Subgroups — #11743746

Order 896.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	#90523	C₂	1	2	yes	maximal, complemented
3	#90520	C₂	1	2	yes	maximal, complemented
4	#90425	C₂	1	1	yes	maximal, characteristic, complemented
5	#90420	C₂	1	1	yes	maximal, characteristic, complemented
6	#90354	C₂	1	2	yes	maximal, complemented
7	#90350	C₂	1	2	yes	maximal, complemented
8	#90345	C₂	1	2	yes	maximal, complemented
9	#90340	C₂	1	2	yes	maximal, complemented
10	#90331	C₂	1	2	yes	maximal, complemented
11	#90328	C₂	1	2	yes	maximal, complemented
12	#90309	C₂	1	1	yes	maximal, characteristic, complemented
13	#90307	C₂	1	1	yes	maximal, characteristic, complemented
14	#90298	C₂	1	1	yes	maximal, characteristic, complemented
15	D₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#90256	C₂	1	1	yes	maximal, characteristic, complemented
17	#90249	C₂	1	1	yes	maximal, characteristic, complemented
18	#90238	C₂	1	1	yes	maximal, characteristic, complemented
19	#90236	C₂	1	1	yes	maximal, characteristic, complemented
20	#90205	C₂	1	1	yes	maximal, characteristic, complemented
21	#90198	C₂	1	1	yes	maximal, characteristic, complemented
22	#90195	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#6455	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	2	yes	complemented
25	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₇	C₂²	1	2	yes	—
27	C₂×#1157	C₂²	1	1	yes	characteristic
28	C₂×#1157	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#123	C₂²	1	2	yes	complemented
32	C₇×#123	C₂²	1	2	yes	complemented
33	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₇×#121	C₂²	1	1	yes	characteristic
35	C₇×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	#6510	C₂²	1	2	yes	complemented
41	#6510	C₂²	1	2	yes	complemented
42	#6509	C₂²	1	2	yes	—
43	#6507	C₂²	1	2	yes	complemented
44	#6503	C₂²	1	2	yes	complemented
45	#6502	C₂²	1	2	yes	—
46	#6502	C₂²	1	1	yes	characteristic, complemented
47	#6502	C₂²	1	2	yes	complemented
48	#6502	C₂²	1	2	yes	complemented
49	#6502	C₂²	1	2	yes	complemented
50	#6501	C₂²	1	1	yes	characteristic
51	#6501	C₂²	1	1	yes	characteristic, complemented
52	#6500	C₂²	1	1	yes	characteristic
53	#6500	C₂²	1	2	yes	—
54	#6499	C₂²	1	2	yes	complemented
55	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
56	D₄×Dic₇	C₂²	1	2	yes	complemented
57	#6493	C₂²	1	1	yes	characteristic
58	#6493	C₂²	1	1	yes	characteristic, complemented
59	#6493	C₂²	1	2	yes	complemented
60	#6492	C₂²	1	2	yes	complemented
61	#6492	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
69	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
70	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
71	#6489	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄×Dic₇	C₂²	1	2	yes	complemented
74	#6461	C₂²	1	2	yes	complemented
75	#6461	C₂²	1	2	yes	complemented
