Subgroups — C₇×#61382 #13238598

Order 1792.

1794 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3388	C₂	1	4	yes	maximal, complemented
4	C₇×#3385	C₂	1	2	yes	maximal, complemented
5	C₇×#3384	C₂	1	4	yes	maximal, complemented
6	C₇×#3384	C₂	1	2	yes	maximal, complemented
7	C₇×#3380	C₂	1	2	yes	maximal, complemented
8	C₇×Q₈×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3163	C₂	1	2	yes	maximal, complemented
11	C₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₇×#3081	C₂	1	2	yes	maximal, complemented
13	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2946	C₂	1	2	yes	maximal
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	C₇×Q₈²	C₂²	1	2	yes	complemented
20	C₇×#557	C₂²	1	2	yes	complemented
21	C₇×#554	—	2	1	no	—
22	C₇×#554	—	2	2	no	—
23	C₇×#554	—	2	2	no	—
24	C₇×#554	C₂²	1	2	yes	—
25	C₇×#554	C₂²	1	4	yes	—
26	C₇×#554	C₂²	1	2	yes	complemented
27	C₇×D₄×Q₈	—	2	1	no	—
28	C₇×D₄×Q₈	—	2	2	no	—
29	C₇×D₄×Q₈	C₂²	1	2	yes	—
30	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
31	C₇×#544	—	2	2	no	—
32	C₇×#544	C₂²	1	2	yes	—
33	C₇×#544	C₂²	1	2	yes	—
34	C₇×#543	—	2	2	no	—
35	C₇×#533	—	2	1	no	—
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
41	C₇×#520	C₂²	1	2	yes	—
42	C₇×#518	C₂²	1	2	yes	—
43	C₄×C₇×#41	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₇×#501	C₂²	1	4	yes	complemented
46	C₇×#501	C₂²	1	4	yes	complemented
47	C₇×#501	C₂²	1	4	yes	complemented
48	C₇×#500	C₂²	1	2	yes	complemented
49	C₇×#499	C₂²	1	4	yes	complemented
50	C₇×#498	C₂²	1	4	yes	complemented
51	C₇×#498	C₂²	1	2	yes	complemented
52	C₇×#479	C₂²	1	2	yes	complemented
53	C₇×#479	C₂²	1	4	yes	complemented
54	C₇×#478	C₂²	1	4	yes	—
55	C₇×#478	C₂²	1	4	yes	—
56	C₇×#478	C₂²	1	2	yes	complemented
57	C₇×#478	C₂²	1	4	yes	complemented
58	C₇×#477	C₂²	1	1	yes	characteristic, complemented
59	C₇×#476	C₂²	1	2	yes	—
60	C₇×#476	C₂²	1	2	yes	—
61	C₇×#476	C₂²	1	4	yes	—
62	C₇×#476	C₂²	1	4	yes	—
63	C₇×#476	C₂²	1	1	yes	characteristic, complemented
64	C₇×#476	C₂²	1	4	yes	complemented
65	C₇×#475	C₂²	1	1	yes	characteristic, complemented
66	C₇×#475	C₂²	1	4	yes	complemented
67	C₇×#474	C₂²	1	4	yes	—
68	C₇×#474	C₂²	1	1	yes	characteristic, complemented
69	C₇×#446	C₂²	1	2	yes	complemented
70	C₇×#446	C₂²	1	4	yes	complemented
71	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
72	C₇×#442	C₂²	1	2	yes	—
73	C₇×#442	C₂²	1	4	yes	—
74	C₇×#440	C₂²	1	2	yes	—
75	C₇×#440	C₂²	1	4	yes	—
76	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
77	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
78	C₄×C₇×D₈	C₂²	1	2	yes	—
79	C₄×C₇×D₈	C₂²	1	4	yes	—
80	C₇×#428	C₂²	1	1	yes	characteristic
81	C₇×#428	C₂²	1	2	yes	—
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#427	C₂²	1	2	yes	—
84	C₂×C₇×#106	C₂²	1	2	yes	—
85	C₇×#424	C₂²	1	2	yes	—
