Subgroups — C₇×#61337 #13238553

Order 1792.

1852 conjugacy classes of subgroups.

The subgroup lattice has 688 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, complemented
2	C₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3371	C₂	1	4	yes	maximal, complemented
4	C₇×#3370	C₂	1	4	yes	maximal, complemented
5	C₇×#3368	C₂	1	4	yes	maximal, complemented
6	C₇×#3366	C₂	1	4	yes	maximal, complemented
7	C₇×#3136	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3081	C₂	1	2	yes	maximal, complemented
10	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3045	C₂	1	2	yes	maximal, complemented
12	C₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2946	C₂	1	2	yes	maximal, complemented
15	C₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₇×#135	C₂²	1	1	yes	characteristic
18	C₇×#559	C₂²	1	4	yes	—
19	C₇×#557	C₂²	1	4	yes	complemented
20	C₇×#554	—	2	4	no	—
21	C₇×#554	C₂²	1	4	yes	complemented
22	C₇×#550	C₂²	1	4	yes	—
23	C₇×#546	—	2	4	no	—
24	C₇×#544	—	2	2	no	—
25	C₇×#544	C₂²	1	2	yes	—
26	C₇×#540	—	2	1	no	—
27	C₇×#540	—	2	1	no	—
28	C₇×#535	C₂²	1	2	yes	—
29	C₇×#533	—	2	1	no	—
30	C₇×#533	C₂²	1	1	yes	characteristic
31	C₇×#532	—	2	2	no	—
32	C₂×C₇×#127	C₂²	1	1	yes	characteristic
33	C₂×C₇×#125	—	2	1	no	—
34	C₂×C₇×#125	C₂²	1	1	yes	characteristic
35	C₇×#520	C₂²	1	2	yes	—
36	C₇×#518	C₂²	1	2	yes	—
37	C₄×C₇×#41	C₂²	1	1	yes	characteristic
38	C₄×C₇×#41	C₂²	1	1	yes	characteristic
39	C₇×#490	C₂²	1	4	yes	—
40	C₇×#490	C₂²	1	4	yes	—
41	C₇×#490	C₂²	1	4	yes	complemented
42	C₇×#489	C₂²	1	4	yes	complemented
43	C₇×#488	C₂²	1	4	yes	complemented
44	C₇×#486	C₂²	1	4	yes	complemented
45	C₇×#479	C₂²	1	4	yes	complemented
46	C₇×#478	C₂²	1	4	yes	complemented
47	C₇×#478	C₂²	1	4	yes	complemented
48	C₇×#478	C₂²	1	4	yes	complemented
49	C₇×#476	C₂²	1	4	yes	complemented
50	C₇×#474	C₂²	1	4	yes	complemented
51	C₇×#464	C₂²	1	4	yes	complemented
52	C₇×#463	C₂²	1	4	yes	complemented
53	C₇×#460	C₂²	1	4	yes	—
54	C₇×#460	C₂²	1	4	yes	complemented
55	C₇×#459	C₂²	1	4	yes	—
56	C₇×#459	C₂²	1	4	yes	complemented
57	C₇×#446	C₂²	1	4	yes	complemented
58	C₇×#446	C₂²	1	4	yes	complemented
59	C₇×#442	C₂²	1	2	yes	complemented
60	C₇×#442	C₂²	1	4	yes	complemented
61	C₇×#441	C₂²	1	2	yes	complemented
62	C₇×#440	C₂²	1	2	yes	complemented
63	C₇×#440	C₂²	1	2	yes	complemented
64	C₇×#440	C₂²	1	4	yes	complemented
65	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
66	C₄×C₇×D₈	C₂²	1	4	yes	complemented
67	C₇×#428	C₂²	1	2	yes	—
68	C₇×#427	C₂²	1	1	yes	characteristic
69	C₇×#424	C₂²	1	2	yes	—
70	C₇×#423	C₂²	1	1	yes	characteristic
71	C₇×#418	C₂²	1	2	yes	—
72	C₇×#417	C₂²	1	2	yes	—
73	C₇×#416	C₂²	1	1	yes	characteristic
74	C₇×#416	C₂²	1	1	yes	characteristic
75	C₂×C₇×#102	C₂²	1	2	yes	—
