Subgroups — C₇×#62824 #13240040

Order 1792.

7330 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3561	C₂	1	8	yes	maximal, complemented
2	C₇×#3558	C₂	1	8	yes	maximal, complemented
3	C₇×#3545	C₂	1	8	yes	maximal, complemented
4	C₇×#3514	C₂	1	16	yes	maximal, complemented
5	C₇×#3510	C₂	1	4	yes	maximal, complemented
6	C₇×#3500	C₂	1	4	yes	maximal, complemented
7	C₇×#3490	C₂	1	8	yes	maximal, complemented
8	C₇×#3486	C₂	1	2	yes	maximal, complemented
9	C₇×#3484	C₂	1	2	yes	maximal, complemented
10	C₇×#3444	C₂	1	2	yes	maximal, complemented
11	C₂²×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₇×#563	C₂²	1	8	yes	complemented
17	C₇×#562	C₂²	1	16	yes	complemented
18	C₇×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₇×#559	C₂²	1	16	yes	complemented
20	C₇×#556	C₂²	1	16	yes	complemented
21	C₇×#555	C₂²	1	16	yes	complemented
22	C₇×#551	C₂²	1	32	yes	complemented
23	C₇×#551	C₂²	1	32	yes	complemented
24	C₇×#551	C₂²	1	16	yes	complemented
25	C₇×D₄×Q₈	C₂²	1	16	yes	complemented
26	C₇×#548	C₂²	1	16	yes	complemented
27	C₇×#548	C₂²	1	16	yes	complemented
28	C₇×#546	C₂²	1	16	yes	complemented
29	C₇×#546	C₂²	1	32	yes	complemented
30	C₇×#546	C₂²	1	32	yes	complemented
31	C₇×#546	C₂²	1	16	yes	complemented
32	C₇×D₄²	C₂²	1	16	yes	complemented
33	C₇×#543	C₂²	1	8	yes	complemented
34	C₇×#542	C₂²	1	16	yes	complemented
35	C₇×#542	C₂²	1	32	yes	complemented
36	C₇×#538	C₂²	1	16	yes	complemented
37	C₇×#538	C₂²	1	16	yes	complemented
38	C₇×#538	C₂²	1	32	yes	complemented
39	C₇×#536	C₂²	1	4	yes	complemented
40	C₇×#536	C₂²	1	8	yes	complemented
41	C₇×#536	C₂²	1	8	yes	complemented
42	C₇×#535	C₂²	1	4	yes	—
43	C₇×#535	C₂²	1	8	yes	complemented
44	C₇×#534	C₂²	1	8	yes	complemented
45	C₇×#534	C₂²	1	8	yes	complemented
46	C₇×#533	C₂²	1	4	yes	complemented
47	C₇×#533	C₂²	1	2	yes	complemented
48	C₇×#532	C₂²	1	2	yes	complemented
49	C₇×#532	C₂²	1	4	yes	complemented
50	C₇×#532	C₂²	1	8	yes	complemented
51	C₇×#529	C₂²	1	8	yes	complemented
52	C₇×#529	C₂²	1	8	yes	complemented
53	C₇×#529	C₂²	1	8	yes	complemented
54	C₇×#529	C₂²	1	16	yes	complemented
55	C₂×C₇×#124	C₂²	1	8	yes	complemented
56	C₂×C₇×#124	C₂²	1	4	yes	complemented
57	C₂×C₇×#124	C₂²	1	8	yes	complemented
58	C₂×C₇×#124	C₂²	1	4	yes	complemented
59	C₂×C₇×#124	C₂²	1	8	yes	complemented
60	C₇×#525	C₂²	1	4	yes	complemented
61	C₇×#525	C₂²	1	8	yes	complemented
62	C₇×#525	C₂²	1	8	yes	complemented
63	C₂×C₇×#120	C₂²	1	8	yes	complemented
64	C₇×#519	C₂²	1	2	yes	complemented
65	C₇×#518	C₂²	1	2	yes	complemented
66	C₇×#518	C₂²	1	16	yes	complemented
67	C₄×C₇×#41	C₂²	1	4	yes	complemented
68	C₄×C₇×#41	C₂²	1	8	yes	complemented
69	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
70	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
71	#62824	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁵×C₇	C₂³	1	2	yes	—
73	C₇×2₋¹⁺⁴	—	4	8	no	—
74	C₇×H(5,𝔽₂)	—	4	8	no	—
75	C₂×C₇×#41	C₂³	1	4	yes	—
76	C₂×C₇×#41	C₂³	1	8	yes	—
77	C₂×C₇×#41	C₂³	1	8	yes	—
78	C₂×C₇×#41	C₂³	1	8	yes	—
79	C₂×C₇×#41	C₂³	1	8	yes	complemented
80	C₂²×C₇×Q₈	—	4	4	no	—
81	C₂²×C₇×Q₈	C₂³	1	2	yes	—
82	C₂²×C₇×Q₈	C₂³	1	2	yes	—
83	C₂²×C₇×Q₈	C₂³	1	8	yes	—
84	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
85	C₂²×C₇×D₄	—	4	4	no	—
86	C₂²×C₇×D₄	C₂³	1	2	yes	—
87	C₂²×C₇×D₄	C₂³	1	2	yes	—
88	C₂²×C₇×D₄	C₂³	1	8	yes	—
89	C₂²×C₇×D₄	C₂³	1	8	yes	—
90	C₂²×C₇×D₄	C₂³	1	8	yes	—
91	C₂²×C₇×D₄	C₂³	1	16	yes	—
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇	C₂³	1	2	yes	—
94	C₂³×C₄×C₇	C₂³	1	2	yes	—
95	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
96	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
97	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
