Subgroups — C₇×#60516 #13237732

Order 1792.

2142 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3449	C₂	1	1	yes	maximal, characteristic
2	C₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3099	C₂	1	4	yes	maximal, complemented
4	C₇×#3098	C₂	1	4	yes	maximal, complemented
5	C₇×#3097	C₂	1	4	yes	maximal, complemented
6	C₇×#3096	C₂	1	4	yes	maximal, complemented
7	C₇×#3091	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	C₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₇×#537	C₂²	1	4	yes	—
18	C₇×#536	—	2	1	no	—
19	C₇×#536	C₂²	1	2	yes	—
20	C₇×#535	—	2	1	no	—
21	C₇×#535	C₂²	1	2	yes	—
22	C₇×#534	—	2	2	no	—
23	C₇×#532	—	2	2	no	—
24	C₇×#525	—	2	2	no	—
25	C₇×#525	C₂²	1	4	yes	—
26	C₇×#520	C₂²	1	4	yes	—
27	C₇×#520	C₂²	1	4	yes	complemented
28	C₇×#519	—	2	1	no	—
29	C₇×#518	—	2	2	no	—
30	C₇×#518	—	2	1	no	—
31	C₄×C₇×#41	—	2	2	no	—
32	C₄×C₇×#41	—	2	2	no	—
33	C₂×C₇×#117	C₂²	1	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	1	yes	characteristic
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₂×C₇×#117	C₂²	1	4	yes	complemented
37	C₇×#485	C₂²	1	8	yes	complemented
38	C₇×#485	C₂²	1	8	yes	complemented
39	C₇×#484	C₂²	1	8	yes	complemented
40	C₇×#483	C₂²	1	8	yes	complemented
41	C₇×#482	C₂²	1	8	yes	complemented
42	C₇×#482	C₂²	1	8	yes	complemented
43	C₇×#481	C₂²	1	8	yes	complemented
44	C₇×#480	C₂²	1	8	yes	complemented
45	C₇×#428	C₂²	1	4	yes	complemented
46	C₇×#428	C₂²	1	4	yes	complemented
47	C₇×#427	C₂²	1	4	yes	complemented
48	C₇×#427	C₂²	1	4	yes	complemented
49	C₇×#427	C₂²	1	4	yes	complemented
50	C₂×C₇×#107	C₂²	1	2	yes	complemented
51	C₂×C₇×#106	C₂²	1	2	yes	complemented
52	C₇×#419	C₂²	1	2	yes	complemented
53	C₇×#418	C₂²	1	2	yes	complemented
54	C₇×#417	C₂²	1	4	yes	complemented
55	C₇×#416	C₂²	1	4	yes	—
56	C₇×#416	C₂²	1	4	yes	—
57	C₇×#416	C₂²	1	2	yes	complemented
58	C₇×#416	C₂²	1	2	yes	complemented
59	C₂×C₇×#103	C₂²	1	2	yes	complemented
60	C₂×C₇×#102	C₂²	1	2	yes	complemented
61	C₇×#408	C₂²	1	4	yes	—
62	C₇×#408	C₂²	1	2	yes	complemented
63	C₇×#408	C₂²	1	2	yes	complemented
64	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
65	#60516	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂×C₇×#41	—	2	1	no	—
67	C₂×C₇×#41	—	2	1	no	—
68	C₂×C₇×#41	—	2	4	no	—
69	C₂×C₇×#41	—	2	4	no	—
70	C₂×C₇×#41	—	2	4	no	—
71	C₂×C₇×#41	—	2	4	no	—
72	C₂×C₇×#41	D₄	1	2	yes	—
73	C₂×C₇×#41	D₄	1	2	yes	—
74	C₂×C₇×#41	C₂³	1	2	yes	—
75	C₂×C₇×#41	C₂³	1	2	yes	—
76	C₂×C₇×#41	C₂³	1	2	yes	—
77	C₂×C₇×#41	C₂³	1	2	yes	—
78	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
