Subgroups — #11744067

Order 896.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#90417	C₂	1	1	yes	maximal, characteristic, complemented
3	#90415	C₂	1	1	yes	maximal, characteristic, complemented
4	#90402	C₂	1	2	yes	maximal, complemented
5	#90400	C₂	1	2	yes	maximal, complemented
6	#90398	C₂	1	2	yes	maximal, complemented
7	#90395	C₂	1	2	yes	maximal, complemented
8	#90368	C₂	1	1	yes	maximal, characteristic, complemented
9	#90367	C₂	1	1	yes	maximal, characteristic, complemented
10	#90365	C₂	1	1	yes	maximal, characteristic, complemented
11	#90359	C₂	1	1	yes	maximal, characteristic, complemented
12	#90338	C₂	1	2	yes	maximal, complemented
13	#90335	C₂	1	2	yes	maximal, complemented
14	#90276	C₂	1	1	yes	maximal, characteristic, complemented
15	#90274	C₂	1	1	yes	maximal, characteristic, complemented
16	#90271	C₂	1	1	yes	maximal, characteristic, complemented
17	#90271	C₂	1	1	yes	maximal, characteristic, complemented
18	#90268	C₂	1	1	yes	maximal, characteristic, complemented
19	#90267	C₂	1	1	yes	maximal, characteristic, complemented
20	#90253	C₂	1	1	yes	maximal, characteristic, complemented
21	#90245	C₂	1	1	yes	maximal, characteristic, complemented
22	#90226	C₂	1	2	yes	maximal, complemented
23	#90218	C₂	1	2	yes	maximal, complemented
24	C₂×#1161	C₂²	1	1	yes	characteristic
25	C₂×#1161	C₂²	1	1	yes	characteristic
26	C₂×#1161	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#1159	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#126	C₂²	1	2	yes	complemented
32	C₇×#126	C₂²	1	2	yes	complemented
33	C₇×#124	C₂²	1	1	yes	characteristic
34	C₇×#124	C₂²	1	1	yes	characteristic
35	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₇×#117	C₂²	1	2	yes	complemented
41	#6510	C₂²	1	1	yes	characteristic
42	#6510	C₂²	1	1	yes	characteristic
43	#6510	C₂²	1	2	yes	complemented
44	#6509	C₂²	1	1	yes	characteristic
45	#6509	C₂²	1	1	yes	characteristic, complemented
46	#6509	C₂²	1	1	yes	characteristic, complemented
47	#6507	C₂²	1	1	yes	characteristic, complemented
48	#6503	C₂²	1	1	yes	characteristic
49	#6501	C₂²	1	1	yes	characteristic
50	#6493	C₂²	1	2	yes	—
51	#6493	C₂²	1	2	yes	complemented
52	#6492	C₂²	1	2	yes	complemented
53	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
54	#6461	C₂²	1	2	yes	—
55	#6461	C₂²	1	1	yes	characteristic
56	#6461	C₂²	1	2	yes	complemented
57	#6461	C₂²	1	1	yes	characteristic, complemented
58	#6460	C₂²	1	1	yes	characteristic
59	#6460	C₂²	1	2	yes	complemented
60	#6459	C₂²	1	2	yes	complemented
61	#6459	C₂²	1	2	yes	complemented
62	#6458	C₂²	1	2	yes	—
63	#6458	C₂²	1	1	yes	characteristic
64	#6458	C₂²	1	2	yes	—
65	#6458	C₂²	1	1	yes	characteristic
66	#6458	C₂²	1	2	yes	complemented
67	#6458	C₂²	1	2	yes	complemented
