Subgroups — C₇×#26749 #13203965

Order 1792.

720 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2489	C₂	1	1	yes	maximal, characteristic
2	C₇×#2362	C₂	1	1	yes	maximal, characteristic
3	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2036	C₂	1	1	yes	maximal, characteristic
5	C₇×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2001	C₂	1	1	yes	maximal, characteristic
7	C₇×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1928	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1924	C₂	1	1	yes	maximal, characteristic
11	C₇×#1921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1873	C₂	1	1	yes	maximal, characteristic
14	C₇×#1825	C₂	1	1	yes	maximal, characteristic
15	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₇×#125	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	1	yes	characteristic
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#103	C₂²	1	1	yes	characteristic
27	C₂×C₇×#103	C₂²	1	1	yes	characteristic
28	C₂×C₇×#103	C₂²	1	1	yes	characteristic
29	C₂×C₇×#103	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×#97	C₂²	1	1	yes	characteristic
33	C₇×#400	—	2	1	no	—
34	C₇×#397	—	2	1	no	—
35	C₇×#391	C₂²	1	1	yes	characteristic
36	C₇×#391	C₂²	1	1	yes	characteristic
37	C₇×#391	C₂²	1	1	yes	characteristic
38	C₇×#389	C₂²	1	1	yes	characteristic
39	C₇×#388	—	2	1	no	—
40	C₇×#388	—	2	1	no	—
41	C₇×#388	—	2	1	no	—
42	C₇×#387	—	2	1	no	—
43	C₇×#382	—	2	1	no	—
44	C₇×#380	C₂²	1	1	yes	characteristic
45	C₄×C₇×C₄⋊C₄	—	2	1	no	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₇×#340	C₂²	1	1	yes	characteristic
50	C₇×#340	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#26749	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₇×Q₁₆	—	2	2	no	—
64	C₂×C₇×Q₁₆	—	4	1	no	—
65	C₂×C₇×Q₁₆	—	4	1	no	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₇×#125	—	2	2	no	—
71	C₇×#125	—	4	1	no	—
72	C₇×C₂²⋊Q₈	—	2	2	no	—
73	C₇×C₂²⋊Q₈	—	2	2	no	—
74	C₇×C₂²⋊Q₈	—	2	2	no	—
75	C₇×C₂²⋊Q₈	—	4	1	no	—
76	C₄×C₇×Q₈	—	2	2	no	—
77	C₄×C₇×Q₈	—	4	1	no	—
78	C₇×#117	—	2	2	no	—
79	C₇×#117	—	4	1	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₇×C₄⋊C₄	—	2	1	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇	—	2	1	no	—
99	C₂×C₄²×C₇	—	2	1	no	—
100	C₂×C₄²×C₇	—	2	1	no	—
101	C₂×C₄²×C₇	—	2	1	no	—
102	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×#107	—	2	2	no	—
105	C₇×C₄⋊C₈	—	4	1	no	—
106	C₇×#103	—	2	2	no	—
107	C₇×#103	—	2	2	no	—
108	C₇×#103	—	2	2	no	—
109	C₇×#103	—	2	2	no	—
110	C₇×#103	—	4	1	no	—
111	C₇×#103	—	4	1	no	—
112	C₇×C₂²⋊C₈	—	4	1	no	—
113	C₇×C₂²⋊C₈	—	4	1	no	—
114	C₇×#97	—	4	1	no	—
115	C₇×#95	—	2	1	no	—
116	C₇×#95	—	2	1	no	—
117	C₇×#95	—	2	1	no	—
118	C₇×#95	—	2	1	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₇×#95	—	2	1	no	—
122	C₇×#95	—	2	1	no	—
123	C₇×#95	—	2	1	no	—
124	C₇×#95	—	2	1	no	—
125	C₇×#95	D₄	1	1	yes	characteristic
