Subgroups — C₇×#61251 #13238467

Order 1792.

1842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	2	yes	maximal, complemented
2	C₇×#3357	C₂	1	2	yes	maximal, complemented
3	C₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₇×#3355	C₂	1	2	yes	maximal, complemented
5	C₇×#3354	C₂	1	2	yes	maximal, complemented
6	C₇×#3353	C₂	1	2	yes	maximal, complemented
7	C₇×#3352	C₂	1	2	yes	maximal, complemented
8	C₇×#3351	C₂	1	4	yes	maximal, complemented
9	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3091	C₂	1	4	yes	maximal, complemented
11	C₇×#3076	C₂	1	2	yes	maximal, complemented
12	C₇×#3054	C₂	1	2	yes	maximal, complemented
13	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2911	C₂	1	2	yes	maximal, complemented
16	C₂×C₇×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
18	C₇×#556	C₂²	1	2	yes	—
19	C₇×#555	C₂²	1	2	yes	—
20	C₇×#554	C₂²	1	2	yes	—
21	C₇×#553	C₂²	1	4	yes	—
22	C₇×#552	—	2	2	no	—
23	C₇×#552	C₂²	1	4	yes	—
24	C₇×#551	—	2	4	no	—
25	C₇×#547	C₂²	1	2	yes	—
26	C₇×#546	—	2	2	no	—
27	C₇×#533	C₂²	1	2	yes	—
28	C₇×#529	—	2	4	no	—
29	C₇×#529	—	2	2	no	—
30	C₇×#525	C₂²	1	4	yes	—
31	C₄×C₇×#41	—	2	2	no	—
32	C₄×C₇×#41	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	4	yes	—
35	C₇×#500	C₂²	1	1	yes	characteristic, complemented
36	C₇×#500	C₂²	1	1	yes	characteristic, complemented
37	C₇×#499	C₂²	1	2	yes	complemented
38	C₇×#499	C₂²	1	2	yes	complemented
39	C₇×#498	C₂²	1	2	yes	complemented
40	C₇×#485	C₂²	1	4	yes	complemented
41	C₇×#485	C₂²	1	4	yes	complemented
42	C₇×#484	C₂²	1	4	yes	complemented
43	C₇×#483	C₂²	1	4	yes	complemented
44	C₇×#482	C₂²	1	4	yes	complemented
45	C₇×#482	C₂²	1	4	yes	complemented
46	C₇×#481	C₂²	1	4	yes	complemented
47	C₇×#480	C₂²	1	4	yes	complemented
48	C₇×#479	C₂²	1	4	yes	complemented
49	C₇×#478	C₂²	1	4	yes	complemented
50	C₇×#477	C₂²	1	2	yes	complemented
51	C₇×#476	C₂²	1	2	yes	complemented
52	C₇×#475	C₂²	1	2	yes	complemented
53	C₇×#474	C₂²	1	2	yes	complemented
54	C₇×#470	C₂²	1	4	yes	complemented
55	C₇×#469	C₂²	1	4	yes	complemented
56	C₇×#468	C₂²	1	4	yes	complemented
57	C₇×#468	C₂²	1	4	yes	complemented
58	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
61	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
62	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
64	C₇×#436	C₂²	1	2	yes	—
65	C₇×#436	C₂²	1	2	yes	—
66	C₇×#436	C₂²	1	2	yes	—
67	C₇×#436	C₂²	1	2	yes	—
68	C₇×#428	C₂²	1	4	yes	complemented
69	C₇×#428	C₂²	1	4	yes	complemented
70	C₇×#428	C₂²	1	4	yes	complemented
71	C₇×#428	C₂²	1	4	yes	complemented
72	C₇×#427	C₂²	1	2	yes	—
73	C₇×#427	C₂²	1	2	yes	—
74	C₇×#427	C₂²	1	1	yes	characteristic
75	C₇×#427	C₂²	1	4	yes	—
76	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
77	C₇×#416	C₂²	1	2	yes	—
78	C₇×#416	C₂²	1	4	yes	—
