Subgroups — C₇×#61477 #13238693

Order 1792.

1772 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3515	C₂	1	2	yes	maximal, complemented
2	C₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3372	C₂	1	2	yes	maximal, complemented
5	C₇×#3338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3336	C₂	1	2	yes	maximal, complemented
7	C₇×#3331	C₂	1	2	yes	maximal, complemented
8	C₇×#3315	C₂	1	4	yes	maximal, complemented
9	C₇×#3283	C₂	1	2	yes	maximal, complemented
10	C₇×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3177	C₂	1	2	yes	maximal, complemented
12	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3120	C₂	1	4	yes	maximal, complemented
14	C₇×#3116	C₂	1	2	yes	maximal, complemented
15	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2951	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#135	C₂²	1	1	yes	characteristic
19	C₂×C₇×#135	C₂²	1	2	yes	—
20	C₇×#557	C₂²	1	2	yes	—
21	C₇×#554	C₂²	1	2	yes	—
22	C₇×#554	C₂²	1	2	yes	—
23	C₇×#553	—	2	2	no	—
24	C₇×#552	—	2	4	no	—
25	C₇×#552	—	2	2	no	—
26	C₇×#552	C₂²	1	4	yes	—
27	C₇×#547	C₂²	1	4	yes	—
28	C₇×#547	C₂²	1	2	yes	—
29	C₇×#541	C₂²	1	4	yes	—
30	C₇×#539	—	2	4	no	—
31	C₇×#533	C₂²	1	2	yes	—
32	C₇×#529	—	2	2	no	—
33	C₇×#529	C₂²	1	1	yes	characteristic
34	C₂×C₇×#125	—	2	2	no	—
35	C₇×#520	C₂²	1	4	yes	—
36	C₄×C₇×#41	C₂²	1	2	yes	—
37	C₇×#500	C₂²	1	1	yes	characteristic
38	C₇×#499	C₂²	1	2	yes	—
39	C₇×#494	C₂²	1	1	yes	characteristic
40	C₇×#494	C₂²	1	2	yes	—
41	C₇×#491	C₂²	1	4	yes	—
42	C₇×#487	C₂²	1	2	yes	—
43	C₇×#485	C₂²	1	4	yes	—
44	C₇×#484	C₂²	1	4	yes	—
45	C₇×#483	C₂²	1	4	yes	—
46	C₇×#479	C₂²	1	4	yes	—
47	C₇×#478	C₂²	1	4	yes	—
48	C₇×#477	C₂²	1	2	yes	—
49	C₇×#476	C₂²	1	2	yes	—
50	C₇×#470	C₂²	1	4	yes	—
51	C₇×#467	C₂²	1	2	yes	—
52	C₇×#467	C₂²	1	2	yes	—
53	C₇×#467	C₂²	1	2	yes	—
54	C₇×#467	C₂²	1	2	yes	—
55	C₇×#462	C₂²	1	4	yes	—
56	C₇×#462	C₂²	1	2	yes	—
57	C₇×#461	C₂²	1	2	yes	—
58	C₇×#461	C₂²	1	4	yes	—
59	C₇×#452	C₂²	1	4	yes	—
60	C₇×#452	C₂²	1	4	yes	—
61	C₇×#452	C₂²	1	4	yes	—
62	C₇×#446	C₂²	1	1	yes	characteristic
63	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
64	C₇×#441	C₂²	1	4	yes	—
65	C₇×#440	C₂²	1	4	yes	—
66	C₇×#440	C₂²	1	4	yes	—
67	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
68	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
69	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
70	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
71	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
72	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
73	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
74	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
75	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
76	C₄×C₇×D₈	C₂²	1	2	yes	—
77	C₇×#436	C₂²	1	1	yes	characteristic
78	C₇×#435	C₂²	1	2	yes	—
79	C₇×C₈×D₄	C₂²	1	2	yes	—
80	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
81	C₇×#433	C₂²	1	2	yes	—
82	C₇×#432	C₂²	1	1	yes	characteristic
83	C₇×#427	C₂²	1	1	yes	characteristic
84	C₂×C₇×#107	C₂²	1	2	yes	—
85	C₇×#417	C₂²	1	4	yes	—
86	C₇×#416	C₂²	1	2	yes	—
87	C₇×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
89	#61477	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂×C₇×#41	C₂³	1	4	yes	—
92	C₇×#135	—	2	4	no	—
93	C₇×#135	—	2	8	no	—
94	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
95	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
101	C₂×C₇×M₁₆	C₂³	1	2	yes	—
102	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×C₈	C₂³	1	2	yes	—
104	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₇×#126	—	2	4	no	—
