Subgroups — C₇×#61325 #13238541

Order 1792.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3370	C₂	1	4	yes	maximal, complemented
4	C₇×#3367	C₂	1	2	yes	maximal, complemented
5	C₇×#3366	C₂	1	2	yes	maximal, complemented
6	C₇×#3361	C₂	1	4	yes	maximal, complemented
7	C₇×#3360	C₂	1	2	yes	maximal, complemented
8	C₇×#3358	C₂	1	2	yes	maximal, complemented
9	C₇×#3136	C₂	1	2	yes	maximal, complemented
10	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3083	C₂	1	2	yes	maximal, complemented
12	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3041	C₂	1	2	yes	maximal, complemented
14	C₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
20	C₇×#559	C₂²	1	4	yes	complemented
21	C₇×#556	C₂²	1	2	yes	complemented
22	C₇×#555	—	2	1	no	—
23	C₇×#554	—	2	1	no	—
24	C₇×#554	—	2	2	no	—
25	C₇×#554	C₂²	1	2	yes	complemented
26	C₇×#554	C₂²	1	4	yes	complemented
27	C₇×#553	—	2	2	no	—
28	C₇×#550	C₂²	1	2	yes	complemented
29	C₇×D₄×Q₈	—	2	1	no	—
30	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
31	C₇×#547	—	2	1	no	—
32	C₇×#544	C₂²	1	2	yes	—
33	C₇×#543	—	2	2	no	—
34	C₇×#538	—	2	2	no	—
35	C₇×#535	C₂²	1	2	yes	—
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#532	C₂²	1	1	yes	characteristic
39	C₇×#525	—	2	2	no	—
40	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
41	C₇×#520	C₂²	1	2	yes	—
42	C₇×#518	C₂²	1	2	yes	—
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₇×#490	C₂²	1	4	yes	complemented
46	C₇×#489	C₂²	1	4	yes	complemented
47	C₇×#488	C₂²	1	4	yes	complemented
48	C₇×#488	C₂²	1	2	yes	complemented
49	C₇×#488	C₂²	1	2	yes	complemented
50	C₇×#487	C₂²	1	1	yes	characteristic, complemented
51	C₇×#487	C₂²	1	1	yes	characteristic, complemented
52	C₇×#486	C₂²	1	1	yes	characteristic, complemented
53	C₇×#486	C₂²	1	4	yes	complemented
54	C₇×#486	C₂²	1	1	yes	characteristic, complemented
55	C₇×#479	C₂²	1	4	yes	complemented
56	C₇×#478	C₂²	1	4	yes	complemented
57	C₇×#478	C₂²	1	4	yes	complemented
58	C₇×#477	C₂²	1	4	yes	complemented
59	C₇×#476	C₂²	1	2	yes	complemented
60	C₇×#474	C₂²	1	2	yes	complemented
61	C₇×#474	C₂²	1	4	yes	complemented
62	C₇×#463	C₂²	1	4	yes	—
63	C₇×#463	C₂²	1	4	yes	—
64	C₇×#463	C₂²	1	4	yes	complemented
65	C₇×#461	C₂²	1	2	yes	complemented
66	C₇×#459	C₂²	1	4	yes	—
67	C₇×#459	C₂²	1	4	yes	—
68	C₇×#459	C₂²	1	2	yes	complemented
69	C₇×#446	C₂²	1	2	yes	complemented
70	C₇×#446	C₂²	1	2	yes	complemented
71	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
72	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
73	C₇×#442	C₂²	1	4	yes	complemented
74	C₇×#440	C₂²	1	4	yes	complemented
75	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
76	C₄×C₇×D₈	C₂²	1	2	yes	—
77	C₄×C₇×D₈	C₂²	1	2	yes	—
78	C₄×C₇×D₈	C₂²	1	2	yes	—
79	C₄×C₇×D₈	C₂²	1	2	yes	—
80	C₄×C₇×D₈	C₂²	1	4	yes	complemented
81	C₇×#428	C₂²	1	2	yes	—
82	C₂×C₇×#107	C₂²	1	1	yes	characteristic
83	C₇×#424	C₂²	1	2	yes	—
84	C₇×#423	C₂²	1	1	yes	characteristic
85	C₇×#418	C₂²	1	2	yes	—
