Subgroups — #13323391

Order 1792.

660 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737383	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#6481	C₂	1	1	yes	maximal, characteristic
4	C₇×#1584	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728710	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728687	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728658	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726322	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726316	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725985	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725984	C₂	1	1	yes	maximal, characteristic
12	#11725977	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725976	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725839	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725823	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6481	C₄	1	1	yes	characteristic
17	C₄×#1161	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₇	C₂²	1	1	yes	characteristic
19	C₇×#446	C₂²	1	1	yes	characteristic
20	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
21	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	#89956	C₄	1	1	yes	characteristic
23	C₄×#1144	C₂²	1	1	yes	characteristic
24	C₄×#1143	C₂²	1	1	yes	characteristic
25	#89796	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
27	#89661	C₄	1	1	yes	characteristic
28	#89653	C₄	1	1	yes	characteristic
29	#89610	C₂²	1	1	yes	characteristic
30	#89608	—	2	1	no	—
31	#89605	—	2	1	no	—
32	#89605	C₂²	1	1	yes	characteristic
33	D₇×C₄⋊C₈	—	2	1	no	—
34	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	#89602	—	2	1	no	—
36	#89602	C₂²	1	1	yes	characteristic
37	#89589	C₄	1	1	yes	characteristic
38	#89575	C₄	1	1	yes	characteristic
39	#89574	C₄	1	1	yes	characteristic
40	#89561	C₄	1	1	yes	characteristic
41	#89479	—	2	1	no	—
42	#89478	—	2	1	no	—
43	C₄×#1132	C₂²	1	1	yes	characteristic
44	#89460	C₂²	1	1	yes	characteristic
45	C₄×#1131	C₂²	1	1	yes	characteristic
46	#89457	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇	—	2	1	no	—
48	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
49	C₈×Dic₁₄	—	2	1	no	—
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
51	C₇×#335	C₂²	1	1	yes	characteristic
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×#322	C₂²	1	1	yes	characteristic
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89279	C₂²	1	1	yes	characteristic
58	#89278	C₂²	1	1	yes	characteristic
59	#89275	C₂²	1	1	yes	characteristic
60	#89274	C₂²	1	1	yes	characteristic
61	#89254	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic
63	#89251	C₂²	1	1	yes	characteristic
64	#89250	C₂²	1	1	yes	characteristic