76	C₂×C₇×#102	C₂²	1	2	yes	—
77	C₇×#405	C₂²	1	2	yes	—
78	C₂×C₇×#97	C₂²	1	1	yes	characteristic
79	#61337	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	4	no	—
81	C₂×C₇×#41	C₂³	1	1	yes	characteristic
82	C₂×C₇×#41	C₂³	1	1	yes	characteristic
83	C₂²×C₇×D₄	—	2	2	no	—
84	C₂²×C₇×D₄	C₂³	1	2	yes	—
85	C₇×AGL(1,ℤ/8)	—	2	8	no	—
86	C₇×#135	—	2	4	no	—
87	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
91	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
92	C₂×C₇×D₈	C₂³	1	4	yes	—
93	C₂×C₇×M₁₆	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	4	no	—
97	C₇×C₄⋊Q₈	—	2	2	no	—
98	C₇×C₄⋊Q₈	D₄	1	2	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₇×#127	—	2	1	no	—
101	C₇×#127	—	2	1	no	—
102	C₇×#127	C₂³	1	4	yes	—
103	C₇×#127	C₂³	1	4	yes	—
104	C₇×#125	—	2	2	no	—
105	C₇×#125	—	2	4	no	—
106	C₇×#125	—	2	4	no	—
107	C₇×#125	—	2	1	no	—
108	C₇×#125	—	2	1	no	—
109	C₇×#125	D₄	1	1	yes	characteristic
110	C₇×#125	D₄	1	1	yes	characteristic
111	C₇×#125	C₂³	1	4	yes	—
112	C₇×#125	C₂³	1	4	yes	—
113	C₇×#124	—	2	4	no	—
114	C₇×#124	C₂³	1	4	yes	—
115	C₇×#123	—	2	4	no	—
116	C₇×#123	—	2	4	no	—
117	C₇×C₂²⋊Q₈	—	2	4	no	—
118	C₇×C₂²⋊Q₈	—	2	4	no	—
119	C₇×C₂²⋊Q₈	—	2	4	no	—
120	C₇×C₂²⋊Q₈	—	2	4	no	—
121	C₇×C₂²⋊Q₈	D₄	1	4	yes	—
122	C₇×#121	—	2	2	no	—
123	C₇×#121	—	2	2	no	—
124	C₇×#121	—	2	4	no	—
125	C₇×#121	—	2	4	no	—
126	C₇×#121	—	2	4	no	—
127	C₇×#120	—	2	4	no	—
128	C₄×C₇×Q₈	—	2	4	no	—
129	C₄×C₇×Q₈	C₂³	1	2	yes	—
130	C₄×C₇×Q₈	C₂³	1	2	yes	—
131	C₄×C₇×Q₈	C₂³	1	4	yes	—
132	C₄×C₇×Q₈	C₂³	1	4	yes	—
133	C₄×C₇×D₄	—	2	2	no	—
134	C₄×C₇×D₄	—	2	2	no	—
135	C₄×C₇×D₄	—	2	2	no	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	—	2	4	no	—
138	C₄×C₇×D₄	—	2	4	no	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₄×C₇×D₄	C₂³	1	4	yes	—
141	C₄×C₇×D₄	C₂³	1	2	yes	—
142	C₄×C₇×D₄	C₂³	1	2	yes	—
143	C₄×C₇×D₄	C₂³	1	4	yes	—
144	C₇×#117	—	2	2	no	—
145	C₇×#117	—	2	1	no	—
146	C₇×#117	—	2	1	no	—
147	C₇×#117	C₂³	1	1	yes	characteristic
148	C₇×#117	C₂³	1	1	yes	characteristic
149	C₇×#117	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	—	2	2	no	—
151	C₂×C₇×C₄⋊C₄	—	2	2	no	—
152	C₂×C₇×C₄⋊C₄	—	2	4	no	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
155	C₂×C₄²×C₇	—	2	1	no	—
156	C₂×C₄²×C₇	—	2	1	no	—
157	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
158	C₇×#107	C₂³	1	2	yes	—
159	C₇×#107	C₂³	1	4	yes	—
160	C₇×#106	C₂³	1	2	yes	—
161	C₇×#106	C₂³	1	4	yes	—
162	C₇×C₄⋊C₈	C₂³	1	4	yes	—
163	C₇×C₄⋊C₈	C₂³	1	4	yes	—
164	C₇×C₄⋊C₈	C₂³	1	4	yes	—
165	C₇×#103	C₂³	1	4	yes	—
166	C₇×#103	C₂³	1	2	yes	—
167	C₇×#103	C₂³	1	2	yes	—
168	C₇×#102	C₂³	1	4	yes	—
169	C₇×#102	C₂³	1	4	yes	—
170	C₇×#102	C₂³	1	4	yes	—
171	C₇×#102	C₂³	1	4	yes	—
172	C₇×#102	C₂³	1	4	yes	—
