Subgroups — C₇×#18659 #13195875

Order 1792.

938 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3514	C₂	1	1	yes	maximal, characteristic
2	C₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1652	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1640	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1639	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1630	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1553	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#559	C₂²	1	1	yes	characteristic
17	C₇×#556	C₂²	1	1	yes	characteristic
18	C₇×#555	—	2	1	no	—
19	C₇×#551	—	2	2	no	—
20	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
21	C₇×#548	—	2	1	no	—
22	C₇×#546	—	2	1	no	—
23	C₇×#546	—	2	1	no	—
24	C₇×D₄²	C₂²	1	1	yes	characteristic
25	C₇×#542	—	2	1	no	—
26	C₇×#538	—	2	2	no	—
27	C₇×#533	C₂²	1	1	yes	characteristic, complemented
28	C₇×#532	C₂²	1	1	yes	characteristic
29	C₇×#529	—	2	1	no	—
30	C₇×#529	C₂²	1	1	yes	characteristic
31	C₂×C₇×#124	—	2	1	no	—
32	C₇×#518	—	2	1	no	—
33	C₄×C₇×#41	C₂²	1	1	yes	characteristic
34	C₇×#499	—	2	1	no	—
35	C₇×#498	C₂²	1	1	yes	characteristic, complemented
36	C₇×#492	C₂²	1	1	yes	characteristic
37	C₇×#488	—	2	1	no	—
38	C₇×#487	C₂²	1	1	yes	characteristic, complemented
39	C₇×#486	C₂²	1	1	yes	characteristic
40	C₇×#485	—	2	1	no	—
41	C₇×#485	—	2	1	no	—
42	C₇×#482	—	2	1	no	—
43	C₇×#477	C₂²	1	1	yes	characteristic, complemented
44	C₇×#477	C₂²	1	1	yes	characteristic, complemented
45	C₇×#476	C₂²	1	1	yes	characteristic
46	C₇×#476	C₂²	1	1	yes	characteristic
47	C₇×#475	C₂²	1	1	yes	characteristic, complemented
48	C₇×#474	C₂²	1	1	yes	characteristic
49	C₇×#465	—	2	2	no	—
50	C₇×#462	C₂²	1	1	yes	characteristic, complemented
51	C₇×#461	C₂²	1	1	yes	characteristic
52	C₇×#452	—	2	1	no	—
53	C₇×#441	—	2	1	no	—
54	C₇×#440	—	2	1	no	—
55	C₄×C₇×SD₁₆	—	2	2	no	—
56	C₇×#432	C₂²	1	1	yes	characteristic, complemented
57	C₇×#431	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
59	C₇×#332	C₂²	1	1	yes	characteristic, complemented
60	C₇×#332	C₂²	1	1	yes	characteristic, complemented
61	C₇×#331	C₂²	1	1	yes	characteristic
62	C₇×#331	C₂²	1	1	yes	characteristic
63	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	#18659	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₇×#41	—	2	1	no	—
73	C₂×C₇×#41	D₄	1	1	yes	characteristic
74	C₂²×C₇×Q₈	—	2	1	no	—
75	C₂²×C₇×D₄	—	2	1	no	—
76	C₂²×C₇×D₄	—	2	1	no	—
77	C₂×C₇×Q₁₆	—	2	1	no	—
78	C₂×C₇×SD₁₆	—	2	2	no	—
79	C₂×C₇×SD₁₆	—	2	1	no	—
80	C₂²×C₇×C₈	—	2	1	no	—
81	C₇×C₄⋊Q₈	—	2	1	no	—
82	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₇×#127	C₂³	1	1	yes	characteristic
86	C₇×#126	—	2	2	no	—
87	C₇×#126	—	2	2	no	—
88	C₇×#126	—	2	1	no	—
89	C₇×#125	—	2	1	no	—
90	C₇×#125	D₄	1	1	yes	characteristic
91	C₇×#124	—	2	2	no	—
92	C₇×#124	—	2	2	no	—
93	C₇×#124	—	2	2	no	—
94	C₇×#124	—	2	1	no	—
95	C₇×#124	—	2	1	no	—
96	C₇×#124	—	2	1	no	—
97	C₇×#124	—	2	1	no	—
98	C₇×#124	D₄	1	1	yes	characteristic
99	C₇×#123	—	2	2	no	—
