Subgroups — C₇×#61340 #13238556

Order 1792.

1792 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3376	C₂	1	4	yes	maximal, complemented
4	C₇×#3372	C₂	1	2	yes	maximal, complemented
5	C₇×#3372	C₂	1	4	yes	maximal, complemented
6	C₇×#3367	C₂	1	2	yes	maximal, complemented
7	C₇×#3360	C₂	1	2	yes	maximal, complemented
8	C₇×#3359	C₂	1	2	yes	maximal, complemented
9	C₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3137	C₂	1	2	yes	maximal, complemented
11	C₇×#3082	C₂	1	2	yes	maximal, complemented
12	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3042	C₂	1	2	yes	maximal
14	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
20	C₇×#557	C₂²	1	2	yes	complemented
21	C₇×#557	C₂²	1	2	yes	complemented
22	C₇×#556	C₂²	1	2	yes	complemented
23	C₇×#556	C₂²	1	2	yes	complemented
24	C₇×#554	—	2	1	no	—
25	C₇×#554	—	2	2	no	—
26	C₇×#554	C₂²	1	2	yes	—
27	C₇×#554	C₂²	1	4	yes	—
28	C₇×#552	—	2	2	no	—
29	C₇×#552	—	2	2	no	—
30	C₇×D₄×Q₈	—	2	1	no	—
31	C₇×D₄×Q₈	C₂²	1	2	yes	—
32	C₇×#544	C₂²	1	2	yes	—
33	C₇×#543	—	2	2	no	—
34	C₇×#541	—	2	2	no	—
35	C₇×#536	C₂²	1	2	yes	—
36	C₇×#533	—	2	1	no	—
37	C₇×#533	—	2	1	no	—
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₇×#533	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
42	C₇×#519	C₂²	1	2	yes	—
43	C₇×#518	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×#491	C₂²	1	4	yes	complemented
47	C₇×#491	C₂²	1	4	yes	complemented
48	C₇×#489	C₂²	1	4	yes	complemented
49	C₇×#488	C₂²	1	4	yes	complemented
50	C₇×#487	C₂²	1	2	yes	complemented
51	C₇×#487	C₂²	1	4	yes	complemented
52	C₇×#487	C₂²	1	2	yes	complemented
53	C₇×#479	C₂²	1	2	yes	complemented
54	C₇×#479	C₂²	1	4	yes	complemented
55	C₇×#479	C₂²	1	4	yes	complemented
56	C₇×#478	C₂²	1	2	yes	complemented
57	C₇×#477	C₂²	1	1	yes	characteristic, complemented
58	C₇×#477	C₂²	1	4	yes	complemented
59	C₇×#476	C₂²	1	1	yes	characteristic, complemented
60	C₇×#475	C₂²	1	1	yes	characteristic, complemented
61	C₇×#475	C₂²	1	4	yes	complemented
62	C₇×#474	C₂²	1	1	yes	characteristic, complemented
63	C₇×#463	C₂²	1	4	yes	—
64	C₇×#463	C₂²	1	4	yes	—
65	C₇×#461	C₂²	1	2	yes	—
66	C₇×#461	C₂²	1	2	yes	—
67	C₇×#461	C₂²	1	4	yes	—
68	C₇×#461	C₂²	1	4	yes	—
69	C₇×#461	C₂²	1	4	yes	—
70	C₇×#446	C₂²	1	2	yes	complemented
71	C₇×#446	C₂²	1	4	yes	complemented
72	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
73	C₇×#442	C₂²	1	2	yes	—
74	C₇×#440	C₂²	1	2	yes	—
75	C₇×#440	C₂²	1	4	yes	—
76	C₇×#440	C₂²	1	4	yes	—
77	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
78	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
79	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
80	C₄×C₇×D₈	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₇×#427	C₂²	1	2	yes	—
83	C₇×#424	C₂²	1	2	yes	—
84	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₇×#419	C₂²	1	2	yes	—
86	C₇×#419	C₂²	1	2	yes	—
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×#103	C₂²	1	2	yes	—
91	C₇×#405	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	#61340	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	C₂³	1	1	yes	characteristic
95	C₂²×C₇×Q₈	—	2	2	no	—
96	C₂²×C₇×Q₈	C₂³	1	2	yes	—
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	—	2	1	no	—