65	#89250	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#17870	—	7	1	no	maximal, Sylow
68	C₂×#1161	C₂×C₄	1	1	yes	characteristic
69	C₂×Q₈×D₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
71	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
73	Q₈×Dic₇	C₂×C₄	1	1	yes	characteristic
74	Q₈×Dic₇	C₂×C₄	1	1	yes	characteristic
75	C₂×#1144	C₂×C₄	1	1	yes	characteristic
76	C₂×#1143	C₂×C₄	1	1	yes	characteristic
77	#6481	—	2	4	no	—
78	C₂×#1132	C₂×C₄	1	1	yes	characteristic
79	C₂×#1131	—	2	1	no	—
80	C₂×#1131	—	2	1	no	—
81	C₂×#1131	C₂×C₄	1	1	yes	characteristic
82	C₂×#1131	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₇	—	2	1	no	—
84	C₂×C₈×D₇	D₄	1	1	yes	characteristic
85	C₂×C₈×D₇	D₄	1	1	yes	characteristic
86	#6456	—	2	1	no	—
87	#6456	C₂×C₄	1	1	yes	characteristic
88	#6455	—	2	1	no	—
89	#6455	C₂×C₄	1	1	yes	characteristic
90	D₇×C₄⋊C₄	—	2	1	no	—
91	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	#6450	—	2	1	no	—
93	#6450	C₂×C₄	1	1	yes	characteristic
94	C₄×D₂₈	—	2	1	no	—
95	C₄×D₂₈	C₂³	1	1	yes	characteristic
96	C₄²×D₇	—	2	1	no	—
97	C₄²×D₇	—	2	1	no	—
98	C₄²×D₇	C₂³	1	1	yes	characteristic
99	C₄×Dic₁₄	—	2	1	no	—
100	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
101	C₇×#107	C₂×C₄	1	1	yes	characteristic
102	C₇×C₄⋊C₈	—	2	1	no	—
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×#103	C₂×C₄	1	1	yes	characteristic
107	C₇×#103	C₂×C₄	1	1	yes	characteristic
108	C₇×#97	—	2	1	no	—
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	#6409	C₂×C₄	1	1	yes	characteristic
114	#6409	C₂×C₄	1	1	yes	characteristic
115	#6395	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₇)⋊C₈	—	2	1	no	—
117	(C₂×D₇)⋊C₈	—	2	1	no	—
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	#6391	C₂×C₄	1	1	yes	characteristic
121	#6390	C₂×C₄	1	1	yes	characteristic
122	#6389	C₂×C₄	1	1	yes	characteristic
123	#6389	C₂×C₄	1	1	yes	characteristic
124	Dic₇⋊C₈	—	2	1	no	—
125	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	2	1	no	—
127	Dic₇⋊C₈	—	2	1	no	—
128	C₈×Dic₇	—	2	1	no	—
129	C₈×Dic₇	—	2	1	no	—
130	C₈×Dic₇	—	2	1	no	—
131	C₈×Dic₇	D₄	1	1	yes	characteristic
132	C₈×Dic₇	D₄	1	1	yes	characteristic
133	#6384	C₂×C₄	1	1	yes	characteristic
134	#6383	C₂×C₄	1	1	yes	characteristic
135	#6382	C₂×C₄	1	1	yes	characteristic
136	#6381	C₂×C₄	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	—	2	1	no	—
138	C₄⋊(C₇⋊C₈)	—	2	1	no	—
139	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
140	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
141	#6377	—	2	1	no	—
142	C₄×C₇⋊C₈	—	2	1	no	—
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
146	#2965	—	7	1	no	—
147	C₂×C₈×Q₈	—	7	1	no	—
148	C₄×#137	—	7	1	no	—
149	#1588	—	7	1	no	—
150	#1588	—	7	1	no	—
151	#1587	—	7	1	no	—
152	#1587	—	7	1	no	—
153	#1584	—	7	1	no	—