86	C₇×#417	C₂²	1	2	yes	—
87	C₇×#416	C₂²	1	2	yes	—
88	C₇×#416	C₂²	1	2	yes	—
89	C₂×C₇×#102	C₂²	1	1	yes	characteristic
90	C₂×C₇×#102	C₂²	1	1	yes	characteristic
91	C₇×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
93	#61325	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	—	2	2	no	—
95	C₂×C₇×#41	C₂³	1	2	yes	—
96	C₂²×C₇×Q₈	—	2	2	no	—
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	—	2	1	no	—
100	C₂³×C₄×C₇	—	2	1	no	—
101	C₇×AGL(1,ℤ/8)	—	2	8	no	—
102	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₇×D₈	—	2	4	no	—
104	C₂×C₇×D₈	C₂³	1	2	yes	—
105	C₂×C₇×D₈	C₂³	1	2	yes	—
106	C₂×C₇×D₈	C₂³	1	4	yes	—
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₇×C₄⋊Q₈	—	2	2	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	1	yes	characteristic
114	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×#127	C₂³	1	1	yes	characteristic
118	C₇×#127	C₂³	1	4	yes	—
119	C₇×#126	—	2	4	no	—
120	C₇×#125	—	2	2	no	—
121	C₇×#125	D₄	1	2	yes	—
122	C₇×#125	C₂³	1	2	yes	—
123	C₇×#125	C₂³	1	4	yes	—
124	C₇×#124	—	2	4	no	—
125	C₇×#124	C₂³	1	2	yes	—
126	C₇×#124	C₂³	1	4	yes	—
127	C₇×#123	—	2	4	no	—
128	C₇×#123	—	2	4	no	—
129	C₇×C₂²⋊Q₈	—	2	2	no	—
130	C₇×C₂²⋊Q₈	—	2	2	no	—
131	C₇×C₂²⋊Q₈	—	2	4	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	4	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	D₄	1	2	yes	—
141	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₇×#121	—	2	1	no	—
143	C₇×#121	—	2	1	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	2	no	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	4	no	—
148	C₇×#120	—	2	4	no	—
149	C₄×C₇×Q₈	—	2	1	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	C₂³	1	4	yes	—
152	C₄×C₇×Q₈	C₂³	1	2	yes	—
153	C₄×C₇×Q₈	C₂³	1	2	yes	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	4	no	—
157	C₄×C₇×D₄	—	2	4	no	—
158	C₄×C₇×D₄	—	2	1	no	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	—	2	1	no	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	4	yes	—
166	C₄×C₇×D₄	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
174	C₇×#117	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	—	2	2	no	—
176	C₂×C₇×C₄⋊C₄	—	2	4	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	1	yes	characteristic
180	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₇×#107	C₂³	1	4	yes	—
185	C₇×#107	C₂³	1	2	yes	—
186	C₇×#107	C₂³	1	2	yes	—
187	C₇×#106	C₂³	1	4	yes	—
188	C₇×C₄⋊C₈	C₂³	1	2	yes	—
189	C₇×C₄⋊C₈	C₂³	1	4	yes	—
190	C₇×C₄⋊C₈	C₂³	1	4	yes	—
191	C₇×C₄⋊C₈	C₂³	1	2	yes	—
192	C₇×#103	C₂³	1	2	yes	—
193	C₇×#103	C₂³	1	4	yes	—
194	C₇×#103	C₂³	1	2	yes	—
195	C₇×#103	C₂³	1	2	yes	—
196	C₇×#103	C₂³	1	2	yes	—
197	C₇×#102	C₂³	1	2	yes	—
198	C₇×#102	C₂³	1	4	yes	—
199	C₇×#102	C₂³	1	4	yes	—
200	C₇×#102	C₂³	1	4	yes	—
201	C₇×#102	C₂³	1	2	yes	—
202	C₇×#102	C₂³	1	2	yes	—
203	C₇×#102	C₂³	1	2	yes	—
204	C₇×#102	C₂³	1	2	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	2	yes	—
207	C₇×#102	C₂³	1	2	yes	—
208	C₇×#97	C₂³	1	4	yes	—