99	C₇×AGL(1,ℤ/8)	—	2	4	no	—
100	C₂×C₇×SD₁₆	—	2	8	no	—
101	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₇×D₈	C₂³	1	2	yes	—
105	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	C₂³	1	2	yes	—
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	—	2	1	no	—
110	C₇×C₄⋊Q₈	—	2	1	no	—
111	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₇×C₄⋊Q₈	C₂³	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	—	2	2	no	—
123	C₇×#125	—	2	4	no	—
124	C₇×#125	—	2	4	no	—
125	C₇×#125	—	2	2	no	—
126	C₇×#125	D₄	1	2	yes	—
127	C₇×#125	C₂³	1	2	yes	—
128	C₇×#125	C₂³	1	4	yes	—
129	C₇×#124	C₂³	1	4	yes	—
130	C₇×#123	—	2	4	no	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	2	no	—
133	C₇×C₂²⋊Q₈	—	2	2	no	—
134	C₇×C₂²⋊Q₈	—	2	4	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	2	no	—
140	C₇×C₂²⋊Q₈	—	2	2	no	—
141	C₇×C₂²⋊Q₈	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	4	no	—
143	C₇×C₂²⋊Q₈	—	2	4	no	—
144	C₇×C₂²⋊Q₈	—	2	4	no	—
145	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
146	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
154	C₄×C₇×Q₈	C₂³	1	4	yes	—
155	C₄×C₇×Q₈	C₂³	1	4	yes	—
156	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
157	C₄×C₇×Q₈	C₂³	1	2	yes	—
158	C₄×C₇×Q₈	C₂³	1	2	yes	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
166	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
167	C₄×C₇×D₄	C₂³	1	2	yes	—
168	C₄×C₇×D₄	C₂³	1	2	yes	—
169	C₄×C₇×D₄	C₂³	1	4	yes	—
170	C₄×C₇×D₄	C₂³	1	4	yes	—
171	C₇×#117	—	2	2	no	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	—	2	4	no	—
174	C₇×#117	—	2	1	no	—
175	C₇×#117	C₂³	1	1	yes	characteristic
176	C₇×#117	C₂³	1	2	yes	—
177	C₇×#117	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	—	2	1	no	—
179	C₂×C₇×C₄⋊C₄	—	2	1	no	—
180	C₂×C₇×C₄⋊C₄	—	2	4	no	—
181	C₂×C₇×C₄⋊C₄	—	2	2	no	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
185	C₂×C₄²×C₇	—	2	1	no	—
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₇×#107	C₂³	1	2	yes	—
188	C₇×#107	C₂³	1	2	yes	—
189	C₇×#107	C₂³	1	2	yes	—
190	C₇×#106	C₂³	1	2	yes	—
191	C₇×#106	C₂³	1	2	yes	—
192	C₇×#106	C₂³	1	2	yes	—
193	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
195	C₇×C₄⋊C₈	C₂³	1	4	yes	—
196	C₇×C₄⋊C₈	C₂³	1	4	yes	—
197	C₇×C₄⋊C₈	C₂³	1	2	yes	—
198	C₇×#103	C₂³	1	4	yes	—
199	C₇×#103	C₂³	1	2	yes	—
200	C₇×#103	C₂³	1	4	yes	—
201	C₇×#103	C₂³	1	4	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#103	C₂³	1	4	yes	—
204	C₇×#103	C₂³	1	4	yes	—
205	C₇×#103	C₂³	1	2	yes	—
206	C₇×#103	C₂³	1	4	yes	—
207	C₇×#102	C₂³	1	2	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×#97	C₂³	1	4	yes	—
213	C₇×#97	C₂³	1	2	yes	—
214	C₄×C₇×C₈	C₂³	1	2	yes	—
215	C₄×C₇×C₈	C₂³	1	4	yes	—
216	#3509	C₂×C₇	1	1	yes	characteristic, complemented
217	#3501	C₂×C₇	1	1	yes	characteristic, complemented
218	#3376	C₂×C₇	1	4	yes	complemented
219	#3372	C₂×C₇	1	2	yes	complemented
220	#3372	C₂×C₇	1	4	yes	complemented
221	#3367	C₂×C₇	1	2	yes	complemented
222	#3360	C₂×C₇	1	2	yes	complemented
223	#3359	C₂×C₇	1	2	yes	complemented
224	#3139	C₂×C₇	1	1	yes	characteristic, complemented
225	#3137	C₂×C₇	1	2	yes	complemented
226	#3082	C₂×C₇	1	2	yes	complemented
227	#3076	C₂×C₇	1	1	yes	characteristic, complemented