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×#405	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	#61382	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	—	2	2	no	—
97	C₂²×C₇×Q₈	—	2	1	no	—
98	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	—	2	1	no	—
100	C₇×AGL(1,ℤ/8)	Q₈	1	8	yes	complemented
101	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₇×D₈	C₂³	1	2	yes	—
103	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
105	C₂²×C₇×C₈	C₂³	1	2	yes	—
106	C₇×C₄⋊Q₈	—	2	2	no	—
107	C₇×C₄⋊Q₈	—	2	2	no	—
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	—	2	4	no	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	—	2	1	no	—
112	C₇×C₄⋊Q₈	—	2	1	no	—
113	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₇×#125	—	2	2	no	—
122	C₇×#125	—	2	4	no	—
123	C₇×#125	—	2	2	no	—
124	C₇×#125	D₄	1	2	yes	—
125	C₇×#125	C₂³	1	4	yes	—
126	C₇×#125	C₂³	1	4	yes	—
127	C₇×#125	C₂³	1	2	yes	—
128	C₇×C₂²⋊Q₈	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	2	no	—
130	C₇×C₂²⋊Q₈	—	2	4	no	—
131	C₇×C₂²⋊Q₈	—	2	1	no	—
132	C₇×C₂²⋊Q₈	—	2	1	no	—
133	C₇×C₂²⋊Q₈	—	2	2	no	—
134	C₇×C₂²⋊Q₈	—	2	4	no	—
135	C₇×C₂²⋊Q₈	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	—	2	4	no	—
141	C₇×C₂²⋊Q₈	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	4	no	—
143	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₄×C₇×Q₈	—	2	2	no	—
146	C₄×C₇×Q₈	—	2	2	no	—
147	C₄×C₇×Q₈	—	2	1	no	—
148	C₄×C₇×Q₈	—	2	1	no	—
149	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
150	C₄×C₇×Q₈	C₂³	1	4	yes	—
151	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
152	C₄×C₇×Q₈	C₂³	1	2	yes	—
153	C₄×C₇×Q₈	C₂³	1	2	yes	—
154	C₄×C₇×D₄	—	2	1	no	—
155	C₄×C₇×D₄	—	2	1	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	4	no	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	C₂³	1	4	yes	—
162	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	4	yes	—
166	C₄×C₇×D₄	C₂³	1	4	yes	—
167	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
168	C₇×#117	—	2	2	no	—
169	C₇×#117	—	2	1	no	—
170	C₇×#117	C₂³	1	1	yes	characteristic
171	C₇×#117	C₂³	1	2	yes	—
172	C₇×#117	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	—	2	1	no	—
174	C₂×C₇×C₄⋊C₄	—	2	2	no	—
175	C₂×C₇×C₄⋊C₄	—	2	4	no	—
176	C₂×C₇×C₄⋊C₄	—	2	2	no	—
177	C₂×C₇×C₄⋊C₄	—	2	2	no	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
182	C₂×C₄²×C₇	—	2	1	no	—
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₇×#107	C₂³	1	2	yes	—
185	C₇×#107	C₂³	1	4	yes	—
186	C₇×#107	C₂³	1	2	yes	—
187	C₇×#107	C₂³	1	2	yes	—
188	C₇×#107	C₂³	1	4	yes	—
189	C₇×#106	C₂³	1	2	yes	—
190	C₇×#106	C₂³	1	4	yes	—
191	C₇×#106	C₂³	1	4	yes	—
192	C₇×#106	C₂³	1	4	yes	—
193	C₇×#106	C₂³	1	2	yes	—
194	C₇×#106	C₂³	1	4	yes	—
195	C₇×#106	C₂³	1	2	yes	—
196	C₇×C₄⋊C₈	C₂³	1	4	yes	—
197	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₇×C₄⋊C₈	C₂³	1	4	yes	—
200	C₇×C₄⋊C₈	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#102	C₂³	1	2	yes	—
205	C₇×#102	C₂³	1	4	yes	—
