Subgroups — #13324430

Order 1792.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736740	C₂	1	1	yes	maximal, characteristic, complemented
2	#11736735	C₂	1	1	yes	maximal, characteristic, complemented
3	#11735977	C₂	1	1	yes	maximal, characteristic
4	C₇×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#11727605	C₂	1	1	yes	maximal, characteristic, complemented
6	#11727490	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727489	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725837	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725836	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725831	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725830	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725809	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#1132	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725806	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₅₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#90170	C₂²	1	1	yes	characteristic
17	#90168	C₂²	1	1	yes	characteristic
18	C₇×#431	C₂²	1	1	yes	characteristic
19	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
21	#89907	C₄	1	1	yes	characteristic
22	#89907	C₄	1	1	yes	characteristic
23	#89906	C₄	1	1	yes	characteristic
24	#89906	C₄	1	1	yes	characteristic
25	#89698	C₂²	1	1	yes	characteristic
26	#89696	C₂²	1	1	yes	characteristic
27	#89612	—	2	1	no	—
28	#89611	—	2	1	no	—
29	#89608	—	2	1	no	—
30	#89608	—	2	1	no	—
31	#89501	—	2	1	no	—
32	#89500	—	2	1	no	—
33	#89499	—	2	1	no	—
34	#89499	—	2	1	no	—
35	#89486	C₄	1	1	yes	characteristic
36	#89485	C₄	1	1	yes	characteristic
37	#89484	C₄	1	1	yes	characteristic
38	#89474	C₄	1	1	yes	characteristic
39	C₄×D₅₆	C₂²	1	1	yes	characteristic
40	C₄×D₅₆	C₂²	1	1	yes	characteristic
41	C₄×#1132	C₂²	1	1	yes	characteristic
42	C₄×#1132	C₂²	1	1	yes	characteristic
43	#89460	C₂²	1	1	yes	characteristic
44	#89460	C₂²	1	1	yes	characteristic
45	#89460	C₂²	1	1	yes	characteristic
46	C₈×D₂₈	C₂²	1	1	yes	characteristic
47	C₈×D₂₈	C₂²	1	1	yes	characteristic
48	C₈×D₂₈	C₂²	1	1	yes	characteristic
49	#89451	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
51	C₇×#322	C₂²	1	1	yes	characteristic
52	C₇×#322	C₂²	1	1	yes	characteristic
53	C₇×C₈²	C₂²	1	1	yes	characteristic
54	C₇×C₈²	C₂²	1	1	yes	characteristic
55	#89254	C₂²	1	1	yes	characteristic
56	#89254	C₂²	1	1	yes	characteristic
57	#89254	C₂²	1	1	yes	characteristic
58	#89254	C₂²	1	1	yes	characteristic
59	#89254	C₂²	1	1	yes	characteristic
60	#89254	C₂²	1	1	yes	characteristic
61	#89253	C₂²	1	1	yes	characteristic
62	#89253	C₂²	1	1	yes	characteristic
63	#89252	C₂²	1	1	yes	characteristic
64	#89252	C₂²	1	1	yes	characteristic
65	#89251	C₂²	1	1	yes	characteristic
66	#89251	C₂²	1	1	yes	characteristic
67	#17968	—	7	1	no	maximal, Sylow