109	C₇×#126	—	2	4	no	—
110	C₇×#126	—	2	4	no	—
111	C₇×#126	D₄	1	2	yes	—
112	C₇×#125	—	2	4	no	—
113	C₇×#125	—	2	4	no	—
114	C₇×#125	—	2	2	no	—
115	C₇×#125	—	2	2	no	—
116	C₇×#125	—	2	4	no	—
117	C₇×#125	—	2	4	no	—
118	C₇×#125	—	2	2	no	—
119	C₇×#125	D₄	1	1	yes	characteristic
120	C₇×#125	C₂³	1	4	yes	—
121	C₇×#124	D₄	1	1	yes	characteristic
122	C₇×#123	—	2	4	no	—
123	C₇×#123	—	2	4	no	—
124	C₇×#123	—	2	4	no	—
125	C₇×#123	—	2	4	no	—
126	C₇×#123	D₄	1	2	yes	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×C₂²⋊Q₈	—	2	4	no	—
131	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₇×#121	—	2	2	no	—
136	C₇×#121	—	2	4	no	—
137	C₇×#121	D₄	1	1	yes	characteristic
138	C₄×C₇×Q₈	—	2	2	no	—
139	C₄×C₇×Q₈	—	2	2	no	—
140	C₄×C₇×Q₈	C₂³	1	2	yes	—
141	C₄×C₇×Q₈	C₂³	1	4	yes	—
142	C₄×C₇×Q₈	C₂³	1	2	yes	—
143	C₄×C₇×Q₈	C₂³	1	4	yes	—
144	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
145	C₄×C₇×D₄	—	2	2	no	—
146	C₄×C₇×D₄	—	2	2	no	—
147	C₄×C₇×D₄	—	2	2	no	—
148	C₄×C₇×D₄	—	2	4	no	—
149	C₄×C₇×D₄	—	2	4	no	—
150	C₄×C₇×D₄	C₂³	1	2	yes	—
151	C₄×C₇×D₄	C₂³	1	4	yes	—
152	C₄×C₇×D₄	C₂³	1	2	yes	—
153	C₄×C₇×D₄	C₂³	1	2	yes	—
154	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₇×#117	—	2	2	no	—
156	C₇×#117	—	2	4	no	—
157	C₇×#117	—	2	4	no	—
158	C₇×#117	—	2	2	no	—
159	C₇×#117	C₂³	1	2	yes	—
160	C₇×#117	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	—	2	4	no	—
162	C₂×C₇×C₄⋊C₄	—	2	2	no	—
163	C₂×C₇×C₄⋊C₄	—	2	4	no	—
164	C₂×C₇×C₄⋊C₄	—	2	2	no	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₄²×C₇	—	2	2	no	—
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₇×#107	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	2	yes	—
170	C₇×#107	C₂³	1	2	yes	—
171	C₇×#107	C₂³	1	4	yes	—
172	C₇×#107	C₂³	1	1	yes	characteristic
173	C₇×#106	C₂³	1	4	yes	—
174	C₇×#106	C₂³	1	2	yes	—
175	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₈	C₂³	1	2	yes	—
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×#103	C₂³	1	4	yes	—
180	C₇×#103	C₂³	1	4	yes	—
181	C₇×#103	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	4	yes	—
183	C₇×#103	C₂³	1	2	yes	—
184	C₇×#103	C₂³	1	4	yes	—
185	C₇×#103	C₂³	1	2	yes	—
186	C₇×#102	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	2	yes	—
188	C₇×#102	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
195	C₄×C₇×C₈	C₂³	1	2	yes	—
196	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	#3515	C₂×C₇	1	2	yes	complemented
200	#3395	C₂×C₇	1	1	yes	characteristic, complemented
201	#3380	C₂×C₇	1	1	yes	characteristic, complemented
202	#3372	C₂×C₇	1	2	yes	complemented
203	#3338	C₂×C₇	1	1	yes	characteristic, complemented
204	#3336	C₂×C₇	1	2	yes	complemented
205	#3331	C₂×C₇	1	2	yes	complemented
206	#3315	C₂×C₇	1	4	yes	complemented
207	#3283	C₂×C₇	1	1	yes	characteristic, complemented
208	#3283	C₂×C₇	1	2	yes	complemented
209	#3177	C₂×C₇	1	2	yes	complemented
210	#3170	C₂×C₇	1	1	yes	characteristic, complemented
211	#3120	C₂×C₇	1	4	yes	complemented
212	#3116	C₂×C₇	1	2	yes	complemented
213	#2966	C₂×C₇	1	1	yes	characteristic, complemented
214	#2951	C₂×C₇	1	2	yes	complemented
215	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
216	C₇×#41	—	2	4	no	—
217	C₇×#41	—	2	8	no	—
218	C₇×#41	—	4	2	no	—
219	C₇×#41	—	4	4	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
223	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
224	C₂×C₇×D₄	—	2	2	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
227	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
228	C₂×C₇×D₄	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇	—	2	4	no	—