100	C₇×#123	—	2	2	no	—
101	C₇×#123	—	2	2	no	—
102	C₇×#123	—	2	1	no	—
103	C₇×C₂²⋊Q₈	—	2	2	no	—
104	C₇×C₂²⋊Q₈	—	2	1	no	—
105	C₇×C₂²⋊Q₈	—	2	1	no	—
106	C₇×C₂²⋊Q₈	—	2	2	no	—
107	C₇×C₂²⋊Q₈	—	2	1	no	—
108	C₇×C₂²⋊Q₈	—	2	1	no	—
109	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
110	C₇×#121	—	2	2	no	—
111	C₇×#121	—	2	2	no	—
112	C₇×#121	—	2	1	no	—
113	C₇×#121	—	2	1	no	—
114	C₇×#121	—	2	1	no	—
115	C₇×#121	D₄	1	1	yes	characteristic
116	C₇×#121	D₄	1	2	yes	—
117	C₇×#120	—	2	2	no	—
118	C₇×#120	—	2	2	no	—
119	C₄×C₇×Q₈	—	2	1	no	—
120	C₄×C₇×Q₈	—	2	1	no	—
121	C₄×C₇×Q₈	—	2	1	no	—
122	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
123	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
124	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₄×C₇×D₄	—	2	2	no	—
126	C₄×C₇×D₄	—	2	2	no	—
127	C₄×C₇×D₄	—	2	1	no	—
128	C₄×C₇×D₄	—	2	1	no	—
129	C₄×C₇×D₄	—	2	1	no	—
130	C₄×C₇×D₄	—	2	1	no	—
131	C₄×C₇×D₄	—	2	1	no	—
132	C₄×C₇×D₄	—	2	1	no	—
133	C₄×C₇×D₄	—	2	1	no	—
134	C₄×C₇×D₄	D₄	1	1	yes	characteristic
135	C₄×C₇×D₄	D₄	1	2	yes	—
136	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
137	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
138	C₇×#117	—	2	2	no	—
139	C₇×#117	—	2	1	no	—
140	C₇×#117	—	2	1	no	—
141	C₇×#117	—	2	1	no	—
142	C₇×#117	—	2	1	no	—
143	C₇×#117	D₄	1	1	yes	characteristic
144	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
145	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
146	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₄²×C₇	—	2	1	no	—
148	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
149	C₇×#107	—	2	1	no	—
150	C₇×#107	—	2	1	no	—
151	C₇×#107	—	2	1	no	—
152	C₇×#106	—	2	1	no	—
153	C₇×#106	—	2	1	no	—
154	C₇×#106	—	2	1	no	—
155	C₇×#106	—	2	2	no	—
156	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₇×#103	—	2	1	no	—
161	C₇×#103	—	2	1	no	—
162	C₇×#103	—	2	1	no	—
163	C₇×#103	—	2	1	no	—
164	C₇×#103	—	2	1	no	—
165	C₇×#103	—	2	2	no	—
166	C₇×#102	—	2	1	no	—
167	C₇×#102	—	2	1	no	—
168	C₇×#102	—	2	1	no	—
169	C₇×#102	—	2	2	no	—
170	C₇×C₂²⋊C₈	—	2	1	no	—
171	C₇×C₂²⋊C₈	—	2	1	no	—
172	C₇×#97	—	2	1	no	—
173	C₄×C₇×C₈	—	2	1	no	—
174	C₄×C₇×C₈	—	2	1	no	—
175	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
177	#3514	C₂×C₇	1	1	yes	characteristic
178	#3233	C₂×C₇	1	1	yes	characteristic, complemented
179	#3167	C₂×C₇	1	1	yes	characteristic, complemented
180	#3116	C₂×C₇	1	1	yes	characteristic, complemented
181	#1652	C₂×C₇	1	1	yes	characteristic, complemented
182	#1651	C₂×C₇	1	1	yes	characteristic, complemented
183	#1640	C₂×C₇	1	1	yes	characteristic, complemented
184	#1639	C₂×C₇	1	1	yes	characteristic, complemented
185	#1638	C₂×C₇	1	1	yes	characteristic, complemented
186	#1637	C₂×C₇	1	1	yes	characteristic, complemented
187	#1630	C₂×C₇	1	1	yes	characteristic, complemented
188	#1629	C₂×C₇	1	1	yes	characteristic, complemented
189	#1553	C₂×C₇	1	1	yes	characteristic, complemented
190	#1494	C₂×C₇	1	1	yes	characteristic, complemented
