Subgroups — C₇×#60879 #13238095

Order 1792.

1654 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3510	C₂	1	1	yes	maximal, characteristic
2	C₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3244	C₂	1	4	yes	maximal, complemented
4	C₇×#3243	C₂	1	4	yes	maximal, complemented
5	C₇×#3233	C₂	1	4	yes	maximal, complemented
6	C₇×#3232	C₂	1	4	yes	maximal, complemented
7	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3097	C₂	1	2	yes	maximal, complemented
12	C₇×#3096	C₂	1	2	yes	maximal
13	C₇×#3082	C₂	1	2	yes	maximal, complemented
14	C₇×#3081	C₂	1	2	yes	maximal, complemented
15	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#559	—	2	2	no	—
17	C₇×#557	—	2	2	no	—
18	C₇×#556	—	2	2	no	—
19	C₇×#554	—	2	4	no	—
20	C₇×#554	—	2	2	no	—
21	C₇×#551	—	2	4	no	—
22	C₇×#544	C₂²	1	2	yes	—
23	C₇×#544	C₂²	1	4	yes	complemented
24	C₇×#542	C₂²	1	4	yes	—
25	C₇×#536	C₂²	1	1	yes	characteristic
26	C₇×#535	C₂²	1	1	yes	characteristic
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#533	C₂²	1	1	yes	characteristic
29	C₇×#533	C₂²	1	2	yes	complemented
30	C₇×#529	C₂²	1	4	yes	—
31	C₂×C₇×#125	C₂²	1	1	yes	characteristic
32	C₂×C₇×#125	C₂²	1	2	yes	complemented
33	C₂×C₇×#124	C₂²	1	1	yes	characteristic
34	C₇×#520	C₂²	1	2	yes	—
35	C₇×#519	C₂²	1	1	yes	characteristic
36	C₇×#518	C₂²	1	1	yes	characteristic
37	C₄×C₇×#41	C₂²	1	1	yes	characteristic
38	C₇×#501	C₂²	1	4	yes	complemented
39	C₇×#500	C₂²	1	2	yes	complemented
40	C₇×#499	C₂²	1	2	yes	complemented
41	C₇×#499	C₂²	1	2	yes	complemented
42	C₇×#499	C₂²	1	4	yes	complemented
43	C₇×#498	C₂²	1	2	yes	complemented
44	C₇×#489	C₂²	1	4	yes	—
45	C₇×#488	C₂²	1	2	yes	—
46	C₇×#488	C₂²	1	4	yes	—
47	C₇×#488	C₂²	1	2	yes	—
48	C₇×#488	C₂²	1	2	yes	—
49	C₇×#488	C₂²	1	2	yes	—
50	C₇×#485	C₂²	1	4	yes	complemented
51	C₇×#485	C₂²	1	4	yes	complemented
52	C₇×#484	C₂²	1	4	yes	complemented
53	C₇×#483	C₂²	1	4	yes	complemented
54	C₇×#482	C₂²	1	4	yes	—
55	C₇×#482	C₂²	1	4	yes	—
56	C₇×#481	C₂²	1	4	yes	—
57	C₇×#480	C₂²	1	4	yes	—
58	C₇×#479	C₂²	1	4	yes	complemented
59	C₇×#479	C₂²	1	4	yes	complemented
60	C₇×#478	C₂²	1	4	yes	—
61	C₇×#478	C₂²	1	4	yes	—
62	C₇×#477	C₂²	1	4	yes	complemented
63	C₇×#476	C₂²	1	4	yes	—
64	C₇×#475	C₂²	1	4	yes	complemented
65	C₇×#474	C₂²	1	4	yes	—
66	C₇×#433	C₂²	1	2	yes	complemented
67	C₇×#433	C₂²	1	2	yes	complemented
68	C₇×#431	C₂²	1	4	yes	complemented
69	C₇×#428	C₂²	1	2	yes	—
70	C₇×#428	C₂²	1	2	yes	—
71	C₇×#427	C₂²	1	2	yes	—
72	C₇×#427	C₂²	1	2	yes	—
73	C₇×#424	C₂²	1	2	yes	—
74	C₇×#419	C₂²	1	2	yes	—
75	C₇×#418	C₂²	1	2	yes	—
76	C₂×C₇×#103	C₂²	1	2	yes	—
77	C₂×C₇×#102	C₂²	1	2	yes	—
78	C₇×#408	C₂²	1	2	yes	—
79	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
81	#60879	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₇×#41	C₂³	1	1	yes	characteristic
