Subgroups — #11743227

Order 896.

1040 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#90396	C₂	1	2	yes	maximal, complemented
3	#90393	C₂	1	2	yes	maximal, complemented
4	#90382	C₂	1	1	yes	maximal, characteristic, complemented
5	#90379	C₂	1	1	yes	maximal, characteristic, complemented
6	#90371	C₂	1	1	yes	maximal, characteristic, complemented
7	D₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	#90355	C₂	1	2	yes	maximal, complemented
9	#90350	C₂	1	2	yes	maximal, complemented
10	#90334	C₂	1	1	yes	maximal, characteristic, complemented
11	#90319	C₂	1	1	yes	maximal, characteristic, complemented
12	#90298	C₂	1	1	yes	maximal, characteristic
13	#90294	C₂	1	1	yes	maximal, characteristic, complemented
14	#90273	C₂	1	1	yes	maximal, characteristic, complemented
15	#90263	C₂	1	1	yes	maximal, characteristic, complemented
16	#90252	C₂	1	1	yes	maximal, characteristic, complemented
17	#90250	C₂	1	2	yes	maximal, complemented
18	#90247	C₂	1	2	yes	maximal, complemented
19	#90236	C₂	1	1	yes	maximal, characteristic, complemented
20	#90224	C₂	1	2	yes	maximal, complemented
21	#90218	C₂	1	2	yes	maximal, complemented
22	#90170	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#1157	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×#1157	C₂²	1	1	yes	characteristic
27	C₇×#126	C₂²	1	2	yes	complemented
28	C₇×#125	C₂²	1	1	yes	characteristic, complemented
29	C₇×#124	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×#121	C₂²	1	1	yes	characteristic
33	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×D₄	C₂²	1	2	yes	complemented
36	C₇×#117	C₂²	1	2	yes	complemented
37	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
38	#6510	C₂²	1	1	yes	characteristic
39	#6509	C₂²	1	1	yes	characteristic, complemented
40	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
41	#6503	C₂²	1	2	yes	—
42	#6501	C₂²	1	1	yes	characteristic
43	#6500	C₂²	1	2	yes	—
44	#6499	C₂²	1	1	yes	characteristic
45	#6499	C₂²	1	2	yes	complemented
46	#6498	C₂²	1	2	yes	complemented
47	D₄×Dic₇	C₂²	1	1	yes	characteristic
48	#6493	C₂²	1	1	yes	characteristic
49	#6492	C₂²	1	2	yes	complemented
50	#6492	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
57	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
58	#6489	C₂²	1	1	yes	characteristic, complemented
59	#6487	C₂²	1	1	yes	characteristic, complemented
60	#6487	C₂²	1	2	yes	complemented
61	#6461	C₂²	1	2	yes	complemented
62	#6461	C₂²	1	2	yes	complemented
63	#6460	C₂²	1	1	yes	characteristic, complemented
64	#6460	C₂²	1	2	yes	complemented
65	#6459	C₂²	1	2	yes	—
66	#6459	C₂²	1	2	yes	—
67	#6459	C₂²	1	2	yes	complemented
68	#6458	C₂²	1	1	yes	characteristic