126	C₇×#95	D₄	1	1	yes	characteristic
127	#2489	C₂×C₇	1	1	yes	characteristic
128	#2362	C₂×C₇	1	1	yes	characteristic
129	#2056	C₂×C₇	1	1	yes	characteristic, complemented
130	#2036	C₂×C₇	1	1	yes	characteristic
131	#2026	C₂×C₇	1	1	yes	characteristic, complemented
132	#2001	C₂×C₇	1	1	yes	characteristic
133	#1989	C₂×C₇	1	1	yes	characteristic, complemented
134	#1935	C₂×C₇	1	1	yes	characteristic, complemented
135	#1928	C₂×C₇	1	1	yes	characteristic, complemented
136	#1924	C₂×C₇	1	1	yes	characteristic
137	#1921	C₂×C₇	1	1	yes	characteristic, complemented
138	#1878	C₂×C₇	1	1	yes	characteristic, complemented
139	#1873	C₂×C₇	1	1	yes	characteristic
140	#1825	C₂×C₇	1	1	yes	characteristic
141	#1763	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×Q₈	—	2	1	no	—
145	C₂×C₇×Q₈	—	2	1	no	—
146	C₂×C₇×Q₈	—	2	1	no	—
147	C₂×C₇×Q₈	—	2	1	no	—
148	C₂×C₇×Q₈	—	2	1	no	—
149	C₂×C₇×Q₈	—	2	1	no	—
150	C₂×C₇×Q₈	—	2	1	no	—
151	C₂×C₇×Q₈	—	2	1	no	—
152	C₂×C₇×Q₈	—	2	1	no	—
153	C₂×C₇×Q₈	—	2	1	no	—
154	C₂×C₇×Q₈	#41	1	2	yes	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
175	C₇×Q₁₆	—	4	4	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	—	2	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	2	1	no	—
196	C₇×C₄⋊C₄	—	2	1	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	—	4	2	no	—
199	C₇×C₄⋊C₄	—	4	2	no	—
200	C₇×C₄⋊C₄	—	4	2	no	—
201	C₇×C₄⋊C₄	—	4	2	no	—
202	C₇×C₄⋊C₄	—	4	2	no	—
203	C₇×C₄⋊C₄	#41	1	2	yes	—
204	C₇×C₄⋊C₄	#41	1	2	yes	—
205	C₇×C₄⋊C₄	#41	1	2	yes	—
206	C₇×C₂²⋊C₄	—	2	4	no	—
207	C₇×C₂²⋊C₄	—	4	1	no	—
208	C₇×C₂²⋊C₄	—	4	1	no	—
209	C₇×C₂²⋊C₄	—	4	2	no	—
210	C₇×C₂²⋊C₄	—	4	2	no	—
211	C₇×C₂²⋊C₄	—	4	2	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	2	1	no	—
214	C₄²×C₇	—	2	1	no	—
215	C₄²×C₇	—	2	1	no	—
216	C₄²×C₇	—	4	2	no	—
217	C₄²×C₇	—	4	2	no	—
218	C₄²×C₇	—	4	2	no	—
219	C₄²×C₇	—	4	2	no	—
220	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
221	C₂×#125	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×#117	C₂²×C₇	1	1	yes	characteristic
226	C₂×#107	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×#103	C₂²×C₇	1	1	yes	characteristic
229	C₂×#103	C₂²×C₇	1	1	yes	characteristic
230	C₂×#103	C₂²×C₇	1	1	yes	characteristic
231	C₂×#103	C₂²×C₇	1	1	yes	characteristic
232	C₂×#103	C₂²×C₇	1	1	yes	characteristic
233	C₂×#103	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₇	1	1	yes	characteristic
237	#400	—	2	1	no	—
238	#397	—	2	1	no	—
239	#391	C₂²×C₇	1	1	yes	characteristic
240	#391	C₂²×C₇	1	1	yes	characteristic
241	#391	C₂²×C₇	1	1	yes	characteristic
242	#389	C₂²×C₇	1	1	yes	characteristic
243	#388	—	2	1	no	—
244	#388	—	2	1	no	—
245	#388	—	2	1	no	—
246	#387	—	2	1	no	—
247	#382	—	2	1	no	—
248	#380	C₂²×C₇	1	1	yes	characteristic
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
253	#340	C₂²×C₇	1	1	yes	characteristic
254	#340	C₂²×C₇	1	1	yes	characteristic