83	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₇×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₇×C₈	C₂³	1	2	yes	—
87	C₇×C₄⋊Q₈	—	2	1	no	—
88	C₇×C₄⋊Q₈	—	2	2	no	—
89	C₇×C₄⋊Q₈	—	2	4	no	—
90	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
91	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
93	C₇×#127	—	2	1	no	—
94	C₇×#126	—	2	4	no	—
95	C₇×#126	—	2	4	no	—
96	C₇×#125	—	2	2	no	—
97	C₇×#125	—	2	4	no	—
98	C₇×#125	—	2	2	no	—
99	C₇×#125	—	2	4	no	—
100	C₇×#125	C₂³	1	4	yes	—
101	C₇×#125	C₂³	1	2	yes	—
102	C₇×#125	C₂³	1	1	yes	characteristic
103	C₇×#125	C₂³	1	1	yes	characteristic
104	C₇×#125	C₂³	1	2	yes	—
105	C₇×#125	C₂³	1	2	yes	—
106	C₇×#124	—	2	1	no	—
107	C₇×#124	—	2	1	no	—
108	C₇×#124	—	2	4	no	—
109	C₇×#124	—	2	2	no	—
110	C₇×#124	C₂³	1	2	yes	—
111	C₇×#124	C₂³	1	2	yes	—
112	C₇×#123	—	2	2	no	—
113	C₇×#123	—	2	4	no	—
114	C₇×#123	—	2	4	no	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	2	no	—
117	C₇×C₂²⋊Q₈	—	2	4	no	—
118	C₇×C₂²⋊Q₈	—	2	4	no	—
119	C₇×C₂²⋊Q₈	—	2	4	no	—
120	C₇×C₂²⋊Q₈	—	2	4	no	—
121	C₇×C₂²⋊Q₈	—	2	4	no	—
122	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₇×#121	C₂³	1	4	yes	—
124	C₇×#120	—	2	2	no	—
125	C₄×C₇×Q₈	—	2	2	no	—
126	C₄×C₇×Q₈	—	2	2	no	—
127	C₄×C₇×Q₈	—	2	2	no	—
128	C₄×C₇×Q₈	—	2	2	no	—
129	C₄×C₇×Q₈	—	2	4	no	—
130	C₄×C₇×Q₈	D₄	1	2	yes	—
131	C₄×C₇×Q₈	C₂³	1	4	yes	—
132	C₄×C₇×D₄	—	2	4	no	—
133	C₄×C₇×D₄	—	2	2	no	—
134	C₄×C₇×D₄	—	2	4	no	—
135	C₄×C₇×D₄	—	2	2	no	—
136	C₄×C₇×D₄	D₄	1	4	yes	—
137	C₄×C₇×D₄	D₄	1	2	yes	—
138	C₄×C₇×D₄	C₂³	1	4	yes	—
139	C₇×#117	—	2	2	no	—
140	C₇×#117	—	2	4	no	—
141	C₇×#117	C₂³	1	4	yes	—
142	C₇×#117	C₂³	1	1	yes	characteristic
143	C₇×#117	C₂³	1	1	yes	characteristic
144	C₇×#117	C₂³	1	2	yes	—
145	C₇×#117	C₂³	1	1	yes	characteristic
146	C₇×#117	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	—	2	2	no	—
148	C₂×C₇×C₄⋊C₄	—	2	4	no	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
152	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
153	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₇	C₂³	1	2	yes	—
155	C₇×#107	C₂³	1	2	yes	—
156	C₇×#107	C₂³	1	4	yes	—
157	C₇×#107	C₂³	1	2	yes	—
158	C₇×#107	C₂³	1	4	yes	—
159	C₇×#107	C₂³	1	2	yes	—
160	C₇×#107	C₂³	1	2	yes	—
161	C₇×#106	C₂³	1	2	yes	—
162	C₇×#106	C₂³	1	4	yes	—
163	C₇×#106	C₂³	1	2	yes	—
164	C₇×#106	C₂³	1	4	yes	—
165	C₇×#106	C₂³	1	2	yes	—
166	C₇×#106	C₂³	1	2	yes	—
167	C₇×C₄⋊C₈	C₂³	1	4	yes	—
168	C₇×C₄⋊C₈	C₂³	1	4	yes	—
169	C₇×#103	C₂³	1	4	yes	—
170	C₇×#103	C₂³	1	4	yes	—
171	C₇×#103	C₂³	1	4	yes	—
172	C₇×#103	C₂³	1	4	yes	—
173	C₇×#102	C₂³	1	4	yes	—
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	4	yes	—
177	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₇×#97	C₂³	1	2	yes	—
180	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
181	C₄×C₇×C₈	C₂³	1	2	yes	—
182	C₄×C₇×C₈	C₂³	1	2	yes	—
183	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
