Subgroups — #11743620

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×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#90424	C₂	1	1	yes	maximal, characteristic, complemented
3	#90419	C₂	1	1	yes	maximal, characteristic, complemented
4	#90396	C₂	1	2	yes	maximal, complemented
5	#90393	C₂	1	2	yes	maximal, complemented
6	#90373	C₂	1	1	yes	maximal, characteristic, complemented
7	#90372	C₂	1	2	yes	maximal, complemented
8	#90370	C₂	1	2	yes	maximal, complemented
9	D₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	#90355	C₂	1	2	yes	maximal, complemented
11	#90349	C₂	1	2	yes	maximal, complemented
12	#90332	C₂	1	2	yes	maximal, complemented
13	#90328	C₂	1	2	yes	maximal, complemented
14	#90319	C₂	1	1	yes	maximal, characteristic, complemented
15	#90315	C₂	1	1	yes	maximal, characteristic, complemented
16	#90298	C₂	1	1	yes	maximal, characteristic
17	#90291	C₂	1	1	yes	maximal, characteristic, complemented
18	#90271	C₂	1	1	yes	maximal, characteristic, complemented
19	#90263	C₂	1	1	yes	maximal, characteristic, complemented
20	#90248	C₂	1	1	yes	maximal, characteristic, complemented
21	#90236	C₂	1	1	yes	maximal, characteristic, complemented
22	#90225	C₂	1	1	yes	maximal, characteristic, complemented
23	#90213	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₇×#126	C₂²	1	2	yes	complemented
29	C₇×#124	C₂²	1	1	yes	characteristic
30	C₇×#124	C₂²	1	2	yes	complemented
31	C₇×#123	C₂²	1	2	yes	complemented
32	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₇×#121	C₂²	1	1	yes	characteristic
35	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₇×#117	C₂²	1	1	yes	characteristic, complemented
38	#6510	C₂²	1	1	yes	characteristic
39	#6510	C₂²	1	2	yes	complemented
40	#6509	C₂²	1	2	yes	—
41	#6509	C₂²	1	2	yes	complemented
42	#6509	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₇	C₂²	1	2	yes	complemented
44	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
45	#6503	C₂²	1	2	yes	—
46	#6501	C₂²	1	1	yes	characteristic
47	#6500	C₂²	1	2	yes	—
48	#6499	C₂²	1	1	yes	characteristic
49	#6498	C₂²	1	2	yes	complemented
50	D₄×Dic₇	C₂²	1	1	yes	characteristic
51	D₄×Dic₇	C₂²	1	2	yes	complemented
52	#6493	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
55	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
56	#6489	C₂²	1	2	yes	complemented
57	#6487	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
59	#6461	C₂²	1	2	yes	complemented
60	#6461	C₂²	1	2	yes	complemented
61	#6461	C₂²	1	2	yes	complemented
62	#6461	C₂²	1	2	yes	complemented
63	#6460	C₂²	1	2	yes	—
64	#6460	C₂²	1	1	yes	characteristic, complemented
65	#6459	C₂²	1	2	yes	complemented
66	#6458	C₂²	1	1	yes	characteristic
67	#6457	C₂²	1	2	yes	—
68	#6457	C₂²	1	2	yes	complemented
69	#6457	C₂²	1	2	yes	complemented
70	#6456	C₂²	1	1	yes	characteristic
71	#6456	C₂²	1	1	yes	characteristic
72	#6456	C₂²	1	1	yes	characteristic
73	#6455	C₂²	1	1	yes	characteristic
74	#6455	C₂²	1	1	yes	characteristic
75	#6455	C₂²	1	2	yes	—
76	#6455	C₂²	1	2	yes	complemented
77	#6453	C₂²	1	1	yes	characteristic, complemented
78	#6453	C₂²	1	1	yes	characteristic, complemented
79	#6451	C₂²	1	2	yes	complemented
80	#6450	C₂²	1	1	yes	characteristic, complemented
81	#6450	C₂²	1	2	yes	complemented
82	#6450	C₂²	1	1	yes	characteristic, complemented
83	#6450	C₂²	1	1	yes	characteristic, complemented
84	#6450	C₂²	1	2	yes	complemented
85	#6449	C₂²	1	2	yes	complemented
86	#6449	C₂²	1	2	yes	complemented
87	#6448	C₂²	1	2	yes	—
88	#6448	C₂²	1	2	yes	—
89	#6448	C₂²	1	2	yes	—
90	#6448	C₂²	1	2	yes	complemented
91	#6448	C₂²	1	2	yes	complemented
92	#6448	C₂²	1	2	yes	complemented
93	#6446	C₂²	1	2	yes	—
94	#6446	C₂²	1	2	yes	complemented
95	#6446	C₂²	1	2	yes	complemented
96	#6445	C₂²	1	2	yes	—
