Subgroups — #11743100

Order 896.

1058 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#90522	C₂	1	1	yes	maximal, characteristic, complemented
3	#90520	C₂	1	1	yes	maximal, characteristic, complemented
4	#90482	C₂	1	1	yes	maximal, characteristic, complemented
5	#90482	C₂	1	1	yes	maximal, characteristic, complemented
6	#90353	C₂	1	2	yes	maximal, complemented
7	#90348	C₂	1	2	yes	maximal, complemented
8	#90334	C₂	1	1	yes	maximal, characteristic, complemented
9	#90332	C₂	1	1	yes	maximal, characteristic, complemented
10	#90324	C₂	1	1	yes	maximal, characteristic, complemented
11	#90319	C₂	1	1	yes	maximal, characteristic, complemented
12	#90307	C₂	1	1	yes	maximal, characteristic, complemented
13	#90303	C₂	1	1	yes	maximal, characteristic, complemented
14	#90298	C₂	1	1	yes	maximal, characteristic, complemented
15	#90294	C₂	1	1	yes	maximal, characteristic, complemented
16	#90286	C₂	1	2	yes	maximal, complemented
17	#90285	C₂	1	2	yes	maximal, complemented
18	#90252	C₂	1	2	yes	maximal, complemented
19	#90251	C₂	1	2	yes	maximal, complemented
20	#90250	C₂	1	2	yes	maximal, complemented
21	#90247	C₂	1	2	yes	maximal, complemented
22	#90224	C₂	1	1	yes	maximal, characteristic, complemented
23	#90223	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#1157	C₂²	1	1	yes	characteristic
29	C₂×#1157	C₂²	1	1	yes	characteristic
30	C₇×#123	C₂²	1	2	yes	complemented
31	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₇×#121	C₂²	1	1	yes	characteristic
34	C₇×#121	C₂²	1	1	yes	characteristic
35	C₇×#120	C₂²	1	2	yes	complemented
36	C₄×C₇×D₄	C₂²	1	2	yes	complemented
37	C₄×C₇×D₄	C₂²	1	2	yes	complemented
38	C₇×#117	C₂²	1	1	yes	characteristic, complemented
39	#6516	C₂²	1	1	yes	characteristic
40	#6516	C₂²	1	2	yes	complemented
41	#6516	C₂²	1	1	yes	characteristic, complemented
42	#6510	C₂²	1	1	yes	characteristic, complemented
43	#6509	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
45	#6503	C₂²	1	2	yes	—
46	#6502	C₂²	1	2	yes	—
47	#6502	C₂²	1	2	yes	complemented
48	#6501	C₂²	1	2	yes	—
49	#6501	C₂²	1	2	yes	complemented
50	#6501	C₂²	1	1	yes	characteristic, complemented
51	#6500	C₂²	1	2	yes	—
52	#6500	C₂²	1	2	yes	—
53	#6500	C₂²	1	2	yes	—
54	#6499	C₂²	1	2	yes	complemented
55	#6499	C₂²	1	2	yes	complemented
56	#6499	C₂²	1	2	yes	complemented
57	#6499	C₂²	1	1	yes	characteristic, complemented
58	#6498	C₂²	1	2	yes	complemented
59	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
60	#6493	C₂²	1	1	yes	characteristic
