Subgroups — #27098577

Order 12032.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257010	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256983	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256382	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256277	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256082	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256071	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255974	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255949	C₂	1	2	yes	maximal, complemented
9	#20255717	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255673	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255652	C₂	1	2	yes	maximal, complemented
12	#20255642	C₂	1	2	yes	maximal, complemented
13	#20255055	C₂	1	1	yes	maximal, characteristic, complemented
14	#20255039	C₂	1	2	yes	maximal, complemented
15	#20254113	C₂	1	2	yes	maximal, complemented
16	#20254106	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253563	C₂	1	2	yes	maximal, complemented
18	#20253539	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253518	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253495	C₂	1	2	yes	maximal, complemented
21	#20252406	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252204	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094056	C₂²	1	2	yes	—
25	#15689858	—	2	1	no	—
26	#15689858	C₂²	1	1	yes	characteristic
27	#15689852	C₂²	1	1	yes	characteristic
28	#15689852	C₂²	1	1	yes	characteristic
29	#15689846	—	2	1	no	—
30	#15689846	C₂²	1	1	yes	characteristic
31	#15689843	—	2	1	no	—
32	#15689843	C₂²	1	1	yes	characteristic
33	#15689821	—	2	2	no	—
34	#15689821	C₂²	1	2	yes	—
35	#15689812	—	2	2	no	—
36	#15689812	C₂²	1	2	yes	—
37	#15689795	C₂²	1	1	yes	characteristic
38	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
39	#15689784	C₂²	1	2	yes	—
40	#15689780	C₂²	1	2	yes	—
41	#15689778	—	2	1	no	—
42	#15689778	C₂²	1	1	yes	characteristic
43	#15689680	—	2	1	no	—
44	#15689680	C₂²	1	1	yes	characteristic
45	#15689673	—	2	1	no	—
46	#15689673	C₂²	1	1	yes	characteristic
47	#15689660	—	2	2	no	—
48	#15689660	C₂²	1	2	yes	—
49	#15689655	—	2	2	no	—
50	#15689655	C₂²	1	2	yes	—
51	C₄×#10625354	C₂²	1	2	yes	—
52	C₄×#10625350	—	2	1	no	—
53	C₄×#10625350	—	2	1	no	—
54	C₄×#10625350	C₂²	1	1	yes	characteristic
55	C₄×Q₈×D₄₇	C₂²	1	2	yes	—
56	#15689528	C₂²	1	1	yes	characteristic
57	#15689524	C₂²	1	2	yes	—
58	#15689504	C₂²	1	2	yes	—
59	#15689496	C₂²	1	1	yes	characteristic
60	#15689479	C₂²	1	2	yes	—
61	#15689476	C₂²	1	2	yes	—
62	#15689474	C₂²	1	1	yes	characteristic
63	#15689470	C₂²	1	1	yes	characteristic
64	#15689466	C₂²	1	2	yes	—
65	#15689457	C₂²	1	2	yes	—
66	#15689453	C₂²	1	2	yes	—
67	#15689447	C₂²	1	2	yes	—
68	#15689445	C₂²	1	2	yes	—
69	#15689443	C₂²	1	2	yes	—
70	#15689433	C₂²	1	2	yes	—
71	#15689432	C₂²	1	2	yes	—
72	#15689432	C₂²	1	2	yes	—
73	#15689426	C₂²	1	2	yes	—
74	#15689408	C₂²	1	1	yes	characteristic
75	#15689408	C₂²	1	1	yes	characteristic
76	#15689408	C₂²	1	1	yes	characteristic
77	#15689403	C₂²	1	1	yes	characteristic
78	#15689380	C₂²	1	2	yes	—
79	#15689375	C₂²	1	2	yes	—
80	#15689370	C₂²	1	2	yes	—
81	#15689369	C₂²	1	2	yes	—
82	#15689369	C₂²	1	2	yes	—
83	#15689366	C₂²	1	2	yes	—
84	#15689348	C₂²	1	2	yes	—
85	#15689347	C₂²	1	2	yes	—
86	#15689343	C₂²	1	2	yes	—
87	#15689337	C₂²	1	2	yes	—
88	#15689333	C₂²	1	1	yes	characteristic
89	#15689333	C₂²	1	1	yes	characteristic
90	#15689323	C₂²	1	1	yes	characteristic
91	#15689318	C₂²	1	1	yes	characteristic
92	#15689288	C₂²	1	2	yes	—
93	#15689279	C₂²	1	2	yes	—
94	#15689277	C₂²	1	2	yes	—
95	#15689268	C₂²	1	2	yes	—
96	#15689267	C₂²	1	2	yes	—
97	#15689263	C₂²	1	2	yes	—
98	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
99	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
100	#15689233	C₂²	1	2	yes	—