68	#6458	C₂²	1	1	yes	characteristic, complemented
69	#6457	C₂²	1	1	yes	characteristic
70	#6457	C₂²	1	2	yes	—
71	#6457	C₂²	1	2	yes	complemented
72	#6457	C₂²	1	2	yes	complemented
73	#6457	C₂²	1	2	yes	complemented
74	#6457	C₂²	1	2	yes	complemented
75	#6457	C₂²	1	2	yes	complemented
76	#6457	C₂²	1	2	yes	complemented
77	#6457	C₂²	1	1	yes	characteristic, complemented
78	#6456	C₂²	1	2	yes	complemented
79	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
80	#6453	C₂²	1	1	yes	characteristic, complemented
81	#6453	C₂²	1	1	yes	characteristic, complemented
82	#6452	C₂²	1	2	yes	complemented
83	#6449	C₂²	1	2	yes	—
84	#6448	C₂²	1	2	yes	complemented
85	#6447	C₂²	1	2	yes	—
86	#6447	C₂²	1	2	yes	—
87	#6447	C₂²	1	2	yes	—
88	#6447	C₂²	1	2	yes	complemented
89	#6447	C₂²	1	2	yes	complemented
90	#6447	C₂²	1	2	yes	complemented
91	#6447	C₂²	1	2	yes	complemented
92	#6446	C₂²	1	2	yes	—
93	#6446	C₂²	1	2	yes	complemented
94	#6445	C₂²	1	2	yes	—
95	#6445	C₂²	1	2	yes	—
96	#6445	C₂²	1	2	yes	—
97	#6445	C₂²	1	2	yes	—
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
100	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
101	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
102	#6441	C₂²	1	2	yes	complemented
103	#6439	C₂²	1	2	yes	—
104	#6438	C₂²	1	2	yes	—
105	#6438	C₂²	1	1	yes	characteristic
106	#6438	C₂²	1	1	yes	characteristic, complemented
107	#6437	C₂²	1	1	yes	characteristic
108	#6437	C₂²	1	2	yes	complemented
109	C₄×D₂₈	C₂²	1	1	yes	characteristic
110	C₄×D₂₈	C₂²	1	1	yes	characteristic
111	C₄×D₂₈	C₂²	1	1	yes	characteristic
112	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₂₈	C₂²	1	2	yes	complemented
114	C₄×D₂₈	C₂²	1	2	yes	complemented
115	C₄×D₂₈	C₂²	1	2	yes	complemented
116	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
117	#6435	C₂²	1	1	yes	characteristic
118	#6435	C₂²	1	2	yes	complemented
119	#6435	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
121	#6433	C₂²	1	2	yes	complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3562	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
135	C₂²×Dic₇	C₂³	1	2	yes	—
136	#1161	—	4	2	no	—
137	#1161	—	4	2	no	—
138	#1161	—	4	2	no	—
139	Q₈×D₇	—	4	2	no	—
140	#1159	—	4	2	no	—
141	D₄×D₇	—	4	2	no	—
142	C₂×D₂₈	C₂³	1	1	yes	characteristic
143	C₂×D₂₈	C₂³	1	1	yes	characteristic
144	C₂×D₂₈	C₂³	1	1	yes	characteristic
145	C₂×D₂₈	C₂³	1	1	yes	characteristic
146	C₂×D₂₈	C₂³	1	2	yes	—
147	C₂×D₂₈	C₂³	1	1	yes	characteristic
148	C₂×D₂₈	C₂³	1	2	yes	—
149	C₂×D₂₈	C₂³	1	2	yes	—
150	C₂×D₂₈	C₂³	1	2	yes	—
151	C₂×D₂₈	C₂³	1	2	yes	—
152	C₂×D₂₈	C₂³	1	2	yes	—
153	C₂×D₂₈	C₂³	1	2	yes	—
154	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₇	C₂³	1	2	yes	—
160	C₂×C₄×D₇	C₂³	1	2	yes	—
161	C₂×C₄×D₇	C₂³	1	2	yes	—
162	C₂×C₄×D₇	C₂³	1	2	yes	—
