Subgroups — C₇×#60489 #13237705

Order 1792.

2002 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3428	C₂	1	1	yes	maximal, characteristic
3	C₇×#3084	C₂	1	4	yes	maximal, complemented
4	C₇×#3083	C₂	1	4	yes	maximal, complemented
5	C₇×#3082	C₂	1	4	yes	maximal, complemented
6	C₇×#3081	C₂	1	4	yes	maximal, complemented
7	C₇×#3076	C₂	1	8	yes	maximal, complemented
8	C₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2896	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#544	—	2	2	no	—
17	C₇×#544	C₂²	1	4	yes	—
18	C₇×#544	C₂²	1	4	yes	complemented
19	C₇×#543	—	2	2	no	—
20	C₇×#533	—	2	2	no	—
21	C₇×#533	—	2	2	no	—
22	C₇×#533	C₂²	1	4	yes	complemented
23	C₇×#520	—	2	2	no	—
24	C₇×#520	C₂²	1	4	yes	—
25	C₇×#519	C₂²	1	2	yes	—
26	C₇×#518	—	2	2	no	—
27	C₇×#518	C₂²	1	2	yes	—
28	C₄×C₇×#41	—	2	2	no	—
29	C₄×C₇×#41	C₂²	1	4	yes	—
30	C₂×C₇×#117	—	2	2	no	—
31	C₂×C₇×#117	C₂²	1	1	yes	characteristic
32	C₂×C₇×#117	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	C₂²	1	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	1	yes	characteristic
35	C₇×#479	C₂²	1	8	yes	complemented
36	C₇×#479	C₂²	1	8	yes	complemented
37	C₇×#478	C₂²	1	8	yes	complemented
38	C₇×#478	C₂²	1	8	yes	complemented
39	C₇×#477	C₂²	1	8	yes	complemented
40	C₇×#476	C₂²	1	8	yes	complemented
41	C₇×#475	C₂²	1	8	yes	complemented
42	C₇×#474	C₂²	1	8	yes	complemented
43	C₇×#428	C₂²	1	4	yes	—
44	C₇×#428	C₂²	1	4	yes	complemented
45	C₇×#427	C₂²	1	4	yes	—
46	C₇×#427	C₂²	1	4	yes	complemented
47	C₇×#427	C₂²	1	4	yes	complemented
48	C₂×C₇×#107	C₂²	1	2	yes	complemented
49	C₂×C₇×#106	C₂²	1	2	yes	complemented
50	C₇×#424	C₂²	1	4	yes	—
51	C₇×#424	C₂²	1	2	yes	complemented
52	C₇×#424	C₂²	1	2	yes	complemented
53	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	complemented
54	C₇×#419	C₂²	1	2	yes	—
55	C₇×#418	C₂²	1	2	yes	—
56	C₇×#417	C₂²	1	4	yes	—
57	C₇×#416	C₂²	1	4	yes	—
58	C₇×#416	C₂²	1	4	yes	—
59	C₇×#416	C₂²	1	2	yes	—
60	C₇×#416	C₂²	1	2	yes	—
61	C₂×C₇×#103	C₂²	1	2	yes	—
62	C₂×C₇×#102	C₂²	1	2	yes	—
63	#60489	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂×C₇×#41	—	2	1	no	—
65	C₂×C₇×#41	—	2	1	no	—
66	C₂×C₇×#41	—	2	4	no	—
67	C₂×C₇×#41	Q₈	1	8	yes	complemented
68	C₂×C₇×#41	C₂³	1	2	yes	—
69	C₂×C₇×#41	C₂³	1	2	yes	—
70	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×D₄	—	2	1	no	—
72	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₇×M₁₆	—	2	4	no	—
76	C₂×C₇×M₁₆	C₂³	1	2	yes	—
77	C₂×C₇×M₁₆	C₂³	1	2	yes	—
78	C₂²×C₇×C₈	—	2	4	no	—
79	C₂²×C₇×C₈	C₂³	1	2	yes	—
80	C₂²×C₇×C₈	C₂³	1	2	yes	—
81	C₂²×C₇×C₈	C₂³	1	2	yes	—
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₇×C₄⋊Q₈	—	2	4	no	—
85	C₇×C₄⋊Q₈	—	2	4	no	—
86	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
87	C₇×#125	—	2	4	no	—
88	C₇×#125	—	2	4	no	—
89	C₇×#125	C₂³	1	8	yes	—
90	C₇×C₂²⋊Q₈	—	2	8	no	—
91	C₇×C₂²⋊Q₈	—	2	8	no	—
92	C₇×C₂²⋊Q₈	—	2	8	no	—
93	C₄×C₇×Q₈	—	2	4	no	—
94	C₄×C₇×Q₈	—	2	8	no	—
95	C₄×C₇×Q₈	C₂³	1	8	yes	—
96	C₄×C₇×D₄	—	2	8	no	—
97	C₄×C₇×D₄	—	2	4	no	—
98	C₄×C₇×D₄	—	2	8	no	—