79	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
80	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
81	#61251	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₇×#41	—	2	2	no	—
83	C₂×C₇×#41	C₂³	1	2	yes	—
84	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₇	C₂³	1	2	yes	—
86	C₇×#135	—	2	4	no	—
87	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
89	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
90	C₂×C₇×M₁₆	—	2	8	no	—
91	C₂×C₇×M₁₆	C₂³	1	4	yes	—
92	C₂×C₇×M₁₆	C₂³	1	4	yes	—
93	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₇×C₈	C₂³	1	2	yes	—
95	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₇×#126	—	2	4	no	—
99	C₇×#126	—	2	4	no	—
100	C₇×#126	—	2	4	no	—
101	C₇×#125	—	2	4	no	—
102	C₇×#125	—	2	2	no	—
103	C₇×#125	C₂³	1	4	yes	—
104	C₇×#124	—	2	2	no	—
105	C₇×#124	—	2	4	no	—
106	C₇×#123	—	2	4	no	—
107	C₇×#123	—	2	4	no	—
108	C₇×#123	—	2	4	no	—
109	C₇×#123	—	2	4	no	—
110	C₇×C₂²⋊Q₈	—	2	2	no	—
111	C₇×C₂²⋊Q₈	—	2	2	no	—
112	C₇×C₂²⋊Q₈	—	2	2	no	—
113	C₇×C₂²⋊Q₈	—	2	4	no	—
114	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
116	C₇×#121	—	2	4	no	—
117	C₇×#121	—	2	2	no	—
118	C₇×#121	C₂³	1	4	yes	—
119	C₇×#121	C₂³	1	4	yes	—
120	C₇×#120	—	2	4	no	—
121	C₄×C₇×Q₈	—	2	2	no	—
122	C₄×C₇×Q₈	—	2	2	no	—
123	C₄×C₇×Q₈	—	2	2	no	—
124	C₄×C₇×Q₈	C₂³	1	2	yes	—
125	C₄×C₇×Q₈	C₂³	1	2	yes	—
126	C₄×C₇×D₄	—	2	2	no	—
127	C₄×C₇×D₄	—	2	4	no	—
128	C₄×C₇×D₄	—	2	2	no	—
129	C₄×C₇×D₄	—	2	2	no	—
130	C₄×C₇×D₄	—	2	4	no	—
131	C₄×C₇×D₄	—	2	4	no	—
132	C₄×C₇×D₄	D₄	1	2	yes	—
133	C₄×C₇×D₄	D₄	1	2	yes	—
134	C₄×C₇×D₄	C₂³	1	2	yes	—
135	C₄×C₇×D₄	C₂³	1	2	yes	—
136	C₄×C₇×D₄	C₂³	1	2	yes	—
137	C₄×C₇×D₄	C₂³	1	2	yes	—
138	C₇×#117	—	2	4	no	—
139	C₇×#117	—	2	4	no	—
140	C₇×#117	—	2	2	no	—
141	C₇×#117	—	2	4	no	—
142	C₇×#117	—	2	2	no	—
143	C₇×#117	C₂³	1	4	yes	—
144	C₇×#117	C₂³	1	4	yes	—
145	C₇×#117	C₂³	1	2	yes	—
146	C₇×#117	C₂³	1	4	yes	—
147	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
151	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
152	C₂×C₄²×C₇	—	2	4	no	—
153	C₂×C₄²×C₇	—	2	2	no	—
154	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
155	C₇×#107	C₂³	1	2	yes	—
156	C₇×#107	C₂³	1	2	yes	—
157	C₇×#107	C₂³	1	4	yes	—
158	C₇×#107	C₂³	1	4	yes	—
159	C₇×#107	C₂³	1	2	yes	—
160	C₇×#107	C₂³	1	2	yes	—
161	C₇×#107	C₂³	1	1	yes	characteristic
162	C₇×#107	C₂³	1	1	yes	characteristic
163	C₇×#106	C₂³	1	4	yes	—
164	C₇×#106	C₂³	1	4	yes	—
165	C₇×#106	C₂³	1	4	yes	—
166	C₇×#106	C₂³	1	4	yes	—
167	C₇×#106	C₂³	1	2	yes	—
168	C₇×C₄⋊C₈	C₂³	1	2	yes	—
169	C₇×C₄⋊C₈	C₂³	1	2	yes	—
170	C₇×#103	C₂³	1	4	yes	—
171	C₇×#103	C₂³	1	4	yes	—
172	C₇×#103	C₂³	1	2	yes	—
173	C₇×#103	C₂³	1	2	yes	—
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	2	yes	—
177	C₇×#102	C₂³	1	2	yes	—
178	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
