Subgroups — #11743430

Order 896.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#536	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	#90508	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#90423	C₂	1	1	yes	maximal, characteristic, complemented
7	#90419	C₂	1	1	yes	maximal, characteristic, complemented
8	#90418	C₂	1	1	yes	maximal, characteristic, complemented
9	#90415	C₂	1	1	yes	maximal, characteristic, complemented
10	#90373	C₂	1	1	yes	maximal, characteristic, complemented
11	#90367	C₂	1	1	yes	maximal, characteristic, complemented
12	D₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
13	#90362	C₂	1	1	yes	maximal, characteristic, complemented
14	#90358	C₂	1	2	yes	maximal, complemented
15	#90353	C₂	1	2	yes	maximal, complemented
16	#90350	C₂	1	2	yes	maximal, complemented
17	#90348	C₂	1	2	yes	maximal, complemented
18	#90337	C₂	1	2	yes	maximal, complemented
19	#90331	C₂	1	2	yes	maximal, complemented
20	#90328	C₂	1	2	yes	maximal, complemented
21	#90325	C₂	1	2	yes	maximal, complemented
22	#90225	C₂	1	1	yes	maximal, characteristic, complemented
23	#90219	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×#1161	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₇×#124	C₂²	1	1	yes	characteristic
33	C₇×#124	C₂²	1	1	yes	characteristic
34	C₇×#123	C₂²	1	2	yes	complemented
35	C₇×#123	C₂²	1	2	yes	complemented
36	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₇×#117	C₂²	1	1	yes	characteristic, complemented
39	#6510	C₂²	1	1	yes	characteristic
40	#6510	C₂²	1	1	yes	characteristic
41	#6510	C₂²	1	2	yes	complemented
42	#6509	C₂²	1	1	yes	characteristic
43	#6509	C₂²	1	1	yes	characteristic
44	#6509	C₂²	1	2	yes	—
45	#6509	C₂²	1	1	yes	characteristic, complemented
46	#6509	C₂²	1	2	yes	complemented
47	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
48	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
50	#6507	C₂²	1	1	yes	characteristic, complemented
51	#6507	C₂²	1	2	yes	complemented
52	#6502	C₂²	1	2	yes	—
53	#6501	C₂²	1	1	yes	characteristic
54	#6501	C₂²	1	2	yes	complemented
55	#6500	C₂²	1	2	yes	—
56	#6499	C₂²	1	1	yes	characteristic
57	#6499	C₂²	1	2	yes	complemented
58	D₄×Dic₇	C₂²	1	1	yes	characteristic
59	#6493	C₂²	1	1	yes	characteristic
60	#6493	C₂²	1	2	yes	complemented
61	#6492	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
67	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
68	#6487	C₂²	1	1	yes	characteristic, complemented
69	#6487	C₂²	1	2	yes	complemented
70	#6487	C₂²	1	2	yes	complemented
71	#6461	C₂²	1	2	yes	complemented
72	#6461	C₂²	1	2	yes	complemented
73	#6461	C₂²	1	1	yes	characteristic, complemented
74	#6461	C₂²	1	2	yes	complemented