173	C₇×#102	C₂³	1	2	yes	—
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	2	yes	—
177	C₇×#97	C₂³	1	4	yes	—
178	C₇×#97	C₂³	1	2	yes	—
179	C₇×#97	C₂³	1	2	yes	—
180	C₄×C₇×C₈	C₂³	1	4	yes	—
181	#3508	C₂×C₇	1	1	yes	characteristic, complemented
182	#3504	C₂×C₇	1	1	yes	characteristic, complemented
183	#3371	C₂×C₇	1	4	yes	complemented
184	#3370	C₂×C₇	1	4	yes	complemented
185	#3368	C₂×C₇	1	4	yes	complemented
186	#3366	C₂×C₇	1	4	yes	complemented
187	#3136	C₂×C₇	1	2	yes	complemented
188	C₂×#490	C₂×C₇	1	1	yes	characteristic, complemented
189	#3081	C₂×C₇	1	2	yes	complemented
190	#3080	C₂×C₇	1	1	yes	characteristic, complemented
191	#3045	C₂×C₇	1	2	yes	complemented
192	#3038	C₂×C₇	1	1	yes	characteristic, complemented
193	#2961	C₂×C₇	1	1	yes	characteristic, complemented
194	#2946	C₂×C₇	1	2	yes	complemented
195	#2943	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂⁴×C₇	—	2	2	no	—
197	C₇×#41	—	2	2	no	—
198	C₇×#41	—	2	2	no	—
199	C₇×#41	—	2	2	no	—
200	C₇×#41	—	8	8	no	—
201	C₇×#41	#41	1	4	yes	complemented
202	C₂×C₇×Q₈	—	2	4	no	—
203	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
204	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
205	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
206	C₂×C₇×D₄	—	2	1	no	—
207	C₂×C₇×D₄	—	2	1	no	—
208	C₂×C₇×D₄	—	2	2	no	—
209	C₂×C₇×D₄	—	2	4	no	—
210	C₂×C₇×D₄	—	2	4	no	—
211	C₂×C₇×D₄	—	2	4	no	—
212	C₂×C₇×D₄	—	2	4	no	—
213	C₂×C₇×D₄	—	2	4	no	—
214	C₂×C₇×D₄	—	2	4	no	—
215	C₂×C₇×D₄	—	8	4	no	—
216	C₂×C₇×D₄	C₂⁴	1	4	yes	—
217	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
218	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₇	—	2	1	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	1	no	—
222	C₂²×C₄×C₇	—	2	2	no	—
223	C₂²×C₄×C₇	—	2	2	no	—
224	C₂²×C₄×C₇	—	2	4	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	C₂⁴	1	1	yes	characteristic
229	C₇×Q₁₆	—	2	2	no	—
230	C₇×SD₁₆	—	2	2	no	—
231	C₇×SD₁₆	—	2	8	no	—
232	C₇×SD₁₆	—	2	2	no	—
233	C₇×D₈	—	2	2	no	—
234	C₇×D₈	—	2	8	no	—
235	C₇×M₁₆	—	2	4	no	—
236	C₂×C₇×C₈	—	2	2	no	—
237	C₂×C₇×C₈	—	2	2	no	—
238	C₂×C₇×C₈	C₂⁴	1	2	yes	—
239	C₂×C₇×C₈	C₂⁴	1	4	yes	—
240	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
241	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
242	C₇×C₄⋊C₄	—	2	4	no	—
243	C₇×C₄⋊C₄	—	2	2	no	—
244	C₇×C₄⋊C₄	—	2	4	no	—
245	C₇×C₄⋊C₄	—	2	4	no	—
246	C₇×C₄⋊C₄	—	2	4	no	—
247	C₇×C₄⋊C₄	—	2	4	no	—
248	C₇×C₄⋊C₄	—	2	2	no	—
249	C₇×C₄⋊C₄	—	2	2	no	—
250	C₇×C₄⋊C₄	—	2	4	no	—
251	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
252	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
253	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
254	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
255	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