228	#3042	C₂×C₇	1	2	yes	—
229	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
230	#2962	C₂×C₇	1	1	yes	characteristic, complemented
231	#2949	C₂×C₇	1	2	yes	complemented
232	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
233	C₂⁴×C₇	—	2	1	no	—
234	C₇×#41	—	2	2	no	—
235	C₇×#41	—	2	2	no	—
236	C₂×C₇×Q₈	—	2	2	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	1	no	—
239	C₂×C₇×Q₈	—	2	4	no	—
240	C₂×C₇×Q₈	—	2	4	no	—
241	C₂×C₇×Q₈	—	2	4	no	—
242	C₂×C₇×Q₈	—	8	4	no	—
243	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
244	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
245	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
246	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
247	C₂×C₇×D₄	—	2	1	no	—
248	C₂×C₇×D₄	—	2	1	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	#41	1	4	yes	—
251	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
252	C₂×C₇×D₄	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇	—	2	2	no	—
254	C₂²×C₄×C₇	—	2	1	no	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	4	no	—
260	C₂²×C₄×C₇	—	2	4	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	8	2	no	—
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₇×SD₁₆	—	2	8	no	—
267	C₇×SD₁₆	—	2	8	no	—
268	C₇×SD₁₆	—	2	4	no	—
269	C₇×D₈	—	2	4	no	—
270	C₇×M₁₆	—	2	2	no	—
271	C₇×M₁₆	—	2	2	no	—
272	C₂×C₇×C₈	—	2	4	no	—
273	C₂×C₇×C₈	C₂⁴	1	2	yes	—
274	C₂×C₇×C₈	C₂⁴	1	2	yes	—
275	C₂×C₇×C₈	C₂⁴	1	2	yes	—
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₇×C₄⋊C₄	—	2	2	no	—
278	C₇×C₄⋊C₄	—	2	1	no	—
279	C₇×C₄⋊C₄	—	2	2	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	2	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	—	2	1	no	—
289	C₇×C₄⋊C₄	—	2	4	no	—
290	C₇×C₄⋊C₄	—	2	4	no	—
291	C₇×C₄⋊C₄	—	2	2	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
297	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	2	no	—
307	C₇×C₂²⋊C₄	—	2	1	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	2	2	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	1	no	—
313	C₇×C₂²⋊C₄	—	2	1	no	—
314	C₇×C₂²⋊C₄	—	2	4	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
317	C₄²×C₇	—	2	1	no	—
318	C₄²×C₇	—	2	1	no	—
319	C₄²×C₇	—	2	1	no	—
320	C₄²×C₇	—	2	4	no	—
321	C₄²×C₇	—	2	4	no	—
322	C₄²×C₇	—	2	2	no	—
323	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₇	C₂⁴	1	1	yes	characteristic
326	C₄²×C₇	C₂⁴	1	4	yes	—
327	C₄²×C₇	C₂⁴	1	1	yes	characteristic
328	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
329	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
330	#557	C₂²×C₇	1	2	yes	complemented
331	#557	C₂²×C₇	1	2	yes	complemented
332	#556	C₂²×C₇	1	2	yes	complemented
333	#556	C₂²×C₇	1	2	yes	complemented
334	#554	—	2	1	no	—
335	#554	—	2	2	no	—
336	#554	C₂²×C₇	1	2	yes	—
337	#554	C₂²×C₇	1	4	yes	—
338	#552	—	2	2	no	—
339	#552	—	2	2	no	—
340	D₄×Q₈	—	2	1	no	—
341	D₄×Q₈	C₂²×C₇	1	2	yes	—
342	#544	C₂²×C₇	1	2	yes	—
343	#543	—	2	2	no	—
344	#541	—	2	2	no	—
345	#536	C₂²×C₇	1	2	yes	—
346	#533	—	2	1	no	—
347	#533	—	2	1	no	—
348	#533	C₂²×C₇	1	1	yes	characteristic
349	#533	C₂²×C₇	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	—	2	2	no	—
352	#519	C₂²×C₇	1	2	yes	—
353	#518	C₂²×C₇	1	2	yes	—