181	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
182	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
183	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
184	#3475	C₂×C₇	1	2	yes	complemented
185	#3357	C₂×C₇	1	2	yes	complemented
186	#3356	C₂×C₇	1	2	yes	complemented
187	#3355	C₂×C₇	1	2	yes	complemented
188	#3354	C₂×C₇	1	2	yes	complemented
189	#3353	C₂×C₇	1	2	yes	complemented
190	#3352	C₂×C₇	1	2	yes	complemented
191	#3351	C₂×C₇	1	4	yes	complemented
192	#3160	C₂×C₇	1	1	yes	characteristic, complemented
193	#3091	C₂×C₇	1	4	yes	complemented
194	#3076	C₂×C₇	1	2	yes	complemented
195	#3054	C₂×C₇	1	2	yes	complemented
196	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
198	#2911	C₂×C₇	1	2	yes	complemented
199	C₂⁴×C₇	C₂×D₄	1	2	yes	—
200	C₇×#41	—	2	4	no	—
201	C₇×#41	—	2	4	no	—
202	C₇×#41	—	4	8	no	—
203	C₂×C₇×Q₈	—	2	2	no	—
204	C₂×C₇×Q₈	—	2	2	no	—
205	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
206	C₂×C₇×D₄	—	2	2	no	—
207	C₂×C₇×D₄	—	2	4	no	—
208	C₂×C₇×D₄	—	2	4	no	—
209	C₂×C₇×D₄	—	4	2	no	—
210	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
211	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
212	C₂×C₇×D₄	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₇	—	2	4	no	—
214	C₂²×C₄×C₇	—	2	4	no	—
215	C₂²×C₄×C₇	—	2	4	no	—
216	C₂²×C₄×C₇	—	2	4	no	—
217	C₂²×C₄×C₇	—	2	2	no	—
218	C₂²×C₄×C₇	—	2	2	no	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
226	C₇×Q₁₆	—	2	2	no	—
227	C₇×SD₁₆	—	2	4	no	—
228	C₇×D₈	—	2	2	no	—
229	C₇×M₁₆	—	2	8	no	—
230	C₇×M₁₆	—	2	8	no	—
231	C₂×C₇×C₈	—	2	4	no	—
232	C₂×C₇×C₈	—	2	2	no	—
233	C₂×C₇×C₈	#41	1	4	yes	complemented
234	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
235	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
236	C₂×C₇×C₈	C₂⁴	1	4	yes	—
237	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
238	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
239	C₇×C₄⋊C₄	—	2	4	no	—
240	C₇×C₄⋊C₄	—	2	4	no	—
241	C₇×C₄⋊C₄	—	2	2	no	—
242	C₇×C₄⋊C₄	—	2	4	no	—
243	C₇×C₄⋊C₄	—	2	4	no	—
244	C₇×C₄⋊C₄	—	2	2	no	—
245	C₇×C₄⋊C₄	—	2	2	no	—
246	C₇×C₄⋊C₄	—	2	4	no	—
247	C₇×C₄⋊C₄	—	2	4	no	—
248	C₇×C₄⋊C₄	—	2	2	no	—
249	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
250	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
251	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
252	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
253	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
254	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
255	C₇×C₂²⋊C₄	—	2	2	no	—
256	C₇×C₂²⋊C₄	—	2	4	no	—
257	C₇×C₂²⋊C₄	—	2	4	no	—
258	C₇×C₂²⋊C₄	—	2	4	no	—
259	C₇×C₂²⋊C₄	—	2	4	no	—
260	C₇×C₂²⋊C₄	—	2	4	no	—
261	C₇×C₂²⋊C₄	—	2	4	no	—
262	C₇×C₂²⋊C₄	—	2	2	no	—
263	C₇×C₂²⋊C₄	—	2	2	no	—
264	C₇×C₂²⋊C₄	—	2	4	no	—
265	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