99	C₄×C₇×D₄	C₂³	1	8	yes	—
100	C₇×#117	—	2	1	no	—
101	C₇×#117	—	2	1	no	—
102	C₇×#117	—	2	1	no	—
103	C₇×#117	—	2	1	no	—
104	C₇×#117	—	2	1	no	—
105	C₇×#117	—	2	1	no	—
106	C₇×#117	—	2	4	no	—
107	C₇×#117	—	2	4	no	—
108	C₇×#117	—	2	4	no	—
109	C₇×#117	D₄	1	2	yes	—
110	C₇×#117	D₄	1	2	yes	—
111	C₇×#117	C₂³	1	2	yes	—
112	C₇×#117	C₂³	1	2	yes	—
113	C₇×#117	C₂³	1	2	yes	—
114	C₇×#117	C₂³	1	2	yes	—
115	C₇×#117	C₂³	1	2	yes	—
116	C₇×#117	C₂³	1	2	yes	—
117	C₇×#117	C₂³	1	2	yes	—
118	C₇×#117	C₂³	1	2	yes	—
119	C₂×C₇×C₄⋊C₄	—	2	4	no	—
120	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
121	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
129	C₂×C₄²×C₇	—	2	1	no	—
130	C₂×C₄²×C₇	—	2	1	no	—
131	C₂×C₄²×C₇	—	2	1	no	—
132	C₂×C₄²×C₇	—	2	4	no	—
133	C₂×C₄²×C₇	C₂³	1	2	yes	—
134	C₇×#107	C₂³	1	4	yes	—
135	C₇×#107	C₂³	1	8	yes	—
136	C₇×#107	C₂³	1	4	yes	—
137	C₇×#106	C₂³	1	4	yes	—
138	C₇×#106	C₂³	1	8	yes	—
139	C₇×#106	C₂³	1	4	yes	—
140	C₇×C₄⋊C₈	C₂³	1	8	yes	—
141	C₇×C₄⋊C₈	C₂³	1	8	yes	—
142	C₇×#103	C₂³	1	4	yes	—
143	C₇×#103	C₂³	1	8	yes	—
144	C₇×#103	C₂³	1	4	yes	—
145	C₇×#102	C₂³	1	4	yes	—
146	C₇×#102	C₂³	1	8	yes	—
147	C₇×#102	C₂³	1	4	yes	—
148	#3458	C₂×C₇	1	1	yes	characteristic, complemented
149	#3428	C₂×C₇	1	1	yes	characteristic
150	#3084	C₂×C₇	1	4	yes	complemented
151	#3083	C₂×C₇	1	4	yes	complemented
152	#3082	C₂×C₇	1	4	yes	complemented
153	#3081	C₂×C₇	1	4	yes	complemented
154	#3076	C₂×C₇	1	8	yes	complemented
155	#2911	C₂×C₇	1	1	yes	characteristic, complemented
156	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
158	#2896	C₂×C₇	1	1	yes	characteristic
159	C₂×#416	C₂×C₇	1	1	yes	characteristic
160	C₂⁴×C₇	—	2	1	no	—
161	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
162	C₇×#41	—	2	8	no	—
163	C₇×#41	—	2	8	no	—
164	C₇×#41	—	2	4	no	—
165	C₇×#41	—	2	4	no	—
166	C₇×#41	C₂×Q₈	1	8	yes	—
167	C₇×#41	C₂×Q₈	1	8	yes	—
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	8	no	—
170	C₂×C₇×Q₈	—	2	2	no	—
171	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	—
172	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
173	C₂×C₇×D₄	—	2	8	no	—
174	C₂×C₇×D₄	—	2	2	no	—
175	C₂×C₇×D₄	—	2	2	no	—
176	C₂×C₇×D₄	—	2	1	no	—
177	C₂×C₇×D₄	—	2	2	no	—
178	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
179	C₂×C₇×D₄	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	8	no	—
182	C₂²×C₄×C₇	—	2	2	no	—
183	C₂²×C₄×C₇	—	2	2	no	—
184	C₂²×C₄×C₇	—	2	2	no	—
185	C₂²×C₄×C₇	—	2	2	no	—
186	C₂²×C₄×C₇	—	2	2	no	—
187	C₂²×C₄×C₇	—	2	8	no	—
188	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
193	C₂²×C₄×C₇	#41	1	4	yes	—
194	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
197	C₇×M₁₆	—	2	4	no	—
198	C₇×M₁₆	—	2	4	no	—
199	C₂×C₇×C₈	—	2	4	no	—
200	C₂×C₇×C₈	—	2	4	no	—
201	C₂×C₇×C₈	—	2	2	no	—
202	C₂×C₇×C₈	—	2	2	no	—
203	C₂×C₇×C₈	—	2	4	no	—
204	C₂×C₇×C₈	C₂⁴	1	2	yes	—
205	C₂×C₇×C₈	C₂⁴	1	4	yes	—
206	C₂×C₇×C₈	C₂⁴	1	2	yes	—
207	C₇×C₄⋊C₄	—	2	2	no	—
208	C₇×C₄⋊C₄	—	2	8	no	—
209	C₇×C₄⋊C₄	—	2	2	no	—
210	C₇×C₄⋊C₄	—	2	2	no	—
211	C₇×C₄⋊C₄	—	2	8	no	—
