Subgroups — C₇×#61480 #13238696

Order 1792.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3519	C₂	1	2	yes	maximal, complemented
2	C₇×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3366	C₂	1	2	yes	maximal, complemented
5	C₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3339	C₂	1	2	yes	maximal, complemented
7	C₇×#3325	C₂	1	2	yes	maximal, complemented
8	C₇×#3318	C₂	1	4	yes	maximal, complemented
9	C₇×D₄×D₈	C₂	1	2	yes	maximal, complemented
10	C₇×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3176	C₂	1	2	yes	maximal, complemented
12	C₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3122	C₂	1	4	yes	maximal, complemented
14	C₇×#3109	C₂	1	2	yes	maximal, complemented
15	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2948	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₇×D₈	C₂²	1	2	yes	—
20	C₇×#555	C₂²	1	2	yes	complemented
21	C₇×#554	C₂²	1	2	yes	complemented
22	C₇×#553	—	2	2	no	—
23	C₇×#553	C₂²	1	4	yes	complemented
24	C₇×#550	C₂²	1	2	yes	complemented
25	C₇×#546	—	2	2	no	—
26	C₇×#546	—	2	4	no	—
27	C₇×D₄²	C₂²	1	4	yes	complemented
28	C₇×D₄²	C₂²	1	2	yes	complemented
29	C₇×#540	C₂²	1	4	yes	complemented
30	C₇×#538	—	2	4	no	—
31	C₇×#532	C₂²	1	2	yes	complemented
32	C₇×#529	C₂²	1	1	yes	characteristic
33	C₇×#525	—	2	2	no	—
34	C₂×C₇×#121	—	2	2	no	—
35	C₇×#518	C₂²	1	4	yes	complemented
36	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
37	C₇×#500	C₂²	1	1	yes	characteristic, complemented
38	C₇×#499	C₂²	1	2	yes	complemented
39	C₇×#493	C₂²	1	1	yes	characteristic, complemented
40	C₇×#493	C₂²	1	2	yes	complemented
41	C₇×#490	C₂²	1	4	yes	complemented
42	C₇×#486	C₂²	1	2	yes	complemented
43	C₇×#482	C₂²	1	4	yes	complemented
44	C₇×#482	C₂²	1	4	yes	complemented
45	C₇×#481	C₂²	1	4	yes	complemented
46	C₇×#478	C₂²	1	4	yes	complemented
47	C₇×#478	C₂²	1	4	yes	complemented
48	C₇×#476	C₂²	1	2	yes	complemented
49	C₇×#476	C₂²	1	2	yes	complemented
50	C₇×#469	C₂²	1	4	yes	complemented
51	C₇×#466	C₂²	1	2	yes	complemented
52	C₇×#466	C₂²	1	2	yes	complemented
53	C₇×#466	C₂²	1	2	yes	complemented
54	C₇×#466	C₂²	1	2	yes	complemented
55	C₇×#459	C₂²	1	2	yes	complemented
56	C₇×#459	C₂²	1	4	yes	complemented
57	C₇×#459	C₂²	1	4	yes	complemented
58	C₇×#459	C₂²	1	2	yes	complemented
59	C₇×#447	C₂²	1	4	yes	complemented
60	C₇×#447	C₂²	1	4	yes	complemented
61	C₇×#447	C₂²	1	4	yes	complemented
62	C₇×#446	C₂²	1	1	yes	characteristic, complemented
63	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₇×#442	C₂²	1	4	yes	complemented
65	C₇×#442	C₂²	1	4	yes	complemented
66	C₇×#442	C₂²	1	4	yes	complemented
67	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
68	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
69	C₄×C₇×D₈	C₂²	1	2	yes	—
70	C₄×C₇×D₈	C₂²	1	2	yes	complemented
71	C₄×C₇×D₈	C₂²	1	2	yes	complemented
72	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₇×D₈	C₂²	1	2	yes	complemented
