Subgroups — C₇×#60725 #13237941

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3180	C₂	1	4	yes	maximal, complemented
4	C₇×#3176	C₂	1	4	yes	maximal, complemented
5	C₇×#3174	C₂	1	4	yes	maximal, complemented
6	C₇×#3171	C₂	1	4	yes	maximal, complemented
7	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3062	C₂	1	4	yes	maximal, complemented
12	C₇×#2946	C₂	1	4	yes	maximal, complemented
13	C₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	—
15	C₂×C₇×#131	C₂²	1	2	yes	—
16	C₇×#559	—	2	2	no	—
17	C₇×#553	—	2	4	no	—
18	C₇×#553	—	2	2	no	—
19	C₇×#552	—	2	2	no	—
20	C₇×#550	—	2	2	no	—
21	C₇×#546	—	2	4	no	—
22	C₇×#541	C₂²	1	2	yes	complemented
23	C₇×#540	C₂²	1	4	yes	—
24	C₇×#540	C₂²	1	2	yes	complemented
25	C₇×#537	C₂²	1	2	yes	—
26	C₇×#535	C₂²	1	2	yes	—
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#532	C₂²	1	1	yes	characteristic
29	C₇×#532	C₂²	1	4	yes	—
30	C₂×C₇×#127	C₂²	1	1	yes	characteristic
31	C₇×#529	C₂²	1	4	yes	complemented
32	C₂×C₇×#125	C₂²	1	1	yes	characteristic
33	C₇×#520	C₂²	1	2	yes	—
34	C₇×#518	C₂²	1	2	yes	—
35	C₄×C₇×#41	C₂²	1	1	yes	characteristic
36	C₇×#501	C₂²	1	4	yes	complemented
37	C₇×#499	C₂²	1	4	yes	complemented
38	C₇×#496	C₂²	1	4	yes	—
39	C₇×#493	C₂²	1	2	yes	—
40	C₇×#492	C₂²	1	2	yes	—
41	C₇×#491	C₂²	1	2	yes	complemented
42	C₇×#490	C₂²	1	2	yes	—
43	C₇×#490	C₂²	1	4	yes	—
44	C₇×#490	C₂²	1	2	yes	—
45	C₇×#490	C₂²	1	2	yes	complemented
46	C₇×#489	C₂²	1	2	yes	complemented
47	C₇×#489	C₂²	1	2	yes	complemented
48	C₇×#469	C₂²	1	8	yes	complemented
49	C₇×#468	C₂²	1	8	yes	complemented
50	C₇×#466	C₂²	1	8	yes	complemented
51	C₇×#465	C₂²	1	8	yes	complemented
52	C₇×#442	C₂²	1	8	yes	complemented
53	C₇×#440	C₂²	1	8	yes	complemented
54	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
55	C₄×C₇×D₈	C₂²	1	8	yes	complemented
56	C₇×#428	C₂²	1	4	yes	—
57	C₇×#416	C₂²	1	4	yes	—
58	C₂×C₇×#102	C₂²	1	4	yes	—
59	C₇×#405	C₂²	1	2	yes	—
60	C₇×#405	C₂²	1	4	yes	complemented
61	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
63	C₂×C₇×#97	C₂²	1	1	yes	characteristic
64	C₂×C₇×#97	C₂²	1	2	yes	complemented
65	#60725	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂×C₇×#41	—	2	4	no	—
67	C₂×C₇×#41	C₂³	1	2	yes	—
68	C₂×C₇×#41	C₂³	1	1	yes	characteristic
69	C₂²×C₇×D₄	—	2	2	no	—
70	C₂²×C₇×D₄	C₂³	1	2	yes	—
71	C₇×AGL(1,ℤ/8)	—	2	16	no	—
72	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₇×D₈	C₂³	1	8	yes	—
74	C₇×#131	—	2	8	no	—
75	C₂×C₇×M₁₆	C₂³	1	4	yes	—
76	C₂×C₇×M₁₆	C₂³	1	2	yes	—