76	#6459	C₂²	1	2	yes	—
77	#6459	C₂²	1	2	yes	complemented
78	#6459	C₂²	1	1	yes	characteristic, complemented
79	#6458	C₂²	1	1	yes	characteristic
80	#6458	C₂²	1	1	yes	characteristic, complemented
81	#6458	C₂²	1	2	yes	complemented
82	#6457	C₂²	1	1	yes	characteristic
83	#6457	C₂²	1	2	yes	complemented
84	#6457	C₂²	1	2	yes	complemented
85	#6456	C₂²	1	2	yes	—
86	#6456	C₂²	1	1	yes	characteristic, complemented
87	#6455	C₂²	1	1	yes	characteristic
88	#6455	C₂²	1	1	yes	characteristic
89	#6455	C₂²	1	2	yes	—
90	#6455	C₂²	1	1	yes	characteristic, complemented
91	#6455	C₂²	1	1	yes	characteristic, complemented
92	#6455	C₂²	1	2	yes	complemented
93	#6455	C₂²	1	1	yes	characteristic, complemented
94	#6455	C₂²	1	2	yes	complemented
95	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	#6453	C₂²	1	1	yes	characteristic, complemented
98	#6452	C₂²	1	2	yes	complemented
99	#6451	C₂²	1	1	yes	characteristic, complemented
100	#6450	C₂²	1	2	yes	complemented
101	#6449	C₂²	1	2	yes	complemented
102	#6448	C₂²	1	2	yes	complemented
103	#6448	C₂²	1	2	yes	complemented
104	#6447	C₂²	1	2	yes	—
105	#6447	C₂²	1	1	yes	characteristic, complemented
106	#6447	C₂²	1	2	yes	complemented
107	#6446	C₂²	1	1	yes	characteristic
108	#6446	C₂²	1	2	yes	complemented
109	#6445	C₂²	1	1	yes	characteristic
110	#6445	C₂²	1	2	yes	—
111	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
112	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
113	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
115	#6442	C₂²	1	2	yes	complemented
116	#6442	C₂²	1	2	yes	complemented
117	#6441	C₂²	1	1	yes	characteristic, complemented
118	#6440	C₂²	1	2	yes	complemented
119	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
121	#6435	C₂²	1	1	yes	characteristic
122	#6433	C₂²	1	1	yes	characteristic, complemented
123	#3494	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	1	yes	characteristic
125	C₂³×D₇	C₂³	1	2	yes	—
126	C₇×#41	—	4	4	no	—
127	C₂×C₇×Q₈	C₂³	1	2	yes	—
128	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₇×D₄	C₂³	1	2	yes	—
130	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₇×D₄	C₂³	1	2	yes	—
132	C₂²×C₄×C₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂³	1	2	yes	—
136	C₂²×C₄×C₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
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	2	yes	—
145	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
146	C₂²×Dic₇	C₂³	1	1	yes	characteristic
147	C₂²×Dic₇	C₂³	1	2	yes	—
148	C₂²×Dic₇	C₂³	1	2	yes	—
149	D₄×D₇	—	2	4	no	—
150	D₄×D₇	—	4	4	no	—
151	#1157	—	2	4	no	—
152	#1157	—	4	4	no	—
153	C₂×D₂₈	C₂³	1	1	yes	characteristic
154	C₂×D₂₈	C₂³	1	1	yes	characteristic
155	C₂×D₂₈	C₂³	1	1	yes	characteristic
156	C₂×D₂₈	C₂³	1	2	yes	—
157	C₂×D₂₈	C₂³	1	2	yes	—
158	C₂×C₄×D₇	—	2	4	no	—