184	#3510	C₂×C₇	1	1	yes	characteristic
185	#3504	C₂×C₇	1	1	yes	characteristic, complemented
186	#3244	C₂×C₇	1	4	yes	complemented
187	#3243	C₂×C₇	1	4	yes	complemented
188	#3233	C₂×C₇	1	4	yes	complemented
189	#3232	C₂×C₇	1	4	yes	complemented
190	#3166	C₂×C₇	1	1	yes	characteristic, complemented
191	#3160	C₂×C₇	1	1	yes	characteristic, complemented
192	#3140	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#488	C₂×C₇	1	1	yes	characteristic, complemented
194	#3097	C₂×C₇	1	2	yes	complemented
195	#3096	C₂×C₇	1	2	yes	—
196	#3082	C₂×C₇	1	2	yes	complemented
197	#3081	C₂×C₇	1	2	yes	complemented
198	#2922	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	—	2	1	no	—
200	C₇×#41	—	2	4	no	—
201	C₂×C₇×Q₈	—	2	1	no	—
202	C₂×C₇×Q₈	—	2	2	no	—
203	C₂×C₇×Q₈	—	2	4	no	—
204	C₂×C₇×Q₈	—	2	2	no	—
205	C₂×C₇×Q₈	—	2	4	no	—
206	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
208	C₂×C₇×D₄	—	2	4	no	—
209	C₂×C₇×D₄	—	2	1	no	—
210	C₂×C₇×D₄	—	2	4	no	—
211	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
212	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
213	C₂×C₇×D₄	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₇	—	2	1	no	—
215	C₂²×C₄×C₇	—	2	4	no	—
216	C₂²×C₄×C₇	—	2	2	no	—
217	C₂²×C₄×C₇	—	2	4	no	—
218	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
222	C₇×M₁₆	—	2	4	no	—
223	C₂×C₇×C₈	—	2	4	no	—
224	C₂×C₇×C₈	C₂⁴	1	2	yes	—
225	C₂×C₇×C₈	C₂⁴	1	2	yes	—
226	C₂×C₇×C₈	C₂⁴	1	4	yes	—
227	C₇×C₄⋊C₄	—	2	4	no	—
228	C₇×C₄⋊C₄	—	2	2	no	—
229	C₇×C₄⋊C₄	—	2	4	no	—
230	C₇×C₄⋊C₄	—	2	4	no	—
231	C₇×C₄⋊C₄	—	2	4	no	—
232	C₇×C₄⋊C₄	—	2	4	no	—
233	C₇×C₄⋊C₄	—	2	2	no	—
234	C₇×C₄⋊C₄	—	2	2	no	—
235	C₇×C₄⋊C₄	—	2	4	no	—
236	C₇×C₄⋊C₄	—	2	4	no	—
237	C₇×C₄⋊C₄	—	2	2	no	—
238	C₇×C₄⋊C₄	—	2	2	no	—
239	C₇×C₄⋊C₄	—	2	4	no	—
240	C₇×C₄⋊C₄	—	2	2	no	—
241	C₇×C₄⋊C₄	—	2	2	no	—
242	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
243	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
244	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
245	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
246	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
247	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
248	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
249	C₇×C₂²⋊C₄	—	2	1	no	—
250	C₇×C₂²⋊C₄	—	2	1	no	—
251	C₇×C₂²⋊C₄	—	2	4	no	—
252	C₇×C₂²⋊C₄	—	2	2	no	—
253	C₇×C₂²⋊C₄	—	2	4	no	—
254	C₇×C₂²⋊C₄	—	2	4	no	—
255	C₇×C₂²⋊C₄	—	2	4	no	—
256	C₇×C₂²⋊C₄	—	2	4	no	—
257	C₇×C₂²⋊C₄	—	2	4	no	—
258	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
259	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
260	C₄²×C₇	—	2	4	no	—
261	C₄²×C₇	—	2	1	no	—
262	C₄²×C₇	—	2	4	no	—
263	C₄²×C₇	—	2	2	no	—
264	C₄²×C₇	—	2	1	no	—
265	C₄²×C₇	C₂×D₄	1	4	yes	—
266	C₄²×C₇	C₂×D₄	1	2	yes	—
267	C₄²×C₇	C₂⁴	1	1	yes	characteristic
