—
477	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
486	C₂²⋊D₄₇	—	4	4	no	—
487	C₂²⋊D₄₇	—	8	2	no	—
488	C₂×Dic₄₇	—	2	1	no	—
489	C₂×Dic₄₇	—	2	2	no	—
490	C₂×Dic₄₇	—	2	2	no	—
491	C₂×Dic₄₇	—	2	1	no	—
492	C₂×Dic₄₇	—	4	2	no	—
493	D₁₈₈	—	2	1	no	—
494	D₁₈₈	—	2	1	no	—
495	D₁₈₈	—	2	1	no	—
496	D₁₈₈	—	4	2	no	—
497	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
498	C₄×D₄₇	—	4	4	no	—
499	C₄×D₄₇	—	4	2	no	—
500	C₄×D₄₇	—	4	2	no	—
501	C₄×D₄₇	—	4	2	no	—
502	C₄×D₄₇	—	4	2	no	—
503	C₄×D₄₇	—	8	2	no	—
504	Dic₉₄	—	2	2	no	—
505	Dic₉₄	—	2	2	no	—
506	Dic₉₄	—	8	1	no	—
507	C₄₇⋊C₈	—	2	1	no	—
508	C₄₇⋊C₈	—	2	1	no	—
509	C₄₇⋊C₈	—	2	1	no	—
510	C₄₇⋊C₈	—	2	2	no	—
511	C₄₇⋊C₈	—	2	1	no	—
512	C₄₇⋊C₈	—	2	2	no	—
513	#62152	—	47	1	no	maximal, Sylow
514	C₂²×C₄₇	—	2	2	no	—
515	C₂²×C₄₇	—	2	1	no	—
516	C₂²×C₄₇	—	2	2	no	—
517	C₂²×C₄₇	—	2	1	no	—
518	C₂²×C₄₇	—	2	1	no	—
519	C₂²×C₄₇	—	2	2	no	—
520	C₂²×C₄₇	—	4	1	no	—
521	C₂²×C₄₇	—	4	1	no	—
522	C₂²×C₄₇	—	4	1	no	—
523	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
524	C₂×D₄₇	—	2	2	no	—
525	C₂×D₄₇	—	4	1	no	—
526	C₂×D₄₇	—	4	1	no	—
527	C₂×D₄₇	—	4	1	no	—
528	C₂×D₄₇	—	4	1	no	—
529	C₂×D₄₇	—	4	1	no	—
530	C₂×D₄₇	—	8	4	no	—
531	C₄×C₄₇	—	2	1	no	—
532	C₄×C₄₇	—	2	2	no	—
533	C₄×C₄₇	—	2	1	no	—
534	C₄×C₄₇	—	2	2	no	—
535	C₄×C₄₇	—	2	1	no	—
536	C₄×C₄₇	—	2	1	no	—
537	C₄×C₄₇	—	2	2	no	—
538	C₄×C₄₇	—	4	1	no	—
539	C₄×C₄₇	—	4	2	no	—
540	C₄×C₄₇	—	4	1	no	—
541	C₄×C₄₇	—	4	1	no	—
542	C₄×C₄₇	—	4	2	no	—
543	C₄×C₄₇	#575	1	2	yes	—
544	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
545	C₄×C₄₇	#585	1	1	yes	characteristic
546	Dic₄₇	—	4	2	no	—
547	Dic₄₇	—	4	2	no	—
548	Dic₄₇	—	4	1	no	—
549	Dic₄₇	—	4	1	no	—
550	#3515	D₄₇	1	1	yes	characteristic, complemented
551	#3475	—	47	1	no	—
552	#3381	—	47	1	no	—
553	#3380	—	47	1	no	—
554	#3364	—	47	1	no	—
555	#3360	—	47	1	no	—
556	#3357	—	47	1	no	—
557	#3354	—	47	1	no	—
558	#3352	—	47	2	no	—
559	#3351	—	47	2	no	—
560	#3331	—	47	1	no	—
561	#3330	—	47	1	no	—
562	#3323	—	47	2	no	—
563	#3322	—	47	2	no	—
564	#3256	—	47	2	no	—
565	#3252	—	47	1	no	—
566	#3232	—	47	2	no	—
567	#3231	—	47	1	no	—
568	#3105	—	47	1	no	—
569	#3102	—	47	2	no	—
570	#3080	—	47	2	no	—
571	#3077	—	47	1	no	—
572	#2991	—	47	1	no	—
573	C₂×C₄₇	—	4	1	no	—
574	C₂×C₄₇	—	4	2	no	—
575	C₂×C₄₇	—	8	1	no	—
576	C₂×C₄₇	#3489	1	1	yes	characteristic
577	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
578	C₂×C₄₇	#3584	1	1	yes	characteristic
579	D₄₇	—	4	2	no	—
580	D₄₇	—	8	1	no	—
581	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
582	#556	—	47	1	no	—
583	#555	—	47	1	no	—
584	#554	—	47	1	no	—
585	#554	C₂×D₄₇	1	1	yes	characteristic, complemented
586	#554	C₂×D₄₇	1	1	yes	characteristic, complemented
587	#553	—	94	1	no	—
588	#553	C₂×D₄₇	1	2	yes	—
589	#552	—	2	2	no	—
590	#552	—	2	1	no	—
591	#552	—	47	2	no	—
592	#552	—	94	1	no	—
593	#552	C₂×D₄₇	1	2	yes	—
594	#551	—	94	2	no	—
595	#547	—	2	1	no	—
596	#547	—	47	1	no	—
597	#547	C₂×D₄₇	1	1	yes	characteristic, complemented