79	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×D₄	—	2	1	no	—
81	C₂²×C₇×D₄	D₄	1	2	yes	—
82	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
83	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇	—	2	1	no	—
85	C₂³×C₄×C₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₇×M₁₆	—	2	4	no	—
88	C₂×C₇×M₁₆	C₂³	1	2	yes	—
89	C₂×C₇×M₁₆	C₂³	1	2	yes	—
90	C₂²×C₇×C₈	—	2	4	no	—
91	C₂²×C₇×C₈	C₂³	1	2	yes	—
92	C₂²×C₇×C₈	C₂³	1	2	yes	—
93	C₂²×C₇×C₈	C₂³	1	2	yes	—
94	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
96	C₇×C₄⋊Q₈	—	2	2	no	—
97	C₇×#127	—	2	2	no	—
98	C₇×#124	—	2	2	no	—
99	C₇×#124	—	2	2	no	—
100	C₇×#123	—	2	4	no	—
101	C₇×#123	—	2	4	no	—
102	C₇×C₂²⋊Q₈	—	2	4	no	—
103	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
104	C₇×#121	—	2	4	no	—
105	C₇×#121	—	2	8	no	—
106	C₇×#121	C₂³	1	8	yes	—
107	C₇×#120	—	2	4	no	—
108	C₇×#120	—	2	4	no	—
109	C₄×C₇×Q₈	—	2	4	no	—
110	C₄×C₇×Q₈	—	2	4	no	—
111	C₄×C₇×D₄	—	2	8	no	—
112	C₄×C₇×D₄	—	2	4	no	—
113	C₄×C₇×D₄	—	2	8	no	—
114	C₄×C₇×D₄	—	2	4	no	—
115	C₄×C₇×D₄	—	2	8	no	—
116	C₇×#117	—	2	1	no	—
117	C₇×#117	—	2	1	no	—
118	C₇×#117	—	2	1	no	—
119	C₇×#117	—	2	1	no	—
120	C₇×#117	—	2	1	no	—
121	C₇×#117	—	2	1	no	—
122	C₇×#117	—	2	4	no	—
123	C₇×#117	—	2	4	no	—
124	C₇×#117	C₂³	1	8	yes	—
125	C₇×#117	C₂³	1	2	yes	—
126	C₇×#117	C₂³	1	2	yes	—
127	C₇×#117	C₂³	1	2	yes	—
128	C₇×#117	C₂³	1	2	yes	—
129	C₇×#117	C₂³	1	2	yes	—
130	C₇×#117	C₂³	1	2	yes	—
131	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
132	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₄²×C₇	—	2	1	no	—
140	C₂×C₄²×C₇	—	2	1	no	—
141	C₂×C₄²×C₇	—	2	1	no	—
142	C₂×C₄²×C₇	—	2	4	no	—
143	C₇×#107	C₂³	1	4	yes	—
144	C₇×#107	C₂³	1	8	yes	—
145	C₇×#107	C₂³	1	4	yes	—
146	C₇×#106	C₂³	1	4	yes	—
147	C₇×#106	C₂³	1	8	yes	—
148	C₇×#106	C₂³	1	4	yes	—
149	C₇×#103	C₂³	1	4	yes	—
150	C₇×#103	C₂³	1	8	yes	—
151	C₇×#103	C₂³	1	4	yes	—
152	C₇×#102	C₂³	1	4	yes	—
153	C₇×#102	C₂³	1	8	yes	—
154	C₇×#102	C₂³	1	4	yes	—
155	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
156	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
157	#3449	C₂×C₇	1	1	yes	characteristic
158	#3428	C₂×C₇	1	1	yes	characteristic, complemented
159	#3099	C₂×C₇	1	4	yes	complemented
160	#3098	C₂×C₇	1	4	yes	complemented
161	#3097	C₂×C₇	1	4	yes	complemented
162	#3096	C₂×C₇	1	4	yes	complemented
163	#3091	C₂×C₇	1	8	yes	complemented
164	#2911	C₂×C₇	1	1	yes	characteristic, complemented
165	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
166	#2896	C₂×C₇	1	1	yes	characteristic, complemented
