Subgroups — C₇×#61278 #13238494

Order 1792.

1860 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3354	C₂	1	2	yes	maximal, complemented
4	C₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₇×#3347	C₂	1	4	yes	maximal, complemented
6	C₇×#3346	C₂	1	4	yes	maximal, complemented
7	C₇×#3340	C₂	1	2	yes	maximal, complemented
8	C₇×#3334	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3098	C₂	1	2	yes	maximal, complemented
11	C₇×#3096	C₂	1	2	yes	maximal, complemented
12	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3062	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2913	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	2	yes	—
20	C₇×#559	—	2	2	no	—
21	C₇×#556	—	2	1	no	—
22	C₇×#556	C₂²	1	2	yes	complemented
23	C₇×#555	C₂²	1	2	yes	—
24	C₇×#555	C₂²	1	2	yes	complemented
25	C₇×#554	C₂²	1	2	yes	complemented
26	C₇×#553	—	2	2	no	—
27	C₇×#553	C₂²	1	4	yes	—
28	C₇×#550	—	2	1	no	—
29	C₇×#548	—	2	2	no	—
30	C₇×#547	C₂²	1	2	yes	—
31	C₇×#547	C₂²	1	2	yes	complemented
32	C₇×#542	—	2	2	no	—
33	C₇×#538	—	2	2	no	—
34	C₇×#537	C₂²	1	2	yes	—
35	C₇×#535	C₂²	1	2	yes	—
36	C₇×#533	—	2	1	no	—
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#532	—	2	1	no	—
39	C₇×#532	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₇×#525	—	2	2	no	—
42	C₇×#520	C₂²	1	2	yes	—
43	C₇×#520	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₇×#501	C₂²	1	4	yes	complemented
47	C₇×#500	C₂²	1	2	yes	complemented
48	C₇×#498	C₂²	1	2	yes	complemented
49	C₇×#485	C₂²	1	4	yes	complemented
50	C₇×#484	C₂²	1	4	yes	complemented
51	C₇×#482	C₂²	1	4	yes	—
52	C₇×#482	C₂²	1	4	yes	—
53	C₇×#482	C₂²	1	4	yes	complemented
54	C₇×#481	C₂²	1	4	yes	—
55	C₇×#480	C₂²	1	4	yes	—
56	C₇×#480	C₂²	1	4	yes	complemented
57	C₇×#479	C₂²	1	2	yes	complemented
58	C₇×#478	C₂²	1	2	yes	complemented
59	C₇×#477	C₂²	1	1	yes	characteristic, complemented
60	C₇×#476	C₂²	1	1	yes	characteristic, complemented
61	C₇×#475	C₂²	1	1	yes	characteristic, complemented
62	C₇×#474	C₂²	1	2	yes	—
63	C₇×#474	C₂²	1	4	yes	—
64	C₇×#474	C₂²	1	2	yes	—
65	C₇×#474	C₂²	1	1	yes	characteristic, complemented
66	C₇×#469	C₂²	1	4	yes	—
67	C₇×#468	C₂²	1	4	yes	—
68	C₇×#466	C₂²	1	4	yes	—
69	C₇×#465	C₂²	1	4	yes	—
70	C₇×#442	C₂²	1	2	yes	—
71	C₇×#440	C₂²	1	2	yes	—
72	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
73	C₄×C₇×D₈	C₂²	1	2	yes	—
74	C₇×#436	C₂²	1	2	yes	complemented
75	C₇×#435	C₂²	1	4	yes	complemented
76	C₇×C₈×D₄	C₂²	1	2	yes	complemented
77	C₇×#428	C₂²	1	2	yes	—
78	C₇×#428	C₂²	1	2	yes	—
79	C₇×#428	C₂²	1	1	yes	characteristic
80	C₇×#428	C₂²	1	4	yes	complemented
81	C₇×#428	C₂²	1	4	yes	complemented
82	C₇×#427	C₂²	1	2	yes	—
83	C₇×#427	C₂²	1	4	yes	complemented
84	C₂×C₇×#107	C₂²	1	2	yes	—
85	C₂×C₇×#107	C₂²	1	4	yes	complemented
86	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₇×#418	C₂²	1	1	yes	characteristic
88	C₇×#417	C₂²	1	1	yes	characteristic
89	C₇×#416	C₂²	1	2	yes	—
