Subgroups — C₇×#60877 #13238093

Order 1792.

1786 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3508	C₂	1	1	yes	maximal, characteristic
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3241	C₂	1	8	yes	maximal, complemented
4	C₇×#3228	C₂	1	2	yes	maximal, complemented
5	C₇×#3228	C₂	1	2	yes	maximal, complemented
6	C₇×#3227	C₂	1	2	yes	maximal, complemented
7	C₇×#3226	C₂	1	2	yes	maximal, complemented
8	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	C₂	1	4	yes	maximal, complemented
13	C₇×#3081	C₂	1	4	yes	maximal, complemented
14	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#559	—	2	1	no	—
16	C₇×#559	—	2	1	no	—
17	C₇×Q₈²	—	2	1	no	—
18	C₇×#557	—	2	1	no	—
19	C₇×#554	—	2	2	no	—
20	C₇×#554	—	2	1	no	—
21	C₇×#550	—	2	1	no	—
22	C₇×#550	—	2	1	no	—
23	C₇×D₄×Q₈	—	2	2	no	—
24	C₇×D₄×Q₈	—	2	1	no	—
25	C₇×#546	—	2	2	no	—
26	C₇×#546	—	2	2	no	—
27	C₇×#544	C₂²	1	2	yes	—
28	C₇×#544	C₂²	1	4	yes	complemented
29	C₇×#540	C₂²	1	4	yes	—
30	C₇×#535	C₂²	1	2	yes	—
31	C₇×#533	C₂²	1	1	yes	characteristic
32	C₇×#533	C₂²	1	1	yes	characteristic
33	C₇×#533	C₂²	1	2	yes	complemented
34	C₇×#532	C₂²	1	2	yes	—
35	C₇×#532	C₂²	1	2	yes	—
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₇×#127	C₂²	1	1	yes	characteristic
39	C₇×#520	C₂²	1	2	yes	—
40	C₇×#518	C₂²	1	2	yes	—
41	C₄×C₇×#41	C₂²	1	1	yes	characteristic
42	C₇×#501	C₂²	1	4	yes	complemented
43	C₇×#500	C₂²	1	1	yes	characteristic, complemented
44	C₇×#500	C₂²	1	1	yes	characteristic, complemented
45	C₇×#500	C₂²	1	2	yes	complemented
46	C₇×#499	C₂²	1	4	yes	complemented
47	C₇×#498	C₂²	1	1	yes	characteristic, complemented
48	C₇×#498	C₂²	1	1	yes	characteristic, complemented
49	C₇×#498	C₂²	1	2	yes	complemented
50	C₇×#490	C₂²	1	4	yes	—
51	C₇×#486	C₂²	1	2	yes	—
52	C₇×#486	C₂²	1	2	yes	—
53	C₇×#486	C₂²	1	2	yes	—
54	C₇×#486	C₂²	1	2	yes	—
55	C₇×#486	C₂²	1	4	yes	—
56	C₇×#482	C₂²	1	8	yes	complemented
57	C₇×#482	C₂²	1	8	yes	complemented
58	C₇×#481	C₂²	1	8	yes	complemented
59	C₇×#480	C₂²	1	8	yes	complemented
60	C₇×#478	C₂²	1	8	yes	complemented
61	C₇×#478	C₂²	1	8	yes	complemented
62	C₇×#476	C₂²	1	8	yes	complemented
63	C₇×#474	C₂²	1	8	yes	complemented
64	C₇×#433	C₂²	1	4	yes	complemented
65	C₇×#431	C₂²	1	2	yes	complemented
66	C₇×#431	C₂²	1	2	yes	complemented
67	C₇×#428	C₂²	1	4	yes	—
68	C₇×#427	C₂²	1	4	yes	—
69	C₇×#424	C₂²	1	2	yes	—
70	C₇×#418	C₂²	1	4	yes	—
71	C₂×C₇×#102	C₂²	1	4	yes	—
72	C₇×#408	C₂²	1	2	yes	—
73	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
75	#60877	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×C₇×#41	—	2	2	no	—
77	C₂×C₇×#41	—	2	2	no	—
78	C₂×C₇×#41	C₂³	1	1	yes	characteristic
