Subgroups — C₇×#18765 #13195981

Order 1792.

902 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3482	C₂	1	1	yes	maximal, characteristic
2	C₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3076	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×#1648	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1647	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×#1636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#557	C₂²	1	1	yes	characteristic
17	C₇×#556	—	2	1	no	—
18	C₇×#556	C₂²	1	1	yes	characteristic
19	C₇×#552	—	2	2	no	—
20	C₇×#552	—	2	1	no	—
21	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
22	C₇×#548	—	2	1	no	—
23	C₇×#547	—	2	1	no	—
24	C₇×#547	C₂²	1	1	yes	characteristic
25	C₇×#533	—	2	1	no	—
26	C₇×#533	C₂²	1	1	yes	characteristic
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#529	—	2	1	no	—
29	C₇×#529	—	2	2	no	—
30	C₄×C₇×#41	—	2	1	no	—
31	C₄×C₇×#41	C₂²	1	1	yes	characteristic
32	C₄×C₇×#41	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	—	2	1	no	—
34	C₇×#500	C₂²	1	1	yes	characteristic
35	C₇×#498	C₂²	1	1	yes	characteristic
36	C₇×#487	C₂²	1	1	yes	characteristic
37	C₇×#487	C₂²	1	1	yes	characteristic
38	C₇×#485	—	2	2	no	—
39	C₇×#485	—	2	1	no	—
40	C₇×#479	—	2	2	no	—
41	C₇×#479	—	2	1	no	—
42	C₇×#478	—	2	1	no	—
43	C₇×#477	C₂²	1	1	yes	characteristic
44	C₇×#477	C₂²	1	1	yes	characteristic
45	C₇×#476	C₂²	1	1	yes	characteristic
46	C₇×#476	C₂²	1	1	yes	characteristic
47	C₇×#475	C₂²	1	1	yes	characteristic
48	C₇×#474	C₂²	1	1	yes	characteristic
49	C₇×#462	C₂²	1	1	yes	characteristic
50	C₇×#461	C₂²	1	1	yes	characteristic
51	C₇×#452	—	2	1	no	—
52	C₇×#441	—	2	1	no	—
53	C₇×#440	—	2	1	no	—
54	C₇×#432	C₂²	1	1	yes	characteristic
55	C₇×#431	C₂²	1	1	yes	characteristic
56	C₇×#427	—	2	1	no	—
57	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₇×#416	—	2	1	no	—
59	C₇×#332	C₂²	1	1	yes	characteristic
60	C₇×#332	C₂²	1	1	yes	characteristic
61	C₇×#332	C₂²	1	1	yes	characteristic
62	C₇×#332	C₂²	1	1	yes	characteristic
63	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
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	#18765	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	C₂×C₇×#41	D₄	1	1	yes	characteristic
75	C₂²×C₇×Q₈	—	2	1	no	—
76	C₂×C₇×Q₁₆	—	2	1	no	—
77	C₂×C₇×SD₁₆	—	2	1	no	—
78	C₂²×C₇×C₈	—	2	1	no	—
79	C₇×C₄⋊Q₈	—	2	1	no	—
80	C₇×C₄⋊Q₈	—	2	1	no	—
81	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#126	—	2	2	no	—
86	C₇×#126	—	2	2	no	—
87	C₇×#126	—	2	2	no	—
88	C₇×#125	—	2	2	no	—
89	C₇×#125	—	2	2	no	—
90	C₇×#125	—	2	1	no	—
91	C₇×#125	—	2	1	no	—
92	C₇×#125	D₄	1	2	yes	—
93	C₇×#124	—	2	2	no	—
94	C₇×#124	—	2	1	no	—
95	C₇×#123	—	2	2	no	—
96	C₇×#123	—	2	2	no	—
97	C₇×#123	—	2	2	no	—
98	C₇×C₂²⋊Q₈	—	2	2	no	—
99	C₇×C₂²⋊Q₈	—	2	1	no	—
100	C₇×C₂²⋊Q₈	—	2	1	no	—
101	C₇×C₂²⋊Q₈	—	2	1	no	—
102	C₇×C₂²⋊Q₈	—	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	1	no	—
107	C₇×#121	—	2	2	no	—
108	C₇×#121	—	2	1	no	—