212	C₇×C₄⋊C₄	—	2	8	no	—
213	C₇×C₄⋊C₄	—	2	8	no	—
214	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
215	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
216	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
217	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
218	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
219	C₇×C₂²⋊C₄	—	2	2	no	—
220	C₇×C₂²⋊C₄	—	2	2	no	—
221	C₇×C₂²⋊C₄	—	2	2	no	—
222	C₇×C₂²⋊C₄	—	2	2	no	—
223	C₇×C₂²⋊C₄	—	2	2	no	—
224	C₇×C₂²⋊C₄	—	2	2	no	—
225	C₇×C₂²⋊C₄	—	2	8	no	—
226	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
227	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
228	C₄²×C₇	—	2	8	no	—
229	C₄²×C₇	—	2	2	no	—
230	C₄²×C₇	—	2	2	no	—
231	C₄²×C₇	—	2	2	no	—
232	C₄²×C₇	—	2	2	no	—
233	C₄²×C₇	—	2	2	no	—
234	C₄²×C₇	—	2	2	no	—
235	C₄²×C₇	C₂×D₄	1	4	yes	—
236	C₄²×C₇	C₂⁴	1	4	yes	—
237	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
240	#544	—	2	2	no	—
241	#544	C₂²×C₇	1	4	yes	—
242	#544	C₂²×C₇	1	4	yes	complemented
243	#543	—	2	2	no	—
244	#533	—	2	2	no	—
245	#533	—	2	2	no	—
246	#533	C₂²×C₇	1	4	yes	complemented
247	#520	—	2	2	no	—
248	#520	C₂²×C₇	1	4	yes	—
249	#519	C₂²×C₇	1	2	yes	—
250	#518	—	2	2	no	—
251	#518	C₂²×C₇	1	2	yes	—
252	C₄×#41	—	2	2	no	—
253	C₄×#41	C₂²×C₇	1	4	yes	—
254	C₂×#117	—	2	2	no	—
255	C₂×#117	C₂²×C₇	1	1	yes	characteristic
256	C₂×#117	C₂²×C₇	1	1	yes	characteristic
257	C₂×#117	C₂²×C₇	1	1	yes	characteristic
258	C₂×#117	C₂²×C₇	1	1	yes	characteristic
259	#479	C₂²×C₇	1	8	yes	complemented
260	#479	C₂²×C₇	1	8	yes	complemented
261	#478	C₂²×C₇	1	8	yes	complemented
262	#478	C₂²×C₇	1	8	yes	complemented
263	#477	C₂²×C₇	1	8	yes	complemented
264	#476	C₂²×C₇	1	8	yes	complemented
265	#475	C₂²×C₇	1	8	yes	complemented
266	#474	C₂²×C₇	1	8	yes	complemented
267	#428	C₂²×C₇	1	4	yes	—
268	#428	C₂²×C₇	1	4	yes	complemented
269	#427	C₂²×C₇	1	4	yes	—
270	#427	C₂²×C₇	1	4	yes	complemented
271	#427	C₂²×C₇	1	4	yes	complemented
272	C₂×#107	C₂²×C₇	1	2	yes	complemented
273	C₂×#106	C₂²×C₇	1	2	yes	complemented
274	#424	C₂²×C₇	1	4	yes	—
275	#424	C₂²×C₇	1	2	yes	complemented
276	#424	C₂²×C₇	1	2	yes	complemented
277	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	complemented
278	#419	C₂²×C₇	1	2	yes	—
279	#418	C₂²×C₇	1	2	yes	—
280	#417	C₂²×C₇	1	4	yes	—
281	#416	C₂²×C₇	1	4	yes	—
282	#416	C₂²×C₇	1	4	yes	—
283	#416	C₂²×C₇	1	2	yes	—
284	#416	C₂²×C₇	1	2	yes	—
285	C₂×#103	C₂²×C₇	1	2	yes	—
286	C₂×#102	C₂²×C₇	1	2	yes	—
287	C₂³×C₇	—	2	2	no	—
288	C₂³×C₇	—	2	4	no	—
289	C₂³×C₇	—	4	2	no	—
290	C₂³×C₇	—	8	2	no	—
291	C₂³×C₇	C₂²⋊Q₈	1	4	yes	—
292	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
295	C₇×Q₈	—	2	4	no	—
296	C₇×Q₈	—	2	2	no	—
297	C₇×Q₈	—	8	8	no	—
298	C₇×Q₈	C₂²×Q₈	1	4	yes	—
299	C₇×D₄	—	2	8	no	—
300	C₇×D₄	—	2	8	no	—
301	C₇×D₄	—	2	4	no	—
302	C₇×D₄	—	2	2	no	—
303	C₇×D₄	C₂²×Q₈	1	4	yes	—
304	C₂×C₄×C₇	—	2	4	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	8	no	—
307	C₂×C₄×C₇	—	2	8	no	—
308	C₂×C₄×C₇	—	2	4	no	—
309	C₂×C₄×C₇	—	2	4	no	—