230	C₂²×C₄×C₇	—	2	2	no	—
231	C₂²×C₄×C₇	—	2	2	no	—
232	C₂²×C₄×C₇	—	2	4	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	4	no	—
235	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
239	C₇×Q₁₆	—	2	4	no	—
240	C₇×Q₁₆	—	2	2	no	—
241	C₇×Q₁₆	—	4	2	no	—
242	C₇×Q₁₆	—	4	4	no	—
243	C₇×SD₁₆	—	2	4	no	—
244	C₇×SD₁₆	—	2	8	no	—
245	C₇×D₈	#41	1	4	yes	—
246	C₇×M₁₆	—	4	2	no	—
247	C₂×C₇×C₈	—	2	2	no	—
248	C₂×C₇×C₈	—	2	4	no	—
249	C₂×C₇×C₈	—	4	1	no	—
250	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
251	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
252	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
253	C₂×C₇×C₈	C₂⁴	1	2	yes	—
254	C₂×C₇×C₈	C₂⁴	1	2	yes	—
255	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
256	C₇×C₄⋊C₄	—	2	4	no	—
257	C₇×C₄⋊C₄	—	2	2	no	—
258	C₇×C₄⋊C₄	—	2	2	no	—
259	C₇×C₄⋊C₄	—	2	4	no	—
260	C₇×C₄⋊C₄	—	2	4	no	—
261	C₇×C₄⋊C₄	—	2	4	no	—
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	4	no	—
265	C₇×C₄⋊C₄	—	2	4	no	—
266	C₇×C₄⋊C₄	—	2	2	no	—
267	C₇×C₄⋊C₄	—	2	2	no	—
268	C₇×C₄⋊C₄	—	2	4	no	—
269	C₇×C₄⋊C₄	—	2	2	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
272	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
273	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
274	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
275	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	2	no	—
285	C₇×C₂²⋊C₄	—	2	2	no	—
286	C₇×C₂²⋊C₄	—	2	4	no	—
287	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
288	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
289	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
290	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
291	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
292	C₄²×C₇	—	2	2	no	—
293	C₄²×C₇	—	2	2	no	—
294	C₄²×C₇	—	2	2	no	—
295	C₄²×C₇	—	2	4	no	—
296	C₄²×C₇	—	2	4	no	—
297	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₇	C₂⁴	1	1	yes	characteristic
300	C₄²×C₇	C₂⁴	1	1	yes	characteristic
301	C₄²×C₇	C₂⁴	1	2	yes	—
302	C₂×#135	C₂²×C₇	1	1	yes	characteristic
303	C₂×#135	C₂²×C₇	1	2	yes	—
304	#557	C₂²×C₇	1	2	yes	—
305	#554	C₂²×C₇	1	2	yes	—
306	#554	C₂²×C₇	1	2	yes	—
307	#553	—	2	2	no	—
308	#552	—	2	4	no	—
309	#552	—	2	2	no	—
310	#552	C₂²×C₇	1	4	yes	—
311	#547	C₂²×C₇	1	2	yes	—
312	#547	C₂²×C₇	1	4	yes	—
313	#541	C₂²×C₇	1	4	yes	—
314	#539	—	2	4	no	—
315	#533	C₂²×C₇	1	2	yes	—
316	#529	—	2	2	no	—
317	#529	C₂²×C₇	1	1	yes	characteristic
318	C₂×#125	—	2	2	no	—
319	#520	C₂²×C₇	1	4	yes	—
320	C₄×#41	C₂²×C₇	1	2	yes	—
321	#500	C₂²×C₇	1	1	yes	characteristic
322	#499	C₂²×C₇	1	2	yes	—
323	#494	C₂²×C₇	1	1	yes	characteristic
324	#494	C₂²×C₇	1	2	yes	—
325	#491	C₂²×C₇	1	4	yes	—
326	#487	C₂²×C₇	1	2	yes	—
327	#485	C₂²×C₇	1	4	yes	—
328	#484	C₂²×C₇	1	4	yes	—
329	#483	C₂²×C₇	1	4	yes	—
330	#479	C₂²×C₇	1	4	yes	—
331	#478	C₂²×C₇	1	4	yes	—
332	#477	C₂²×C₇	1	2	yes	—
333	#476	C₂²×C₇	1	2	yes	—
334	#470	C₂²×C₇	1	4	yes	—
335	#467	C₂²×C₇	1	2	yes	—
336	#467	C₂²×C₇	1	2	yes	—
337	#467	C₂²×C₇	1	2	yes	—
338	#467	C₂²×C₇	1	2	yes	—
339	#462	C₂²×C₇	1	2	yes	—
340	#462	C₂²×C₇	1	4	yes	—
341	#461	C₂²×C₇	1	2	yes	—
342	#461	C₂²×C₇	1	4	yes	—
343	#452	C₂²×C₇	1	4	yes	—
344	#452	C₂²×C₇	1	4	yes	—
345	#452	C₂²×C₇	1	4	yes	—
346	#446	C₂²×C₇	1	1	yes	characteristic
347	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
348	#441	C₂²×C₇	1	4	yes	—
349	#440	C₂²×C₇	1	4	yes	—
350	#440	C₂²×C₇	1	4	yes	—
351	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
352	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
353	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