354	C₄×#41	C₂²×C₇	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
356	#491	C₂²×C₇	1	4	yes	complemented
357	#491	C₂²×C₇	1	4	yes	complemented
358	#489	C₂²×C₇	1	4	yes	complemented
359	#488	C₂²×C₇	1	4	yes	complemented
360	#487	C₂²×C₇	1	2	yes	complemented
361	#487	C₂²×C₇	1	4	yes	complemented
362	#487	C₂²×C₇	1	2	yes	complemented
363	#479	C₂²×C₇	1	2	yes	complemented
364	#479	C₂²×C₇	1	4	yes	complemented
365	#479	C₂²×C₇	1	4	yes	complemented
366	#478	C₂²×C₇	1	2	yes	complemented
367	#477	C₂²×C₇	1	1	yes	characteristic, complemented
368	#477	C₂²×C₇	1	4	yes	complemented
369	#476	C₂²×C₇	1	1	yes	characteristic, complemented
370	#475	C₂²×C₇	1	1	yes	characteristic, complemented
371	#475	C₂²×C₇	1	4	yes	complemented
372	#474	C₂²×C₇	1	1	yes	characteristic, complemented
373	#463	C₂²×C₇	1	4	yes	—
374	#463	C₂²×C₇	1	4	yes	—
375	#461	C₂²×C₇	1	2	yes	—
376	#461	C₂²×C₇	1	4	yes	—
377	#461	C₂²×C₇	1	2	yes	—
378	#461	C₂²×C₇	1	4	yes	—
379	#461	C₂²×C₇	1	4	yes	—
380	#446	C₂²×C₇	1	2	yes	complemented
381	#446	C₂²×C₇	1	4	yes	complemented
382	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
383	#442	C₂²×C₇	1	2	yes	—
384	#440	C₂²×C₇	1	4	yes	—
385	#440	C₂²×C₇	1	2	yes	—
386	#440	C₂²×C₇	1	4	yes	—
387	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
388	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
389	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
390	C₄×D₈	C₂²×C₇	1	2	yes	—
391	#428	C₂²×C₇	1	1	yes	characteristic
392	#427	C₂²×C₇	1	2	yes	—
393	#424	C₂²×C₇	1	2	yes	—
394	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
395	#419	C₂²×C₇	1	2	yes	—
396	#419	C₂²×C₇	1	2	yes	—
397	#418	C₂²×C₇	1	1	yes	characteristic
398	#417	C₂²×C₇	1	1	yes	characteristic
399	#416	C₂²×C₇	1	2	yes	—
400	C₂×#103	C₂²×C₇	1	2	yes	—
401	#405	C₂²×C₇	1	2	yes	—
402	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	—	2	4	no	—
405	C₂³×C₇	—	2	1	no	—
406	C₂³×C₇	—	8	1	no	—
407	C₂³×C₇	—	8	1	no	—
408	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
409	C₇×Q₈	—	2	4	no	—
410	C₇×Q₈	—	2	4	no	—
411	C₇×Q₈	—	2	1	no	—
412	C₇×Q₈	—	2	4	no	—
413	C₇×Q₈	—	2	1	no	—
414	C₇×Q₈	—	4	2	no	—
415	C₇×Q₈	—	4	4	no	—
416	C₇×Q₈	—	4	2	no	—
417	C₇×Q₈	—	8	1	no	—
418	C₇×Q₈	—	8	4	no	—
419	C₇×D₄	—	2	4	no	—
420	C₇×D₄	—	2	1	no	—
421	C₇×D₄	—	2	2	no	—
422	C₇×D₄	—	2	1	no	—
423	C₇×D₄	—	4	2	no	—
424	C₇×D₄	C₂×#41	1	4	yes	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	1	no	—
427	C₂×C₄×C₇	—	2	1	no	—
428	C₂×C₄×C₇	—	2	4	no	—
429	C₂×C₄×C₇	—	2	1	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	4	1	no	—
434	C₂×C₄×C₇	—	4	2	no	—
435	C₂×C₄×C₇	—	4	4	no	—
436	C₂×C₄×C₇	—	4	2	no	—
437	C₂×C₄×C₇	—	4	2	no	—
438	C₂×C₄×C₇	—	4	4	no	—
439	C₂×C₄×C₇	—	8	4	no	—
440	C₂×C₄×C₇	—	8	2	no	—
441	C₂×C₄×C₇	—	8	4	no	—
442	C₂×C₄×C₇	—	8	1	no	—
443	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
445	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
446	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂×#41	1	2	yes	—
451	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
452	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
453	C₇×C₈	—	2	2	no	—
454	C₇×C₈	—	2	2	no	—
455	C₇×C₈	—	2	2	no	—
456	C₇×C₈	—	2	2	no	—
457	C₂×#41	C₂³×C₇	1	1	yes	characteristic
458	C₂²×Q₈	—	2	2	no	—