266	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
267	C₄²×C₇	—	2	4	no	—
268	C₄²×C₇	—	2	2	no	—
269	C₄²×C₇	—	2	4	no	—
270	C₄²×C₇	—	2	2	no	—
271	C₄²×C₇	—	2	2	no	—
272	C₄²×C₇	—	2	4	no	—
273	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₇	C₂⁴	1	1	yes	characteristic
276	C₄²×C₇	C₂⁴	1	1	yes	characteristic
277	C₂×#135	C₂²×C₇	1	1	yes	characteristic
278	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
279	#556	C₂²×C₇	1	2	yes	—
280	#555	C₂²×C₇	1	2	yes	—
281	#554	C₂²×C₇	1	2	yes	—
282	#553	C₂²×C₇	1	4	yes	—
283	#552	—	2	2	no	—
284	#552	C₂²×C₇	1	4	yes	—
285	#551	—	2	4	no	—
286	#547	C₂²×C₇	1	2	yes	—
287	#546	—	2	2	no	—
288	#533	C₂²×C₇	1	2	yes	—
289	#529	—	2	4	no	—
290	#529	—	2	2	no	—
291	#525	C₂²×C₇	1	4	yes	—
292	C₄×#41	—	2	2	no	—
293	C₄×#41	C₂²×C₇	1	2	yes	—
294	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
295	C₂×#117	C₂²×C₇	1	4	yes	—
296	#500	C₂²×C₇	1	1	yes	characteristic, complemented
297	#500	C₂²×C₇	1	1	yes	characteristic, complemented
298	#499	C₂²×C₇	1	2	yes	complemented
299	#499	C₂²×C₇	1	2	yes	complemented
300	#498	C₂²×C₇	1	2	yes	complemented
301	#485	C₂²×C₇	1	4	yes	complemented
302	#485	C₂²×C₇	1	4	yes	complemented
303	#484	C₂²×C₇	1	4	yes	complemented
304	#483	C₂²×C₇	1	4	yes	complemented
305	#482	C₂²×C₇	1	4	yes	complemented
306	#482	C₂²×C₇	1	4	yes	complemented
307	#481	C₂²×C₇	1	4	yes	complemented
308	#480	C₂²×C₇	1	4	yes	complemented
309	#479	C₂²×C₇	1	4	yes	complemented
310	#478	C₂²×C₇	1	4	yes	complemented
311	#477	C₂²×C₇	1	2	yes	complemented
312	#476	C₂²×C₇	1	2	yes	complemented
313	#475	C₂²×C₇	1	2	yes	complemented
314	#474	C₂²×C₇	1	2	yes	complemented
315	#470	C₂²×C₇	1	4	yes	complemented
316	#469	C₂²×C₇	1	4	yes	complemented
317	#468	C₂²×C₇	1	4	yes	complemented
318	#468	C₂²×C₇	1	4	yes	complemented
319	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
320	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
321	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
322	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
323	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
324	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
325	#436	C₂²×C₇	1	2	yes	—
326	#436	C₂²×C₇	1	2	yes	—
327	#436	C₂²×C₇	1	2	yes	—
328	#436	C₂²×C₇	1	2	yes	—
329	#428	C₂²×C₇	1	4	yes	complemented
330	#428	C₂²×C₇	1	4	yes	complemented
331	#428	C₂²×C₇	1	4	yes	complemented
332	#428	C₂²×C₇	1	4	yes	complemented
333	#427	C₂²×C₇	1	4	yes	—
334	#427	C₂²×C₇	1	2	yes	—
335	#427	C₂²×C₇	1	2	yes	—
336	#427	C₂²×C₇	1	1	yes	characteristic
337	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
338	#416	C₂²×C₇	1	4	yes	—
339	#416	C₂²×C₇	1	2	yes	—
340	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
341	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
342	C₂³×C₇	—	2	4	no	—