167	C₂×#416	C₂×C₇	1	1	yes	characteristic, complemented
168	C₂×#408	C₂×C₇	1	1	yes	characteristic, complemented
169	C₂⁴×C₇	—	2	1	no	—
170	C₂⁴×C₇	C₂×D₄	1	2	yes	—
171	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
172	C₇×#41	—	2	8	no	—
173	C₇×#41	—	2	8	no	—
174	C₇×#41	—	2	4	no	—
175	C₇×#41	—	2	4	no	—
176	C₇×#41	—	2	4	no	—
177	C₇×#41	—	2	4	no	—
178	C₇×#41	—	2	4	no	—
179	C₇×#41	—	2	4	no	—
180	C₇×#41	—	2	4	no	—
181	C₇×#41	—	2	4	no	—
182	C₇×#41	—	4	4	no	—
183	C₇×#41	—	4	4	no	—
184	C₂×C₇×Q₈	—	2	4	no	—
185	C₂×C₇×Q₈	—	2	1	no	—
186	C₂×C₇×Q₈	—	2	2	no	—
187	C₂×C₇×Q₈	—	2	2	no	—
188	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
189	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
190	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
191	C₂×C₇×D₄	—	2	8	no	—
192	C₂×C₇×D₄	—	2	2	no	—
193	C₂×C₇×D₄	—	2	2	no	—
194	C₂×C₇×D₄	—	2	8	no	—
195	C₂×C₇×D₄	—	2	4	no	—
196	C₂×C₇×D₄	—	2	1	no	—
197	C₂×C₇×D₄	—	2	2	no	—
198	C₂×C₇×D₄	—	2	2	no	—
199	C₂×C₇×D₄	—	4	4	no	—
200	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
201	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
202	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
203	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
204	C₂×C₇×D₄	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₇	—	2	4	no	—
206	C₂²×C₄×C₇	—	2	4	no	—
207	C₂²×C₄×C₇	—	2	1	no	—
208	C₂²×C₄×C₇	—	2	8	no	—
209	C₂²×C₄×C₇	—	2	2	no	—
210	C₂²×C₄×C₇	—	2	2	no	—
211	C₂²×C₄×C₇	—	2	2	no	—
212	C₂²×C₄×C₇	—	2	2	no	—
213	C₂²×C₄×C₇	—	2	2	no	—
214	C₂²×C₄×C₇	—	4	4	no	—
215	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₇	#41	1	4	yes	—
221	C₂²×C₄×C₇	#41	1	4	yes	—
222	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
226	C₇×M₁₆	—	2	4	no	—
227	C₇×M₁₆	—	2	4	no	—
228	C₂×C₇×C₈	—	2	4	no	—
229	C₂×C₇×C₈	—	2	4	no	—
230	C₂×C₇×C₈	—	2	2	no	—
231	C₂×C₇×C₈	—	2	2	no	—
232	C₂×C₇×C₈	—	2	4	no	—
233	C₂×C₇×C₈	C₂⁴	1	2	yes	—
234	C₂×C₇×C₈	C₂⁴	1	4	yes	—
235	C₂×C₇×C₈	C₂⁴	1	2	yes	—
236	C₇×C₄⋊C₄	—	2	8	no	—
237	C₇×C₄⋊C₄	—	2	2	no	—
238	C₇×C₄⋊C₄	—	2	2	no	—
239	C₇×C₄⋊C₄	—	2	2	no	—
240	C₇×C₄⋊C₄	—	2	8	no	—
241	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
242	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
243	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
244	C₇×C₂²⋊C₄	—	2	2	no	—
245	C₇×C₂²⋊C₄	—	2	2	no	—
246	C₇×C₂²⋊C₄	—	2	8	no	—
247	C₇×C₂²⋊C₄	—	2	2	no	—
248	C₇×C₂²⋊C₄	—	2	2	no	—
249	C₇×C₂²⋊C₄	—	2	2	no	—
250	C₇×C₂²⋊C₄	—	2	2	no	—
251	C₇×C₂²⋊C₄	—	2	8	no	—
252	C₇×C₂²⋊C₄	—	2	8	no	—
253	C₄²×C₇	—	2	8	no	—