68	C₂×#1157	—	2	1	no	—
69	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₇×C₈	—	2	1	no	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	#6493	—	2	1	no	—
74	#6493	C₂×C₄	1	1	yes	characteristic
75	#6493	C₂×C₄	1	1	yes	characteristic
76	#6493	C₂×C₄	1	1	yes	characteristic
77	#6492	—	2	1	no	—
78	C₄×C₂²⋊D₇	—	2	1	no	—
79	#6487	C₂×C₄	1	1	yes	characteristic
80	C₂×#1136	—	2	1	no	—
81	C₂×D₅₆	C₂×C₄	1	1	yes	characteristic
82	C₂×D₅₆	C₂×C₄	1	1	yes	characteristic
83	C₂×#1132	C₂×C₄	1	1	yes	characteristic
84	C₂×#1132	C₂×C₄	1	1	yes	characteristic
85	C₂×#1131	—	2	1	no	—
86	C₂×#1131	—	2	1	no	—
87	C₂×#1131	—	2	1	no	—
88	C₂×C₈×D₇	—	2	1	no	—
89	C₂×C₈×D₇	—	2	1	no	—
90	C₂×C₈×D₇	—	2	1	no	—
91	#6439	—	2	1	no	—
92	#6438	—	2	1	no	—
93	#6438	C₂×C₄	1	1	yes	characteristic
94	#6437	C₂×C₄	1	1	yes	characteristic
95	C₄×D₂₈	—	2	1	no	—
96	C₄×D₂₈	C₂³	1	1	yes	characteristic
97	C₄×D₂₈	C₂³	1	1	yes	characteristic
98	C₄×D₂₈	C₂³	1	1	yes	characteristic
99	#6435	—	2	1	no	—
100	#6433	C₂×C₄	1	1	yes	characteristic
101	#6432	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
105	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
106	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
107	C₇×#97	C₂×C₄	1	1	yes	characteristic
108	C₇×#97	C₂×C₄	1	1	yes	characteristic
109	C₄×C₇×C₈	—	2	1	no	—
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
117	#6395	C₂×C₄	1	1	yes	characteristic
118	#6395	C₂×C₄	1	1	yes	characteristic
119	#6395	C₂×C₄	1	1	yes	characteristic
120	#6395	C₂×C₄	1	1	yes	characteristic
121	#6395	C₂×C₄	1	1	yes	characteristic
122	#6395	C₂×C₄	1	1	yes	characteristic
123	(C₂×D₇)⋊C₈	—	2	1	no	—
124	(C₂×D₇)⋊C₈	—	2	1	no	—
125	(C₂×D₇)⋊C₈	—	2	1	no	—
126	(C₂×D₇)⋊C₈	—	2	1	no	—
127	(C₂×D₇)⋊C₈	—	2	1	no	—
128	(C₂×D₇)⋊C₈	—	2	1	no	—
129	#6392	C₂×C₄	1	1	yes	characteristic
130	#6392	C₂×C₄	1	1	yes	characteristic
131	#6391	C₂×C₄	1	1	yes	characteristic
132	#6391	C₂×C₄	1	1	yes	characteristic
133	#6390	C₂×C₄	1	1	yes	characteristic
134	#6390	C₂×C₄	1	1	yes	characteristic
135	#6389	—	2	1	no	—
136	Dic₇⋊C₈	—	2	1	no	—
137	Dic₇⋊C₈	—	2	1	no	—
138	C₈×Dic₇	—	2	1	no	—
139	C₄⋊(C₇⋊C₈)	—	2	1	no	—
140	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
141	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
142	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
143	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
144	#6377	—	2	1	no	—
145	#3171	—	7	1	no	—
146	#2993	—	7	1	no	—
147	#2981	—	7	1	no	—
148	#1594	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1590	—	7	1	no	—
151	#1589	—	7	1	no	—
152	#1580	—	7	1	no	—
153	SD₁₆⋊C₈	—	7	1	no	—
154	C₈×SD₁₆	—	7	1	no	—
155	C₈×D₈	—	7	1	no	—
156	#1569	—	7	1	no	—
157	#1494	—	7	1	no	—
158	#1492	—	7	1	no	—
159	C₈×M₁₆	D₇	1	1	yes	characteristic, complemented