154	#1584	D₇	1	1	yes	characteristic, complemented
155	#1583	—	7	1	no	—
156	#1583	—	7	1	no	—
157	#1565	—	7	1	no	—
158	#1479	—	7	1	no	—
159	#1477	—	7	1	no	—
160	#1451	—	7	1	no	—
161	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	#1161	—	2	2	no	—
164	#1161	—	2	2	no	—
165	Q₈×D₇	—	2	2	no	—
166	Q₈×D₇	M₁₆	1	4	yes	complemented
167	C₂×D₂₈	—	2	1	no	—
168	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₇	—	2	1	no	—
170	C₂×C₄×D₇	—	2	1	no	—
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×D₇	#41	1	1	yes	characteristic
177	C₂×Dic₁₄	—	2	1	no	—
178	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
179	C₇×Q₁₆	—	2	2	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	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	C₂×D₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₇	—	2	1	no	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	C₂⁴	1	1	yes	characteristic
194	#1144	—	2	2	no	—
195	#1143	—	2	2	no	—
196	(C₂×D₇)⋊C₄	—	2	1	no	—
197	(C₂×D₇)⋊C₄	—	2	1	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	C₄⋊Dic₇	—	2	1	no	—
200	C₄⋊Dic₇	—	2	1	no	—
201	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
203	Dic₇⋊C₄	—	2	1	no	—
204	Dic₇⋊C₄	—	2	1	no	—
205	Dic₇⋊C₄	—	2	1	no	—
206	C₄×Dic₇	—	2	1	no	—
207	C₄×Dic₇	—	2	1	no	—
208	C₄×Dic₇	—	2	1	no	—
209	C₄×Dic₇	—	2	1	no	—
210	C₄×Dic₇	—	2	1	no	—
211	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
213	C₄×Dic₇	#41	1	1	yes	characteristic
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
221	#1132	—	2	2	no	—
222	#1131	—	2	2	no	—
223	#1131	—	2	2	no	—
224	#1131	—	4	2	no	—
225	#1131	—	4	2	no	—
226	C₈×D₇	—	2	2	no	—
227	C₈×D₇	—	4	1	no	—
228	C₈×D₇	—	4	2	no	—
229	C₂×#137	—	7	1	no	—
230	C₄×#41	—	7	1	no	—
231	C₂×C₄×Q₈	—	7	1	no	—
232	#446	—	7	1	no	—
233	#446	C₂×D₇	1	1	yes	characteristic
234	C₈×Q₈	—	7	1	no	—
235	C₈×Q₈	—	7	1	no	—
236	C₈×Q₈	—	7	1	no	—
237	C₈×Q₈	—	14	1	no	—
238	C₈×Q₈	—	14	1	no	—
239	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
240	#441	—	7	1	no	—
241	#441	—	7	1	no	—
242	#440	—	7	1	no	—
243	#440	—	7	1	no	—
244	C₄×Q₁₆	—	7	1	no	—
245	C₄×Q₁₆	C₂×D₇	1	1	yes	characteristic
246	C₄×SD₁₆	—	7	1	no	—
247	C₄×SD₁₆	—	7	1	no	—
248	#436	—	7	1	no	—
249	#436	—	7	1	no	—
250	#435	—	14	1	no	—
251	#435	—	14	1	no	—
252	#431	—	7	1	no	—
253	#431	—	7	1	no	—
254	#431	—	14	1	no	—
255	#428	—	7	1	no	—
256	C₂×C₄⋊C₈	—	7	1	no	—
257	C₂×C₄⋊C₈	—	14	1	no	—
258	#419	—	7	1	no	—
259	#417	—	7	1	no	—
260	C₄×M₁₆	—	7	1	no	—
261	C₄×M₁₆	—	14	1	no	—
262	C₂×C₄×C₈	—	7	1	no	—
263	C₂×C₄×C₈	—	14	1	no	—
264	#335	—	7	1	no	—
265	#335	C₂×D₇	1	1	yes	characteristic
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	Q₈⋊C₈	—	7	1	no	—
269	Q₈⋊C₈	—	7	1	no	—
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