209	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
210	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
211	C₄×C₇×C₈	C₂³	1	4	yes	—
212	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
213	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
214	#3506	C₂×C₇	1	1	yes	characteristic, complemented
215	#3501	C₂×C₇	1	1	yes	characteristic, complemented
216	#3370	C₂×C₇	1	4	yes	complemented
217	#3367	C₂×C₇	1	2	yes	complemented
218	#3366	C₂×C₇	1	2	yes	complemented
219	#3361	C₂×C₇	1	4	yes	complemented
220	#3360	C₂×C₇	1	2	yes	complemented
221	#3358	C₂×C₇	1	2	yes	complemented
222	#3136	C₂×C₇	1	2	yes	complemented
223	#3131	C₂×C₇	1	1	yes	characteristic, complemented
224	#3083	C₂×C₇	1	2	yes	complemented
225	#3077	C₂×C₇	1	1	yes	characteristic, complemented
226	#3041	C₂×C₇	1	2	yes	complemented
227	#3036	C₂×C₇	1	1	yes	characteristic, complemented
228	#2960	C₂×C₇	1	1	yes	characteristic, complemented
229	#2946	C₂×C₇	1	2	yes	complemented
230	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
231	C₂⁴×C₇	—	2	1	no	—
232	C₂⁴×C₇	—	2	1	no	—
233	C₇×#41	—	2	4	no	—
234	C₇×#41	—	2	4	no	—
235	C₇×#41	—	8	4	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	4	no	—
239	C₂×C₇×Q₈	—	8	4	no	—
240	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
241	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
242	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	1	no	—
245	C₂×C₇×D₄	—	2	1	no	—
246	C₂×C₇×D₄	—	2	1	no	—
247	C₂×C₇×D₄	—	2	4	no	—
248	C₂×C₇×D₄	—	2	1	no	—
249	C₂×C₇×D₄	—	2	4	no	—
250	C₂×C₇×D₄	—	2	2	no	—
251	C₂×C₇×D₄	—	2	2	no	—
252	C₂×C₇×D₄	—	2	2	no	—
253	C₂×C₇×D₄	#41	1	4	yes	complemented
254	C₂×C₇×D₄	C₂⁴	1	2	yes	—
255	C₂×C₇×D₄	C₂⁴	1	2	yes	—
256	C₂×C₇×D₄	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	1	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	2	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	2	no	—
265	C₂²×C₄×C₇	—	2	4	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	8	2	no	—
268	C₂²×C₄×C₇	—	8	2	no	—
269	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₇×SD₁₆	—	2	8	no	—
273	C₇×D₈	—	2	4	no	—
274	C₇×D₈	—	2	4	no	—
275	C₇×D₈	—	2	8	no	—
276	C₇×M₁₆	—	2	4	no	—
277	C₂×C₇×C₈	—	2	2	no	—
278	C₂×C₇×C₈	—	2	2	no	—
279	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
280	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
281	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
282	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
283	C₂×C₇×C₈	C₂⁴	1	4	yes	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	4	no	—
288	C₇×C₄⋊C₄	—	2	4	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	1	no	—
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	C₂×D₄	1	2	yes	—
300	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
301	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