256	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
257	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
258	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
259	C₇×C₂²⋊C₄	—	2	1	no	—
260	C₇×C₂²⋊C₄	—	2	1	no	—
261	C₇×C₂²⋊C₄	—	2	4	no	—
262	C₇×C₂²⋊C₄	—	2	4	no	—
263	C₇×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	4	yes	—
269	C₄²×C₇	—	2	1	no	—
270	C₄²×C₇	—	2	1	no	—
271	C₄²×C₇	—	2	2	no	—
272	C₄²×C₇	—	2	2	no	—
273	C₄²×C₇	—	2	4	no	—
274	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₇	C₂⁴	1	4	yes	—
277	C₄²×C₇	C₂⁴	1	2	yes	—
278	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
279	C₂×#135	C₂²×C₇	1	1	yes	characteristic
280	#559	C₂²×C₇	1	4	yes	—
281	#557	C₂²×C₇	1	4	yes	complemented
282	#554	—	2	4	no	—
283	#554	C₂²×C₇	1	4	yes	complemented
284	#550	C₂²×C₇	1	4	yes	—
285	#546	—	2	4	no	—
286	#544	—	2	2	no	—
287	#544	C₂²×C₇	1	2	yes	—
288	#540	—	2	1	no	—
289	#540	—	2	1	no	—
290	#535	C₂²×C₇	1	2	yes	—
291	#533	—	2	1	no	—
292	#533	C₂²×C₇	1	1	yes	characteristic
293	#532	—	2	2	no	—
294	C₂×#127	C₂²×C₇	1	1	yes	characteristic
295	C₂×#125	—	2	1	no	—
296	C₂×#125	C₂²×C₇	1	1	yes	characteristic
297	#520	C₂²×C₇	1	2	yes	—
298	#518	C₂²×C₇	1	2	yes	—
299	C₄×#41	C₂²×C₇	1	1	yes	characteristic
300	C₄×#41	C₂²×C₇	1	1	yes	characteristic
301	#490	C₂²×C₇	1	4	yes	—
302	#490	C₂²×C₇	1	4	yes	—
303	#490	C₂²×C₇	1	4	yes	complemented
304	#489	C₂²×C₇	1	4	yes	complemented
305	#488	C₂²×C₇	1	4	yes	complemented
306	#486	C₂²×C₇	1	4	yes	complemented
307	#479	C₂²×C₇	1	4	yes	complemented
308	#478	C₂²×C₇	1	4	yes	complemented
309	#478	C₂²×C₇	1	4	yes	complemented
310	#478	C₂²×C₇	1	4	yes	complemented
311	#476	C₂²×C₇	1	4	yes	complemented
312	#474	C₂²×C₇	1	4	yes	complemented
313	#464	C₂²×C₇	1	4	yes	complemented
314	#463	C₂²×C₇	1	4	yes	complemented
315	#460	C₂²×C₇	1	4	yes	—
316	#460	C₂²×C₇	1	4	yes	complemented
317	#459	C₂²×C₇	1	4	yes	—
318	#459	C₂²×C₇	1	4	yes	complemented
319	#446	C₂²×C₇	1	4	yes	complemented
320	#446	C₂²×C₇	1	4	yes	complemented
321	#442	C₂²×C₇	1	2	yes	complemented
322	#442	C₂²×C₇	1	4	yes	complemented
323	#441	C₂²×C₇	1	2	yes	complemented
324	#440	C₂²×C₇	1	2	yes	complemented
325	#440	C₂²×C₇	1	4	yes	complemented
326	#440	C₂²×C₇	1	2	yes	complemented
327	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
328	C₄×D₈	C₂²×C₇	1	4	yes	complemented
329	#428	C₂²×C₇	1	2	yes	—
330	#427	C₂²×C₇	1	1	yes	characteristic
331	#424	C₂²×C₇	1	2	yes	—
332	#423	C₂²×C₇	1	1	yes	characteristic
333	#418	C₂²×C₇	1	2	yes	—
334	#417	C₂²×C₇	1	2	yes	—
335	#416	C₂²×C₇	1	1	yes	characteristic
336	#416	C₂²×C₇	1	1	yes	characteristic
337	C₂×#102	C₂²×C₇	1	2	yes	—
338	C₂×#102	C₂²×C₇	1	2	yes	—
339	#405	C₂²×C₇	1	2	yes	—