79	C₂²×C₇×Q₈	—	2	1	no	—
80	C₂²×C₇×Q₈	—	2	2	no	—
81	C₂²×C₇×D₄	—	2	1	no	—
82	C₂²×C₇×D₄	—	2	1	no	—
83	C₂²×C₇×D₄	C₂³	1	2	yes	—
84	C₂×C₇×M₁₆	C₂³	1	2	yes	—
85	C₂²×C₇×C₈	C₂³	1	2	yes	—
86	C₇×C₄⋊Q₈	—	2	2	no	—
87	C₇×C₄⋊Q₈	—	2	4	no	—
88	C₇×C₄⋊Q₈	—	2	1	no	—
89	C₇×C₄⋊Q₈	—	2	1	no	—
90	C₇×C₄⋊Q₈	—	2	2	no	—
91	C₇×C₄⋊Q₈	—	2	2	no	—
92	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₇×#127	—	2	2	no	—
100	C₇×#127	—	2	1	no	—
101	C₇×#127	—	2	1	no	—
102	C₇×#127	C₂³	1	2	yes	—
103	C₇×#127	C₂³	1	2	yes	—
104	C₇×#125	—	2	2	no	—
105	C₇×#125	—	2	4	no	—
106	C₇×#125	C₂³	1	4	yes	—
107	C₇×#125	C₂³	1	2	yes	—
108	C₇×#125	C₂³	1	2	yes	—
109	C₇×#124	—	2	2	no	—
110	C₇×#124	—	2	2	no	—
111	C₇×#124	—	2	2	no	—
112	C₇×#123	—	2	4	no	—
113	C₇×#123	—	2	4	no	—
114	C₇×C₂²⋊Q₈	—	2	1	no	—
115	C₇×C₂²⋊Q₈	—	2	1	no	—
116	C₇×C₂²⋊Q₈	—	2	1	no	—
117	C₇×C₂²⋊Q₈	—	2	1	no	—
118	C₇×C₂²⋊Q₈	—	2	2	no	—
119	C₇×C₂²⋊Q₈	—	2	2	no	—
120	C₇×C₂²⋊Q₈	—	2	4	no	—
121	C₇×C₂²⋊Q₈	—	2	4	no	—
122	C₇×C₂²⋊Q₈	—	2	4	no	—
123	C₇×#121	—	2	2	no	—
124	C₇×#121	—	2	2	no	—
125	C₇×#121	—	2	4	no	—
126	C₇×#121	—	2	4	no	—
127	C₇×#121	C₂³	1	4	yes	—
128	C₇×#121	C₂³	1	4	yes	—
129	C₇×#120	—	2	4	no	—
130	C₄×C₇×Q₈	—	2	2	no	—
131	C₄×C₇×Q₈	—	2	1	no	—
132	C₄×C₇×Q₈	—	2	1	no	—
133	C₄×C₇×Q₈	—	2	1	no	—
134	C₄×C₇×Q₈	—	2	1	no	—
135	C₄×C₇×Q₈	—	2	2	no	—
136	C₄×C₇×Q₈	—	2	2	no	—
137	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
138	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
139	C₄×C₇×D₄	—	2	4	no	—
140	C₄×C₇×D₄	—	2	2	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	—	2	2	no	—
143	C₄×C₇×D₄	—	2	2	no	—
144	C₄×C₇×D₄	—	2	2	no	—
145	C₄×C₇×D₄	D₄	1	2	yes	—
146	C₄×C₇×D₄	D₄	1	2	yes	—
147	C₄×C₇×D₄	D₄	1	1	yes	characteristic
148	C₄×C₇×D₄	D₄	1	1	yes	characteristic
149	C₄×C₇×D₄	C₂³	1	4	yes	—
150	C₄×C₇×D₄	C₂³	1	4	yes	—
151	C₇×#117	C₂³	1	4	yes	—
152	C₇×#117	C₂³	1	2	yes	—
153	C₇×#117	C₂³	1	2	yes	—
154	C₇×#117	C₂³	1	1	yes	characteristic
155	C₇×#117	C₂³	1	2	yes	—
156	C₂×C₇×C₄⋊C₄	—	2	1	no	—
157	C₂×C₇×C₄⋊C₄	—	2	2	no	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
161	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₇	C₂³	1	2	yes	—
163	C₇×#107	C₂³	1	4	yes	—
164	C₇×#107	C₂³	1	8	yes	—
165	C₇×#107	C₂³	1	4	yes	—
166	C₇×#106	C₂³	1	4	yes	—
167	C₇×#106	C₂³	1	8	yes	—
168	C₇×#106	C₂³	1	4	yes	—
169	C₇×C₄⋊C₈	C₂³	1	4	yes	—
170	C₇×C₄⋊C₈	C₂³	1	4	yes	—
171	C₇×#102	C₂³	1	8	yes	—
172	C₇×#102	C₂³	1	8	yes	—
173	C₇×#102	C₂³	1	8	yes	—
174	C₇×#102	C₂³	1	8	yes	—
175	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₇×#97	C₂³	1	2	yes	—
178	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₄×C₇×C₈	C₂³	1	2	yes	—
180	C₄×C₇×C₈	C₂³	1	2	yes	—