206	C₇×#102	C₂³	1	2	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×#97	C₂³	1	2	yes	—
212	C₇×#97	C₂³	1	4	yes	—
213	C₄×C₇×C₈	C₂³	1	4	yes	—
214	C₄×C₇×C₈	C₂³	1	2	yes	—
215	#3503	C₂×C₇	1	1	yes	characteristic, complemented
216	#3501	C₂×C₇	1	1	yes	characteristic, complemented
217	#3388	C₂×C₇	1	4	yes	complemented
218	#3385	C₂×C₇	1	2	yes	complemented
219	#3384	C₂×C₇	1	2	yes	complemented
220	#3384	C₂×C₇	1	4	yes	complemented
221	#3380	C₂×C₇	1	2	yes	complemented
222	Q₈×SD₁₆	C₂×C₇	1	2	yes	complemented
223	#3165	C₂×C₇	1	1	yes	characteristic, complemented
224	#3163	C₂×C₇	1	2	yes	complemented
225	#3084	C₂×C₇	1	2	yes	complemented
226	#3081	C₂×C₇	1	2	yes	complemented
227	#3076	C₂×C₇	1	1	yes	characteristic, complemented
228	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
229	#2962	C₂×C₇	1	1	yes	characteristic, complemented
230	#2946	C₂×C₇	1	2	yes	—
231	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
232	C₂⁴×C₇	—	2	1	no	—
233	C₇×#41	—	2	2	no	—
234	C₇×#41	C₂×Q₈	1	4	yes	complemented
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	2	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	4	no	—
239	C₂×C₇×Q₈	—	2	4	no	—
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	8	4	no	—
242	C₂×C₇×Q₈	—	8	2	no	—
243	C₂×C₇×Q₈	—	8	4	no	—
244	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
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	1	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	C₂×Q₈	1	4	yes	complemented
251	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
252	C₂×C₇×D₄	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇	—	2	1	no	—
254	C₂²×C₄×C₇	—	2	1	no	—
255	C₂²×C₄×C₇	—	2	2	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	—	2	4	no	—
263	C₂²×C₄×C₇	—	8	2	no	—
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₇×SD₁₆	C₂×Q₈	1	8	yes	complemented
268	C₇×D₈	C₂×Q₈	1	8	yes	complemented
269	C₇×M₁₆	—	2	2	no	—
270	C₇×M₁₆	C₂×Q₈	1	4	yes	complemented
271	C₂×C₇×C₈	—	2	4	no	—
272	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	C₇×C₄⋊C₄	—	2	2	no	—
277	C₇×C₄⋊C₄	—	2	1	no	—
278	C₇×C₄⋊C₄	—	2	2	no	—
279	C₇×C₄⋊C₄	—	2	2	no	—
280	C₇×C₄⋊C₄	—	2	4	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	4	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	2	no	—
290	C₇×C₄⋊C₄	—	2	1	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	4	no	—
293	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
294	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
295	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
296	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	4	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	2	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	1	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	2	no	—
310	C₇×C₂²⋊C₄	—	2	2	no	—
311	C₇×C₂²⋊C₄	—	2	1	no	—
312	C₇×C₂²⋊C₄	—	2	1	no	—
313	C₇×C₂²⋊C₄	—	2	4	no	—
314	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