163	C₂×C₄×D₇	C₂³	1	2	yes	—
164	C₂×C₄×D₇	C₂³	1	2	yes	—
165	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₄	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₄²×C₇	C₂³	1	2	yes	—
182	C₄²×C₇	C₂³	1	1	yes	characteristic
183	C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₄²×C₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₇	C₂³	1	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
209	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₇	C₂³	1	2	yes	—
211	C₄⋊Dic₇	C₂³	1	2	yes	—
212	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₇⋊C₄	C₂³	1	2	yes	—
218	Dic₇⋊C₄	C₂³	1	2	yes	—
219	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	Dic₇⋊C₄	C₂³	1	2	yes	—
222	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₇⋊C₄	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	2	yes	—
226	C₄×Dic₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₇	C₂³	1	1	yes	characteristic
229	#562	—	7	2	no	—
230	#560	—	7	2	no	—
231	#559	—	7	1	no	—
232	#556	D₇	1	1	yes	characteristic, complemented
233	#553	—	7	2	no	—
234	#551	—	7	2	no	—
235	#550	—	7	1	no	—
236	#548	—	7	1	no	—
237	#548	—	7	1	no	—
238	#547	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	1	no	—
241	#541	—	7	1	no	—
242	#540	—	7	1	no	—
243	#540	—	7	2	no	—
244	#539	—	7	2	no	—
245	#538	—	7	2	no	—
246	#538	—	7	2	no	—
247	#536	—	7	1	no	—
248	#535	—	7	1	no	—
249	#532	—	7	1	no	—
250	#529	—	7	1	no	—
251	#529	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	2	yes	—
253	C₂²×D₇	—	4	2	no	—
254	C₂²×D₇	—	4	2	no	—
255	C₂²×D₇	—	4	2	no	—
256	C₂²×D₇	C₂⁴	1	1	yes	characteristic
257	C₂²×D₇	C₂⁴	1	2	yes	—
258	C₂²×D₇	C₂⁴	1	1	yes	characteristic
259	C₂²×D₇	C₂⁴	1	1	yes	characteristic
260	C₂²×D₇	C₂⁴	1	2	yes	—
261	C₇×Q₈	—	2	2	no	—
262	C₇×Q₈	—	2	2	no	—
263	C₇×Q₈	—	4	1	no	—
264	C₇×D₄	—	2	2	no	—
265	C₂×C₄×C₇	—	4	2	no	—
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂×C₄×C₇	C₂⁴	1	2	yes	—
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂²⋊D₇	—	4	2	no	—
277	C₂²⋊D₇	—	4	2	no	—
278	C₂²⋊D₇	—	4	2	no	—
279	C₂²⋊D₇	—	4	2	no	—
280	C₂²⋊D₇	—	4	2	no	—
281	C₂×Dic₇	—	4	2	no	—
282	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₇	C₂⁴	1	2	yes	—
286	C₂×Dic₇	C₂⁴	1	2	yes	—
287	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
289	D₂₈	—	2	2	no	—
290	D₂₈	—	2	2	no	—
291	D₂₈	—	4	1	no	—
292	D₂₈	—	4	1	no	—
293	D₂₈	—	4	1	no	—
294	D₂₈	—	4	2	no	—
295	D₂₈	—	4	2	no	—
296	D₂₈	—	4	2	no	—
297	D₂₈	—	4	2	no	—
298	D₂₈	—	4	2	no	—
299	D₂₈	—	4	2	no	—
300	D₂₈	—	4	2	no	—
301	C₄×D₇	—	2	2	no	—
302	C₄×D₇	—	2	2	no	—
303	C₄×D₇	—	2	2	no	—
304	C₄×D₇	—	4	2	no	—
305	C₄×D₇	—	4	2	no	—
306	C₄×D₇	—	4	1	no	—
307	C₄×D₇	—	4	1	no	—
308	C₄×D₇	—	4	2	no	—
309	C₄×D₇	—	4	2	no	—
310	C₄×D₇	—	4	2	no	—
311	C₄×D₇	—	4	2	no	—
312	Dic₁₄	—	2	2	no	—