77	C₂²×C₇×C₈	C₂³	1	4	yes	—
78	C₂²×C₇×C₈	C₂³	1	2	yes	—
79	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₇×#127	—	2	2	no	—
82	C₇×#127	—	2	2	no	—
83	C₇×#127	C₂³	1	2	yes	—
84	C₇×#127	C₂³	1	2	yes	—
85	C₇×#127	C₂³	1	1	yes	characteristic
86	C₇×#126	—	2	4	no	—
87	C₇×#126	—	2	4	no	—
88	C₇×#125	—	2	4	no	—
89	C₇×#125	—	2	2	no	—
90	C₇×#125	C₂³	1	2	yes	—
91	C₇×#125	C₂³	1	2	yes	—
92	C₇×#125	C₂³	1	2	yes	—
93	C₇×#124	—	2	2	no	—
94	C₇×#124	—	2	4	no	—
95	C₇×#124	C₂³	1	2	yes	—
96	C₇×#123	—	2	4	no	—
97	C₇×#123	—	2	8	no	—
98	C₇×#123	—	2	4	no	—
99	C₇×C₂²⋊Q₈	—	2	2	no	—
100	C₇×C₂²⋊Q₈	—	2	2	no	—
101	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
102	C₇×#121	—	2	2	no	—
103	C₇×#121	—	2	4	no	—
104	C₇×#121	—	2	4	no	—
105	C₇×#121	—	2	2	no	—
106	C₇×#121	—	2	8	no	—
107	C₇×#121	—	2	4	no	—
108	C₇×#121	C₂³	1	4	yes	—
109	C₇×#121	C₂³	1	8	yes	—
110	C₇×#120	—	2	4	no	—
111	C₄×C₇×Q₈	—	2	2	no	—
112	C₄×C₇×Q₈	D₄	1	2	yes	—
113	C₄×C₇×Q₈	C₂³	1	4	yes	—
114	C₄×C₇×D₄	—	2	4	no	—
115	C₄×C₇×D₄	—	2	4	no	—
116	C₄×C₇×D₄	—	2	4	no	—
117	C₄×C₇×D₄	—	2	4	no	—
118	C₄×C₇×D₄	—	2	2	no	—
119	C₄×C₇×D₄	D₄	1	4	yes	—
120	C₄×C₇×D₄	D₄	1	2	yes	—
121	C₄×C₇×D₄	C₂³	1	8	yes	—
122	C₄×C₇×D₄	C₂³	1	4	yes	—
123	C₇×#117	—	2	2	no	—
124	C₇×#117	—	2	4	no	—
125	C₇×#117	C₂³	1	2	yes	—
126	C₇×#117	C₂³	1	1	yes	characteristic
127	C₇×#117	C₂³	1	2	yes	—
128	C₂×C₇×C₄⋊C₄	—	2	2	no	—
129	C₂×C₇×C₄⋊C₄	—	2	2	no	—
130	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
132	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₇	C₂³	1	2	yes	—
134	C₇×#107	C₂³	1	8	yes	—
135	C₇×#106	C₂³	1	8	yes	—
136	C₇×#103	C₂³	1	4	yes	—
137	C₇×#103	C₂³	1	4	yes	—
138	C₇×#102	C₂³	1	4	yes	—
139	C₇×#102	C₂³	1	8	yes	—
140	C₇×#102	C₂³	1	8	yes	—
141	C₇×#102	C₂³	1	4	yes	—
142	C₇×#97	C₂³	1	1	yes	characteristic
143	C₇×#97	C₂³	1	1	yes	characteristic
144	C₇×#97	C₂³	1	2	yes	—
145	C₇×#97	C₂³	1	2	yes	—
146	C₇×#97	C₂³	1	4	yes	—
147	C₄×C₇×C₈	C₂³	1	2	yes	—
148	C₄×C₇×C₈	C₂³	1	4	yes	—
149	#3512	C₂×C₇	1	1	yes	characteristic, complemented
150	#3508	C₂×C₇	1	1	yes	characteristic, complemented
151	#3180	C₂×C₇	1	4	yes	complemented
152	#3176	C₂×C₇	1	4	yes	complemented
153	#3174	C₂×C₇	1	4	yes	complemented
154	#3171	C₂×C₇	1	4	yes	complemented
155	#3166	C₂×C₇	1	1	yes	characteristic, complemented
156	#3151	C₂×C₇	1	1	yes	characteristic, complemented
157	#3135	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂×#490	C₂×C₇	1	1	yes	characteristic, complemented
159	#3062	C₂×C₇	1	4	yes	complemented
160	#2946	C₂×C₇	1	4	yes	complemented