159	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₇	C₂³	1	2	yes	—
164	C₂×C₄×D₇	C₂³	1	2	yes	—
165	C₂×C₄×D₇	C₂³	1	2	yes	—
166	C₂×C₄×D₇	C₂³	1	2	yes	—
167	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
168	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₄	C₂³	1	2	yes	—
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	1	yes	characteristic
175	C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₄²×C₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
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	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
202	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₇	C₂³	1	2	yes	—
211	C₄⋊Dic₇	C₂³	1	2	yes	—
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	Dic₇⋊C₄	C₂³	1	2	yes	—
214	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
222	C₄×Dic₇	C₂³	1	1	yes	characteristic
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	2	yes	—
228	C₄×Dic₇	C₂³	1	2	yes	—
229	#555	—	7	1	no	—
230	#555	—	7	1	no	—
231	#553	—	7	1	no	—
232	#553	—	7	1	no	—
233	#553	—	7	1	no	—
234	#553	—	7	1	no	—
235	#551	—	7	2	no	—
236	#551	—	7	2	no	—
237	#547	—	7	1	no	—
238	#547	D₇	1	1	yes	characteristic, complemented
239	#546	—	7	2	no	—
240	#546	—	7	2	no	—
241	#544	—	7	1	no	—
242	#542	—	7	2	no	—
243	#540	—	7	2	no	—
244	#535	—	7	1	no	—
245	#532	—	7	2	no	—
246	#529	—	7	2	no	—
247	#525	—	7	1	no	—
248	C₂×#121	—	7	1	no	—
249	#520	—	7	1	no	—
250	#518	—	7	1	no	—
251	C₂×#117	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	2	yes	—
253	C₂³×C₇	C₂⁴	1	1	yes	characteristic
254	C₂³×C₇	C₂⁴	1	1	yes	characteristic
255	C₂²×D₇	—	2	2	no	—
256	C₂²×D₇	—	2	2	no	—
257	C₂²×D₇	—	2	4	no	—
258	C₂²×D₇	—	4	1	no	—
259	C₂²×D₇	—	4	2	no	—
260	C₂²×D₇	—	4	2	no	—
261	C₂²×D₇	C₂⁴	1	1	yes	characteristic
262	C₂²×D₇	C₂⁴	1	2	yes	—
263	C₂²×D₇	C₂⁴	1	1	yes	characteristic
264	C₂²×D₇	C₂⁴	1	1	yes	characteristic
265	C₇×Q₈	—	4	2	no	—
266	C₇×D₄	—	2	4	no	—
267	C₇×D₄	—	2	2	no	—
268	C₇×D₄	—	2	2	no	—
269	C₇×D₄	—	4	2	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	—	4	2	no	—
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂²⋊D₇	—	2	2	no	—
284	C₂²⋊D₇	—	2	4	no	—
285	C₂²⋊D₇	—	2	2	no	—
286	C₂²⋊D₇	—	2	2	no	—
287	C₂²⋊D₇	—	2	4	no	—
288	C₂²⋊D₇	—	4	2	no	—
289	C₂²⋊D₇	—	4	1	no	—
290	C₂²⋊D₇	—	4	2	no	—
291	C₂²⋊D₇	—	4	2	no	—
292	C₂×Dic₇	—	2	2	no	—
293	C₂×Dic₇	—	4	2	no	—
294	C₂×Dic₇	—	4	2	no	—
295	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇	C₂⁴	1	2	yes	—
297	C₂×Dic₇	C₂⁴	1	2	yes	—
298	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₇	C₂⁴	1	2	yes	—
300	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	D₂₈	—	2	2	no	—
304	D₂₈	—	2	2	no	—
305	D₂₈	—	4	1	no	—
306	D₂₈	—	4	2	no	—
307	D₂₈	—	4	2	no	—
308	C₄×D₇	—	2	2	no	—
309	C₄×D₇	—	2	2	no	—
310	C₄×D₇	—	2	2	no	—
311	C₄×D₇	—	2	2	no	—
312	C₄×D₇	—	4	2	no	—
313	C₄×D₇	—	4	2	no	—
314	C₄×D₇	—	4	2	no	—