254	C₄²×C₇	—	2	2	no	—
255	C₄²×C₇	—	2	2	no	—
256	C₄²×C₇	—	2	2	no	—
257	C₄²×C₇	—	2	2	no	—
258	C₄²×C₇	—	2	2	no	—
259	C₄²×C₇	—	2	2	no	—
260	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
261	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
262	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
263	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
264	#537	C₂²×C₇	1	4	yes	—
265	#536	—	2	1	no	—
266	#536	C₂²×C₇	1	2	yes	—
267	#535	—	2	1	no	—
268	#535	C₂²×C₇	1	2	yes	—
269	#534	—	2	2	no	—
270	#532	—	2	2	no	—
271	#525	—	2	2	no	—
272	#525	C₂²×C₇	1	4	yes	—
273	#520	C₂²×C₇	1	4	yes	—
274	#520	C₂²×C₇	1	4	yes	complemented
275	#519	—	2	1	no	—
276	#518	—	2	2	no	—
277	#518	—	2	1	no	—
278	C₄×#41	—	2	2	no	—
279	C₄×#41	—	2	2	no	—
280	C₂×#117	C₂²×C₇	1	1	yes	characteristic
281	C₂×#117	C₂²×C₇	1	1	yes	characteristic
282	C₂×#117	C₂²×C₇	1	1	yes	characteristic
283	C₂×#117	C₂²×C₇	1	4	yes	complemented
284	#485	C₂²×C₇	1	8	yes	complemented
285	#485	C₂²×C₇	1	8	yes	complemented
286	#484	C₂²×C₇	1	8	yes	complemented
287	#483	C₂²×C₇	1	8	yes	complemented
288	#482	C₂²×C₇	1	8	yes	complemented
289	#482	C₂²×C₇	1	8	yes	complemented
290	#481	C₂²×C₇	1	8	yes	complemented
291	#480	C₂²×C₇	1	8	yes	complemented
292	#428	C₂²×C₇	1	4	yes	complemented
293	#428	C₂²×C₇	1	4	yes	complemented
294	#427	C₂²×C₇	1	4	yes	complemented
295	#427	C₂²×C₇	1	4	yes	complemented
296	#427	C₂²×C₇	1	4	yes	complemented
297	C₂×#107	C₂²×C₇	1	2	yes	complemented
298	C₂×#106	C₂²×C₇	1	2	yes	complemented
299	#419	C₂²×C₇	1	2	yes	complemented
300	#418	C₂²×C₇	1	2	yes	complemented
301	#417	C₂²×C₇	1	4	yes	complemented
302	#416	C₂²×C₇	1	4	yes	—
303	#416	C₂²×C₇	1	4	yes	—
304	#416	C₂²×C₇	1	2	yes	complemented
305	#416	C₂²×C₇	1	2	yes	complemented
306	C₂×#103	C₂²×C₇	1	2	yes	complemented
307	C₂×#102	C₂²×C₇	1	2	yes	complemented
308	#408	C₂²×C₇	1	4	yes	—
309	#408	C₂²×C₇	1	2	yes	complemented
310	#408	C₂²×C₇	1	2	yes	complemented
311	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	complemented
312	C₂³×C₇	—	2	4	no	—
313	C₂³×C₇	—	2	2	no	—
314	C₂³×C₇	—	4	2	no	—
315	C₂³×C₇	—	4	4	no	—
316	C₂³×C₇	—	4	2	no	—
317	C₂³×C₇	—	8	2	no	—
318	C₂³×C₇	#123	1	4	yes	—
319	C₂³×C₇	C₂²×D₄	1	4	yes	—
320	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
322	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
323	C₇×Q₈	—	2	4	no	—
324	C₇×Q₈	—	2	4	no	—
325	C₇×Q₈	—	2	2	no	—
326	C₇×Q₈	—	2	2	no	—
327	C₇×Q₈	—	4	2	no	—
328	C₇×D₄	—	2	8	no	—
329	C₇×D₄	—	2	8	no	—
330	C₇×D₄	—	2	4	no	—
331	C₇×D₄	—	2	4	no	—
332	C₇×D₄	—	2	2	no	—