98	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
99	C₇×#127	C₂³	1	8	yes	—
100	C₇×#127	C₂³	1	2	yes	complemented
101	C₇×#126	C₂³	1	16	yes	complemented
102	C₇×#126	C₂³	1	32	yes	complemented
103	C₇×#126	C₂³	1	32	yes	complemented
104	C₇×#125	C₂³	1	4	yes	complemented
105	C₇×#125	C₂³	1	8	yes	complemented
106	C₇×#124	C₂³	1	8	yes	—
107	C₇×#124	C₂³	1	8	yes	—
108	C₇×#124	C₂³	1	16	yes	—
109	C₇×#124	C₂³	1	16	yes	—
110	C₇×#124	C₂³	1	8	yes	—
111	C₇×#124	C₂³	1	8	yes	—
112	C₇×#124	C₂³	1	8	yes	—
113	C₇×#124	C₂³	1	4	yes	complemented
114	C₇×#124	C₂³	1	8	yes	complemented
115	C₇×#124	C₂³	1	32	yes	complemented
116	C₇×#124	C₂³	1	8	yes	complemented
117	C₇×#124	C₂³	1	16	yes	complemented
118	C₇×#124	C₂³	1	32	yes	complemented
119	C₇×#123	C₂³	1	8	yes	—
120	C₇×#123	C₂³	1	16	yes	—
121	C₇×#123	C₂³	1	16	yes	—
122	C₇×#123	C₂³	1	16	yes	—
123	C₇×#123	C₂³	1	32	yes	complemented
124	C₇×#123	C₂³	1	32	yes	complemented
125	C₇×#123	C₂³	1	32	yes	complemented
126	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
127	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
128	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
130	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
131	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
132	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
133	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
134	C₇×#121	C₂³	1	8	yes	—
135	C₇×#121	C₂³	1	8	yes	—
136	C₇×#121	C₂³	1	8	yes	—
137	C₇×#121	C₂³	1	16	yes	—
138	C₇×#121	C₂³	1	16	yes	—
139	C₇×#121	C₂³	1	32	yes	—
140	C₇×#121	C₂³	1	32	yes	complemented
141	C₇×#121	C₂³	1	32	yes	complemented
142	C₇×#120	C₂³	1	8	yes	—
143	C₇×#120	C₂³	1	16	yes	—
144	C₇×#120	C₂³	1	32	yes	—
145	C₇×#120	C₂³	1	16	yes	—
146	C₇×#120	C₂³	1	32	yes	complemented
147	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
148	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
149	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
150	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
151	C₄×C₇×D₄	C₂³	1	16	yes	—
152	C₄×C₇×D₄	C₂³	1	16	yes	—
153	C₄×C₇×D₄	C₂³	1	16	yes	—
154	C₄×C₇×D₄	C₂³	1	32	yes	—
155	C₄×C₇×D₄	C₂³	1	16	yes	—
156	C₄×C₇×D₄	C₂³	1	8	yes	complemented
157	C₄×C₇×D₄	C₂³	1	8	yes	complemented
158	C₄×C₇×D₄	C₂³	1	8	yes	complemented
159	C₄×C₇×D₄	C₂³	1	32	yes	complemented
160	C₄×C₇×D₄	C₂³	1	32	yes	complemented
161	C₇×#117	C₂³	1	4	yes	—
162	C₇×#117	C₂³	1	8	yes	—
163	C₇×#117	C₂³	1	8	yes	—
164	C₇×#117	C₂³	1	8	yes	complemented
165	C₇×#117	C₂³	1	16	yes	complemented
166	C₇×#117	C₂³	1	32	yes	complemented
167	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
174	C₂×C₄²×C₇	C₂³	1	4	yes	—
175	C₂×C₄²×C₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₇	C₂³	1	4	yes	—
178	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
179	#3561	C₂×C₇	1	8	yes	complemented
180	#3558	C₂×C₇	1	8	yes	complemented
181	#3545	C₂×C₇	1	8	yes	complemented
182	#3514	C₂×C₇	1	16	yes	complemented
183	#3510	C₂×C₇	1	4	yes	complemented
184	#3500	C₂×C₇	1	4	yes	complemented
185	#3490	C₂×C₇	1	8	yes	complemented
186	#3486	C₂×C₇	1	2	yes	complemented
187	#3484	C₂×C₇	1	2	yes	complemented
188	#3444	C₂×C₇	1	2	yes	complemented
189	C₂²×#124	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂⁴×C₇	—	4	4	no	—
191	C₂⁴×C₇	—	4	8	no	—
192	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₇	C₂⁴	1	4	yes	—
194	C₂⁴×C₇	C₂⁴	1	8	yes	—
195	C₂⁴×C₇	C₂⁴	1	8	yes	—
196	C₇×#41	—	2	16	no	—
197	C₇×#41	—	4	16	no	—
198	C₇×#41	—	4	16	no	—
199	C₇×#41	—	4	16	no	—
200	C₇×#41	—	4	16	no	—
201	C₂×C₇×Q₈	—	2	8	no	—
202	C₂×C₇×Q₈	—	4	4	no	—
203	C₂×C₇×Q₈	—	4	16	no	—
204	C₂×C₇×Q₈	—	4	16	no	—