160	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	#41	1	1	yes	characteristic
163	C₂×C₂²⋊D₇	—	2	1	no	—
164	C₂×C₂²⋊D₇	—	2	1	no	—
165	C₂×C₂²⋊D₇	—	2	1	no	—
166	#1157	—	8	1	no	—
167	#1157	—	8	1	no	—
168	C₂×D₂₈	—	2	1	no	—
169	C₂×D₂₈	—	2	1	no	—
170	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×C₄×D₇	—	2	1	no	—
175	C₂×C₄×D₇	—	2	1	no	—
176	C₂×Dic₁₄	—	2	1	no	—
177	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
178	C₇×M₁₆	—	2	2	no	—
179	C₇×M₁₆	—	2	2	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	4	2	no	—
183	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₇	#41	1	1	yes	characteristic
194	C₄²×C₇	C₂⁴	1	1	yes	characteristic
195	C₂²⋊Dic₇	—	2	1	no	—
196	(C₂×D₇)⋊C₄	—	2	1	no	—
197	(C₂×D₇)⋊C₄	—	2	1	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	(C₂×D₇)⋊C₄	—	2	1	no	—
200	(C₂×D₇)⋊C₄	—	2	1	no	—
201	(C₂×D₇)⋊C₄	—	2	1	no	—
202	(C₂×D₇)⋊C₄	—	2	1	no	—
203	(C₂×D₇)⋊C₄	—	2	1	no	—
204	C₄⋊Dic₇	—	2	1	no	—
205	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
207	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
209	Dic₇⋊C₄	—	2	1	no	—
210	Dic₇⋊C₄	—	2	1	no	—
211	Dic₇⋊C₄	—	2	1	no	—
212	Dic₇⋊C₄	—	2	1	no	—
213	C₄×Dic₇	—	2	1	no	—
214	#1136	—	8	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	D₅₆	—	2	2	no	—
220	D₅₆	—	2	2	no	—
221	#1132	—	2	2	no	—
222	#1132	—	2	2	no	—
223	#1131	—	8	1	no	—
224	#1131	—	8	1	no	—
225	#1131	—	8	1	no	—
226	C₈×D₇	—	8	1	no	—
227	C₈×D₇	—	8	1	no	—
228	C₈×D₇	—	8	1	no	—
229	#532	—	7	1	no	—
230	#529	—	7	1	no	—
231	#501	—	7	1	no	—
232	#496	—	7	1	no	—
233	#490	—	7	1	no	—
234	#489	—	7	1	no	—
235	#469	—	7	1	no	—
236	#469	—	7	1	no	—
237	#468	—	7	1	no	—
238	#468	—	7	1	no	—
239	#446	—	7	1	no	—
240	C₈×Q₈	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×D₈	—	7	1	no	—
244	C₄×D₈	—	7	1	no	—
245	#436	—	7	1	no	—
246	#436	—	7	1	no	—
247	#436	—	7	1	no	—
248	#436	—	14	1	no	—
249	#435	—	14	1	no	—
250	#435	—	14	1	no	—
251	#435	—	14	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	—	7	1	no	—
254	C₈×D₄	—	7	1	no	—
255	#433	—	14	1	no	—
256	#432	—	7	1	no	—
257	#431	C₂×D₇	1	1	yes	characteristic
258	#424	—	14	1	no	—
259	#423	—	7	1	no	—
260	#408	—	14	1	no	—
261	#408	—	14	1	no	—
262	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
264	#335	—	7	1	no	—
265	#335	—	7	1	no	—
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	Q₈⋊C₈	—	7	1	no	—
269	Q₈⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	—	7	1	no	—
272	D₄⋊C₈	—	7	1	no	—
273	D₄⋊C₈	—	7	1	no	—
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	#322	C₂×D₇	1	1	yes	characteristic
277	#322	C₂×D₇	1	1	yes	characteristic
278	C₈²	C₂×D₇	1	1	yes	characteristic
279	C₈²	C₂×D₇	1	1	yes	characteristic
280	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
281	C₂²×D₇	—	2	1	no	—
282	C₂²×D₇	—	2	1	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