61	#6493	C₂²	1	1	yes	characteristic
62	#6493	C₂²	1	1	yes	characteristic
63	#6493	C₂²	1	1	yes	characteristic
64	#6492	C₂²	1	1	yes	characteristic
65	#6492	C₂²	1	1	yes	characteristic, complemented
66	#6492	C₂²	1	2	yes	complemented
67	#6492	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
75	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
76	#6489	C₂²	1	1	yes	characteristic, complemented
77	#6489	C₂²	1	1	yes	characteristic, complemented
78	#6487	C₂²	1	1	yes	characteristic, complemented
79	#6487	C₂²	1	1	yes	characteristic, complemented
80	#6487	C₂²	1	1	yes	characteristic, complemented
81	#6487	C₂²	1	1	yes	characteristic, complemented
82	#6487	C₂²	1	2	yes	complemented
83	#6461	C₂²	1	2	yes	complemented
84	#6461	C₂²	1	2	yes	complemented
85	#6460	C₂²	1	1	yes	characteristic, complemented
86	#6460	C₂²	1	2	yes	complemented
87	#6459	C₂²	1	2	yes	complemented
88	#6458	C₂²	1	1	yes	characteristic, complemented
89	#6457	C₂²	1	2	yes	complemented
90	#6456	C₂²	1	1	yes	characteristic, complemented
91	#6456	C₂²	1	2	yes	complemented
92	#6455	C₂²	1	1	yes	characteristic, complemented
93	#6455	C₂²	1	1	yes	characteristic, complemented
94	#6451	C₂²	1	1	yes	characteristic, complemented
95	#6451	C₂²	1	1	yes	characteristic, complemented
96	#6451	C₂²	1	2	yes	complemented
97	#6450	C₂²	1	1	yes	characteristic, complemented
98	#6450	C₂²	1	2	yes	complemented
99	#6448	C₂²	1	2	yes	—
100	#6448	C₂²	1	2	yes	—
101	#6448	C₂²	1	2	yes	—
102	#6448	C₂²	1	2	yes	complemented
103	#6448	C₂²	1	2	yes	complemented
104	#6448	C₂²	1	2	yes	complemented
105	#6448	C₂²	1	2	yes	complemented
106	#6448	C₂²	1	2	yes	complemented
107	#6447	C₂²	1	2	yes	complemented
108	#6447	C₂²	1	2	yes	complemented
109	#6446	C₂²	1	2	yes	complemented
110	#6446	C₂²	1	2	yes	complemented
111	#6446	C₂²	1	2	yes	complemented
112	#6445	C₂²	1	2	yes	complemented
113	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	#6442	C₂²	1	2	yes	complemented
115	#6442	C₂²	1	2	yes	complemented
116	#6442	C₂²	1	2	yes	complemented
117	#6441	C₂²	1	2	yes	complemented
118	#6440	C₂²	1	2	yes	complemented
119	#6439	C₂²	1	2	yes	complemented
120	#6438	C₂²	1	2	yes	complemented
121	#6435	C₂²	1	2	yes	complemented
122	C₄×Dic₁₄	C₂²	1	2	yes	complemented
123	#3540	—	7	1	no	maximal, Sylow
124	C₂⁴×C₇	C₂³	1	1	yes	characteristic
125	C₂³×D₇	C₂³	1	2	yes	—
126	C₇×#41	—	4	2	no	—
127	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₇×D₄	C₂³	1	2	yes	—
130	C₂×C₇×D₄	C₂³	1	2	yes	—
131	C₂×C₇×D₄	C₂³	1	2	yes	—