268	C₄²×C₇	C₂⁴	1	1	yes	characteristic
269	C₄²×C₇	C₂⁴	1	2	yes	—
270	#559	—	2	2	no	—
271	#557	—	2	2	no	—
272	#556	—	2	2	no	—
273	#554	—	2	4	no	—
274	#554	—	2	2	no	—
275	#551	—	2	4	no	—
276	#544	C₂²×C₇	1	2	yes	—
277	#544	C₂²×C₇	1	4	yes	complemented
278	#542	C₂²×C₇	1	4	yes	—
279	#536	C₂²×C₇	1	1	yes	characteristic
280	#535	C₂²×C₇	1	1	yes	characteristic
281	#533	C₂²×C₇	1	1	yes	characteristic
282	#533	C₂²×C₇	1	1	yes	characteristic
283	#533	C₂²×C₇	1	2	yes	complemented
284	#529	C₂²×C₇	1	4	yes	—
285	C₂×#125	C₂²×C₇	1	1	yes	characteristic
286	C₂×#125	C₂²×C₇	1	2	yes	complemented
287	C₂×#124	C₂²×C₇	1	1	yes	characteristic
288	#520	C₂²×C₇	1	2	yes	—
289	#519	C₂²×C₇	1	1	yes	characteristic
290	#518	C₂²×C₇	1	1	yes	characteristic
291	C₄×#41	C₂²×C₇	1	1	yes	characteristic
292	#501	C₂²×C₇	1	4	yes	complemented
293	#500	C₂²×C₇	1	2	yes	complemented
294	#499	C₂²×C₇	1	2	yes	complemented
295	#499	C₂²×C₇	1	2	yes	complemented
296	#499	C₂²×C₇	1	4	yes	complemented
297	#498	C₂²×C₇	1	2	yes	complemented
298	#489	C₂²×C₇	1	4	yes	—
299	#488	C₂²×C₇	1	4	yes	—
300	#488	C₂²×C₇	1	2	yes	—
301	#488	C₂²×C₇	1	2	yes	—
302	#488	C₂²×C₇	1	2	yes	—
303	#488	C₂²×C₇	1	2	yes	—
304	#485	C₂²×C₇	1	4	yes	complemented
305	#485	C₂²×C₇	1	4	yes	complemented
306	#484	C₂²×C₇	1	4	yes	complemented
307	#483	C₂²×C₇	1	4	yes	complemented
308	#482	C₂²×C₇	1	4	yes	—
309	#482	C₂²×C₇	1	4	yes	—
310	#481	C₂²×C₇	1	4	yes	—
311	#480	C₂²×C₇	1	4	yes	—
312	#479	C₂²×C₇	1	4	yes	complemented
313	#479	C₂²×C₇	1	4	yes	complemented
314	#478	C₂²×C₇	1	4	yes	—
315	#478	C₂²×C₇	1	4	yes	—
316	#477	C₂²×C₇	1	4	yes	complemented
317	#476	C₂²×C₇	1	4	yes	—
318	#475	C₂²×C₇	1	4	yes	complemented
319	#474	C₂²×C₇	1	4	yes	—
320	#433	C₂²×C₇	1	2	yes	complemented
321	#433	C₂²×C₇	1	2	yes	complemented
322	#431	C₂²×C₇	1	4	yes	complemented
323	#428	C₂²×C₇	1	2	yes	—
324	#428	C₂²×C₇	1	2	yes	—
325	#427	C₂²×C₇	1	2	yes	—
326	#427	C₂²×C₇	1	2	yes	—
327	#424	C₂²×C₇	1	2	yes	—
328	#419	C₂²×C₇	1	2	yes	—
329	#418	C₂²×C₇	1	2	yes	—
330	C₂×#103	C₂²×C₇	1	2	yes	—
331	C₂×#102	C₂²×C₇	1	2	yes	—
332	#408	C₂²×C₇	1	2	yes	—
333	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
335	C₂³×C₇	—	2	2	no	—
336	C₂³×C₇	—	4	2	no	—
337	C₂³×C₇	—	8	2	no	—
338	C₂³×C₇	C₂²×D₄	1	2	yes	—
339	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
340	C₇×Q₈	—	2	2	no	—
341	C₇×Q₈	—	2	4	no	—
342	C₇×Q₈	—	4	2	no	—
343	C₇×Q₈	—	8	4	no	—
344	C₇×Q₈	—	8	2	no	—
345	C₇×Q₈	—	8	2	no	—
346	C₇×D₄	—	2	4	no	—
347	C₇×D₄	—	2	2	no	—
348	C₇×D₄	—	2	4	no	—
349	C₇×D₄	—	4	2	no	—
350	C₇×D₄	—	8	4	no	—
351	C₂×C₄×C₇	—	2	4	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	2	no	—
354	C₂×C₄×C₇	—	2	2	no	—
355	C₂×C₄×C₇	—	2	2	no	—
356	C₂×C₄×C₇	—	2	4	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	4	4	no	—
359	C₂×C₄×C₇	—	4	2	no	—
360	C₂×C₄×C₇	—	4	2	no	—
361	C₂×C₄×C₇	—	8	4	no	—