315	C₄×D₇	—	4	2	no	—
316	C₄×D₇	#41	1	4	yes	complemented
317	Dic₁₄	—	2	2	no	—
318	Dic₁₄	—	4	2	no	—
319	C₂×#41	—	7	1	no	—
320	C₂×#41	—	7	2	no	—
321	C₂×#41	C₂×D₇	1	2	yes	complemented
322	C₂²×D₄	—	7	1	no	—
323	C₂²×D₄	—	7	2	no	—
324	C₂³×C₄	—	7	1	no	—
325	C₄⋊Q₈	—	7	2	no	—
326	C₄⋊Q₈	—	7	1	no	—
327	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
328	#127	—	7	2	no	—
329	#126	—	7	2	no	—
330	#126	—	7	2	no	—
331	#126	—	7	2	no	—
332	#126	—	7	2	no	—
333	#125	—	7	2	no	—
334	#125	—	7	1	no	—
335	#125	—	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	#123	—	7	2	no	—
342	#123	—	7	2	no	—
343	#123	—	7	1	no	—
344	#123	—	7	2	no	—
345	#123	—	7	2	no	—
346	#123	—	7	1	no	—
347	#123	—	7	2	no	—
348	#123	—	7	2	no	—
349	#123	C₂×D₇	1	2	yes	complemented
350	#123	C₂×D₇	1	2	yes	complemented
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	—	7	1	no	—
353	C₂²⋊Q₈	—	7	2	no	—
354	C₂²⋊Q₈	—	7	2	no	—
355	C₂²⋊Q₈	—	7	1	no	—
356	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
357	#121	—	7	2	no	—
358	#121	—	7	1	no	—
359	#121	—	7	1	no	—
360	#121	—	7	2	no	—
361	#121	—	7	2	no	—
362	#121	—	7	1	no	—
363	#121	—	7	2	no	—
364	#121	—	7	1	no	—
365	#121	—	7	1	no	—
366	#121	—	7	2	no	—
367	#121	—	7	1	no	—
368	#121	—	7	1	no	—
369	#121	—	7	2	no	—
370	#121	—	7	2	no	—
371	#121	—	7	1	no	—
372	#121	—	7	2	no	—
373	#121	C₂×D₇	1	1	yes	characteristic
374	#121	C₂×D₇	1	1	yes	characteristic, complemented
375	#120	—	7	1	no	—
376	#120	—	7	2	no	—
377	#120	—	7	1	no	—
378	#120	—	7	2	no	—
379	C₄×Q₈	—	7	2	no	—
380	C₄×D₄	—	7	1	no	—
381	C₄×D₄	—	7	2	no	—
382	C₄×D₄	—	7	2	no	—
383	C₄×D₄	—	7	2	no	—
384	C₄×D₄	—	7	2	no	—
385	C₄×D₄	—	7	1	no	—
386	C₄×D₄	—	7	1	no	—
387	C₄×D₄	—	7	2	no	—
388	C₄×D₄	—	7	2	no	—
389	C₄×D₄	—	7	1	no	—
390	C₄×D₄	—	7	2	no	—
391	C₄×D₄	—	7	2	no	—
392	C₄×D₄	—	7	2	no	—
393	C₄×D₄	—	7	1	no	—
394	C₄×D₄	—	7	1	no	—
395	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
396	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
397	#117	—	7	1	no	—
398	#117	—	7	1	no	—
399	#117	—	7	1	no	—
400	#117	—	7	2	no	—
401	#117	—	7	2	no	—
402	#117	—	7	1	no	—
403	#117	—	7	1	no	—
404	#117	—	7	1	no	—
405	#117	—	7	2	no	—
406	#117	—	7	2	no	—
407	#117	—	7	1	no	—
408	C₂×C₄⋊C₄	—	7	1	no	—
409	C₂×C₄⋊C₄	—	7	1	no	—
410	C₂×C₄⋊C₄	—	7	1	no	—
411	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
412	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
413	C₂×C₂²⋊C₄	—	7	2	no	—
414	C₂×C₂²⋊C₄	—	7	2	no	—
415	C₂×C₂²⋊C₄	—	7	2	no	—
416	C₂×C₂²⋊C₄	—	7	2	no	—
417	C₂×C₄²	—	7	2	no	—
418	C₂²×C₇	—	2	1	no	—
419	C₂²×C₇	—	2	1	no	—
420	C₂²×C₇	—	2	1	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	—	2	2	no	—
423	C₂²×C₇	—	2	1	no	—
424	C₂²×C₇	—	2	2	no	—
425	C₂²×C₇	—	2	1	no	—
426	C₂²×C₇	H(5,𝔽₂)	1	2	yes	—
427	C₂²×C₇	C₂⁵	1	1	yes	characteristic
428	C₂×D₇	—	2	1	no	—
429	C₂×D₇	—	2	1	no	—