315	C₄²×C₇	—	2	1	no	—
316	C₄²×C₇	—	2	1	no	—
317	C₄²×C₇	—	2	1	no	—
318	C₄²×C₇	—	2	4	no	—
319	C₄²×C₇	—	2	2	no	—
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	4	yes	—
324	C₄²×C₇	C₂⁴	1	1	yes	characteristic
325	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
326	Q₈²	C₂²×C₇	1	2	yes	complemented
327	#557	C₂²×C₇	1	2	yes	complemented
328	#554	—	2	1	no	—
329	#554	—	2	2	no	—
330	#554	—	2	2	no	—
331	#554	C₂²×C₇	1	2	yes	—
332	#554	C₂²×C₇	1	4	yes	—
333	#554	C₂²×C₇	1	2	yes	complemented
334	D₄×Q₈	—	2	1	no	—
335	D₄×Q₈	—	2	2	no	—
336	D₄×Q₈	C₂²×C₇	1	2	yes	—
337	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
338	#544	—	2	2	no	—
339	#544	C₂²×C₇	1	2	yes	—
340	#544	C₂²×C₇	1	2	yes	—
341	#543	—	2	2	no	—
342	#533	—	2	1	no	—
343	#533	C₂²×C₇	1	1	yes	characteristic
344	#533	C₂²×C₇	1	1	yes	characteristic
345	C₂×C₄⋊Q₈	—	2	1	no	—
346	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
347	C₂×C₂²⋊Q₈	—	2	2	no	—
348	#520	C₂²×C₇	1	2	yes	—
349	#518	C₂²×C₇	1	2	yes	—
350	C₄×#41	C₂²×C₇	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
352	#501	C₂²×C₇	1	4	yes	complemented
353	#501	C₂²×C₇	1	4	yes	complemented
354	#501	C₂²×C₇	1	4	yes	complemented
355	#500	C₂²×C₇	1	2	yes	complemented
356	#499	C₂²×C₇	1	4	yes	complemented
357	#498	C₂²×C₇	1	4	yes	complemented
358	#498	C₂²×C₇	1	2	yes	complemented
359	#479	C₂²×C₇	1	2	yes	complemented
360	#479	C₂²×C₇	1	4	yes	complemented
361	#478	C₂²×C₇	1	4	yes	—
362	#478	C₂²×C₇	1	4	yes	—
363	#478	C₂²×C₇	1	2	yes	complemented
364	#478	C₂²×C₇	1	4	yes	complemented
365	#477	C₂²×C₇	1	1	yes	characteristic, complemented
366	#476	C₂²×C₇	1	4	yes	—
367	#476	C₂²×C₇	1	2	yes	—
368	#476	C₂²×C₇	1	2	yes	—
369	#476	C₂²×C₇	1	4	yes	—
370	#476	C₂²×C₇	1	1	yes	characteristic, complemented
371	#476	C₂²×C₇	1	4	yes	complemented
372	#475	C₂²×C₇	1	1	yes	characteristic, complemented
373	#475	C₂²×C₇	1	4	yes	complemented
374	#474	C₂²×C₇	1	4	yes	—
375	#474	C₂²×C₇	1	1	yes	characteristic, complemented
376	#446	C₂²×C₇	1	2	yes	complemented
377	#446	C₂²×C₇	1	4	yes	complemented
378	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
379	#442	C₂²×C₇	1	2	yes	—
380	#442	C₂²×C₇	1	4	yes	—
381	#440	C₂²×C₇	1	4	yes	—
382	#440	C₂²×C₇	1	2	yes	—
383	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
384	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
385	C₄×D₈	C₂²×C₇	1	2	yes	—
386	C₄×D₈	C₂²×C₇	1	4	yes	—
387	#428	C₂²×C₇	1	2	yes	—
388	#428	C₂²×C₇	1	1	yes	characteristic
389	#428	C₂²×C₇	1	2	yes	—
390	#427	C₂²×C₇	1	2	yes	—
391	C₂×#106	C₂²×C₇	1	2	yes	—
392	#424	C₂²×C₇	1	2	yes	—
393	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
394	#418	C₂²×C₇	1	1	yes	characteristic
395	#417	C₂²×C₇	1	1	yes	characteristic
396	#416	C₂²×C₇	1	2	yes	—
397	C₂×#102	C₂²×C₇	1	2	yes	—
398	#405	C₂²×C₇	1	2	yes	—
399	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