459	C₂²×Q₈	C₂³×C₇	1	2	yes	—
460	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
461	C₂³×C₄	—	2	1	no	—
462	AGL(1,ℤ/8)	—	2	4	no	—
463	C₂×SD₁₆	—	2	8	no	—
464	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
465	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
466	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
467	C₂×D₈	C₂³×C₇	1	2	yes	—
468	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₇	1	2	yes	—
471	C₄⋊Q₈	—	2	2	no	—
472	C₄⋊Q₈	—	2	1	no	—
473	C₄⋊Q₈	—	2	1	no	—
474	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
475	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
477	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
478	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
479	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#125	—	2	2	no	—
485	#125	—	2	2	no	—
486	#125	—	2	4	no	—
487	#125	—	2	4	no	—
488	#125	—	2	2	no	—
489	#125	C₇×D₄	1	2	yes	—
490	#125	C₂³×C₇	1	2	yes	—
491	#125	C₂³×C₇	1	4	yes	—
492	#124	C₂³×C₇	1	4	yes	—
493	#123	—	2	4	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
509	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
518	C₄×Q₈	C₂³×C₇	1	4	yes	—
519	C₄×Q₈	C₂³×C₇	1	4	yes	—
520	C₄×Q₈	C₂³×C₇	1	2	yes	—
521	C₄×Q₈	C₂³×C₇	1	2	yes	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	C₂³×C₇	1	2	yes	—
529	C₄×D₄	C₂³×C₇	1	2	yes	—
530	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
531	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
532	C₄×D₄	C₂³×C₇	1	4	yes	—
533	C₄×D₄	C₂³×C₇	1	4	yes	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	—	2	4	no	—
537	#117	—	2	1	no	—
538	#117	C₂³×C₇	1	1	yes	characteristic
539	#117	C₂³×C₇	1	2	yes	—
540	#117	C₂³×C₇	1	2	yes	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	4	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	4	no	—
548	C₂×C₄²	—	2	1	no	—
549	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
550	#107	C₂³×C₇	1	2	yes	—
551	#107	C₂³×C₇	1	2	yes	—
552	#107	C₂³×C₇	1	2	yes	—
553	#106	C₂³×C₇	1	2	yes	—
554	#106	C₂³×C₇	1	2	yes	—
555	#106	C₂³×C₇	1	2	yes	—
556	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
557	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
558	C₄⋊C₈	C₂³×C₇	1	2	yes	—
559	C₄⋊C₈	C₂³×C₇	1	4	yes	—
560	C₄⋊C₈	C₂³×C₇	1	4	yes	—
561	#103	C₂³×C₇	1	4	yes	—
562	#103	C₂³×C₇	1	4	yes	—
563	#103	C₂³×C₇	1	2	yes	—
564	#103	C₂³×C₇	1	2	yes	—
565	#103	C₂³×C₇	1	2	yes	—
566	#103	C₂³×C₇	1	4	yes	—
567	#103	C₂³×C₇	1	4	yes	—
568	#103	C₂³×C₇	1	4	yes	—
569	#103	C₂³×C₇	1	4	yes	—
570	#102	C₂³×C₇	1	2	yes	—
571	#102	C₂³×C₇	1	2	yes	—
572	#102	C₂³×C₇	1	2	yes	—
573	#102	C₂³×C₇	1	2	yes	—
574	#102	C₂³×C₇	1	2	yes	—
575	#97	C₂³×C₇	1	2	yes	—
576	#97	C₂³×C₇	1	4	yes	—
577	C₄×C₈	C₂³×C₇	1	2	yes	—
578	C₄×C₈	C₂³×C₇	1	4	yes	—
579	C₂²×C₇	—	2	1	no	—
580	C₂²×C₇	—	2	1	no	—
581	C₂²×C₇	—	2	4	no	—
582	C₂²×C₇	—	4	2	no	—
583	C₂²×C₇	—	4	2	no	—
584	C₂²×C₇	—	4	1	no	—
585	C₂²×C₇	—	4	1	no	—
586	C₂²×C₇	—	4	1	no	—
587	C₂²×C₇	—	8	4	no	—
588	C₂²×C₇	#548	1	2	yes	—
589	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
590	C₄×C₇	—	2	1	no	—
591	C₄×C₇	—	2	1	no	—
592	C₄×C₇	—	2	4	no	—
593	C₄×C₇	—	2	1	no	—
594	C₄×C₇	—	2	4	no	—
595	C₄×C₇	—	4	1	no	—
596	C₄×C₇	—	4	2	no	—
597	C₄×C₇	—	4	1	no	—