290	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
295	C₂²⋊D₇	—	8	1	no	—
296	C₂²⋊D₇	—	8	1	no	—
297	C₂²⋊D₇	—	8	1	no	—
298	C₂×Dic₇	—	2	1	no	—
299	C₂×Dic₇	—	2	1	no	—
300	C₂×Dic₇	—	2	1	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	D₂₈	—	2	1	no	—
304	D₂₈	—	2	1	no	—
305	D₂₈	—	2	1	no	—
306	D₂₈	—	2	1	no	—
307	D₂₈	—	2	1	no	—
308	D₂₈	—	2	1	no	—
309	D₂₈	—	8	1	no	—
310	D₂₈	—	8	1	no	—
311	C₄×D₇	—	4	1	no	—
312	C₄×D₇	—	4	1	no	—
313	C₄×D₇	—	4	1	no	—
314	C₄×D₇	—	4	1	no	—
315	C₄×D₇	—	4	1	no	—
316	C₄×D₇	—	4	1	no	—
317	Dic₁₄	—	2	1	no	—
318	Dic₁₄	—	2	1	no	—
319	Dic₁₄	—	8	1	no	—
320	C₇×C₈	—	2	2	no	—
321	C₇×C₈	—	2	1	no	—
322	C₇×C₈	—	2	1	no	—
323	C₇×C₈	—	2	1	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	2	1	no	—
326	C₇×C₈	—	2	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇×C₈	#131	1	2	yes	—
329	C₇×C₈	#131	1	2	yes	—
330	C₇⋊C₈	—	4	1	no	—
331	C₇⋊C₈	—	4	1	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₂×#41	—	14	1	no	—
335	C₂×SD₁₆	—	7	1	no	—
336	C₂×SD₁₆	—	7	1	no	—
337	C₂×D₈	—	7	1	no	—
338	C₂×D₈	—	7	1	no	—
339	C₂×M₁₆	—	14	1	no	—
340	C₂×M₁₆	—	14	1	no	—
341	C₂×M₁₆	—	14	1	no	—
342	C₂×M₁₆	—	14	1	no	—
343	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
344	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	—	14	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₄⋊Q₈	—	7	1	no	—
350	#127	—	7	1	no	—
351	#126	—	14	1	no	—
352	#125	—	7	1	no	—
353	#124	—	7	1	no	—
354	#124	—	14	1	no	—
355	#123	—	14	1	no	—
356	C₂²⋊Q₈	—	7	1	no	—
357	#121	—	7	1	no	—
358	#121	—	7	1	no	—
359	#121	—	7	1	no	—
360	#121	—	14	1	no	—
361	C₄×Q₈	—	7	1	no	—
362	C₄×D₄	—	7	1	no	—
363	C₄×D₄	—	7	1	no	—
364	C₄×D₄	—	7	1	no	—
365	C₄×D₄	—	14	1	no	—
366	C₄×D₄	—	14	1	no	—
367	#117	—	14	1	no	—
368	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
369	#107	—	7	1	no	—
370	#107	—	7	1	no	—
371	#106	—	7	1	no	—
372	#106	—	7	1	no	—
373	C₄⋊C₈	—	7	1	no	—
374	C₄⋊C₈	—	7	1	no	—
375	C₄⋊C₈	—	7	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	14	1	no	—
378	C₄⋊C₈	—	14	1	no	—
379	C₄⋊C₈	—	14	1	no	—
380	C₄⋊C₈	D₂₈	1	1	yes	characteristic
381	C₄⋊C₈	D₂₈	1	1	yes	characteristic
382	#103	—	7	1	no	—
383	#103	—	7	1	no	—
384	#102	—	7	1	no	—
385	#102	—	7	1	no	—
386	#102	—	7	1	no	—
387	#102	—	7	1	no	—
388	#102	—	7	1	no	—
389	#102	—	7	1	no	—
390	C₂²⋊C₈	—	14	1	no	—
391	C₂²⋊C₈	—	14	1	no	—
392	C₂²⋊C₈	—	14	1	no	—
393	C₂²⋊C₈	—	14	1	no	—
394	C₂²⋊C₈	—	14	1	no	—
395	C₂²⋊C₈	—	14	1	no	—
396	C₂²⋊C₈	—	14	1	no	—
397	C₂²⋊C₈	D₂₈	1	1	yes	characteristic
398	C₂²⋊C₈	D₂₈	1	1	yes	characteristic
399	#97	—	14	1	no	—
400	#97	—	14	1	no	—
401	#97	C₄×D₇	1	1	yes	characteristic
402	#97	C₄×D₇	1	1	yes	characteristic
403	C₄×C₈	—	2	1	no	—
404	C₄×C₈	—	14	1	no	—
405	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
406	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