333	C₇×D₄	—	2	2	no	—
334	C₇×D₄	—	4	4	no	—
335	C₇×D₄	—	4	4	no	—
336	C₇×D₄	—	4	2	no	—
337	C₇×D₄	—	8	8	no	—
338	C₂×C₄×C₇	—	2	4	no	—
339	C₂×C₄×C₇	—	2	8	no	—
340	C₂×C₄×C₇	—	2	4	no	—
341	C₂×C₄×C₇	—	2	4	no	—
342	C₂×C₄×C₇	—	2	4	no	—
343	C₂×C₄×C₇	—	2	4	no	—
344	C₂×C₄×C₇	—	2	4	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	4	2	no	—
347	C₂×C₄×C₇	—	4	4	no	—
348	C₂×C₄×C₇	—	4	4	no	—
349	C₂×C₄×C₇	—	8	2	no	—
350	C₂×C₄×C₇	—	8	2	no	—
351	C₂×C₄×C₇	—	8	8	no	—
352	C₂×C₄×C₇	—	8	2	no	—
353	C₂×C₄×C₇	#123	1	4	yes	—
354	C₂×C₄×C₇	#123	1	4	yes	—
355	C₂×C₄×C₇	#123	1	4	yes	—
356	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₇	C₂×#41	1	2	yes	—
361	C₂×C₄×C₇	C₂×#41	1	2	yes	—
362	C₂×C₄×C₇	C₂×#41	1	2	yes	—
363	C₂×C₄×C₇	C₂×#41	1	2	yes	—
364	C₂×C₄×C₇	C₂×#41	1	2	yes	—
365	C₂×C₄×C₇	C₂×#41	1	2	yes	—
366	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
367	C₇×C₈	—	2	2	no	—
368	C₇×C₈	—	2	2	no	—
369	C₇×C₈	—	2	4	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	4	no	—
373	C₂×#41	—	2	4	no	—
374	C₂×#41	—	2	4	no	—
375	C₂×#41	—	2	4	no	—
376	C₂×#41	C₇×D₄	1	2	yes	—
377	C₂×#41	C₇×D₄	1	2	yes	—
378	C₂×#41	C₂³×C₇	1	2	yes	—
379	C₂×#41	C₂³×C₇	1	2	yes	—
380	C₂×#41	C₂³×C₇	1	2	yes	—
381	C₂×#41	C₂³×C₇	1	2	yes	—
382	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²×D₄	—	2	1	no	—
385	C₂²×D₄	C₇×D₄	1	2	yes	—
386	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	C₂³×C₇	1	2	yes	—
390	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
391	C₂×M₁₆	—	2	4	no	—
392	C₂×M₁₆	C₂³×C₇	1	2	yes	—
393	C₂×M₁₆	C₂³×C₇	1	2	yes	—
394	C₂²×C₈	—	2	4	no	—
395	C₂²×C₈	C₂³×C₇	1	2	yes	—
396	C₂²×C₈	C₂³×C₇	1	2	yes	—
397	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₇	1	2	yes	—
400	C₄⋊Q₈	—	2	2	no	—
401	#127	—	2	2	no	—
402	#124	—	2	2	no	—
403	#124	—	2	2	no	—
404	#123	—	2	4	no	—
405	#123	—	2	4	no	—
406	C₂²⋊Q₈	—	2	4	no	—
407	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
408	#121	—	2	4	no	—
409	#121	—	2	8	no	—
410	#121	C₂³×C₇	1	8	yes	—
411	#120	—	2	4	no	—
412	#120	—	2	4	no	—
413	C₄×Q₈	—	2	4	no	—
414	C₄×Q₈	—	2	4	no	—
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	4	no	—
417	C₄×D₄	—	2	8	no	—
418	C₄×D₄	—	2	4	no	—
419	C₄×D₄	—	2	8	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	1	no	—
423	#117	—	2	1	no	—
424	#117	—	2	1	no	—
425	#117	—	2	1	no	—
426	#117	—	2	4	no	—
427	#117	—	2	4	no	—
428	#117	C₂³×C₇	1	2	yes	—
429	#117	C₂³×C₇	1	2	yes	—
430	#117	C₂³×C₇	1	2	yes	—
431	#117	C₂³×C₇	1	2	yes	—
432	#117	C₂³×C₇	1	2	yes	—
433	#117	C₂³×C₇	1	2	yes	—
434	#117	C₂³×C₇	1	8	yes	—