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×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₇×C₂²⋊C₄	—	2	2	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	2	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₇×C₂²⋊C₄	—	2	4	no	—
314	C₇×C₂²⋊C₄	—	2	4	no	—
315	C₇×C₂²⋊C₄	—	2	2	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	2	no	—
318	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
319	C₄²×C₇	—	2	4	no	—
320	C₄²×C₇	—	2	2	no	—
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	1	yes	characteristic
324	C₄²×C₇	C₂⁴	1	1	yes	characteristic
325	C₄²×C₇	C₂⁴	1	4	yes	—
326	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
327	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
328	#559	C₂²×C₇	1	4	yes	complemented
329	#556	C₂²×C₇	1	2	yes	complemented
330	#555	—	2	1	no	—
331	#554	—	2	1	no	—
332	#554	—	2	2	no	—
333	#554	C₂²×C₇	1	2	yes	complemented
334	#554	C₂²×C₇	1	4	yes	complemented
335	#553	—	2	2	no	—
336	#550	C₂²×C₇	1	2	yes	complemented
337	D₄×Q₈	—	2	1	no	—
338	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
339	#547	—	2	1	no	—
340	#544	C₂²×C₇	1	2	yes	—
341	#543	—	2	2	no	—
342	#538	—	2	2	no	—
343	#535	C₂²×C₇	1	2	yes	—
344	#533	C₂²×C₇	1	1	yes	characteristic
345	#533	C₂²×C₇	1	1	yes	characteristic
346	#532	C₂²×C₇	1	1	yes	characteristic
347	#525	—	2	2	no	—
348	C₂×C₂²⋊Q₈	—	2	2	no	—
349	#520	C₂²×C₇	1	2	yes	—
350	#518	C₂²×C₇	1	2	yes	—
351	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
353	#490	C₂²×C₇	1	4	yes	complemented
354	#489	C₂²×C₇	1	4	yes	complemented
355	#488	C₂²×C₇	1	4	yes	complemented
356	#488	C₂²×C₇	1	2	yes	complemented
357	#488	C₂²×C₇	1	2	yes	complemented
358	#487	C₂²×C₇	1	1	yes	characteristic, complemented
359	#487	C₂²×C₇	1	1	yes	characteristic, complemented
360	#486	C₂²×C₇	1	1	yes	characteristic, complemented
361	#486	C₂²×C₇	1	4	yes	complemented
362	#486	C₂²×C₇	1	1	yes	characteristic, complemented
363	#479	C₂²×C₇	1	4	yes	complemented
364	#478	C₂²×C₇	1	4	yes	complemented
365	#478	C₂²×C₇	1	4	yes	complemented
366	#477	C₂²×C₇	1	4	yes	complemented
367	#476	C₂²×C₇	1	2	yes	complemented
368	#474	C₂²×C₇	1	2	yes	complemented
369	#474	C₂²×C₇	1	4	yes	complemented
370	#463	C₂²×C₇	1	4	yes	—
371	#463	C₂²×C₇	1	4	yes	—
372	#463	C₂²×C₇	1	4	yes	complemented
373	#461	C₂²×C₇	1	2	yes	complemented
374	#459	C₂²×C₇	1	4	yes	—
375	#459	C₂²×C₇	1	4	yes	—
376	#459	C₂²×C₇	1	2	yes	complemented
377	#446	C₂²×C₇	1	2	yes	complemented
378	#446	C₂²×C₇	1	2	yes	complemented
379	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
380	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
381	#442	C₂²×C₇	1	4	yes	complemented
382	#440	C₂²×C₇	1	4	yes	complemented
383	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
384	C₄×D₈	C₂²×C₇	1	2	yes	—
385	C₄×D₈	C₂²×C₇	1	2	yes	—
386	C₄×D₈	C₂²×C₇	1	2	yes	—
387	C₄×D₈	C₂²×C₇	1	2	yes	—
388	C₄×D₈	C₂²×C₇	1	4	yes	complemented
389	#428	C₂²×C₇	1	2	yes	—
390	C₂×#107	C₂²×C₇	1	1	yes	characteristic
391	#424	C₂²×C₇	1	2	yes	—
392	#423	C₂²×C₇	1	1	yes	characteristic
393	#418	C₂²×C₇	1	2	yes	—