181	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
182	#3508	C₂×C₇	1	1	yes	characteristic
183	#3503	C₂×C₇	1	1	yes	characteristic, complemented
184	#3241	C₂×C₇	1	8	yes	complemented
185	#3228	C₂×C₇	1	2	yes	complemented
186	#3228	C₂×C₇	1	2	yes	complemented
187	#3227	C₂×C₇	1	2	yes	complemented
188	#3226	C₂×C₇	1	2	yes	complemented
189	#3165	C₂×C₇	1	1	yes	characteristic, complemented
190	#3160	C₂×C₇	1	1	yes	characteristic, complemented
191	#3138	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
193	#3096	C₂×C₇	1	4	yes	complemented
194	#3081	C₂×C₇	1	4	yes	complemented
195	#2922	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂⁴×C₇	—	2	2	no	—
197	C₇×#41	—	2	4	no	—
198	C₇×#41	—	8	4	no	—
199	C₇×#41	—	8	4	no	—
200	C₂×C₇×Q₈	—	2	1	no	—
201	C₂×C₇×Q₈	—	2	1	no	—
202	C₂×C₇×Q₈	—	2	1	no	—
203	C₂×C₇×Q₈	—	2	1	no	—
204	C₂×C₇×Q₈	—	2	2	no	—
205	C₂×C₇×Q₈	—	2	4	no	—
206	C₂×C₇×Q₈	—	2	2	no	—
207	C₂×C₇×Q₈	—	8	2	no	—
208	C₂×C₇×Q₈	—	8	4	no	—
209	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
210	C₂×C₇×D₄	—	2	4	no	—
211	C₂×C₇×D₄	—	2	4	no	—
212	C₂×C₇×D₄	—	2	2	no	—
213	C₂×C₇×D₄	—	2	2	no	—
214	C₂×C₇×D₄	—	2	2	no	—
215	C₂×C₇×D₄	—	2	2	no	—
216	C₂×C₇×D₄	—	2	2	no	—
217	C₂×C₇×D₄	—	2	8	no	—
218	C₂×C₇×D₄	—	8	2	no	—
219	C₂×C₇×D₄	—	8	2	no	—
220	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
221	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇×D₄	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₇	—	2	4	no	—
224	C₂²×C₄×C₇	—	2	2	no	—
225	C₂²×C₄×C₇	—	2	4	no	—
226	C₂²×C₄×C₇	—	2	4	no	—
227	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
233	C₇×M₁₆	—	2	4	no	—
234	C₂×C₇×C₈	—	2	4	no	—
235	C₂×C₇×C₈	C₂⁴	1	2	yes	—
236	C₂×C₇×C₈	C₂⁴	1	2	yes	—
237	C₂×C₇×C₈	C₂⁴	1	4	yes	—
238	C₇×C₄⋊C₄	—	2	2	no	—
239	C₇×C₄⋊C₄	—	2	1	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	2	no	—
244	C₇×C₄⋊C₄	—	2	1	no	—
245	C₇×C₄⋊C₄	—	2	1	no	—
246	C₇×C₄⋊C₄	—	2	1	no	—
247	C₇×C₄⋊C₄	—	2	2	no	—
248	C₇×C₄⋊C₄	—	2	2	no	—
249	C₇×C₄⋊C₄	—	2	4	no	—
250	C₇×C₄⋊C₄	—	2	2	no	—
251	C₇×C₄⋊C₄	—	2	4	no	—
252	C₇×C₄⋊C₄	—	2	2	no	—
253	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
254	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
255	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
256	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
257	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
258	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
259	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₇×C₂²⋊C₄	—	2	2	no	—
263	C₇×C₂²⋊C₄	—	2	4	no	—
264	C₇×C₂²⋊C₄	—	2	2	no	—
265	C₇×C₂²⋊C₄	—	2	4	no	—
266	C₇×C₂²⋊C₄	—	2	4	no	—
267	C₇×C₂²⋊C₄	—	2	4	no	—