191	#1476	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂⁴×C₇	—	2	2	no	—
193	C₇×#41	—	2	2	no	—
194	C₇×#41	—	4	1	no	—
195	C₇×#41	—	8	1	no	—
196	C₇×#41	—	8	1	no	—
197	C₂×C₇×Q₈	—	2	2	no	—
198	C₂×C₇×Q₈	—	2	1	no	—
199	C₂×C₇×Q₈	—	2	1	no	—
200	C₂×C₇×Q₈	—	2	1	no	—
201	C₂×C₇×Q₈	—	8	1	no	—
202	C₂×C₇×Q₈	—	8	1	no	—
203	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₇×D₄	—	2	2	no	—
206	C₂×C₇×D₄	—	2	1	no	—
207	C₂×C₇×D₄	—	2	2	no	—
208	C₂×C₇×D₄	—	2	1	no	—
209	C₂×C₇×D₄	—	2	2	no	—
210	C₂×C₇×D₄	—	2	1	no	—
211	C₂×C₇×D₄	—	2	1	no	—
212	C₂×C₇×D₄	—	4	2	no	—
213	C₂×C₇×D₄	—	4	2	no	—
214	C₂×C₇×D₄	—	8	1	no	—
215	C₂×C₇×D₄	—	8	1	no	—
216	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
217	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	1	no	—
222	C₂²×C₄×C₇	—	2	1	no	—
223	C₂²×C₄×C₇	—	2	1	no	—
224	C₂²×C₄×C₇	—	2	1	no	—
225	C₂²×C₄×C₇	—	2	2	no	—
226	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
229	C₇×Q₁₆	—	4	2	no	—
230	C₇×SD₁₆	—	4	4	no	—
231	C₇×SD₁₆	—	4	2	no	—
232	C₂×C₇×C₈	—	2	1	no	—
233	C₂×C₇×C₈	—	2	1	no	—
234	C₂×C₇×C₈	—	2	1	no	—
235	C₂×C₇×C₈	—	2	1	no	—
236	C₂×C₇×C₈	—	2	1	no	—
237	C₂×C₇×C₈	—	2	1	no	—
238	C₂×C₇×C₈	—	4	2	no	—
239	C₇×C₄⋊C₄	—	2	2	no	—
240	C₇×C₄⋊C₄	—	2	2	no	—
241	C₇×C₄⋊C₄	—	2	1	no	—
242	C₇×C₄⋊C₄	—	2	1	no	—
243	C₇×C₄⋊C₄	—	2	1	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	1	no	—
248	C₇×C₄⋊C₄	—	2	1	no	—
249	C₇×C₄⋊C₄	—	2	1	no	—
250	C₇×C₄⋊C₄	—	2	1	no	—
251	C₇×C₄⋊C₄	—	2	1	no	—
252	C₇×C₄⋊C₄	—	4	1	no	—
253	C₇×C₄⋊C₄	—	4	1	no	—
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	1	yes	characteristic
257	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
258	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₇×C₂²⋊C₄	—	2	2	no	—
260	C₇×C₂²⋊C₄	—	2	2	no	—
261	C₇×C₂²⋊C₄	—	2	2	no	—
262	C₇×C₂²⋊C₄	—	2	2	no	—
263	C₇×C₂²⋊C₄	—	2	2	no	—
264	C₇×C₂²⋊C₄	—	2	2	no	—
265	C₇×C₂²⋊C₄	—	2	2	no	—
266	C₇×C₂²⋊C₄	—	2	1	no	—
267	C₇×C₂²⋊C₄	—	2	1	no	—
268	C₇×C₂²⋊C₄	—	2	1	no	—
269	C₇×C₂²⋊C₄	—	2	1	no	—
270	C₇×C₂²⋊C₄	—	2	1	no	—
271	C₇×C₂²⋊C₄	—	2	1	no	—
272	C₇×C₂²⋊C₄	—	2	2	no	—
273	C₇×C₂²⋊C₄	—	2	2	no	—
274	C₇×C₂²⋊C₄	—	2	1	no	—
275	C₇×C₂²⋊C₄	—	2	1	no	—
276	C₇×C₂²⋊C₄	—	4	1	no	—
277	C₄²×C₇	—	2	2	no	—
278	C₄²×C₇	—	2	1	no	—
279	C₄²×C₇	—	2	1	no	—
280	C₄²×C₇	—	2	1	no	—
281	C₄²×C₇	—	2	1	no	—
282	C₄²×C₇	—	4	1	no	—
283	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₇	C₂⁴	1	1	yes	characteristic
287	#559	C₂²×C₇	1	1	yes	characteristic
288	#556	C₂²×C₇	1	1	yes	characteristic
289	#555	—	2	1	no	—
290	#551	—	2	2	no	—
291	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
292	#548	—	2	1	no	—
293	#546	—	2	1	no	—
294	#546	—	2	1	no	—
295	D₄²	C₂²×C₇	1	1	yes	characteristic
296	#542	—	2	1	no	—
297	#538	—	2	2	no	—
298	#533	C₂²×C₇	1	1	yes	characteristic, complemented
299	#532	C₂²×C₇	1	1	yes	characteristic
300	#529	—	2	1	no	—
301	#529	C₂²×C₇	1	1	yes	characteristic
302	C₂×#124	—	2	1	no	—
303	#518	—	2	1	no	—
304	C₄×#41	C₂²×C₇	1	1	yes	characteristic
305	#499	—	2	1	no	—
306	#498	C₂²×C₇	1	1	yes	characteristic, complemented