132	C₂²×C₄×C₇	—	4	2	no	—
133	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
151	C₂²×Dic₇	C₂³	1	2	yes	—
152	Q₈×D₇	—	4	2	no	—
153	D₄×D₇	—	4	2	no	—
154	#1157	—	4	2	no	—
155	#1157	—	4	2	no	—
156	C₂×D₂₈	C₂³	1	1	yes	characteristic
157	C₂×D₂₈	C₂³	1	2	yes	—
158	C₂×D₂₈	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
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×Dic₁₄	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₄	C₂³	1	2	yes	—
166	C₂×Dic₁₄	C₂³	1	2	yes	—
167	C₂×Dic₁₄	C₂³	1	2	yes	—
168	C₂×Dic₁₄	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×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₇×C₂²⋊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	C₄²×C₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₇	C₂³	1	2	yes	—
189	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
201	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
206	C₄⋊Dic₇	C₂³	1	2	yes	—
207	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₇	C₂³	1	2	yes	—
210	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
212	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₇⋊C₄	C₂³	1	2	yes	—
214	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	2	yes	—
217	Dic₇⋊C₄	C₂³	1	2	yes	—
218	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₇⋊C₄	C₂³	1	2	yes	—
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
222	C₄×Dic₇	C₂³	1	2	yes	—
223	C₄×Dic₇	C₂³	1	2	yes	—
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	2	yes	—
226	C₄×Dic₇	C₂³	1	2	yes	—
227	C₄×Dic₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₇	C₂³	1	1	yes	characteristic
229	H(3,𝔽₄)	—	7	2	no	—
230	#560	—	7	2	no	—
231	#559	—	7	2	no	—
232	#556	—	7	1	no	—
233	#556	—	7	1	no	—
234	#555	—	7	1	no	—
235	#555	—	7	1	no	—
236	#551	—	7	2	no	—
237	#548	—	7	1	no	—
238	#548	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	1	no	—
241	#542	—	7	2	no	—
242	#542	—	7	1	no	—
243	#542	—	7	1	no	—
244	#542	—	7	2	no	—
245	#538	—	7	2	no	—
246	#538	—	7	2	no	—
247	#536	—	7	1	no	—
248	#535	—	7	1	no	—
249	#525	—	7	1	no	—
250	#525	—	7	1	no	—
251	#525	D₇	1	1	yes	characteristic, complemented
252	C₂³×C₇	—	4	1	no	—
253	C₂³×C₇	—	4	1	no	—
254	C₂³×C₇	—	4	1	no	—
255	C₂³×C₇	C₂⁴	1	2	yes	—
256	C₂³×C₇	C₂⁴	1	1	yes	characteristic
257	C₂³×C₇	C₂⁴	1	1	yes	characteristic
258	C₂³×C₇	C₂⁴	1	1	yes	characteristic
259	C₂²×D₇	—	4	2	no	—
260	C₂²×D₇	—	4	2	no	—
261	C₂²×D₇	—	4	2	no	—
262	C₂²×D₇	C₂⁴	1	1	yes	characteristic
263	C₂²×D₇	C₂⁴	1	2	yes	—
264	C₂²×D₇	C₂⁴	1	1	yes	characteristic