268	C₇×C₂²⋊C₄	—	2	4	no	—
269	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
270	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
271	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
272	C₄²×C₇	—	2	2	no	—
273	C₄²×C₇	—	2	4	no	—
274	C₄²×C₇	—	2	2	no	—
275	C₄²×C₇	C₂×D₄	1	2	yes	—
276	C₄²×C₇	C₂×D₄	1	2	yes	—
277	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₇	C₂⁴	1	1	yes	characteristic
280	C₄²×C₇	C₂⁴	1	1	yes	characteristic
281	C₄²×C₇	C₂⁴	1	2	yes	—
282	#559	—	2	1	no	—
283	#559	—	2	1	no	—
284	Q₈²	—	2	1	no	—
285	#557	—	2	1	no	—
286	#554	—	2	2	no	—
287	#554	—	2	1	no	—
288	#550	—	2	1	no	—
289	#550	—	2	1	no	—
290	D₄×Q₈	—	2	2	no	—
291	D₄×Q₈	—	2	1	no	—
292	#546	—	2	2	no	—
293	#546	—	2	2	no	—
294	#544	C₂²×C₇	1	2	yes	—
295	#544	C₂²×C₇	1	4	yes	complemented
296	#540	C₂²×C₇	1	4	yes	—
297	#535	C₂²×C₇	1	2	yes	—
298	#533	C₂²×C₇	1	1	yes	characteristic
299	#533	C₂²×C₇	1	1	yes	characteristic
300	#533	C₂²×C₇	1	2	yes	complemented
301	#532	C₂²×C₇	1	2	yes	—
302	#532	C₂²×C₇	1	2	yes	—
303	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
304	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
305	C₂×#127	C₂²×C₇	1	1	yes	characteristic
306	#520	C₂²×C₇	1	2	yes	—
307	#518	C₂²×C₇	1	2	yes	—
308	C₄×#41	C₂²×C₇	1	1	yes	characteristic
309	#501	C₂²×C₇	1	4	yes	complemented
310	#500	C₂²×C₇	1	1	yes	characteristic, complemented
311	#500	C₂²×C₇	1	1	yes	characteristic, complemented
312	#500	C₂²×C₇	1	2	yes	complemented
313	#499	C₂²×C₇	1	4	yes	complemented
314	#498	C₂²×C₇	1	1	yes	characteristic, complemented
315	#498	C₂²×C₇	1	1	yes	characteristic, complemented
316	#498	C₂²×C₇	1	2	yes	complemented
317	#490	C₂²×C₇	1	4	yes	—
318	#486	C₂²×C₇	1	2	yes	—
319	#486	C₂²×C₇	1	2	yes	—
320	#486	C₂²×C₇	1	4	yes	—
321	#486	C₂²×C₇	1	2	yes	—
322	#486	C₂²×C₇	1	2	yes	—
323	#482	C₂²×C₇	1	8	yes	complemented
324	#482	C₂²×C₇	1	8	yes	complemented
325	#481	C₂²×C₇	1	8	yes	complemented
326	#480	C₂²×C₇	1	8	yes	complemented
327	#478	C₂²×C₇	1	8	yes	complemented
328	#478	C₂²×C₇	1	8	yes	complemented
329	#476	C₂²×C₇	1	8	yes	complemented
330	#474	C₂²×C₇	1	8	yes	complemented
331	#433	C₂²×C₇	1	4	yes	complemented
332	#431	C₂²×C₇	1	2	yes	complemented
333	#431	C₂²×C₇	1	2	yes	complemented
334	#428	C₂²×C₇	1	4	yes	—
335	#427	C₂²×C₇	1	4	yes	—
336	#424	C₂²×C₇	1	2	yes	—
337	#418	C₂²×C₇	1	4	yes	—
338	C₂×#102	C₂²×C₇	1	4	yes	—
339	#408	C₂²×C₇	1	2	yes	—
340	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
341	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
342	C₂³×C₇	—	2	4	no	—
343	C₂³×C₇	—	4	4	no	—
344	C₂³×C₇	—	8	2	no	—
345	C₂³×C₇	—	8	2	no	—
346	C₂³×C₇	C₂²×D₄	1	2	yes	—