354	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
355	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
356	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
357	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
358	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
359	C₄×D₈	C₂²×C₇	1	2	yes	—
360	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
361	#436	C₂²×C₇	1	1	yes	characteristic
362	#435	C₂²×C₇	1	2	yes	—
363	C₈×D₄	C₂²×C₇	1	2	yes	—
364	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
365	#433	C₂²×C₇	1	2	yes	—
366	#432	C₂²×C₇	1	1	yes	characteristic
367	#427	C₂²×C₇	1	1	yes	characteristic
368	C₂×#107	C₂²×C₇	1	2	yes	—
369	#417	C₂²×C₇	1	4	yes	—
370	#416	C₂²×C₇	1	2	yes	—
371	#405	C₂²×C₇	1	2	yes	—
372	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
373	C₂³×C₇	—	2	2	no	—
374	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₇	C₂²×D₄	1	2	yes	—
376	C₇×Q₈	—	2	2	no	—
377	C₇×Q₈	—	2	2	no	—
378	C₇×Q₈	—	2	4	no	—
379	C₇×Q₈	—	2	4	no	—
380	C₇×Q₈	—	2	2	no	—
381	C₇×Q₈	—	8	2	no	—
382	C₇×D₄	—	2	2	no	—
383	C₇×D₄	—	2	2	no	—
384	C₇×D₄	—	4	2	no	—
385	C₇×D₄	—	4	4	no	—
386	C₇×D₄	—	4	8	no	—
387	C₇×D₄	C₂×#41	1	4	yes	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	1	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	1	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	4	no	—
397	C₂×C₄×C₇	—	2	4	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	—	4	4	no	—
400	C₂×C₄×C₇	—	4	8	no	—
401	C₂×C₄×C₇	—	4	4	no	—
402	C₂×C₄×C₇	—	8	2	no	—
403	C₂×C₄×C₇	—	8	4	no	—
404	C₂×C₄×C₇	—	8	4	no	—
405	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
414	C₇×C₈	—	2	1	no	—
415	C₇×C₈	—	2	2	no	—
416	C₇×C₈	—	2	1	no	—
417	C₇×C₈	—	2	1	no	—
418	C₇×C₈	—	2	2	no	—
419	C₇×C₈	C₂×#41	1	2	yes	—
420	C₂×#41	C₂³×C₇	1	2	yes	—
421	C₂×#41	C₂³×C₇	1	4	yes	—
422	#135	—	2	4	no	—
423	#135	—	2	8	no	—
424	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
425	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
426	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
427	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
428	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
429	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
430	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
431	C₂×M₁₆	C₂³×C₇	1	2	yes	—
432	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₇	1	2	yes	—
434	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
435	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
436	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
437	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
438	#126	—	2	4	no	—
439	#126	—	2	4	no	—
440	#126	—	2	4	no	—
441	#126	C₇×D₄	1	2	yes	—
442	#125	—	2	4	no	—
443	#125	—	2	4	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	4	no	—
447	#125	—	2	4	no	—
448	#125	—	2	2	no	—
449	#125	C₇×D₄	1	1	yes	characteristic
450	#125	C₂³×C₇	1	4	yes	—
451	#124	C₇×D₄	1	1	yes	characteristic
452	#123	—	2	4	no	—
453	#123	—	2	4	no	—
454	#123	—	2	4	no	—
455	#123	—	2	4	no	—
456	#123	C₇×D₄	1	2	yes	—
457	C₂²⋊Q₈	—	2	2	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	4	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
462	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
463	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
464	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
465	#121	—	2	2	no	—
466	#121	—	2	4	no	—
467	#121	C₇×D₄	1	1	yes	characteristic
468	C₄×Q₈	—	2	2	no	—
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	C₂³×C₇	1	2	yes	—
471	C₄×Q₈	C₂³×C₇	1	2	yes	—