340	C₂×#97	C₂²×C₇	1	1	yes	characteristic
341	C₂³×C₇	—	2	1	no	—
342	C₂³×C₇	—	2	4	no	—
343	C₂³×C₇	—	2	1	no	—
344	C₂³×C₇	—	4	4	no	—
345	C₂³×C₇	—	8	2	no	—
346	C₂³×C₇	—	8	2	no	—
347	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
348	C₇×Q₈	—	2	1	no	—
349	C₇×Q₈	—	2	1	no	—
350	C₇×Q₈	—	2	1	no	—
351	C₇×Q₈	—	4	4	no	—
352	C₇×Q₈	—	8	4	no	—
353	C₇×Q₈	C₂×#41	1	2	yes	—
354	C₇×D₄	—	2	4	no	—
355	C₇×D₄	—	2	4	no	—
356	C₇×D₄	—	2	1	no	—
357	C₇×D₄	—	2	1	no	—
358	C₇×D₄	—	2	4	no	—
359	C₇×D₄	—	2	1	no	—
360	C₇×D₄	—	4	8	no	—
361	C₇×D₄	—	4	2	no	—
362	C₇×D₄	—	4	4	no	—
363	C₇×D₄	—	8	4	no	—
364	C₇×D₄	—	8	4	no	—
365	C₇×D₄	—	8	4	no	—
366	C₇×D₄	C₂×#41	1	2	yes	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	4	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	4	no	—
373	C₂×C₄×C₇	—	4	2	no	—
374	C₂×C₄×C₇	—	4	4	no	—
375	C₂×C₄×C₇	—	4	2	no	—
376	C₂×C₄×C₇	—	8	2	no	—
377	C₂×C₄×C₇	—	8	4	no	—
378	C₂×C₄×C₇	—	8	4	no	—
379	C₂×C₄×C₇	—	8	4	no	—
380	C₂×C₄×C₇	—	8	2	no	—
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	4	yes	—
384	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₇	C₂×#41	1	2	yes	—
387	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
388	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
389	C₇×C₈	—	2	1	no	—
390	C₇×C₈	—	2	1	no	—
391	C₇×C₈	—	2	4	no	—
392	C₇×C₈	—	2	2	no	—
393	C₂×#41	—	2	4	no	—
394	C₂×#41	C₂³×C₇	1	1	yes	characteristic
395	C₂×#41	C₂³×C₇	1	1	yes	characteristic
396	C₂²×D₄	—	2	2	no	—
397	C₂²×D₄	C₂³×C₇	1	2	yes	—
398	AGL(1,ℤ/8)	—	2	8	no	—
399	#135	—	2	4	no	—
400	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
401	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
402	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
403	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
404	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
405	C₂×D₈	C₂³×C₇	1	4	yes	—
406	C₂×M₁₆	C₂³×C₇	1	2	yes	—
407	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
409	C₄⋊Q₈	—	2	4	no	—
410	C₄⋊Q₈	—	2	2	no	—
411	C₄⋊Q₈	C₇×D₄	1	2	yes	—
412	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
413	#127	—	2	1	no	—
414	#127	—	2	1	no	—
415	#127	C₂³×C₇	1	4	yes	—
416	#127	C₂³×C₇	1	4	yes	—
417	#125	—	2	2	no	—
418	#125	—	2	4	no	—
419	#125	—	2	4	no	—
420	#125	—	2	1	no	—
421	#125	—	2	1	no	—
422	#125	C₇×D₄	1	1	yes	characteristic
423	#125	C₇×D₄	1	1	yes	characteristic
424	#125	C₂³×C₇	1	4	yes	—
425	#125	C₂³×C₇	1	4	yes	—
426	#124	—	2	4	no	—
427	#124	C₂³×C₇	1	4	yes	—
428	#123	—	2	4	no	—
429	#123	—	2	4	no	—
430	C₂²⋊Q₈	—	2	4	no	—
431	C₂²⋊Q₈	—	2	4	no	—
432	C₂²⋊Q₈	—	2	4	no	—
433	C₂²⋊Q₈	—	2	4	no	—
434	C₂²⋊Q₈	C₇×D₄	1	4	yes	—
435	#121	—	2	2	no	—
436	#121	—	2	2	no	—
437	#121	—	2	4	no	—
438	#121	—	2	4	no	—
439	#121	—	2	4	no	—
440	#120	—	2	4	no	—