347	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
348	C₇×Q₈	—	2	2	no	—
349	C₇×Q₈	—	4	2	no	—
350	C₇×Q₈	—	4	4	no	—
351	C₇×Q₈	—	4	2	no	—
352	C₇×Q₈	—	4	2	no	—
353	C₇×Q₈	—	4	2	no	—
354	C₇×Q₈	—	8	4	no	—
355	C₇×Q₈	—	8	2	no	—
356	C₇×D₄	—	2	4	no	—
357	C₇×D₄	—	2	2	no	—
358	C₇×D₄	—	2	8	no	—
359	C₇×D₄	—	4	4	no	—
360	C₇×D₄	—	4	4	no	—
361	C₇×D₄	—	4	4	no	—
362	C₇×D₄	—	8	2	no	—
363	C₇×D₄	—	8	2	no	—
364	C₇×D₄	—	8	4	no	—
365	C₇×D₄	—	8	4	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	4	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	4	no	—
370	C₂×C₄×C₇	—	2	4	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	4	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	8	4	no	—
377	C₂×C₄×C₇	—	8	4	no	—
378	C₂×C₄×C₇	—	8	2	no	—
379	C₂×C₄×C₇	—	8	4	no	—
380	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
389	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
390	C₇×C₈	—	2	2	no	—
391	C₇×C₈	—	2	2	no	—
392	C₇×C₈	—	2	4	no	—
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	C₂³×C₇	1	1	yes	characteristic
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	—	2	2	no	—
398	C₂²×D₄	—	2	1	no	—
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	C₂³×C₇	1	2	yes	—
401	C₂×M₁₆	C₂³×C₇	1	2	yes	—
402	C₂²×C₈	C₂³×C₇	1	2	yes	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	4	no	—
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	—	2	1	no	—
407	C₄⋊Q₈	—	2	2	no	—
408	C₄⋊Q₈	—	2	2	no	—
409	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
410	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
411	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
412	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
413	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
414	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
415	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
416	#127	—	2	2	no	—
417	#127	—	2	1	no	—
418	#127	—	2	1	no	—
419	#127	C₂³×C₇	1	2	yes	—
420	#127	C₂³×C₇	1	2	yes	—
421	#125	—	2	2	no	—
422	#125	—	2	4	no	—
423	#125	C₂³×C₇	1	2	yes	—
424	#125	C₂³×C₇	1	2	yes	—
425	#125	C₂³×C₇	1	4	yes	—
426	#124	—	2	2	no	—
427	#124	—	2	2	no	—
428	#124	—	2	2	no	—
429	#123	—	2	4	no	—
430	#123	—	2	4	no	—
431	C₂²⋊Q₈	—	2	1	no	—
432	C₂²⋊Q₈	—	2	1	no	—
433	C₂²⋊Q₈	—	2	1	no	—
434	C₂²⋊Q₈	—	2	1	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	4	no	—
438	C₂²⋊Q₈	—	2	4	no	—
439	C₂²⋊Q₈	—	2	4	no	—
440	#121	—	2	2	no	—
441	#121	—	2	2	no	—
442	#121	—	2	4	no	—
443	#121	—	2	4	no	—
444	#121	C₂³×C₇	1	4	yes	—
445	#121	C₂³×C₇	1	4	yes	—
446	#120	—	2	4	no	—
447	C₄×Q₈	—	2	2	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