313	Dic₁₄	—	4	2	no	—
314	C₂×#41	—	7	1	no	—
315	C₂×#41	—	7	1	no	—
316	C₂×#41	—	7	1	no	—
317	C₂×#41	—	7	1	no	—
318	C₂²×Q₈	—	7	1	no	—
319	C₂²×D₄	—	7	1	no	—
320	C₄⋊Q₈	—	7	1	no	—
321	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
322	#127	—	7	1	no	—
323	#127	—	7	1	no	—
324	#127	—	7	2	no	—
325	#126	—	7	2	no	—
326	#126	—	7	1	no	—
327	#126	—	7	1	no	—
328	#126	—	7	2	no	—
329	#126	—	7	2	no	—
330	#126	C₂×D₇	1	2	yes	complemented
331	#126	C₂×D₇	1	2	yes	complemented
332	#125	—	7	1	no	—
333	#125	—	7	1	no	—
334	#125	—	7	2	no	—
335	#125	—	7	2	no	—
336	#124	—	7	1	no	—
337	#124	—	7	1	no	—
338	#124	—	7	2	no	—
339	#124	—	7	2	no	—
340	#124	—	7	1	no	—
341	#124	—	7	1	no	—
342	#124	—	7	2	no	—
343	#124	C₂×D₇	1	1	yes	characteristic
344	#124	C₂×D₇	1	1	yes	characteristic
345	#123	—	7	2	no	—
346	#123	—	7	1	no	—
347	#123	—	7	1	no	—
348	#123	—	7	2	no	—
349	#123	—	7	2	no	—
350	#123	—	7	2	no	—
351	#123	—	7	2	no	—
352	#123	—	7	2	no	—
353	#123	—	7	2	no	—
354	#123	—	7	2	no	—
355	#123	—	7	2	no	—
356	#123	—	7	2	no	—
357	#123	—	7	2	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	1	no	—
360	C₂²⋊Q₈	—	7	1	no	—
361	C₂²⋊Q₈	—	7	2	no	—
362	C₂²⋊Q₈	—	7	2	no	—
363	C₂²⋊Q₈	—	7	2	no	—
364	C₂²⋊Q₈	—	7	1	no	—
365	C₂²⋊Q₈	—	7	2	no	—
366	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
367	#121	—	7	1	no	—
368	#121	—	7	2	no	—
369	#121	—	7	2	no	—
370	#121	—	7	1	no	—
371	#121	—	7	1	no	—
372	#121	—	7	2	no	—
373	#121	—	7	2	no	—
374	#121	—	7	2	no	—
375	#121	—	7	2	no	—
376	#121	—	7	1	no	—
377	#121	—	7	2	no	—
378	#121	—	7	2	no	—
379	#121	—	7	2	no	—
380	#121	—	7	2	no	—
381	#121	—	7	2	no	—
382	#121	—	7	2	no	—
383	#121	—	7	2	no	—
384	#120	—	7	2	no	—
385	#120	—	7	2	no	—
386	#120	—	7	2	no	—
387	#120	—	7	2	no	—
388	C₄×Q₈	—	7	1	no	—
389	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
390	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
391	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
392	C₄×D₄	—	7	2	no	—
393	C₄×D₄	—	7	2	no	—
394	C₄×D₄	—	7	2	no	—
395	C₄×D₄	—	7	2	no	—
396	C₄×D₄	—	7	2	no	—
397	C₄×D₄	—	7	1	no	—
398	C₄×D₄	—	7	1	no	—
399	C₄×D₄	—	7	1	no	—
400	C₄×D₄	—	7	1	no	—
401	C₄×D₄	—	7	2	no	—
402	C₄×D₄	—	7	1	no	—
403	C₄×D₄	—	7	2	no	—
404	C₄×D₄	C₂×D₇	1	1	yes	characteristic
405	#117	—	7	1	no	—
406	#117	—	7	1	no	—
407	#117	—	7	2	no	—
408	#117	C₂×D₇	1	2	yes	complemented
409	C₂×C₄⋊C₄	—	7	2	no	—
410	C₂×C₂²⋊C₄	—	7	2	no	—
411	C₂×C₂²⋊C₄	—	7	2	no	—
412	C₂×C₄²	—	7	1	no	—
413	C₂²×C₇	—	2	2	no	—
414	C₂²×C₇	—	2	2	no	—
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	C₂⁵	1	1	yes	characteristic
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	2	1	no	—
419	C₂×D₇	—	2	1	no	—
420	C₂×D₇	—	2	2	no	—
421	C₂×D₇	—	2	2	no	—
422	C₂×D₇	—	2	1	no	—
423	C₂×D₇	—	2	1	no	—