598	#546	—	47	2	no	—
599	#541	—	2	1	no	—
600	#539	—	2	2	no	—
601	#533	—	47	1	no	—
602	#533	C₂×D₄₇	1	1	yes	characteristic
603	#529	—	47	2	no	—
604	#529	—	94	2	no	—
605	#529	C₂×D₄₇	1	1	yes	characteristic
606	#529	C₂×D₄₇	1	2	yes	complemented
607	C₂×#125	C₂×D₄₇	1	2	yes	complemented
608	#525	—	94	1	no	—
609	#520	—	2	1	no	—
610	C₄×#41	—	47	2	no	—
611	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
612	C₂×C₄×D₄	—	47	1	no	—
613	C₂×#117	—	94	1	no	—
614	#500	—	47	1	no	—
615	#499	—	47	2	no	—
616	#499	—	47	2	no	—
617	#498	—	47	1	no	—
618	#488	—	47	2	no	—
619	#488	—	47	2	no	—
620	#487	—	47	1	no	—
621	#487	—	47	1	no	—
622	#485	—	47	2	no	—
623	#485	—	47	2	no	—
624	#485	—	47	2	no	—
625	#484	—	47	1	no	—
626	#484	—	47	2	no	—
627	#483	—	47	2	no	—
628	#482	—	47	2	no	—
629	#481	—	47	1	no	—
630	#481	—	47	2	no	—
631	#480	—	47	2	no	—
632	#479	—	47	2	no	—
633	#479	—	47	2	no	—
634	#479	—	47	2	no	—
635	#479	—	47	2	no	—
636	#479	—	47	2	no	—
637	#479	—	47	2	no	—
638	#478	—	47	2	no	—
639	#478	—	47	2	no	—
640	#478	—	47	1	no	—
641	#478	—	47	2	no	—
642	#478	—	47	2	no	—
643	#478	—	47	1	no	—
644	#478	—	47	2	no	—
645	#477	—	47	1	no	—
646	#476	—	47	1	no	—
647	#476	—	47	1	no	—
648	#476	—	47	1	no	—
649	#474	—	47	1	no	—
650	#474	—	47	1	no	—
651	#470	—	47	2	no	—
652	#470	—	47	2	no	—
653	#469	—	47	2	no	—
654	#468	—	47	2	no	—
655	#468	—	47	2	no	—
656	#468	—	47	2	no	—
657	#464	—	47	2	no	—
658	#464	—	47	2	no	—
659	#463	—	47	1	no	—
660	#463	—	47	1	no	—
661	#463	—	47	2	no	—
662	#462	—	47	1	no	—
663	#461	—	47	1	no	—
664	#452	—	47	2	no	—
665	#450	—	47	1	no	—
666	#449	—	47	2	no	—
667	#447	—	47	1	no	—
668	C₈×Q₈	—	47	1	no	—
669	C₈×Q₈	—	47	1	no	—
670	C₄×Q₁₆	—	47	2	no	—
671	C₄×SD₁₆	—	47	1	no	—
672	C₄×SD₁₆	—	47	1	no	—
673	C₄×SD₁₆	—	47	2	no	—
674	C₄×SD₁₆	—	47	2	no	—
675	C₄×D₈	—	47	1	no	—
676	C₄×D₈	—	47	1	no	—
677	C₄×D₈	—	47	2	no	—
678	#436	—	47	1	no	—
679	#436	—	47	1	no	—
680	#436	—	47	2	no	—
681	#436	—	47	2	no	—
682	#431	—	47	2	no	—
683	#431	—	47	1	no	—
684	#428	—	47	2	no	—
685	#428	—	47	2	no	—
686	#428	—	47	2	no	—
687	#423	—	47	1	no	—
688	#423	—	47	2	no	—
689	#418	—	47	2	no	—
690	#417	—	47	2	no	—
691	#417	—	47	2	no	—
692	C₄₇	#62152	1	1	yes	characteristic, complemented, Sylow
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	47	2	no	—
695	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
696	C₂²×D₄	—	47	1	no	—
697	C₂³×C₄	—	94	1	no	—
698	C₂×Q₁₆	—	47	2	no	—
699	C₂×SD₁₆	—	47	1	no	—
700	C₂×SD₁₆	—	47	1	no	—
701	C₂×SD₁₆	—	47	2	no	—
702	C₂×D₈	—	47	1	no	—
703	C₂×D₈	—	47	1	no	—
704	C₂×M₁₆	—	47	2	no	—
705	C₂×M₁₆	—	47	2	no	—
706	C₂×M₁₆	—	47	2	no	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	47	1	no	—
709	C₄⋊Q₈	—	47	1	no	—
710	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
711	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	1	no	—
715	#126	—	2	2	no	—
716	#126	—	94	2	no	—
717	#126	—	94	2	no	—