310	C₂×C₄×C₇	—	2	4	no	—
311	C₂×C₄×C₇	—	4	4	no	—
312	C₂×C₄×C₇	—	8	8	no	—
313	C₂×C₄×C₇	—	8	2	no	—
314	C₂×C₄×C₇	—	8	2	no	—
315	C₂×C₄×C₇	—	8	2	no	—
316	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
317	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
318	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
319	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
320	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
324	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
325	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
326	C₂×C₄×C₇	C₂×#41	1	2	yes	—
327	C₂×C₄×C₇	C₂×#41	1	2	yes	—
328	C₂×C₄×C₇	C₂×#41	1	2	yes	—
329	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
330	C₇×C₈	—	2	2	no	—
331	C₇×C₈	—	2	2	no	—
332	C₇×C₈	—	2	4	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	4	no	—
336	C₂×#41	C₇×Q₈	1	8	yes	complemented
337	C₂×#41	C₂³×C₇	1	2	yes	—
338	C₂×#41	C₂³×C₇	1	2	yes	—
339	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
344	C₂×M₁₆	—	2	4	no	—
345	C₂×M₁₆	C₂³×C₇	1	2	yes	—
346	C₂×M₁₆	C₂³×C₇	1	2	yes	—
347	C₂²×C₈	—	2	4	no	—
348	C₂²×C₈	C₂³×C₇	1	2	yes	—
349	C₂²×C₈	C₂³×C₇	1	2	yes	—
350	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₇	1	2	yes	—
353	C₄⋊Q₈	—	2	4	no	—
354	C₄⋊Q₈	—	2	4	no	—
355	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
356	#125	—	2	4	no	—
357	#125	—	2	4	no	—
358	#125	C₂³×C₇	1	8	yes	—
359	C₂²⋊Q₈	—	2	8	no	—
360	C₂²⋊Q₈	—	2	8	no	—
361	C₂²⋊Q₈	—	2	8	no	—
362	C₄×Q₈	—	2	4	no	—
363	C₄×Q₈	—	2	8	no	—
364	C₄×Q₈	C₂³×C₇	1	8	yes	—
365	C₄×D₄	—	2	8	no	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	—	2	8	no	—
368	C₄×D₄	C₂³×C₇	1	8	yes	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	4	no	—
376	#117	—	2	4	no	—
377	#117	—	2	4	no	—
378	#117	C₇×D₄	1	2	yes	—
379	#117	C₇×D₄	1	2	yes	—
380	#117	C₂³×C₇	1	2	yes	—
381	#117	C₂³×C₇	1	2	yes	—
382	#117	C₂³×C₇	1	2	yes	—
383	#117	C₂³×C₇	1	2	yes	—
384	#117	C₂³×C₇	1	2	yes	—
385	#117	C₂³×C₇	1	2	yes	—
386	#117	C₂³×C₇	1	2	yes	—
387	#117	C₂³×C₇	1	2	yes	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	4	no	—
397	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	4	no	—
402	C₂×C₄²	C₂³×C₇	1	2	yes	—
403	#107	C₂³×C₇	1	4	yes	—
404	#107	C₂³×C₇	1	4	yes	—
405	#107	C₂³×C₇	1	8	yes	—
406	#106	C₂³×C₇	1	4	yes	—
407	#106	C₂³×C₇	1	4	yes	—
408	#106	C₂³×C₇	1	8	yes	—
409	C₄⋊C₈	C₂³×C₇	1	8	yes	—
410	C₄⋊C₈	C₂³×C₇	1	8	yes	—
411	#103	C₂³×C₇	1	4	yes	—
412	#103	C₂³×C₇	1	4	yes	—
413	#103	C₂³×C₇	1	8	yes	—
414	#102	C₂³×C₇	1	4	yes	—
415	#102	C₂³×C₇	1	4	yes	—
416	#102	C₂³×C₇	1	8	yes	—
417	C₂²×C₇	—	2	2	no	—
418	C₂²×C₇	—	2	2	no	—
419	C₂²×C₇	—	2	2	no	—
420	C₂²×C₇	—	2	4	no	—
421	C₂²×C₇	—	4	4	no	—
422	C₂²×C₇	—	4	4	no	—
423	C₂²×C₇	—	8	4	no	—
424	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
425	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
426	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
427	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₇	—	2	8	no	—
429	C₄×C₇	—	2	4	no	—
430	C₄×C₇	—	4	4	no	—
431	C₄×C₇	—	4	4	no	—