430	C₂×D₇	—	2	1	no	—
431	C₂×D₇	—	2	1	no	—
432	C₂×D₇	—	2	2	no	—
433	C₂×D₇	—	2	1	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	—	4	4	no	—
440	C₂×D₇	—	8	4	no	—
441	C₂×D₇	C₂×#41	1	2	yes	—
442	C₄×C₇	—	2	1	no	—
443	C₄×C₇	—	2	1	no	—
444	C₄×C₇	—	2	2	no	—
445	C₄×C₇	—	2	2	no	—
446	C₄×C₇	—	2	2	no	—
447	C₄×C₇	—	2	1	no	—
448	C₄×C₇	—	2	1	no	—
449	C₄×C₇	C₂×#41	1	2	yes	—
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	2	no	—
457	Dic₇	C₂×#41	1	2	yes	—
458	C₂⁴	—	7	1	no	—
459	C₂⁴	—	7	2	no	—
460	#41	—	4	4	no	—
461	#41	—	14	4	no	—
462	#41	—	28	4	no	—
463	C₂×Q₈	—	7	1	no	—
464	C₂×Q₈	—	7	2	no	—
465	C₂×Q₈	C₂²×D₇	1	2	yes	—
466	C₂×D₄	—	7	1	no	—
467	C₂×D₄	—	7	2	no	—
468	C₂×D₄	—	7	1	no	—
469	C₂×D₄	—	7	1	no	—
470	C₂×D₄	—	7	2	no	—
471	C₂×D₄	—	7	1	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	7	2	no	—
474	C₂×D₄	—	7	2	no	—
475	C₂×D₄	—	7	1	no	—
476	C₂×D₄	—	7	1	no	—
477	C₂×D₄	—	7	1	no	—
478	C₂×D₄	—	7	2	no	—
479	C₂×D₄	—	7	2	no	—
480	C₂×D₄	—	14	4	no	—
481	C₂×D₄	—	28	4	no	—
482	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₇	1	2	yes	—
484	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₇	1	2	yes	—
486	C₂²×C₄	—	7	1	no	—
487	C₂²×C₄	—	7	1	no	—
488	C₂²×C₄	—	7	2	no	—
489	C₂²×C₄	—	7	2	no	—
490	C₂²×C₄	—	7	1	no	—
491	C₂²×C₄	—	7	1	no	—
492	C₂²×C₄	—	7	1	no	—
493	C₂²×C₄	—	7	1	no	—
494	C₂²×C₄	—	7	2	no	—
495	C₂²×C₄	—	7	2	no	—
496	C₂²×C₄	—	7	2	no	—
497	C₂²×C₄	—	7	2	no	—
498	C₂²×C₄	—	14	4	no	—
499	C₂²×C₄	C₂²×D₇	1	2	yes	—
500	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₇	1	2	yes	—
503	C₂²×C₄	C₂²×D₇	1	2	yes	—
504	C₄⋊C₄	—	7	2	no	—
505	C₄⋊C₄	—	7	2	no	—
506	C₄⋊C₄	—	7	1	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	2	no	—
513	C₄⋊C₄	—	7	1	no	—
514	C₄⋊C₄	—	7	1	no	—
515	C₄⋊C₄	—	7	1	no	—
516	C₄⋊C₄	—	7	1	no	—
517	C₄⋊C₄	—	7	2	no	—
518	C₄⋊C₄	—	7	1	no	—
519	C₄⋊C₄	—	7	2	no	—
520	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₇	1	2	yes	—
525	C₄⋊C₄	C₂²×D₇	1	2	yes	—
526	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
527	C₂²⋊C₄	—	7	2	no	—
528	C₂²⋊C₄	—	7	2	no	—
529	C₂²⋊C₄	—	7	2	no	—
530	C₂²⋊C₄	—	7	1	no	—
531	C₂²⋊C₄	—	7	1	no	—
532	C₂²⋊C₄	—	7	2	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	1	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	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	2	no	—
545	C₂²⋊C₄	—	7	1	no	—
546	C₂²⋊C₄	—	7	2	no	—
547	C₂²⋊C₄	—	7	1	no	—
548	C₂²⋊C₄	—	7	1	no	—
549	C₂²⋊C₄	—	7	1	no	—
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	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
555	C₄²	—	7	2	no	—
556	C₄²	—	7	2	no	—
557	C₄²	—	7	2	no	—
558	C₄²	—	7	2	no	—
559	C₄²	—	7	2	no	—
560	C₄²	—	7	2	no	—
561	C₄²	—	7	1	no	—
562	C₄²	C₂²×D₇	1	1	yes	characteristic
563	C₂×C₇	—	2	2	no	—
564	C₂×C₇	—	4	2	no	—
565	C₂×C₇	—	4	1	no	—
566	C₂×C₇	C₂²×#41	1	1	yes	characteristic