74	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₇×D₈	C₂²	1	2	yes	complemented
76	C₄×C₇×D₈	C₂²	1	2	yes	complemented
77	C₇×#436	C₂²	1	1	yes	characteristic, complemented
78	C₇×#435	C₂²	1	2	yes	complemented
79	C₇×C₈×D₄	C₂²	1	2	yes	complemented
80	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
81	C₇×#433	C₂²	1	2	yes	complemented
82	C₇×#432	C₂²	1	1	yes	characteristic, complemented
83	C₇×#427	C₂²	1	2	yes	complemented
84	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
85	C₇×#418	C₂²	1	4	yes	complemented
86	C₂×C₇×#102	C₂²	1	2	yes	complemented
87	C₇×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
89	#61480	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	2	no	—
91	C₂×C₇×#41	—	2	2	no	—
92	C₂²×C₇×D₄	—	2	2	no	—
93	C₂²×C₇×D₄	—	2	4	no	—
94	C₂²×C₇×D₄	C₂³	1	2	yes	—
95	C₂²×C₇×D₄	C₂³	1	4	yes	—
96	C₂³×C₄×C₇	—	2	2	no	—
97	C₂×C₇×D₈	—	2	4	no	—
98	C₂×C₇×D₈	—	2	8	no	—
99	C₂×C₇×D₈	C₂³	1	2	yes	—
100	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
101	C₂×C₇×D₈	C₂³	1	2	yes	—
102	C₂×C₇×D₈	C₂³	1	4	yes	—
103	C₂×C₇×D₈	C₂³	1	2	yes	—
104	C₂×C₇×D₈	C₂³	1	4	yes	—
105	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	2	yes	—
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₇×#127	C₂³	1	2	yes	—
112	C₇×#127	C₂³	1	4	yes	—
113	C₇×#126	—	2	4	no	—
114	C₇×#126	D₄	1	2	yes	—
115	C₇×#125	D₄	1	1	yes	characteristic
116	C₇×#125	C₂³	1	4	yes	—
117	C₇×#124	—	2	4	no	—
118	C₇×#124	—	2	2	no	—
119	C₇×#124	D₄	1	1	yes	characteristic
120	C₇×#123	—	2	4	no	—
121	C₇×#123	—	2	4	no	—
122	C₇×#123	—	2	4	no	—
123	C₇×#123	D₄	1	2	yes	—
124	C₇×C₂²⋊Q₈	—	2	2	no	—
125	C₇×C₂²⋊Q₈	—	2	4	no	—
126	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₇×#121	—	2	4	no	—
128	C₇×#121	—	2	2	no	—
129	C₇×#121	—	2	2	no	—
130	C₇×#121	—	2	2	no	—
131	C₇×#121	—	2	2	no	—
132	C₇×#121	—	2	4	no	—
133	C₇×#121	—	2	4	no	—
134	C₇×#121	—	2	4	no	—
135	C₇×#121	—	2	4	no	—
136	C₇×#121	D₄	1	1	yes	characteristic
137	C₇×#121	C₂³	1	4	yes	—
138	C₇×#121	C₂³	1	4	yes	—
139	C₇×#121	C₂³	1	4	yes	—
140	C₇×#120	—	2	4	no	—
141	C₇×#120	—	2	4	no	—
142	C₇×#120	—	2	4	no	—
143	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
144	C₄×C₇×D₄	—	2	4	no	—
145	C₄×C₇×D₄	—	2	4	no	—
146	C₄×C₇×D₄	—	2	4	no	—
147	C₄×C₇×D₄	—	2	2	no	—
148	C₄×C₇×D₄	—	2	2	no	—
149	C₄×C₇×D₄	—	2	2	no	—
150	C₄×C₇×D₄	C₂³	1	2	yes	—
151	C₄×C₇×D₄	C₂³	1	2	yes	—
152	C₄×C₇×D₄	C₂³	1	4	yes	—
153	C₄×C₇×D₄	C₂³	1	4	yes	—
154	C₄×C₇×D₄	C₂³	1	2	yes	—
155	C₄×C₇×D₄	C₂³	1	2	yes	—
156	C₄×C₇×D₄	C₂³	1	4	yes	—
157	C₄×C₇×D₄	C₂³	1	2	yes	—
158	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
159	C₇×#117	—	2	2	no	—
160	C₇×#117	C₂³	1	4	yes	—
161	C₇×#117	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	—	2	2	no	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
165	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