432	C₄×C₇	—	4	4	no	—
433	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
434	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
435	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
436	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
437	C₄×C₇	C₂²×#41	1	1	yes	characteristic
438	C₂⁴	—	2	1	no	—
439	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
440	#41	—	2	8	no	—
441	#41	—	2	8	no	—
442	#41	—	2	4	no	—
443	#41	—	2	4	no	—
444	#41	C₂×C₇×Q₈	1	8	yes	—
445	#41	C₂×C₇×Q₈	1	8	yes	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	8	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	—
450	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
457	C₂×D₄	C₂⁴×C₇	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
467	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
471	C₂²×C₄	C₇×#41	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
475	M₁₆	—	2	4	no	—
476	M₁₆	—	2	4	no	—
477	C₂×C₈	—	2	4	no	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	4	no	—
482	C₂×C₈	C₂⁴×C₇	1	2	yes	—
483	C₂×C₈	C₂⁴×C₇	1	4	yes	—
484	C₂×C₈	C₂⁴×C₇	1	2	yes	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	8	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	8	no	—
492	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
493	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
494	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
505	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	8	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	C₂×C₇×D₄	1	4	yes	—
514	C₄²	C₂⁴×C₇	1	4	yes	—
515	C₂×C₇	—	2	2	no	—
516	C₂×C₇	—	2	2	no	—
517	C₂×C₇	—	2	2	no	—
518	C₂×C₇	—	4	4	no	—
519	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
520	C₂×C₇	#3584	1	2	yes	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	8	2	no	—
525	C₂³	C₇×C₂²⋊Q₈	1	4	yes	—
526	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
527	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
528	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
529	Q₈	—	2	2	no	—
530	Q₈	—	2	4	no	—
531	Q₈	—	8	8	no	—
532	Q₈	C₂²×C₇×Q₈	1	4	yes	—
533	D₄	—	2	8	no	—
534	D₄	—	2	8	no	—
535	D₄	—	2	2	no	—
536	D₄	—	2	4	no	—
537	D₄	C₂²×C₇×Q₈	1	4	yes	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	8	8	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
551	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
552	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
553	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
554	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
555	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
556	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
557	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
558	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
559	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
560	C₂×C₄	C₂×C₇×#41	1	2	yes	—
561	C₂×C₄	C₂×C₇×#41	1	2	yes	—
562	C₂×C₄	C₂×C₇×#41	1	2	yes	—
563	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