75	#6460	C₂²	1	2	yes	—
76	#6460	C₂²	1	2	yes	complemented
77	#6459	C₂²	1	2	yes	—
78	#6459	C₂²	1	1	yes	characteristic
79	#6459	C₂²	1	2	yes	complemented
80	#6459	C₂²	1	2	yes	complemented
81	#6459	C₂²	1	2	yes	complemented
82	#6459	C₂²	1	2	yes	complemented
83	#6457	C₂²	1	1	yes	characteristic
84	#6457	C₂²	1	2	yes	complemented
85	#6457	C₂²	1	2	yes	complemented
86	#6456	C₂²	1	2	yes	—
87	#6455	C₂²	1	2	yes	—
88	#6455	C₂²	1	2	yes	complemented
89	#6453	C₂²	1	2	yes	complemented
90	#6452	C₂²	1	1	yes	characteristic, complemented
91	#6451	C₂²	1	2	yes	complemented
92	#6450	C₂²	1	2	yes	complemented
93	#6449	C₂²	1	2	yes	complemented
94	#6448	C₂²	1	2	yes	—
95	#6448	C₂²	1	2	yes	—
96	#6448	C₂²	1	2	yes	complemented
97	#6448	C₂²	1	1	yes	characteristic, complemented
98	#6448	C₂²	1	2	yes	complemented
99	#6447	C₂²	1	1	yes	characteristic
100	#6447	C₂²	1	2	yes	—
101	#6446	C₂²	1	1	yes	characteristic
102	#6446	C₂²	1	2	yes	—
103	#6446	C₂²	1	2	yes	complemented
104	#6445	C₂²	1	2	yes	—
105	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
106	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
107	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
108	#6442	C₂²	1	2	yes	complemented
109	#6442	C₂²	1	1	yes	characteristic, complemented
110	#6442	C₂²	1	2	yes	complemented
111	#6442	C₂²	1	2	yes	complemented
112	#6441	C₂²	1	2	yes	complemented
113	#6441	C₂²	1	2	yes	complemented
114	#6440	C₂²	1	2	yes	complemented
115	#6438	C₂²	1	1	yes	characteristic
116	C₄×D₂₈	C₂²	1	1	yes	characteristic
117	C₄×D₂₈	C₂²	1	1	yes	characteristic
118	#6435	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₇	C₂²	1	1	yes	characteristic
120	#6432	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3561	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₇×#41	—	4	2	no	—
126	C₂×C₇×Q₈	—	4	2	no	—
127	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₇×Q₈	C₂³	1	2	yes	—
131	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₂×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂³	1	2	yes	—
135	C₂²×C₄×C₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₇	C₂³	1	2	yes	—
142	#1161	—	4	2	no	—
143	Q₈×D₇	—	4	2	no	—
144	Q₈×D₇	—	4	2	no	—
145	D₄×D₇	—	4	2	no	—
146	C₂×D₂₈	C₂³	1	1	yes	characteristic
147	C₂×D₂₈	C₂³	1	1	yes	characteristic
148	C₂×D₂₈	C₂³	1	2	yes	—
149	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₇	C₂³	1	2	yes	—
154	C₂×C₄×D₇	C₂³	1	2	yes	—
155	C₂×C₄×D₇	C₂³	1	2	yes	—
156	C₂×C₄×D₇	C₂³	1	2	yes	—
157	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
158	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
159	C₂×Dic₁₄	C₂³	1	2	yes	—
160	C₂×Dic₁₄	C₂³	1	2	yes	—
161	C₂×Dic₁₄	C₂³	1	2	yes	—