205	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
206	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
207	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
208	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
209	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
210	C₂×C₇×D₄	—	2	8	no	—
211	C₂×C₇×D₄	—	4	16	no	—
212	C₂×C₇×D₄	—	4	16	no	—
213	C₂×C₇×D₄	—	4	4	no	—
214	C₂×C₇×D₄	—	4	32	no	—
215	C₂×C₇×D₄	—	4	16	no	—
216	C₂×C₇×D₄	C₂⁴	1	16	yes	—
217	C₂×C₇×D₄	C₂⁴	1	8	yes	—
218	C₂×C₇×D₄	C₂⁴	1	8	yes	—
219	C₂×C₇×D₄	C₂⁴	1	4	yes	—
220	C₂×C₇×D₄	C₂⁴	1	32	yes	—
221	C₂×C₇×D₄	C₂⁴	1	8	yes	—
222	C₂×C₇×D₄	C₂⁴	1	8	yes	—
223	C₂×C₇×D₄	C₂⁴	1	16	yes	—
224	C₂×C₇×D₄	C₂⁴	1	8	yes	—
225	C₂²×C₄×C₇	—	2	4	no	—
226	C₂²×C₄×C₇	—	4	4	no	—
227	C₂²×C₄×C₇	—	4	4	no	—
228	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
232	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
237	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
238	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
239	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
240	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
241	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
242	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
243	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
244	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
245	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
246	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
247	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
248	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
249	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
250	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
251	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
252	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
253	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
254	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
255	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
256	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
257	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
258	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
259	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
260	C₄²×C₇	C₂⁴	1	2	yes	—
261	C₄²×C₇	C₂⁴	1	2	yes	—
262	C₄²×C₇	C₂⁴	1	2	yes	—
263	C₄²×C₇	C₂⁴	1	4	yes	—
264	C₄²×C₇	C₂⁴	1	4	yes	—
265	C₄²×C₇	C₂⁴	1	2	yes	—
266	C₄²×C₇	C₂⁴	1	16	yes	—
267	C₄²×C₇	C₂⁴	1	8	yes	—
268	C₄²×C₇	C₂⁴	1	16	yes	—
269	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	complemented
270	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	complemented
271	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
272	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
273	#563	C₂²×C₇	1	8	yes	complemented
274	#562	C₂²×C₇	1	16	yes	complemented
275	H(3,𝔽₄)	C₂²×C₇	1	8	yes	complemented
276	#559	C₂²×C₇	1	16	yes	complemented
277	#556	C₂²×C₇	1	16	yes	complemented
278	#555	C₂²×C₇	1	16	yes	complemented
279	#551	C₂²×C₇	1	32	yes	complemented
280	#551	C₂²×C₇	1	32	yes	complemented
281	#551	C₂²×C₇	1	16	yes	complemented
282	D₄×Q₈	C₂²×C₇	1	16	yes	complemented
283	#548	C₂²×C₇	1	16	yes	complemented
284	#548	C₂²×C₇	1	16	yes	complemented
285	#546	C₂²×C₇	1	16	yes	complemented
286	#546	C₂²×C₇	1	32	yes	complemented
287	#546	C₂²×C₇	1	32	yes	complemented
288	#546	C₂²×C₇	1	16	yes	complemented
289	D₄²	C₂²×C₇	1	16	yes	complemented
290	#543	C₂²×C₇	1	8	yes	complemented
291	#542	C₂²×C₇	1	16	yes	complemented
292	#542	C₂²×C₇	1	32	yes	complemented
293	#538	C₂²×C₇	1	16	yes	complemented
294	#538	C₂²×C₇	1	16	yes	complemented
295	#538	C₂²×C₇	1	32	yes	complemented