166	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₇×#107	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	2	yes	—
170	C₇×#107	C₂³	1	2	yes	—
171	C₇×#107	C₂³	1	2	yes	—
172	C₇×#107	C₂³	1	1	yes	characteristic
173	C₇×#106	C₂³	1	4	yes	—
174	C₇×#106	C₂³	1	4	yes	—
175	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₈	C₂³	1	2	yes	—
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×#102	C₂³	1	4	yes	—
180	C₇×#102	C₂³	1	4	yes	—
181	C₇×#102	C₂³	1	4	yes	—
182	C₇×#102	C₂³	1	4	yes	—
183	C₇×#102	C₂³	1	2	yes	—
184	C₇×#102	C₂³	1	4	yes	—
185	C₇×#102	C₂³	1	2	yes	—
186	C₇×#102	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	2	yes	—
188	C₇×#102	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
195	C₄×C₇×C₈	C₂³	1	2	yes	—
196	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	#3519	C₂×C₇	1	2	yes	complemented
200	#3391	C₂×C₇	1	1	yes	characteristic, complemented
201	#3380	C₂×C₇	1	1	yes	characteristic, complemented
202	#3366	C₂×C₇	1	2	yes	complemented
203	#3341	C₂×C₇	1	1	yes	characteristic, complemented
204	#3339	C₂×C₇	1	2	yes	complemented
205	#3325	C₂×C₇	1	2	yes	complemented
206	#3318	C₂×C₇	1	4	yes	complemented
207	D₄×D₈	C₂×C₇	1	2	yes	complemented
208	D₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
209	#3176	C₂×C₇	1	2	yes	complemented
210	#3169	C₂×C₇	1	1	yes	characteristic, complemented
211	#3122	C₂×C₇	1	4	yes	complemented
212	#3109	C₂×C₇	1	2	yes	complemented
213	#2966	C₂×C₇	1	1	yes	characteristic, complemented
214	#2948	C₂×C₇	1	2	yes	complemented
215	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂⁴×C₇	—	2	2	no	—
217	C₂⁴×C₇	—	2	4	no	—
218	C₇×#41	—	8	4	no	—
219	C₇×#41	—	8	4	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇×D₄	—	2	4	no	—
223	C₂×C₇×D₄	—	2	8	no	—
224	C₂×C₇×D₄	—	2	4	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	—	2	4	no	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	2	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	2	no	—
232	C₂×C₇×D₄	—	2	4	no	—
233	C₂×C₇×D₄	—	4	2	no	—
234	C₂×C₇×D₄	—	4	4	no	—
235	C₂×C₇×D₄	—	8	4	no	—
236	C₂×C₇×D₄	—	8	8	no	—
237	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
238	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
239	C₂×C₇×D₄	C₂⁴	1	4	yes	—
240	C₂×C₇×D₄	C₂⁴	1	2	yes	—
241	C₂×C₇×D₄	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	2	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	4	no	—
247	C₂²×C₄×C₇	—	2	4	no	—
248	C₂²×C₄×C₇	—	2	4	no	—
249	C₂²×C₄×C₇	—	2	2	no	—
250	C₂²×C₄×C₇	—	8	4	no	—
251	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₇×D₈	—	2	4	no	—
256	C₇×D₈	—	2	8	no	—
257	C₇×D₈	—	2	2	no	—
258	C₇×D₈	—	2	4	no	—
259	C₇×D₈	—	4	2	no	—
260	C₇×D₈	—	4	4	no	—
261	C₇×D₈	#41	1	4	yes	complemented
262	C₇×M₁₆	—	4	2	no	—
263	C₂×C₇×C₈	—	2	2	no	—
264	C₂×C₇×C₈	—	2	4	no	—
265	C₂×C₇×C₈	—	4	1	no	—
266	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₂×C₇×C₈	C₂⁴	1	2	yes	—