162	C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇	C₂³	1	2	yes	—
183	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
191	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₇	C₂³	1	2	yes	—
204	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₇	C₂³	1	2	yes	—
206	C₄⋊Dic₇	C₂³	1	2	yes	—
207	C₄⋊Dic₇	C₂³	1	2	yes	—
208	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₇⋊C₄	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₇⋊C₄	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	2	yes	—
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	1	yes	characteristic
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	C₄×Dic₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₇	C₂³	1	2	yes	—
224	C₄×Dic₇	C₂³	1	1	yes	characteristic
225	C₄×Dic₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₇	C₂³	1	2	yes	—
227	C₄×Dic₇	C₂³	1	2	yes	—
228	C₄×Dic₇	C₂³	1	2	yes	—
229	#563	—	7	2	no	—
230	#562	—	7	2	no	—
231	#556	—	7	1	no	—
232	#556	—	7	1	no	—
233	#551	—	7	2	no	—
234	#551	—	7	2	no	—
235	D₄×Q₈	—	7	1	no	—
236	D₄×Q₈	—	7	1	no	—
237	#548	—	7	1	no	—
238	#548	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	1	no	—
241	#543	—	7	2	no	—
242	#542	—	7	1	no	—
243	#542	—	7	2	no	—
244	#542	—	7	2	no	—
245	#542	—	7	1	no	—
246	#538	—	7	2	no	—
247	#536	—	7	1	no	—
248	#536	D₇	1	1	yes	characteristic, complemented
249	#533	—	7	1	no	—
250	#529	—	7	1	no	—
251	C₂×#124	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	2	yes	—
253	C₂³×C₇	C₂⁴	1	1	yes	characteristic
254	C₂²×D₇	—	2	4	no	—
255	C₂²×D₇	—	4	2	no	—
256	C₂²×D₇	—	4	2	no	—
257	C₂²×D₇	C₂⁴	1	2	yes	—
258	C₂²×D₇	C₂⁴	1	1	yes	characteristic
259	C₂²×D₇	C₂⁴	1	1	yes	characteristic
260	C₇×Q₈	—	2	2	no	—
261	C₇×Q₈	—	2	2	no	—
262	C₇×Q₈	—	2	2	no	—
263	C₇×Q₈	—	4	2	no	—
264	C₇×D₄	—	2	2	no	—
265	C₇×D₄	—	4	2	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	4	2	no	—
268	C₂×C₄×C₇	—	4	2	no	—
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂⁴	1	2	yes	—
273	C₂×C₄×C₇	C₂⁴	1	2	yes	—
274	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²⋊D₇	—	2	2	no	—
279	C₂²⋊D₇	—	4	2	no	—
280	C₂²⋊D₇	—	4	2	no	—
281	C₂²⋊D₇	—	4	1	no	—
282	C₂²⋊D₇	—	4	2	no	—
283	C₂×Dic₇	—	4	2	no	—
284	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₇	C₂⁴	1	2	yes	—
288	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₇	C₂⁴	1	2	yes	—
290	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₇	C₂⁴	1	2	yes	—
292	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
293	D₂₈	—	2	2	no	—
294	D₂₈	—	2	2	no	—
295	D₂₈	—	4	2	no	—
296	C₄×D₇	—	2	2	no	—
297	C₄×D₇	—	2	2	no	—
298	C₄×D₇	—	2	2	no	—
299	C₄×D₇	—	4	1	no	—
300	C₄×D₇	—	4	2	no	—
301	C₄×D₇	—	4	2	no	—
302	C₄×D₇	—	4	2	no	—
303	C₄×D₇	—	4	2	no	—