343	C₂³×C₇	—	2	2	no	—
344	C₂³×C₇	—	4	2	no	—
345	C₂³×C₇	—	4	2	no	—
346	C₂³×C₇	C₂²×D₄	1	4	yes	—
347	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
348	C₇×Q₈	—	2	2	no	—
349	C₇×Q₈	—	2	2	no	—
350	C₇×Q₈	—	4	4	no	—
351	C₇×Q₈	—	8	2	no	—
352	C₇×D₄	—	2	4	no	—
353	C₇×D₄	—	2	2	no	—
354	C₇×D₄	—	2	2	no	—
355	C₇×D₄	—	4	2	no	—
356	C₇×D₄	—	4	8	no	—
357	C₇×D₄	—	4	4	no	—
358	C₇×D₄	—	8	4	no	—
359	C₂×C₄×C₇	—	2	4	no	—
360	C₂×C₄×C₇	—	2	8	no	—
361	C₂×C₄×C₇	—	2	2	no	—
362	C₂×C₄×C₇	—	2	4	no	—
363	C₂×C₄×C₇	—	2	4	no	—
364	C₂×C₄×C₇	—	2	2	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	4	no	—
368	C₂×C₄×C₇	—	2	4	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	4	8	no	—
371	C₂×C₄×C₇	—	4	4	no	—
372	C₂×C₄×C₇	—	4	4	no	—
373	C₂×C₄×C₇	—	8	2	no	—
374	C₂×C₄×C₇	—	8	4	no	—
375	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₇	C₂×#41	1	2	yes	—
382	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
383	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
384	C₇×C₈	—	2	4	no	—
385	C₇×C₈	—	2	1	no	—
386	C₇×C₈	—	2	1	no	—
387	C₇×C₈	C₂×#41	1	2	yes	—
388	C₇×C₈	C₂×#41	1	2	yes	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	C₂³×C₇	1	2	yes	—
391	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₇	1	2	yes	—
393	#135	—	2	4	no	—
394	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
395	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
396	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
397	C₂×M₁₆	—	2	8	no	—
398	C₂×M₁₆	C₂³×C₇	1	4	yes	—
399	C₂×M₁₆	C₂³×C₇	1	4	yes	—
400	C₂²×C₈	C₂³×C₇	1	2	yes	—
401	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
403	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
404	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
405	#126	—	2	4	no	—
406	#126	—	2	4	no	—
407	#126	—	2	4	no	—
408	#125	—	2	4	no	—
409	#125	—	2	2	no	—
410	#125	C₂³×C₇	1	4	yes	—
411	#124	—	2	2	no	—
412	#124	—	2	4	no	—
413	#123	—	2	4	no	—
414	#123	—	2	4	no	—
415	#123	—	2	4	no	—
416	#123	—	2	4	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	4	no	—
421	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
422	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
423	#121	—	2	4	no	—
424	#121	—	2	2	no	—
425	#121	C₂³×C₇	1	4	yes	—
426	#121	C₂³×C₇	1	4	yes	—
427	#120	—	2	4	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	C₂³×C₇	1	2	yes	—
432	C₄×Q₈	C₂³×C₇	1	2	yes	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	4	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	C₇×D₄	1	2	yes	—
440	C₄×D₄	C₇×D₄	1	2	yes	—
441	C₄×D₄	C₂³×C₇	1	2	yes	—
442	C₄×D₄	C₂³×C₇	1	2	yes	—
443	C₄×D₄	C₂³×C₇	1	2	yes	—
444	C₄×D₄	C₂³×C₇	1	2	yes	—
445	#117	—	2	4	no	—
446	#117	—	2	4	no	—
447	#117	—	2	2	no	—
448	#117	—	2	4	no	—
449	#117	—	2	2	no	—
450	#117	C₂³×C₇	1	2	yes	—
451	#117	C₂³×C₇	1	4	yes	—