296	#536	C₂²×C₇	1	4	yes	complemented
297	#536	C₂²×C₇	1	8	yes	complemented
298	#536	C₂²×C₇	1	8	yes	complemented
299	#535	C₂²×C₇	1	4	yes	—
300	#535	C₂²×C₇	1	8	yes	complemented
301	#534	C₂²×C₇	1	8	yes	complemented
302	#534	C₂²×C₇	1	8	yes	complemented
303	#533	C₂²×C₇	1	2	yes	complemented
304	#533	C₂²×C₇	1	4	yes	complemented
305	#532	C₂²×C₇	1	2	yes	complemented
306	#532	C₂²×C₇	1	4	yes	complemented
307	#532	C₂²×C₇	1	8	yes	complemented
308	#529	C₂²×C₇	1	8	yes	complemented
309	#529	C₂²×C₇	1	8	yes	complemented
310	#529	C₂²×C₇	1	8	yes	complemented
311	#529	C₂²×C₇	1	16	yes	complemented
312	C₂×#124	C₂²×C₇	1	4	yes	complemented
313	C₂×#124	C₂²×C₇	1	8	yes	complemented
314	C₂×#124	C₂²×C₇	1	4	yes	complemented
315	C₂×#124	C₂²×C₇	1	8	yes	complemented
316	C₂×#124	C₂²×C₇	1	8	yes	complemented
317	#525	C₂²×C₇	1	4	yes	complemented
318	#525	C₂²×C₇	1	8	yes	complemented
319	#525	C₂²×C₇	1	8	yes	complemented
320	C₂×#120	C₂²×C₇	1	8	yes	complemented
321	#519	C₂²×C₇	1	2	yes	complemented
322	#518	C₂²×C₇	1	2	yes	complemented
323	#518	C₂²×C₇	1	16	yes	complemented
324	C₄×#41	C₂²×C₇	1	4	yes	complemented
325	C₄×#41	C₂²×C₇	1	8	yes	complemented
326	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
327	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
328	C₂³×C₇	—	2	2	no	—
329	C₂³×C₇	—	2	4	no	—
330	C₂³×C₇	—	2	8	no	—
331	C₂³×C₇	—	2	16	no	—
332	C₂³×C₇	—	4	8	no	—
333	C₂³×C₇	—	4	8	no	—
334	C₂³×C₇	—	4	8	no	—
335	C₂³×C₇	—	4	8	no	—
336	C₂³×C₇	—	4	16	no	—
337	C₂³×C₇	—	8	16	no	—
338	C₂³×C₇	C₂⁵	1	8	yes	—
339	C₂³×C₇	C₂⁵	1	8	yes	—
340	C₂³×C₇	C₂⁵	1	1	yes	characteristic
341	C₂³×C₇	C₂⁵	1	2	yes	—
342	C₇×Q₈	—	2	16	no	—
343	C₇×Q₈	—	2	8	no	—
344	C₇×Q₈	—	4	8	no	—
345	C₇×Q₈	—	4	8	no	—
346	C₇×Q₈	—	4	8	no	—
347	C₇×D₄	—	2	16	no	—
348	C₇×D₄	—	2	32	no	—
349	C₇×D₄	—	2	16	no	—
350	C₇×D₄	—	2	8	no	—
351	C₇×D₄	—	4	8	no	—
352	C₇×D₄	—	4	16	no	—
353	C₇×D₄	—	4	32	no	—
354	C₇×D₄	—	4	8	no	—
355	C₇×D₄	—	4	8	no	—
356	C₂×C₄×C₇	—	2	2	no	—
357	C₂×C₄×C₇	—	2	8	no	—
358	C₂×C₄×C₇	—	2	8	no	—
359	C₂×C₄×C₇	—	2	8	no	—
360	C₂×C₄×C₇	—	2	16	no	—
361	C₂×C₄×C₇	—	4	2	no	—
362	C₂×C₄×C₇	—	4	4	no	—
363	C₂×C₄×C₇	—	4	2	no	—
364	C₂×C₄×C₇	—	4	8	no	—
365	C₂×C₄×C₇	—	4	16	no	—
366	C₂×C₄×C₇	—	4	8	no	—
367	C₂×C₄×C₇	—	4	16	no	—
368	C₂×C₄×C₇	—	4	16	no	—
369	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
370	C₂×C₄×C₇	C₂⁵	1	4	yes	—
371	C₂×C₄×C₇	C₂⁵	1	4	yes	—
372	C₂×C₄×C₇	C₂⁵	1	16	yes	—
373	C₂×C₄×C₇	C₂⁵	1	2	yes	—
374	C₂×C₄×C₇	C₂⁵	1	8	yes	—
375	C₂×C₄×C₇	C₂⁵	1	8	yes	—
376	C₂×C₄×C₇	C₂⁵	1	2	yes	—
377	C₂⁵	C₂³×C₇	1	2	yes	—
378	2₋¹⁺⁴	—	4	8	no	—
379	H(5,𝔽₂)	—	4	8	no	—
380	C₂×#41	C₂³×C₇	1	4	yes	—
381	C₂×#41	C₂³×C₇	1	8	yes	—
382	C₂×#41	C₂³×C₇	1	8	yes	—
383	C₂×#41	C₂³×C₇	1	8	yes	—
384	C₂×#41	C₂³×C₇	1	8	yes	complemented
385	C₂²×Q₈	—	4	4	no	—
386	C₂²×Q₈	C₂³×C₇	1	2	yes	—
387	C₂²×Q₈	C₂³×C₇	1	2	yes	—
388	C₂²×Q₈	C₂³×C₇	1	8	yes	—
389	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
390	C₂²×D₄	—	4	4	no	—
391	C₂²×D₄	C₂³×C₇	1	2	yes	—
392	C₂²×D₄	C₂³×C₇	1	16	yes	—
393	C₂²×D₄	C₂³×C₇	1	8	yes	—
394	C₂²×D₄	C₂³×C₇	1	2	yes	—
395	C₂²×D₄	C₂³×C₇	1	8	yes	—
396	C₂²×D₄	C₂³×C₇	1	8	yes	—
397	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₇	1	2	yes	—
399	C₂³×C₄	C₂³×C₇	1	2	yes	—
400	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
401	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
402	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
403	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
404	#127	C₂³×C₇	1	8	yes	—
405	#127	C₂³×C₇	1	2	yes	complemented
406	#126	C₂³×C₇	1	16	yes	complemented
407	#126	C₂³×C₇	1	32	yes	complemented
408	#126	C₂³×C₇	1	32	yes	complemented
409	#125	C₂³×C₇	1	4	yes	complemented