362	C₂×C₄×C₇	—	8	2	no	—
363	C₂×C₄×C₇	—	8	4	no	—
364	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
366	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
370	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
371	C₇×C₈	—	2	2	no	—
372	C₇×C₈	—	2	2	no	—
373	C₇×C₈	—	2	4	no	—
374	C₂×#41	C₂³×C₇	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
377	C₂×M₁₆	C₂³×C₇	1	2	yes	—
378	C₂²×C₈	C₂³×C₇	1	2	yes	—
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	—	2	2	no	—
381	C₄⋊Q₈	—	2	4	no	—
382	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
383	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
384	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
385	#127	—	2	1	no	—
386	#126	—	2	4	no	—
387	#126	—	2	4	no	—
388	#125	—	2	2	no	—
389	#125	—	2	4	no	—
390	#125	—	2	2	no	—
391	#125	—	2	4	no	—
392	#125	C₂³×C₇	1	2	yes	—
393	#125	C₂³×C₇	1	2	yes	—
394	#125	C₂³×C₇	1	1	yes	characteristic
395	#125	C₂³×C₇	1	4	yes	—
396	#125	C₂³×C₇	1	2	yes	—
397	#125	C₂³×C₇	1	1	yes	characteristic
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#124	—	2	4	no	—
401	#124	—	2	2	no	—
402	#124	C₂³×C₇	1	2	yes	—
403	#124	C₂³×C₇	1	2	yes	—
404	#123	—	2	2	no	—
405	#123	—	2	4	no	—
406	#123	—	2	4	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	4	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
415	#121	C₂³×C₇	1	4	yes	—
416	#120	—	2	2	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	4	no	—
422	C₄×Q₈	C₇×D₄	1	2	yes	—
423	C₄×Q₈	C₂³×C₇	1	4	yes	—
424	C₄×D₄	—	2	4	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	C₇×D₄	1	4	yes	—
429	C₄×D₄	C₇×D₄	1	2	yes	—
430	C₄×D₄	C₂³×C₇	1	4	yes	—
431	#117	—	2	2	no	—
432	#117	—	2	4	no	—
433	#117	C₂³×C₇	1	1	yes	characteristic
434	#117	C₂³×C₇	1	1	yes	characteristic
435	#117	C₂³×C₇	1	2	yes	—
436	#117	C₂³×C₇	1	4	yes	—
437	#117	C₂³×C₇	1	1	yes	characteristic
438	#117	C₂³×C₇	1	2	yes	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	4	no	—
441	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₂²⋊C₄	—	2	2	no	—
445	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₇	1	2	yes	—
447	#107	C₂³×C₇	1	2	yes	—
448	#107	C₂³×C₇	1	2	yes	—
449	#107	C₂³×C₇	1	2	yes	—
450	#107	C₂³×C₇	1	2	yes	—
451	#107	C₂³×C₇	1	4	yes	—
452	#107	C₂³×C₇	1	4	yes	—
453	#106	C₂³×C₇	1	2	yes	—
454	#106	C₂³×C₇	1	2	yes	—
455	#106	C₂³×C₇	1	2	yes	—
456	#106	C₂³×C₇	1	2	yes	—
457	#106	C₂³×C₇	1	4	yes	—
458	#106	C₂³×C₇	1	4	yes	—
459	C₄⋊C₈	C₂³×C₇	1	4	yes	—
460	C₄⋊C₈	C₂³×C₇	1	4	yes	—
461	#103	C₂³×C₇	1	4	yes	—
462	#103	C₂³×C₇	1	4	yes	—
463	#103	C₂³×C₇	1	4	yes	—
464	#103	C₂³×C₇	1	4	yes	—
465	#102	C₂³×C₇	1	4	yes	—
466	#102	C₂³×C₇	1	4	yes	—
467	#102	C₂³×C₇	1	4	yes	—
468	#102	C₂³×C₇	1	4	yes	—
469	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
470	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
471	#97	C₂³×C₇	1	2	yes	—