307	#492	C₂²×C₇	1	1	yes	characteristic
308	#488	—	2	1	no	—
309	#487	C₂²×C₇	1	1	yes	characteristic, complemented
310	#486	C₂²×C₇	1	1	yes	characteristic
311	#485	—	2	1	no	—
312	#485	—	2	1	no	—
313	#482	—	2	1	no	—
314	#477	C₂²×C₇	1	1	yes	characteristic, complemented
315	#477	C₂²×C₇	1	1	yes	characteristic, complemented
316	#476	C₂²×C₇	1	1	yes	characteristic
317	#476	C₂²×C₇	1	1	yes	characteristic
318	#475	C₂²×C₇	1	1	yes	characteristic, complemented
319	#474	C₂²×C₇	1	1	yes	characteristic
320	#465	—	2	2	no	—
321	#462	C₂²×C₇	1	1	yes	characteristic, complemented
322	#461	C₂²×C₇	1	1	yes	characteristic
323	#452	—	2	1	no	—
324	#441	—	2	1	no	—
325	#440	—	2	1	no	—
326	C₄×SD₁₆	—	2	2	no	—
327	#432	C₂²×C₇	1	1	yes	characteristic, complemented
328	#431	C₂²×C₇	1	1	yes	characteristic, complemented
329	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
330	#332	C₂²×C₇	1	1	yes	characteristic, complemented
331	#332	C₂²×C₇	1	1	yes	characteristic, complemented
332	#331	C₂²×C₇	1	1	yes	characteristic
333	#331	C₂²×C₇	1	1	yes	characteristic
334	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
335	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
336	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
337	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
338	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
339	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
340	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
341	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
342	C₂³×C₇	—	2	1	no	—
343	C₂³×C₇	—	2	1	no	—
344	C₂³×C₇	—	2	2	no	—
345	C₂³×C₇	—	4	4	no	—
346	C₂³×C₇	—	8	2	no	—
347	C₂³×C₇	—	8	2	no	—
348	C₂³×C₇	#120	1	1	yes	characteristic
349	C₇×Q₈	—	2	1	no	—
350	C₇×Q₈	—	2	1	no	—
351	C₇×Q₈	—	2	1	no	—
352	C₇×Q₈	—	2	1	no	—
353	C₇×Q₈	—	4	2	no	—
354	C₇×Q₈	—	4	1	no	—
355	C₇×Q₈	—	4	1	no	—
356	C₇×Q₈	—	4	1	no	—
357	C₇×Q₈	—	4	1	no	—
358	C₇×Q₈	—	8	2	no	—
359	C₇×D₄	—	2	1	no	—
360	C₇×D₄	—	2	1	no	—
361	C₇×D₄	—	2	1	no	—
362	C₇×D₄	—	4	2	no	—
363	C₇×D₄	—	4	2	no	—
364	C₇×D₄	—	4	4	no	—
365	C₇×D₄	—	4	1	no	—
366	C₇×D₄	—	4	1	no	—
367	C₇×D₄	—	4	1	no	—
368	C₇×D₄	—	4	1	no	—
369	C₇×D₄	—	8	1	no	—
370	C₇×D₄	—	8	2	no	—
371	C₇×D₄	—	8	2	no	—
372	C₇×D₄	#135	1	2	yes	—
373	C₂×C₄×C₇	—	2	1	no	—
374	C₂×C₄×C₇	—	2	1	no	—
375	C₂×C₄×C₇	—	2	1	no	—
376	C₂×C₄×C₇	—	2	1	no	—
377	C₂×C₄×C₇	—	2	1	no	—
378	C₂×C₄×C₇	—	2	1	no	—
379	C₂×C₄×C₇	—	2	1	no	—
380	C₂×C₄×C₇	—	2	1	no	—
381	C₂×C₄×C₇	—	2	1	no	—
382	C₂×C₄×C₇	—	2	1	no	—
383	C₂×C₄×C₇	—	2	2	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	2	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	1	no	—
388	C₂×C₄×C₇	—	4	1	no	—
389	C₂×C₄×C₇	—	4	1	no	—
390	C₂×C₄×C₇	—	4	1	no	—
391	C₂×C₄×C₇	—	4	1	no	—
392	C₂×C₄×C₇	—	8	1	no	—
393	C₂×C₄×C₇	—	8	2	no	—
394	C₂×C₄×C₇	—	8	2	no	—
395	C₂×C₄×C₇	—	8	2	no	—
396	C₂×C₄×C₇	#120	1	1	yes	characteristic
397	C₂×C₄×C₇	#120	1	1	yes	characteristic
398	C₂×C₄×C₇	#120	1	1	yes	characteristic