718	#126	—	94	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	1	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	47	2	no	—
725	#125	—	94	2	no	—
726	#125	—	94	1	no	—
727	#125	C₂²×D₄₇	1	1	yes	characteristic
728	#125	C₂²×D₄₇	1	2	yes	—
729	#125	C₂²×D₄₇	1	2	yes	—
730	#125	C₂²×D₄₇	1	2	yes	—
731	#124	—	47	2	no	—
732	#124	—	94	2	no	—
733	#124	C₂²×D₄₇	1	1	yes	characteristic
734	#123	—	2	2	no	—
735	#123	—	2	1	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	94	2	no	—
740	#123	—	94	2	no	—
741	#123	—	94	2	no	—
742	#123	—	94	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	47	2	no	—
750	C₂²⋊Q₈	—	47	2	no	—
751	C₂²⋊Q₈	—	94	1	no	—
752	C₂²⋊Q₈	—	94	1	no	—
753	C₂²⋊Q₈	—	94	1	no	—
754	C₂²⋊Q₈	—	94	2	no	—
755	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
757	#121	—	2	2	no	—
758	#121	—	47	2	no	—
759	#121	—	94	1	no	—
760	#121	—	94	1	no	—
761	#121	—	94	2	no	—
762	#121	C₂²×D₄₇	1	1	yes	characteristic
763	#121	C₂²×D₄₇	1	2	yes	—
764	#120	—	94	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	47	2	no	—
769	C₄×Q₈	—	47	2	no	—
770	C₄×Q₈	—	94	1	no	—
771	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
772	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
773	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
774	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	47	1	no	—
780	C₄×D₄	—	47	1	no	—
781	C₄×D₄	—	47	1	no	—
782	C₄×D₄	—	47	1	no	—
783	C₄×D₄	—	47	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	—	94	2	no	—
787	C₄×D₄	—	94	1	no	—
788	C₄×D₄	—	94	1	no	—
789	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
790	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
791	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
792	C₄×D₄	C₂²×D₄₇	1	2	yes	—
793	C₄×D₄	C₂²×D₄₇	1	2	yes	—
794	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
795	#117	—	2	2	no	—
796	#117	—	2	1	no	—
797	#117	—	2	2	no	—
798	#117	—	47	2	no	—
799	#117	—	94	1	no	—
800	#117	—	94	1	no	—
801	#117	—	94	1	no	—
802	#117	—	94	2	no	—
803	#117	—	94	2	no	—
804	#117	—	94	2	no	—
805	#117	C₂²⋊D₄₇	1	1	yes	characteristic
806	#117	C₂²⋊D₄₇	1	2	yes	—
807	#117	C₂²×D₄₇	1	2	yes	—
808	C₂×C₄⋊C₄	—	2	2	no	—
809	C₂×C₄⋊C₄	—	2	2	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	47	1	no	—
812	C₂×C₄⋊C₄	—	94	1	no	—
813	C₂×C₄⋊C₄	—	94	1	no	—
814	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
815	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
816	C₂×C₂²⋊C₄	—	94	1	no	—
817	C₂×C₂²⋊C₄	—	94	2	no	—
818	C₂×C₄²	—	94	2	no	—
819	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
820	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
821	#107	—	47	1	no	—
822	#107	—	47	2	no	—
823	#107	—	47	2	no	—
824	#107	—	47	2	no	—
825	#107	—	47	2	no	—
826	#107	—	47	1	no	—
827	#107	—	47	2	no	—
828	#106	—	47	2	no	—
829	#106	—	47	1	no	—
830	#106	—	47	2	no	—
831	#106	—	47	2	no	—
832	#106	—	47	2	no	—
833	#106	—	47	1	no	—
834	#106	—	47	2	no	—
835	C₄⋊C₈	—	47	1	no	—
836	C₄⋊C₈	—	47	2	no	—
837	C₄⋊C₈	—	47	1	no	—