441	C₄×Q₈	—	2	4	no	—
442	C₄×Q₈	C₂³×C₇	1	2	yes	—
443	C₄×Q₈	C₂³×C₇	1	2	yes	—
444	C₄×Q₈	C₂³×C₇	1	4	yes	—
445	C₄×Q₈	C₂³×C₇	1	4	yes	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	2	4	no	—
452	C₄×D₄	C₂³×C₇	1	2	yes	—
453	C₄×D₄	C₂³×C₇	1	2	yes	—
454	C₄×D₄	C₂³×C₇	1	4	yes	—
455	C₄×D₄	C₂³×C₇	1	4	yes	—
456	C₄×D₄	C₂³×C₇	1	4	yes	—
457	#117	—	2	2	no	—
458	#117	—	2	1	no	—
459	#117	—	2	1	no	—
460	#117	C₂³×C₇	1	1	yes	characteristic
461	#117	C₂³×C₇	1	1	yes	characteristic
462	#117	C₂³×C₇	1	2	yes	—
463	C₂×C₄⋊C₄	—	2	2	no	—
464	C₂×C₄⋊C₄	—	2	2	no	—
465	C₂×C₄⋊C₄	—	2	4	no	—
466	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	2	1	no	—
470	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
471	#107	C₂³×C₇	1	2	yes	—
472	#107	C₂³×C₇	1	4	yes	—
473	#106	C₂³×C₇	1	2	yes	—
474	#106	C₂³×C₇	1	4	yes	—
475	C₄⋊C₈	C₂³×C₇	1	4	yes	—
476	C₄⋊C₈	C₂³×C₇	1	4	yes	—
477	C₄⋊C₈	C₂³×C₇	1	4	yes	—
478	#103	C₂³×C₇	1	2	yes	—
479	#103	C₂³×C₇	1	2	yes	—
480	#103	C₂³×C₇	1	4	yes	—
481	#102	C₂³×C₇	1	4	yes	—
482	#102	C₂³×C₇	1	4	yes	—
483	#102	C₂³×C₇	1	4	yes	—
484	#102	C₂³×C₇	1	4	yes	—
485	#102	C₂³×C₇	1	2	yes	—
486	#102	C₂³×C₇	1	2	yes	—
487	#102	C₂³×C₇	1	4	yes	—
488	#102	C₂³×C₇	1	4	yes	—
489	#102	C₂³×C₇	1	4	yes	—
490	#97	C₂³×C₇	1	2	yes	—
491	#97	C₂³×C₇	1	2	yes	—
492	#97	C₂³×C₇	1	4	yes	—
493	C₄×C₈	C₂³×C₇	1	4	yes	—
494	C₂²×C₇	—	2	2	no	—
495	C₂²×C₇	—	2	2	no	—
496	C₂²×C₇	—	4	2	no	—
497	C₂²×C₇	—	4	2	no	—
498	C₂²×C₇	—	4	4	no	—
499	C₂²×C₇	—	4	4	no	—
500	C₂²×C₇	—	4	1	no	—
501	C₂²×C₇	—	4	4	no	—
502	C₂²×C₇	—	16	4	no	—
503	C₂²×C₇	#548	1	2	yes	—
504	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₇	—	2	2	no	—
506	C₄×C₇	—	2	2	no	—
507	C₄×C₇	—	2	4	no	—
508	C₄×C₇	—	2	4	no	—
509	C₄×C₇	—	2	2	no	—
510	C₄×C₇	—	4	2	no	—
511	C₄×C₇	—	4	4	no	—
512	C₄×C₇	—	4	2	no	—
513	C₄×C₇	—	4	1	no	—
514	C₄×C₇	#548	1	2	yes	—
515	C₄×C₇	C₂²×#41	1	1	yes	characteristic
516	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
517	C₂⁴	—	2	2	no	—
518	#41	—	2	2	no	—
519	#41	—	2	2	no	—
520	#41	—	2	2	no	—
521	#41	—	8	8	no	—
522	#41	C₇×#41	1	4	yes	complemented
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
525	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
526	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	8	4	no	—
537	C₂×D₄	C₂⁴×C₇	1	4	yes	—
538	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
539	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
550	Q₁₆	—	2	2	no	—
551	SD₁₆	—	2	2	no	—
552	SD₁₆	—	2	8	no	—
553	SD₁₆	—	2	2	no	—
554	D₈	—	2	2	no	—
555	D₈	—	2	8	no	—
556	M₁₆	—	2	4	no	—
557	C₂×C₈	—	2	2	no	—
558	C₂×C₈	—	2	2	no	—
559	C₂×C₈	C₂⁴×C₇	1	2	yes	—
560	C₂×C₈	C₂⁴×C₇	1	4	yes	—
561	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
562	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