270	C₂×C₇×C₈	C₂⁴	1	2	yes	—
271	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	—	2	2	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
277	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₇×C₂²⋊C₄	—	2	4	no	—
286	C₇×C₂²⋊C₄	—	2	2	no	—
287	C₇×C₂²⋊C₄	—	2	4	no	—
288	C₇×C₂²⋊C₄	—	2	2	no	—
289	C₇×C₂²⋊C₄	—	2	4	no	—
290	C₇×C₂²⋊C₄	—	2	2	no	—
291	C₇×C₂²⋊C₄	—	2	4	no	—
292	C₇×C₂²⋊C₄	—	2	2	no	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
297	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
298	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
299	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
301	C₄²×C₇	—	2	4	no	—
302	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₇	C₂⁴	1	1	yes	characteristic
305	C₄²×C₇	C₂⁴	1	1	yes	characteristic
306	C₄²×C₇	C₂⁴	1	2	yes	—
307	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
308	C₂²×D₈	C₂²×C₇	1	2	yes	—
309	#555	C₂²×C₇	1	2	yes	complemented
310	#554	C₂²×C₇	1	2	yes	complemented
311	#553	—	2	2	no	—
312	#553	C₂²×C₇	1	4	yes	complemented
313	#550	C₂²×C₇	1	2	yes	complemented
314	#546	—	2	2	no	—
315	#546	—	2	4	no	—
316	D₄²	C₂²×C₇	1	4	yes	complemented
317	D₄²	C₂²×C₇	1	2	yes	complemented
318	#540	C₂²×C₇	1	4	yes	complemented
319	#538	—	2	4	no	—
320	#532	C₂²×C₇	1	2	yes	complemented
321	#529	C₂²×C₇	1	1	yes	characteristic
322	#525	—	2	2	no	—
323	C₂×#121	—	2	2	no	—
324	#518	C₂²×C₇	1	4	yes	complemented
325	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
326	#500	C₂²×C₇	1	1	yes	characteristic, complemented
327	#499	C₂²×C₇	1	2	yes	complemented
328	#493	C₂²×C₇	1	1	yes	characteristic, complemented
329	#493	C₂²×C₇	1	2	yes	complemented
330	#490	C₂²×C₇	1	4	yes	complemented
331	#486	C₂²×C₇	1	2	yes	complemented
332	#482	C₂²×C₇	1	4	yes	complemented
333	#482	C₂²×C₇	1	4	yes	complemented
334	#481	C₂²×C₇	1	4	yes	complemented
335	#478	C₂²×C₇	1	4	yes	complemented
336	#478	C₂²×C₇	1	4	yes	complemented
337	#476	C₂²×C₇	1	2	yes	complemented
338	#476	C₂²×C₇	1	2	yes	complemented
339	#469	C₂²×C₇	1	4	yes	complemented
340	#466	C₂²×C₇	1	2	yes	complemented
341	#466	C₂²×C₇	1	2	yes	complemented
342	#466	C₂²×C₇	1	2	yes	complemented
343	#466	C₂²×C₇	1	2	yes	complemented
344	#459	C₂²×C₇	1	2	yes	complemented
345	#459	C₂²×C₇	1	2	yes	complemented
346	#459	C₂²×C₇	1	4	yes	complemented
347	#459	C₂²×C₇	1	4	yes	complemented
348	#447	C₂²×C₇	1	4	yes	complemented
349	#447	C₂²×C₇	1	4	yes	complemented
350	#447	C₂²×C₇	1	4	yes	complemented
351	#446	C₂²×C₇	1	1	yes	characteristic, complemented
352	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
353	#442	C₂²×C₇	1	4	yes	complemented
354	#442	C₂²×C₇	1	4	yes	complemented
355	#442	C₂²×C₇	1	4	yes	complemented
356	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
357	C₄×D₈	C₂²×C₇	1	2	yes	—
358	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
359	C₄×D₈	C₂²×C₇	1	2	yes	complemented