455	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	2	no	—
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	C₇×D₄	1	2	yes	—
463	C₄×D₄	C₇×D₄	1	2	yes	—
464	C₄×D₄	C₇×D₄	1	1	yes	characteristic
465	C₄×D₄	C₇×D₄	1	1	yes	characteristic
466	C₄×D₄	C₂³×C₇	1	4	yes	—
467	C₄×D₄	C₂³×C₇	1	4	yes	—
468	#117	C₂³×C₇	1	2	yes	—
469	#117	C₂³×C₇	1	2	yes	—
470	#117	C₂³×C₇	1	4	yes	—
471	#117	C₂³×C₇	1	1	yes	characteristic
472	#117	C₂³×C₇	1	2	yes	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
477	C₂×C₂²⋊C₄	—	2	4	no	—
478	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₇	1	2	yes	—
480	#107	C₂³×C₇	1	4	yes	—
481	#107	C₂³×C₇	1	4	yes	—
482	#107	C₂³×C₇	1	8	yes	—
483	#106	C₂³×C₇	1	4	yes	—
484	#106	C₂³×C₇	1	4	yes	—
485	#106	C₂³×C₇	1	8	yes	—
486	C₄⋊C₈	C₂³×C₇	1	4	yes	—
487	C₄⋊C₈	C₂³×C₇	1	4	yes	—
488	#102	C₂³×C₇	1	8	yes	—
489	#102	C₂³×C₇	1	8	yes	—
490	#102	C₂³×C₇	1	8	yes	—
491	#102	C₂³×C₇	1	8	yes	—
492	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
494	#97	C₂³×C₇	1	2	yes	—
495	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
496	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
497	C₄×C₈	C₂³×C₇	1	2	yes	—
498	C₄×C₈	C₂³×C₇	1	2	yes	—
499	C₂²×C₇	—	2	1	no	—
500	C₂²×C₇	—	2	1	no	—
501	C₂²×C₇	—	2	2	no	—
502	C₂²×C₇	—	2	2	no	—
503	C₂²×C₇	—	2	2	no	—
504	C₂²×C₇	—	4	4	no	—
505	C₂²×C₇	—	4	4	no	—
506	C₂²×C₇	—	4	4	no	—
507	C₂²×C₇	—	16	4	no	—
508	C₂²×C₇	#536	1	2	yes	—
509	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₇	—	2	2	no	—
511	C₄×C₇	—	2	2	no	—
512	C₄×C₇	—	2	1	no	—
513	C₄×C₇	—	2	2	no	—
514	C₄×C₇	—	2	1	no	—
515	C₄×C₇	—	4	2	no	—
516	C₄×C₇	—	4	4	no	—
517	C₄×C₇	—	4	2	no	—
518	C₄×C₇	—	4	2	no	—
519	C₄×C₇	—	4	2	no	—
520	C₄×C₇	#536	1	2	yes	—
521	C₄×C₇	#576	1	2	yes	—
522	C₄×C₇	#577	1	2	yes	—
523	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
524	C₂⁴	—	2	2	no	—
525	#41	—	2	4	no	—
526	#41	—	8	4	no	—
527	#41	—	8	4	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	8	2	no	—
536	C₂×Q₈	—	8	4	no	—
537	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	8	no	—
546	C₂×D₄	—	8	2	no	—
547	C₂×D₄	—	8	2	no	—
548	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
549	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
550	C₂×D₄	C₂⁴×C₇	1	4	yes	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	2	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	1	yes	characteristic
557	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
558	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
561	M₁₆	—	2	4	no	—
562	C₂×C₈	—	2	4	no	—
563	C₂×C₈	C₂⁴×C₇	1	2	yes	—
564	C₂×C₈	C₂⁴×C₇	1	2	yes	—
565	C₂×C₈	C₂⁴×C₇	1	4	yes	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