424	C₂×D₇	—	2	2	no	—
425	C₂×D₇	—	2	2	no	—
426	C₂×D₇	—	2	1	no	—
427	C₂×D₇	—	2	2	no	—
428	C₂×D₇	—	2	2	no	—
429	C₂×D₇	—	2	1	no	—
430	C₂×D₇	—	2	1	no	—
431	C₂×D₇	—	2	1	no	—
432	C₂×D₇	—	8	4	no	—
433	C₄×C₇	—	2	2	no	—
434	C₄×C₇	—	2	2	no	—
435	C₄×C₇	—	2	1	no	—
436	C₄×C₇	—	2	1	no	—
437	C₄×C₇	—	2	1	no	—
438	C₄×C₇	—	2	1	no	—
439	C₄×C₇	—	2	2	no	—
440	C₄×C₇	—	2	1	no	—
441	C₄×C₇	—	2	1	no	—
442	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
443	Dic₇	—	2	2	no	—
444	Dic₇	—	2	1	no	—
445	Dic₇	—	2	1	no	—
446	Dic₇	—	2	1	no	—
447	Dic₇	—	2	2	no	—
448	Dic₇	—	2	1	no	—
449	Dic₇	—	2	1	no	—
450	C₂⁴	—	7	2	no	—
451	#41	—	28	2	no	—
452	#41	—	28	2	no	—
453	#41	—	28	2	no	—
454	#41	—	28	2	no	—
455	C₂×Q₈	—	7	1	no	—
456	C₂×Q₈	—	7	2	no	—
457	C₂×Q₈	—	28	2	no	—
458	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
459	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
460	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
461	C₂×D₄	—	7	2	no	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	7	2	no	—
464	C₂×D₄	—	7	2	no	—
465	C₂×D₄	—	7	2	no	—
466	C₂×D₄	—	7	1	no	—
467	C₂×D₄	—	7	1	no	—
468	C₂×D₄	—	7	1	no	—
469	C₂×D₄	—	7	1	no	—
470	C₂×D₄	—	7	2	no	—
471	C₂×D₄	—	7	2	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	7	2	no	—
474	C₂×D₄	—	7	1	no	—
475	C₂×D₄	—	7	2	no	—
476	C₂×D₄	—	7	2	no	—
477	C₂×D₄	—	7	2	no	—
478	C₂×D₄	—	28	2	no	—
479	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
480	C₂²×C₄	—	7	2	no	—
481	C₂²×C₄	—	7	1	no	—
482	C₂²×C₄	—	7	1	no	—
483	C₂²×C₄	—	7	1	no	—
484	C₂²×C₄	—	7	1	no	—
485	C₂²×C₄	—	7	1	no	—
486	C₂²×C₄	—	7	2	no	—
487	C₂²×C₄	—	7	2	no	—
488	C₂²×C₄	—	7	2	no	—
489	C₂²×C₄	—	7	2	no	—
490	C₂²×C₄	—	7	2	no	—
491	C₂²×C₄	—	7	2	no	—
492	C₂²×C₄	C₂²×D₇	1	2	yes	—
493	C₄⋊C₄	—	7	2	no	—
494	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	1	no	—
496	C₄⋊C₄	—	7	1	no	—
497	C₄⋊C₄	—	7	2	no	—
498	C₄⋊C₄	—	7	1	no	—
499	C₄⋊C₄	—	7	1	no	—
500	C₄⋊C₄	—	7	2	no	—
501	C₄⋊C₄	—	7	2	no	—
502	C₄⋊C₄	—	7	2	no	—
503	C₄⋊C₄	—	7	1	no	—
504	C₄⋊C₄	—	7	1	no	—
505	C₄⋊C₄	—	7	1	no	—
506	C₄⋊C₄	—	7	2	no	—
507	C₄⋊C₄	—	7	2	no	—
508	C₄⋊C₄	—	7	1	no	—
509	C₄⋊C₄	C₂²×D₇	1	2	yes	—
510	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	—	7	1	no	—
519	C₂²⋊C₄	—	7	1	no	—
520	C₂²⋊C₄	—	7	2	no	—
521	C₂²⋊C₄	—	7	2	no	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	1	no	—
525	C₂²⋊C₄	—	7	1	no	—
526	C₂²⋊C₄	—	7	2	no	—
527	C₂²⋊C₄	—	7	1	no	—
528	C₂²⋊C₄	—	7	1	no	—
529	C₂²⋊C₄	—	7	1	no	—
530	C₂²⋊C₄	—	7	1	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	2	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	2	no	—
535	C₂²⋊C₄	—	7	1	no	—
536	C₂²⋊C₄	—	7	2	no	—
537	C₂²⋊C₄	—	7	2	no	—
538	C₂²⋊C₄	—	7	2	no	—
539	C₂²⋊C₄	—	7	1	no	—
540	C₂²⋊C₄	—	7	2	no	—
541	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