410	#125	C₂³×C₇	1	8	yes	complemented
411	#124	C₂³×C₇	1	8	yes	—
412	#124	C₂³×C₇	1	8	yes	—
413	#124	C₂³×C₇	1	16	yes	—
414	#124	C₂³×C₇	1	16	yes	—
415	#124	C₂³×C₇	1	8	yes	—
416	#124	C₂³×C₇	1	8	yes	—
417	#124	C₂³×C₇	1	8	yes	—
418	#124	C₂³×C₇	1	4	yes	complemented
419	#124	C₂³×C₇	1	8	yes	complemented
420	#124	C₂³×C₇	1	32	yes	complemented
421	#124	C₂³×C₇	1	8	yes	complemented
422	#124	C₂³×C₇	1	16	yes	complemented
423	#124	C₂³×C₇	1	32	yes	complemented
424	#123	C₂³×C₇	1	8	yes	—
425	#123	C₂³×C₇	1	16	yes	—
426	#123	C₂³×C₇	1	16	yes	—
427	#123	C₂³×C₇	1	16	yes	—
428	#123	C₂³×C₇	1	32	yes	complemented
429	#123	C₂³×C₇	1	32	yes	complemented
430	#123	C₂³×C₇	1	32	yes	complemented
431	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
432	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
433	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
434	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
435	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
436	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
437	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
438	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
439	#121	C₂³×C₇	1	8	yes	—
440	#121	C₂³×C₇	1	8	yes	—
441	#121	C₂³×C₇	1	8	yes	—
442	#121	C₂³×C₇	1	16	yes	—
443	#121	C₂³×C₇	1	16	yes	—
444	#121	C₂³×C₇	1	32	yes	—
445	#121	C₂³×C₇	1	32	yes	complemented
446	#121	C₂³×C₇	1	32	yes	complemented
447	#120	C₂³×C₇	1	8	yes	—
448	#120	C₂³×C₇	1	16	yes	—
449	#120	C₂³×C₇	1	32	yes	—
450	#120	C₂³×C₇	1	16	yes	—
451	#120	C₂³×C₇	1	32	yes	complemented
452	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
453	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
454	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
455	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
456	C₄×D₄	C₂³×C₇	1	16	yes	—
457	C₄×D₄	C₂³×C₇	1	16	yes	—
458	C₄×D₄	C₂³×C₇	1	16	yes	—
459	C₄×D₄	C₂³×C₇	1	32	yes	—
460	C₄×D₄	C₂³×C₇	1	16	yes	—
461	C₄×D₄	C₂³×C₇	1	8	yes	complemented
462	C₄×D₄	C₂³×C₇	1	8	yes	complemented
463	C₄×D₄	C₂³×C₇	1	8	yes	complemented
464	C₄×D₄	C₂³×C₇	1	32	yes	complemented
465	C₄×D₄	C₂³×C₇	1	32	yes	complemented
466	#117	C₂³×C₇	1	4	yes	—
467	#117	C₂³×C₇	1	8	yes	—
468	#117	C₂³×C₇	1	8	yes	—
469	#117	C₂³×C₇	1	8	yes	complemented
470	#117	C₂³×C₇	1	16	yes	complemented
471	#117	C₂³×C₇	1	32	yes	complemented
472	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
479	C₂×C₄²	C₂³×C₇	1	4	yes	—
480	C₂×C₄²	C₂³×C₇	1	2	yes	—
481	C₂×C₄²	C₂³×C₇	1	2	yes	—
482	C₂×C₄²	C₂³×C₇	1	4	yes	—
483	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
484	C₂²×C₇	—	2	8	no	—
485	C₂²×C₇	—	2	2	no	—
486	C₂²×C₇	—	2	2	no	—
487	C₂²×C₇	—	2	2	no	—
488	C₂²×C₇	—	2	8	no	—
489	C₂²×C₇	—	2	8	no	—
490	C₂²×C₇	—	2	16	no	—
491	C₂²×C₇	—	2	16	no	—
492	C₂²×C₇	—	8	8	no	—
493	C₂²×C₇	—	8	16	no	—
494	C₂²×C₇	—	16	8	no	—
495	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
496	C₂²×C₇	#585	1	4	yes	—
497	C₂²×C₇	C₂⁶	1	1	yes	characteristic
498	C₄×C₇	—	2	2	no	—
499	C₄×C₇	—	2	8	no	—
500	C₄×C₇	—	2	8	no	—
501	C₄×C₇	—	2	4	no	—
502	C₄×C₇	—	2	4	no	—
503	C₄×C₇	—	2	16	no	—
504	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
505	C₂⁴	—	4	4	no	—
506	C₂⁴	—	4	8	no	—
507	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
508	C₂⁴	C₂⁴×C₇	1	4	yes	—
509	C₂⁴	C₂⁴×C₇	1	8	yes	—
510	C₂⁴	C₂⁴×C₇	1	8	yes	—
511	#41	—	2	16	no	—
512	#41	—	4	16	no	—
513	#41	—	4	16	no	—
514	#41	—	4	16	no	—
515	#41	—	4	16	no	—
516	C₂×Q₈	—	2	8	no	—
517	C₂×Q₈	—	4	4	no	—
518	C₂×Q₈	—	4	16	no	—
519	C₂×Q₈	—	4	16	no	—
520	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
521	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
522	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