101	#15689228	C₂²	1	2	yes	—
102	#15689228	C₂²	1	2	yes	—
103	#15689225	C₂²	1	2	yes	—
104	#15689225	C₂²	1	2	yes	—
105	#15689221	C₂²	1	2	yes	—
106	Q₁₆×Dic₄₇	C₂²	1	2	yes	—
107	#15689215	C₂²	1	2	yes	—
108	#15689210	C₂²	1	2	yes	—
109	#15689208	C₂²	1	2	yes	—
110	#15689202	C₂²	1	1	yes	characteristic
111	#15689202	C₂²	1	1	yes	characteristic
112	#15689199	C₂²	1	2	yes	—
113	#15689199	C₂²	1	2	yes	—
114	#15689180	C₂²	1	1	yes	characteristic
115	#15689178	C₂²	1	2	yes	—
116	#15689162	C₂²	1	2	yes	—
117	#15689130	C₂²	1	2	yes	—
118	#15689123	C₂²	1	2	yes	—
119	#15689075	C₂²	1	2	yes	—
120	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
123	C₄₇×#441	C₂²	1	1	yes	characteristic
124	C₄₇×#441	C₂²	1	1	yes	characteristic
125	C₄₇×#440	C₂²	1	1	yes	characteristic
126	C₄₇×#440	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
128	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
131	C₄₇×#428	C₂²	1	1	yes	characteristic
132	C₄₇×#419	C₂²	1	1	yes	characteristic
133	C₄₇×#417	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625354	C₂³	1	2	yes	—
136	C₂×#10625350	—	2	1	no	—
137	C₂×#10625350	—	2	1	no	—
138	C₂×#10625350	D₄	1	1	yes	characteristic
139	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
140	#13094056	—	2	8	no	—
141	C₂×#10625337	C₂³	1	2	yes	—
142	C₂×#10625337	C₂³	1	2	yes	—
143	C₂×#10625325	C₂³	1	2	yes	—
144	C₂×#10625325	C₂³	1	2	yes	—
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625334	C₂³	1	2	yes	—
147	C₂×#10625324	C₂³	1	2	yes	—
148	C₂×#10625324	C₂³	1	2	yes	—
149	#13094024	—	2	1	no	—
150	#13094024	—	2	1	no	—
151	#13094024	—	2	1	no	—
152	#13094024	C₂³	1	1	yes	characteristic
153	#13094024	C₂³	1	1	yes	characteristic
154	#13094024	C₂³	1	1	yes	characteristic
155	#13094021	—	2	1	no	—
156	#13094021	C₂³	1	1	yes	characteristic
157	#13094019	—	2	2	no	—
158	#13094019	—	2	2	no	—
159	#13094019	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094017	—	2	2	no	—
162	#13094017	—	2	2	no	—
163	#13094016	—	2	1	no	—
164	#13094016	—	2	2	no	—
165	#13094015	—	2	2	no	—
166	#13094015	—	2	2	no	—
167	#13094015	C₂³	1	2	yes	—
168	#13094015	C₂³	1	2	yes	—
169	#13094013	—	2	2	no	—
170	#13094013	C₂³	1	2	yes	—
171	#13094012	—	2	1	no	—
172	#13094012	—	2	1	no	—
173	#13094012	—	2	1	no	—
174	#13094011	—	2	2	no	—
175	#13094011	C₂³	1	2	yes	—
176	#13094009	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094009	—	2	2	no	—
179	#13094006	—	2	2	no	—
180	#13094006	—	2	2	no	—
181	#13094006	—	2	2	no	—
182	#13094004	—	2	2	no	—
183	#13094004	C₂³	1	2	yes	—
184	#13094003	—	2	1	no	—
185	#13094003	—	2	1	no	—
186	#13094003	—	2	1	no	—
187	#13094003	—	2	2	no	—
188	#13094003	C₂³	1	2	yes	—
189	#13094000	—	2	2	no	—
190	#13094000	C₂³	1	2	yes	—
191	#13093999	—	2	2	no	—
192	#13093999	C₂³	1	2	yes	—
193	#13093998	—	2	1	no	—
194	#13093998	—	2	2	no	—
195	#13093998	—	2	2	no	—
196	#13093998	C₂³	1	2	yes	—
197	#13093995	—	2	2	no	—
198	#13093995	C₂³	1	2	yes	—
199	Q₈×Dic₄₇	C₂³	1	2	yes	—
200	Q₈×Dic₄₇	C₂³	1	2	yes	—
201	C₄×Dic₉₄	—	2	1	no	—
202	C₄×Dic₉₄	—	2	1	no	—
203	C₄×Dic₉₄	—	2	1	no	—
204	C₄×Dic₉₄	—	2	1	no	—
205	C₄×Dic₉₄	—	2	2	no	—
206	C₄×Dic₉₄	D₄	1	1	yes	characteristic
207	C₄×Dic₉₄	C₂³	1	2	yes	—
208	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
209	#13093989	—	2	2	no	—
210	#13093989	C₂³	1	2	yes	—
211	C₄×D₁₈₈	—	2	1	no	—
212	C₄×D₁₈₈	—	2	2	no	—
213	C₄×D₁₈₈	—	2	2	no	—
214	C₄×D₁₈₈	—	2	1	no	—
215	C₄×D₁₈₈	—	2	1	no	—
216	C₄×D₁₈₈	—	2	1	no	—
217	C₄×D₁₈₈	D₄	1	1	yes	characteristic
218	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
219	C₄×D₁₈₈	C₂³	1	2	yes	—
220	#13093986	—	2	2	no	—
221	#13093986	C₂³	1	2	yes	—
222	C₄×C₂²⋊D₄₇	—	2	2	no	—
223	C₄×C₂²⋊D₄₇	—	2	2	no	—
224	C₄×C₂²⋊D₄₇	—	2	2	no	—
225	C₄×C₂²⋊D₄₇	—	2	2	no	—
226	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
227	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
228	#13093983	—	2	1	no	—