109	C₄×C₇×Q₈	—	2	2	no	—
110	C₄×C₇×Q₈	—	2	2	no	—
111	C₄×C₇×Q₈	—	2	1	no	—
112	C₄×C₇×Q₈	—	2	1	no	—
113	C₄×C₇×Q₈	—	2	1	no	—
114	C₄×C₇×Q₈	—	2	1	no	—
115	C₄×C₇×Q₈	—	2	1	no	—
116	C₄×C₇×Q₈	—	2	1	no	—
117	C₄×C₇×Q₈	—	2	1	no	—
118	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
119	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
120	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
121	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
122	C₄×C₇×D₄	—	2	2	no	—
123	C₄×C₇×D₄	—	2	2	no	—
124	C₄×C₇×D₄	—	2	1	no	—
125	C₄×C₇×D₄	—	2	1	no	—
126	C₄×C₇×D₄	—	2	1	no	—
127	C₄×C₇×D₄	—	2	1	no	—
128	C₄×C₇×D₄	—	2	1	no	—
129	C₄×C₇×D₄	D₄	1	1	yes	characteristic
130	C₄×C₇×D₄	D₄	1	1	yes	characteristic
131	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
133	C₇×#117	—	2	2	no	—
134	C₇×#117	—	2	2	no	—
135	C₇×#117	—	2	1	no	—
136	C₇×#117	—	2	1	no	—
137	C₇×#117	—	2	1	no	—
138	C₇×#117	—	2	1	no	—
139	C₇×#117	D₄	1	1	yes	characteristic
140	C₇×#117	D₄	1	2	yes	—
141	C₇×#117	D₄	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	—	2	2	no	—
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄²×C₇	—	2	2	no	—
145	C₂×C₄²×C₇	—	2	1	no	—
146	C₂×C₄²×C₇	—	2	1	no	—
147	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
148	C₇×#107	—	2	1	no	—
149	C₇×#107	—	2	1	no	—
150	C₇×#107	—	2	1	no	—
151	C₇×#107	—	2	2	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	—	2	1	no	—
157	C₇×C₄⋊C₈	—	2	1	no	—
158	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	2	2	no	—
167	C₇×#103	—	2	1	no	—
168	C₇×#103	—	2	1	no	—
169	C₇×#102	—	2	1	no	—
170	C₇×#102	—	2	1	no	—
171	C₇×#102	—	2	1	no	—
172	C₇×C₂²⋊C₈	—	2	1	no	—
173	C₇×C₂²⋊C₈	—	2	1	no	—
174	C₇×#97	—	2	1	no	—
175	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
177	#3482	C₂×C₇	1	1	yes	characteristic
178	#3231	C₂×C₇	1	1	yes	characteristic, complemented
179	#3116	C₂×C₇	1	1	yes	characteristic, complemented
180	#3076	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	#1648	C₂×C₇	1	1	yes	characteristic, complemented
184	#1647	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	#1636	C₂×C₇	1	1	yes	characteristic, complemented
188	#1635	C₂×C₇	1	1	yes	characteristic, complemented
189	#1552	C₂×C₇	1	1	yes	characteristic, complemented
190	#1488	C₂×C₇	1	1	yes	characteristic, complemented
191	#1477	C₂×C₇	1	1	yes	characteristic, complemented
192	C₇×#41	—	2	2	no	—
193	C₇×#41	—	2	2	no	—
194	C₇×#41	—	4	1	no	—
195	C₇×#41	—	4	1	no	—
196	C₇×#41	—	4	2	no	—
197	C₇×#41	—	4	2	no	—
198	C₂×C₇×Q₈	—	2	2	no	—
199	C₂×C₇×Q₈	—	2	1	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	—	4	2	no	—
204	C₂×C₇×Q₈	—	4	2	no	—
205	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₇×D₄	—	2	2	no	—
208	C₂×C₇×D₄	—	2	1	no	—
209	C₂×C₇×D₄	—	2	1	no	—
210	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₇	—	2	2	no	—
213	C₂²×C₄×C₇	—	2	2	no	—
214	C₂²×C₄×C₇	—	2	1	no	—
215	C₂²×C₄×C₇	—	2	1	no	—
216	C₂²×C₄×C₇	—	2	1	no	—
217	C₂²×C₄×C₇	—	2	1	no	—