69	#6457	C₂²	1	2	yes	—
70	#6457	C₂²	1	2	yes	complemented
71	#6457	C₂²	1	2	yes	complemented
72	#6456	C₂²	1	1	yes	characteristic
73	#6456	C₂²	1	2	yes	complemented
74	#6455	C₂²	1	1	yes	characteristic
75	#6455	C₂²	1	1	yes	characteristic
76	#6455	C₂²	1	2	yes	—
77	#6455	C₂²	1	2	yes	complemented
78	#6451	C₂²	1	1	yes	characteristic, complemented
79	#6451	C₂²	1	1	yes	characteristic, complemented
80	#6451	C₂²	1	2	yes	complemented
81	#6450	C₂²	1	2	yes	complemented
82	#6450	C₂²	1	2	yes	complemented
83	#6450	C₂²	1	1	yes	characteristic, complemented
84	#6450	C₂²	1	2	yes	complemented
85	#6448	C₂²	1	2	yes	—
86	#6448	C₂²	1	2	yes	—
87	#6448	C₂²	1	2	yes	—
88	#6448	C₂²	1	2	yes	complemented
89	#6448	C₂²	1	2	yes	complemented
90	#6448	C₂²	1	2	yes	complemented
91	#6446	C₂²	1	2	yes	—
92	#6446	C₂²	1	2	yes	complemented
93	#6446	C₂²	1	2	yes	complemented
94	#6445	C₂²	1	2	yes	—
95	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
96	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
97	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
99	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
100	#6442	C₂²	1	2	yes	complemented
101	#6442	C₂²	1	2	yes	complemented
102	#6442	C₂²	1	2	yes	complemented
103	#6441	C₂²	1	2	yes	complemented
104	#6440	C₂²	1	2	yes	complemented
105	#6439	C₂²	1	2	yes	complemented
106	#6439	C₂²	1	2	yes	complemented
107	#6438	C₂²	1	1	yes	characteristic
108	#6438	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	#6435	C₂²	1	1	yes	characteristic
113	#6435	C₂²	1	2	yes	—
114	#6435	C₂²	1	2	yes	complemented
115	#6435	C₂²	1	1	yes	characteristic, complemented
116	C₄²×D₇	C₂²	1	1	yes	characteristic
117	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
118	#6433	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	2	yes	complemented
123	#3510	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₄	C₂³	1	2	yes	—
128	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂³	1	2	yes	—
130	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
137	C₂²×Dic₇	C₂³	1	2	yes	—
138	Q₈×D₇	—	2	4	no	—
139	D₄×D₇	—	2	4	no	—
140	#1157	—	2	4	no	—
141	C₂×D₂₈	C₂³	1	1	yes	characteristic
142	C₂×D₂₈	C₂³	1	1	yes	characteristic
143	C₂×D₂₈	C₂³	1	2	yes	—
144	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₇	C₂³	1	2	yes	—
146	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₇	C₂³	1	2	yes	—
151	C₂×C₄×D₇	C₂³	1	2	yes	—
152	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
153	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
155	C₂×Dic₁₄	C₂³	1	2	yes	—
156	C₂×Dic₁₄	C₂³	1	2	yes	—
157	C₂×Dic₁₄	C₂³	1	2	yes	—
158	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₄²×C₇	C₂³	1	2	yes	—