582	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
583	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
584	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
586	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
587	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
588	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
589	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
598	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
599	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	4	no	—
602	C₄²	—	2	2	no	—
603	C₄²	C₂×C₇×D₄	1	2	yes	—
604	C₄²	C₂×C₇×D₄	1	2	yes	—
605	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
606	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
607	C₄²	C₂⁴×C₇	1	1	yes	characteristic
608	C₄²	C₂⁴×C₇	1	1	yes	characteristic
609	C₄²	C₂⁴×C₇	1	2	yes	—
610	C₂×C₇	—	2	2	no	—
611	C₂×C₇	—	4	2	no	—
612	C₂×C₇	—	8	4	no	—
613	C₂×C₇	C₂×#536	1	1	yes	characteristic
614	C₂×C₇	C₂×#576	1	1	yes	characteristic
615	C₂×C₇	C₂×#577	1	1	yes	characteristic
616	C₂³	—	2	4	no	—
617	C₂³	—	4	4	no	—
618	C₂³	—	8	2	no	—
619	C₂³	—	8	2	no	—
620	C₂³	C₂²×C₇×D₄	1	2	yes	—
621	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
622	Q₈	—	2	2	no	—
623	Q₈	—	4	2	no	—
624	Q₈	—	4	4	no	—
625	Q₈	—	4	2	no	—
626	Q₈	—	4	2	no	—
627	Q₈	—	4	2	no	—
628	Q₈	—	8	4	no	—
629	Q₈	—	8	2	no	—
630	D₄	—	2	4	no	—
631	D₄	—	2	8	no	—
632	D₄	—	2	2	no	—
633	D₄	—	4	4	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	4	no	—
636	D₄	—	8	2	no	—
637	D₄	—	8	2	no	—
638	D₄	—	8	4	no	—
639	D₄	—	8	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	8	4	no	—
651	C₂×C₄	—	8	4	no	—
652	C₂×C₄	—	8	2	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
655	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
656	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
657	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
658	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
659	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
660	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
661	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
662	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
663	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
664	C₈	—	2	2	no	—
665	C₈	—	2	2	no	—
666	C₈	—	2	4	no	—
667	C₇	#60877	1	1	yes	characteristic, direct product factor, Sylow
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	16	4	no	—
677	C₂²	C₇×#536	1	2	yes	—
678	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	C₇×#536	1	2	yes	—
690	C₄	C₇×#576	1	2	yes	—
691	C₄	C₇×#577	1	2	yes	—
692	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	8	4	no	—