265	C₇×Q₈	—	2	2	no	—
266	C₇×D₄	—	2	2	no	—
267	C₇×D₄	—	4	2	no	—
268	C₇×D₄	—	4	2	no	—
269	C₇×D₄	—	4	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	4	1	no	—
274	C₂×C₄×C₇	—	4	1	no	—
275	C₂×C₄×C₇	—	4	1	no	—
276	C₂×C₄×C₇	—	4	2	no	—
277	C₂×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₂²⋊D₇	—	4	2	no	—
285	C₂²⋊D₇	—	4	1	no	—
286	C₂²⋊D₇	—	4	1	no	—
287	C₂²⋊D₇	—	4	2	no	—
288	C₂²⋊D₇	—	4	1	no	—
289	C₂²⋊D₇	—	4	1	no	—
290	C₂²⋊D₇	—	4	2	no	—
291	C₂²⋊D₇	—	4	2	no	—
292	C₂²⋊D₇	—	4	2	no	—
293	C₂²⋊D₇	—	4	1	no	—
294	C₂²⋊D₇	—	4	1	no	—
295	C₂×Dic₇	—	4	2	no	—
296	C₂×Dic₇	C₂⁴	1	2	yes	—
297	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇	C₂⁴	1	2	yes	—
301	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₇	C₂⁴	1	2	yes	—
305	D₂₈	—	2	2	no	—
306	D₂₈	—	4	2	no	—
307	D₂₈	—	4	1	no	—
308	C₄×D₇	—	2	2	no	—
309	C₄×D₇	—	2	2	no	—
310	C₄×D₇	—	4	2	no	—
311	C₄×D₇	—	4	2	no	—
312	C₄×D₇	—	4	2	no	—
313	Dic₁₄	—	2	2	no	—
314	Dic₁₄	—	4	2	no	—
315	Dic₁₄	—	4	2	no	—
316	Dic₁₄	—	4	1	no	—
317	Dic₁₄	—	4	2	no	—
318	C₂×#41	—	7	1	no	—
319	C₂×#41	—	7	1	no	—
320	C₂×#41	C₂×D₇	1	1	yes	characteristic
321	C₂²×Q₈	—	7	1	no	—
322	C₂²×D₄	—	7	1	no	—
323	C₂³×C₄	C₂×D₇	1	1	yes	characteristic, complemented
324	C₄⋊Q₈	—	7	2	no	—
325	C₄⋊Q₈	—	7	1	no	—
326	C₄⋊Q₈	—	7	1	no	—
327	#127	—	7	2	no	—
328	#126	—	7	2	no	—
329	#126	—	7	2	no	—
330	#126	—	7	2	no	—
331	#126	—	7	2	no	—
332	#126	—	7	2	no	—
333	#126	—	7	2	no	—
334	#124	—	7	1	no	—
335	#124	—	7	1	no	—
336	#124	—	7	2	no	—
337	#124	—	7	2	no	—
338	#124	—	7	2	no	—
339	#124	—	7	2	no	—
340	#124	—	7	2	no	—
341	#124	—	7	2	no	—
342	#124	—	7	2	no	—
343	#124	—	7	2	no	—
344	#124	—	7	2	no	—
345	#124	—	7	2	no	—
346	#124	—	7	2	no	—
347	#124	—	7	2	no	—
348	#123	—	7	2	no	—
349	#123	—	7	2	no	—
350	#123	—	7	1	no	—
351	#123	—	7	1	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	C₂×D₇	1	2	yes	complemented
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	1	no	—
360	C₂²⋊Q₈	—	7	1	no	—
361	C₂²⋊Q₈	—	7	1	no	—
362	C₂²⋊Q₈	—	7	1	no	—
363	C₂²⋊Q₈	—	7	2	no	—
364	C₂²⋊Q₈	—	7	1	no	—
365	C₂²⋊Q₈	—	7	2	no	—
366	C₂²⋊Q₈	—	7	2	no	—
367	C₂²⋊Q₈	—	7	2	no	—
368	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
369	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
370	#121	—	7	1	no	—
371	#121	—	7	2	no	—
372	#121	—	7	2	no	—
373	#121	—	7	2	no	—
374	#121	—	7	2	no	—
375	#121	—	7	1	no	—
376	#121	—	7	1	no	—
377	#121	—	7	1	no	—
378	#121	—	7	1	no	—
379	#121	—	7	1	no	—
380	#121	—	7	2	no	—
381	#121	—	7	2	no	—