171	C₄²×C₇	C₂³	1	1	yes	characteristic
172	C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₇	C₂³	1	2	yes	—
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	1	yes	characteristic
180	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
181	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
197	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₇	C₂³	1	2	yes	—
201	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂³	1	2	yes	—
203	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₇⋊C₄	C₂³	1	2	yes	—
205	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₇⋊C₄	C₂³	1	2	yes	—
209	Dic₇⋊C₄	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	2	yes	—
211	Dic₇⋊C₄	C₂³	1	2	yes	—
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	Dic₇⋊C₄	C₂³	1	2	yes	—
214	Dic₇⋊C₄	C₂³	1	2	yes	—
215	C₄×Dic₇	C₂³	1	1	yes	characteristic
216	C₄×Dic₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₇	C₂³	1	2	yes	—
220	C₄×Dic₇	C₂³	1	2	yes	—
221	C₄×Dic₇	C₂³	1	2	yes	—
222	C₄×Dic₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	2	yes	—
226	#559	—	7	2	no	—
227	#559	—	7	2	no	—
228	#556	—	7	2	no	—
229	#556	—	7	2	no	—
230	#551	—	7	2	no	—
231	#551	—	7	2	no	—
232	#551	—	7	2	no	—
233	#551	—	7	2	no	—
234	#542	—	7	1	no	—
235	#542	—	7	1	no	—
236	#542	—	7	1	no	—
237	#542	—	7	1	no	—
238	#536	—	7	1	no	—
239	#535	—	7	1	no	—
240	#533	—	7	1	no	—
241	#529	—	7	1	no	—
242	#529	—	7	1	no	—
243	#529	—	7	1	no	—
244	#529	D₇	1	1	yes	characteristic, complemented
245	C₂×#124	—	7	1	no	—
246	#519	—	7	1	no	—
247	#518	—	7	1	no	—
248	C₄×#41	—	7	1	no	—
249	C₂³×C₇	C₂⁴	1	2	yes	—
250	C₂³×C₇	C₂⁴	1	1	yes	characteristic
251	C₂²×D₇	—	2	4	no	—
252	C₂²×D₇	—	4	2	no	—
253	C₂²×D₇	—	4	2	no	—
254	C₂²×D₇	C₂⁴	1	2	yes	—
255	C₂²×D₇	C₂⁴	1	1	yes	characteristic
256	C₂²×D₇	C₂⁴	1	1	yes	characteristic
257	C₇×Q₈	—	2	2	no	—
258	C₇×D₄	—	2	2	no	—
259	C₇×D₄	—	4	2	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	4	2	no	—
262	C₂×C₄×C₇	—	4	1	no	—
263	C₂×C₄×C₇	—	4	1	no	—
264	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	2	yes	—
268	C₂×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂²⋊D₇	—	2	2	no	—
274	C₂²⋊D₇	—	2	2	no	—
275	C₂²⋊D₇	—	2	4	no	—
276	C₂²⋊D₇	—	4	2	no	—
277	C₂²⋊D₇	—	4	2	no	—
278	C₂×Dic₇	—	4	2	no	—
279	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₇	C₂⁴	1	2	yes	—
282	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₇	C₂⁴	1	2	yes	—
284	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₇	C₂⁴	1	2	yes	—
287	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
288	D₂₈	—	2	2	no	—
289	D₂₈	—	2	2	no	—
290	D₂₈	—	4	2	no	—
291	C₄×D₇	—	2	4	no	—
292	C₄×D₇	—	2	2	no	—
293	C₄×D₇	—	4	1	no	—