161	#2875	C₂×C₇	1	1	yes	characteristic, complemented
162	C₂⁴×C₇	—	2	2	no	—
163	C₇×#41	—	2	4	no	—
164	C₇×#41	—	2	8	no	—
165	C₇×#41	—	8	8	no	—
166	C₂×C₇×Q₈	—	2	2	no	—
167	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
169	C₂×C₇×D₄	—	2	2	no	—
170	C₂×C₇×D₄	—	2	4	no	—
171	C₂×C₇×D₄	—	2	8	no	—
172	C₂×C₇×D₄	—	2	2	no	—
173	C₂×C₇×D₄	—	2	4	no	—
174	C₂×C₇×D₄	—	2	2	no	—
175	C₂×C₇×D₄	—	2	4	no	—
176	C₂×C₇×D₄	—	2	8	no	—
177	C₂×C₇×D₄	—	8	4	no	—
178	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
179	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂×C₇×D₄	C₂⁴	1	2	yes	—
181	C₂×C₇×D₄	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₇	—	2	2	no	—
183	C₂²×C₄×C₇	—	2	2	no	—
184	C₂²×C₄×C₇	—	2	8	no	—
185	C₂²×C₄×C₇	—	2	4	no	—
186	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	C₇×SD₁₆	—	2	16	no	—
191	C₇×D₈	—	2	16	no	—
192	C₇×M₁₆	—	2	8	no	—
193	C₇×M₁₆	#41	1	8	yes	complemented
194	C₂×C₇×C₈	—	2	4	no	—
195	C₂×C₇×C₈	—	2	8	no	—
196	C₂×C₇×C₈	C₂⁴	1	2	yes	—
197	C₂×C₇×C₈	C₂⁴	1	2	yes	—
198	C₂×C₇×C₈	C₂⁴	1	4	yes	—
199	C₇×C₄⋊C₄	—	2	2	no	—
200	C₇×C₄⋊C₄	—	2	4	no	—
201	C₇×C₄⋊C₄	—	2	4	no	—
202	C₇×C₄⋊C₄	—	2	4	no	—
203	C₇×C₄⋊C₄	—	2	4	no	—
204	C₇×C₄⋊C₄	—	2	2	no	—
205	C₇×C₄⋊C₄	—	2	2	no	—
206	C₇×C₄⋊C₄	—	2	4	no	—
207	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
208	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
210	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
211	C₇×C₂²⋊C₄	—	2	2	no	—
212	C₇×C₂²⋊C₄	—	2	4	no	—
213	C₇×C₂²⋊C₄	—	2	8	no	—
214	C₇×C₂²⋊C₄	—	2	2	no	—
215	C₇×C₂²⋊C₄	—	2	4	no	—
216	C₇×C₂²⋊C₄	—	2	4	no	—
217	C₇×C₂²⋊C₄	—	2	2	no	—
218	C₇×C₂²⋊C₄	—	2	8	no	—
219	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
220	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
221	C₄²×C₇	—	2	4	no	—
222	C₄²×C₇	—	2	2	no	—
223	C₄²×C₇	C₂×D₄	1	4	yes	—
224	C₄²×C₇	C₂×D₄	1	2	yes	—
225	C₄²×C₇	C₂⁴	1	2	yes	—
226	C₄²×C₇	C₂⁴	1	1	yes	characteristic
227	C₄²×C₇	C₂⁴	1	1	yes	characteristic
228	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	—
229	C₂×#131	C₂²×C₇	1	2	yes	—
230	#559	—	2	2	no	—
231	#553	—	2	4	no	—
232	#553	—	2	2	no	—
233	#552	—	2	2	no	—
234	#550	—	2	2	no	—
235	#546	—	2	4	no	—
236	#541	C₂²×C₇	1	2	yes	complemented
237	#540	C₂²×C₇	1	4	yes	—
238	#540	C₂²×C₇	1	2	yes	complemented
239	#537	C₂²×C₇	1	2	yes	—
240	#535	C₂²×C₇	1	2	yes	—
241	#533	C₂²×C₇	1	1	yes	characteristic
242	#532	C₂²×C₇	1	1	yes	characteristic
243	#532	C₂²×C₇	1	4	yes	—
244	C₂×#127	C₂²×C₇	1	1	yes	characteristic