472	C₄×Q₈	C₂³×C₇	1	4	yes	—
473	C₄×Q₈	C₂³×C₇	1	4	yes	—
474	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	C₂³×C₇	1	2	yes	—
481	C₄×D₄	C₂³×C₇	1	2	yes	—
482	C₄×D₄	C₂³×C₇	1	4	yes	—
483	C₄×D₄	C₂³×C₇	1	2	yes	—
484	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
485	#117	—	2	2	no	—
486	#117	—	2	4	no	—
487	#117	—	2	4	no	—
488	#117	—	2	2	no	—
489	#117	C₂³×C₇	1	2	yes	—
490	#117	C₂³×C₇	1	2	yes	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	—	2	2	no	—
495	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
496	C₂×C₄²	—	2	2	no	—
497	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
498	#107	C₂³×C₇	1	1	yes	characteristic
499	#107	C₂³×C₇	1	2	yes	—
500	#107	C₂³×C₇	1	4	yes	—
501	#107	C₂³×C₇	1	1	yes	characteristic
502	#107	C₂³×C₇	1	2	yes	—
503	#106	C₂³×C₇	1	2	yes	—
504	#106	C₂³×C₇	1	4	yes	—
505	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
506	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
507	C₄⋊C₈	C₂³×C₇	1	2	yes	—
508	C₄⋊C₈	C₂³×C₇	1	2	yes	—
509	#103	C₂³×C₇	1	2	yes	—
510	#103	C₂³×C₇	1	2	yes	—
511	#103	C₂³×C₇	1	4	yes	—
512	#103	C₂³×C₇	1	4	yes	—
513	#103	C₂³×C₇	1	4	yes	—
514	#103	C₂³×C₇	1	4	yes	—
515	#103	C₂³×C₇	1	4	yes	—
516	#102	C₂³×C₇	1	2	yes	—
517	#102	C₂³×C₇	1	2	yes	—
518	#102	C₂³×C₇	1	4	yes	—
519	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
520	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
521	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
522	#97	C₂³×C₇	1	2	yes	—
523	#97	C₂³×C₇	1	2	yes	—
524	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
525	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
526	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
527	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
528	C₄×C₈	C₂³×C₇	1	2	yes	—
529	C₂²×C₇	—	2	1	no	—
530	C₂²×C₇	—	2	2	no	—
531	C₂²×C₇	—	2	1	no	—
532	C₂²×C₇	—	2	2	no	—
533	C₂²×C₇	—	2	4	no	—
534	C₂²×C₇	—	2	1	no	—
535	C₂²×C₇	—	2	2	no	—
536	C₂²×C₇	—	4	2	no	—
537	C₂²×C₇	—	4	2	no	—
538	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₇	—	2	1	no	—
540	C₄×C₇	—	2	1	no	—
541	C₄×C₇	—	2	2	no	—
542	C₄×C₇	—	2	1	no	—
543	C₄×C₇	—	2	2	no	—
544	C₄×C₇	—	2	1	no	—
545	C₄×C₇	—	2	2	no	—
546	C₄×C₇	—	4	2	no	—
547	C₄×C₇	—	4	4	no	—
548	C₄×C₇	—	4	2	no	—
549	C₄×C₇	—	4	4	no	—
550	C₄×C₇	—	4	2	no	—
551	C₄×C₇	#578	1	2	yes	—
552	C₄×C₇	C₂²×#41	1	1	yes	characteristic
553	C₄×C₇	#585	1	1	yes	characteristic
554	#41	—	2	4	no	—
555	#41	—	2	8	no	—
556	#41	—	4	2	no	—
557	#41	—	4	4	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
560	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
561	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
565	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
566	C₂×D₄	C₂⁴×C₇	1	2	yes	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
574	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
577	Q₁₆	—	2	2	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	—	4	2	no	—
580	Q₁₆	—	4	4	no	—
581	SD₁₆	—	2	4	no	—
582	SD₁₆	—	2	8	no	—
583	D₈	C₇×#41	1	4	yes	—
584	M₁₆	—	4	2	no	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	4	no	—
587	C₂×C₈	—	4	1	no	—
588	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
589	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
590	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
591	C₂×C₈	C₂⁴×C₇	1	2	yes	—
592	C₂×C₈	C₂⁴×C₇	1	2	yes	—
593	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
610	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
611	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