229	#13093983	—	2	1	no	—
230	#13093983	—	2	2	no	—
231	#13093983	D₄	1	1	yes	characteristic
232	#13093982	—	2	2	no	—
233	#13093982	C₂³	1	2	yes	—
234	#13093981	—	2	2	no	—
235	#13093981	—	2	2	no	—
236	#13093981	D₄	1	2	yes	—
237	C₄⋊C₄×D₄₇	—	2	2	no	—
238	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
239	C₄²×D₄₇	—	2	2	no	—
240	C₄²×D₄₇	—	2	2	no	—
241	C₄²×D₄₇	C₂³	1	2	yes	—
242	#13093958	C₂³	1	2	yes	—
243	#13093958	C₂³	1	2	yes	—
244	#13093957	C₂³	1	2	yes	—
245	#13093955	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	#13093949	C₂³	1	2	yes	—
253	#13093949	C₂³	1	2	yes	—
254	#13093948	C₂³	1	2	yes	—
255	#13093948	C₂³	1	2	yes	—
256	#13093948	C₂³	1	2	yes	—
257	#13093947	C₂³	1	2	yes	—
258	#13093947	C₂³	1	2	yes	—
259	#13093946	C₂³	1	2	yes	—
260	#13093946	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093944	C₂³	1	2	yes	—
263	#13093944	C₂³	1	2	yes	—
264	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	#13093935	C₂³	1	2	yes	—
268	C₈×Dic₄₇	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
271	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
272	#137×C₄₇	—	2	4	no	—
273	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₄₇	—	2	1	no	—
280	C₄×Q₈×C₄₇	—	2	1	no	—
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₇	—	2	1	no	—
288	C₄×D₄×C₄₇	—	2	1	no	—
289	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	#117×C₄₇	—	2	1	no	—
292	#117×C₄₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₇	—	2	1	no	—
296	C₂×C₄²×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	#106×C₄₇	C₂³	1	1	yes	characteristic
302	#103×C₄₇	C₂³	1	1	yes	characteristic
303	#103×C₄₇	C₂³	1	1	yes	characteristic
304	#103×C₄₇	C₂³	1	1	yes	characteristic
305	#103×C₄₇	C₂³	1	1	yes	characteristic
306	#103×C₄₇	C₂³	1	1	yes	characteristic
307	#103×C₄₇	C₂³	1	1	yes	characteristic
308	#102×C₄₇	C₂³	1	1	yes	characteristic
309	#102×C₄₇	C₂³	1	1	yes	characteristic
310	#97×C₄₇	C₂³	1	1	yes	characteristic
311	#97×C₄₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	#41×C₄₇	—	2	2	no	—
315	#41×C₄₇	—	4	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₇	—	2	1	no	—
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	—	2	1	no	—
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₄₇	—	2	2	no	—
333	C₂×C₂²⋊D₄₇	—	2	2	no	—
334	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
335	#10625354	—	2	4	no	—
336	#10625354	—	4	2	no	—
337	Q₈×D₄₇	—	2	4	no	—
338	Q₈×D₄₇	—	4	2	no	—
339	#10625350	—	4	2	no	—
340	#10625350	—	4	4	no	—
341	#10625350	—	4	4	no	—
342	C₂×D₁₈₈	—	2	2	no	—
343	C₂×D₁₈₈	—	2	1	no	—
344	C₂×D₁₈₈	—	2	2	no	—
345	C₂×D₁₈₈	—	2	1	no	—
346	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
347	C₂×D₁₈₈	C₂⁴	1	2	yes	—
348	C₂×C₄×D₄₇	—	2	2	no	—
349	C₂×C₄×D₄₇	—	2	2	no	—
350	C₂×C₄×D₄₇	—	2	2	no	—
351	C₂×C₄×D₄₇	—	2	2	no	—
352	C₂×C₄×D₄₇	—	2	2	no	—
353	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
354	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
355	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
356	C₂×Dic₉₄	—	2	1	no	—
357	C₂×Dic₉₄	—	2	1	no	—
358	C₂×Dic₉₄	—	2	2	no	—
359	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
360	C₂×Dic₉₄	C₂⁴	1	2	yes	—
361	Q₁₆×C₄₇	—	2	2	no	—
362	Q₁₆×C₄₇	#41	1	4	yes	complemented
363	SD₁₆×C₄₇	—	2	2	no	—
364	SD₁₆×C₄₇	—	2	2	no	—
365	M₁₆×C₄₇	—	2	2	no	—
366	M₁₆×C₄₇	—	4	1	no	—
367	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	—	2	1	no	—
374	C₄⋊C₄×C₄₇	—	2	1	no	—
375	C₄⋊C₄×C₄₇	—	2	1	no	—
376	C₄⋊C₄×C₄₇	—	2	1	no	—
377	C₄⋊C₄×C₄₇	—	2	1	no	—
378	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
382	C₂²⋊C₄×C₄₇	—	2	1	no	—
383	C₂²⋊C₄×C₄₇	—	2	1	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	1	no	—
387	C₄²×C₄₇	—	2	1	no	—
388	C₄²×C₄₇	—	2	1	no	—
389	C₄²×C₄₇	—	2	1	no	—
390	C₄²×C₄₇	—	2	1	no	—
391	C₄²×C₄₇	—	2	1	no	—
392	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₂²⋊Dic₄₇	—	2	2	no	—