546	C₄²	—	7	1	no	—
547	C₄²	—	7	1	no	—
548	C₄²	—	7	1	no	—
549	C₄²	—	7	2	no	—
550	C₄²	C₂²×D₇	1	1	yes	characteristic
551	C₄²	C₂²×D₇	1	2	yes	—
552	C₄²	C₂²×D₇	1	1	yes	characteristic
553	C₄²	C₂²×D₇	1	1	yes	characteristic
554	C₄²	C₂²×D₇	1	2	yes	—
555	C₂×C₇	—	4	2	no	—
556	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂×C₇	#585	1	1	yes	characteristic
558	C₂×C₇	#585	1	1	yes	characteristic
559	D₇	—	4	1	no	—
560	D₇	—	4	1	no	—
561	D₇	—	4	2	no	—
562	D₇	—	4	2	no	—
563	D₇	—	4	1	no	—
564	C₂³	—	7	1	no	—
565	C₂³	—	7	2	no	—
566	C₂³	—	7	1	no	—
567	C₂³	—	7	1	no	—
568	C₂³	—	7	2	no	—
569	C₂³	—	28	2	no	—
570	C₂³	—	28	2	no	—
571	C₂³	—	28	2	no	—
572	C₂³	C₂³×D₇	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	14	2	no	—
577	Q₈	—	28	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	14	2	no	—
580	D₄	—	14	2	no	—
581	D₄	—	28	2	no	—
582	D₄	—	28	2	no	—
583	D₄	—	28	1	no	—
584	D₄	—	28	2	no	—
585	D₄	—	28	1	no	—
586	D₄	—	28	2	no	—
587	D₄	—	28	1	no	—
588	D₄	—	28	2	no	—
589	D₄	—	28	2	no	—
590	D₄	—	28	2	no	—
591	D₄	—	28	2	no	—
592	D₄	—	28	2	no	—
593	D₄	—	28	2	no	—
594	D₄	—	28	2	no	—
595	D₄	—	28	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	7	1	no	—
598	C₂×C₄	—	7	1	no	—
599	C₂×C₄	—	7	1	no	—
600	C₂×C₄	—	7	2	no	—
601	C₂×C₄	—	7	2	no	—
602	C₂×C₄	—	7	1	no	—
603	C₂×C₄	—	7	1	no	—
604	C₂×C₄	—	14	2	no	—
605	C₂×C₄	—	14	2	no	—
606	C₂×C₄	—	14	2	no	—
607	C₂×C₄	—	28	1	no	—
608	C₂×C₄	—	28	2	no	—
609	C₂×C₄	—	28	1	no	—
610	C₂×C₄	—	28	2	no	—
611	C₂×C₄	—	28	2	no	—
612	C₂×C₄	—	28	2	no	—
613	C₂×C₄	—	28	2	no	—
614	C₂×C₄	—	28	2	no	—
615	C₂×C₄	—	28	2	no	—
616	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₇	1	2	yes	—
621	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₇	1	2	yes	—
624	C₂×C₄	C₂³×D₇	1	2	yes	—
625	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
626	C₇	#3562	1	1	yes	characteristic, complemented, Sylow
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	14	1	no	—
631	C₂²	—	14	1	no	—
632	C₂²	—	14	1	no	—
633	C₂²	—	14	2	no	—
634	C₂²	—	14	2	no	—
635	C₂²	—	14	1	no	—
636	C₂²	—	14	1	no	—
637	C₂²	—	14	2	no	—
638	C₂²	—	14	2	no	—
639	C₂²	—	14	1	no	—
640	C₂²	—	14	1	no	—
641	C₂²	—	14	2	no	—
642	C₂²	—	14	2	no	—
643	C₂²	—	14	1	no	—
644	C₂²	—	14	1	no	—
645	C₂²	—	56	4	no	—
646	C₂²	C₂⁴×D₇	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	14	1	no	—
657	C₄	—	14	1	no	—
658	C₄	—	14	1	no	—
659	C₄	—	14	2	no	—
660	C₄	—	14	1	no	—
661	C₄	—	14	2	no	—
662	C₄	—	14	1	no	—
663	C₄	#6553	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	28	1	no	—
666	C₂	—	28	2	no	—
667	C₂	—	28	1	no	—
668	C₂	—	28	1	no	—
669	C₂	—	28	2	no	—
670	C₂	C₂×#6553	1	1	yes	characteristic
671	C₂	#90616	1	1	yes	characteristic
672	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#556	C₂