360	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
361	C₄×D₈	C₂²×C₇	1	2	yes	complemented
362	C₄×D₈	C₂²×C₇	1	2	yes	complemented
363	C₄×D₈	C₂²×C₇	1	2	yes	complemented
364	C₄×D₈	C₂²×C₇	1	2	yes	complemented
365	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
366	#436	C₂²×C₇	1	1	yes	characteristic, complemented
367	#435	C₂²×C₇	1	2	yes	complemented
368	C₈×D₄	C₂²×C₇	1	2	yes	complemented
369	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
370	#433	C₂²×C₇	1	2	yes	complemented
371	#432	C₂²×C₇	1	1	yes	characteristic, complemented
372	#427	C₂²×C₇	1	2	yes	complemented
373	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
374	#418	C₂²×C₇	1	4	yes	complemented
375	C₂×#102	C₂²×C₇	1	2	yes	complemented
376	#405	C₂²×C₇	1	2	yes	complemented
377	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	2	4	no	—
381	C₂³×C₇	—	4	4	no	—
382	C₂³×C₇	—	4	8	no	—
383	C₂³×C₇	—	4	4	no	—
384	C₂³×C₇	—	8	2	no	—
385	C₂³×C₇	—	8	4	no	—
386	C₂³×C₇	—	8	4	no	—
387	C₂³×C₇	C₂²×D₄	1	2	yes	—
388	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
389	C₇×Q₈	—	2	2	no	—
390	C₇×Q₈	—	8	2	no	—
391	C₇×D₄	—	2	4	no	—
392	C₇×D₄	—	2	2	no	—
393	C₇×D₄	—	2	2	no	—
394	C₇×D₄	—	2	4	no	—
395	C₇×D₄	—	2	2	no	—
396	C₇×D₄	—	2	2	no	—
397	C₇×D₄	—	2	4	no	—
398	C₇×D₄	—	4	4	no	—
399	C₇×D₄	—	4	8	no	—
400	C₇×D₄	—	4	8	no	—
401	C₇×D₄	—	4	4	no	—
402	C₇×D₄	—	8	4	no	—
403	C₇×D₄	—	8	2	no	—
404	C₇×D₄	—	8	4	no	—
405	C₇×D₄	—	8	4	no	—
406	C₇×D₄	—	8	4	no	—
407	C₇×D₄	C₂×#41	1	4	yes	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	1	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	1	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	4	4	no	—
418	C₂×C₄×C₇	—	4	4	no	—
419	C₂×C₄×C₇	—	8	2	no	—
420	C₂×C₄×C₇	—	8	2	no	—
421	C₂×C₄×C₇	—	8	4	no	—
422	C₂×C₄×C₇	—	8	4	no	—
423	C₂×C₄×C₇	—	8	4	no	—
424	C₂×C₄×C₇	—	8	2	no	—
425	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
434	C₇×C₈	—	2	1	no	—
435	C₇×C₈	—	2	2	no	—
436	C₇×C₈	—	2	1	no	—
437	C₇×C₈	—	2	1	no	—
438	C₇×C₈	—	2	2	no	—
439	C₇×C₈	C₂×#41	1	2	yes	—
440	C₂×#41	—	2	2	no	—
441	C₂×#41	—	2	2	no	—
442	C₂²×D₄	—	2	2	no	—
443	C₂²×D₄	—	2	4	no	—
444	C₂²×D₄	C₂³×C₇	1	2	yes	—
445	C₂²×D₄	C₂³×C₇	1	4	yes	—
446	C₂³×C₄	—	2	2	no	—
447	C₂×D₈	—	2	4	no	—
448	C₂×D₈	—	2	8	no	—
449	C₂×D₈	C₂³×C₇	1	2	yes	—
450	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
451	C₂×D₈	C₂³×C₇	1	2	yes	—
452	C₂×D₈	C₂³×C₇	1	4	yes	—
453	C₂×D₈	C₂³×C₇	1	2	yes	—
454	C₂×D₈	C₂³×C₇	1	4	yes	—
455	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
456	C₂×M₁₆	C₂³×C₇	1	2	yes	—
457	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₇	1	2	yes	—
459	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
460	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
461	#127	C₂³×C₇	1	2	yes	—
462	#127	C₂³×C₇	1	4	yes	—
463	#126	—	2	4	no	—
464	#126	C₇×D₄	1	2	yes	—
465	#125	C₇×D₄	1	1	yes	characteristic