407	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
408	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
409	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
415	C₂×D₇	—	4	1	no	—
416	C₂×D₇	—	4	1	no	—
417	C₂×D₇	—	4	1	no	—
418	C₂×D₇	—	4	1	no	—
419	C₂×D₇	—	4	1	no	—
420	C₂×D₇	—	4	1	no	—
421	C₂×D₇	—	4	1	no	—
422	C₂×D₇	—	4	1	no	—
423	C₂×D₇	—	4	1	no	—
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	C₂×#131	1	1	yes	characteristic
429	C₄×C₇	C₂×#131	1	1	yes	characteristic
430	C₄×C₇	#576	1	1	yes	characteristic
431	C₄×C₇	#577	1	1	yes	characteristic
432	Dic₇	—	4	1	no	—
433	Dic₇	—	4	1	no	—
434	Dic₇	—	4	1	no	—
435	Dic₇	—	4	1	no	—
436	Dic₇	—	4	1	no	—
437	#41	—	56	1	no	—
438	#41	—	56	1	no	—
439	C₂×Q₈	—	7	1	no	—
440	C₂×Q₈	—	14	1	no	—
441	C₂×D₄	—	7	1	no	—
442	C₂×D₄	—	7	1	no	—
443	C₂×D₄	—	7	1	no	—
444	C₂×D₄	—	14	1	no	—
445	C₂×D₄	—	14	1	no	—
446	C₂×D₄	—	14	1	no	—
447	C₂×D₄	—	14	1	no	—
448	C₂×D₄	—	14	1	no	—
449	C₂²×C₄	—	14	1	no	—
450	C₂²×C₄	—	14	1	no	—
451	C₂²×C₄	—	14	1	no	—
452	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₂₈	1	1	yes	characteristic
454	C₂²×C₄	#1157	1	1	yes	characteristic
455	SD₁₆	—	14	2	no	—
456	SD₁₆	—	14	2	no	—
457	D₈	—	14	2	no	—
458	D₈	—	14	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	56	1	no	—
462	M₁₆	—	56	1	no	—
463	M₁₆	—	56	1	no	—
464	M₁₆	—	56	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	4	2	no	—
468	C₂×C₈	—	14	1	no	—
469	C₂×C₈	—	14	1	no	—
470	C₂×C₈	—	14	1	no	—
471	C₂×C₈	—	14	1	no	—
472	C₂×C₈	—	56	1	no	—
473	C₂×C₈	—	56	1	no	—
474	C₂×C₈	—	56	1	no	—
475	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
477	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
478	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
479	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
480	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
481	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
482	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	14	1	no	—
488	C₄⋊C₄	—	14	1	no	—
489	C₄⋊C₄	—	14	1	no	—
490	C₄⋊C₄	—	14	1	no	—
491	C₄⋊C₄	—	14	1	no	—
492	C₂²⋊C₄	—	14	1	no	—
493	C₂²⋊C₄	—	14	1	no	—
494	C₂²⋊C₄	—	14	1	no	—
495	C₂²⋊C₄	—	14	1	no	—
496	C₂²⋊C₄	—	14	1	no	—
497	C₂²⋊C₄	—	14	1	no	—
498	C₂²⋊C₄	—	14	1	no	—
499	C₂²⋊C₄	—	14	1	no	—
500	C₂²⋊C₄	—	14	1	no	—
501	C₄²	—	14	1	no	—
502	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
503	C₄²	C₂×D₂₈	1	1	yes	characteristic
504	C₄²	#1157	1	1	yes	characteristic
505	C₄²	C₂³×D₇	1	1	yes	characteristic
506	C₂×C₇	—	4	1	no	—
507	C₂×C₇	#2931	1	1	yes	characteristic
508	C₂×C₇	#2946	1	1	yes	characteristic
509	C₂×C₇	#2956	1	1	yes	characteristic
510	D₇	—	8	1	no	—
511	D₇	—	8	1	no	—
512	D₇	—	8	1	no	—
513	C₂³	—	14	1	no	—
514	C₂³	—	14	1	no	—
515	C₂³	—	14	1	no	—
516	C₂³	C₄×D₂₈	1	1	yes	characteristic