90	C₂×C₇×#102	C₂²	1	2	yes	—
91	C₇×#408	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	#61278	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	—	2	2	no	—
95	C₂×C₇×#41	—	2	2	no	—
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂×C₇×#41	C₂³	1	2	yes	—
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	—	2	1	no	—
101	C₇×AGL(1,ℤ/8)	—	2	4	no	—
102	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₇×D₈	C₂³	1	2	yes	—
104	C₇×#131	—	2	8	no	—
105	C₂×C₇×M₁₆	C₂³	1	4	yes	—
106	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	4	yes	—
109	C₂²×C₇×C₈	C₂³	1	2	yes	—
110	C₇×C₄⋊Q₈	—	2	1	no	—
111	C₇×C₄⋊Q₈	—	2	1	no	—
112	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×#127	—	2	2	no	—
118	C₇×#127	D₄	1	1	yes	characteristic
119	C₇×#126	—	2	4	no	—
120	C₇×#126	—	2	4	no	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	C₂³	1	2	yes	—
123	C₇×#124	—	2	2	no	—
124	C₇×#124	—	2	2	no	—
125	C₇×#124	—	2	4	no	—
126	C₇×#124	—	2	4	no	—
127	C₇×#124	D₄	1	2	yes	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	1	no	—
133	C₇×C₂²⋊Q₈	—	2	1	no	—
134	C₇×C₂²⋊Q₈	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₇×#121	—	2	2	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	4	no	—
142	C₇×#121	—	2	4	no	—
143	C₇×#121	D₄	1	2	yes	—
144	C₇×#121	D₄	1	2	yes	—
145	C₇×#121	C₂³	1	4	yes	—
146	C₇×#121	C₂³	1	4	yes	—
147	C₇×#121	C₂³	1	4	yes	—
148	C₇×#120	—	2	4	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
155	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
156	C₄×C₇×D₄	—	2	4	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	4	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	—	2	1	no	—
163	C₄×C₇×D₄	—	2	4	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	C₂³	1	2	yes	—
167	C₄×C₇×D₄	C₂³	1	2	yes	—
168	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
169	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
170	C₄×C₇×D₄	C₂³	1	2	yes	—
171	C₄×C₇×D₄	C₂³	1	2	yes	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	—	2	2	no	—
174	C₇×#117	—	2	1	no	—
175	C₇×#117	C₂³	1	4	yes	—
176	C₇×#117	C₂³	1	4	yes	—
177	C₇×#117	C₂³	1	1	yes	characteristic
178	C₇×#117	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	—	2	1	no	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₄²×C₇	—	2	1	no	—
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₇×#107	C₂³	1	4	yes	—
188	C₇×#107	C₂³	1	4	yes	—
189	C₇×#107	C₂³	1	4	yes	—
190	C₇×#107	C₂³	1	2	yes	—
191	C₇×#107	C₂³	1	2	yes	—
192	C₇×#107	C₂³	1	4	yes	—
193	C₇×#107	C₂³	1	2	yes	—
194	C₇×#106	C₂³	1	4	yes	—
195	C₇×#106	C₂³	1	2	yes	—
196	C₇×#106	C₂³	1	2	yes	—
197	C₇×#106	C₂³	1	4	yes	—
198	C₇×#106	C₂³	1	2	yes	—
199	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₇×C₄⋊C₈	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#103	C₂³	1	2	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	4	yes	—
207	C₇×#102	C₂³	1	4	yes	—
208	C₇×#102	C₂³	1	2	yes	—
209	C₇×#102	C₂³	1	2	yes	—