218	C₂²×C₄×C₇	—	2	1	no	—
219	C₂²×C₄×C₇	—	2	1	no	—
220	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
223	C₇×Q₁₆	—	4	2	no	—
224	C₇×SD₁₆	—	4	2	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	—	2	1	no	—
227	C₂×C₇×C₈	—	2	1	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	—	2	1	no	—
231	C₂×C₇×C₈	—	4	2	no	—
232	C₇×C₄⋊C₄	—	2	2	no	—
233	C₇×C₄⋊C₄	—	2	2	no	—
234	C₇×C₄⋊C₄	—	2	2	no	—
235	C₇×C₄⋊C₄	—	2	2	no	—
236	C₇×C₄⋊C₄	—	2	2	no	—
237	C₇×C₄⋊C₄	—	2	2	no	—
238	C₇×C₄⋊C₄	—	2	1	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	—	4	1	no	—
251	C₇×C₄⋊C₄	—	4	1	no	—
252	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
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×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
263	C₇×C₂²⋊C₄	—	2	1	no	—
264	C₇×C₂²⋊C₄	—	2	2	no	—
265	C₇×C₂²⋊C₄	—	2	1	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	—	4	1	no	—
270	C₄²×C₇	—	2	2	no	—
271	C₄²×C₇	—	2	2	no	—
272	C₄²×C₇	—	2	1	no	—
273	C₄²×C₇	—	2	1	no	—
274	C₄²×C₇	—	2	1	no	—
275	C₄²×C₇	—	2	2	no	—
276	C₄²×C₇	—	2	1	no	—
277	C₄²×C₇	—	2	1	no	—
278	C₄²×C₇	—	2	1	no	—
279	C₄²×C₇	—	4	1	no	—
280	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₇	C₂⁴	1	1	yes	characteristic
284	#557	C₂²×C₇	1	1	yes	characteristic
285	#556	—	2	1	no	—
286	#556	C₂²×C₇	1	1	yes	characteristic
287	#552	—	2	2	no	—
288	#552	—	2	1	no	—
289	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
290	#548	—	2	1	no	—
291	#547	—	2	1	no	—
292	#547	C₂²×C₇	1	1	yes	characteristic
293	#533	—	2	1	no	—
294	#533	C₂²×C₇	1	1	yes	characteristic
295	#533	C₂²×C₇	1	1	yes	characteristic
296	#529	—	2	1	no	—
297	#529	—	2	2	no	—
298	C₄×#41	—	2	1	no	—
299	C₄×#41	C₂²×C₇	1	1	yes	characteristic
300	C₄×#41	C₂²×C₇	1	1	yes	characteristic
301	C₂×C₄×Q₈	—	2	1	no	—
302	#500	C₂²×C₇	1	1	yes	characteristic
303	#498	C₂²×C₇	1	1	yes	characteristic
304	#487	C₂²×C₇	1	1	yes	characteristic
305	#487	C₂²×C₇	1	1	yes	characteristic
306	#485	—	2	1	no	—
307	#485	—	2	2	no	—
308	#479	—	2	2	no	—
309	#479	—	2	1	no	—
310	#478	—	2	1	no	—
311	#477	C₂²×C₇	1	1	yes	characteristic
312	#477	C₂²×C₇	1	1	yes	characteristic
313	#476	C₂²×C₇	1	1	yes	characteristic
314	#476	C₂²×C₇	1	1	yes	characteristic
315	#475	C₂²×C₇	1	1	yes	characteristic
316	#474	C₂²×C₇	1	1	yes	characteristic
317	#462	C₂²×C₇	1	1	yes	characteristic
318	#461	C₂²×C₇	1	1	yes	characteristic
319	#452	—	2	1	no	—
320	#441	—	2	1	no	—
321	#440	—	2	1	no	—
322	#432	C₂²×C₇	1	1	yes	characteristic
323	#431	C₂²×C₇	1	1	yes	characteristic
324	#427	—	2	1	no	—
325	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
326	#416	—	2	1	no	—
327	#332	C₂²×C₇	1	1	yes	characteristic
328	#332	C₂²×C₇	1	1	yes	characteristic
329	#332	C₂²×C₇	1	1	yes	characteristic
330	#332	C₂²×C₇	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
334	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
336	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