517	Q₈	—	14	1	no	—
518	Q₈	—	14	1	no	—
519	Q₈	—	56	1	no	—
520	D₄	—	14	1	no	—
521	D₄	—	14	1	no	—
522	D₄	—	14	1	no	—
523	D₄	—	14	1	no	—
524	D₄	—	14	1	no	—
525	D₄	—	14	1	no	—
526	D₄	—	56	1	no	—
527	D₄	—	56	1	no	—
528	D₄	—	56	1	no	—
529	D₄	—	56	1	no	—
530	D₄	—	56	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	14	1	no	—
537	C₂×C₄	—	14	1	no	—
538	C₂×C₄	—	14	1	no	—
539	C₂×C₄	—	14	1	no	—
540	C₂×C₄	—	14	1	no	—
541	C₂×C₄	—	28	1	no	—
542	C₂×C₄	—	28	1	no	—
543	C₂×C₄	—	28	1	no	—
544	C₂×C₄	—	28	1	no	—
545	C₂×C₄	—	28	1	no	—
546	C₂×C₄	—	28	1	no	—
547	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
548	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
549	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₂₈	1	1	yes	characteristic
552	C₂×C₄	C₂×#1157	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	28	1	no	—
562	C₈	—	28	1	no	—
563	C₈	—	28	1	no	—
564	C₈	—	28	1	no	—
565	C₈	#6464	1	2	yes	—
566	C₈	#6464	1	2	yes	—
567	C₇	#17968	1	1	yes	characteristic, complemented, Sylow
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	28	1	no	—
572	C₂²	—	28	1	no	—
573	C₂²	—	28	1	no	—
574	C₂²	—	28	1	no	—
575	C₂²	—	28	1	no	—
576	C₂²	—	28	1	no	—
577	C₂²	—	28	1	no	—
578	C₂²	—	28	1	no	—
579	C₂²	—	28	1	no	—
580	C₂²	C₂×C₄×D₂₈	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	28	1	no	—
586	C₄	—	28	1	no	—
587	C₄	—	28	1	no	—
588	C₄	—	28	1	no	—
589	C₄	—	28	1	no	—
590	C₄	C₂×#6464	1	1	yes	characteristic
591	C₄	C₂×#6464	1	1	yes	characteristic
592	C₄	#90442	1	1	yes	characteristic
593	C₄	#90443	1	1	yes	characteristic
594	C₂	—	4	1	no	—
595	C₂	—	56	1	no	—
596	C₂	—	56	1	no	—
597	C₂	—	56	1	no	—
598	C₂	#11735903	1	1	yes	characteristic
599	C₂	#11735986	1	1	yes	characteristic
600	C₂	#11736005	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₈
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×C₈×M₁₆	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#11735977	C₂
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₈×M₁₆	D₇
hypocenter	C₇	#17968
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
1. #11736740	C₂	semidirect
2. #11736735	C₂	semidirect
4. C₇×C₈×M₁₆	C₂	semidirect
5. #11727605	C₂	semidirect
6. #11727490	C₂	semidirect
7. #11727489	C₂	semidirect
8. #11725837	C₂	semidirect
9. #11725836	C₂	semidirect
10. #11725831	C₂	semidirect
11. #11725830	C₂	semidirect
12. #11725809	C₂	semidirect
13. C₈×#1132	C₂	semidirect
14. #11725806	C₂	semidirect
15. C₈×D₅₆	C₂	semidirect
159. C₈×M₁₆	D₇	semidirect
567. C₇	#17968	semidirect

Maximal subgroups

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

subgroup	index
#11736740	2
#11736735	2
#11735977	2
C₇×C₈×M₁₆	2
#11727605	2
#11727490	2
#11727489	2
#11725837	2
#11725836	2
#11725831	2
#11725830	2
#11725809	2
C₈×#1132	2
#11725806	2
C₈×D₅₆	2
#17968	7