210	C₇×#102	C₂³	1	2	yes	—
211	C₇×#102	C₂³	1	2	yes	—
212	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₇×#97	C₂³	1	2	yes	—
215	C₄×C₇×C₈	C₂³	1	2	yes	—
216	#3511	C₂×C₇	1	1	yes	characteristic, complemented
217	#3506	C₂×C₇	1	1	yes	characteristic, complemented
218	#3354	C₂×C₇	1	2	yes	complemented
219	#3353	C₂×C₇	1	2	yes	complemented
220	#3347	C₂×C₇	1	4	yes	complemented
221	#3346	C₂×C₇	1	4	yes	complemented
222	#3340	C₂×C₇	1	2	yes	complemented
223	#3334	C₂×C₇	1	2	yes	complemented
224	#3165	C₂×C₇	1	1	yes	characteristic, complemented
225	#3098	C₂×C₇	1	2	yes	complemented
226	#3096	C₂×C₇	1	2	yes	complemented
227	#3076	C₂×C₇	1	1	yes	characteristic, complemented
228	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
229	#3062	C₂×C₇	1	2	yes	complemented
230	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
231	#2935	C₂×C₇	1	1	yes	characteristic, complemented
232	#2913	C₂×C₇	1	2	yes	complemented
233	C₂⁴×C₇	—	2	1	no	—
234	C₇×#41	—	2	4	no	—
235	C₇×#41	—	2	4	no	—
236	C₇×#41	—	2	2	no	—
237	C₇×#41	—	2	2	no	—
238	C₇×#41	—	8	4	no	—
239	C₇×#41	—	8	4	no	—
240	C₂×C₇×Q₈	—	2	1	no	—
241	C₂×C₇×Q₈	—	2	2	no	—
242	C₂×C₇×Q₈	—	2	1	no	—
243	C₂×C₇×Q₈	—	2	2	no	—
244	C₂×C₇×Q₈	—	8	2	no	—
245	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
246	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
247	C₂×C₇×D₄	—	2	1	no	—
248	C₂×C₇×D₄	—	2	4	no	—
249	C₂×C₇×D₄	—	2	4	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	1	no	—
252	C₂×C₇×D₄	—	2	2	no	—
253	C₂×C₇×D₄	—	2	2	no	—
254	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
255	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
256	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
257	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
258	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
259	C₂×C₇×D₄	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	—	2	1	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	4	no	—
263	C₂²×C₄×C₇	—	2	4	no	—
264	C₂²×C₄×C₇	—	2	1	no	—
265	C₂²×C₄×C₇	—	2	1	no	—
266	C₂²×C₄×C₇	—	2	1	no	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	8	2	no	—
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₇×SD₁₆	—	2	4	no	—
275	C₇×D₈	—	2	4	no	—
276	C₇×M₁₆	—	2	2	no	—
277	C₇×M₁₆	—	2	8	no	—
278	C₇×M₁₆	#41	1	4	yes	complemented
279	C₂×C₇×C₈	—	2	4	no	—
280	C₂×C₇×C₈	—	2	8	no	—
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₂×C₇×C₈	C₂⁴	1	2	yes	—
283	C₂×C₇×C₈	C₂⁴	1	2	yes	—
284	C₂×C₇×C₈	C₂⁴	1	2	yes	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	4	no	—
290	C₇×C₄⋊C₄	—	2	4	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	1	no	—
294	C₇×C₄⋊C₄	—	2	2	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
301	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₇×C₂²⋊C₄	—	2	1	no	—
307	C₇×C₂²⋊C₄	—	2	2	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₇×C₂²⋊C₄	—	2	1	no	—
314	C₇×C₂²⋊C₄	—	2	1	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	4	no	—