97	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
99	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
100	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
101	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
104	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
105	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
106	#6442	C₂²	1	2	yes	complemented
107	#6442	C₂²	1	2	yes	complemented
108	#6442	C₂²	1	2	yes	complemented
109	#6441	C₂²	1	2	yes	complemented
110	#6440	C₂²	1	2	yes	complemented
111	#6438	C₂²	1	1	yes	characteristic
112	C₄×D₂₈	C₂²	1	1	yes	characteristic
113	C₄×D₂₈	C₂²	1	2	yes	complemented
114	#6435	C₂²	1	2	yes	—
115	#6435	C₂²	1	1	yes	characteristic
116	#6435	C₂²	1	2	yes	complemented
117	#6435	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₇	C₂²	1	1	yes	characteristic
119	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
120	#6432	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	2	yes	complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, 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×Q₈	C₂³	1	2	yes	—
127	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₄	C₂³	1	2	yes	—
129	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇	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	2	yes	—
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂²×Dic₇	C₂³	1	2	yes	—
137	C₂²×Dic₇	C₂³	1	1	yes	characteristic
138	C₂²×Dic₇	C₂³	1	1	yes	characteristic
139	Q₈×D₇	—	2	4	no	—
140	D₄×D₇	—	2	4	no	—
141	#1157	—	2	4	no	—
142	C₂×D₂₈	C₂³	1	1	yes	characteristic
143	C₂×D₂₈	C₂³	1	1	yes	characteristic
144	C₂×D₂₈	C₂³	1	2	yes	—
145	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₇	C₂³	1	2	yes	—
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	1	yes	characteristic
151	C₂×C₄×D₇	C₂³	1	2	yes	—
152	C₂×C₄×D₇	C₂³	1	2	yes	—
153	C₂×C₄×D₇	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	1	yes	characteristic
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	1	yes	characteristic
161	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×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	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₄²×C₇	C₂³	1	2	yes	—
174	C₄²×C₇	C₂³	1	1	yes	characteristic
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	2	yes	—
180	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₇	C₂³	1	2	yes	—
198	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₇	C₂³	1	2	yes	—
200	C₄⋊Dic₇	C₂³	1	2	yes	—
201	C₄⋊Dic₇	C₂³	1	2	yes	—
202	C₄⋊Dic₇	C₂³	1	2	yes	—
203	Dic₇⋊C₄	C₂³	1	2	yes	—
204	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₇⋊C₄	C₂³	1	2	yes	—
206	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₇⋊C₄	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	2	yes	—
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	C₄×Dic₇	C₂³	1	2	yes	—
214	C₄×Dic₇	C₂³	1	2	yes	—
215	C₄×Dic₇	C₂³	1	2	yes	—
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	1	yes	characteristic
220	C₄×Dic₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₇	C₂³	1	2	yes	—
223	C₄×Dic₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₇	C₂³	1	1	yes	characteristic
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	D₇	1	1	yes	characteristic, complemented
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	—	7	1	no	—
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×Q₈	—	4	2	no	—
259	C₇×D₄	—	2	2	no	—
260	C₇×D₄	—	4	2	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	—	4	2	no	—
263	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₇	—	2	2	no	—
273	C₂²⋊D₇	—	2	2	no	—
274	C₂²⋊D₇	—	2	4	no	—
275	C₂²⋊D₇	—	4	2	no	—
276	C₂²⋊D₇	—	4	2	no	—
277	C₂×Dic₇	—	4	2	no	—
278	C₂×Dic₇	—	4	1	no	—
279	C₂×Dic₇	—	4	1	no	—
280	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₇	C₂⁴	1	2	yes	—