598	C₄×C₇	—	4	4	no	—
599	C₄×C₇	—	4	1	no	—
600	C₄×C₇	—	4	2	no	—
601	C₄×C₇	—	4	2	no	—
602	C₄×C₇	#548	1	2	yes	—
603	C₄×C₇	#577	1	2	yes	—
604	C₄×C₇	C₂²×#41	1	1	yes	characteristic
605	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
606	C₂⁴	—	2	1	no	—
607	#41	—	2	2	no	—
608	#41	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	2	4	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	8	4	no	—
616	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
617	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
618	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
619	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	C₇×#41	1	4	yes	—
624	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
625	C₂×D₄	C₂⁴×C₇	1	2	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
637	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
639	SD₁₆	—	2	8	no	—
640	SD₁₆	—	2	8	no	—
641	SD₁₆	—	2	4	no	—
642	D₈	—	2	4	no	—
643	M₁₆	—	2	2	no	—
644	M₁₆	—	2	2	no	—
645	C₂×C₈	—	2	4	no	—
646	C₂×C₈	C₂⁴×C₇	1	2	yes	—
647	C₂×C₈	C₂⁴×C₇	1	2	yes	—
648	C₂×C₈	C₂⁴×C₇	1	2	yes	—
649	C₂×C₈	C₂⁴×C₇	1	2	yes	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
669	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
670	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
671	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
672	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
673	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
674	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
675	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
676	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
697	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
698	C₄²	C₂⁴×C₇	1	1	yes	characteristic
699	C₄²	C₂⁴×C₇	1	4	yes	—
700	C₄²	C₂⁴×C₇	1	1	yes	characteristic
701	C₂×C₇	—	2	2	no	—
702	C₂×C₇	—	4	4	no	—
703	C₂×C₇	—	8	1	no	—
704	C₂×C₇	C₂×#548	1	1	yes	characteristic
705	C₂×C₇	C₂×#577	1	1	yes	characteristic
706	C₂×C₇	#3586	1	1	yes	characteristic
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	8	1	no	—
711	C₂³	—	8	1	no	—
712	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
713	Q₈	—	2	4	no	—
714	Q₈	—	2	4	no	—
715	Q₈	—	2	1	no	—
716	Q₈	—	2	4	no	—
717	Q₈	—	2	1	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	4	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	8	1	no	—
722	Q₈	—	8	4	no	—
723	D₄	—	2	1	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	4	no	—
727	D₄	—	4	2	no	—
728	D₄	C₂×C₇×#41	1	4	yes	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	—	8	2	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
748	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
749	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
750	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
751	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
752	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
753	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
754	C₂×C₄	C₂×C₇×#41	1	2	yes	—
755	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
756	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	—	2	2	no	—
761	C₇	#61340	1	1	yes	characteristic, direct product factor, Sylow