399	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
402	C₇×C₈	—	2	2	no	—
403	C₇×C₈	—	4	1	no	—
404	C₇×C₈	—	4	1	no	—
405	C₇×C₈	—	4	1	no	—
406	C₇×C₈	—	4	1	no	—
407	C₇×C₈	—	4	1	no	—
408	C₂×#41	—	2	1	no	—
409	C₂×#41	C₇×D₄	1	1	yes	characteristic
410	C₂²×Q₈	—	2	1	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂×Q₁₆	—	2	1	no	—
414	C₂×SD₁₆	—	2	2	no	—
415	C₂×SD₁₆	—	2	1	no	—
416	C₂²×C₈	—	2	1	no	—
417	C₄⋊Q₈	—	2	1	no	—
418	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
419	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
420	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
421	#127	C₂³×C₇	1	1	yes	characteristic
422	#126	—	2	2	no	—
423	#126	—	2	2	no	—
424	#126	—	2	1	no	—
425	#125	—	2	1	no	—
426	#125	C₇×D₄	1	1	yes	characteristic
427	#124	—	2	2	no	—
428	#124	—	2	2	no	—
429	#124	—	2	2	no	—
430	#124	—	2	1	no	—
431	#124	—	2	1	no	—
432	#124	—	2	1	no	—
433	#124	—	2	1	no	—
434	#124	C₇×D₄	1	1	yes	characteristic
435	#123	—	2	2	no	—
436	#123	—	2	2	no	—
437	#123	—	2	2	no	—
438	#123	—	2	1	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	—	2	1	no	—
445	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
446	#121	—	2	2	no	—
447	#121	—	2	2	no	—
448	#121	—	2	1	no	—
449	#121	—	2	1	no	—
450	#121	—	2	1	no	—
451	#121	C₇×D₄	1	1	yes	characteristic
452	#121	C₇×D₄	1	2	yes	—
453	#120	—	2	2	no	—
454	#120	—	2	2	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	—	2	1	no	—
457	C₄×Q₈	—	2	1	no	—
458	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
459	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
460	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	—	2	1	no	—
470	C₄×D₄	C₇×D₄	1	1	yes	characteristic
471	C₄×D₄	C₇×D₄	1	2	yes	—
472	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
473	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
474	#117	—	2	2	no	—
475	#117	—	2	1	no	—
476	#117	—	2	1	no	—
477	#117	—	2	1	no	—
478	#117	—	2	1	no	—
479	#117	C₇×D₄	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₂²⋊C₄	—	2	2	no	—
482	C₂×C₂²⋊C₄	—	2	2	no	—
483	C₂×C₄²	—	2	1	no	—
484	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
485	#107	—	2	1	no	—
486	#107	—	2	1	no	—
487	#107	—	2	1	no	—
488	#106	—	2	2	no	—
489	#106	—	2	1	no	—
490	#106	—	2	1	no	—
491	#106	—	2	1	no	—
492	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
493	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
494	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
495	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
496	#103	—	2	1	no	—
497	#103	—	2	1	no	—
498	#103	—	2	1	no	—
499	#103	—	2	2	no	—
500	#103	—	2	1	no	—
501	#103	—	2	1	no	—
502	#102	—	2	2	no	—
503	#102	—	2	1	no	—
504	#102	—	2	1	no	—
505	#102	—	2	1	no	—
506	C₂²⋊C₈	—	2	1	no	—
507	C₂²⋊C₈	—	2	1	no	—
508	#97	—	2	1	no	—
509	C₄×C₈	—	2	1	no	—
510	C₄×C₈	—	2	1	no	—
511	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
512	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
513	C₂²×C₇	—	2	1	no	—
514	C₂²×C₇	—	2	2	no	—
515	C₂²×C₇	—	2	1	no	—