466	#125	C₂³×C₇	1	4	yes	—
467	#124	—	2	4	no	—
468	#124	—	2	2	no	—
469	#124	C₇×D₄	1	1	yes	characteristic
470	#123	—	2	4	no	—
471	#123	—	2	4	no	—
472	#123	—	2	4	no	—
473	#123	C₇×D₄	1	2	yes	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
477	#121	—	2	4	no	—
478	#121	—	2	2	no	—
479	#121	—	2	2	no	—
480	#121	—	2	2	no	—
481	#121	—	2	2	no	—
482	#121	—	2	4	no	—
483	#121	—	2	4	no	—
484	#121	—	2	4	no	—
485	#121	—	2	4	no	—
486	#121	C₇×D₄	1	1	yes	characteristic
487	#121	C₂³×C₇	1	4	yes	—
488	#121	C₂³×C₇	1	4	yes	—
489	#121	C₂³×C₇	1	4	yes	—
490	#120	—	2	4	no	—
491	#120	—	2	4	no	—
492	#120	—	2	4	no	—
493	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	C₂³×C₇	1	2	yes	—
501	C₄×D₄	C₂³×C₇	1	2	yes	—
502	C₄×D₄	C₂³×C₇	1	2	yes	—
503	C₄×D₄	C₂³×C₇	1	2	yes	—
504	C₄×D₄	C₂³×C₇	1	4	yes	—
505	C₄×D₄	C₂³×C₇	1	4	yes	—
506	C₄×D₄	C₂³×C₇	1	4	yes	—
507	C₄×D₄	C₂³×C₇	1	2	yes	—
508	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
509	#117	—	2	2	no	—
510	#117	C₂³×C₇	1	4	yes	—
511	#117	C₂³×C₇	1	2	yes	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
514	C₂×C₂²⋊C₄	—	2	2	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
518	#107	C₂³×C₇	1	1	yes	characteristic
519	#107	C₂³×C₇	1	1	yes	characteristic
520	#107	C₂³×C₇	1	2	yes	—
521	#107	C₂³×C₇	1	2	yes	—
522	#107	C₂³×C₇	1	2	yes	—
523	#106	C₂³×C₇	1	4	yes	—
524	#106	C₂³×C₇	1	4	yes	—
525	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
526	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
527	C₄⋊C₈	C₂³×C₇	1	2	yes	—
528	C₄⋊C₈	C₂³×C₇	1	2	yes	—
529	#102	C₂³×C₇	1	2	yes	—
530	#102	C₂³×C₇	1	2	yes	—
531	#102	C₂³×C₇	1	2	yes	—
532	#102	C₂³×C₇	1	2	yes	—
533	#102	C₂³×C₇	1	4	yes	—
534	#102	C₂³×C₇	1	4	yes	—
535	#102	C₂³×C₇	1	4	yes	—
536	#102	C₂³×C₇	1	4	yes	—
537	#102	C₂³×C₇	1	4	yes	—
538	#102	C₂³×C₇	1	4	yes	—
539	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
540	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
541	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
542	#97	C₂³×C₇	1	2	yes	—
543	#97	C₂³×C₇	1	2	yes	—
544	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
546	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
548	C₄×C₈	C₂³×C₇	1	2	yes	—
549	C₂²×C₇	—	2	1	no	—
550	C₂²×C₇	—	2	1	no	—
551	C₂²×C₇	—	2	2	no	—
552	C₂²×C₇	—	2	4	no	—
553	C₂²×C₇	—	2	2	no	—
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	4	2	no	—
556	C₂²×C₇	—	4	2	no	—
557	C₂²×C₇	—	4	2	no	—
558	C₂²×C₇	—	4	4	no	—
559	C₂²×C₇	—	4	2	no	—
560	C₂²×C₇	—	4	4	no	—
561	C₂²×C₇	—	4	4	no	—
562	C₂²×C₇	—	4	2	no	—
563	C₂²×C₇	—	8	8	no	—
564	C₂²×C₇	—	16	8	no	—
565	C₂²×C₇	#576	1	2	yes	—
566	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
567	C₄×C₇	—	2	1	no	—
568	C₄×C₇	—	2	2	no	—
569	C₄×C₇	—	2	1	no	—
570	C₄×C₇	—	2	1	no	—
571	C₄×C₇	—	2	1	no	—
572	C₄×C₇	—	2	2	no	—
573	C₄×C₇	—	2	2	no	—
574	C₄×C₇	—	4	2	no	—
575	C₄×C₇	—	4	2	no	—
576	C₄×C₇	—	4	4	no	—