245	#529	C₂²×C₇	1	4	yes	complemented
246	C₂×#125	C₂²×C₇	1	1	yes	characteristic
247	#520	C₂²×C₇	1	2	yes	—
248	#518	C₂²×C₇	1	2	yes	—
249	C₄×#41	C₂²×C₇	1	1	yes	characteristic
250	#501	C₂²×C₇	1	4	yes	complemented
251	#499	C₂²×C₇	1	4	yes	complemented
252	#496	C₂²×C₇	1	4	yes	—
253	#493	C₂²×C₇	1	2	yes	—
254	#492	C₂²×C₇	1	2	yes	—
255	#491	C₂²×C₇	1	2	yes	complemented
256	#490	C₂²×C₇	1	2	yes	—
257	#490	C₂²×C₇	1	4	yes	—
258	#490	C₂²×C₇	1	2	yes	—
259	#490	C₂²×C₇	1	2	yes	complemented
260	#489	C₂²×C₇	1	2	yes	complemented
261	#489	C₂²×C₇	1	2	yes	complemented
262	#469	C₂²×C₇	1	8	yes	complemented
263	#468	C₂²×C₇	1	8	yes	complemented
264	#466	C₂²×C₇	1	8	yes	complemented
265	#465	C₂²×C₇	1	8	yes	complemented
266	#442	C₂²×C₇	1	8	yes	complemented
267	#440	C₂²×C₇	1	8	yes	complemented
268	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
269	C₄×D₈	C₂²×C₇	1	8	yes	complemented
270	#428	C₂²×C₇	1	4	yes	—
271	#416	C₂²×C₇	1	4	yes	—
272	C₂×#102	C₂²×C₇	1	4	yes	—
273	#405	C₂²×C₇	1	2	yes	—
274	#405	C₂²×C₇	1	4	yes	complemented
275	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
276	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
277	C₂×#97	C₂²×C₇	1	1	yes	characteristic
278	C₂×#97	C₂²×C₇	1	2	yes	complemented
279	C₂³×C₇	—	2	2	no	—
280	C₂³×C₇	—	2	4	no	—
281	C₂³×C₇	—	4	4	no	—
282	C₂³×C₇	—	8	4	no	—
283	C₂³×C₇	C₂²×D₄	1	2	yes	—
284	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
285	C₇×Q₈	—	2	2	no	—
286	C₇×Q₈	—	2	4	no	—
287	C₇×Q₈	—	4	4	no	—
288	C₇×D₄	—	2	4	no	—
289	C₇×D₄	—	2	2	no	—
290	C₇×D₄	—	2	4	no	—
291	C₇×D₄	—	2	8	no	—
292	C₇×D₄	—	4	8	no	—
293	C₇×D₄	—	4	4	no	—
294	C₇×D₄	—	4	4	no	—
295	C₇×D₄	—	8	2	no	—
296	C₇×D₄	—	8	4	no	—
297	C₇×D₄	—	8	4	no	—
298	C₇×D₄	—	8	8	no	—
299	C₂×C₄×C₇	—	2	4	no	—
300	C₂×C₄×C₇	—	2	2	no	—
301	C₂×C₄×C₇	—	2	4	no	—
302	C₂×C₄×C₇	—	2	4	no	—
303	C₂×C₄×C₇	—	4	2	no	—
304	C₂×C₄×C₇	—	4	4	no	—
305	C₂×C₄×C₇	—	4	4	no	—
306	C₂×C₄×C₇	—	8	4	no	—
307	C₂×C₄×C₇	—	8	8	no	—
308	C₂×C₄×C₇	—	8	2	no	—
309	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₇	C₂×#41	1	4	yes	—
315	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
316	C₇×C₈	—	2	2	no	—
317	C₇×C₈	—	2	2	no	—
318	C₇×C₈	C₂×#41	1	8	yes	—
319	C₂×#41	—	2	4	no	—
320	C₂×#41	C₂³×C₇	1	2	yes	—
321	C₂×#41	C₂³×C₇	1	1	yes	characteristic
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	C₂³×C₇	1	2	yes	—
324	AGL(1,ℤ/8)	—	2	16	no	—
325	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
326	C₂×D₈	C₂³×C₇	1	8	yes	—
327	#131	—	2	8	no	—
328	C₂×M₁₆	C₂³×C₇	1	4	yes	—