400	C₂³×C₇	—	2	1	no	—
401	C₂³×C₇	—	2	2	no	—
402	C₂³×C₇	—	2	4	no	—
403	C₂³×C₇	—	8	1	no	—
404	C₂³×C₇	—	8	1	no	—
405	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
406	C₇×Q₈	—	2	4	no	—
407	C₇×Q₈	—	2	1	no	—
408	C₇×Q₈	—	4	2	no	—
409	C₇×Q₈	—	4	4	no	—
410	C₇×Q₈	—	4	2	no	—
411	C₇×Q₈	—	8	1	no	—
412	C₇×Q₈	—	8	2	no	—
413	C₇×Q₈	—	8	4	no	—
414	C₇×Q₈	—	8	4	no	—
415	C₇×Q₈	C₂²×Q₈	1	2	yes	—
416	C₇×D₄	—	2	4	no	—
417	C₇×D₄	—	2	4	no	—
418	C₇×D₄	—	2	2	no	—
419	C₇×D₄	—	2	1	no	—
420	C₇×D₄	C₂²×Q₈	1	2	yes	—
421	C₇×D₄	C₂²×Q₈	1	4	yes	—
422	C₂×C₄×C₇	—	2	1	no	—
423	C₂×C₄×C₇	—	2	4	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	1	no	—
426	C₂×C₄×C₇	—	2	1	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	4	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	4	1	no	—
432	C₂×C₄×C₇	—	4	2	no	—
433	C₂×C₄×C₇	—	4	2	no	—
434	C₂×C₄×C₇	—	4	4	no	—
435	C₂×C₄×C₇	—	8	4	no	—
436	C₂×C₄×C₇	—	8	2	no	—
437	C₂×C₄×C₇	—	8	4	no	—
438	C₂×C₄×C₇	—	8	4	no	—
439	C₂×C₄×C₇	—	8	1	no	—
440	C₂×C₄×C₇	—	8	2	no	—
441	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
443	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
449	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
450	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
451	C₇×C₈	—	2	2	no	—
452	C₇×C₈	—	2	2	no	—
453	C₇×C₈	—	2	2	no	—
454	C₇×C₈	C₂²×Q₈	1	4	yes	—
455	C₂×#41	C₂³×C₇	1	1	yes	characteristic
456	C₂²×Q₈	—	2	2	no	—
457	C₂²×Q₈	—	2	2	no	—
458	C₂²×Q₈	—	2	1	no	—
459	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	AGL(1,ℤ/8)	C₇×Q₈	1	8	yes	complemented
462	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
463	C₂×D₈	C₂³×C₇	1	2	yes	—
464	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
465	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₇	1	2	yes	—
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	—	2	2	no	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	—	2	4	no	—
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	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
481	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
482	#125	—	2	2	no	—
483	#125	—	2	4	no	—
484	#125	—	2	2	no	—
485	#125	C₇×D₄	1	2	yes	—
486	#125	C₂³×C₇	1	2	yes	—
487	#125	C₂³×C₇	1	4	yes	—
488	#125	C₂³×C₇	1	4	yes	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
505	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	1	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
511	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
512	C₄×Q₈	C₂³×C₇	1	4	yes	—
513	C₄×Q₈	C₂³×C₇	1	2	yes	—
514	C₄×Q₈	C₂³×C₇	1	2	yes	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	C₂³×C₇	1	2	yes	—
523	C₄×D₄	C₂³×C₇	1	2	yes	—
524	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
525	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
526	C₄×D₄	C₂³×C₇	1	4	yes	—
527	C₄×D₄	C₂³×C₇	1	4	yes	—
528	C₄×D₄	C₂³×C₇	1	4	yes	—
529	#117	—	2	2	no	—
530	#117	—	2	1	no	—