567	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₇	#585	1	1	yes	characteristic
569	D₇	—	2	2	no	—
570	D₇	—	4	1	no	—
571	D₇	—	4	1	no	—
572	D₇	—	4	2	no	—
573	C₂³	—	7	1	no	—
574	C₂³	—	7	2	no	—
575	C₂³	—	7	1	no	—
576	C₂³	—	7	1	no	—
577	C₂³	—	14	2	no	—
578	C₂³	—	14	4	no	—
579	C₂³	—	14	2	no	—
580	C₂³	—	28	1	no	—
581	C₂³	—	28	2	no	—
582	C₂³	—	28	2	no	—
583	C₂³	C₂³×D₇	1	2	yes	—
584	C₂³	C₂³×D₇	1	1	yes	characteristic
585	C₂³	C₂³×D₇	1	1	yes	characteristic
586	Q₈	—	4	2	no	—
587	Q₈	—	14	2	no	—
588	Q₈	—	28	2	no	—
589	D₄	—	2	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	14	2	no	—
594	D₄	—	14	4	no	—
595	D₄	—	14	2	no	—
596	D₄	—	14	2	no	—
597	D₄	—	14	4	no	—
598	D₄	—	14	2	no	—
599	D₄	—	14	2	no	—
600	D₄	—	28	1	no	—
601	D₄	—	28	2	no	—
602	D₄	—	28	2	no	—
603	D₄	—	28	1	no	—
604	D₄	—	28	2	no	—
605	D₄	—	28	2	no	—
606	D₄	—	28	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	7	1	no	—
613	C₂×C₄	—	7	4	no	—
614	C₂×C₄	—	7	1	no	—
615	C₂×C₄	—	7	2	no	—
616	C₂×C₄	—	7	1	no	—
617	C₂×C₄	—	7	2	no	—
618	C₂×C₄	—	7	1	no	—
619	C₂×C₄	—	7	1	no	—
620	C₂×C₄	—	7	2	no	—
621	C₂×C₄	—	14	2	no	—
622	C₂×C₄	—	14	2	no	—
623	C₂×C₄	—	14	2	no	—
624	C₂×C₄	—	14	2	no	—
625	C₂×C₄	—	14	2	no	—
626	C₂×C₄	—	28	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	—	28	2	no	—
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	2	yes	—
636	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
640	C₇	#3494	1	1	yes	characteristic, complemented, Sylow
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	7	2	no	—
650	C₂²	—	14	1	no	—
651	C₂²	—	14	1	no	—
652	C₂²	—	14	1	no	—
653	C₂²	—	14	2	no	—
654	C₂²	—	14	1	no	—
655	C₂²	—	14	1	no	—
656	C₂²	—	14	1	no	—
657	C₂²	—	14	2	no	—
658	C₂²	—	14	2	no	—
659	C₂²	—	14	1	no	—
660	C₂²	—	14	1	no	—
661	C₂²	—	28	4	no	—
662	C₂²	—	56	4	no	—
663	C₂²	#6548	1	2	yes	—
664	C₂²	C₂⁴×D₇	1	1	yes	characteristic
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	7	2	no	—
673	C₄	—	14	2	no	—
674	C₄	—	14	1	no	—
675	C₄	—	14	1	no	—
676	C₄	—	14	1	no	—
677	C₄	—	14	2	no	—
678	C₄	—	14	1	no	—
679	C₄	—	14	2	no	—
680	C₄	D₇×#41	1	2	yes	—
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	14	2	no	—
685	C₂	—	28	1	no	—
686	C₂	—	28	2	no	—
687	C₂	—	28	1	no	—
688	C₂	C₂×#6548	1	1	yes	characteristic
689	C₂	C₂×D₇×#41	1	1	yes	characteristic
690	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#547	C₂
hypercenter	#547	D₇
hypocenter	C₇	#3494
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₇×#547	C₂	semidirect
2. #90523	C₂	semidirect
3. #90520	C₂	semidirect
4. #90425	C₂	semidirect
5. #90420	C₂	semidirect
6. #90354	C₂	semidirect
7. #90350	C₂	semidirect
8. #90345	C₂	semidirect
9. #90340	C₂	semidirect
10. #90331	C₂	semidirect
11. #90328	C₂	semidirect
12. #90309	C₂	semidirect
13. #90307	C₂	semidirect
14. #90298	C₂	semidirect
15. D₇×#121	C₂	semidirect