472	C₄×C₈	C₂³×C₇	1	2	yes	—
473	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
474	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
475	C₄×C₈	C₂³×C₇	1	2	yes	—
476	C₂²×C₇	—	2	2	no	—
477	C₂²×C₇	—	2	4	no	—
478	C₂²×C₇	—	2	2	no	—
479	C₂²×C₇	—	4	4	no	—
480	C₂²×C₇	—	4	2	no	—
481	C₂²×C₇	—	16	2	no	—
482	C₂²×C₇	#536	1	2	yes	—
483	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
484	C₄×C₇	—	2	2	no	—
485	C₄×C₇	—	2	4	no	—
486	C₄×C₇	—	2	2	no	—
487	C₄×C₇	—	2	2	no	—
488	C₄×C₇	—	4	2	no	—
489	C₄×C₇	—	4	4	no	—
490	C₄×C₇	—	4	2	no	—
491	C₄×C₇	—	4	2	no	—
492	C₄×C₇	—	4	2	no	—
493	C₄×C₇	—	4	2	no	—
494	C₄×C₇	#536	1	2	yes	—
495	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
496	C₂⁴	—	2	1	no	—
497	#41	—	2	4	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
504	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
509	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
510	C₂×D₄	C₂⁴×C₇	1	2	yes	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
516	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
517	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
519	M₁₆	—	2	4	no	—
520	C₂×C₈	—	2	4	no	—
521	C₂×C₈	C₂⁴×C₇	1	2	yes	—
522	C₂×C₈	C₂⁴×C₇	1	2	yes	—
523	C₂×C₈	C₂⁴×C₇	1	4	yes	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
540	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
541	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
542	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
543	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
544	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
545	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
556	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	2	2	no	—
561	C₄²	—	2	1	no	—
562	C₄²	C₂×C₇×D₄	1	4	yes	—
563	C₄²	C₂×C₇×D₄	1	2	yes	—
564	C₄²	C₂⁴×C₇	1	1	yes	characteristic
565	C₄²	C₂⁴×C₇	1	1	yes	characteristic
566	C₄²	C₂⁴×C₇	1	2	yes	—
567	C₂×C₇	—	2	2	no	—
568	C₂×C₇	—	4	2	no	—
569	C₂×C₇	—	8	2	no	—
570	C₂×C₇	C₂×#536	1	1	yes	characteristic
571	C₂×C₇	#3584	1	2	yes	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	8	2	no	—
575	C₂³	C₂²×C₇×D₄	1	2	yes	—
576	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	2	4	no	—
579	Q₈	—	4	2	no	—
580	Q₈	—	8	4	no	—
581	Q₈	—	8	2	no	—
582	Q₈	—	8	2	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	8	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	8	4	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	—	8	4	no	—
601	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
602	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
603	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
604	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
605	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
606	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