304	Dic₁₄	—	2	2	no	—
305	Dic₁₄	—	4	1	no	—
306	Dic₁₄	—	4	2	no	—
307	Dic₁₄	—	4	2	no	—
308	Dic₁₄	—	4	2	no	—
309	C₂×#41	—	7	1	no	—
310	C₂×#41	C₂×D₇	1	1	yes	characteristic
311	C₂²×Q₈	—	7	1	no	—
312	C₂²×Q₈	—	7	1	no	—
313	C₂²×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
314	C₂²×D₄	—	7	1	no	—
315	C₄⋊Q₈	—	7	1	no	—
316	C₄⋊Q₈	—	7	2	no	—
317	C₄⋊Q₈	—	7	2	no	—
318	C₄⋊Q₈	—	7	1	no	—
319	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
320	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
321	#126	—	7	1	no	—
322	#126	—	7	2	no	—
323	#126	—	7	2	no	—
324	#126	—	7	2	no	—
325	#126	—	7	1	no	—
326	#126	—	7	2	no	—
327	#126	—	7	2	no	—
328	#126	—	7	2	no	—
329	#125	—	7	1	no	—
330	#125	—	7	2	no	—
331	#124	—	7	1	no	—
332	#124	—	7	1	no	—
333	#124	—	7	2	no	—
334	#124	—	7	1	no	—
335	#124	—	7	2	no	—
336	#124	—	7	2	no	—
337	#124	—	7	2	no	—
338	#124	—	7	1	no	—
339	#124	—	7	2	no	—
340	#124	—	7	2	no	—
341	#124	—	7	1	no	—
342	#124	C₂×D₇	1	1	yes	characteristic
343	#124	C₂×D₇	1	1	yes	characteristic
344	#123	—	7	2	no	—
345	#123	—	7	1	no	—
346	#123	—	7	2	no	—
347	#123	—	7	2	no	—
348	#123	—	7	1	no	—
349	#123	—	7	2	no	—
350	#123	—	7	2	no	—
351	#123	—	7	2	no	—
352	#123	C₂×D₇	1	2	yes	complemented
353	#123	C₂×D₇	1	2	yes	complemented
354	C₂²⋊Q₈	—	7	1	no	—
355	C₂²⋊Q₈	—	7	1	no	—
356	C₂²⋊Q₈	—	7	1	no	—
357	C₂²⋊Q₈	—	7	2	no	—
358	C₂²⋊Q₈	—	7	2	no	—
359	C₂²⋊Q₈	—	7	1	no	—
360	C₂²⋊Q₈	—	7	2	no	—
361	C₂²⋊Q₈	—	7	2	no	—
362	C₂²⋊Q₈	—	7	1	no	—
363	C₂²⋊Q₈	—	7	2	no	—
364	C₂²⋊Q₈	—	7	2	no	—
365	C₂²⋊Q₈	—	7	2	no	—
366	C₂²⋊Q₈	—	7	2	no	—
367	C₂²⋊Q₈	—	7	2	no	—
368	C₂²⋊Q₈	—	7	2	no	—
369	C₂²⋊Q₈	—	7	2	no	—
370	C₂²⋊Q₈	—	7	2	no	—
371	C₂²⋊Q₈	—	7	2	no	—
372	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
373	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
374	#121	—	7	2	no	—
375	#121	—	7	1	no	—
376	#121	—	7	2	no	—
377	#121	—	7	2	no	—
378	#121	—	7	1	no	—
379	#121	—	7	1	no	—
380	#121	—	7	2	no	—
381	#120	—	7	2	no	—
382	#120	—	7	2	no	—
383	C₄×Q₈	—	7	1	no	—
384	C₄×Q₈	—	7	1	no	—
385	C₄×Q₈	—	7	1	no	—
386	C₄×Q₈	—	7	2	no	—
387	C₄×Q₈	—	7	1	no	—
388	C₄×Q₈	—	7	1	no	—
389	C₄×D₄	—	7	1	no	—
390	C₄×D₄	—	7	1	no	—
391	C₄×D₄	—	7	1	no	—
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	1	no	—
397	C₄×D₄	—	7	1	no	—
398	#117	—	7	2	no	—
399	#117	—	7	2	no	—
400	#117	—	7	2	no	—
401	#117	—	7	1	no	—
402	#117	C₂×D₇	1	1	yes	characteristic, complemented
403	C₂×C₂²⋊C₄	—	7	2	no	—
404	C₂×C₂²⋊C₄	—	7	2	no	—
405	C₂×C₂²⋊C₄	—	7	2	no	—
406	C₂×C₂²⋊C₄	—	7	2	no	—
407	C₂×C₄²	—	7	1	no	—
408	C₂²×C₇	—	2	2	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	—	2	1	no	—
411	C₂²×C₇	—	2	2	no	—
412	C₂²×C₇	—	2	2	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	C₂⁵	1	1	yes	characteristic