337	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
338	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
339	C₂³×C₇	—	2	1	no	—
340	C₂³×C₇	—	2	1	no	—
341	C₂³×C₇	#120	1	1	yes	characteristic
342	C₇×Q₈	—	2	1	no	—
343	C₇×Q₈	—	2	1	no	—
344	C₇×Q₈	—	2	1	no	—
345	C₇×Q₈	—	4	4	no	—
346	C₇×Q₈	—	4	2	no	—
347	C₇×Q₈	—	4	1	no	—
348	C₇×Q₈	—	4	1	no	—
349	C₇×Q₈	—	4	1	no	—
350	C₇×Q₈	—	4	1	no	—
351	C₇×Q₈	—	4	1	no	—
352	C₇×Q₈	—	4	1	no	—
353	C₇×Q₈	#137	1	2	yes	—
354	C₇×D₄	—	2	1	no	—
355	C₇×D₄	—	2	1	no	—
356	C₇×D₄	—	2	1	no	—
357	C₇×D₄	—	4	2	no	—
358	C₇×D₄	—	4	2	no	—
359	C₇×D₄	—	4	4	no	—
360	C₇×D₄	#135	1	2	yes	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	no	—
363	C₂×C₄×C₇	—	2	1	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	2	1	no	—
366	C₂×C₄×C₇	—	2	1	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	1	no	—
371	C₂×C₄×C₇	—	2	1	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	4	1	no	—
374	C₂×C₄×C₇	—	4	2	no	—
375	C₂×C₄×C₇	—	4	2	no	—
376	C₂×C₄×C₇	—	4	2	no	—
377	C₂×C₄×C₇	—	4	2	no	—
378	C₂×C₄×C₇	—	4	4	no	—
379	C₂×C₄×C₇	—	4	4	no	—
380	C₂×C₄×C₇	—	4	1	no	—
381	C₂×C₄×C₇	—	4	1	no	—
382	C₂×C₄×C₇	—	4	1	no	—
383	C₂×C₄×C₇	—	4	1	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	1	no	—
386	C₂×C₄×C₇	#120	1	1	yes	characteristic
387	C₂×C₄×C₇	#120	1	1	yes	characteristic
388	C₂×C₄×C₇	#120	1	1	yes	characteristic
389	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
392	C₇×C₈	—	4	1	no	—
393	C₇×C₈	—	4	1	no	—
394	C₇×C₈	—	4	1	no	—
395	C₇×C₈	—	4	1	no	—
396	C₇×C₈	—	4	1	no	—
397	C₇×C₈	—	4	1	no	—
398	C₂×#41	—	2	1	no	—
399	C₂×#41	C₇×D₄	1	1	yes	characteristic
400	C₂×#41	C₇×D₄	1	1	yes	characteristic
401	C₂²×Q₈	—	2	1	no	—
402	C₂×Q₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	—	2	1	no	—
407	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
408	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
409	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
410	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
411	#126	—	2	2	no	—
412	#126	—	2	2	no	—
413	#126	—	2	2	no	—
414	#125	—	2	2	no	—
415	#125	—	2	2	no	—
416	#125	—	2	1	no	—
417	#125	—	2	1	no	—
418	#125	C₇×D₄	1	2	yes	—
419	#124	—	2	2	no	—
420	#124	—	2	1	no	—
421	#123	—	2	2	no	—
422	#123	—	2	2	no	—
423	#123	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	1	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	C₂²⋊Q₈	—	2	1	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	1	no	—
431	C₂²⋊Q₈	—	2	1	no	—
432	C₂²⋊Q₈	—	2	1	no	—
433	#121	—	2	2	no	—
434	#121	—	2	1	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	—	2	1	no	—
442	C₄×Q₈	—	2	1	no	—
443	C₄×Q₈	—	2	1	no	—
444	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
445	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
446	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
447	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	C₇×D₄	1	1	yes	characteristic
456	C₄×D₄	C₇×D₄	1	1	yes	characteristic