435	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	4	no	—
447	#107	C₂³×C₇	1	4	yes	—
448	#107	C₂³×C₇	1	4	yes	—
449	#107	C₂³×C₇	1	8	yes	—
450	#106	C₂³×C₇	1	4	yes	—
451	#106	C₂³×C₇	1	4	yes	—
452	#106	C₂³×C₇	1	8	yes	—
453	#103	C₂³×C₇	1	4	yes	—
454	#103	C₂³×C₇	1	4	yes	—
455	#103	C₂³×C₇	1	8	yes	—
456	#102	C₂³×C₇	1	4	yes	—
457	#102	C₂³×C₇	1	4	yes	—
458	#102	C₂³×C₇	1	8	yes	—
459	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
460	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
461	C₂²×C₇	—	2	2	no	—
462	C₂²×C₇	—	2	2	no	—
463	C₂²×C₇	—	2	2	no	—
464	C₂²×C₇	—	2	8	no	—
465	C₂²×C₇	—	2	4	no	—
466	C₂²×C₇	—	4	4	no	—
467	C₂²×C₇	—	4	4	no	—
468	C₂²×C₇	—	4	2	no	—
469	C₂²×C₇	—	8	4	no	—
470	C₂²×C₇	—	8	4	no	—
471	C₂²×C₇	C₂×#123	1	2	yes	—
472	C₂²×C₇	C₂×#123	1	2	yes	—
473	C₂²×C₇	C₂×#123	1	2	yes	—
474	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
475	C₄×C₇	—	2	4	no	—
476	C₄×C₇	—	4	4	no	—
477	C₄×C₇	—	4	4	no	—
478	C₄×C₇	—	4	4	no	—
479	C₄×C₇	—	4	2	no	—
480	C₄×C₇	C₂×#123	1	2	yes	—
481	C₄×C₇	C₂×#123	1	2	yes	—
482	C₄×C₇	C₂×#123	1	2	yes	—
483	C₄×C₇	C₂²×#41	1	1	yes	characteristic
484	C₄×C₇	C₂²×#41	1	1	yes	characteristic
485	C₂⁴	—	2	1	no	—
486	C₂⁴	C₂×C₇×D₄	1	2	yes	—
487	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
488	#41	—	2	8	no	—
489	#41	—	2	8	no	—
490	#41	—	2	4	no	—
491	#41	—	2	4	no	—
492	#41	—	2	4	no	—
493	#41	—	2	4	no	—
494	#41	—	2	4	no	—
495	#41	—	2	4	no	—
496	#41	—	2	4	no	—
497	#41	—	2	4	no	—
498	#41	—	4	4	no	—
499	#41	—	4	4	no	—
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
505	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
506	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
517	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
518	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
519	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
520	C₂×D₄	C₂⁴×C₇	1	2	yes	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
532	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
533	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
536	C₂²×C₄	C₇×#41	1	4	yes	—
537	C₂²×C₄	C₇×#41	1	4	yes	—
538	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
542	M₁₆	—	2	4	no	—
543	M₁₆	—	2	4	no	—
544	C₂×C₈	—	2	4	no	—
545	C₂×C₈	—	2	4	no	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	4	no	—
549	C₂×C₈	C₂⁴×C₇	1	2	yes	—
550	C₂×C₈	C₂⁴×C₇	1	4	yes	—
551	C₂×C₈	C₂⁴×C₇	1	2	yes	—
552	C₄⋊C₄	—	2	8	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
558	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