318	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
319	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
320	C₄²×C₇	—	2	1	no	—
321	C₄²×C₇	—	2	1	no	—
322	C₄²×C₇	—	2	1	no	—
323	C₄²×C₇	—	2	4	no	—
324	C₄²×C₇	—	2	4	no	—
325	C₄²×C₇	—	2	2	no	—
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂⁴	1	1	yes	characteristic
329	C₄²×C₇	C₂⁴	1	1	yes	characteristic
330	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
331	C₂×#131	C₂²×C₇	1	2	yes	—
332	#559	—	2	2	no	—
333	#556	—	2	1	no	—
334	#556	C₂²×C₇	1	2	yes	complemented
335	#555	C₂²×C₇	1	2	yes	—
336	#555	C₂²×C₇	1	2	yes	complemented
337	#554	C₂²×C₇	1	2	yes	complemented
338	#553	—	2	2	no	—
339	#553	C₂²×C₇	1	4	yes	—
340	#550	—	2	1	no	—
341	#548	—	2	2	no	—
342	#547	C₂²×C₇	1	2	yes	—
343	#547	C₂²×C₇	1	2	yes	complemented
344	#542	—	2	2	no	—
345	#538	—	2	2	no	—
346	#537	C₂²×C₇	1	2	yes	—
347	#535	C₂²×C₇	1	2	yes	—
348	#533	—	2	1	no	—
349	#533	C₂²×C₇	1	1	yes	characteristic
350	#532	—	2	1	no	—
351	#532	C₂²×C₇	1	1	yes	characteristic
352	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
353	#525	—	2	2	no	—
354	#520	C₂²×C₇	1	2	yes	—
355	#520	C₂²×C₇	1	2	yes	—
356	C₄×#41	C₂²×C₇	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
358	#501	C₂²×C₇	1	4	yes	complemented
359	#500	C₂²×C₇	1	2	yes	complemented
360	#498	C₂²×C₇	1	2	yes	complemented
361	#485	C₂²×C₇	1	4	yes	complemented
362	#484	C₂²×C₇	1	4	yes	complemented
363	#482	C₂²×C₇	1	4	yes	—
364	#482	C₂²×C₇	1	4	yes	—
365	#482	C₂²×C₇	1	4	yes	complemented
366	#481	C₂²×C₇	1	4	yes	—
367	#480	C₂²×C₇	1	4	yes	—
368	#480	C₂²×C₇	1	4	yes	complemented
369	#479	C₂²×C₇	1	2	yes	complemented
370	#478	C₂²×C₇	1	2	yes	complemented
371	#477	C₂²×C₇	1	1	yes	characteristic, complemented
372	#476	C₂²×C₇	1	1	yes	characteristic, complemented
373	#475	C₂²×C₇	1	1	yes	characteristic, complemented
374	#474	C₂²×C₇	1	2	yes	—
375	#474	C₂²×C₇	1	4	yes	—
376	#474	C₂²×C₇	1	2	yes	—
377	#474	C₂²×C₇	1	1	yes	characteristic, complemented
378	#469	C₂²×C₇	1	4	yes	—
379	#468	C₂²×C₇	1	4	yes	—
380	#466	C₂²×C₇	1	4	yes	—
381	#465	C₂²×C₇	1	4	yes	—
382	#442	C₂²×C₇	1	2	yes	—
383	#440	C₂²×C₇	1	2	yes	—
384	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
385	C₄×D₈	C₂²×C₇	1	2	yes	—
386	#436	C₂²×C₇	1	2	yes	complemented
387	#435	C₂²×C₇	1	4	yes	complemented
388	C₈×D₄	C₂²×C₇	1	2	yes	complemented
389	#428	C₂²×C₇	1	2	yes	—
390	#428	C₂²×C₇	1	2	yes	—
391	#428	C₂²×C₇	1	1	yes	characteristic
392	#428	C₂²×C₇	1	4	yes	complemented
393	#428	C₂²×C₇	1	4	yes	complemented
394	#427	C₂²×C₇	1	2	yes	—
395	#427	C₂²×C₇	1	4	yes	complemented
396	C₂×#107	C₂²×C₇	1	2	yes	—
397	C₂×#107	C₂²×C₇	1	4	yes	complemented
398	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
399	#418	C₂²×C₇	1	1	yes	characteristic
400	#417	C₂²×C₇	1	1	yes	characteristic
401	#416	C₂²×C₇	1	2	yes	—
402	C₂×#102	C₂²×C₇	1	2	yes	—
403	#408	C₂²×C₇	1	2	yes	—
404	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