329	C₂×M₁₆	C₂³×C₇	1	2	yes	—
330	C₂²×C₈	C₂³×C₇	1	2	yes	—
331	C₂²×C₈	C₂³×C₇	1	4	yes	—
332	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
334	#127	—	2	2	no	—
335	#127	—	2	2	no	—
336	#127	C₂³×C₇	1	2	yes	—
337	#127	C₂³×C₇	1	2	yes	—
338	#127	C₂³×C₇	1	1	yes	characteristic
339	#126	—	2	4	no	—
340	#126	—	2	4	no	—
341	#125	—	2	4	no	—
342	#125	—	2	2	no	—
343	#125	C₂³×C₇	1	2	yes	—
344	#125	C₂³×C₇	1	2	yes	—
345	#125	C₂³×C₇	1	2	yes	—
346	#124	—	2	2	no	—
347	#124	—	2	4	no	—
348	#124	C₂³×C₇	1	2	yes	—
349	#123	—	2	4	no	—
350	#123	—	2	8	no	—
351	#123	—	2	4	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
355	#121	—	2	2	no	—
356	#121	—	2	4	no	—
357	#121	—	2	4	no	—
358	#121	—	2	2	no	—
359	#121	—	2	8	no	—
360	#121	—	2	4	no	—
361	#121	C₂³×C₇	1	4	yes	—
362	#121	C₂³×C₇	1	8	yes	—
363	#120	—	2	4	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	C₇×D₄	1	2	yes	—
366	C₄×Q₈	C₂³×C₇	1	4	yes	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	4	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	C₇×D₄	1	4	yes	—
373	C₄×D₄	C₇×D₄	1	2	yes	—
374	C₄×D₄	C₂³×C₇	1	8	yes	—
375	C₄×D₄	C₂³×C₇	1	4	yes	—
376	#117	—	2	2	no	—
377	#117	—	2	4	no	—
378	#117	C₂³×C₇	1	2	yes	—
379	#117	C₂³×C₇	1	1	yes	characteristic
380	#117	C₂³×C₇	1	2	yes	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
384	C₂×C₂²⋊C₄	—	2	4	no	—
385	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₇	1	2	yes	—
387	#107	C₂³×C₇	1	8	yes	—
388	#106	C₂³×C₇	1	8	yes	—
389	#103	C₂³×C₇	1	4	yes	—
390	#103	C₂³×C₇	1	4	yes	—
391	#102	C₂³×C₇	1	8	yes	—
392	#102	C₂³×C₇	1	8	yes	—
393	#102	C₂³×C₇	1	4	yes	—
394	#102	C₂³×C₇	1	4	yes	—
395	#97	C₂³×C₇	1	1	yes	characteristic
396	#97	C₂³×C₇	1	1	yes	characteristic
397	#97	C₂³×C₇	1	2	yes	—
398	#97	C₂³×C₇	1	2	yes	—
399	#97	C₂³×C₇	1	4	yes	—
400	C₄×C₈	C₂³×C₇	1	2	yes	—
401	C₄×C₈	C₂³×C₇	1	4	yes	—
402	C₂²×C₇	—	2	2	no	—
403	C₂²×C₇	—	2	4	no	—
404	C₂²×C₇	—	2	2	no	—
405	C₂²×C₇	—	4	2	no	—
406	C₂²×C₇	—	4	8	no	—
407	C₂²×C₇	—	4	2	no	—
408	C₂²×C₇	—	4	2	no	—
409	C₂²×C₇	—	4	4	no	—
410	C₂²×C₇	—	16	4	no	—
411	C₂²×C₇	#532	1	2	yes	—
412	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₇	—	2	2	no	—
414	C₄×C₇	—	2	4	no	—
415	C₄×C₇	—	2	2	no	—
416	C₄×C₇	—	2	2	no	—
417	C₄×C₇	—	4	4	no	—
418	C₄×C₇	—	4	4	no	—
419	C₄×C₇	—	4	2	no	—
420	C₄×C₇	#532	1	2	yes	—
421	C₄×C₇	C₂²×#41	1	2	yes	—
422	C₂⁴	—	2	2	no	—
423	#41	—	2	4	no	—
424	#41	—	2	8	no	—
425	#41	—	8	8	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