559	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	8	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	8	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₂×C₇	—	2	2	no	—
577	C₂×C₇	—	2	2	no	—
578	C₂×C₇	—	2	2	no	—
579	C₂×C₇	—	4	4	no	—
580	C₂×C₇	—	8	2	no	—
581	C₂×C₇	C₂²×#123	1	1	yes	characteristic
582	C₂×C₇	#3584	1	2	yes	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	4	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	8	2	no	—
589	C₂³	C₇×#123	1	4	yes	—
590	C₂³	C₂²×C₇×D₄	1	4	yes	—
591	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
592	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
593	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
594	Q₈	—	2	4	no	—
595	Q₈	—	2	4	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	4	2	no	—
599	D₄	—	2	8	no	—
600	D₄	—	2	8	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	4	4	no	—
606	D₄	—	4	4	no	—
607	D₄	—	4	2	no	—
608	D₄	—	8	8	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	8	8	no	—
623	C₂×C₄	—	8	2	no	—
624	C₂×C₄	C₇×#123	1	4	yes	—
625	C₂×C₄	C₇×#123	1	4	yes	—
626	C₂×C₄	C₇×#123	1	4	yes	—
627	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
628	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
629	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
630	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
631	C₂×C₄	C₂×C₇×#41	1	2	yes	—
632	C₂×C₄	C₂×C₇×#41	1	2	yes	—
633	C₂×C₄	C₂×C₇×#41	1	2	yes	—
634	C₂×C₄	C₂×C₇×#41	1	2	yes	—
635	C₂×C₄	C₂×C₇×#41	1	2	yes	—
636	C₂×C₄	C₂×C₇×#41	1	2	yes	—
637	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	4	no	—
641	C₇	#60516	1	1	yes	characteristic, direct product factor, Sylow
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	8	4	no	—
651	C₂²	—	8	4	no	—
652	C₂²	C₂×C₇×#123	1	2	yes	—
653	C₂²	C₂×C₇×#123	1	2	yes	—
654	C₂²	C₂×C₇×#123	1	2	yes	—
655	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
656	C₄	—	2	4	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	4	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	2	no	—
661	C₄	C₂×C₇×#123	1	2	yes	—
662	C₄	C₂×C₇×#123	1	2	yes	—
663	C₄	C₂×C₇×#123	1	2	yes	—
664	C₄	C₂²×C₇×#41	1	1	yes	characteristic
665	C₄	C₂²×C₇×#41	1	1	yes	characteristic
666	C₂	—	2	2	no	—
667	C₂	—	2	2	no	—
668	C₂	—	2	2	no	—
669	C₂	—	4	4	no	—
670	C₂	—	8	2	no	—
671	C₂	C₂²×C₇×#123	1	1	yes	characteristic
672	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	C₇×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3428	C₂	semidirect
3. C₇×#3099	C₂	semidirect