273	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	#322	—	7	1	no	—
277	#322	—	7	1	no	—
278	#322	—	7	1	no	—
279	#322	C₂×D₇	1	1	yes	characteristic
280	C₂²×D₇	—	2	1	no	—
281	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
282	C₇×Q₈	—	2	1	no	—
283	C₇×Q₈	—	2	1	no	—
284	C₇×Q₈	—	2	1	no	—
285	C₇×Q₈	C₂×M₁₆	1	2	yes	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
293	C₂×Dic₇	—	2	1	no	—
294	C₂×Dic₇	—	2	1	no	—
295	C₂×Dic₇	—	2	1	no	—
296	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
297	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
298	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
299	D₂₈	—	2	1	no	—
300	D₂₈	—	2	1	no	—
301	D₂₈	—	4	2	no	—
302	C₄×D₇	—	2	4	no	—
303	C₄×D₇	—	2	1	no	—
304	C₄×D₇	—	2	1	no	—
305	C₄×D₇	—	4	1	no	—
306	C₄×D₇	—	4	2	no	—
307	C₄×D₇	—	4	2	no	—
308	C₄×D₇	—	4	1	no	—
309	C₄×D₇	—	4	1	no	—
310	C₄×D₇	—	4	2	no	—
311	C₄×D₇	C₂×M₁₆	1	2	yes	—
312	C₄×D₇	#131	1	2	yes	—
313	Dic₁₄	—	2	1	no	—
314	Dic₁₄	—	2	4	no	—
315	Dic₁₄	C₂×M₁₆	1	2	yes	—
316	C₇×C₈	—	2	1	no	—
317	C₇×C₈	—	2	1	no	—
318	C₇×C₈	—	2	1	no	—
319	C₇×C₈	—	4	1	no	—
320	C₇×C₈	—	4	1	no	—
321	C₇×C₈	—	4	1	no	—
322	C₇×C₈	#137	1	2	yes	complemented
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	—	4	1	no	—
329	C₇⋊C₈	—	4	1	no	—
330	C₂×#41	—	7	1	no	—
331	C₂²×Q₈	—	7	1	no	—
332	#137	—	14	4	no	—
333	C₂×Q₁₆	—	7	1	no	—
334	C₂×Q₁₆	C₄×D₇	1	1	yes	characteristic
335	C₂×SD₁₆	—	7	1	no	—
336	C₂×SD₁₆	—	7	1	no	—
337	C₂×M₁₆	—	7	1	no	—
338	C₂×M₁₆	—	7	1	no	—
339	C₂×M₁₆	—	14	1	no	—
340	C₂×M₁₆	—	14	1	no	—
341	C₂²×C₈	—	7	1	no	—
342	C₂²×C₈	—	7	1	no	—
343	C₂²×C₈	—	14	1	no	—
344	C₄×Q₈	—	7	1	no	—
345	C₄×Q₈	—	7	1	no	—
346	C₄×Q₈	—	7	1	no	—
347	C₄×Q₈	—	7	1	no	—
348	C₄×Q₈	—	14	1	no	—
349	C₄×Q₈	—	14	1	no	—
350	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
351	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
352	C₄×D₄	—	7	1	no	—
353	C₄×D₄	—	7	1	no	—
354	C₄×D₄	—	14	1	no	—
355	C₄×D₄	—	14	1	no	—
356	#117	—	7	1	no	—
357	#117	—	14	1	no	—
358	C₂×C₄⋊C₄	—	7	1	no	—
359	C₂×C₄⋊C₄	—	14	1	no	—
360	C₂×C₄²	—	7	1	no	—
361	C₂×C₄²	—	14	1	no	—
362	C₂×C₄²	—	14	1	no	—
363	#107	—	7	1	no	—
364	#107	C₄×D₇	1	1	yes	characteristic
365	#106	—	7	1	no	—
366	#106	—	7	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	7	1	no	—
370	C₄⋊C₈	—	7	1	no	—
371	C₄⋊C₈	—	14	1	no	—
372	C₄⋊C₈	—	14	1	no	—
373	C₄⋊C₈	—	14	1	no	—
374	C₄⋊C₈	—	14	1	no	—
375	C₄⋊C₈	—	14	1	no	—
376	C₄⋊C₈	—	14	1	no	—
377	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
378	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
379	#103	—	7	1	no	—
380	#103	—	7	1	no	—
381	#103	—	7	1	no	—
382	#103	—	7	1	no	—
383	#103	C₄×D₇	1	1	yes	characteristic
384	#103	C₄×D₇	1	1	yes	characteristic
385	#102	—	7	1	no	—
386	#102	—	7	1	no	—
387	C₂²⋊C₈	—	14	1	no	—
388	C₂²⋊C₈	—	14	1	no	—