394	#417	C₂²×C₇	1	2	yes	—
395	#416	C₂²×C₇	1	2	yes	—
396	#416	C₂²×C₇	1	2	yes	—
397	C₂×#102	C₂²×C₇	1	1	yes	characteristic
398	C₂×#102	C₂²×C₇	1	1	yes	characteristic
399	#405	C₂²×C₇	1	2	yes	—
400	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
401	C₂³×C₇	—	2	2	no	—
402	C₂³×C₇	—	2	4	no	—
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	—	2	2	no	—
405	C₂³×C₇	—	4	2	no	—
406	C₂³×C₇	—	8	1	no	—
407	C₂³×C₇	—	8	1	no	—
408	C₂³×C₇	—	8	1	no	—
409	C₂³×C₇	—	8	1	no	—
410	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₇×Q₈	—	2	4	no	—
412	C₇×Q₈	—	2	2	no	—
413	C₇×Q₈	—	2	2	no	—
414	C₇×Q₈	—	4	2	no	—
415	C₇×Q₈	—	4	2	no	—
416	C₇×Q₈	—	8	1	no	—
417	C₇×Q₈	—	8	4	no	—
418	C₇×D₄	—	2	4	no	—
419	C₇×D₄	—	2	2	no	—
420	C₇×D₄	—	2	2	no	—
421	C₇×D₄	—	2	2	no	—
422	C₇×D₄	—	2	2	no	—
423	C₇×D₄	—	2	2	no	—
424	C₇×D₄	—	4	4	no	—
425	C₇×D₄	—	4	2	no	—
426	C₇×D₄	—	4	2	no	—
427	C₇×D₄	—	8	1	no	—
428	C₇×D₄	—	8	4	no	—
429	C₇×D₄	—	8	4	no	—
430	C₇×D₄	C₂×#41	1	4	yes	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	4	1	no	—
438	C₂×C₄×C₇	—	4	4	no	—
439	C₂×C₄×C₇	—	4	4	no	—
440	C₂×C₄×C₇	—	4	4	no	—
441	C₂×C₄×C₇	—	8	4	no	—
442	C₂×C₄×C₇	—	8	2	no	—
443	C₂×C₄×C₇	—	8	2	no	—
444	C₂×C₄×C₇	—	8	4	no	—
445	C₂×C₄×C₇	—	8	4	no	—
446	C₂×C₄×C₇	—	8	1	no	—
447	C₂×C₄×C₇	—	8	1	no	—
448	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
449	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
456	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
457	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
458	C₇×C₈	—	2	1	no	—
459	C₇×C₈	—	2	1	no	—
460	C₇×C₈	—	2	4	no	—
461	C₇×C₈	—	2	1	no	—
462	C₇×C₈	—	2	1	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	C₂³×C₇	1	2	yes	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	—	2	1	no	—
470	AGL(1,ℤ/8)	—	2	8	no	—
471	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
472	C₂×D₈	—	2	4	no	—
473	C₂×D₈	C₂³×C₇	1	2	yes	—
474	C₂×D₈	C₂³×C₇	1	2	yes	—
475	C₂×D₈	C₂³×C₇	1	4	yes	—
476	C₂×M₁₆	C₂³×C₇	1	2	yes	—
477	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
481	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
485	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
486	#127	C₂³×C₇	1	1	yes	characteristic
487	#127	C₂³×C₇	1	4	yes	—
488	#126	—	2	4	no	—
489	#125	—	2	2	no	—
490	#125	C₇×D₄	1	2	yes	—
491	#125	C₂³×C₇	1	2	yes	—
492	#125	C₂³×C₇	1	4	yes	—
493	#124	—	2	4	no	—
494	#124	C₂³×C₇	1	2	yes	—
495	#124	C₂³×C₇	1	4	yes	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	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	—	2	4	no	—
509	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
510	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
511	#121	—	2	1	no	—
512	#121	—	2	1	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	4	no	—
517	#120	—	2	4	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	C₂³×C₇	1	4	yes	—
521	C₄×Q₈	C₂³×C₇	1	2	yes	—
522	C₄×Q₈	C₂³×C₇	1	2	yes	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	C₂³×C₇	1	2	yes	—