382	#121	C₂×D₇	1	1	yes	characteristic
383	#121	C₂×D₇	1	1	yes	characteristic
384	#120	—	7	1	no	—
385	#120	—	7	2	no	—
386	#120	—	7	1	no	—
387	#120	—	7	2	no	—
388	#120	—	7	2	no	—
389	#120	—	7	2	no	—
390	#120	—	7	2	no	—
391	#120	C₂×D₇	1	2	yes	complemented
392	C₄×Q₈	—	7	1	no	—
393	C₄×Q₈	—	7	1	no	—
394	C₄×Q₈	—	7	2	no	—
395	C₄×Q₈	—	7	2	no	—
396	C₄×D₄	—	7	1	no	—
397	C₄×D₄	—	7	2	no	—
398	C₄×D₄	—	7	1	no	—
399	C₄×D₄	—	7	1	no	—
400	C₄×D₄	—	7	1	no	—
401	C₄×D₄	—	7	1	no	—
402	C₄×D₄	—	7	2	no	—
403	C₄×D₄	—	7	2	no	—
404	C₄×D₄	—	7	2	no	—
405	C₄×D₄	—	7	1	no	—
406	C₄×D₄	C₂×D₇	1	2	yes	complemented
407	C₄×D₄	C₂×D₇	1	2	yes	complemented
408	#117	—	7	1	no	—
409	#117	—	7	1	no	—
410	#117	—	7	1	no	—
411	#117	—	7	1	no	—
412	#117	—	7	2	no	—
413	#117	—	7	2	no	—
414	#117	C₂×D₇	1	1	yes	characteristic, complemented
415	C₂×C₂²⋊C₄	—	7	2	no	—
416	C₂×C₂²⋊C₄	—	7	2	no	—
417	C₂²×C₇	—	2	1	no	—
418	C₂²×C₇	—	2	1	no	—
419	C₂²×C₇	—	2	2	no	—
420	C₂²×C₇	—	2	1	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	—	2	1	no	—
423	C₂²×C₇	—	2	1	no	—
424	C₂²×C₇	—	2	1	no	—
425	C₂²×C₇	—	2	1	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	1	no	—
428	C₂²×C₇	—	2	1	no	—
429	C₂²×C₇	—	4	4	no	—
430	C₂²×C₇	C₂⁵	1	1	yes	characteristic
431	C₂×D₇	—	2	1	no	—
432	C₂×D₇	—	2	1	no	—
433	C₂×D₇	—	2	2	no	—
434	C₂×D₇	—	2	2	no	—
435	C₂×D₇	—	2	1	no	—
436	C₂×D₇	—	2	2	no	—
437	C₂×D₇	—	2	1	no	—
438	C₂×D₇	—	2	1	no	—
439	C₂×D₇	—	2	1	no	—
440	C₂×D₇	—	8	4	no	—
441	C₄×C₇	—	2	2	no	—
442	C₄×C₇	—	2	1	no	—
443	C₄×C₇	—	2	1	no	—
444	C₄×C₇	—	2	1	no	—
445	C₄×C₇	—	2	2	no	—
446	C₄×C₇	—	2	2	no	—
447	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
448	Dic₇	—	2	2	no	—
449	Dic₇	—	2	1	no	—
450	Dic₇	—	2	1	no	—
451	Dic₇	—	2	1	no	—
452	Dic₇	—	2	1	no	—
453	Dic₇	—	2	2	no	—
454	Dic₇	—	2	2	no	—
455	Dic₇	—	2	1	no	—
456	Dic₇	—	2	1	no	—
457	C₂⁴	—	7	2	no	—
458	C₂⁴	C₂²×D₇	1	1	yes	characteristic
459	#41	—	4	2	no	—
460	#41	—	28	2	no	—
461	#41	—	28	2	no	—
462	C₂×Q₈	—	7	1	no	—
463	C₂×Q₈	—	7	2	no	—
464	C₂×Q₈	—	7	2	no	—
465	C₂×Q₈	—	7	2	no	—
466	C₂×Q₈	—	7	1	no	—
467	C₂×Q₈	—	28	2	no	—
468	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
469	C₂×D₄	—	7	1	no	—
470	C₂×D₄	—	7	1	no	—
471	C₂×D₄	—	7	2	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	7	1	no	—
474	C₂×D₄	—	7	1	no	—
475	C₂×D₄	—	7	2	no	—
476	C₂×D₄	—	7	1	no	—
477	C₂×D₄	—	7	2	no	—
478	C₂×D₄	—	7	1	no	—
479	C₂×D₄	—	7	2	no	—
480	C₂×D₄	—	7	1	no	—
481	C₂×D₄	—	7	2	no	—
482	C₂×D₄	—	7	1	no	—
483	C₂×D₄	—	28	2	no	—