516	C₂²×C₇	—	2	1	no	—
517	C₂²×C₇	—	4	1	no	—
518	C₂²×C₇	—	4	1	no	—
519	C₂²×C₇	—	4	1	no	—
520	C₂²×C₇	—	4	2	no	—
521	C₂²×C₇	—	4	2	no	—
522	C₂²×C₇	—	4	1	no	—
523	C₂²×C₇	—	4	2	no	—
524	C₂²×C₇	—	4	1	no	—
525	C₂²×C₇	—	16	4	no	—
526	C₂²×C₇	C₂×#120	1	1	yes	characteristic
527	C₄×C₇	—	2	1	no	—
528	C₄×C₇	—	2	1	no	—
529	C₄×C₇	—	2	1	no	—
530	C₄×C₇	—	2	1	no	—
531	C₄×C₇	—	4	1	no	—
532	C₄×C₇	—	4	1	no	—
533	C₄×C₇	—	4	1	no	—
534	C₄×C₇	—	4	2	no	—
535	C₄×C₇	—	4	1	no	—
536	C₄×C₇	—	4	1	no	—
537	C₄×C₇	—	4	1	no	—
538	C₄×C₇	—	8	1	no	—
539	C₄×C₇	—	8	1	no	—
540	C₄×C₇	C₂×#135	1	1	yes	characteristic
541	C₄×C₇	#575	1	1	yes	characteristic
542	C₄×C₇	#577	1	1	yes	characteristic
543	C₄×C₇	#577	1	1	yes	characteristic
544	C₂⁴	—	2	2	no	—
545	#41	—	2	2	no	—
546	#41	—	4	1	no	—
547	#41	—	8	1	no	—
548	#41	—	8	1	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	8	1	no	—
554	C₂×Q₈	—	8	1	no	—
555	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
556	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	8	1	no	—
567	C₂×D₄	—	8	1	no	—
568	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
569	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
570	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
579	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
580	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
581	Q₁₆	—	4	2	no	—
582	SD₁₆	—	4	4	no	—
583	SD₁₆	—	4	2	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	4	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	4	1	no	—
605	C₄⋊C₄	—	4	1	no	—
606	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
607	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
608	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
609	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
610	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	4	1	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	4	1	no	—
635	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
636	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
637	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
638	C₄²	C₂⁴×C₇	1	1	yes	characteristic
639	C₂×C₇	—	4	1	no	—
640	C₂×C₇	—	4	2	no	—
641	C₂×C₇	—	8	2	no	—
642	C₂×C₇	—	8	1	no	—
643	C₂×C₇	#3002	1	1	yes	characteristic
644	C₂×C₇	#3009	1	1	yes	characteristic
645	C₂×C₇	#3018	1	1	yes	characteristic
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	8	2	no	—
651	C₂³	—	8	2	no	—
652	C₂³	C₇×#120	1	1	yes	characteristic
653	Q₈	—	2	1	no	—
654	Q₈	—	2	1	no	—
655	Q₈	—	2	1	no	—
656	Q₈	—	2	1	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	1	no	—
659	Q₈	—	4	1	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	8	2	no	—
663	D₄	—	2	1	no	—
664	D₄	—	2	1	no	—
665	D₄	—	2	1	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	8	1	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	2	no	—
676	D₄	C₇×#135	1	2	yes	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	8	1	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	C₇×#120	1	1	yes	characteristic