696	C₂	C₂×C₇×#536	1	1	yes	characteristic
697	C₂	C₂×C₇×#576	1	1	yes	characteristic
698	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3508	C₂
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×#3503	C₂	semidirect
3. C₇×#3241	C₂	semidirect
4. C₇×#3228	C₂	semidirect
5. C₇×#3228	C₂	semidirect
6. C₇×#3227	C₂	semidirect
7. C₇×#3226	C₂	semidirect
8. C₇×#3165	C₂	semidirect
9. C₇×#3160	C₂	semidirect
10. C₇×#3138	C₂	semidirect
11. C₂×C₇×#486	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3081	C₂	semidirect
14. C₇×#2922	C₂	semidirect
28. C₇×#544	C₂²	semidirect
33. C₇×#533	C₂²	semidirect
37. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
42. C₇×#501	C₂²	semidirect
43. C₇×#500	C₂²	semidirect
44. C₇×#500	C₂²	semidirect
45. C₇×#500	C₂²	semidirect
46. C₇×#499	C₂²	semidirect
47. C₇×#498	C₂²	semidirect
48. C₇×#498	C₂²	semidirect
49. C₇×#498	C₂²	semidirect
56. C₇×#482	C₂²	semidirect
57. C₇×#482	C₂²	semidirect
58. C₇×#481	C₂²	semidirect
59. C₇×#480	C₂²	semidirect
60. C₇×#478	C₂²	semidirect
61. C₇×#478	C₂²	semidirect
62. C₇×#476	C₂²	semidirect
63. C₇×#474	C₂²	semidirect
64. C₇×#433	C₂²	semidirect
65. C₇×#431	C₂²	semidirect
66. C₇×#431	C₂²	semidirect
75. #60877	C₇	direct (N × H)
183. #3503	C₂×C₇	semidirect
184. #3241	C₂×C₇	semidirect
185. #3228	C₂×C₇	semidirect
186. #3228	C₂×C₇	semidirect
187. #3227	C₂×C₇	semidirect
188. #3226	C₂×C₇	semidirect
189. #3165	C₂×C₇	semidirect
190. #3160	C₂×C₇	semidirect
191. #3138	C₂×C₇	semidirect
192. C₂×#486	C₂×C₇	semidirect
193. #3096	C₂×C₇	semidirect
194. #3081	C₂×C₇	semidirect
195. #2922	C₂×C₇	semidirect
295. #544	C₂²×C₇	semidirect
300. #533	C₂²×C₇	semidirect
304. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
309. #501	C₂²×C₇	semidirect
310. #500	C₂²×C₇	semidirect
311. #500	C₂²×C₇	semidirect
312. #500	C₂²×C₇	semidirect
313. #499	C₂²×C₇	semidirect
314. #498	C₂²×C₇	semidirect
315. #498	C₂²×C₇	semidirect
316. #498	C₂²×C₇	semidirect
323. #482	C₂²×C₇	semidirect
324. #482	C₂²×C₇	semidirect
325. #481	C₂²×C₇	semidirect
326. #480	C₂²×C₇	semidirect
327. #478	C₂²×C₇	semidirect
328. #478	C₂²×C₇	semidirect
329. #476	C₂²×C₇	semidirect
330. #474	C₂²×C₇	semidirect
331. #433	C₂²×C₇	semidirect
332. #431	C₂²×C₇	semidirect
333. #431	C₂²×C₇	semidirect
667. C₇	#60877	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×#3508	2
C₇×#3503	2
C₇×#3241	2
C₇×#3228	2
C₇×#3227	2
C₇×#3226	2
C₇×#3165	2
C₇×#3160	2
C₇×#3138	2
C₂×C₇×#486	2
C₇×#3096	2
C₇×#3081	2
C₇×#2922	2
#60877	7

Subgroups — C7×#60877 #13238093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60877 #13238093