534	C₄×D₄	C₂³×C₇	1	2	yes	—
535	C₄×D₄	C₂³×C₇	1	2	yes	—
536	C₄×D₄	C₂³×C₇	1	2	yes	—
537	C₄×D₄	C₂³×C₇	1	4	yes	—
538	C₄×D₄	C₂³×C₇	1	4	yes	—
539	C₄×D₄	C₂³×C₇	1	4	yes	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	C₂³×C₇	1	2	yes	—
543	#117	C₂³×C₇	1	2	yes	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	4	no	—
546	C₂×C₄⋊C₄	—	2	2	no	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	4	no	—
552	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
553	#107	C₂³×C₇	1	2	yes	—
554	#107	C₂³×C₇	1	2	yes	—
555	#107	C₂³×C₇	1	4	yes	—
556	#106	C₂³×C₇	1	4	yes	—
557	C₄⋊C₈	C₂³×C₇	1	2	yes	—
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	2	yes	—
562	#103	C₂³×C₇	1	2	yes	—
563	#103	C₂³×C₇	1	2	yes	—
564	#103	C₂³×C₇	1	2	yes	—
565	#103	C₂³×C₇	1	4	yes	—
566	#102	C₂³×C₇	1	2	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	#102	C₂³×C₇	1	2	yes	—
573	#102	C₂³×C₇	1	2	yes	—
574	#102	C₂³×C₇	1	4	yes	—
575	#102	C₂³×C₇	1	4	yes	—
576	#102	C₂³×C₇	1	4	yes	—
577	#97	C₂³×C₇	1	4	yes	—
578	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
579	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
580	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
581	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
582	C₄×C₈	C₂³×C₇	1	4	yes	—
583	C₂²×C₇	—	2	1	no	—
584	C₂²×C₇	—	2	1	no	—
585	C₂²×C₇	—	2	4	no	—
586	C₂²×C₇	—	4	2	no	—
587	C₂²×C₇	—	4	2	no	—
588	C₂²×C₇	—	4	2	no	—
589	C₂²×C₇	—	4	2	no	—
590	C₂²×C₇	—	4	2	no	—
591	C₂²×C₇	—	4	2	no	—
592	C₂²×C₇	—	4	2	no	—
593	C₂²×C₇	—	4	2	no	—
594	C₂²×C₇	—	8	4	no	—
595	C₂²×C₇	—	8	4	no	—
596	C₂²×C₇	#548	1	2	yes	—
597	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₇	—	2	1	no	—
599	C₄×C₇	—	2	1	no	—
600	C₄×C₇	—	2	4	no	—
601	C₄×C₇	—	2	1	no	—
602	C₄×C₇	—	2	4	no	—
603	C₄×C₇	—	4	2	no	—
604	C₄×C₇	—	4	2	no	—
605	C₄×C₇	—	4	2	no	—
606	C₄×C₇	—	4	2	no	—
607	C₄×C₇	—	4	2	no	—
608	C₄×C₇	#548	1	2	yes	—
609	C₄×C₇	#576	1	2	yes	—
610	C₄×C₇	C₂²×#41	1	1	yes	characteristic
611	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	#41	—	2	4	no	—
615	#41	—	2	4	no	—
616	#41	—	8	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	4	no	—
620	C₂×Q₈	—	8	4	no	—
621	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
622	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
623	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	C₇×#41	1	4	yes	complemented
635	C₂×D₄	C₂⁴×C₇	1	2	yes	—
636	C₂×D₄	C₂⁴×C₇	1	2	yes	—
637	C₂×D₄	C₂⁴×C₇	1	2	yes	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	8	2	no	—
649	C₂²×C₄	—	8	2	no	—
650	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
651	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
653	SD₁₆	—	2	8	no	—
654	D₈	—	2	4	no	—
655	D₈	—	2	4	no	—
656	D₈	—	2	8	no	—
657	M₁₆	—	2	4	no	—
658	C₂×C₈	—	2	2	no	—
659	C₂×C₈	—	2	2	no	—
660	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
661	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
662	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