4. C₇×#3098	C₂	semidirect
5. C₇×#3097	C₂	semidirect
6. C₇×#3096	C₂	semidirect
7. C₇×#3091	C₂	semidirect
8. C₇×#2911	C₂	semidirect
9. C₂×C₇×#427	C₂	semidirect
10. C₇×#2896	C₂	semidirect
11. C₂×C₇×#416	C₂	semidirect
12. C₂×C₇×#408	C₂	semidirect
27. C₇×#520	C₂²	semidirect
36. C₂×C₇×#117	C₂²	semidirect
37. C₇×#485	C₂²	semidirect
38. C₇×#485	C₂²	semidirect
39. C₇×#484	C₂²	semidirect
40. C₇×#483	C₂²	semidirect
41. C₇×#482	C₂²	semidirect
42. C₇×#482	C₂²	semidirect
43. C₇×#481	C₂²	semidirect
44. C₇×#480	C₂²	semidirect
45. C₇×#428	C₂²	semidirect
46. C₇×#428	C₂²	semidirect
47. C₇×#427	C₂²	semidirect
48. C₇×#427	C₂²	semidirect
49. C₇×#427	C₂²	semidirect
50. C₂×C₇×#107	C₂²	semidirect
51. C₂×C₇×#106	C₂²	semidirect
52. C₇×#419	C₂²	semidirect
53. C₇×#418	C₂²	semidirect
54. C₇×#417	C₂²	semidirect
57. C₇×#416	C₂²	semidirect
58. C₇×#416	C₂²	semidirect
59. C₂×C₇×#103	C₂²	semidirect
60. C₂×C₇×#102	C₂²	semidirect
62. C₇×#408	C₂²	semidirect
63. C₇×#408	C₂²	semidirect
64. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
65. #60516	C₇	direct (N × H)
158. #3428	C₂×C₇	semidirect
159. #3099	C₂×C₇	semidirect
160. #3098	C₂×C₇	semidirect
161. #3097	C₂×C₇	semidirect
162. #3096	C₂×C₇	semidirect
163. #3091	C₂×C₇	semidirect
164. #2911	C₂×C₇	semidirect
165. C₂×#427	C₂×C₇	semidirect
166. #2896	C₂×C₇	semidirect
167. C₂×#416	C₂×C₇	semidirect
168. C₂×#408	C₂×C₇	semidirect
274. #520	C₂²×C₇	semidirect
283. C₂×#117	C₂²×C₇	semidirect
284. #485	C₂²×C₇	semidirect
285. #485	C₂²×C₇	semidirect
286. #484	C₂²×C₇	semidirect
287. #483	C₂²×C₇	semidirect
288. #482	C₂²×C₇	semidirect
289. #482	C₂²×C₇	semidirect
290. #481	C₂²×C₇	semidirect
291. #480	C₂²×C₇	semidirect
292. #428	C₂²×C₇	semidirect
293. #428	C₂²×C₇	semidirect
294. #427	C₂²×C₇	semidirect
295. #427	C₂²×C₇	semidirect
296. #427	C₂²×C₇	semidirect
297. C₂×#107	C₂²×C₇	semidirect
298. C₂×#106	C₂²×C₇	semidirect
299. #419	C₂²×C₇	semidirect
300. #418	C₂²×C₇	semidirect
301. #417	C₂²×C₇	semidirect
304. #416	C₂²×C₇	semidirect
305. #416	C₂²×C₇	semidirect
306. C₂×#103	C₂²×C₇	semidirect
307. C₂×#102	C₂²×C₇	semidirect
309. #408	C₂²×C₇	semidirect
310. #408	C₂²×C₇	semidirect
311. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
641. C₇	#60516	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×#3449	2
C₇×#3428	2
C₇×#3099	2
C₇×#3098	2
C₇×#3097	2
C₇×#3096	2
C₇×#3091	2
C₇×#2911	2
C₂×C₇×#427	2
C₇×#2896	2
C₂×C₇×#416	2
C₂×C₇×#408	2
#60516	7

Subgroups — C7×#60516 #13237732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60516 #13237732