255	#340	C₂²×C₇	1	1	yes	characteristic
256	#340	C₂²×C₇	1	1	yes	characteristic
257	#340	C₂²×C₇	1	1	yes	characteristic
258	#340	C₂²×C₇	1	1	yes	characteristic
259	#340	C₂²×C₇	1	1	yes	characteristic
260	#340	C₂²×C₇	1	1	yes	characteristic
261	#336	C₂²×C₇	1	1	yes	characteristic
262	#336	C₂²×C₇	1	1	yes	characteristic
263	C₂³×C₇	—	2	1	no	—
264	C₂³×C₇	—	2	1	no	—
265	C₂³×C₇	—	2	1	no	—
266	C₂³×C₇	—	2	1	no	—
267	C₂³×C₇	—	2	1	no	—
268	C₂³×C₇	—	2	1	no	—
269	C₂³×C₇	—	2	1	no	—
270	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
271	C₇×Q₈	—	2	2	no	—
272	C₇×Q₈	—	2	2	no	—
273	C₇×Q₈	—	4	1	no	—
274	C₇×Q₈	—	4	1	no	—
275	C₇×Q₈	—	4	1	no	—
276	C₇×Q₈	—	4	1	no	—
277	C₇×Q₈	—	4	1	no	—
278	C₇×Q₈	—	4	1	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	1	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	—	4	1	no	—
315	C₂×C₄×C₇	—	4	1	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	1	no	—
318	C₂×C₄×C₇	—	4	1	no	—
319	C₂×C₄×C₇	—	4	1	no	—
320	C₂×C₄×C₇	—	4	1	no	—
321	C₂×C₄×C₇	—	4	1	no	—
322	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
328	C₇×C₈	—	4	1	no	—
329	C₇×C₈	—	4	1	no	—
330	C₇×C₈	—	4	1	no	—
331	C₇×C₈	—	4	1	no	—
332	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×Q₁₆	—	4	1	no	—
337	C₂×Q₁₆	—	4	1	no	—
338	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
342	#125	—	2	2	no	—
343	#125	—	4	1	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	4	1	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	4	1	no	—
350	#117	—	2	2	no	—
351	#117	—	4	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	#107	—	2	2	no	—
377	C₄⋊C₈	—	4	1	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#103	—	4	1	no	—
383	#103	—	4	1	no	—
384	C₂²⋊C₈	—	4	1	no	—
385	C₂²⋊C₈	—	4	1	no	—
386	#97	—	4	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	C₇×D₄	1	1	yes	characteristic
398	#95	C₇×D₄	1	1	yes	characteristic
399	C₂²×C₇	—	4	1	no	—
400	C₂²×C₇	—	4	1	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	—	4	1	no	—
404	C₂²×C₇	—	4	1	no	—
405	C₂²×C₇	—	4	1	no	—
406	C₂²×C₇	#525	1	1	yes	characteristic
407	C₂²×C₇	#546	1	1	yes	characteristic
408	C₂²×C₇	#546	1	1	yes	characteristic
409	C₂²×C₇	#575	1	1	yes	characteristic
410	C₂²×C₇	#575	1	1	yes	characteristic
411	C₂²×C₇	#578	1	1	yes	characteristic
412	C₂²×C₇	#578	1	1	yes	characteristic
413	C₄×C₇	—	4	2	no	—
414	C₄×C₇	—	4	1	no	—
415	C₄×C₇	—	4	2	no	—
416	C₄×C₇	—	4	1	no	—
417	C₄×C₇	—	4	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	—	4	2	no	—
420	C₄×C₇	—	4	2	no	—
421	C₄×C₇	—	4	1	no	—
422	C₄×C₇	—	8	1	no	—
423	C₄×C₇	—	8	1	no	—
424	C₄×C₇	—	8	1	no	—
425	C₄×C₇	—	8	1	no	—
426	C₄×C₇	#529	1	1	yes	characteristic
427	C₄×C₇	#538	1	1	yes	characteristic
428	C₄×C₇	#555	1	1	yes	characteristic
429	C₄×C₇	#559	1	1	yes	characteristic
430	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	C₇×#41	1	2	yes	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