663	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
664	C₂×C₈	C₂⁴×C₇	1	4	yes	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
678	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
679	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
680	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
681	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
682	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
703	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
704	C₄²	C₂⁴×C₇	1	1	yes	characteristic
705	C₄²	C₂⁴×C₇	1	1	yes	characteristic
706	C₄²	C₂⁴×C₇	1	4	yes	—
707	C₂×C₇	—	2	2	no	—
708	C₂×C₇	—	4	4	no	—
709	C₂×C₇	—	8	2	no	—
710	C₂×C₇	—	8	2	no	—
711	C₂×C₇	C₂×#548	1	1	yes	characteristic
712	C₂×C₇	C₂×#576	1	1	yes	characteristic
713	C₂×C₇	#3584	1	1	yes	characteristic
714	C₂³	—	2	2	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	8	1	no	—
720	C₂³	—	8	1	no	—
721	C₂³	—	8	1	no	—
722	C₂³	—	8	1	no	—
723	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
724	Q₈	—	2	4	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	Q₈	—	8	4	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	2	no	—
740	D₄	—	8	1	no	—
741	D₄	—	8	4	no	—
742	D₄	—	8	4	no	—
743	D₄	C₂×C₇×#41	1	4	yes	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	8	4	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	—	8	1	no	—
761	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
762	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
763	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
764	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
766	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂×C₇×#41	1	2	yes	—
769	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
770	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
771	C₈	—	2	1	no	—
772	C₈	—	2	1	no	—
773	C₈	—	2	4	no	—
774	C₈	—	2	1	no	—
775	C₈	—	2	1	no	—
776	C₇	#61325	1	1	yes	characteristic, direct product factor, Sylow
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	4	no	—
789	C₂²	—	8	4	no	—
790	C₂²	C₇×#548	1	2	yes	—
791	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	4	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	C₇×#548	1	2	yes	—
803	C₄	C₇×#576	1	2	yes	—
804	C₄	C₂²×C₇×#41	1	1	yes	characteristic
805	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
806	C₂	—	2	2	no	—
807	C₂	—	4	4	no	—
808	C₂	—	8	2	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂×C₇×#548	1	1	yes	characteristic
811	C₂	C₂×C₇×#576	1	1	yes	characteristic
812	C₂	C₇×#3584	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3506	C₂	semidirect
2. C₇×#3501	C₂	semidirect
3. C₇×#3370	C₂	semidirect
4. C₇×#3367	C₂	semidirect
5. C₇×#3366	C₂	semidirect
6. C₇×#3361	C₂	semidirect
7. C₇×#3360	C₂	semidirect
8. C₇×#3358	C₂	semidirect
9. C₇×#3136	C₂	semidirect
10. C₇×#3131	C₂	semidirect
11. C₇×#3083	C₂	semidirect
12. C₇×#3077	C₂	semidirect
13. C₇×#3041	C₂	semidirect