397	C₂²⋊Dic₄₇	—	2	2	no	—
398	C₂²⋊Dic₄₇	—	2	2	no	—
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
401	#10625337	—	2	4	no	—
402	#10625337	—	4	2	no	—
403	#10625336	—	2	4	no	—
404	#10625334	—	4	2	no	—
405	(C₂×D₄₇)⋊C₄	—	2	2	no	—
406	(C₂×D₄₇)⋊C₄	—	2	2	no	—
407	(C₂×D₄₇)⋊C₄	—	2	2	no	—
408	(C₂×D₄₇)⋊C₄	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	2	no	—
411	(C₂×D₄₇)⋊C₄	—	2	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
415	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
421	C₄⋊Dic₄₇	—	2	2	no	—
422	C₄⋊Dic₄₇	—	2	2	no	—
423	C₄⋊Dic₄₇	—	2	2	no	—
424	C₄⋊Dic₄₇	—	2	2	no	—
425	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
426	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
427	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
428	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
429	Dic₄₇⋊C₄	—	2	2	no	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	Dic₄₇⋊C₄	—	2	2	no	—
434	Dic₄₇⋊C₄	—	2	2	no	—
435	Dic₄₇⋊C₄	—	2	2	no	—
436	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
437	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
438	C₄×Dic₄₇	—	2	2	no	—
439	C₄×Dic₄₇	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	—	2	2	no	—
442	C₄×Dic₄₇	—	2	2	no	—
443	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
444	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
445	C₄×Dic₄₇	C₂⁴	1	2	yes	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	#10625325	—	2	4	no	—
449	#10625325	—	4	2	no	—
450	#10625324	—	2	4	no	—
451	#10625324	—	4	2	no	—
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₄₇	—	2	2	no	—
455	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
456	Q₈×C₄₇	—	2	1	no	—
457	Q₈×C₄₇	—	2	1	no	—
458	Q₈×C₄₇	—	2	1	no	—
459	Q₈×C₄₇	—	2	1	no	—
460	Q₈×C₄₇	—	4	2	no	—
461	Q₈×C₄₇	C₂×#41	1	2	yes	—
462	Q₈×C₄₇	C₂×#41	1	2	yes	—
463	D₄×C₄₇	—	2	1	no	—
464	D₄×C₄₇	—	2	1	no	—
465	D₄×C₄₇	—	4	2	no	—
466	C₂×C₄×C₄₇	—	2	1	no	—
467	C₂×C₄×C₄₇	—	2	1	no	—
468	C₂×C₄×C₄₇	—	2	2	no	—
469	C₂×C₄×C₄₇	—	2	1	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	2	1	no	—
474	C₂×C₄×C₄₇	—	2	1	no	—
475	C₂×C₄×C₄₇	—	2	1	no	—
476	C₂×C₄×C₄₇	—	4	1	no	—
477	C₂×C₄×C₄₇	—	4	2	no	—
478	C₂×C₄×C₄₇	—	4	2	no	—
479	C₂×C₄×C₄₇	—	4	2	no	—
480	C₂×C₄×C₄₇	—	4	2	no	—
481	C₂×C₄×C₄₇	—	8	1	no	—
482	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
488	C₂²⋊D₄₇	—	4	2	no	—
489	C₂²⋊D₄₇	—	4	4	no	—
490	C₂²⋊D₄₇	—	4	4	no	—
491	C₂×Dic₄₇	—	2	2	no	—
492	C₂×Dic₄₇	—	2	2	no	—
493	C₂×Dic₄₇	—	2	2	no	—
494	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
495	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
496	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
497	D₁₈₈	—	2	2	no	—
498	D₁₈₈	—	2	2	no	—
499	D₁₈₈	—	2	2	no	—
500	D₁₈₈	—	4	4	no	—
501	D₁₈₈	—	4	2	no	—
502	D₁₈₈	—	8	1	no	—
503	D₁₈₈	—	8	2	no	—
504	C₄×D₄₇	—	2	2	no	—
505	C₄×D₄₇	—	2	2	no	—
506	C₄×D₄₇	—	4	2	no	—
507	C₄×D₄₇	—	4	2	no	—
508	C₄×D₄₇	—	4	4	no	—
509	C₄×D₄₇	—	4	4	no	—
510	C₄×D₄₇	—	4	4	no	—
511	C₄×D₄₇	—	4	4	no	—
512	C₄×D₄₇	—	8	2	no	—
513	Dic₉₄	—	2	2	no	—
514	Dic₉₄	—	2	2	no	—
515	Dic₉₄	—	2	2	no	—
516	Dic₉₄	—	4	4	no	—
517	Dic₉₄	—	4	2	no	—
518	Dic₉₄	—	4	2	no	—
519	C₈×C₄₇	—	2	1	no	—
520	C₈×C₄₇	—	2	1	no	—
521	C₈×C₄₇	—	2	1	no	—
522	C₈×C₄₇	C₂×#41	1	2	yes	—
523	C₄₇⋊C₈	—	2	2	no	—
524	C₄₇⋊C₈	—	2	2	no	—
525	#61467	—	47	1	no	maximal, Sylow
526	C₂²×C₄₇	—	2	1	no	—
527	C₂²×C₄₇	—	2	1	no	—
528	C₂²×C₄₇	—	2	1	no	—
529	C₂²×C₄₇	—	4	1	no	—
530	C₂²×C₄₇	—	4	1	no	—
531	C₂²×C₄₇	—	4	1	no	—
532	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
533	C₂×D₄₇	—	2	2	no	—
534	C₂×D₄₇	—	2	2	no	—
535	C₂×D₄₇	—	2	2	no	—
536	C₂×D₄₇	—	4	2	no	—
537	C₂×D₄₇	—	4	2	no	—
538	C₂×D₄₇	—	4	2	no	—
539	C₄×C₄₇	—	2	1	no	—
540	C₄×C₄₇	—	2	1	no	—
541	C₄×C₄₇	—	2	2	no	—
542	C₄×C₄₇	—	2	2	no	—
543	C₄×C₄₇	—	2	1	no	—
544	C₄×C₄₇	—	2	1	no	—
545	C₄×C₄₇	—	4	1	no	—
546	C₄×C₄₇	—	4	1	no	—