457	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
458	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
459	#117	—	2	2	no	—
460	#117	—	2	2	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	#117	—	2	1	no	—
464	#117	—	2	1	no	—
465	#117	C₇×D₄	1	1	yes	characteristic
466	#117	C₇×D₄	1	1	yes	characteristic
467	#117	C₇×D₄	1	2	yes	—
468	C₂×C₄⋊C₄	—	2	2	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄²	—	2	2	no	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	—	2	1	no	—
473	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
474	#107	—	2	1	no	—
475	#107	—	2	1	no	—
476	#107	—	2	1	no	—
477	#107	—	2	2	no	—
478	#106	—	2	1	no	—
479	#106	—	2	1	no	—
480	#106	—	2	1	no	—
481	#106	—	2	2	no	—
482	C₄⋊C₈	—	2	1	no	—
483	C₄⋊C₈	—	2	1	no	—
484	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
485	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
486	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
487	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
488	#103	—	2	1	no	—
489	#103	—	2	1	no	—
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	1	no	—
493	#103	—	2	2	no	—
494	#103	—	2	2	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	C₂²⋊C₈	—	2	1	no	—
499	C₂²⋊C₈	—	2	1	no	—
500	#97	—	2	1	no	—
501	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
502	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
503	C₂²×C₇	—	2	1	no	—
504	C₂²×C₇	—	2	2	no	—
505	C₂²×C₇	—	2	1	no	—
506	C₂²×C₇	—	2	1	no	—
507	C₂²×C₇	—	4	1	no	—
508	C₂²×C₇	—	4	1	no	—
509	C₂²×C₇	—	4	1	no	—
510	C₂²×C₇	—	4	1	no	—
511	C₂²×C₇	—	4	1	no	—
512	C₂²×C₇	C₂×#120	1	1	yes	characteristic
513	C₄×C₇	—	2	1	no	—
514	C₄×C₇	—	2	1	no	—
515	C₄×C₇	—	2	2	no	—
516	C₄×C₇	—	2	1	no	—
517	C₄×C₇	—	2	1	no	—
518	C₄×C₇	—	4	1	no	—
519	C₄×C₇	—	4	1	no	—
520	C₄×C₇	—	4	2	no	—
521	C₄×C₇	—	4	2	no	—
522	C₄×C₇	—	4	1	no	—
523	C₄×C₇	—	4	1	no	—
524	C₄×C₇	—	4	1	no	—
525	C₄×C₇	—	8	1	no	—
526	C₄×C₇	—	8	1	no	—
527	C₄×C₇	C₂×#135	1	1	yes	characteristic
528	C₄×C₇	C₂×#137	1	1	yes	characteristic
529	C₄×C₇	#575	1	1	yes	characteristic
530	C₄×C₇	#575	1	1	yes	characteristic
531	#41	—	2	2	no	—
532	#41	—	2	2	no	—
533	#41	—	4	1	no	—
534	#41	—	4	1	no	—
535	#41	—	4	2	no	—
536	#41	—	4	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	4	2	no	—
543	C₂×Q₈	—	4	2	no	—
544	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
545	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
550	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
560	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
561	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
562	Q₁₆	—	4	2	no	—
563	SD₁₆	—	4	2	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	4	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
592	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
593	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
594	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
595	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