523	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
524	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	4	16	no	—
527	C₂×D₄	—	4	16	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	32	no	—
530	C₂×D₄	—	4	16	no	—
531	C₂×D₄	C₂⁴×C₇	1	16	yes	—
532	C₂×D₄	C₂⁴×C₇	1	8	yes	—
533	C₂×D₄	C₂⁴×C₇	1	8	yes	—
534	C₂×D₄	C₂⁴×C₇	1	4	yes	—
535	C₂×D₄	C₂⁴×C₇	1	32	yes	—
536	C₂×D₄	C₂⁴×C₇	1	8	yes	—
537	C₂×D₄	C₂⁴×C₇	1	8	yes	—
538	C₂×D₄	C₂⁴×C₇	1	16	yes	—
539	C₂×D₄	C₂⁴×C₇	1	8	yes	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
547	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
552	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
553	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
554	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
555	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
556	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
557	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
558	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
559	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
560	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
561	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
562	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
563	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
564	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
565	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
566	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
567	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
568	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
569	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
570	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
571	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
572	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
573	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
574	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
575	C₄²	C₂⁴×C₇	1	2	yes	—
576	C₄²	C₂⁴×C₇	1	2	yes	—
577	C₄²	C₂⁴×C₇	1	2	yes	—
578	C₄²	C₂⁴×C₇	1	4	yes	—
579	C₄²	C₂⁴×C₇	1	4	yes	—
580	C₄²	C₂⁴×C₇	1	2	yes	—
581	C₄²	C₂⁴×C₇	1	16	yes	—
582	C₄²	C₂⁴×C₇	1	8	yes	—
583	C₄²	C₂⁴×C₇	1	16	yes	—
584	C₂×C₇	—	2	2	no	—
585	C₂×C₇	—	2	4	no	—
586	C₂×C₇	—	4	8	no	—
587	C₂×C₇	—	4	8	no	—
588	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×C₇	C₂×#585	1	2	yes	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	8	no	—
593	C₂³	—	2	16	no	—
594	C₂³	—	4	8	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	8	no	—
598	C₂³	—	4	16	no	—
599	C₂³	—	8	16	no	—
600	C₂³	C₂⁵×C₇	1	8	yes	—
601	C₂³	C₂⁵×C₇	1	8	yes	—
602	C₂³	C₂⁵×C₇	1	1	yes	characteristic
603	C₂³	C₂⁵×C₇	1	2	yes	—
604	Q₈	—	2	16	no	—
605	Q₈	—	2	8	no	—
606	Q₈	—	4	8	no	—
607	Q₈	—	4	8	no	—
608	Q₈	—	4	8	no	—
609	D₄	—	2	16	no	—
610	D₄	—	2	32	no	—
611	D₄	—	2	16	no	—
612	D₄	—	2	8	no	—
613	D₄	—	4	8	no	—
614	D₄	—	4	16	no	—
615	D₄	—	4	32	no	—
616	D₄	—	4	8	no	—
617	D₄	—	4	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	16	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	16	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	16	no	—
630	C₂×C₄	—	4	16	no	—
631	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
632	C₂×C₄	C₂⁵×C₇	1	4	yes	—
633	C₂×C₄	C₂⁵×C₇	1	4	yes	—
634	C₂×C₄	C₂⁵×C₇	1	16	yes	—
635	C₂×C₄	C₂⁵×C₇	1	2	yes	—
636	C₂×C₄	C₂⁵×C₇	1	8	yes	—
637	C₂×C₄	C₂⁵×C₇	1	8	yes	—
638	C₂×C₄	C₂⁵×C₇	1	2	yes	—
639	C₇	#62824	1	1	yes	characteristic, direct product factor, Sylow
640	C₂²	—	2	8	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	2	16	no	—
648	C₂²	—	8	8	no	—
649	C₂²	—	8	16	no	—
650	C₂²	—	16	8	no	—