294	C₄×D₇	—	4	1	no	—
295	C₄×D₇	—	4	2	no	—
296	C₄×D₇	—	4	2	no	—
297	C₄×D₇	—	4	1	no	—
298	C₄×D₇	—	4	1	no	—
299	C₄×D₇	#41	1	4	yes	—
300	Dic₁₄	—	2	2	no	—
301	Dic₁₄	—	2	2	no	—
302	Dic₁₄	—	2	4	no	—
303	Dic₁₄	—	4	2	no	—
304	Dic₁₄	—	4	2	no	—
305	C₂×#41	—	7	1	no	—
306	C₂²×Q₈	—	7	1	no	—
307	C₂²×D₄	—	7	1	no	—
308	C₄⋊Q₈	—	7	1	no	—
309	C₄⋊Q₈	—	7	1	no	—
310	C₄⋊Q₈	—	7	2	no	—
311	#127	—	7	2	no	—
312	#126	—	7	2	no	—
313	#126	—	7	2	no	—
314	#126	—	7	2	no	—
315	#126	—	7	2	no	—
316	#126	—	7	2	no	—
317	#126	—	7	2	no	—
318	#126	—	7	2	no	—
319	#126	C₂×D₇	1	2	yes	complemented
320	#125	—	7	1	no	—
321	#125	C₂×D₇	1	1	yes	characteristic, complemented
322	#124	—	7	1	no	—
323	#124	—	7	1	no	—
324	#124	—	7	2	no	—
325	#124	—	7	2	no	—
326	#124	—	7	2	no	—
327	#124	—	7	2	no	—
328	#124	—	7	2	no	—
329	#124	—	7	2	no	—
330	#124	—	7	2	no	—
331	#124	—	7	1	no	—
332	#124	—	7	2	no	—
333	#124	C₂×D₇	1	1	yes	characteristic
334	#123	—	7	2	no	—
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	#123	—	7	2	no	—
338	#123	—	7	2	no	—
339	#123	—	7	2	no	—
340	#123	—	7	2	no	—
341	#123	—	7	2	no	—
342	#123	—	7	2	no	—
343	#123	C₂×D₇	1	2	yes	complemented
344	C₂²⋊Q₈	—	7	1	no	—
345	C₂²⋊Q₈	—	7	1	no	—
346	C₂²⋊Q₈	—	7	2	no	—
347	C₂²⋊Q₈	—	7	1	no	—
348	C₂²⋊Q₈	—	7	2	no	—
349	C₂²⋊Q₈	—	7	2	no	—
350	C₂²⋊Q₈	—	7	2	no	—
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	—	7	2	no	—
353	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
354	#121	—	7	1	no	—
355	#121	—	7	1	no	—
356	#121	—	7	1	no	—
357	#121	C₂×D₇	1	1	yes	characteristic
358	#120	—	7	2	no	—
359	#120	—	7	2	no	—
360	C₄×Q₈	—	7	1	no	—
361	C₄×Q₈	—	7	1	no	—
362	C₄×Q₈	—	7	2	no	—
363	C₄×Q₈	—	7	2	no	—
364	C₄×Q₈	—	7	2	no	—
365	C₄×Q₈	—	7	1	no	—
366	C₄×Q₈	—	7	1	no	—
367	C₄×Q₈	—	7	1	no	—
368	C₄×Q₈	—	7	2	no	—
369	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
370	C₄×D₄	—	7	1	no	—
371	C₄×D₄	—	7	1	no	—
372	C₄×D₄	—	7	1	no	—
373	C₄×D₄	—	7	1	no	—
374	C₄×D₄	—	7	1	no	—
375	C₄×D₄	—	7	2	no	—
376	C₄×D₄	—	7	2	no	—
377	C₄×D₄	—	7	1	no	—
378	C₄×D₄	—	7	2	no	—
379	C₄×D₄	—	7	2	no	—
380	C₄×D₄	—	7	2	no	—
381	C₄×D₄	—	7	1	no	—
382	C₄×D₄	—	7	1	no	—
383	C₄×D₄	—	7	1	no	—
384	C₄×D₄	C₂×D₇	1	1	yes	characteristic
385	C₄×D₄	C₂×D₇	1	2	yes	complemented
386	#117	—	7	1	no	—
387	#117	—	7	1	no	—
388	#117	—	7	1	no	—
389	#117	—	7	2	no	—
390	#117	—	7	2	no	—
391	#117	—	7	2	no	—
392	#117	—	7	1	no	—
393	#117	—	7	1	no	—
394	#117	—	7	2	no	—
395	#117	—	7	2	no	—
396	#117	C₂×D₇	1	2	yes	complemented
397	C₂×C₂²⋊C₄	—	7	2	no	—
398	C₂×C₂²⋊C₄	—	7	2	no	—
399	C₂×C₂²⋊C₄	—	7	2	no	—
400	C₂×C₂²⋊C₄	—	7	2	no	—
401	C₂×C₄²	—	7	1	no	—
402	C₂×C₄²	—	7	1	no	—
403	C₂×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	2	no	—