428	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	8	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	8	4	no	—
438	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
439	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
440	C₂×D₄	C₂⁴×C₇	1	2	yes	—
441	C₂×D₄	C₂⁴×C₇	1	4	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	8	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
447	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
450	SD₁₆	—	2	16	no	—
451	D₈	—	2	16	no	—
452	M₁₆	—	2	8	no	—
453	M₁₆	C₇×#41	1	8	yes	complemented
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	—	2	8	no	—
456	C₂×C₈	C₂⁴×C₇	1	2	yes	—
457	C₂×C₈	C₂⁴×C₇	1	2	yes	—
458	C₂×C₈	C₂⁴×C₇	1	4	yes	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
468	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
480	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
481	C₄²	—	2	4	no	—
482	C₄²	—	2	2	no	—
483	C₄²	C₂×C₇×D₄	1	4	yes	—
484	C₄²	C₂×C₇×D₄	1	2	yes	—
485	C₄²	C₂⁴×C₇	1	2	yes	—
486	C₄²	C₂⁴×C₇	1	1	yes	characteristic
487	C₄²	C₂⁴×C₇	1	1	yes	characteristic
488	C₂×C₇	—	2	2	no	—
489	C₂×C₇	—	4	2	no	—
490	C₂×C₇	—	8	2	no	—
491	C₂×C₇	—	8	4	no	—
492	C₂×C₇	C₂×#532	1	1	yes	characteristic
493	C₂×C₇	#3585	1	2	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	8	4	no	—
498	C₂³	C₂²×C₇×D₄	1	2	yes	—
499	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
500	Q₈	—	2	2	no	—
501	Q₈	—	2	4	no	—
502	Q₈	—	4	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	8	no	—
506	D₄	—	2	2	no	—
507	D₄	—	4	8	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	4	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	4	no	—
512	D₄	—	8	4	no	—
513	D₄	—	8	8	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	8	4	no	—
522	C₂×C₄	—	8	8	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
525	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
526	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
527	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
528	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂×C₇×#41	1	4	yes	—
530	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	C₂×C₇×#41	1	8	yes	—
534	C₇	#60725	1	1	yes	characteristic, direct product factor, Sylow
535	C₂²	—	2	2	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	8	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	16	4	no	—
544	C₂²	C₇×#532	1	2	yes	—
545	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	4	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	C₇×#532	1	2	yes	—