14. C₇×#3036	C₂	semidirect
15. C₇×#2960	C₂	semidirect
16. C₇×#2946	C₂	semidirect
17. C₂×C₄×C₇×D₈	C₂	semidirect
20. C₇×#559	C₂²	semidirect
21. C₇×#556	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
28. C₇×#550	C₂²	semidirect
30. C₇×D₄×Q₈	C₂²	semidirect
45. C₇×#490	C₂²	semidirect
46. C₇×#489	C₂²	semidirect
47. C₇×#488	C₂²	semidirect
48. C₇×#488	C₂²	semidirect
49. C₇×#488	C₂²	semidirect
50. C₇×#487	C₂²	semidirect
51. C₇×#487	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#486	C₂²	semidirect
55. C₇×#479	C₂²	semidirect
56. C₇×#478	C₂²	semidirect
57. C₇×#478	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#474	C₂²	semidirect
61. C₇×#474	C₂²	semidirect
64. C₇×#463	C₂²	semidirect
65. C₇×#461	C₂²	semidirect
68. C₇×#459	C₂²	semidirect
69. C₇×#446	C₂²	semidirect
70. C₇×#446	C₂²	semidirect
71. C₇×C₈×Q₈	C₂²	semidirect
72. C₇×C₈×Q₈	C₂²	semidirect
73. C₇×#442	C₂²	semidirect
74. C₇×#440	C₂²	semidirect
75. C₄×C₇×SD₁₆	C₂²	semidirect
80. C₄×C₇×D₈	C₂²	semidirect
93. #61325	C₇	direct (N × H)
214. #3506	C₂×C₇	semidirect
215. #3501	C₂×C₇	semidirect
216. #3370	C₂×C₇	semidirect
217. #3367	C₂×C₇	semidirect
218. #3366	C₂×C₇	semidirect
219. #3361	C₂×C₇	semidirect
220. #3360	C₂×C₇	semidirect
221. #3358	C₂×C₇	semidirect
222. #3136	C₂×C₇	semidirect
223. #3131	C₂×C₇	semidirect
224. #3083	C₂×C₇	semidirect
225. #3077	C₂×C₇	semidirect
226. #3041	C₂×C₇	semidirect
227. #3036	C₂×C₇	semidirect
228. #2960	C₂×C₇	semidirect
229. #2946	C₂×C₇	semidirect
230. C₂×C₄×D₈	C₂×C₇	semidirect
253. C₂×C₇×D₄	#41	semidirect
328. #559	C₂²×C₇	semidirect
329. #556	C₂²×C₇	semidirect
333. #554	C₂²×C₇	semidirect
334. #554	C₂²×C₇	semidirect
336. #550	C₂²×C₇	semidirect
338. D₄×Q₈	C₂²×C₇	semidirect
353. #490	C₂²×C₇	semidirect
354. #489	C₂²×C₇	semidirect
355. #488	C₂²×C₇	semidirect
356. #488	C₂²×C₇	semidirect
357. #488	C₂²×C₇	semidirect
358. #487	C₂²×C₇	semidirect
359. #487	C₂²×C₇	semidirect
360. #486	C₂²×C₇	semidirect
361. #486	C₂²×C₇	semidirect
362. #486	C₂²×C₇	semidirect
363. #479	C₂²×C₇	semidirect
364. #478	C₂²×C₇	semidirect
365. #478	C₂²×C₇	semidirect
366. #477	C₂²×C₇	semidirect
367. #476	C₂²×C₇	semidirect
368. #474	C₂²×C₇	semidirect
369. #474	C₂²×C₇	semidirect
372. #463	C₂²×C₇	semidirect
373. #461	C₂²×C₇	semidirect
376. #459	C₂²×C₇	semidirect
377. #446	C₂²×C₇	semidirect
378. #446	C₂²×C₇	semidirect
379. C₈×Q₈	C₂²×C₇	semidirect
380. C₈×Q₈	C₂²×C₇	semidirect
381. #442	C₂²×C₇	semidirect
382. #440	C₂²×C₇	semidirect
383. C₄×SD₁₆	C₂²×C₇	semidirect
388. C₄×D₈	C₂²×C₇	semidirect
634. C₂×D₄	C₇×#41	semidirect
776. C₇	#61325	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×#3506	2
C₇×#3501	2
C₇×#3370	2
C₇×#3367	2
C₇×#3366	2
C₇×#3361	2
C₇×#3360	2
C₇×#3358	2
C₇×#3136	2
C₇×#3131	2
C₇×#3083	2
C₇×#3077	2
C₇×#3041	2
C₇×#3036	2
C₇×#2960	2
C₇×#2946	2
C₂×C₄×C₇×D₈	2
#61325	7

Subgroups — C7×#61325 #13238541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61325 #13238541