612	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
613	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
614	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
617	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
626	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
627	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
628	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
629	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
636	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
637	C₄²	C₂⁴×C₇	1	1	yes	characteristic
638	C₄²	C₂⁴×C₇	1	1	yes	characteristic
639	C₄²	C₂⁴×C₇	1	2	yes	—
640	C₂×C₇	—	4	1	no	—
641	C₂×C₇	—	4	2	no	—
642	C₂×C₇	—	4	4	no	—
643	C₂×C₇	D₄×#41	1	1	yes	characteristic
644	C₂×C₇	C₂×#578	1	1	yes	characteristic
645	C₂×C₇	#3584	1	1	yes	characteristic
646	C₂³	—	2	2	no	—
647	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
648	C₂³	C₂²×C₇×D₄	1	2	yes	—
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	4	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	8	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	8	no	—
660	D₄	C₂×C₇×#41	1	4	yes	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	8	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	8	2	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
681	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
682	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
683	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
684	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
685	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
686	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
687	C₈	—	2	1	no	—
688	C₈	—	2	2	no	—
689	C₈	—	2	1	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	2	no	—
692	C₈	C₂×C₇×#41	1	2	yes	—
693	C₇	#61477	1	1	yes	characteristic, direct product factor, Sylow
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	4	no	—
716	C₄	C₇×#578	1	2	yes	—
717	C₄	C₂²×C₇×#41	1	1	yes	characteristic
718	C₄	C₇×#585	1	1	yes	characteristic
719	C₂	—	4	1	no	—
720	C₂	—	4	2	no	—
721	C₂	—	4	4	no	—
722	C₂	C₇×D₄×#41	1	1	yes	characteristic
723	C₂	C₂×C₇×#578	1	1	yes	characteristic
724	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3515	C₂	semidirect
2. C₇×#3395	C₂	semidirect
3. C₇×#3380	C₂	semidirect
4. C₇×#3372	C₂	semidirect
5. C₇×#3338	C₂	semidirect
6. C₇×#3336	C₂	semidirect
7. C₇×#3331	C₂	semidirect
8. C₇×#3315	C₂	semidirect
9. C₇×#3283	C₂	semidirect
10. C₇×#3283	C₂	semidirect
11. C₇×#3177	C₂	semidirect
12. C₇×#3170	C₂	semidirect
13. C₇×#3120	C₂	semidirect
14. C₇×#3116	C₂	semidirect
15. C₇×#2966	C₂	semidirect
16. C₇×#2951	C₂	semidirect
17. C₄×C₇×#135	C₂	semidirect
89. #61477	C₇	direct (N × H)
199. #3515	C₂×C₇	semidirect
200. #3395	C₂×C₇	semidirect
201. #3380	C₂×C₇	semidirect
202. #3372	C₂×C₇	semidirect
203. #3338	C₂×C₇	semidirect
204. #3336	C₂×C₇	semidirect
205. #3331	C₂×C₇	semidirect
206. #3315	C₂×C₇	semidirect
207. #3283	C₂×C₇	semidirect
208. #3283	C₂×C₇	semidirect
209. #3177	C₂×C₇	semidirect
210. #3170	C₂×C₇	semidirect
211. #3120	C₂×C₇	semidirect
212. #3116	C₂×C₇	semidirect
213. #2966	C₂×C₇	semidirect
214. #2951	C₂×C₇	semidirect
215. C₄×#135	C₂×C₇	semidirect
693. C₇	#61477	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×#3515	2
C₇×#3395	2
C₇×#3380	2
C₇×#3372	2
C₇×#3338	2
C₇×#3336	2
C₇×#3331	2
C₇×#3315	2
C₇×#3283	2
C₇×#3177	2
C₇×#3170	2
C₇×#3120	2
C₇×#3116	2
C₇×#2966	2
C₇×#2951	2
C₄×C₇×#135	2
#61477	7

Subgroups — C7×#61477 #13238693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61477 #13238693