389	C₂²⋊C₈	—	14	1	no	—
390	C₂²⋊C₈	—	14	1	no	—
391	#97	—	2	1	no	—
392	#97	—	7	1	no	—
393	#97	—	7	1	no	—
394	#97	—	14	1	no	—
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	—	7	1	no	—
397	C₄×C₈	—	7	1	no	—
398	C₄×C₈	—	7	1	no	—
399	C₄×C₈	—	7	1	no	—
400	C₄×C₈	—	7	1	no	—
401	C₄×C₈	—	14	1	no	—
402	C₄×C₈	—	14	1	no	—
403	C₄×C₈	—	14	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	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
409	C₂×D₇	—	2	1	no	—
410	C₂×D₇	—	2	1	no	—
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₂×D₇	—	4	1	no	—
414	C₂×D₇	#435	1	2	yes	—
415	C₄×C₇	—	2	2	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	—	4	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	—	4	1	no	—
420	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
421	C₄×C₇	C₂×#131	1	1	yes	characteristic
422	C₄×C₇	C₂×#137	1	1	yes	characteristic
423	C₄×C₇	#575	1	1	yes	characteristic
424	Dic₇	—	2	2	no	—
425	Dic₇	—	2	1	no	—
426	Dic₇	—	2	1	no	—
427	Dic₇	—	4	1	no	—
428	Dic₇	—	4	1	no	—
429	Dic₇	#435	1	2	yes	—
430	#41	—	14	2	no	—
431	#41	—	14	2	no	—
432	C₂×Q₈	—	7	4	no	—
433	C₂×Q₈	—	7	1	no	—
434	C₂×Q₈	—	14	1	no	—
435	C₂×Q₈	—	14	2	no	—
436	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
437	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
438	C₂×D₄	—	7	1	no	—
439	C₂×D₄	—	14	1	no	—
440	C₂²×C₄	—	7	1	no	—
441	C₂²×C₄	—	7	1	no	—
442	C₂²×C₄	—	7	1	no	—
443	C₂²×C₄	—	14	1	no	—
444	C₂²×C₄	—	14	1	no	—
445	C₂²×C₄	—	14	1	no	—
446	C₂²×C₄	—	14	1	no	—
447	C₂²×C₄	—	14	1	no	—
448	Q₁₆	—	2	2	no	—
449	Q₁₆	—	14	2	no	—
450	SD₁₆	—	14	2	no	—
451	SD₁₆	—	14	2	no	—
452	M₁₆	—	14	2	no	—
453	M₁₆	—	14	2	no	—
454	M₁₆	—	28	2	no	—
455	M₁₆	—	28	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	7	1	no	—
460	C₂×C₈	—	7	1	no	—
461	C₂×C₈	—	7	1	no	—
462	C₂×C₈	—	7	1	no	—
463	C₂×C₈	—	14	2	no	—
464	C₂×C₈	—	14	1	no	—
465	C₂×C₈	—	14	1	no	—
466	C₂×C₈	—	14	1	no	—
467	C₂×C₈	—	28	1	no	—
468	C₂×C₈	—	28	2	no	—
469	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
471	C₂×C₈	D₄×D₇	1	1	yes	characteristic
472	C₂×C₈	D₄×D₇	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	7	1	no	—
476	C₄⋊C₄	—	7	1	no	—
477	C₄⋊C₄	—	14	1	no	—
478	C₄⋊C₄	—	14	1	no	—
479	C₄⋊C₄	—	14	1	no	—
480	C₄⋊C₄	—	14	1	no	—
481	C₄⋊C₄	—	14	1	no	—
482	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
483	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
484	C₂²⋊C₄	—	14	1	no	—
485	C₂²⋊C₄	—	14	1	no	—
486	C₂²⋊C₄	—	14	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	7	1	no	—
490	C₄²	—	7	1	no	—
491	C₄²	—	7	1	no	—
492	C₄²	—	14	1	no	—
493	C₄²	—	14	1	no	—
494	C₄²	—	14	1	no	—
495	C₄²	—	14	1	no	—
496	C₄²	—	14	1	no	—
497	C₄²	C₂³×D₇	1	1	yes	characteristic
498	C₂×C₇	C₂×#435	1	1	yes	characteristic