16. #90256	C₂	semidirect
17. #90249	C₂	semidirect
18. #90238	C₂	semidirect
19. #90236	C₂	semidirect
20. #90205	C₂	semidirect
21. #90198	C₂	semidirect
22. #90195	C₂	semidirect
23. C₂×#6455	C₂	semidirect
24. C₂×C₇×#41	C₂²	semidirect
28. C₂×#1157	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×#123	C₂²	semidirect
32. C₇×#123	C₂²	semidirect
33. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₇×#121	C₂²	semidirect
36. C₄×C₇×D₄	C₂²	semidirect
37. C₄×C₇×D₄	C₂²	semidirect
38. C₂×C₇×C₄⋊C₄	C₂²	semidirect
39. C₂×C₇×C₄⋊C₄	C₂²	semidirect
40. #6510	C₂²	semidirect
41. #6510	C₂²	semidirect
43. #6507	C₂²	semidirect
44. #6503	C₂²	semidirect
46. #6502	C₂²	semidirect
47. #6502	C₂²	semidirect
48. #6502	C₂²	semidirect
49. #6502	C₂²	semidirect
51. #6501	C₂²	semidirect
54. #6499	C₂²	semidirect
55. D₄×Dic₇	C₂²	semidirect
56. D₄×Dic₇	C₂²	semidirect
58. #6493	C₂²	semidirect
59. #6493	C₂²	semidirect
60. #6492	C₂²	semidirect
61. #6492	C₂²	semidirect
63. C₄×C₂²⋊D₇	C₂²	semidirect
64. C₄×C₂²⋊D₇	C₂²	semidirect
65. C₄×C₂²⋊D₇	C₂²	semidirect
66. C₄×C₂²⋊D₇	C₂²	semidirect
67. C₄×C₂²⋊D₇	C₂²	semidirect
68. C₄×C₂²⋊D₇	C₂²	semidirect
71. #6489	C₂²	semidirect
72. C₂×C₄⋊Dic₇	C₂²	semidirect
73. C₂×C₄×Dic₇	C₂²	semidirect
74. #6461	C₂²	semidirect
75. #6461	C₂²	semidirect
77. #6459	C₂²	semidirect
78. #6459	C₂²	semidirect
80. #6458	C₂²	semidirect
81. #6458	C₂²	semidirect
83. #6457	C₂²	semidirect
84. #6457	C₂²	semidirect
86. #6456	C₂²	semidirect
90. #6455	C₂²	semidirect
91. #6455	C₂²	semidirect
92. #6455	C₂²	semidirect
93. #6455	C₂²	semidirect
94. #6455	C₂²	semidirect
96. D₇×C₄⋊C₄	C₂²	semidirect
97. #6453	C₂²	semidirect
98. #6452	C₂²	semidirect
99. #6451	C₂²	semidirect
100. #6450	C₂²	semidirect
101. #6449	C₂²	semidirect
102. #6448	C₂²	semidirect
103. #6448	C₂²	semidirect
105. #6447	C₂²	semidirect
106. #6447	C₂²	semidirect
108. #6446	C₂²	semidirect
111. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
112. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
115. #6442	C₂²	semidirect
116. #6442	C₂²	semidirect
117. #6441	C₂²	semidirect
118. #6440	C₂²	semidirect
119. C₄×D₂₈	C₂²	semidirect
120. C₄×D₂₈	C₂²	semidirect
122. #6433	C₂²	semidirect
238. #547	D₇	semidirect
316. C₄×D₇	#41	semidirect
321. C₂×#41	C₂×D₇	semidirect
327. C₄⋊Q₈	C₂×D₇	semidirect
349. #123	C₂×D₇	semidirect
350. #123	C₂×D₇	semidirect
356. C₂²⋊Q₈	C₂×D₇	semidirect
374. #121	C₂×D₇	semidirect
395. C₄×D₄	C₂×D₇	semidirect
396. C₄×D₄	C₂×D₇	semidirect
411. C₂×C₄⋊C₄	C₂×D₇	semidirect
412. C₂×C₄⋊C₄	C₂×D₇	semidirect
640. C₇	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₇×#547	2
#90523	2
#90520	2
#90425	2
#90420	2
#90354	2
#90350	2
#90345	2
#90340	2
#90331	2
#90328	2
#90309	2
#90307	2
#90298	2
D₇×#121	2
#90256	2
#90249	2
#90238	2
#90236	2
#90205	2
#90198	2
#90195	2
C₂×#6455	2
#3494	7