838	C₄⋊C₈	—	47	1	no	—
839	C₄⋊C₈	—	47	2	no	—
840	C₄⋊C₈	—	47	2	no	—
841	C₄⋊C₈	—	47	1	no	—
842	#103	—	47	1	no	—
843	#103	—	47	1	no	—
844	#103	—	47	2	no	—
845	#103	—	47	2	no	—
846	#103	—	47	2	no	—
847	#103	—	47	2	no	—
848	#103	—	47	2	no	—
849	#103	—	47	2	no	—
850	#103	—	47	2	no	—
851	#102	—	47	1	no	—
852	#102	—	47	1	no	—
853	#102	—	47	2	no	—
854	#102	—	47	1	no	—
855	#102	—	47	1	no	—
856	#102	—	47	2	no	—
857	#102	—	47	2	no	—
858	#102	—	47	2	no	—
859	#102	—	47	2	no	—
860	#102	—	47	1	no	—
861	#102	—	47	1	no	—
862	C₂²⋊C₈	—	47	1	no	—
863	C₂²⋊C₈	—	47	2	no	—
864	C₂²⋊C₈	—	47	1	no	—
865	C₂²⋊C₈	—	47	2	no	—
866	C₄×C₈	—	47	1	no	—
867	C₄×C₈	—	47	1	no	—
868	C₄×C₈	—	47	2	no	—
869	C₄×C₈	—	47	2	no	—
870	C₂⁴	—	94	1	no	—
871	#41	—	4	2	no	—
872	#41	—	4	4	no	—
873	#41	—	94	4	no	—
874	#41	—	188	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	47	2	no	—
878	C₂×Q₈	—	94	1	no	—
879	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
880	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	47	1	no	—
884	C₂×D₄	—	47	1	no	—
885	C₂×D₄	—	94	2	no	—
886	C₂×D₄	—	94	2	no	—
887	C₂×D₄	—	94	2	no	—
888	C₂×D₄	—	94	1	no	—
889	C₂×D₄	—	188	1	no	—
890	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
891	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
892	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	94	1	no	—
898	C₂²×C₄	—	94	2	no	—
899	C₂²×C₄	—	94	1	no	—
900	C₂²×C₄	—	94	2	no	—
901	C₂²×C₄	—	94	1	no	—
902	C₂²×C₄	—	94	1	no	—
903	C₂²×C₄	—	94	1	no	—
904	C₂²×C₄	—	188	4	no	—
905	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
906	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
907	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
908	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
909	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
910	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
911	Q₁₆	—	188	2	no	—
912	SD₁₆	—	94	2	no	—
913	SD₁₆	—	188	2	no	—
914	SD₁₆	—	188	1	no	—
915	D₈	—	94	2	no	—
916	D₈	—	188	1	no	—
917	M₁₆	—	188	2	no	—
918	M₁₆	—	188	2	no	—
919	M₁₆	—	188	2	no	—
920	C₂×C₈	—	47	1	no	—
921	C₂×C₈	—	47	1	no	—
922	C₂×C₈	—	47	2	no	—
923	C₂×C₈	—	47	2	no	—
924	C₂×C₈	—	47	1	no	—
925	C₂×C₈	—	47	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	47	1	no	—
943	C₄⋊C₄	—	47	1	no	—
944	C₄⋊C₄	—	47	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	2	no	—
947	C₄⋊C₄	—	94	2	no	—
948	C₄⋊C₄	—	94	2	no	—
949	C₄⋊C₄	—	94	2	no	—
950	C₄⋊C₄	—	94	2	no	—
951	C₄⋊C₄	—	94	1	no	—
952	C₄⋊C₄	—	94	1	no	—
953	C₄⋊C₄	—	94	1	no	—
954	C₄⋊C₄	—	94	1	no	—
955	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
956	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
958	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
959	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
960	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
961	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
962	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	94	2	no	—