547	C₄×C₄₇	—	4	1	no	—
548	C₄×C₄₇	—	4	1	no	—
549	C₄×C₄₇	—	4	1	no	—
550	C₄×C₄₇	#575	1	2	yes	—
551	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
552	C₄×C₄₇	#585	1	1	yes	characteristic
553	Dic₄₇	—	2	2	no	—
554	Dic₄₇	—	2	2	no	—
555	Dic₄₇	—	2	2	no	—
556	Dic₄₇	—	4	2	no	—
557	Dic₄₇	—	4	2	no	—
558	Dic₄₇	—	4	2	no	—
559	#3482	—	47	1	no	—
560	#3480	—	47	1	no	—
561	#3394	—	47	1	no	—
562	#3383	—	47	1	no	—
563	#3365	—	47	1	no	—
564	#3364	—	47	1	no	—
565	#3353	—	47	1	no	—
566	#3351	—	47	2	no	—
567	#3332	—	47	1	no	—
568	#3328	—	47	1	no	—
569	#3327	—	47	2	no	—
570	#3326	—	47	2	no	—
571	#3278	—	47	1	no	—
572	#3277	—	47	2	no	—
573	#3183	—	47	2	no	—
574	#3182	—	47	1	no	—
575	#3117	—	47	2	no	—
576	#3115	—	47	1	no	—
577	#3113	—	47	1	no	—
578	#3111	—	47	2	no	—
579	#2971	—	47	1	no	—
580	C₄×#137	—	47	2	no	—
581	C₄×#137	D₄₇	1	1	yes	characteristic, complemented
582	C₂×C₄₇	—	4	1	no	—
583	C₂×C₄₇	—	8	1	no	—
584	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
585	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
586	C₂×C₄₇	#3586	1	1	yes	characteristic
587	D₄₇	—	4	2	no	—
588	D₄₇	—	8	2	no	—
589	C₂×#137	—	47	2	no	—
590	C₂×#137	C₂×D₄₇	1	1	yes	characteristic
591	#559	—	47	1	no	—
592	#559	—	94	1	no	—
593	#557	—	47	1	no	—
594	#557	—	47	1	no	—
595	#556	—	47	1	no	—
596	#556	—	47	1	no	—
597	#556	—	94	1	no	—
598	#556	—	94	1	no	—
599	#553	—	47	2	no	—
600	#553	—	94	2	no	—
601	#552	—	47	2	no	—
602	#552	—	94	2	no	—
603	#550	—	47	1	no	—
604	D₄×Q₈	—	47	1	no	—
605	#548	—	47	2	no	—
606	#548	—	47	2	no	—
607	#547	—	47	1	no	—
608	#547	—	94	1	no	—
609	#533	—	47	1	no	—
610	#533	—	94	1	no	—
611	#532	—	47	1	no	—
612	#532	—	94	1	no	—
613	#529	—	47	2	no	—
614	#529	—	47	2	no	—
615	#529	—	94	2	no	—
616	#529	—	94	2	no	—
617	C₄×#41	—	47	1	no	—
618	C₄×#41	—	47	2	no	—
619	C₄×#41	—	94	1	no	—
620	C₄×#41	—	94	1	no	—
621	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
622	C₂×C₄×Q₈	—	47	2	no	—
623	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
624	#500	—	47	1	no	—
625	#499	—	47	2	no	—
626	#495	—	47	2	no	—
627	#492	—	47	1	no	—
628	#488	—	47	2	no	—
629	#488	—	47	2	no	—
630	#487	—	47	1	no	—
631	#486	—	47	1	no	—
632	#485	—	47	2	no	—
633	#484	—	47	2	no	—
634	#483	—	47	2	no	—
635	#482	—	47	2	no	—
636	#482	—	47	2	no	—
637	#481	—	47	2	no	—
638	#479	—	47	2	no	—
639	#479	—	47	2	no	—
640	#479	—	47	2	no	—
641	#478	—	47	2	no	—
642	#475	—	47	1	no	—
643	#475	—	47	1	no	—
644	#475	—	47	1	no	—
645	#474	—	47	1	no	—
646	#470	—	47	2	no	—
647	#469	—	47	2	no	—
648	#468	—	47	2	no	—
649	#468	—	47	2	no	—
650	#468	—	47	2	no	—
651	#468	—	47	2	no	—
652	#464	—	47	2	no	—
653	#464	—	47	2	no	—
654	#464	—	47	2	no	—
655	#463	—	47	2	no	—
656	#462	—	47	1	no	—
657	#462	—	47	1	no	—
658	#460	—	47	1	no	—
659	#459	—	47	1	no	—
660	#452	—	47	2	no	—
661	#451	—	47	2	no	—
662	#451	—	47	2	no	—
663	#449	—	47	2	no	—
664	#449	—	47	2	no	—
665	#448	—	47	2	no	—
666	C₈×Q₈	—	47	1	no	—
667	C₈×Q₈	—	47	1	no	—
668	#442	—	47	2	no	—
669	#441	—	47	2	no	—
670	#441	—	47	2	no	—
671	#441	C₂×D₄₇	1	1	yes	characteristic
672	#441	C₂×D₄₇	1	1	yes	characteristic
673	#440	—	47	2	no	—
674	#440	—	47	2	no	—
675	#440	—	47	2	no	—
676	#440	C₂×D₄₇	1	1	yes	characteristic
677	#440	C₂×D₄₇	1	1	yes	characteristic
678	C₄×Q₁₆	—	47	2	no	—
679	C₄×Q₁₆	—	47	2	no	—
680	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
681	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
682	C₄×SD₁₆	—	47	2	no	—
683	C₄×SD₁₆	—	47	2	no	—
684	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
685	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
686	#436	—	47	2	no	—
687	#436	—	47	2	no	—
688	#436	—	47	1	no	—
689	#436	—	47	1	no	—
690	#432	—	47	1	no	—
691	#432	—	47	2	no	—
692	#428	—	47	2	no	—
693	#428	C₂×D₄₇	1	1	yes	characteristic
694	#419	—	47	2	no	—
695	#419	C₂×D₄₇	1	1	yes	characteristic
696	#417	—	47	2	no	—