415	C₂×D₇	—	2	1	no	—
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	2	2	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	—	8	4	no	—
424	C₂×D₇	2₋¹⁺⁴	1	2	yes	—
425	C₄×C₇	—	2	2	no	—
426	C₄×C₇	—	2	2	no	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	2	1	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	—	2	1	no	—
432	C₄×C₇	—	2	1	no	—
433	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
434	Dic₇	—	2	2	no	—
435	Dic₇	—	2	1	no	—
436	Dic₇	—	2	1	no	—
437	Dic₇	—	2	1	no	—
438	Dic₇	—	2	1	no	—
439	Dic₇	—	2	1	no	—
440	Dic₇	—	2	2	no	—
441	Dic₇	—	2	1	no	—
442	Dic₇	—	2	2	no	—
443	C₂⁴	—	7	2	no	—
444	#41	—	4	2	no	—
445	#41	—	28	2	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	—	7	1	no	—
448	C₂×Q₈	—	7	1	no	—
449	C₂×Q₈	—	7	2	no	—
450	C₂×Q₈	—	7	2	no	—
451	C₂×Q₈	—	7	2	no	—
452	C₂×Q₈	—	28	2	no	—
453	C₂×Q₈	—	28	2	no	—
454	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
455	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
456	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
457	C₂×Q₈	C₂²×D₇	1	2	yes	—
458	C₂×D₄	—	7	1	no	—
459	C₂×D₄	—	7	2	no	—
460	C₂×D₄	—	7	2	no	—
461	C₂×D₄	—	7	1	no	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	7	1	no	—
464	C₂×D₄	—	7	1	no	—
465	C₂×D₄	—	7	2	no	—
466	C₂×D₄	—	28	2	no	—
467	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
468	C₂×D₄	C₂²×D₇	1	2	yes	—
469	C₂²×C₄	—	7	2	no	—
470	C₂²×C₄	—	7	1	no	—
471	C₂²×C₄	—	7	1	no	—
472	C₂²×C₄	—	7	1	no	—
473	C₂²×C₄	—	7	1	no	—
474	C₂²×C₄	—	7	2	no	—
475	C₂²×C₄	—	7	2	no	—
476	C₂²×C₄	—	7	2	no	—
477	C₂²×C₄	—	7	2	no	—
478	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
479	C₂²×C₄	C₂²×D₇	1	2	yes	—
480	C₂²×C₄	C₂²×D₇	1	2	yes	—
481	C₄⋊C₄	—	7	1	no	—
482	C₄⋊C₄	—	7	1	no	—
483	C₄⋊C₄	—	7	2	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	2	no	—
487	C₄⋊C₄	—	7	2	no	—
488	C₄⋊C₄	—	7	2	no	—
489	C₄⋊C₄	—	7	1	no	—
490	C₄⋊C₄	—	7	2	no	—
491	C₄⋊C₄	—	7	2	no	—
492	C₄⋊C₄	—	7	1	no	—
493	C₄⋊C₄	—	7	2	no	—
494	C₄⋊C₄	—	7	1	no	—
495	C₄⋊C₄	—	7	2	no	—
496	C₄⋊C₄	—	7	1	no	—
497	C₄⋊C₄	—	7	1	no	—
498	C₄⋊C₄	—	7	1	no	—
499	C₄⋊C₄	—	7	2	no	—
500	C₄⋊C₄	—	7	2	no	—
501	C₄⋊C₄	—	7	2	no	—
502	C₄⋊C₄	C₂²×D₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₇	1	2	yes	—
504	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₇	1	2	yes	—
507	C₄⋊C₄	C₂²×D₇	1	2	yes	—
508	C₂²⋊C₄	—	7	2	no	—
509	C₂²⋊C₄	—	7	2	no	—
510	C₂²⋊C₄	—	7	2	no	—
511	C₂²⋊C₄	—	7	1	no	—
512	C₂²⋊C₄	—	7	2	no	—
513	C₂²⋊C₄	—	7	1	no	—
514	C₂²⋊C₄	—	7	2	no	—
515	C₂²⋊C₄	—	7	1	no	—
516	C₂²⋊C₄	—	7	1	no	—
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	2	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	2	no	—