973	C₂²⋊C₄	—	94	2	no	—
974	C₂²⋊C₄	—	94	2	no	—
975	C₂²⋊C₄	—	94	1	no	—
976	C₂²⋊C₄	—	94	2	no	—
977	C₂²⋊C₄	—	94	2	no	—
978	C₂²⋊C₄	—	94	1	no	—
979	C₂²⋊C₄	—	94	1	no	—
980	C₂²⋊C₄	—	94	1	no	—
981	C₂²⋊C₄	—	94	2	no	—
982	C₂²⋊C₄	—	94	2	no	—
983	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
984	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
985	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	94	2	no	—
990	C₄²	—	94	2	no	—
991	C₄²	—	94	2	no	—
992	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
993	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
994	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
995	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
996	C₄²	C₂³×D₄₇	1	1	yes	characteristic
997	C₄²	C₂³×D₄₇	1	2	yes	—
998	C₄²	C₂³×D₄₇	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	94	1	no	—
1001	C₂³	—	94	1	no	—
1002	C₂³	—	376	1	no	—
1003	C₂³	—	188	2	no	—
1004	C₂³	—	188	2	no	—
1005	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1006	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	8	1	no	—
1012	Q₈	—	94	2	no	—
1013	Q₈	—	94	2	no	—
1014	Q₈	—	376	1	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	8	1	no	—
1021	D₄	—	47	2	no	—
1022	D₄	—	94	1	no	—
1023	D₄	—	94	1	no	—
1024	D₄	—	94	1	no	—
1025	D₄	—	376	2	no	—
1026	D₄	—	188	2	no	—
1027	D₄	—	188	4	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	1	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	94	1	no	—
1046	C₂×C₄	—	94	2	no	—
1047	C₂×C₄	—	94	2	no	—
1048	C₂×C₄	—	94	1	no	—
1049	C₂×C₄	—	376	2	no	—
1050	C₂×C₄	—	188	4	no	—
1051	C₂×C₄	—	188	2	no	—
1052	C₂×C₄	—	188	2	no	—
1053	C₂×C₄	—	188	2	no	—
1054	C₂×C₄	—	188	2	no	—
1055	C₂×C₄	—	188	2	no	—
1056	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1057	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1058	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1059	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1060	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1061	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1062	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1063	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1064	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1065	C₈	—	94	1	no	—
1066	C₈	—	94	1	no	—
1067	C₈	—	94	1	no	—
1068	C₈	—	94	2	no	—
1069	C₈	—	94	1	no	—
1070	C₈	—	94	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	94	2	no	—
1081	C₂²	—	376	4	no	—
1082	C₂²	—	188	1	no	—
1083	C₂²	—	188	1	no	—
1084	C₂²	—	188	1	no	—
1085	C₂²	—	188	1	no	—
1086	C₂²	—	188	1	no	—
1087	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1088	C₄	—	2	2	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	188	2	no	—
1101	C₄	—	188	1	no	—
1102	C₄	—	188	1	no	—
1103	C₄	—	188	2	no	—
1104	C₄	#15689921	1	2	yes	—
1105	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1106	C₄	#15689960	1	1	yes	characteristic
1107	C₂	—	4	1	no	—
1108	C₂	—	4	2	no	—