697	#417	C₂×D₄₇	1	1	yes	characteristic
698	C₄×M₁₆	—	47	2	no	—
699	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
700	C₄₇	#61467	1	1	yes	characteristic, complemented, Sylow
701	C₂×#41	—	47	1	no	—
702	C₂×#41	—	47	2	no	—
703	C₂×#41	—	94	1	no	—
704	C₂×#41	—	94	1	no	—
705	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
706	C₂²×Q₈	—	47	2	no	—
707	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
708	#137	—	2	4	no	—
709	#137	—	94	8	no	—
710	C₂×Q₁₆	—	47	2	no	—
711	C₂×Q₁₆	—	47	2	no	—
712	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
713	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
714	C₂×SD₁₆	—	47	2	no	—
715	C₂×SD₁₆	—	47	2	no	—
716	C₂×SD₁₆	—	47	2	no	—
717	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
718	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
719	C₂×D₈	—	47	2	no	—
720	C₂×M₁₆	—	47	2	no	—
721	C₂×M₁₆	—	47	2	no	—
722	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
723	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
724	C₄⋊Q₈	—	47	1	no	—
725	C₄⋊Q₈	—	47	1	no	—
726	C₄⋊Q₈	—	47	1	no	—
727	C₄⋊Q₈	—	94	1	no	—
728	C₄⋊Q₈	—	94	1	no	—
729	C₄⋊Q₈	—	94	1	no	—
730	#127	—	47	1	no	—
731	#127	—	94	1	no	—
732	#126	—	94	2	no	—
733	#126	—	94	2	no	—
734	#126	—	94	2	no	—
735	#126	—	94	2	no	—
736	#126	—	94	2	no	—
737	#126	—	94	2	no	—
738	#125	—	47	2	no	—
739	#125	—	47	2	no	—
740	#125	—	94	2	no	—
741	#125	—	94	2	no	—
742	#125	—	94	2	no	—
743	#125	—	94	1	no	—
744	#124	—	47	2	no	—
745	#124	—	47	2	no	—
746	#124	—	94	1	no	—
747	#124	—	94	1	no	—
748	#124	—	94	2	no	—
749	#124	—	94	2	no	—
750	#124	—	94	1	no	—
751	#123	—	94	2	no	—
752	#123	—	94	2	no	—
753	#123	—	94	2	no	—
754	#123	—	94	2	no	—
755	#123	—	94	2	no	—
756	#123	—	94	2	no	—
757	C₂²⋊Q₈	—	47	2	no	—
758	C₂²⋊Q₈	—	47	2	no	—
759	C₂²⋊Q₈	—	47	2	no	—
760	C₂²⋊Q₈	—	94	2	no	—
761	C₂²⋊Q₈	—	94	1	no	—
762	C₂²⋊Q₈	—	94	2	no	—
763	C₂²⋊Q₈	—	94	2	no	—
764	C₂²⋊Q₈	—	94	1	no	—
765	C₂²⋊Q₈	—	94	1	no	—
766	#121	—	47	2	no	—
767	#121	—	47	2	no	—
768	#121	—	47	2	no	—
769	#121	—	94	2	no	—
770	#121	—	94	2	no	—
771	#121	—	94	2	no	—
772	#121	—	94	2	no	—
773	#121	—	94	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	47	1	no	—
777	C₄×Q₈	—	47	1	no	—
778	C₄×Q₈	—	47	2	no	—
779	C₄×Q₈	—	47	2	no	—
780	C₄×Q₈	—	47	2	no	—
781	C₄×Q₈	—	47	2	no	—
782	C₄×Q₈	—	94	2	no	—
783	C₄×Q₈	—	94	1	no	—
784	C₄×Q₈	—	94	1	no	—
785	C₄×Q₈	—	94	1	no	—
786	C₄×Q₈	—	94	2	no	—
787	C₄×Q₈	—	94	1	no	—
788	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
790	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
791	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
792	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
793	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	47	2	no	—
797	C₄×D₄	—	47	2	no	—
798	C₄×D₄	—	47	2	no	—
799	C₄×D₄	—	47	1	no	—
800	C₄×D₄	—	47	1	no	—
801	C₄×D₄	—	47	2	no	—
802	C₄×D₄	—	94	1	no	—
803	C₄×D₄	—	94	1	no	—
804	C₄×D₄	—	94	2	no	—
805	C₄×D₄	—	94	2	no	—
806	C₄×D₄	—	94	1	no	—
807	C₄×D₄	—	94	2	no	—
808	C₄×D₄	—	94	2	no	—
809	C₄×D₄	—	94	2	no	—
810	C₄×D₄	—	94	2	no	—
811	C₄×D₄	—	94	2	no	—
812	C₄×D₄	—	94	1	no	—
813	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
814	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
815	#117	—	2	1	no	—
816	#117	—	47	1	no	—
817	#117	—	47	2	no	—
818	#117	—	47	2	no	—
819	#117	—	94	2	no	—
820	#117	—	94	2	no	—
821	#117	—	94	2	no	—
822	#117	—	94	2	no	—
823	#117	—	94	1	no	—
824	#117	—	94	1	no	—
825	#117	C₂²×D₄₇	1	1	yes	characteristic
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	47	2	no	—
828	C₂×C₄⋊C₄	—	94	2	no	—
829	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	47	2	no	—
833	C₂×C₄²	—	94	2	no	—
834	C₂×C₄²	—	94	2	no	—
835	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
836	#107	—	47	2	no	—
837	#107	—	47	2	no	—
838	#107	—	47	2	no	—
839	#107	C₂²×D₄₇	1	1	yes	characteristic
840	#107	C₂²×D₄₇	1	1	yes	characteristic