577	C₄×C₇	#576	1	2	yes	—
578	C₄×C₇	C₂²×#41	1	1	yes	characteristic
579	C₄×C₇	#585	1	1	yes	characteristic
580	C₂⁴	—	2	2	no	—
581	C₂⁴	—	2	4	no	—
582	#41	—	8	4	no	—
583	#41	—	8	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	8	4	no	—
600	C₂×D₄	—	8	8	no	—
601	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
602	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
603	C₂×D₄	C₂⁴×C₇	1	2	yes	—
604	C₂×D₄	C₂⁴×C₇	1	4	yes	—
605	C₂×D₄	C₂⁴×C₇	1	2	yes	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	8	4	no	—
615	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
619	D₈	—	2	4	no	—
620	D₈	—	2	8	no	—
621	D₈	—	2	2	no	—
622	D₈	—	2	4	no	—
623	D₈	—	4	2	no	—
624	D₈	—	4	4	no	—
625	D₈	C₇×#41	1	4	yes	complemented
626	M₁₆	—	4	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	4	no	—
629	C₂×C₈	—	4	1	no	—
630	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₇	1	2	yes	—
634	C₂×C₈	C₂⁴×C₇	1	2	yes	—
635	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
642	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
643	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
644	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
645	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
661	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
662	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
663	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
664	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
665	C₄²	—	2	4	no	—
666	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
667	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
668	C₄²	C₂⁴×C₇	1	1	yes	characteristic
669	C₄²	C₂⁴×C₇	1	1	yes	characteristic
670	C₄²	C₂⁴×C₇	1	2	yes	—
671	C₂×C₇	—	2	2	no	—
672	C₂×C₇	—	4	2	no	—
673	C₂×C₇	—	4	4	no	—
674	C₂×C₇	—	8	2	no	—
675	C₂×C₇	—	8	4	no	—
676	C₂×C₇	D₄×#41	1	1	yes	characteristic
677	C₂×C₇	C₂×#576	1	1	yes	characteristic
678	C₂×C₇	C₂×#576	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	8	no	—
684	C₂³	—	4	4	no	—
685	C₂³	—	8	2	no	—
686	C₂³	—	8	4	no	—
687	C₂³	—	8	4	no	—
688	C₂³	C₂²×C₇×D₄	1	2	yes	—
689	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	8	2	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	4	no	—
698	D₄	—	2	2	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	8	no	—
701	D₄	—	4	8	no	—
702	D₄	—	4	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	D₄	C₂×C₇×#41	1	4	yes	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	2	no	—
726	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
727	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
729	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
730	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
731	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
732	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
733	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