573	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
574	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
575	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
576	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
577	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
578	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
579	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	4	no	—
595	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
596	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
597	C₄²	C₂⁴×C₇	1	4	yes	—
598	C₄²	C₂⁴×C₇	1	2	yes	—
599	C₂×C₇	—	2	2	no	—
600	C₂×C₇	—	4	2	no	—
601	C₂×C₇	—	8	1	no	—
602	C₂×C₇	—	8	4	no	—
603	C₂×C₇	C₂×#548	1	1	yes	characteristic
604	C₂×C₇	#3585	1	2	yes	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	4	4	no	—
609	C₂³	—	8	2	no	—
610	C₂³	—	8	2	no	—
611	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
612	Q₈	—	2	1	no	—
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	Q₈	—	4	4	no	—
616	Q₈	—	8	4	no	—
617	Q₈	C₂×C₇×#41	1	2	yes	—
618	D₄	—	2	4	no	—
619	D₄	—	2	4	no	—
620	D₄	—	2	1	no	—
621	D₄	—	2	1	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	1	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	2	no	—
626	D₄	—	4	4	no	—
627	D₄	—	8	4	no	—
628	D₄	—	8	4	no	—
629	D₄	—	8	4	no	—
630	D₄	C₂×C₇×#41	1	2	yes	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	8	2	no	—
641	C₂×C₄	—	8	4	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	—	8	4	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
646	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
647	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
648	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
649	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
650	C₂×C₄	C₂×C₇×#41	1	2	yes	—
651	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
652	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
653	C₈	—	2	1	no	—
654	C₈	—	2	1	no	—
655	C₈	—	2	4	no	—
656	C₈	—	2	2	no	—
657	C₇	#61337	1	1	yes	characteristic, direct product factor, Sylow
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	16	4	no	—
667	C₂²	C₇×#548	1	2	yes	—
668	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
669	C₄	—	2	2	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	4	no	—
672	C₄	—	2	4	no	—
673	C₄	—	2	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	4	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	C₇×#548	1	2	yes	—
679	C₄	C₂²×C₇×#41	1	1	yes	characteristic
680	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	8	4	no	—
684	C₂	—	8	1	no	—
685	C₂	C₂×C₇×#548	1	1	yes	characteristic
686	C₂	C₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3508	C₂	semidirect