484	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₇	1	2	yes	—
486	C₂×D₄	C₂²×D₇	1	2	yes	—
487	C₂×D₄	C₂²×D₇	1	2	yes	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	7	2	no	—
490	C₂²×C₄	—	7	1	no	—
491	C₂²×C₄	—	7	1	no	—
492	C₂²×C₄	—	7	2	no	—
493	C₂²×C₄	—	7	2	no	—
494	C₂²×C₄	—	7	2	no	—
495	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₇	1	2	yes	—
499	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
502	C₄⋊C₄	—	7	1	no	—
503	C₄⋊C₄	—	7	1	no	—
504	C₄⋊C₄	—	7	2	no	—
505	C₄⋊C₄	—	7	2	no	—
506	C₄⋊C₄	—	7	2	no	—
507	C₄⋊C₄	—	7	1	no	—
508	C₄⋊C₄	—	7	1	no	—
509	C₄⋊C₄	—	7	2	no	—
510	C₄⋊C₄	—	7	2	no	—
511	C₄⋊C₄	—	7	2	no	—
512	C₄⋊C₄	—	7	1	no	—
513	C₄⋊C₄	—	7	1	no	—
514	C₄⋊C₄	—	7	1	no	—
515	C₄⋊C₄	—	7	1	no	—
516	C₄⋊C₄	—	7	2	no	—
517	C₄⋊C₄	—	7	2	no	—
518	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₇	1	2	yes	—
521	C₄⋊C₄	C₂²×D₇	1	2	yes	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	2	no	—
525	C₂²⋊C₄	—	7	1	no	—
526	C₂²⋊C₄	—	7	1	no	—
527	C₂²⋊C₄	—	7	1	no	—
528	C₂²⋊C₄	—	7	1	no	—
529	C₂²⋊C₄	—	7	2	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	1	no	—
533	C₂²⋊C₄	—	7	1	no	—
534	C₂²⋊C₄	—	7	2	no	—
535	C₂²⋊C₄	—	7	1	no	—
536	C₂²⋊C₄	—	7	1	no	—
537	C₂²⋊C₄	—	7	2	no	—
538	C₂²⋊C₄	—	7	2	no	—
539	C₂²⋊C₄	—	7	2	no	—
540	C₂²⋊C₄	—	7	2	no	—
541	C₂²⋊C₄	—	7	2	no	—
542	C₂²⋊C₄	—	7	2	no	—
543	C₂²⋊C₄	—	7	2	no	—
544	C₂²⋊C₄	—	7	1	no	—
545	C₂²⋊C₄	—	7	1	no	—
546	C₂²⋊C₄	—	7	2	no	—
547	C₂²⋊C₄	—	7	2	no	—
548	C₂²⋊C₄	—	7	2	no	—
549	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
554	C₄²	—	7	2	no	—
555	C₄²	—	7	2	no	—
556	C₄²	—	7	1	no	—
557	C₄²	—	7	1	no	—
558	C₄²	—	7	2	no	—
559	C₄²	—	7	2	no	—
560	C₄²	—	7	2	no	—
561	C₄²	C₂²×D₇	1	2	yes	—
562	C₂×C₇	—	4	2	no	—
563	C₂×C₇	—	4	1	no	—
564	C₂×C₇	—	4	1	no	—
565	C₂×C₇	—	4	1	no	—
566	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₇	#585	1	1	yes	characteristic
568	C₂×C₇	#585	1	1	yes	characteristic
569	D₇	—	4	1	no	—
570	D₇	—	4	2	no	—
571	D₇	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	7	1	no	—
576	C₂³	—	7	2	no	—
577	C₂³	—	7	1	no	—
578	C₂³	—	28	2	no	—
579	C₂³	—	28	2	no	—
580	C₂³	—	28	2	no	—
581	C₂³	C₂³×D₇	1	2	yes	—
582	C₂³	C₂³×D₇	1	1	yes	characteristic
583	C₂³	C₂³×D₇	1	1	yes	characteristic
584	C₂³	C₂³×D₇	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	14	2	no	—
587	Q₈	—	28	2	no	—
588	Q₈	—	28	2	no	—
589	Q₈	—	28	2	no	—
590	Q₈	—	28	1	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	14	2	no	—
596	D₄	—	28	2	no	—
597	D₄	—	28	1	no	—
598	D₄	—	28	1	no	—
599	D₄	—	28	1	no	—