564	C₈	—	2	2	no	—
565	C₈	—	2	2	no	—
566	C₈	—	2	4	no	—
567	C₇	#60489	1	1	yes	characteristic, direct product factor, Sylow
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	8	4	no	—
575	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
576	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
577	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
578	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
579	C₄	—	2	8	no	—
580	C₄	—	2	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	4	no	—
584	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
585	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
586	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
587	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
588	C₄	C₂²×C₇×#41	1	1	yes	characteristic
589	C₂	—	2	2	no	—
590	C₂	—	2	2	no	—
591	C₂	—	2	2	no	—
592	C₂	—	4	4	no	—
593	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
594	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
prime radical	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3458	C₂	semidirect
3. C₇×#3084	C₂	semidirect
4. C₇×#3083	C₂	semidirect
5. C₇×#3082	C₂	semidirect
6. C₇×#3081	C₂	semidirect
7. C₇×#3076	C₂	semidirect
8. C₇×#2911	C₂	semidirect
9. C₂×C₇×#427	C₂	semidirect
10. C₂×C₇×#424	C₂	semidirect
18. C₇×#544	C₂²	semidirect
22. C₇×#533	C₂²	semidirect
35. C₇×#479	C₂²	semidirect
36. C₇×#479	C₂²	semidirect
37. C₇×#478	C₂²	semidirect
38. C₇×#478	C₂²	semidirect
39. C₇×#477	C₂²	semidirect
40. C₇×#476	C₂²	semidirect
41. C₇×#475	C₂²	semidirect
42. C₇×#474	C₂²	semidirect
44. C₇×#428	C₂²	semidirect
46. C₇×#427	C₂²	semidirect
47. C₇×#427	C₂²	semidirect
48. C₂×C₇×#107	C₂²	semidirect
49. C₂×C₇×#106	C₂²	semidirect
51. C₇×#424	C₂²	semidirect
52. C₇×#424	C₂²	semidirect
53. C₂×C₇×C₄⋊C₈	C₂²	semidirect
63. #60489	C₇	direct (N × H)
67. C₂×C₇×#41	Q₈	semidirect
148. #3458	C₂×C₇	semidirect
150. #3084	C₂×C₇	semidirect
151. #3083	C₂×C₇	semidirect
152. #3082	C₂×C₇	semidirect
153. #3081	C₂×C₇	semidirect
154. #3076	C₂×C₇	semidirect
155. #2911	C₂×C₇	semidirect
156. C₂×#427	C₂×C₇	semidirect
157. C₂×#424	C₂×C₇	semidirect
242. #544	C₂²×C₇	semidirect
246. #533	C₂²×C₇	semidirect
259. #479	C₂²×C₇	semidirect
260. #479	C₂²×C₇	semidirect
261. #478	C₂²×C₇	semidirect
262. #478	C₂²×C₇	semidirect
263. #477	C₂²×C₇	semidirect
264. #476	C₂²×C₇	semidirect
265. #475	C₂²×C₇	semidirect
266. #474	C₂²×C₇	semidirect
268. #428	C₂²×C₇	semidirect
270. #427	C₂²×C₇	semidirect
271. #427	C₂²×C₇	semidirect
272. C₂×#107	C₂²×C₇	semidirect
273. C₂×#106	C₂²×C₇	semidirect
275. #424	C₂²×C₇	semidirect
276. #424	C₂²×C₇	semidirect
277. C₂×C₄⋊C₈	C₂²×C₇	semidirect
336. C₂×#41	C₇×Q₈	semidirect
567. C₇	#60489	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×#3458	2
C₇×#3428	2
C₇×#3084	2
C₇×#3083	2
C₇×#3082	2
C₇×#3081	2
C₇×#3076	2
C₇×#2911	2
C₂×C₇×#427	2
C₂×C₇×#424	2
C₇×#2896	2
C₂×C₇×#416	2
#60489	7

Subgroups — C7×#60489 #13237705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60489 #13237705