2. C₇×#3504	C₂	semidirect
3. C₇×#3371	C₂	semidirect
4. C₇×#3370	C₂	semidirect
5. C₇×#3368	C₂	semidirect
6. C₇×#3366	C₂	semidirect
7. C₇×#3136	C₂	semidirect
8. C₂×C₇×#490	C₂	semidirect
9. C₇×#3081	C₂	semidirect
10. C₇×#3080	C₂	semidirect
11. C₇×#3045	C₂	semidirect
12. C₇×#3038	C₂	semidirect
13. C₇×#2961	C₂	semidirect
14. C₇×#2946	C₂	semidirect
15. C₇×#2943	C₂	semidirect
19. C₇×#557	C₂²	semidirect
21. C₇×#554	C₂²	semidirect
41. C₇×#490	C₂²	semidirect
42. C₇×#489	C₂²	semidirect
43. C₇×#488	C₂²	semidirect
44. C₇×#486	C₂²	semidirect
45. C₇×#479	C₂²	semidirect
46. C₇×#478	C₂²	semidirect
47. C₇×#478	C₂²	semidirect
48. C₇×#478	C₂²	semidirect
49. C₇×#476	C₂²	semidirect
50. C₇×#474	C₂²	semidirect
51. C₇×#464	C₂²	semidirect
52. C₇×#463	C₂²	semidirect
54. C₇×#460	C₂²	semidirect
56. C₇×#459	C₂²	semidirect
57. C₇×#446	C₂²	semidirect
58. C₇×#446	C₂²	semidirect
59. C₇×#442	C₂²	semidirect
60. C₇×#442	C₂²	semidirect
61. C₇×#441	C₂²	semidirect
62. C₇×#440	C₂²	semidirect
63. C₇×#440	C₂²	semidirect
64. C₇×#440	C₂²	semidirect
65. C₄×C₇×SD₁₆	C₂²	semidirect
66. C₄×C₇×D₈	C₂²	semidirect
79. #61337	C₇	direct (N × H)
181. #3508	C₂×C₇	semidirect
182. #3504	C₂×C₇	semidirect
183. #3371	C₂×C₇	semidirect
184. #3370	C₂×C₇	semidirect
185. #3368	C₂×C₇	semidirect
186. #3366	C₂×C₇	semidirect
187. #3136	C₂×C₇	semidirect
188. C₂×#490	C₂×C₇	semidirect
189. #3081	C₂×C₇	semidirect
190. #3080	C₂×C₇	semidirect
191. #3045	C₂×C₇	semidirect
192. #3038	C₂×C₇	semidirect
193. #2961	C₂×C₇	semidirect
194. #2946	C₂×C₇	semidirect
195. #2943	C₂×C₇	semidirect
201. C₇×#41	#41	semidirect
281. #557	C₂²×C₇	semidirect
283. #554	C₂²×C₇	semidirect
303. #490	C₂²×C₇	semidirect
304. #489	C₂²×C₇	semidirect
305. #488	C₂²×C₇	semidirect
306. #486	C₂²×C₇	semidirect
307. #479	C₂²×C₇	semidirect
308. #478	C₂²×C₇	semidirect
309. #478	C₂²×C₇	semidirect
310. #478	C₂²×C₇	semidirect
311. #476	C₂²×C₇	semidirect
312. #474	C₂²×C₇	semidirect
313. #464	C₂²×C₇	semidirect
314. #463	C₂²×C₇	semidirect
316. #460	C₂²×C₇	semidirect
318. #459	C₂²×C₇	semidirect
319. #446	C₂²×C₇	semidirect
320. #446	C₂²×C₇	semidirect
321. #442	C₂²×C₇	semidirect
322. #442	C₂²×C₇	semidirect
323. #441	C₂²×C₇	semidirect
324. #440	C₂²×C₇	semidirect
325. #440	C₂²×C₇	semidirect
326. #440	C₂²×C₇	semidirect
327. C₄×SD₁₆	C₂²×C₇	semidirect
328. C₄×D₈	C₂²×C₇	semidirect
522. #41	C₇×#41	semidirect
657. C₇	#61337	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×#3504	2
C₇×#3371	2
C₇×#3370	2
C₇×#3368	2
C₇×#3366	2
C₇×#3136	2
C₂×C₇×#490	2
C₇×#3081	2
C₇×#3080	2
C₇×#3045	2
C₇×#3038	2
C₇×#2961	2
C₇×#2946	2
C₇×#2943	2
#61337	7

Subgroups — C7×#61337 #13238553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61337 #13238553