hypercenter	#556	D₇
hypocenter	C₇	#3562
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₇×#556	C₂	semidirect
2. #90417	C₂	semidirect
3. #90415	C₂	semidirect
4. #90402	C₂	semidirect
5. #90400	C₂	semidirect
6. #90398	C₂	semidirect
7. #90395	C₂	semidirect
8. #90368	C₂	semidirect
9. #90367	C₂	semidirect
10. #90365	C₂	semidirect
11. #90359	C₂	semidirect
12. #90338	C₂	semidirect
13. #90335	C₂	semidirect
14. #90276	C₂	semidirect
15. #90274	C₂	semidirect
16. #90271	C₂	semidirect
17. #90271	C₂	semidirect
18. #90268	C₂	semidirect
19. #90267	C₂	semidirect
20. #90253	C₂	semidirect
21. #90245	C₂	semidirect
22. #90226	C₂	semidirect
23. #90218	C₂	semidirect
26. C₂×#1161	C₂²	semidirect
27. C₂×Q₈×D₇	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×#126	C₂²	semidirect
32. C₇×#126	C₂²	semidirect
35. C₇×C₂²⋊Q₈	C₂²	semidirect
36. C₄×C₇×Q₈	C₂²	semidirect
37. C₄×C₇×Q₈	C₂²	semidirect
38. C₄×C₇×Q₈	C₂²	semidirect
40. C₇×#117	C₂²	semidirect
43. #6510	C₂²	semidirect
45. #6509	C₂²	semidirect
46. #6509	C₂²	semidirect
47. #6507	C₂²	semidirect
51. #6493	C₂²	semidirect
52. #6492	C₂²	semidirect
56. #6461	C₂²	semidirect
57. #6461	C₂²	semidirect
59. #6460	C₂²	semidirect
60. #6459	C₂²	semidirect
61. #6459	C₂²	semidirect
66. #6458	C₂²	semidirect
67. #6458	C₂²	semidirect
68. #6458	C₂²	semidirect
71. #6457	C₂²	semidirect
72. #6457	C₂²	semidirect
73. #6457	C₂²	semidirect
74. #6457	C₂²	semidirect
75. #6457	C₂²	semidirect
76. #6457	C₂²	semidirect
77. #6457	C₂²	semidirect
78. #6456	C₂²	semidirect
79. D₇×C₄⋊C₄	C₂²	semidirect
80. #6453	C₂²	semidirect
81. #6453	C₂²	semidirect
82. #6452	C₂²	semidirect
84. #6448	C₂²	semidirect
88. #6447	C₂²	semidirect
89. #6447	C₂²	semidirect
90. #6447	C₂²	semidirect
91. #6447	C₂²	semidirect
93. #6446	C₂²	semidirect
98. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
102. #6441	C₂²	semidirect
106. #6438	C₂²	semidirect
108. #6437	C₂²	semidirect
112. C₄×D₂₈	C₂²	semidirect
113. C₄×D₂₈	C₂²	semidirect
114. C₄×D₂₈	C₂²	semidirect
115. C₄×D₂₈	C₂²	semidirect
116. C₄×D₂₈	C₂²	semidirect
118. #6435	C₂²	semidirect
119. #6435	C₂²	semidirect
120. C₄²×D₇	C₂²	semidirect
121. #6433	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
232. #556	D₇	semidirect
321. C₄⋊Q₈	C₂×D₇	semidirect
330. #126	C₂×D₇	semidirect
331. #126	C₂×D₇	semidirect
366. C₂²⋊Q₈	C₂×D₇	semidirect
389. C₄×Q₈	C₂×D₇	semidirect
390. C₄×Q₈	C₂×D₇	semidirect
391. C₄×Q₈	C₂×D₇	semidirect
408. #117	C₂×D₇	semidirect
626. C₇	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₇×#556	2
#90417	2
#90415	2
#90402	2
#90400	2
#90398	2
#90395	2
#90368	2
#90367	2
#90365	2
#90359	2
#90338	2
#90335	2
#90276	2
#90274	2
#90271	2
#90268	2
#90267	2
#90253	2
#90245	2
#90226	2
#90218	2
#3562	7