406	C₂²×C₇	—	2	2	no	—
407	C₂²×C₇	—	2	1	no	—
408	C₂²×C₇	—	2	2	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	C₂⁵	1	1	yes	characteristic
411	C₂×D₇	—	2	1	no	—
412	C₂×D₇	—	2	1	no	—
413	C₂×D₇	—	2	1	no	—
414	C₂×D₇	—	2	2	no	—
415	C₂×D₇	—	2	1	no	—
416	C₂×D₇	—	2	2	no	—
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	2	2	no	—
419	C₂×D₇	—	8	4	no	—
420	C₂×D₇	C₂×#41	1	2	yes	—
421	C₄×C₇	—	2	2	no	—
422	C₄×C₇	—	2	1	no	—
423	C₄×C₇	—	2	2	no	—
424	C₄×C₇	—	2	2	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	C₂×#41	1	2	yes	—
430	Dic₇	—	2	2	no	—
431	Dic₇	—	2	1	no	—
432	Dic₇	—	2	1	no	—
433	Dic₇	—	2	1	no	—
434	Dic₇	—	2	2	no	—
435	Dic₇	—	2	2	no	—
436	Dic₇	—	2	1	no	—
437	Dic₇	—	2	1	no	—
438	Dic₇	C₂×#41	1	2	yes	—
439	C₂⁴	—	7	2	no	—
440	#41	—	14	4	no	—
441	C₂×Q₈	—	7	1	no	—
442	C₂×Q₈	—	7	2	no	—
443	C₂×Q₈	—	7	1	no	—
444	C₂×Q₈	—	7	2	no	—
445	C₂×Q₈	—	7	2	no	—
446	C₂×Q₈	—	14	4	no	—
447	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
448	C₂×D₄	—	7	1	no	—
449	C₂×D₄	—	7	2	no	—
450	C₂×D₄	—	7	1	no	—
451	C₂×D₄	—	7	2	no	—
452	C₂×D₄	—	7	2	no	—
453	C₂×D₄	—	7	1	no	—
454	C₂×D₄	—	7	1	no	—
455	C₂×D₄	—	7	2	no	—
456	C₂×D₄	—	14	4	no	—
457	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
458	C₂×D₄	C₂²×D₇	1	2	yes	—
459	C₂²×C₄	—	7	1	no	—
460	C₂²×C₄	—	7	2	no	—
461	C₂²×C₄	—	7	1	no	—
462	C₂²×C₄	—	7	2	no	—
463	C₂²×C₄	—	7	1	no	—
464	C₂²×C₄	—	7	1	no	—
465	C₂²×C₄	—	7	1	no	—
466	C₂²×C₄	—	7	1	no	—
467	C₂²×C₄	—	7	2	no	—
468	C₂²×C₄	—	7	2	no	—
469	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²×D₇	1	2	yes	—
473	C₄⋊C₄	—	7	2	no	—
474	C₄⋊C₄	—	7	1	no	—
475	C₄⋊C₄	—	7	1	no	—
476	C₄⋊C₄	—	7	1	no	—
477	C₄⋊C₄	—	7	1	no	—
478	C₄⋊C₄	—	7	2	no	—
479	C₄⋊C₄	—	7	2	no	—
480	C₄⋊C₄	—	7	2	no	—
481	C₄⋊C₄	—	7	2	no	—
482	C₄⋊C₄	—	7	2	no	—
483	C₄⋊C₄	—	7	2	no	—
484	C₄⋊C₄	—	7	2	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	7	1	no	—
488	C₄⋊C₄	—	7	1	no	—
489	C₄⋊C₄	—	7	2	no	—
490	C₄⋊C₄	—	7	2	no	—
491	C₄⋊C₄	C₂²×D₇	1	2	yes	—
492	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₇	1	2	yes	—
495	C₄⋊C₄	C₂²×D₇	1	2	yes	—
496	C₄⋊C₄	C₂²×D₇	1	2	yes	—
497	C₂²⋊C₄	—	7	2	no	—
498	C₂²⋊C₄	—	7	2	no	—
499	C₂²⋊C₄	—	7	2	no	—
500	C₂²⋊C₄	—	7	1	no	—
501	C₂²⋊C₄	—	7	1	no	—
502	C₂²⋊C₄	—	7	2	no	—
503	C₂²⋊C₄	—	7	2	no	—
504	C₂²⋊C₄	—	7	1	no	—
505	C₂²⋊C₄	—	7	1	no	—
506	C₂²⋊C₄	—	7	2	no	—
507	C₂²⋊C₄	—	7	2	no	—
508	C₂²⋊C₄	—	7	2	no	—
509	C₂²⋊C₄	—	7	2	no	—
510	C₂²⋊C₄	—	7	2	no	—
511	C₂²⋊C₄	—	7	2	no	—
512	C₂²⋊C₄	—	7	2	no	—
513	C₂²⋊C₄	—	7	2	no	—
514	C₂²⋊C₄	—	7	1	no	—
515	C₂²⋊C₄	—	7	1	no	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
525	C₄²	—	7	1	no	—
526	C₄²	—	7	1	no	—
527	C₄²	—	7	1	no	—
528	C₄²	—	7	1	no	—
529	C₄²	—	7	1	no	—