651	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
652	C₂²	C₇×#585	1	4	yes	—
653	C₂²	C₂⁶×C₇	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	16	no	—
660	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
661	C₂	—	2	2	no	—
662	C₂	—	2	4	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	8	no	—
665	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂	C₂×C₇×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3561	C₂	semidirect
2. C₇×#3558	C₂	semidirect
3. C₇×#3545	C₂	semidirect
4. C₇×#3514	C₂	semidirect
5. C₇×#3510	C₂	semidirect
6. C₇×#3500	C₂	semidirect
7. C₇×#3490	C₂	semidirect
8. C₇×#3486	C₂	semidirect
9. C₇×#3484	C₂	semidirect
10. C₇×#3444	C₂	semidirect
11. C₂²×C₇×#124	C₂	semidirect
12. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
14. C₂³×C₇×Q₈	C₂²	semidirect
16. C₇×#563	C₂²	semidirect
17. C₇×#562	C₂²	semidirect
18. C₇×H(3,𝔽₄)	C₂²	semidirect
19. C₇×#559	C₂²	semidirect
20. C₇×#556	C₂²	semidirect
21. C₇×#555	C₂²	semidirect
22. C₇×#551	C₂²	semidirect
23. C₇×#551	C₂²	semidirect
24. C₇×#551	C₂²	semidirect
25. C₇×D₄×Q₈	C₂²	semidirect
26. C₇×#548	C₂²	semidirect
27. C₇×#548	C₂²	semidirect
28. C₇×#546	C₂²	semidirect
29. C₇×#546	C₂²	semidirect
30. C₇×#546	C₂²	semidirect
31. C₇×#546	C₂²	semidirect
32. C₇×D₄²	C₂²	semidirect
33. C₇×#543	C₂²	semidirect
34. C₇×#542	C₂²	semidirect
35. C₇×#542	C₂²	semidirect
36. C₇×#538	C₂²	semidirect
37. C₇×#538	C₂²	semidirect
38. C₇×#538	C₂²	semidirect
39. C₇×#536	C₂²	semidirect
40. C₇×#536	C₂²	semidirect
41. C₇×#536	C₂²	semidirect
43. C₇×#535	C₂²	semidirect
44. C₇×#534	C₂²	semidirect
45. C₇×#534	C₂²	semidirect
46. C₇×#533	C₂²	semidirect
47. C₇×#533	C₂²	semidirect
48. C₇×#532	C₂²	semidirect
49. C₇×#532	C₂²	semidirect
50. C₇×#532	C₂²	semidirect
51. C₇×#529	C₂²	semidirect
52. C₇×#529	C₂²	semidirect
53. C₇×#529	C₂²	semidirect
54. C₇×#529	C₂²	semidirect
55. C₂×C₇×#124	C₂²	semidirect
56. C₂×C₇×#124	C₂²	semidirect
57. C₂×C₇×#124	C₂²	semidirect
58. C₂×C₇×#124	C₂²	semidirect
59. C₂×C₇×#124	C₂²	semidirect
60. C₇×#525	C₂²	semidirect
61. C₇×#525	C₂²	semidirect
62. C₇×#525	C₂²	semidirect
63. C₂×C₇×#120	C₂²	semidirect
64. C₇×#519	C₂²	semidirect
65. C₇×#518	C₂²	semidirect
66. C₇×#518	C₂²	semidirect
67. C₄×C₇×#41	C₂²	semidirect
68. C₄×C₇×#41	C₂²	semidirect
69. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
70. C₂²×C₄²×C₇	C₂²	semidirect
71. #62824	C₇	direct (N × H)
79. C₂×C₇×#41	C₂³	semidirect
84. C₂²×C₇×Q₈	C₂³	semidirect
95. C₇×C₄⋊Q₈	C₂³	semidirect
96. C₇×C₄⋊Q₈	C₂³	semidirect
97. C₇×C₄⋊Q₈	C₂³	semidirect
98. C₇×C₄⋊Q₈	C₂³	semidirect
100. C₇×#127	C₂³	semidirect
101. C₇×#126	C₂³	semidirect
102. C₇×#126	C₂³	semidirect
103. C₇×#126	C₂³	semidirect
104. C₇×#125	C₂³	semidirect
105. C₇×#125	C₂³	semidirect
113. C₇×#124	C₂³	semidirect
114. C₇×#124	C₂³	semidirect
115. C₇×#124	C₂³	semidirect
116. C₇×#124	C₂³	semidirect
117. C₇×#124	C₂³	semidirect
118. C₇×#124	C₂³	semidirect
123. C₇×#123	C₂³	semidirect
124. C₇×#123	C₂³	semidirect
125. C₇×#123	C₂³	semidirect
130. C₇×C₂²⋊Q₈	C₂³	semidirect
131. C₇×C₂²⋊Q₈	C₂³	semidirect
132. C₇×C₂²⋊Q₈	C₂³	semidirect
133. C₇×C₂²⋊Q₈	C₂³	semidirect
140. C₇×#121	C₂³	semidirect
141. C₇×#121	C₂³	semidirect
146. C₇×#120	C₂³	semidirect
147. C₄×C₇×Q₈	C₂³	semidirect
148. C₄×C₇×Q₈	C₂³	semidirect
149. C₄×C₇×Q₈	C₂³	semidirect
150. C₄×C₇×Q₈	C₂³	semidirect
156. C₄×C₇×D₄	C₂³	semidirect
157. C₄×C₇×D₄	C₂³	semidirect
158. C₄×C₇×D₄	C₂³	semidirect
159. C₄×C₇×D₄	C₂³	semidirect
160. C₄×C₇×D₄	C₂³	semidirect
164. C₇×#117	C₂³	semidirect
165. C₇×#117	C₂³	semidirect
166. C₇×#117	C₂³	semidirect
173. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
178. C₂×C₄²×C₇	C₂³	semidirect