1109	C₂	—	8	1	no	—
1110	C₂	—	376	1	no	—
1111	C₂	—	188	2	no	—
1112	C₂	#20257061	1	1	yes	characteristic
1113	C₂	C₂×#15689921	1	1	yes	characteristic
1114	C₂	#20258159	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×#3515	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3515	D₄₇
hypocenter	C₄₇	#62152
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3515

Complements

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

N	H ≅ G/N	type
1. #20256952	C₂	semidirect
2. #20256259	C₂	semidirect
3. #20256251	C₂	semidirect
4. #20256073	C₂	semidirect
5. #20256037	C₂	semidirect
6. #20256014	C₂	semidirect
7. #20255983	C₂	semidirect
8. #20255957	C₂	semidirect
9. #20255942	C₂	semidirect
10. #20255698	C₂	semidirect
11. #20255687	C₂	semidirect
12. #20255598	C₂	semidirect
13. #20255583	C₂	semidirect
14. #20254784	C₂	semidirect
15. #20254761	C₂	semidirect
16. #20254556	C₂	semidirect
17. #20254547	C₂	semidirect
18. #20253431	C₂	semidirect
19. #20253400	C₂	semidirect
20. #20253206	C₂	semidirect
21. #20253181	C₂	semidirect
22. #20252520	C₂	semidirect
23. C₄₇×#3515	C₂	semidirect
40. #15689526	C₂²	semidirect
41. #15689522	C₂²	semidirect
42. #15689522	C₂²	semidirect
43. #15689519	C₂²	semidirect
46. #15689475	C₂²	semidirect
47. #15689475	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689458	C₂²	semidirect
53. #15689453	C₂²	semidirect
54. #15689444	C₂²	semidirect
58. #15689430	C₂²	semidirect
59. #15689427	C₂²	semidirect
60. #15689427	C₂²	semidirect
61. #15689427	C₂²	semidirect
62. #15689427	C₂²	semidirect
63. #15689427	C₂²	semidirect
64. #15689423	C₂²	semidirect
71. #15689418	C₂²	semidirect
72. #15689413	C₂²	semidirect
78. #15689379	C₂²	semidirect
82. #15689367	C₂²	semidirect
84. #15689342	C₂²	semidirect
88. #15689333	C₂²	semidirect
89. #15689328	C₂²	semidirect
94. Q₈×C₄₇⋊C₈	C₂²	semidirect
95. Q₈×C₄₇⋊C₈	C₂²	semidirect
96. C₄×#10625337	C₂²	semidirect
100. C₄×#10625335	C₂²	semidirect
106. #15689201	C₂²	semidirect
107. #15689201	C₂²	semidirect
109. #15689176	C₂²	semidirect
111. #15689163	C₂²	semidirect
112. #15689163	C₂²	semidirect
114. #15689147	C₂²	semidirect
118. C₄₇×#557	C₂²	semidirect
119. C₄₇×#554	C₂²	semidirect
120. C₄₇×#554	C₂²	semidirect
126. C₄₇×#547	C₂²	semidirect
131. C₄₇×#529	C₂²	semidirect
132. C₂×#125×C₄₇	C₂²	semidirect
550. #3515	D₄₇	semidirect
581. #557	C₂×D₄₇	semidirect
585. #554	C₂×D₄₇	semidirect
586. #554	C₂×D₄₇	semidirect
597. #547	C₂×D₄₇	semidirect
606. #529	C₂×D₄₇	semidirect
607. C₂×#125	C₂×D₄₇	semidirect
692. C₄₇	#62152	semidirect

Maximal subgroups

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

subgroup	index
#20256952	2
#20256259	2
#20256251	2
#20256073	2
#20256037	2
#20256014	2
#20255983	2
#20255957	2
#20255942	2
#20255698	2
#20255687	2
#20255598	2
#20255583	2
#20254784	2
#20254761	2
#20254556	2
#20254547	2
#20253431	2
#20253400	2
#20253206	2
#20253181	2
#20252520	2
C₄₇×#3515	2
#62152	47