841	#106	—	47	2	no	—
842	#106	—	47	2	no	—
843	#106	—	47	2	no	—
844	#106	C₂²×D₄₇	1	1	yes	characteristic
845	#106	C₂²×D₄₇	1	1	yes	characteristic
846	C₄⋊C₈	—	47	2	no	—
847	C₄⋊C₈	—	47	2	no	—
848	C₄⋊C₈	—	47	1	no	—
849	C₄⋊C₈	—	47	1	no	—
850	#103	—	47	2	no	—
851	#103	—	47	2	no	—
852	#103	—	47	2	no	—
853	#103	—	47	2	no	—
854	#103	—	47	2	no	—
855	#103	—	47	2	no	—
856	#103	—	47	2	no	—
857	#103	C₂²×D₄₇	1	1	yes	characteristic
858	#103	C₂²×D₄₇	1	1	yes	characteristic
859	#103	C₂²×D₄₇	1	1	yes	characteristic
860	#103	C₂²×D₄₇	1	1	yes	characteristic
861	#103	C₂²×D₄₇	1	1	yes	characteristic
862	#103	C₂²×D₄₇	1	1	yes	characteristic
863	#102	—	47	2	no	—
864	#102	—	47	2	no	—
865	#102	—	47	2	no	—
866	#102	—	47	2	no	—
867	#102	—	47	2	no	—
868	#102	C₂²×D₄₇	1	1	yes	characteristic
869	#102	C₂²×D₄₇	1	1	yes	characteristic
870	C₂²⋊C₈	—	47	2	no	—
871	C₂²⋊C₈	—	47	2	no	—
872	C₂²⋊C₈	—	47	2	no	—
873	#97	—	47	2	no	—
874	#97	C₂²×D₄₇	1	1	yes	characteristic
875	#97	C₂²×D₄₇	1	1	yes	characteristic
876	C₄×C₈	—	47	2	no	—
877	C₄×C₈	—	47	2	no	—
878	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
879	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
880	#41	—	2	2	no	—
881	#41	—	4	1	no	—
882	#41	—	94	4	no	—
883	#41	—	188	2	no	—
884	#41	—	188	4	no	—
885	#41	—	188	4	no	—
886	#41	—	188	2	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	4	1	no	—
890	C₂×Q₈	—	47	1	no	—
891	C₂×Q₈	—	47	2	no	—
892	C₂×Q₈	—	94	2	no	—
893	C₂×Q₈	—	94	1	no	—
894	C₂×Q₈	—	94	1	no	—
895	C₂×Q₈	—	94	4	no	—
896	C₂×Q₈	—	188	2	no	—
897	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
898	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
899	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	47	2	no	—
902	C₂×D₄	—	47	1	no	—
903	C₂×D₄	—	47	2	no	—
904	C₂×D₄	—	94	2	no	—
905	C₂×D₄	—	94	2	no	—
906	C₂×D₄	—	94	2	no	—
907	C₂×D₄	—	94	2	no	—
908	C₂×D₄	—	94	1	no	—
909	C₂×D₄	—	94	1	no	—
910	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	47	2	no	—
917	C₂²×C₄	—	47	2	no	—
918	C₂²×C₄	—	47	2	no	—
919	C₂²×C₄	—	94	2	no	—
920	C₂²×C₄	—	94	2	no	—
921	C₂²×C₄	—	94	2	no	—
922	C₂²×C₄	—	94	2	no	—
923	C₂²×C₄	—	94	2	no	—
924	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
925	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
926	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
927	Q₁₆	—	2	2	no	—
928	Q₁₆	—	94	4	no	—
929	Q₁₆	—	188	2	no	—
930	Q₁₆	#10625350	1	4	yes	complemented
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	2	2	no	—
933	SD₁₆	—	94	4	no	—
934	SD₁₆	—	94	4	no	—
935	SD₁₆	—	188	2	no	—
936	D₈	—	188	2	no	—
937	M₁₆	—	2	2	no	—
938	M₁₆	—	4	1	no	—
939	M₁₆	—	94	4	no	—
940	M₁₆	—	188	2	no	—
941	C₂×C₈	—	47	2	no	—
942	C₂×C₈	—	47	2	no	—
943	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
944	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
946	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	47	2	no	—
955	C₄⋊C₄	—	47	2	no	—
956	C₄⋊C₄	—	47	1	no	—
957	C₄⋊C₄	—	47	1	no	—
958	C₄⋊C₄	—	47	2	no	—
959	C₄⋊C₄	—	47	2	no	—
960	C₄⋊C₄	—	94	2	no	—
961	C₄⋊C₄	—	94	2	no	—
962	C₄⋊C₄	—	94	2	no	—
963	C₄⋊C₄	—	94	2	no	—
964	C₄⋊C₄	—	94	2	no	—
965	C₄⋊C₄	—	94	2	no	—
966	C₄⋊C₄	—	94	2	no	—
967	C₄⋊C₄	—	94	2	no	—
968	C₄⋊C₄	—	94	2	no	—
969	C₄⋊C₄	—	94	2	no	—
970	C₄⋊C₄	—	94	2	no	—
971	C₄⋊C₄	—	94	2	no	—
972	C₄⋊C₄	—	94	1	no	—
973	C₄⋊C₄	—	94	1	no	—
974	C₄⋊C₄	—	94	1	no	—
975	C₄⋊C₄	—	94	1	no	—
976	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
979	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	47	2	no	—
984	C₂²⋊C₄	—	47	2	no	—
985	C₂²⋊C₄	—	47	2	no	—
986	C₂²⋊C₄	—	94	2	no	—
987	C₂²⋊C₄	—	94	2	no	—
988	C₂²⋊C₄	—	94	2	no	—
989	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	—	94	2	no	—
991	C₂²⋊C₄	—	94	2	no	—
992	C₂²⋊C₄	—	94	2	no	—
993	C₂²⋊C₄	—	94	2	no	—
994	C₂²⋊C₄	—	94	2	no	—
995	C₂²⋊C₄	—	94	2	no	—
996	C₂²⋊C₄	—	94	2	no	—
997	C₂²⋊C₄	—	94	2	no	—