405	C₂³×C₇	—	2	1	no	—
406	C₂³×C₇	—	2	2	no	—
407	C₂³×C₇	—	4	2	no	—
408	C₂³×C₇	—	8	1	no	—
409	C₂³×C₇	—	8	1	no	—
410	C₂³×C₇	C₂²×D₄	1	4	yes	—
411	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
412	C₇×Q₈	—	2	4	no	—
413	C₇×Q₈	—	2	1	no	—
414	C₇×Q₈	—	2	1	no	—
415	C₇×Q₈	—	4	4	no	—
416	C₇×Q₈	—	4	2	no	—
417	C₇×Q₈	—	8	1	no	—
418	C₇×Q₈	—	8	2	no	—
419	C₇×D₄	—	2	8	no	—
420	C₇×D₄	—	2	4	no	—
421	C₇×D₄	—	2	4	no	—
422	C₇×D₄	—	2	1	no	—
423	C₇×D₄	—	2	2	no	—
424	C₇×D₄	—	2	2	no	—
425	C₇×D₄	—	2	1	no	—
426	C₇×D₄	—	4	2	no	—
427	C₇×D₄	—	4	2	no	—
428	C₇×D₄	—	4	2	no	—
429	C₇×D₄	—	8	4	no	—
430	C₇×D₄	—	8	4	no	—
431	C₇×D₄	—	8	4	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	4	no	—
434	C₂×C₄×C₇	—	2	4	no	—
435	C₂×C₄×C₇	—	2	1	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	1	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	1	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	4	no	—
442	C₂×C₄×C₇	—	4	1	no	—
443	C₂×C₄×C₇	—	4	2	no	—
444	C₂×C₄×C₇	—	4	2	no	—
445	C₂×C₄×C₇	—	4	4	no	—
446	C₂×C₄×C₇	—	4	2	no	—
447	C₂×C₄×C₇	—	8	2	no	—
448	C₂×C₄×C₇	—	8	1	no	—
449	C₂×C₄×C₇	—	8	2	no	—
450	C₂×C₄×C₇	—	8	4	no	—
451	C₂×C₄×C₇	—	8	4	no	—
452	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
453	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂×#41	1	2	yes	—
459	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
460	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
461	C₇×C₈	—	2	2	no	—
462	C₇×C₈	—	2	2	no	—
463	C₇×C₈	—	2	2	no	—
464	C₇×C₈	C₂×#41	1	4	yes	—
465	C₂×#41	—	2	2	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	C₂³×C₇	1	1	yes	characteristic
468	C₂×#41	C₂³×C₇	1	2	yes	—
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	AGL(1,ℤ/8)	—	2	4	no	—
473	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
474	C₂×D₈	C₂³×C₇	1	2	yes	—
475	#131	—	2	8	no	—
476	C₂×M₁₆	C₂³×C₇	1	4	yes	—
477	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
478	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₇	1	2	yes	—
480	C₂²×C₈	C₂³×C₇	1	4	yes	—
481	C₄⋊Q₈	—	2	1	no	—
482	C₄⋊Q₈	—	2	1	no	—
483	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
485	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
486	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
488	#127	—	2	2	no	—
489	#127	C₇×D₄	1	1	yes	characteristic
490	#126	—	2	4	no	—
491	#126	—	2	4	no	—
492	#125	—	2	2	no	—
493	#125	C₂³×C₇	1	2	yes	—
494	#124	—	2	2	no	—
495	#124	—	2	2	no	—
496	#124	—	2	4	no	—
497	#124	—	2	4	no	—
498	#124	C₇×D₄	1	2	yes	—
499	#123	—	2	4	no	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	1	no	—
504	C₂²⋊Q₈	—	2	1	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	—	2	4	no	—
514	#121	C₇×D₄	1	2	yes	—
515	#121	C₇×D₄	1	2	yes	—
516	#121	C₂³×C₇	1	4	yes	—
517	#121	C₂³×C₇	1	4	yes	—
518	#121	C₂³×C₇	1	4	yes	—
519	#120	—	2	4	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