600	D₄	—	28	2	no	—
601	D₄	—	28	2	no	—
602	D₄	—	28	2	no	—
603	D₄	—	28	1	no	—
604	D₄	—	28	1	no	—
605	D₄	—	28	2	no	—
606	D₄	—	28	1	no	—
607	D₄	—	28	1	no	—
608	D₄	—	28	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	7	1	no	—
617	C₂×C₄	—	7	1	no	—
618	C₂×C₄	—	7	2	no	—
619	C₂×C₄	—	7	2	no	—
620	C₂×C₄	—	7	1	no	—
621	C₂×C₄	—	7	1	no	—
622	C₂×C₄	—	7	1	no	—
623	C₂×C₄	—	7	1	no	—
624	C₂×C₄	—	7	2	no	—
625	C₂×C₄	—	14	2	no	—
626	C₂×C₄	—	14	2	no	—
627	C₂×C₄	—	28	2	no	—
628	C₂×C₄	—	28	2	no	—
629	C₂×C₄	—	28	2	no	—
630	C₂×C₄	—	28	2	no	—
631	C₂×C₄	C₂³×D₇	1	2	yes	—
632	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₇	1	2	yes	—
634	C₂×C₄	C₂³×D₇	1	2	yes	—
635	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
638	C₇	#3540	1	1	yes	characteristic, complemented, Sylow
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	14	1	no	—
653	C₂²	—	14	1	no	—
654	C₂²	—	14	2	no	—
655	C₂²	—	14	2	no	—
656	C₂²	—	14	1	no	—
657	C₂²	—	14	1	no	—
658	C₂²	—	14	2	no	—
659	C₂²	—	14	1	no	—
660	C₂²	—	14	1	no	—
661	C₂²	—	56	4	no	—
662	C₂²	C₂⁴×D₇	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	14	1	no	—
670	C₄	—	14	1	no	—
671	C₄	—	14	2	no	—
672	C₄	—	14	1	no	—
673	C₄	—	14	1	no	—
674	C₄	—	14	2	no	—
675	C₄	—	14	2	no	—
676	C₄	—	14	1	no	—
677	C₄	—	14	1	no	—
678	C₄	#6548	1	2	yes	—
679	C₂	—	4	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	4	1	no	—
682	C₂	—	4	2	no	—
683	C₂	—	28	1	no	—
684	C₂	—	28	2	no	—
685	C₂	—	28	1	no	—
686	C₂	C₂×#6548	1	1	yes	characteristic
687	C₂	#90616	1	1	yes	characteristic
688	C₂	#90616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#525	C₂
hypercenter	#525	D₇
hypocenter	C₇	#3540
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₇×#525	C₂	semidirect
2. #90522	C₂	semidirect
3. #90520	C₂	semidirect
4. #90482	C₂	semidirect
5. #90482	C₂	semidirect
6. #90353	C₂	semidirect
7. #90348	C₂	semidirect
8. #90334	C₂	semidirect
9. #90332	C₂	semidirect
10. #90324	C₂	semidirect
11. #90319	C₂	semidirect
12. #90307	C₂	semidirect
13. #90303	C₂	semidirect
14. #90298	C₂	semidirect
15. #90294	C₂	semidirect
16. #90286	C₂	semidirect
17. #90285	C₂	semidirect
18. #90252	C₂	semidirect
19. #90251	C₂	semidirect
20. #90250	C₂	semidirect
21. #90247	C₂	semidirect
22. #90224	C₂	semidirect
23. #90223	C₂	semidirect
25. C₂³×C₄×C₇	C₂²	semidirect
26. C₂×Q₈×D₇	C₂²	semidirect
27. C₂×D₄×D₇	C₂²	semidirect
30. C₇×#123	C₂²	semidirect
31. C₇×C₂²⋊Q₈	C₂²	semidirect
32. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₇×#120	C₂²	semidirect