452	#117	C₂³×C₇	1	4	yes	—
453	#117	C₂³×C₇	1	4	yes	—
454	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
457	C₂×C₂²⋊C₄	—	2	4	no	—
458	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
459	C₂×C₄²	—	2	4	no	—
460	C₂×C₄²	—	2	2	no	—
461	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
462	#107	C₂³×C₇	1	1	yes	characteristic
463	#107	C₂³×C₇	1	1	yes	characteristic
464	#107	C₂³×C₇	1	2	yes	—
465	#107	C₂³×C₇	1	2	yes	—
466	#107	C₂³×C₇	1	4	yes	—
467	#107	C₂³×C₇	1	4	yes	—
468	#107	C₂³×C₇	1	2	yes	—
469	#107	C₂³×C₇	1	2	yes	—
470	#106	C₂³×C₇	1	2	yes	—
471	#106	C₂³×C₇	1	4	yes	—
472	#106	C₂³×C₇	1	4	yes	—
473	#106	C₂³×C₇	1	4	yes	—
474	#106	C₂³×C₇	1	4	yes	—
475	C₄⋊C₈	C₂³×C₇	1	2	yes	—
476	C₄⋊C₈	C₂³×C₇	1	2	yes	—
477	#103	C₂³×C₇	1	2	yes	—
478	#103	C₂³×C₇	1	2	yes	—
479	#103	C₂³×C₇	1	4	yes	—
480	#103	C₂³×C₇	1	4	yes	—
481	#102	C₂³×C₇	1	2	yes	—
482	#102	C₂³×C₇	1	2	yes	—
483	#102	C₂³×C₇	1	4	yes	—
484	#102	C₂³×C₇	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
487	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
488	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
489	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
490	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
491	C₂²×C₇	—	2	1	no	—
492	C₂²×C₇	—	2	1	no	—
493	C₂²×C₇	—	2	4	no	—
494	C₂²×C₇	—	2	4	no	—
495	C₂²×C₇	—	2	4	no	—
496	C₂²×C₇	—	4	2	no	—
497	C₂²×C₇	—	4	2	no	—
498	C₂²×C₇	—	4	2	no	—
499	C₂²×C₇	—	8	4	no	—
500	C₂²×C₇	#547	1	2	yes	—
501	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
502	C₄×C₇	—	2	1	no	—
503	C₄×C₇	—	2	1	no	—
504	C₄×C₇	—	2	4	no	—
505	C₄×C₇	—	2	1	no	—
506	C₄×C₇	—	4	2	no	—
507	C₄×C₇	—	4	4	no	—
508	C₄×C₇	—	4	2	no	—
509	C₄×C₇	—	4	2	no	—
510	C₄×C₇	—	4	4	no	—
511	C₄×C₇	#547	1	2	yes	—
512	C₄×C₇	#575	1	2	yes	—
513	C₄×C₇	C₂²×#41	1	1	yes	characteristic
514	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	C₂⁴	C₂×C₇×D₄	1	2	yes	—
516	#41	—	2	4	no	—
517	#41	—	2	4	no	—
518	#41	—	4	8	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
527	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
528	C₂×D₄	C₂⁴×C₇	1	2	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
537	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
539	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
542	Q₁₆	—	2	2	no	—
543	SD₁₆	—	2	4	no	—
544	D₈	—	2	2	no	—
545	M₁₆	—	2	8	no	—
546	M₁₆	—	2	8	no	—
547	C₂×C₈	—	2	4	no	—
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	C₇×#41	1	4	yes	complemented
550	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
551	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
552	C₂×C₈	C₂⁴×C₇	1	4	yes	—
553	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
554	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
566	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