526	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	C₂³×C₇	1	2	yes	—
538	C₄×D₄	C₂³×C₇	1	2	yes	—
539	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
540	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
541	C₄×D₄	C₂³×C₇	1	2	yes	—
542	C₄×D₄	C₂³×C₇	1	2	yes	—
543	#117	—	2	2	no	—
544	#117	—	2	2	no	—
545	#117	—	2	1	no	—
546	#117	C₂³×C₇	1	1	yes	characteristic
547	#117	C₂³×C₇	1	2	yes	—
548	#117	C₂³×C₇	1	4	yes	—
549	#117	C₂³×C₇	1	4	yes	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
558	#107	C₂³×C₇	1	4	yes	—
559	#107	C₂³×C₇	1	4	yes	—
560	#107	C₂³×C₇	1	2	yes	—
561	#107	C₂³×C₇	1	2	yes	—
562	#107	C₂³×C₇	1	4	yes	—
563	#107	C₂³×C₇	1	2	yes	—
564	#107	C₂³×C₇	1	4	yes	—
565	#106	C₂³×C₇	1	2	yes	—
566	#106	C₂³×C₇	1	2	yes	—
567	#106	C₂³×C₇	1	2	yes	—
568	#106	C₂³×C₇	1	4	yes	—
569	#106	C₂³×C₇	1	4	yes	—
570	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
571	C₄⋊C₈	C₂³×C₇	1	2	yes	—
572	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
573	#103	C₂³×C₇	1	2	yes	—
574	#103	C₂³×C₇	1	2	yes	—
575	#103	C₂³×C₇	1	2	yes	—
576	#102	C₂³×C₇	1	4	yes	—
577	#102	C₂³×C₇	1	4	yes	—
578	#102	C₂³×C₇	1	2	yes	—
579	#102	C₂³×C₇	1	2	yes	—
580	#102	C₂³×C₇	1	2	yes	—
581	#102	C₂³×C₇	1	2	yes	—
582	#102	C₂³×C₇	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
584	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
585	#97	C₂³×C₇	1	2	yes	—
586	C₄×C₈	C₂³×C₇	1	2	yes	—
587	C₂²×C₇	—	2	1	no	—
588	C₂²×C₇	—	2	1	no	—
589	C₂²×C₇	—	2	4	no	—
590	C₂²×C₇	—	2	4	no	—
591	C₂²×C₇	—	2	4	no	—
592	C₂²×C₇	—	4	1	no	—
593	C₂²×C₇	—	4	2	no	—
594	C₂²×C₇	—	4	1	no	—
595	C₂²×C₇	—	4	2	no	—
596	C₂²×C₇	—	4	2	no	—
597	C₂²×C₇	—	4	1	no	—
598	C₂²×C₇	—	8	4	no	—
599	C₂²×C₇	#547	1	2	yes	—
600	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
601	C₄×C₇	—	2	1	no	—
602	C₄×C₇	—	2	1	no	—
603	C₄×C₇	—	2	4	no	—
604	C₄×C₇	—	2	1	no	—
605	C₄×C₇	—	4	1	no	—
606	C₄×C₇	—	4	2	no	—
607	C₄×C₇	—	4	1	no	—
608	C₄×C₇	—	4	2	no	—
609	C₄×C₇	—	4	1	no	—
610	C₄×C₇	—	4	2	no	—
611	C₄×C₇	—	4	4	no	—
612	C₄×C₇	#547	1	2	yes	—
613	C₄×C₇	#576	1	2	yes	—
614	C₄×C₇	C₂²×#41	1	1	yes	characteristic
615	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
616	C₂⁴	—	2	1	no	—
617	#41	—	2	4	no	—
618	#41	—	2	4	no	—
619	#41	—	2	2	no	—
620	#41	—	2	2	no	—
621	#41	—	8	4	no	—
622	#41	—	8	4	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	8	2	no	—
628	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
629	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
638	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
639	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
640	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
641	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
642	C₂×D₄	C₂⁴×C₇	1	2	yes	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	8	2	no	—
653	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
654	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
656	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