499	C₂×C₇	C₄×#137	1	1	yes	characteristic
500	C₂×C₇	#2955	1	1	yes	characteristic
501	D₇	—	2	2	no	—
502	D₇	—	8	1	no	—
503	C₂³	—	7	1	no	—
504	C₂³	—	14	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	7	2	no	—
509	Q₈	—	14	4	no	—
510	Q₈	—	14	1	no	—
511	Q₈	D₇×M₁₆	1	2	yes	—
512	D₄	—	14	1	no	—
513	D₄	—	14	1	no	—
514	D₄	—	28	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	7	1	no	—
520	C₂×C₄	—	7	2	no	—
521	C₂×C₄	—	7	2	no	—
522	C₂×C₄	—	7	1	no	—
523	C₂×C₄	—	7	1	no	—
524	C₂×C₄	—	14	4	no	—
525	C₂×C₄	—	14	1	no	—
526	C₂×C₄	—	14	1	no	—
527	C₂×C₄	—	14	1	no	—
528	C₂×C₄	—	14	1	no	—
529	C₂×C₄	—	14	1	no	—
530	C₂×C₄	—	28	1	no	—
531	C₂×C₄	—	28	2	no	—
532	C₂×C₄	—	28	2	no	—
533	C₂×C₄	—	28	2	no	—
534	C₂×C₄	—	28	1	no	—
535	C₂×C₄	—	28	1	no	—
536	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
537	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
538	C₂×C₄	D₇×#41	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	14	1	no	—
546	C₈	—	14	1	no	—
547	C₈	—	14	1	no	—
548	C₈	—	14	1	no	—
549	C₈	—	28	1	no	—
550	C₈	—	28	1	no	—
551	C₈	—	28	1	no	—
552	C₈	#6481	1	2	yes	complemented
553	C₇	#17870	1	1	yes	characteristic, complemented, Sylow
554	C₂²	—	7	2	no	—
555	C₂²	—	14	1	no	—
556	C₂²	—	14	1	no	—
557	C₂²	—	28	1	no	—
558	C₂²	—	28	1	no	—
559	C₂²	—	28	1	no	—
560	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	7	2	no	—
567	C₄	—	14	1	no	—
568	C₄	—	14	2	no	—
569	C₄	—	14	1	no	—
570	C₄	—	28	1	no	—
571	C₄	—	28	1	no	—
572	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
573	C₄	D₇×#131	1	1	yes	characteristic
574	C₄	C₂×#6481	1	1	yes	characteristic
575	C₄	#90459	1	1	yes	characteristic
576	C₂	—	14	2	no	—
577	C₂	—	56	1	no	—
578	C₂	D₇×#435	1	1	yes	characteristic
579	C₂	C₄×#6481	1	1	yes	characteristic
580	C₂	#11737342	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#1584	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×#1161	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1584	D₇
hypocenter	C₇	#17870
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈×D₇	C₂	semidirect
4. C₇×#1584	C₂	semidirect
5. #11728710	C₂	semidirect
6. #11728687	C₂	semidirect
7. #11728658	C₂	semidirect
8. #11726322	C₂	semidirect
9. #11726316	C₂	semidirect
10. #11725985	C₂	semidirect
12. #11725977	C₂	semidirect
13. #11725976	C₂	semidirect
14. #11725839	C₂	semidirect
15. #11725823	C₂	semidirect
154. #1584	D₇	semidirect
166. Q₈×D₇	M₁₆	semidirect
322. C₇×C₈	#137	semidirect
552. C₈	#6481	semidirect
553. C₇	#17870	semidirect

Maximal subgroups

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

subgroup	index
#11737383	2
C₈×Q₈×D₇	2
C₄×#6481	2
C₇×#1584	2
#11728710	2
#11728687	2
#11728658	2
#11726322	2
#11726316	2
#11725985	2
#11725984	2
#11725977	2
#11725976	2
#11725839	2
#11725823	2
#17870	7