554	C₄	C₂²×C₇×#41	1	2	yes	—
555	C₂	—	2	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	4	no	—
558	C₂	—	8	2	no	—
559	C₂	C₂×C₇×#532	1	1	yes	characteristic
560	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3508	C₂	semidirect
3. C₇×#3180	C₂	semidirect
4. C₇×#3176	C₂	semidirect
5. C₇×#3174	C₂	semidirect
6. C₇×#3171	C₂	semidirect
7. C₇×#3166	C₂	semidirect
8. C₇×#3151	C₂	semidirect
9. C₇×#3135	C₂	semidirect
10. C₂×C₇×#490	C₂	semidirect
11. C₇×#3062	C₂	semidirect
12. C₇×#2946	C₂	semidirect
13. C₇×#2875	C₂	semidirect
22. C₇×#541	C₂²	semidirect
24. C₇×#540	C₂²	semidirect
31. C₇×#529	C₂²	semidirect
36. C₇×#501	C₂²	semidirect
37. C₇×#499	C₂²	semidirect
41. C₇×#491	C₂²	semidirect
45. C₇×#490	C₂²	semidirect
46. C₇×#489	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#469	C₂²	semidirect
49. C₇×#468	C₂²	semidirect
50. C₇×#466	C₂²	semidirect
51. C₇×#465	C₂²	semidirect
52. C₇×#442	C₂²	semidirect
53. C₇×#440	C₂²	semidirect
54. C₄×C₇×SD₁₆	C₂²	semidirect
55. C₄×C₇×D₈	C₂²	semidirect
60. C₇×#405	C₂²	semidirect
62. C₄×C₇×M₁₆	C₂²	semidirect
64. C₂×C₇×#97	C₂²	semidirect
65. #60725	C₇	direct (N × H)
149. #3512	C₂×C₇	semidirect
150. #3508	C₂×C₇	semidirect
151. #3180	C₂×C₇	semidirect
152. #3176	C₂×C₇	semidirect
153. #3174	C₂×C₇	semidirect
154. #3171	C₂×C₇	semidirect
155. #3166	C₂×C₇	semidirect
156. #3151	C₂×C₇	semidirect
157. #3135	C₂×C₇	semidirect
158. C₂×#490	C₂×C₇	semidirect
159. #3062	C₂×C₇	semidirect
160. #2946	C₂×C₇	semidirect
161. #2875	C₂×C₇	semidirect
193. C₇×M₁₆	#41	semidirect
236. #541	C₂²×C₇	semidirect
238. #540	C₂²×C₇	semidirect
245. #529	C₂²×C₇	semidirect
250. #501	C₂²×C₇	semidirect
251. #499	C₂²×C₇	semidirect
255. #491	C₂²×C₇	semidirect
259. #490	C₂²×C₇	semidirect
260. #489	C₂²×C₇	semidirect
261. #489	C₂²×C₇	semidirect
262. #469	C₂²×C₇	semidirect
263. #468	C₂²×C₇	semidirect
264. #466	C₂²×C₇	semidirect
265. #465	C₂²×C₇	semidirect
266. #442	C₂²×C₇	semidirect
267. #440	C₂²×C₇	semidirect
268. C₄×SD₁₆	C₂²×C₇	semidirect
269. C₄×D₈	C₂²×C₇	semidirect
274. #405	C₂²×C₇	semidirect
276. C₄×M₁₆	C₂²×C₇	semidirect
278. C₂×#97	C₂²×C₇	semidirect
453. M₁₆	C₇×#41	semidirect
534. C₇	#60725	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×#3512	2
C₇×#3508	2
C₇×#3180	2
C₇×#3176	2
C₇×#3174	2
C₇×#3171	2
C₇×#3166	2
C₇×#3151	2
C₇×#3135	2
C₂×C₇×#490	2
C₇×#3062	2
C₇×#2946	2
C₇×#2875	2
#60725	7

Subgroups — C7×#60725 #13237941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60725 #13237941