998	C₂²⋊C₄	—	94	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	47	2	no	—
1007	C₄²	—	47	2	no	—
1008	C₄²	—	47	2	no	—
1009	C₄²	—	94	2	no	—
1010	C₄²	—	94	2	no	—
1011	C₄²	—	94	2	no	—
1012	C₄²	—	94	2	no	—
1013	C₄²	—	94	2	no	—
1014	C₄²	D₄×D₄₇	1	1	yes	characteristic
1015	C₄²	D₄×D₄₇	1	1	yes	characteristic
1016	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1017	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1018	C₂³	—	2	1	no	—
1019	C₂³	—	47	2	no	—
1020	C₂³	—	94	2	no	—
1021	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	94	2	no	—
1028	Q₈	—	94	2	no	—
1029	Q₈	—	94	2	no	—
1030	Q₈	—	188	4	no	—
1031	Q₈	—	188	2	no	—
1032	Q₈	—	188	2	no	—
1033	Q₈	C₂×#10625350	1	2	yes	—
1034	Q₈	C₂×#10625350	1	2	yes	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	94	2	no	—
1039	D₄	—	94	2	no	—
1040	D₄	—	94	2	no	—
1041	D₄	—	376	1	no	—
1042	D₄	—	376	2	no	—
1043	D₄	—	188	4	no	—
1044	D₄	—	188	2	no	—
1045	D₄	—	188	4	no	—
1046	D₄	—	188	4	no	—
1047	D₄	—	188	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	1	no	—
1064	C₂×C₄	—	47	2	no	—
1065	C₂×C₄	—	47	2	no	—
1066	C₂×C₄	—	47	2	no	—
1067	C₂×C₄	—	94	2	no	—
1068	C₂×C₄	—	94	2	no	—
1069	C₂×C₄	—	94	2	no	—
1070	C₂×C₄	—	94	2	no	—
1071	C₂×C₄	—	94	2	no	—
1072	C₂×C₄	—	376	2	no	—
1073	C₂×C₄	—	188	2	no	—
1074	C₂×C₄	—	188	2	no	—
1075	C₂×C₄	—	188	4	no	—
1076	C₂×C₄	—	188	4	no	—
1077	C₂×C₄	—	188	4	no	—
1078	C₂×C₄	—	188	4	no	—
1079	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1080	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1081	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1082	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1083	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1084	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1085	C₈	—	2	1	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	94	2	no	—
1089	C₈	—	94	2	no	—
1090	C₈	C₂×#10625350	1	2	yes	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	94	2	no	—
1098	C₂²	—	94	2	no	—
1099	C₂²	—	94	2	no	—
1100	C₂²	—	188	2	no	—
1101	C₂²	—	188	2	no	—
1102	C₂²	—	188	2	no	—
1103	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	94	2	no	—
1116	C₄	—	94	2	no	—
1117	C₄	—	94	2	no	—
1118	C₄	—	188	2	no	—
1119	C₄	—	188	2	no	—
1120	C₄	—	188	2	no	—
1121	C₄	#15689922	1	2	yes	—
1122	C₄	C₂²×#10625350	1	1	yes	characteristic
1123	C₄	#15689959	1	1	yes	characteristic
1124	C₂	—	4	1	no	—
1125	C₂	—	8	1	no	—
1126	C₂	—	376	2	no	—
1127	C₂	—	188	2	no	—
1128	C₂	D₄×#10625350	1	1	yes	characteristic
1129	C₂	C₂×#15689922	1	1	yes	characteristic
1130	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	C₄×#137×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×#137	D₄₇
hypocenter	C₄₇	#61467
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
1. #20257010	C₂	semidirect
2. #20256983	C₂	semidirect
3. #20256382	C₂	semidirect
4. #20256277	C₂	semidirect
5. #20256082	C₂	semidirect
6. #20256071	C₂	semidirect
7. #20255974	C₂	semidirect
8. #20255949	C₂	semidirect
9. #20255717	C₂	semidirect
10. #20255673	C₂	semidirect
11. #20255652	C₂	semidirect
12. #20255642	C₂	semidirect
13. #20255055	C₂	semidirect
14. #20255039	C₂	semidirect
15. #20254113	C₂	semidirect
16. #20254106	C₂	semidirect
17. #20253563	C₂	semidirect
18. #20253539	C₂	semidirect
19. #20253518	C₂	semidirect
20. #20253495	C₂	semidirect
21. #20252406	C₂	semidirect
22. #20252204	C₂	semidirect
23. C₄×#137×C₄₇	C₂	semidirect
362. Q₁₆×C₄₇	#41	semidirect
581. C₄×#137	D₄₇	semidirect
700. C₄₇	#61467	semidirect
930. Q₁₆	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257010	2
#20256983	2
#20256382	2
#20256277	2
#20256082	2
#20256071	2
#20255974	2
#20255949	2
#20255717	2
#20255673	2
#20255652	2
#20255642	2
#20255055	2
#20255039	2
#20254113	2
#20254106	2
#20253563	2
#20253539	2
#20253518	2
#20253495	2
#20252406	2
#20252204	2
C₄×#137×C₄₇	2
#61467	47