531	#117	C₂³×C₇	1	1	yes	characteristic
532	#117	C₂³×C₇	1	2	yes	—
533	#117	C₂³×C₇	1	2	yes	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	—	2	4	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	2	no	—
539	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
545	#107	C₂³×C₇	1	2	yes	—
546	#107	C₂³×C₇	1	2	yes	—
547	#107	C₂³×C₇	1	2	yes	—
548	#107	C₂³×C₇	1	4	yes	—
549	#107	C₂³×C₇	1	4	yes	—
550	#106	C₂³×C₇	1	4	yes	—
551	#106	C₂³×C₇	1	4	yes	—
552	#106	C₂³×C₇	1	2	yes	—
553	#106	C₂³×C₇	1	2	yes	—
554	#106	C₂³×C₇	1	4	yes	—
555	#106	C₂³×C₇	1	2	yes	—
556	#106	C₂³×C₇	1	4	yes	—
557	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
558	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
559	C₄⋊C₈	C₂³×C₇	1	2	yes	—
560	C₄⋊C₈	C₂³×C₇	1	4	yes	—
561	C₄⋊C₈	C₂³×C₇	1	4	yes	—
562	#103	C₂³×C₇	1	2	yes	—
563	#103	C₂³×C₇	1	2	yes	—
564	#103	C₂³×C₇	1	2	yes	—
565	#102	C₂³×C₇	1	4	yes	—
566	#102	C₂³×C₇	1	4	yes	—
567	#102	C₂³×C₇	1	2	yes	—
568	#102	C₂³×C₇	1	2	yes	—
569	#102	C₂³×C₇	1	2	yes	—
570	#102	C₂³×C₇	1	2	yes	—
571	#102	C₂³×C₇	1	2	yes	—
572	#97	C₂³×C₇	1	2	yes	—
573	#97	C₂³×C₇	1	4	yes	—
574	C₄×C₈	C₂³×C₇	1	2	yes	—
575	C₄×C₈	C₂³×C₇	1	4	yes	—
576	C₂²×C₇	—	2	1	no	—
577	C₂²×C₇	—	2	1	no	—
578	C₂²×C₇	—	2	2	no	—
579	C₂²×C₇	—	2	4	no	—
580	C₂²×C₇	—	4	1	no	—
581	C₂²×C₇	—	4	2	no	—
582	C₂²×C₇	—	4	2	no	—
583	C₂²×C₇	—	4	1	no	—
584	C₂²×C₇	—	8	4	no	—
585	C₂²×C₇	D₄×Q₈	1	2	yes	—
586	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
587	C₄×C₇	—	2	1	no	—
588	C₄×C₇	—	2	1	no	—
589	C₄×C₇	—	2	4	no	—
590	C₄×C₇	—	2	2	no	—
591	C₄×C₇	—	2	1	no	—
592	C₄×C₇	—	2	4	no	—
593	C₄×C₇	—	4	1	no	—
594	C₄×C₇	—	4	4	no	—
595	C₄×C₇	—	4	2	no	—
596	C₄×C₇	—	4	1	no	—
597	C₄×C₇	—	4	2	no	—
598	C₄×C₇	—	4	2	no	—
599	C₄×C₇	D₄×Q₈	1	2	yes	—
600	C₄×C₇	#577	1	2	yes	—
601	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
602	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
603	C₂⁴	—	2	1	no	—
604	#41	—	2	2	no	—
605	#41	C₂×C₇×Q₈	1	4	yes	complemented
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	8	4	no	—
613	C₂×Q₈	—	8	2	no	—
614	C₂×Q₈	—	8	4	no	—
615	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
616	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	C₂×C₇×Q₈	1	4	yes	complemented
622	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
623	C₂×D₄	C₂⁴×C₇	1	2	yes	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	8	2	no	—
635	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
636	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
638	SD₁₆	C₂×C₇×Q₈	1	8	yes	complemented
639	D₈	C₂×C₇×Q₈	1	8	yes	complemented
640	M₁₆	—	2	2	no	—
641	M₁₆	C₂×C₇×Q₈	1	4	yes	complemented
642	C₂×C₈	—	2	4	no	—
643	C₂×C₈	C₂⁴×C₇	1	2	yes	—
644	C₂×C₈	C₂⁴×C₇	1	2	yes	—
645	C₂×C₈	C₂⁴×C₇	1	2	yes	—
646	C₂×C₈	C₂⁴×C₇	1	2	yes	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
665	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