567	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
568	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
569	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
570	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
582	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
583	C₄²	—	2	2	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
590	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
591	C₄²	C₂⁴×C₇	1	1	yes	characteristic
592	C₄²	C₂⁴×C₇	1	1	yes	characteristic
593	C₂×C₇	—	2	2	no	—
594	C₂×C₇	—	4	4	no	—
595	C₂×C₇	—	8	2	no	—
596	C₂×C₇	C₂×#547	1	1	yes	characteristic
597	C₂×C₇	C₂×#575	1	1	yes	characteristic
598	C₂×C₇	#3584	1	1	yes	characteristic
599	C₂³	—	2	4	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	4	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	C₂²×C₇×D₄	1	4	yes	—
604	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	2	2	no	—
607	Q₈	—	4	4	no	—
608	Q₈	—	8	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	4	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	8	no	—
614	D₄	—	4	4	no	—
615	D₄	—	8	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	8	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	4	no	—
632	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
633	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
634	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
635	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
636	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
637	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
638	C₂×C₄	C₂×C₇×#41	1	2	yes	—
639	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
640	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
641	C₈	—	2	4	no	—
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	C₂×C₇×#41	1	2	yes	—
645	C₈	C₂×C₇×#41	1	2	yes	—
646	C₇	#61251	1	1	yes	characteristic, direct product factor, Sylow
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	8	4	no	—
656	C₂²	C₇×#547	1	2	yes	—
657	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	4	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	C₇×#547	1	2	yes	—
668	C₄	C₇×#575	1	2	yes	—
669	C₄	C₂²×C₇×#41	1	1	yes	characteristic
670	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
671	C₂	—	2	2	no	—
672	C₂	—	4	4	no	—
673	C₂	—	8	2	no	—
674	C₂	C₂×C₇×#547	1	1	yes	characteristic
675	C₂	C₂×C₇×#575	1	1	yes	characteristic
676	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₇×#3357	C₂	semidirect
3. C₇×#3356	C₂	semidirect
4. C₇×#3355	C₂	semidirect
5. C₇×#3354	C₂	semidirect
6. C₇×#3353	C₂	semidirect
7. C₇×#3352	C₂	semidirect
8. C₇×#3351	C₂	semidirect
9. C₇×#3160	C₂	semidirect
10. C₇×#3091	C₂	semidirect
11. C₇×#3076	C₂	semidirect
12. C₇×#3054	C₂	semidirect
13. C₄×C₇×#135	C₂	semidirect
14. C₂×C₇×#436	C₂	semidirect