285	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₇	C₂⁴	1	2	yes	—
287	C₂×Dic₇	C₂⁴	1	2	yes	—
288	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
289	D₂₈	—	2	2	no	—
290	D₂₈	—	2	2	no	—
291	D₂₈	—	4	2	no	—
292	C₄×D₇	—	2	4	no	—
293	C₄×D₇	—	2	2	no	—
294	C₄×D₇	—	4	2	no	—
295	C₄×D₇	—	4	1	no	—
296	C₄×D₇	—	4	1	no	—
297	C₄×D₇	—	4	1	no	—
298	C₄×D₇	—	4	2	no	—
299	C₄×D₇	—	4	1	no	—
300	C₄×D₇	#41	1	4	yes	—
301	Dic₁₄	—	2	2	no	—
302	Dic₁₄	—	2	2	no	—
303	Dic₁₄	—	2	4	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	2	no	—
309	C₄⋊Q₈	—	7	1	no	—
310	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
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	—	7	1	no	—
322	#124	—	7	1	no	—
323	#124	—	7	2	no	—
324	#124	—	7	1	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	C₂×D₇	1	1	yes	characteristic
333	#124	C₂×D₇	1	2	yes	complemented
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	2	no	—
346	C₂²⋊Q₈	—	7	2	no	—
347	C₂²⋊Q₈	—	7	1	no	—
348	C₂²⋊Q₈	—	7	1	no	—
349	C₂²⋊Q₈	—	7	2	no	—
350	C₂²⋊Q₈	—	7	2	no	—
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
353	C₂²⋊Q₈	C₂×D₇	1	2	yes	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	2	no	—
362	C₄×Q₈	—	7	1	no	—
363	C₄×Q₈	—	7	1	no	—
364	C₄×Q₈	—	7	1	no	—
365	C₄×Q₈	—	7	2	no	—
366	C₄×Q₈	—	7	2	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	2	no	—
372	C₄×D₄	—	7	2	no	—
373	C₄×D₄	—	7	2	no	—
374	C₄×D₄	—	7	1	no	—
375	C₄×D₄	—	7	1	no	—
376	C₄×D₄	—	7	1	no	—
377	C₄×D₄	—	7	1	no	—
378	C₄×D₄	—	7	1	no	—
379	C₄×D₄	—	7	1	no	—
380	C₄×D₄	—	7	1	no	—
381	C₄×D₄	—	7	2	no	—
382	C₄×D₄	—	7	2	no	—
383	C₄×D₄	—	7	1	no	—
384	C₄×D₄	—	7	2	no	—
385	C₄×D₄	C₂×D₇	1	1	yes	characteristic
386	#117	—	7	2	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	1	yes	characteristic, 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	—	7	1	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	2	no	—
406	C₂²×C₇	—	2	1	no	—
407	C₂²×C₇	—	2	2	no	—
408	C₂²×C₇	—	2	1	no	—
409	C₂²×C₇	—	2	2	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	1	no	—
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	2	2	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	2	2	no	—
429	C₄×C₇	C₂×#41	1	2	yes	—
430	Dic₇	—	2	2	no	—
431	Dic₇	—	2	1	no	—
432	Dic₇	—	2	2	no	—
433	Dic₇	—	2	2	no	—
434	Dic₇	—	2	1	no	—
435	Dic₇	—	2	1	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	—	14	4	no	—
446	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₇	1	2	yes	—
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	1	no	—
461	C₂²×C₄	—	7	1	no	—
462	C₂²×C₄	—	7	2	no	—
463	C₂²×C₄	—	7	1	no	—
464	C₂²×C₄	—	7	2	no	—
465	C₂²×C₄	—	7	1	no	—
466	C₂²×C₄	—	7	1	no	—
467	C₂²×C₄	—	7	1	no	—
468	C₂²×C₄	—	7	1	no	—
469	C₂²×C₄	—	7	2	no	—
470	C₂²×C₄	—	7	2	no	—
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	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	2	no	—
490	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₇	1	2	yes	—
493	C₄⋊C₄	C₂²×D₇	1	2	yes	—
494	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	2	no	—
501	C₂²⋊C₄	—	7	2	no	—
502	C₂²⋊C₄	—	7	1	no	—
503	C₂²⋊C₄	—	7	1	no	—
504	C₂²⋊C₄	—	7	2	no	—
505	C₂²⋊C₄	—	7	2	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	1	no	—
513	C₂²⋊C₄	—	7	1	no	—
514	C₂²⋊C₄	—	7	2	no	—
515	C₂²⋊C₄	—	7	2	no	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
519	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	1	no	—
532	C₄²	—	7	1	no	—
533	C₄²	—	7	2	no	—
534	C₄²	—	7	2	no	—
535	C₄²	—	7	2	no	—
536	C₄²	—	7	2	no	—
537	C₄²	—	7	2	no	—
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	—	4	2	no	—
559	Q₈	—	14	4	no	—
560	Q₈	—	14	2	no	—
561	Q₈	—	14	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	2	no	—
575	C₂×C₄	—	7	1	no	—
576	C₂×C₄	—	7	4	no	—