657	SD₁₆	—	2	4	no	—
658	D₈	—	2	4	no	—
659	M₁₆	—	2	2	no	—
660	M₁₆	—	2	8	no	—
661	M₁₆	C₇×#41	1	4	yes	complemented
662	C₂×C₈	—	2	4	no	—
663	C₂×C₈	—	2	8	no	—
664	C₂×C₈	C₂⁴×C₇	1	2	yes	—
665	C₂×C₈	C₂⁴×C₇	1	2	yes	—
666	C₂×C₈	C₂⁴×C₇	1	2	yes	—
667	C₂×C₈	C₂⁴×C₇	1	2	yes	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
682	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
684	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
685	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
688	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
702	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	4	no	—
708	C₄²	—	2	2	no	—
709	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
710	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
711	C₄²	C₂⁴×C₇	1	1	yes	characteristic
712	C₄²	C₂⁴×C₇	1	1	yes	characteristic
713	C₂×C₇	—	2	2	no	—
714	C₂×C₇	—	4	4	no	—
715	C₂×C₇	—	8	1	no	—
716	C₂×C₇	—	8	2	no	—
717	C₂×C₇	C₂×#547	1	1	yes	characteristic
718	C₂×C₇	C₂×#576	1	1	yes	characteristic
719	C₂×C₇	#3586	1	1	yes	characteristic
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	4	2	no	—
723	C₂³	—	8	1	no	—
724	C₂³	—	8	1	no	—
725	C₂³	C₂²×C₇×D₄	1	4	yes	—
726	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
727	Q₈	—	2	4	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	4	4	no	—
731	Q₈	—	4	2	no	—
732	Q₈	—	8	1	no	—
733	Q₈	—	8	2	no	—
734	D₄	—	2	8	no	—
735	D₄	—	2	1	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	8	4	no	—
745	D₄	—	8	4	no	—
746	D₄	—	8	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	8	2	no	—
763	C₂×C₄	—	8	1	no	—
764	C₂×C₄	—	8	2	no	—
765	C₂×C₄	—	8	4	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
768	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
769	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
770	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
771	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
772	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
773	C₂×C₄	C₂×C₇×#41	1	2	yes	—
774	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
775	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
776	C₈	—	2	2	no	—
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	C₂×C₇×#41	1	4	yes	—
780	C₇	#61278	1	1	yes	characteristic, direct product factor, Sylow
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	4	no	—
793	C₂²	C₇×#547	1	2	yes	—
794	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	4	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	4	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	1	no	—
806	C₄	C₇×#547	1	2	yes	—
807	C₄	C₇×#576	1	2	yes	—
808	C₄	C₂²×C₇×#41	1	1	yes	characteristic
809	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
810	C₂	—	2	2	no	—
811	C₂	—	4	4	no	—
812	C₂	—	8	2	no	—
813	C₂	—	8	1	no	—
814	C₂	C₂×C₇×#547	1	1	yes	characteristic
815	C₂	C₂×C₇×#576	1	1	yes	characteristic