15. C₇×#2911	C₂	semidirect
35. C₇×#500	C₂²	semidirect
36. C₇×#500	C₂²	semidirect
37. C₇×#499	C₂²	semidirect
38. C₇×#499	C₂²	semidirect
39. C₇×#498	C₂²	semidirect
40. C₇×#485	C₂²	semidirect
41. C₇×#485	C₂²	semidirect
42. C₇×#484	C₂²	semidirect
43. C₇×#483	C₂²	semidirect
44. C₇×#482	C₂²	semidirect
45. C₇×#482	C₂²	semidirect
46. C₇×#481	C₂²	semidirect
47. C₇×#480	C₂²	semidirect
48. C₇×#479	C₂²	semidirect
49. C₇×#478	C₂²	semidirect
50. C₇×#477	C₂²	semidirect
51. C₇×#476	C₂²	semidirect
52. C₇×#475	C₂²	semidirect
53. C₇×#474	C₂²	semidirect
54. C₇×#470	C₂²	semidirect
55. C₇×#469	C₂²	semidirect
56. C₇×#468	C₂²	semidirect
57. C₇×#468	C₂²	semidirect
58. C₄×C₇×Q₁₆	C₂²	semidirect
59. C₄×C₇×Q₁₆	C₂²	semidirect
60. C₄×C₇×SD₁₆	C₂²	semidirect
61. C₄×C₇×SD₁₆	C₂²	semidirect
62. C₄×C₇×D₈	C₂²	semidirect
63. C₄×C₇×D₈	C₂²	semidirect
68. C₇×#428	C₂²	semidirect
69. C₇×#428	C₂²	semidirect
70. C₇×#428	C₂²	semidirect
71. C₇×#428	C₂²	semidirect
81. #61251	C₇	direct (N × H)
184. #3475	C₂×C₇	semidirect
185. #3357	C₂×C₇	semidirect
186. #3356	C₂×C₇	semidirect
187. #3355	C₂×C₇	semidirect
188. #3354	C₂×C₇	semidirect
189. #3353	C₂×C₇	semidirect
190. #3352	C₂×C₇	semidirect
191. #3351	C₂×C₇	semidirect
192. #3160	C₂×C₇	semidirect
193. #3091	C₂×C₇	semidirect
194. #3076	C₂×C₇	semidirect
195. #3054	C₂×C₇	semidirect
196. C₄×#135	C₂×C₇	semidirect
197. C₂×#436	C₂×C₇	semidirect
198. #2911	C₂×C₇	semidirect
233. C₂×C₇×C₈	#41	semidirect
296. #500	C₂²×C₇	semidirect
297. #500	C₂²×C₇	semidirect
298. #499	C₂²×C₇	semidirect
299. #499	C₂²×C₇	semidirect
300. #498	C₂²×C₇	semidirect
301. #485	C₂²×C₇	semidirect
302. #485	C₂²×C₇	semidirect
303. #484	C₂²×C₇	semidirect
304. #483	C₂²×C₇	semidirect
305. #482	C₂²×C₇	semidirect
306. #482	C₂²×C₇	semidirect
307. #481	C₂²×C₇	semidirect
308. #480	C₂²×C₇	semidirect
309. #479	C₂²×C₇	semidirect
310. #478	C₂²×C₇	semidirect
311. #477	C₂²×C₇	semidirect
312. #476	C₂²×C₇	semidirect
313. #475	C₂²×C₇	semidirect
314. #474	C₂²×C₇	semidirect
315. #470	C₂²×C₇	semidirect
316. #469	C₂²×C₇	semidirect
317. #468	C₂²×C₇	semidirect
318. #468	C₂²×C₇	semidirect
319. C₄×Q₁₆	C₂²×C₇	semidirect
320. C₄×Q₁₆	C₂²×C₇	semidirect
321. C₄×SD₁₆	C₂²×C₇	semidirect
322. C₄×SD₁₆	C₂²×C₇	semidirect
323. C₄×D₈	C₂²×C₇	semidirect
324. C₄×D₈	C₂²×C₇	semidirect
329. #428	C₂²×C₇	semidirect
330. #428	C₂²×C₇	semidirect
331. #428	C₂²×C₇	semidirect
332. #428	C₂²×C₇	semidirect
549. C₂×C₈	C₇×#41	semidirect
646. C₇	#61251	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3475	2
C₇×#3357	2
C₇×#3356	2
C₇×#3355	2
C₇×#3354	2
C₇×#3353	2
C₇×#3352	2
C₇×#3351	2
C₇×#3160	2
C₇×#3091	2
C₇×#3076	2
C₇×#3054	2
C₄×C₇×#135	2
C₂×C₇×#436	2
C₇×#2911	2
#61251	7

Subgroups — C7×#61251 #13238467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61251 #13238467