666	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
667	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
668	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
669	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
672	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
673	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
686	C₄²	—	2	1	no	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
692	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
693	C₄²	C₂⁴×C₇	1	1	yes	characteristic
694	C₄²	C₂⁴×C₇	1	4	yes	—
695	C₄²	C₂⁴×C₇	1	1	yes	characteristic
696	C₂×C₇	—	2	2	no	—
697	C₂×C₇	—	4	2	no	—
698	C₂×C₇	—	4	4	no	—
699	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
700	C₂×C₇	C₂×#577	1	1	yes	characteristic
701	C₂×C₇	#3585	1	1	yes	characteristic
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	8	1	no	—
706	C₂³	—	8	1	no	—
707	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
708	Q₈	—	2	1	no	—
709	Q₈	—	2	4	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	4	no	—
712	Q₈	—	4	2	no	—
713	Q₈	—	8	1	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	2	no	—
716	Q₈	—	8	4	no	—
717	Q₈	C₂²×C₇×Q₈	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	2	no	—
720	D₄	—	2	1	no	—
721	D₄	—	2	4	no	—
722	D₄	C₂²×C₇×Q₈	1	2	yes	—
723	D₄	C₂²×C₇×Q₈	1	4	yes	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	2	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	—	8	1	no	—
742	C₂×C₄	—	8	2	no	—
743	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
744	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
745	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
746	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
747	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
748	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
749	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
750	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
751	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
752	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	C₂²×C₇×Q₈	1	4	yes	—
757	C₇	#61382	1	1	yes	characteristic, direct product factor, Sylow
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	8	4	no	—
767	C₂²	C₇×D₄×Q₈	1	2	yes	—
768	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
769	C₄	—	2	1	no	—
770	C₄	—	2	4	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	4	no	—
780	C₄	—	4	2	no	—
781	C₄	C₇×D₄×Q₈	1	2	yes	—
782	C₄	C₇×#577	1	2	yes	—
783	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
784	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	4	4	no	—
787	C₂	—	4	2	no	—
788	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
789	C₂	C₂×C₇×#577	1	1	yes	characteristic
790	C₂	C₇×#3585	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×#3503	C₂	semidirect
2. C₇×#3501	C₂	semidirect
3. C₇×#3388	C₂	semidirect
4. C₇×#3385	C₂	semidirect