463	Q₁₆	—	4	4	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	C₇×#41	1	2	yes	—
492	C₄⋊C₄	C₇×#41	1	2	yes	—
493	C₄⋊C₄	C₇×#41	1	2	yes	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	4	2	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₂×C₇	—	8	1	no	—
509	C₂×C₇	#2459	1	1	yes	characteristic
510	C₂×C₇	#3111	1	1	yes	characteristic
511	C₂×C₇	#3127	1	1	yes	characteristic
512	C₂×C₇	#3313	1	1	yes	characteristic
513	C₂×C₇	#3315	1	1	yes	characteristic
514	C₂×C₇	#3315	1	1	yes	characteristic
515	C₂×C₇	#3327	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
524	Q₈	—	2	2	no	—
525	Q₈	—	2	2	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	4	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
576	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
577	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
578	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
579	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	1	no	—
585	C₇	#26749	1	1	yes	characteristic, direct product factor, Sylow
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₇×#525	1	1	yes	characteristic
594	C₂²	C₇×#546	1	1	yes	characteristic
595	C₂²	C₇×#546	1	1	yes	characteristic
596	C₂²	C₇×#575	1	1	yes	characteristic
597	C₂²	C₇×#575	1	1	yes	characteristic
598	C₂²	C₇×#578	1	1	yes	characteristic
599	C₂²	C₇×#578	1	1	yes	characteristic
600	C₄	—	4	1	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	1	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	C₇×#529	1	1	yes	characteristic
614	C₄	C₇×#538	1	1	yes	characteristic
615	C₄	C₇×#555	1	1	yes	characteristic
616	C₄	C₇×#559	1	1	yes	characteristic
617	C₂	—	8	1	no	—
618	C₂	C₇×#2459	1	1	yes	characteristic
619	C₂	C₇×#3111	1	1	yes	characteristic
620	C₂	C₇×#3127	1	1	yes	characteristic
621	C₂	C₇×#3313	1	1	yes	characteristic
622	C₂	C₇×#3315	1	1	yes	characteristic
623	C₂	C₇×#3315	1	1	yes	characteristic
624	C₂	C₇×#3327	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2056	C₂	semidirect
5. C₇×#2026	C₂	semidirect
7. C₇×#1989	C₂	semidirect
8. C₇×#1935	C₂	semidirect
9. C₇×#1928	C₂	semidirect
11. C₇×#1921	C₂	semidirect
12. C₇×#1878	C₂	semidirect
15. C₇×#1763	C₂	semidirect
59. #26749	C₇	direct (N × H)
129. #2056	C₂×C₇	semidirect
131. #2026	C₂×C₇	semidirect
133. #1989	C₂×C₇	semidirect
134. #1935	C₂×C₇	semidirect
135. #1928	C₂×C₇	semidirect
137. #1921	C₂×C₇	semidirect
138. #1878	C₂×C₇	semidirect
141. #1763	C₂×C₇	semidirect
585. C₇	#26749	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×#2489	2
C₇×#2362	2
C₇×#2056	2
C₇×#2036	2
C₇×#2026	2
C₇×#2001	2
C₇×#1989	2
C₇×#1935	2
C₇×#1928	2
C₇×#1924	2
C₇×#1921	2
C₇×#1878	2
C₇×#1873	2
C₇×#1825	2
C₇×#1763	2
#26749	7

Subgroups — C7×#26749 #13203965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26749 #13203965