525	C₂²⋊C₄	—	7	2	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	1	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
537	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
538	C₄²	—	7	1	no	—
539	C₄²	—	7	1	no	—
540	C₄²	—	7	1	no	—
541	C₄²	—	7	2	no	—
542	C₄²	—	7	2	no	—
543	C₄²	—	7	1	no	—
544	C₄²	—	7	2	no	—
545	C₄²	—	7	2	no	—
546	C₄²	C₂²×D₇	1	1	yes	characteristic
547	C₄²	C₂²×D₇	1	1	yes	characteristic
548	C₂×C₇	—	4	2	no	—
549	C₂×C₇	—	4	1	no	—
550	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂×C₇	#585	1	1	yes	characteristic
553	D₇	—	2	2	no	—
554	D₇	—	4	1	no	—
555	D₇	—	4	2	no	—
556	C₂³	—	7	1	no	—
557	C₂³	—	7	2	no	—
558	C₂³	—	7	1	no	—
559	C₂³	—	14	4	no	—
560	C₂³	—	28	2	no	—
561	C₂³	—	28	2	no	—
562	C₂³	C₂³×D₇	1	2	yes	—
563	C₂³	C₂³×D₇	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	14	2	no	—
569	Q₈	—	28	1	no	—
570	Q₈	—	28	2	no	—
571	Q₈	—	28	2	no	—
572	Q₈	—	28	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	14	2	no	—
576	D₄	—	14	2	no	—
577	D₄	—	14	2	no	—
578	D₄	—	28	2	no	—
579	D₄	—	28	2	no	—
580	D₄	—	28	2	no	—
581	D₄	—	28	1	no	—
582	D₄	—	28	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	7	1	no	—
587	C₂×C₄	—	7	1	no	—
588	C₂×C₄	—	7	1	no	—
589	C₂×C₄	—	7	2	no	—
590	C₂×C₄	—	7	2	no	—
591	C₂×C₄	—	7	1	no	—
592	C₂×C₄	—	7	1	no	—
593	C₂×C₄	—	7	2	no	—
594	C₂×C₄	—	7	1	no	—
595	C₂×C₄	—	14	2	no	—
596	C₂×C₄	—	14	2	no	—
597	C₂×C₄	—	14	2	no	—
598	C₂×C₄	—	28	2	no	—
599	C₂×C₄	—	28	1	no	—
600	C₂×C₄	—	28	2	no	—
601	C₂×C₄	—	28	2	no	—
602	C₂×C₄	—	28	2	no	—
603	C₂×C₄	—	28	2	no	—
604	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₇	1	2	yes	—
608	C₂×C₄	C₂³×D₇	1	2	yes	—
609	C₂×C₄	C₂³×D₇	1	2	yes	—
610	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
613	C₇	#3561	1	1	yes	characteristic, complemented, Sylow
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	7	2	no	—
621	C₂²	—	14	1	no	—
622	C₂²	—	14	1	no	—
623	C₂²	—	14	1	no	—
624	C₂²	—	14	2	no	—
625	C₂²	—	14	1	no	—
626	C₂²	—	14	2	no	—
627	C₂²	—	14	2	no	—
628	C₂²	—	14	1	no	—
629	C₂²	—	56	4	no	—
630	C₂²	C₂⁴×D₇	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	14	1	no	—
640	C₄	—	14	1	no	—
641	C₄	—	14	2	no	—
642	C₄	—	14	1	no	—
643	C₄	—	14	1	no	—
644	C₄	—	14	1	no	—
645	C₄	—	14	1	no	—
646	C₄	—	14	2	no	—
647	C₄	—	14	2	no	—
648	C₄	#6548	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	14	2	no	—
652	C₂	—	28	2	no	—
653	C₂	—	28	1	no	—
654	C₂	C₂×#6548	1	1	yes	characteristic
655	C₂	D₇×2₋¹⁺⁴	1	1	yes	characteristic
656	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#536	C₂
hypercenter	#536	D₇
hypocenter	C₇	#3561
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₇×#536	C₂	semidirect
2. #90522	C₂	semidirect