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	8	4	no	—
771	C₂²	C₇×#548	1	2	yes	—
772	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	4	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	4	no	—
785	C₄	C₇×#548	1	2	yes	—
786	C₄	C₇×#577	1	2	yes	—
787	C₄	C₂²×C₇×#41	1	1	yes	characteristic
788	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
789	C₂	—	2	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	1	no	—
792	C₂	C₂×C₇×#548	1	1	yes	characteristic
793	C₂	C₂×C₇×#577	1	1	yes	characteristic
794	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×AGL(1,ℤ/8)	C₂²
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×#3509	C₂	semidirect
2. C₇×#3501	C₂	semidirect
3. C₇×#3376	C₂	semidirect
4. C₇×#3372	C₂	semidirect
5. C₇×#3372	C₂	semidirect
6. C₇×#3367	C₂	semidirect
7. C₇×#3360	C₂	semidirect
8. C₇×#3359	C₂	semidirect
9. C₇×#3139	C₂	semidirect
10. C₇×#3137	C₂	semidirect
11. C₇×#3082	C₂	semidirect
12. C₇×#3076	C₂	semidirect
14. C₂×C₇×#461	C₂	semidirect
15. C₇×#2962	C₂	semidirect
16. C₇×#2949	C₂	semidirect
20. C₇×#557	C₂²	semidirect
21. C₇×#557	C₂²	semidirect
22. C₇×#556	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
46. C₇×#491	C₂²	semidirect
47. C₇×#491	C₂²	semidirect
48. C₇×#489	C₂²	semidirect
49. C₇×#488	C₂²	semidirect
50. C₇×#487	C₂²	semidirect
51. C₇×#487	C₂²	semidirect
52. C₇×#487	C₂²	semidirect
53. C₇×#479	C₂²	semidirect
54. C₇×#479	C₂²	semidirect
55. C₇×#479	C₂²	semidirect
56. C₇×#478	C₂²	semidirect
57. C₇×#477	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
61. C₇×#475	C₂²	semidirect
62. C₇×#474	C₂²	semidirect
70. C₇×#446	C₂²	semidirect
71. C₇×#446	C₂²	semidirect
72. C₇×C₈×Q₈	C₂²	semidirect
93. #61340	C₇	direct (N × H)
216. #3509	C₂×C₇	semidirect
217. #3501	C₂×C₇	semidirect
218. #3376	C₂×C₇	semidirect
219. #3372	C₂×C₇	semidirect
220. #3372	C₂×C₇	semidirect
221. #3367	C₂×C₇	semidirect
222. #3360	C₂×C₇	semidirect
223. #3359	C₂×C₇	semidirect
224. #3139	C₂×C₇	semidirect
225. #3137	C₂×C₇	semidirect
226. #3082	C₂×C₇	semidirect
227. #3076	C₂×C₇	semidirect
229. C₂×#461	C₂×C₇	semidirect
230. #2962	C₂×C₇	semidirect
231. #2949	C₂×C₇	semidirect
330. #557	C₂²×C₇	semidirect
331. #557	C₂²×C₇	semidirect
332. #556	C₂²×C₇	semidirect
333. #556	C₂²×C₇	semidirect
356. #491	C₂²×C₇	semidirect
357. #491	C₂²×C₇	semidirect
358. #489	C₂²×C₇	semidirect
359. #488	C₂²×C₇	semidirect
360. #487	C₂²×C₇	semidirect
361. #487	C₂²×C₇	semidirect
362. #487	C₂²×C₇	semidirect
363. #479	C₂²×C₇	semidirect
364. #479	C₂²×C₇	semidirect
365. #479	C₂²×C₇	semidirect
366. #478	C₂²×C₇	semidirect
367. #477	C₂²×C₇	semidirect
368. #477	C₂²×C₇	semidirect
369. #476	C₂²×C₇	semidirect
370. #475	C₂²×C₇	semidirect
371. #475	C₂²×C₇	semidirect
372. #474	C₂²×C₇	semidirect
380. #446	C₂²×C₇	semidirect
381. #446	C₂²×C₇	semidirect
382. C₈×Q₈	C₂²×C₇	semidirect
761. C₇	#61340	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×#3509	2
C₇×#3501	2
C₇×#3376	2
C₇×#3372	2
C₇×#3367	2
C₇×#3360	2
C₇×#3359	2
C₇×#3139	2
C₇×#3137	2
C₇×#3082	2
C₇×#3076	2
C₇×#3042	2
C₂×C₇×#461	2
C₇×#2962	2
C₇×#2949	2
C₄×C₇×AGL(1,ℤ/8)	2
#61340	7

Subgroups — C7×#61340 #13238556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61340 #13238556