577	C₂×C₄	—	7	1	no	—
578	C₂×C₄	—	7	1	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	2	no	—
585	C₂×C₄	—	14	4	no	—
586	C₂×C₄	—	14	2	no	—
587	C₂×C₄	—	28	1	no	—
588	C₂×C₄	—	28	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	1	no	—
595	C₂×C₄	—	28	2	no	—
596	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₇	1	2	yes	—
598	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₇	1	2	yes	—
602	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₇	1	2	yes	—
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	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	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	2	no	—
619	C₂²	—	14	1	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	2	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	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	1	no	—
637	C₄	—	14	1	no	—
638	C₄	—	14	2	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	#90618	1	1	yes	characteristic
648	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#542	C₂
prime radical	#90298	C₂
hypercenter	#542	D₇
hypocenter	C₇	#3510
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₇×#542	C₂	semidirect
2. #90424	C₂	semidirect
3. #90419	C₂	semidirect
4. #90396	C₂	semidirect
5. #90393	C₂	semidirect
6. #90373	C₂	semidirect
7. #90372	C₂	semidirect
8. #90370	C₂	semidirect
9. D₇×#124	C₂	semidirect
10. #90355	C₂	semidirect
11. #90349	C₂	semidirect
12. #90332	C₂	semidirect
13. #90328	C₂	semidirect
14. #90319	C₂	semidirect
15. #90315	C₂	semidirect
17. #90291	C₂	semidirect
18. #90271	C₂	semidirect
19. #90263	C₂	semidirect
20. #90248	C₂	semidirect
21. #90236	C₂	semidirect
22. #90225	C₂	semidirect
23. #90213	C₂	semidirect
27. C₇×C₄⋊Q₈	C₂²	semidirect
28. C₇×#126	C₂²	semidirect
30. C₇×#124	C₂²	semidirect
31. C₇×#123	C₂²	semidirect
32. C₇×C₂²⋊Q₈	C₂²	semidirect
33. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₄×C₇×Q₈	C₂²	semidirect
37. C₇×#117	C₂²	semidirect
39. #6510	C₂²	semidirect
41. #6509	C₂²	semidirect
42. #6509	C₂²	semidirect
43. Q₈×Dic₇	C₂²	semidirect
44. Q₈×Dic₇	C₂²	semidirect
49. #6498	C₂²	semidirect
51. D₄×Dic₇	C₂²	semidirect
54. C₄×C₂²⋊D₇	C₂²	semidirect
56. #6489	C₂²	semidirect
57. #6487	C₂²	semidirect
58. C₂×C₄×Dic₇	C₂²	semidirect
59. #6461	C₂²	semidirect
60. #6461	C₂²	semidirect
61. #6461	C₂²	semidirect
62. #6461	C₂²	semidirect
64. #6460	C₂²	semidirect
65. #6459	C₂²	semidirect
68. #6457	C₂²	semidirect
69. #6457	C₂²	semidirect
76. #6455	C₂²	semidirect
77. #6453	C₂²	semidirect
78. #6453	C₂²	semidirect
79. #6451	C₂²	semidirect
80. #6450	C₂²	semidirect
81. #6450	C₂²	semidirect
82. #6450	C₂²	semidirect
83. #6450	C₂²	semidirect
84. #6450	C₂²	semidirect
85. #6449	C₂²	semidirect
86. #6449	C₂²	semidirect
90. #6448	C₂²	semidirect
91. #6448	C₂²	semidirect
92. #6448	C₂²	semidirect
94. #6446	C₂²	semidirect
95. #6446	C₂²	semidirect
100. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
106. #6442	C₂²	semidirect
107. #6442	C₂²	semidirect
108. #6442	C₂²	semidirect
109. #6441	C₂²	semidirect
110. #6440	C₂²	semidirect
113. C₄×D₂₈	C₂²	semidirect
116. #6435	C₂²	semidirect
117. #6435	C₂²	semidirect
119. C₄²×D₇	C₂²	semidirect
120. #6432	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
237. #542	D₇	semidirect
310. C₄⋊Q₈	C₂×D₇	semidirect
319. #126	C₂×D₇	semidirect
333. #124	C₂×D₇	semidirect
343. #123	C₂×D₇	semidirect
352. C₂²⋊Q₈	C₂×D₇	semidirect
353. C₂²⋊Q₈	C₂×D₇	semidirect
369. C₄×Q₈	C₂×D₇	semidirect
396. #117	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×#542	2
#90424	2
#90419	2
#90396	2
#90393	2
#90373	2
#90372	2
#90370	2
D₇×#124	2
#90355	2
#90349	2
#90332	2
#90328	2
#90319	2
#90315	2
#90298	2
#90291	2
#90271	2
#90263	2
#90248	2
#90236	2
#90225	2
#90213	2
#3510	7