816	C₂	C₇×#3586	1	1	yes	characteristic

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3511	C₂	semidirect
2. C₇×#3506	C₂	semidirect
3. C₇×#3354	C₂	semidirect
4. C₇×#3353	C₂	semidirect
5. C₇×#3347	C₂	semidirect
6. C₇×#3346	C₂	semidirect
7. C₇×#3340	C₂	semidirect
8. C₇×#3334	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3098	C₂	semidirect
11. C₇×#3096	C₂	semidirect
12. C₇×#3076	C₂	semidirect
13. C₂×C₇×#474	C₂	semidirect
14. C₇×#3062	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×#2935	C₂	semidirect
17. C₇×#2913	C₂	semidirect
22. C₇×#556	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
31. C₇×#547	C₂²	semidirect
46. C₇×#501	C₂²	semidirect
47. C₇×#500	C₂²	semidirect
48. C₇×#498	C₂²	semidirect
49. C₇×#485	C₂²	semidirect
50. C₇×#484	C₂²	semidirect
53. C₇×#482	C₂²	semidirect
56. C₇×#480	C₂²	semidirect
57. C₇×#479	C₂²	semidirect
58. C₇×#478	C₂²	semidirect
59. C₇×#477	C₂²	semidirect
60. C₇×#476	C₂²	semidirect
61. C₇×#475	C₂²	semidirect
65. C₇×#474	C₂²	semidirect
74. C₇×#436	C₂²	semidirect
75. C₇×#435	C₂²	semidirect
76. C₇×C₈×D₄	C₂²	semidirect
80. C₇×#428	C₂²	semidirect
81. C₇×#428	C₂²	semidirect
83. C₇×#427	C₂²	semidirect
85. C₂×C₇×#107	C₂²	semidirect
93. #61278	C₇	direct (N × H)
216. #3511	C₂×C₇	semidirect
217. #3506	C₂×C₇	semidirect
218. #3354	C₂×C₇	semidirect
219. #3353	C₂×C₇	semidirect
220. #3347	C₂×C₇	semidirect
221. #3346	C₂×C₇	semidirect
222. #3340	C₂×C₇	semidirect
223. #3334	C₂×C₇	semidirect
224. #3165	C₂×C₇	semidirect
225. #3098	C₂×C₇	semidirect
226. #3096	C₂×C₇	semidirect
227. #3076	C₂×C₇	semidirect
228. C₂×#474	C₂×C₇	semidirect
229. #3062	C₂×C₇	semidirect
230. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
231. #2935	C₂×C₇	semidirect
232. #2913	C₂×C₇	semidirect
278. C₇×M₁₆	#41	semidirect
334. #556	C₂²×C₇	semidirect
336. #555	C₂²×C₇	semidirect
337. #554	C₂²×C₇	semidirect
343. #547	C₂²×C₇	semidirect
358. #501	C₂²×C₇	semidirect
359. #500	C₂²×C₇	semidirect
360. #498	C₂²×C₇	semidirect
361. #485	C₂²×C₇	semidirect
362. #484	C₂²×C₇	semidirect
365. #482	C₂²×C₇	semidirect
368. #480	C₂²×C₇	semidirect
369. #479	C₂²×C₇	semidirect
370. #478	C₂²×C₇	semidirect
371. #477	C₂²×C₇	semidirect
372. #476	C₂²×C₇	semidirect
373. #475	C₂²×C₇	semidirect
377. #474	C₂²×C₇	semidirect
386. #436	C₂²×C₇	semidirect
387. #435	C₂²×C₇	semidirect
388. C₈×D₄	C₂²×C₇	semidirect
392. #428	C₂²×C₇	semidirect
393. #428	C₂²×C₇	semidirect
395. #427	C₂²×C₇	semidirect
397. C₂×#107	C₂²×C₇	semidirect
661. M₁₆	C₇×#41	semidirect
780. C₇	#61278	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×#3511	2
C₇×#3506	2
C₇×#3354	2
C₇×#3353	2
C₇×#3347	2
C₇×#3346	2
C₇×#3340	2
C₇×#3334	2
C₇×#3165	2
C₇×#3098	2
C₇×#3096	2
C₇×#3076	2
C₂×C₇×#474	2
C₇×#3062	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2935	2
C₇×#2913	2
#61278	7

Subgroups — C7×#61278 #13238494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61278 #13238494