3. #90520	C₂	semidirect
4. #90508	C₂	semidirect
5. Q₈×C₂²⋊D₇	C₂	semidirect
6. #90423	C₂	semidirect
7. #90419	C₂	semidirect
8. #90418	C₂	semidirect
9. #90415	C₂	semidirect
10. #90373	C₂	semidirect
11. #90367	C₂	semidirect
12. D₇×#124	C₂	semidirect
13. #90362	C₂	semidirect
14. #90358	C₂	semidirect
15. #90353	C₂	semidirect
16. #90350	C₂	semidirect
17. #90348	C₂	semidirect
18. #90337	C₂	semidirect
19. #90331	C₂	semidirect
20. #90328	C₂	semidirect
21. #90325	C₂	semidirect
22. #90225	C₂	semidirect
23. #90219	C₂	semidirect
25. C₂²×C₇×Q₈	C₂²	semidirect
28. C₂×Q₈×D₇	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×C₄⋊Q₈	C₂²	semidirect
34. C₇×#123	C₂²	semidirect
35. C₇×#123	C₂²	semidirect
36. C₇×C₂²⋊Q₈	C₂²	semidirect
37. C₇×C₂²⋊Q₈	C₂²	semidirect
38. C₇×#117	C₂²	semidirect
41. #6510	C₂²	semidirect
45. #6509	C₂²	semidirect
46. #6509	C₂²	semidirect
47. Q₈×Dic₇	C₂²	semidirect
48. Q₈×Dic₇	C₂²	semidirect
49. Q₈×Dic₇	C₂²	semidirect
50. #6507	C₂²	semidirect
51. #6507	C₂²	semidirect
54. #6501	C₂²	semidirect
57. #6499	C₂²	semidirect
60. #6493	C₂²	semidirect
64. C₄×C₂²⋊D₇	C₂²	semidirect
65. C₄×C₂²⋊D₇	C₂²	semidirect
66. C₄×C₂²⋊D₇	C₂²	semidirect
68. #6487	C₂²	semidirect
69. #6487	C₂²	semidirect
70. #6487	C₂²	semidirect
71. #6461	C₂²	semidirect
72. #6461	C₂²	semidirect
73. #6461	C₂²	semidirect
74. #6461	C₂²	semidirect
76. #6460	C₂²	semidirect
79. #6459	C₂²	semidirect
80. #6459	C₂²	semidirect
81. #6459	C₂²	semidirect
82. #6459	C₂²	semidirect
84. #6457	C₂²	semidirect
85. #6457	C₂²	semidirect
88. #6455	C₂²	semidirect
89. #6453	C₂²	semidirect
90. #6452	C₂²	semidirect
91. #6451	C₂²	semidirect
92. #6450	C₂²	semidirect
93. #6449	C₂²	semidirect
96. #6448	C₂²	semidirect
97. #6448	C₂²	semidirect
98. #6448	C₂²	semidirect
103. #6446	C₂²	semidirect
108. #6442	C₂²	semidirect
109. #6442	C₂²	semidirect
110. #6442	C₂²	semidirect
111. #6442	C₂²	semidirect
112. #6441	C₂²	semidirect
113. #6441	C₂²	semidirect
114. #6440	C₂²	semidirect
118. #6435	C₂²	semidirect
120. #6432	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
248. #536	D₇	semidirect
313. C₂²×Q₈	C₂×D₇	semidirect
319. C₄⋊Q₈	C₂×D₇	semidirect
320. C₄⋊Q₈	C₂×D₇	semidirect
352. #123	C₂×D₇	semidirect
353. #123	C₂×D₇	semidirect
372. C₂²⋊Q₈	C₂×D₇	semidirect
373. C₂²⋊Q₈	C₂×D₇	semidirect
402. #117	C₂×D₇	semidirect
613. C₇	#3561	semidirect

Maximal subgroups

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

subgroup	index
C₇×#536	2
#90522	2
#90520	2
#90508	2
Q₈×C₂²⋊D₇	2
#90423	2
#90419	2
#90418	2
#90415	2
#90373	2
#90367	2
D₇×#124	2
#90362	2
#90358	2
#90353	2
#90350	2
#90348	2
#90337	2
#90331	2
#90328	2
#90325	2
#90225	2
#90219	2
#3561	7