607	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
608	C₈	—	2	2	no	—
609	C₈	—	2	2	no	—
610	C₈	—	2	4	no	—
611	C₇	#60879	1	1	yes	characteristic, direct product factor, Sylow
612	C₂²	—	2	2	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	16	2	no	—
618	C₂²	C₇×#536	1	2	yes	—
619	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	4	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	C₇×#536	1	2	yes	—
631	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	8	2	no	—
635	C₂	C₂×C₇×#536	1	1	yes	characteristic
636	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3504	C₂	semidirect
3. C₇×#3244	C₂	semidirect
4. C₇×#3243	C₂	semidirect
5. C₇×#3233	C₂	semidirect
6. C₇×#3232	C₂	semidirect
7. C₇×#3166	C₂	semidirect
8. C₇×#3160	C₂	semidirect
9. C₇×#3140	C₂	semidirect
10. C₂×C₇×#488	C₂	semidirect
11. C₇×#3097	C₂	semidirect
13. C₇×#3082	C₂	semidirect
14. C₇×#3081	C₂	semidirect
15. C₇×#2922	C₂	semidirect
23. C₇×#544	C₂²	semidirect
29. C₇×#533	C₂²	semidirect
32. C₂×C₇×#125	C₂²	semidirect
38. C₇×#501	C₂²	semidirect
39. C₇×#500	C₂²	semidirect
40. C₇×#499	C₂²	semidirect
41. C₇×#499	C₂²	semidirect
42. C₇×#499	C₂²	semidirect
43. C₇×#498	C₂²	semidirect
50. C₇×#485	C₂²	semidirect
51. C₇×#485	C₂²	semidirect
52. C₇×#484	C₂²	semidirect
53. C₇×#483	C₂²	semidirect
58. C₇×#479	C₂²	semidirect
59. C₇×#479	C₂²	semidirect
62. C₇×#477	C₂²	semidirect
64. C₇×#475	C₂²	semidirect
66. C₇×#433	C₂²	semidirect
67. C₇×#433	C₂²	semidirect
68. C₇×#431	C₂²	semidirect
81. #60879	C₇	direct (N × H)
185. #3504	C₂×C₇	semidirect
186. #3244	C₂×C₇	semidirect
187. #3243	C₂×C₇	semidirect
188. #3233	C₂×C₇	semidirect
189. #3232	C₂×C₇	semidirect
190. #3166	C₂×C₇	semidirect
191. #3160	C₂×C₇	semidirect
192. #3140	C₂×C₇	semidirect
193. C₂×#488	C₂×C₇	semidirect
194. #3097	C₂×C₇	semidirect
196. #3082	C₂×C₇	semidirect
197. #3081	C₂×C₇	semidirect
198. #2922	C₂×C₇	semidirect
277. #544	C₂²×C₇	semidirect
283. #533	C₂²×C₇	semidirect
286. C₂×#125	C₂²×C₇	semidirect
292. #501	C₂²×C₇	semidirect
293. #500	C₂²×C₇	semidirect
294. #499	C₂²×C₇	semidirect
295. #499	C₂²×C₇	semidirect
296. #499	C₂²×C₇	semidirect
297. #498	C₂²×C₇	semidirect
304. #485	C₂²×C₇	semidirect
305. #485	C₂²×C₇	semidirect
306. #484	C₂²×C₇	semidirect
307. #483	C₂²×C₇	semidirect
312. #479	C₂²×C₇	semidirect
313. #479	C₂²×C₇	semidirect
316. #477	C₂²×C₇	semidirect
318. #475	C₂²×C₇	semidirect
320. #433	C₂²×C₇	semidirect
321. #433	C₂²×C₇	semidirect
322. #431	C₂²×C₇	semidirect
611. C₇	#60879	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×#3510	2
C₇×#3504	2
C₇×#3244	2
C₇×#3243	2
C₇×#3233	2
C₇×#3232	2
C₇×#3166	2
C₇×#3160	2
C₇×#3140	2
C₂×C₇×#488	2
C₇×#3097	2
C₇×#3096	2
C₇×#3082	2
C₇×#3081	2
C₇×#2922	2
#60879	7

Subgroups — C7×#60879 #13238095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60879 #13238095