179. #3561	C₂×C₇	semidirect
180. #3558	C₂×C₇	semidirect
181. #3545	C₂×C₇	semidirect
182. #3514	C₂×C₇	semidirect
183. #3510	C₂×C₇	semidirect
184. #3500	C₂×C₇	semidirect
185. #3490	C₂×C₇	semidirect
186. #3486	C₂×C₇	semidirect
187. #3484	C₂×C₇	semidirect
188. #3444	C₂×C₇	semidirect
189. C₂²×#124	C₂×C₇	semidirect
269. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
270. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
271. C₂³×Q₈	C₂²×C₇	semidirect
273. #563	C₂²×C₇	semidirect
274. #562	C₂²×C₇	semidirect
275. H(3,𝔽₄)	C₂²×C₇	semidirect
276. #559	C₂²×C₇	semidirect
277. #556	C₂²×C₇	semidirect
278. #555	C₂²×C₇	semidirect
279. #551	C₂²×C₇	semidirect
280. #551	C₂²×C₇	semidirect
281. #551	C₂²×C₇	semidirect
282. D₄×Q₈	C₂²×C₇	semidirect
283. #548	C₂²×C₇	semidirect
284. #548	C₂²×C₇	semidirect
285. #546	C₂²×C₇	semidirect
286. #546	C₂²×C₇	semidirect
287. #546	C₂²×C₇	semidirect
288. #546	C₂²×C₇	semidirect
289. D₄²	C₂²×C₇	semidirect
290. #543	C₂²×C₇	semidirect
291. #542	C₂²×C₇	semidirect
292. #542	C₂²×C₇	semidirect
293. #538	C₂²×C₇	semidirect
294. #538	C₂²×C₇	semidirect
295. #538	C₂²×C₇	semidirect
296. #536	C₂²×C₇	semidirect
297. #536	C₂²×C₇	semidirect
298. #536	C₂²×C₇	semidirect
300. #535	C₂²×C₇	semidirect
301. #534	C₂²×C₇	semidirect
302. #534	C₂²×C₇	semidirect
303. #533	C₂²×C₇	semidirect
304. #533	C₂²×C₇	semidirect
305. #532	C₂²×C₇	semidirect
306. #532	C₂²×C₇	semidirect
307. #532	C₂²×C₇	semidirect
308. #529	C₂²×C₇	semidirect
309. #529	C₂²×C₇	semidirect
310. #529	C₂²×C₇	semidirect
311. #529	C₂²×C₇	semidirect
312. C₂×#124	C₂²×C₇	semidirect
313. C₂×#124	C₂²×C₇	semidirect
314. C₂×#124	C₂²×C₇	semidirect
315. C₂×#124	C₂²×C₇	semidirect
316. C₂×#124	C₂²×C₇	semidirect
317. #525	C₂²×C₇	semidirect
318. #525	C₂²×C₇	semidirect
319. #525	C₂²×C₇	semidirect
320. C₂×#120	C₂²×C₇	semidirect
321. #519	C₂²×C₇	semidirect
322. #518	C₂²×C₇	semidirect
323. #518	C₂²×C₇	semidirect
324. C₄×#41	C₂²×C₇	semidirect
325. C₄×#41	C₂²×C₇	semidirect
326. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
327. C₂²×C₄²	C₂²×C₇	semidirect
384. C₂×#41	C₂³×C₇	semidirect
389. C₂²×Q₈	C₂³×C₇	semidirect
400. C₄⋊Q₈	C₂³×C₇	semidirect
401. C₄⋊Q₈	C₂³×C₇	semidirect
402. C₄⋊Q₈	C₂³×C₇	semidirect
403. C₄⋊Q₈	C₂³×C₇	semidirect
405. #127	C₂³×C₇	semidirect
406. #126	C₂³×C₇	semidirect
407. #126	C₂³×C₇	semidirect
408. #126	C₂³×C₇	semidirect
409. #125	C₂³×C₇	semidirect
410. #125	C₂³×C₇	semidirect
418. #124	C₂³×C₇	semidirect
419. #124	C₂³×C₇	semidirect
420. #124	C₂³×C₇	semidirect
421. #124	C₂³×C₇	semidirect
422. #124	C₂³×C₇	semidirect
423. #124	C₂³×C₇	semidirect
428. #123	C₂³×C₇	semidirect
429. #123	C₂³×C₇	semidirect
430. #123	C₂³×C₇	semidirect
435. C₂²⋊Q₈	C₂³×C₇	semidirect
436. C₂²⋊Q₈	C₂³×C₇	semidirect
437. C₂²⋊Q₈	C₂³×C₇	semidirect
438. C₂²⋊Q₈	C₂³×C₇	semidirect
445. #121	C₂³×C₇	semidirect
446. #121	C₂³×C₇	semidirect
451. #120	C₂³×C₇	semidirect
452. C₄×Q₈	C₂³×C₇	semidirect
453. C₄×Q₈	C₂³×C₇	semidirect
454. C₄×Q₈	C₂³×C₇	semidirect
455. C₄×Q₈	C₂³×C₇	semidirect
461. C₄×D₄	C₂³×C₇	semidirect
462. C₄×D₄	C₂³×C₇	semidirect
463. C₄×D₄	C₂³×C₇	semidirect
464. C₄×D₄	C₂³×C₇	semidirect
465. C₄×D₄	C₂³×C₇	semidirect
469. #117	C₂³×C₇	semidirect
470. #117	C₂³×C₇	semidirect
471. #117	C₂³×C₇	semidirect
478. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
483. C₂×C₄²	C₂³×C₇	semidirect
639. C₇	#62824	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×#3561	2
C₇×#3558	2
C₇×#3545	2
C₇×#3514	2
C₇×#3510	2
C₇×#3500	2
C₇×#3490	2
C₇×#3486	2
C₇×#3484	2
C₇×#3444	2
C₂²×C₇×#124	2
#62824	7

Subgroups — C7×#62824 #13240040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62824 #13240040