36. C₄×C₇×D₄	C₂²	semidirect
37. C₄×C₇×D₄	C₂²	semidirect
38. C₇×#117	C₂²	semidirect
40. #6516	C₂²	semidirect
41. #6516	C₂²	semidirect
42. #6510	C₂²	semidirect
43. #6509	C₂²	semidirect
44. Q₈×Dic₇	C₂²	semidirect
47. #6502	C₂²	semidirect
49. #6501	C₂²	semidirect
50. #6501	C₂²	semidirect
54. #6499	C₂²	semidirect
55. #6499	C₂²	semidirect
56. #6499	C₂²	semidirect
57. #6499	C₂²	semidirect
58. #6498	C₂²	semidirect
59. D₄×Dic₇	C₂²	semidirect
65. #6492	C₂²	semidirect
66. #6492	C₂²	semidirect
67. #6492	C₂²	semidirect
70. C₄×C₂²⋊D₇	C₂²	semidirect
71. C₄×C₂²⋊D₇	C₂²	semidirect
72. C₄×C₂²⋊D₇	C₂²	semidirect
73. C₄×C₂²⋊D₇	C₂²	semidirect
74. C₄×C₂²⋊D₇	C₂²	semidirect
75. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
76. #6489	C₂²	semidirect
77. #6489	C₂²	semidirect
78. #6487	C₂²	semidirect
79. #6487	C₂²	semidirect
80. #6487	C₂²	semidirect
81. #6487	C₂²	semidirect
82. #6487	C₂²	semidirect
83. #6461	C₂²	semidirect
84. #6461	C₂²	semidirect
85. #6460	C₂²	semidirect
86. #6460	C₂²	semidirect
87. #6459	C₂²	semidirect
88. #6458	C₂²	semidirect
89. #6457	C₂²	semidirect
90. #6456	C₂²	semidirect
91. #6456	C₂²	semidirect
92. #6455	C₂²	semidirect
93. #6455	C₂²	semidirect
94. #6451	C₂²	semidirect
95. #6451	C₂²	semidirect
96. #6451	C₂²	semidirect
97. #6450	C₂²	semidirect
98. #6450	C₂²	semidirect
102. #6448	C₂²	semidirect
103. #6448	C₂²	semidirect
104. #6448	C₂²	semidirect
105. #6448	C₂²	semidirect
106. #6448	C₂²	semidirect
107. #6447	C₂²	semidirect
108. #6447	C₂²	semidirect
109. #6446	C₂²	semidirect
110. #6446	C₂²	semidirect
111. #6446	C₂²	semidirect
112. #6445	C₂²	semidirect
113. D₇×C₂²⋊C₄	C₂²	semidirect
114. #6442	C₂²	semidirect
115. #6442	C₂²	semidirect
116. #6442	C₂²	semidirect
117. #6441	C₂²	semidirect
118. #6440	C₂²	semidirect
119. #6439	C₂²	semidirect
120. #6438	C₂²	semidirect
121. #6435	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
251. #525	D₇	semidirect
323. C₂³×C₄	C₂×D₇	semidirect
357. #123	C₂×D₇	semidirect
368. C₂²⋊Q₈	C₂×D₇	semidirect
369. C₂²⋊Q₈	C₂×D₇	semidirect
391. #120	C₂×D₇	semidirect
406. C₄×D₄	C₂×D₇	semidirect
407. C₄×D₄	C₂×D₇	semidirect
414. #117	C₂×D₇	semidirect
638. C₇	#3540	semidirect

Maximal subgroups

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

subgroup	index
C₇×#525	2
#90522	2
#90520	2
#90482	2
#90353	2
#90348	2
#90334	2
#90332	2
#90324	2
#90319	2
#90307	2
#90303	2
#90298	2
#90294	2
#90286	2
#90285	2
#90252	2
#90251	2
#90250	2
#90247	2
#90224	2
#90223	2
#3540	7