596	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	4	1	no	—
619	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
620	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
621	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
622	C₄²	C₂⁴×C₇	1	1	yes	characteristic
623	C₂×C₇	—	4	1	no	—
624	C₂×C₇	—	4	2	no	—
625	C₂×C₇	—	8	1	no	—
626	C₂×C₇	#3002	1	1	yes	characteristic
627	C₂×C₇	#3007	1	1	yes	characteristic
628	C₂×C₇	#3020	1	1	yes	characteristic
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	C₇×#120	1	1	yes	characteristic
632	Q₈	—	2	1	no	—
633	Q₈	—	2	1	no	—
634	Q₈	—	2	1	no	—
635	Q₈	—	4	4	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	C₇×#137	1	2	yes	—
644	D₄	—	2	1	no	—
645	D₄	—	2	1	no	—
646	D₄	—	2	1	no	—
647	D₄	—	4	2	no	—
648	D₄	—	4	2	no	—
649	D₄	—	4	4	no	—
650	D₄	C₇×#135	1	2	yes	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	C₇×#120	1	1	yes	characteristic
677	C₂×C₄	C₇×#120	1	1	yes	characteristic
678	C₂×C₄	C₇×#120	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	1	yes	characteristic
682	C₈	—	4	1	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₇	#18765	1	1	yes	characteristic, direct product factor, Sylow
689	C₂²	—	2	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	C₂×C₇×#120	1	1	yes	characteristic
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	C₂×C₇×#135	1	1	yes	characteristic
714	C₄	C₂×C₇×#137	1	1	yes	characteristic
715	C₄	C₇×#575	1	1	yes	characteristic
716	C₄	C₇×#575	1	1	yes	characteristic
717	C₂	—	4	1	no	—
718	C₂	—	4	2	no	—
719	C₂	—	8	1	no	—
720	C₂	C₇×#3002	1	1	yes	characteristic
721	C₂	C₇×#3007	1	1	yes	characteristic
722	C₂	C₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3482	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×#3231	C₂	semidirect
3. C₇×#3116	C₂	semidirect
4. C₇×#3076	C₂	semidirect
5. C₇×#1652	C₂	semidirect
6. C₇×#1651	C₂	semidirect
7. C₇×#1648	C₂	semidirect
8. C₇×#1647	C₂	semidirect
9. C₇×#1638	C₂	semidirect
10. C₇×#1637	C₂	semidirect
11. C₇×#1636	C₂	semidirect
12. C₇×#1635	C₂	semidirect
13. C₇×#1552	C₂	semidirect
14. C₇×#1488	C₂	semidirect
15. C₇×#1477	C₂	semidirect
71. #18765	C₇	direct (N × H)
178. #3231	C₂×C₇	semidirect
179. #3116	C₂×C₇	semidirect
180. #3076	C₂×C₇	semidirect
181. #1652	C₂×C₇	semidirect
182. #1651	C₂×C₇	semidirect
183. #1648	C₂×C₇	semidirect
184. #1647	C₂×C₇	semidirect
185. #1638	C₂×C₇	semidirect
186. #1637	C₂×C₇	semidirect
187. #1636	C₂×C₇	semidirect
188. #1635	C₂×C₇	semidirect
189. #1552	C₂×C₇	semidirect
190. #1488	C₂×C₇	semidirect
191. #1477	C₂×C₇	semidirect
688. C₇	#18765	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×#3482	2
C₇×#3231	2
C₇×#3116	2
C₇×#3076	2
C₇×#1652	2
C₇×#1651	2
C₇×#1648	2
C₇×#1647	2
C₇×#1638	2
C₇×#1637	2
C₇×#1636	2
C₇×#1635	2
C₇×#1552	2
C₇×#1488	2
C₇×#1477	2
#18765	7

Subgroups — C7×#18765 #13195981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#18765 #13195981