701	C₂×C₄	C₇×#120	1	1	yes	characteristic
702	C₂×C₄	C₇×#120	1	1	yes	characteristic
703	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₈	—	4	1	no	—
711	C₈	—	4	1	no	—
712	C₇	#18659	1	1	yes	characteristic, direct product factor, Sylow
713	C₂²	—	2	1	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	16	4	no	—
726	C₂²	C₂×C₇×#120	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	8	1	no	—
739	C₄	—	8	1	no	—
740	C₄	C₂×C₇×#135	1	1	yes	characteristic
741	C₄	C₇×#575	1	1	yes	characteristic
742	C₄	C₇×#577	1	1	yes	characteristic
743	C₄	C₇×#577	1	1	yes	characteristic
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	—	8	1	no	—
747	C₂	—	8	2	no	—
748	C₂	C₇×#3002	1	1	yes	characteristic
749	C₂	C₇×#3009	1	1	yes	characteristic
750	C₂	C₇×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3514	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3233	C₂	semidirect
3. C₇×#3167	C₂	semidirect
4. C₇×#3116	C₂	semidirect
5. C₇×#1652	C₂	semidirect
6. C₇×#1651	C₂	semidirect
7. C₇×#1640	C₂	semidirect
8. C₇×#1639	C₂	semidirect
9. C₇×#1638	C₂	semidirect
10. C₇×#1637	C₂	semidirect
11. C₇×#1630	C₂	semidirect
12. C₇×#1629	C₂	semidirect
13. C₇×#1553	C₂	semidirect
14. C₇×#1494	C₂	semidirect
15. C₇×#1476	C₂	semidirect
27. C₇×#533	C₂²	semidirect
35. C₇×#498	C₂²	semidirect
38. C₇×#487	C₂²	semidirect
43. C₇×#477	C₂²	semidirect
44. C₇×#477	C₂²	semidirect
47. C₇×#475	C₂²	semidirect
50. C₇×#462	C₂²	semidirect
56. C₇×#432	C₂²	semidirect
57. C₇×#431	C₂²	semidirect
58. C₂×C₄×C₇×C₈	C₂²	semidirect
59. C₇×#332	C₂²	semidirect
60. C₇×#332	C₂²	semidirect
63. C₇×Q₈⋊C₈	C₂²	semidirect
64. C₇×Q₈⋊C₈	C₂²	semidirect
65. C₇×Q₈⋊C₈	C₂²	semidirect
66. C₇×Q₈⋊C₈	C₂²	semidirect
71. #18659	C₇	direct (N × H)
178. #3233	C₂×C₇	semidirect
179. #3167	C₂×C₇	semidirect
180. #3116	C₂×C₇	semidirect
181. #1652	C₂×C₇	semidirect
182. #1651	C₂×C₇	semidirect
183. #1640	C₂×C₇	semidirect
184. #1639	C₂×C₇	semidirect
185. #1638	C₂×C₇	semidirect
186. #1637	C₂×C₇	semidirect
187. #1630	C₂×C₇	semidirect
188. #1629	C₂×C₇	semidirect
189. #1553	C₂×C₇	semidirect
190. #1494	C₂×C₇	semidirect
191. #1476	C₂×C₇	semidirect
298. #533	C₂²×C₇	semidirect
306. #498	C₂²×C₇	semidirect
309. #487	C₂²×C₇	semidirect
314. #477	C₂²×C₇	semidirect
315. #477	C₂²×C₇	semidirect
318. #475	C₂²×C₇	semidirect
321. #462	C₂²×C₇	semidirect
327. #432	C₂²×C₇	semidirect
328. #431	C₂²×C₇	semidirect
329. C₂×C₄×C₈	C₂²×C₇	semidirect
330. #332	C₂²×C₇	semidirect
331. #332	C₂²×C₇	semidirect
334. Q₈⋊C₈	C₂²×C₇	semidirect
335. Q₈⋊C₈	C₂²×C₇	semidirect
336. Q₈⋊C₈	C₂²×C₇	semidirect
337. Q₈⋊C₈	C₂²×C₇	semidirect
712. C₇	#18659	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×#3514	2
C₇×#3233	2
C₇×#3167	2
C₇×#3116	2
C₇×#1652	2
C₇×#1651	2
C₇×#1640	2
C₇×#1639	2
C₇×#1638	2
C₇×#1637	2
C₇×#1630	2
C₇×#1629	2
C₇×#1553	2
C₇×#1494	2
C₇×#1476	2
#18659	7

Subgroups — C7×#18659 #13195875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#18659 #13195875