530	C₄²	—	7	1	no	—
531	C₄²	—	7	2	no	—
532	C₄²	—	7	2	no	—
533	C₄²	—	7	2	no	—
534	C₄²	—	7	2	no	—
535	C₄²	—	7	2	no	—
536	C₄²	C₂²×D₇	1	1	yes	characteristic
537	C₄²	C₂²×D₇	1	1	yes	characteristic
538	C₄²	C₂²×D₇	1	1	yes	characteristic
539	C₄²	C₂²×D₇	1	1	yes	characteristic
540	C₄²	C₂²×D₇	1	2	yes	—
541	C₂×C₇	—	4	2	no	—
542	C₂×C₇	—	4	1	no	—
543	C₂×C₇	C₂²×#41	1	1	yes	characteristic
544	C₂×C₇	#585	1	1	yes	characteristic
545	C₂×C₇	#585	1	1	yes	characteristic
546	D₇	—	2	2	no	—
547	D₇	—	4	1	no	—
548	D₇	—	4	2	no	—
549	C₂³	—	7	1	no	—
550	C₂³	—	7	2	no	—
551	C₂³	—	7	1	no	—
552	C₂³	—	14	4	no	—
553	C₂³	—	28	2	no	—
554	C₂³	—	28	2	no	—
555	C₂³	C₂³×D₇	1	2	yes	—
556	C₂³	C₂³×D₇	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	14	4	no	—
559	Q₈	—	14	2	no	—
560	Q₈	—	14	2	no	—
561	Q₈	—	28	2	no	—
562	Q₈	—	28	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	14	2	no	—
566	D₄	—	14	4	no	—
567	D₄	—	14	2	no	—
568	D₄	—	14	2	no	—
569	D₄	—	14	2	no	—
570	D₄	—	28	2	no	—
571	D₄	—	28	2	no	—
572	D₄	—	28	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	7	1	no	—
578	C₂×C₄	—	7	4	no	—
579	C₂×C₄	—	7	1	no	—
580	C₂×C₄	—	7	1	no	—
581	C₂×C₄	—	7	2	no	—
582	C₂×C₄	—	7	2	no	—
583	C₂×C₄	—	7	1	no	—
584	C₂×C₄	—	7	1	no	—
585	C₂×C₄	—	7	1	no	—
586	C₂×C₄	—	7	2	no	—
587	C₂×C₄	—	14	4	no	—
588	C₂×C₄	—	14	2	no	—
589	C₂×C₄	—	28	1	no	—
590	C₂×C₄	—	28	1	no	—
591	C₂×C₄	—	28	2	no	—
592	C₂×C₄	—	28	1	no	—
593	C₂×C₄	—	28	1	no	—
594	C₂×C₄	—	28	2	no	—
595	C₂×C₄	—	28	2	no	—
596	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₇	1	2	yes	—
600	C₂×C₄	C₂³×D₇	1	2	yes	—
601	C₂×C₄	C₂³×D₇	1	2	yes	—
602	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
605	C₇	#3510	1	1	yes	characteristic, complemented, Sylow
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	7	2	no	—
613	C₂²	—	14	1	no	—
614	C₂²	—	14	1	no	—
615	C₂²	—	14	1	no	—
616	C₂²	—	14	2	no	—
617	C₂²	—	14	1	no	—
618	C₂²	—	14	1	no	—
619	C₂²	—	14	2	no	—
620	C₂²	—	14	2	no	—
621	C₂²	—	56	4	no	—
622	C₂²	C₂⁴×D₇	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	7	2	no	—
632	C₄	—	14	1	no	—
633	C₄	—	14	2	no	—
634	C₄	—	14	1	no	—
635	C₄	—	14	1	no	—
636	C₄	—	14	2	no	—
637	C₄	—	14	1	no	—
638	C₄	—	14	1	no	—
639	C₄	—	14	2	no	—
640	C₄	D₇×#41	1	2	yes	—
641	C₂	—	4	2	no	—
642	C₂	—	4	1	no	—
643	C₂	—	14	2	no	—
644	C₂	—	28	2	no	—
645	C₂	—	28	1	no	—
646	C₂	C₂×D₇×#41	1	1	yes	characteristic
647	C₂	#90616	1	1	yes	characteristic
648	C₂	#90616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#529	C₂
prime radical	#90298	C₂
hypercenter	#529	D₇
hypocenter	C₇	#3510
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₇×#529	C₂	semidirect
2. #90396	C₂	semidirect