5. C₇×#3384	C₂	semidirect
6. C₇×#3384	C₂	semidirect
7. C₇×#3380	C₂	semidirect
8. C₇×Q₈×SD₁₆	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3163	C₂	semidirect
11. C₇×#3084	C₂	semidirect
12. C₇×#3081	C₂	semidirect
13. C₇×#3076	C₂	semidirect
14. C₂×C₇×#476	C₂	semidirect
15. C₇×#2962	C₂	semidirect
19. C₇×Q₈²	C₂²	semidirect
20. C₇×#557	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
30. C₇×D₄×Q₈	C₂²	semidirect
45. C₇×#501	C₂²	semidirect
46. C₇×#501	C₂²	semidirect
47. C₇×#501	C₂²	semidirect
48. C₇×#500	C₂²	semidirect
49. C₇×#499	C₂²	semidirect
50. C₇×#498	C₂²	semidirect
51. C₇×#498	C₂²	semidirect
52. C₇×#479	C₂²	semidirect
53. C₇×#479	C₂²	semidirect
56. C₇×#478	C₂²	semidirect
57. C₇×#478	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
63. C₇×#476	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#475	C₂²	semidirect
68. C₇×#474	C₂²	semidirect
69. C₇×#446	C₂²	semidirect
70. C₇×#446	C₂²	semidirect
71. C₇×C₈×Q₈	C₂²	semidirect
93. #61382	C₇	direct (N × H)
100. C₇×AGL(1,ℤ/8)	Q₈	semidirect
215. #3503	C₂×C₇	semidirect
216. #3501	C₂×C₇	semidirect
217. #3388	C₂×C₇	semidirect
218. #3385	C₂×C₇	semidirect
219. #3384	C₂×C₇	semidirect
220. #3384	C₂×C₇	semidirect
221. #3380	C₂×C₇	semidirect
222. Q₈×SD₁₆	C₂×C₇	semidirect
223. #3165	C₂×C₇	semidirect
224. #3163	C₂×C₇	semidirect
225. #3084	C₂×C₇	semidirect
226. #3081	C₂×C₇	semidirect
227. #3076	C₂×C₇	semidirect
228. C₂×#476	C₂×C₇	semidirect
229. #2962	C₂×C₇	semidirect
234. C₇×#41	C₂×Q₈	semidirect
250. C₂×C₇×D₄	C₂×Q₈	semidirect
267. C₇×SD₁₆	C₂×Q₈	semidirect
268. C₇×D₈	C₂×Q₈	semidirect
270. C₇×M₁₆	C₂×Q₈	semidirect
326. Q₈²	C₂²×C₇	semidirect
327. #557	C₂²×C₇	semidirect
333. #554	C₂²×C₇	semidirect
337. D₄×Q₈	C₂²×C₇	semidirect
352. #501	C₂²×C₇	semidirect
353. #501	C₂²×C₇	semidirect
354. #501	C₂²×C₇	semidirect
355. #500	C₂²×C₇	semidirect
356. #499	C₂²×C₇	semidirect
357. #498	C₂²×C₇	semidirect
358. #498	C₂²×C₇	semidirect
359. #479	C₂²×C₇	semidirect
360. #479	C₂²×C₇	semidirect
363. #478	C₂²×C₇	semidirect
364. #478	C₂²×C₇	semidirect
365. #477	C₂²×C₇	semidirect
370. #476	C₂²×C₇	semidirect
371. #476	C₂²×C₇	semidirect
372. #475	C₂²×C₇	semidirect
373. #475	C₂²×C₇	semidirect
375. #474	C₂²×C₇	semidirect
376. #446	C₂²×C₇	semidirect
377. #446	C₂²×C₇	semidirect
378. C₈×Q₈	C₂²×C₇	semidirect
461. AGL(1,ℤ/8)	C₇×Q₈	semidirect
605. #41	C₂×C₇×Q₈	semidirect
621. C₂×D₄	C₂×C₇×Q₈	semidirect
638. SD₁₆	C₂×C₇×Q₈	semidirect
639. D₈	C₂×C₇×Q₈	semidirect
641. M₁₆	C₂×C₇×Q₈	semidirect
757. C₇	#61382	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×#3503	2
C₇×#3501	2
C₇×#3388	2
C₇×#3385	2
C₇×#3384	2
C₇×#3380	2
C₇×Q₈×SD₁₆	2
C₇×#3165	2
C₇×#3163	2
C₇×#3084	2
C₇×#3081	2
C₇×#3076	2
C₂×C₇×#476	2
C₇×#2962	2
C₇×#2946	2
C₄×C₇×AGL(1,ℤ/8)	2
#61382	7

Subgroups — C7×#61382 #13238598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61382 #13238598