3. #90393	C₂	semidirect
4. #90382	C₂	semidirect
5. #90379	C₂	semidirect
6. #90371	C₂	semidirect
7. D₇×#124	C₂	semidirect
8. #90355	C₂	semidirect
9. #90350	C₂	semidirect
10. #90334	C₂	semidirect
11. #90319	C₂	semidirect
13. #90294	C₂	semidirect
14. #90273	C₂	semidirect
15. #90263	C₂	semidirect
16. #90252	C₂	semidirect
17. #90250	C₂	semidirect
18. #90247	C₂	semidirect
19. #90236	C₂	semidirect
20. #90224	C₂	semidirect
21. #90218	C₂	semidirect
22. #90170	C₂	semidirect
23. C₄×#1157	C₂	semidirect
27. C₇×#126	C₂²	semidirect
28. C₇×#125	C₂²	semidirect
30. C₇×#123	C₂²	semidirect
31. C₇×C₂²⋊Q₈	C₂²	semidirect
33. C₄×C₇×Q₈	C₂²	semidirect
35. C₄×C₇×D₄	C₂²	semidirect
36. C₇×#117	C₂²	semidirect
37. C₂×C₄²×C₇	C₂²	semidirect
39. #6509	C₂²	semidirect
40. Q₈×Dic₇	C₂²	semidirect
45. #6499	C₂²	semidirect
46. #6498	C₂²	semidirect
49. #6492	C₂²	semidirect
50. #6492	C₂²	semidirect
54. C₄×C₂²⋊D₇	C₂²	semidirect
55. C₄×C₂²⋊D₇	C₂²	semidirect
56. C₄×C₂²⋊D₇	C₂²	semidirect
58. #6489	C₂²	semidirect
59. #6487	C₂²	semidirect
60. #6487	C₂²	semidirect
61. #6461	C₂²	semidirect
62. #6461	C₂²	semidirect
63. #6460	C₂²	semidirect
64. #6460	C₂²	semidirect
67. #6459	C₂²	semidirect
70. #6457	C₂²	semidirect
71. #6457	C₂²	semidirect
73. #6456	C₂²	semidirect
77. #6455	C₂²	semidirect
78. #6451	C₂²	semidirect
79. #6451	C₂²	semidirect
80. #6451	C₂²	semidirect
81. #6450	C₂²	semidirect
82. #6450	C₂²	semidirect
83. #6450	C₂²	semidirect
84. #6450	C₂²	semidirect
88. #6448	C₂²	semidirect
89. #6448	C₂²	semidirect
90. #6448	C₂²	semidirect
92. #6446	C₂²	semidirect
93. #6446	C₂²	semidirect
96. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
100. #6442	C₂²	semidirect
101. #6442	C₂²	semidirect
102. #6442	C₂²	semidirect
103. #6441	C₂²	semidirect
104. #6440	C₂²	semidirect
105. #6439	C₂²	semidirect
106. #6439	C₂²	semidirect
108. #6438	C₂²	semidirect
114. #6435	C₂²	semidirect
115. #6435	C₂²	semidirect
117. C₄²×D₇	C₂²	semidirect
118. #6433	C₂²	semidirect
119. C₄×Dic₁₄	C₂²	semidirect
120. C₄×Dic₁₄	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
244. #529	D₇	semidirect
319. #126	C₂×D₇	semidirect
321. #125	C₂×D₇	semidirect
343. #123	C₂×D₇	semidirect
353. C₂²⋊Q₈	C₂×D₇	semidirect
369. C₄×Q₈	C₂×D₇	semidirect
385. C₄×D₄	C₂×D₇	semidirect
396. #117	C₂×D₇	semidirect
403. C₂×C₄²	C₂×D₇	semidirect
605. C₇	#3510	semidirect

Maximal subgroups

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

subgroup	index
C₇×#529	2
#90396	2
#90393	2
#90382	2
#90379	2
#90371	2
D₇×#124	2
#90355	2
#90350	2
#90334	2
#90319	2
#90298	2
#90294	2
#90273	2
#90263	2
#90252	2
#90250	2
#90247	2
#90236	2
#90224	2
#90218	2
#90170	2
C₄×#1157	2
#3510	7