734	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
735	C₈	—	2	1	no	—
736	C₈	—	2	2	no	—
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	2	no	—
740	C₈	C₂×C₇×#41	1	2	yes	—
741	C₇	#61480	1	1	yes	characteristic, direct product factor, Sylow
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	8	8	no	—
757	C₂²	—	16	8	no	—
758	C₂²	C₇×#576	1	2	yes	—
759	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	4	no	—
770	C₄	C₇×#576	1	2	yes	—
771	C₄	C₂²×C₇×#41	1	1	yes	characteristic
772	C₄	C₇×#585	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	8	2	no	—
777	C₂	—	8	4	no	—
778	C₂	C₇×D₄×#41	1	1	yes	characteristic
779	C₂	C₂×C₇×#576	1	1	yes	characteristic
780	C₂	C₂×C₇×#576	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3519	C₂	semidirect
2. C₇×#3391	C₂	semidirect
3. C₇×#3380	C₂	semidirect
4. C₇×#3366	C₂	semidirect
5. C₇×#3341	C₂	semidirect
6. C₇×#3339	C₂	semidirect
7. C₇×#3325	C₂	semidirect
8. C₇×#3318	C₂	semidirect
9. C₇×D₄×D₈	C₂	semidirect
10. C₇×D₄×D₈	C₂	semidirect
11. C₇×#3176	C₂	semidirect
12. C₇×#3169	C₂	semidirect
13. C₇×#3122	C₂	semidirect
14. C₇×#3109	C₂	semidirect
15. C₇×#2966	C₂	semidirect
16. C₇×#2948	C₂	semidirect
17. C₂×C₄×C₇×D₈	C₂	semidirect
20. C₇×#555	C₂²	semidirect
21. C₇×#554	C₂²	semidirect
23. C₇×#553	C₂²	semidirect
24. C₇×#550	C₂²	semidirect
27. C₇×D₄²	C₂²	semidirect
28. C₇×D₄²	C₂²	semidirect
29. C₇×#540	C₂²	semidirect
31. C₇×#532	C₂²	semidirect
35. C₇×#518	C₂²	semidirect
36. C₂×C₄×C₇×D₄	C₂²	semidirect
37. C₇×#500	C₂²	semidirect
38. C₇×#499	C₂²	semidirect
39. C₇×#493	C₂²	semidirect
40. C₇×#493	C₂²	semidirect
41. C₇×#490	C₂²	semidirect
42. C₇×#486	C₂²	semidirect
43. C₇×#482	C₂²	semidirect
44. C₇×#482	C₂²	semidirect
45. C₇×#481	C₂²	semidirect
46. C₇×#478	C₂²	semidirect
47. C₇×#478	C₂²	semidirect
48. C₇×#476	C₂²	semidirect
49. C₇×#476	C₂²	semidirect
50. C₇×#469	C₂²	semidirect
51. C₇×#466	C₂²	semidirect
52. C₇×#466	C₂²	semidirect
53. C₇×#466	C₂²	semidirect
54. C₇×#466	C₂²	semidirect
55. C₇×#459	C₂²	semidirect
56. C₇×#459	C₂²	semidirect
57. C₇×#459	C₂²	semidirect
58. C₇×#459	C₂²	semidirect
59. C₇×#447	C₂²	semidirect
60. C₇×#447	C₂²	semidirect
61. C₇×#447	C₂²	semidirect
62. C₇×#446	C₂²	semidirect
63. C₇×C₈×Q₈	C₂²	semidirect
64. C₇×#442	C₂²	semidirect
65. C₇×#442	C₂²	semidirect
66. C₇×#442	C₂²	semidirect
70. C₄×C₇×D₈	C₂²	semidirect
71. C₄×C₇×D₈	C₂²	semidirect
72. C₄×C₇×D₈	C₂²	semidirect
73. C₄×C₇×D₈	C₂²	semidirect
74. C₄×C₇×D₈	C₂²	semidirect
75. C₄×C₇×D₈	C₂²	semidirect
76. C₄×C₇×D₈	C₂²	semidirect
77. C₇×#436	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
79. C₇×C₈×D₄	C₂²	semidirect
80. C₇×C₈×D₄	C₂²	semidirect
81. C₇×#433	C₂²	semidirect
82. C₇×#432	C₂²	semidirect
83. C₇×#427	C₂²	semidirect
84. C₂×C₇×#107	C₂²	semidirect
85. C₇×#418	C₂²	semidirect
86. C₂×C₇×#102	C₂²	semidirect
87. C₇×#405	C₂²	semidirect
88. C₂×C₄×C₇×C₈	C₂²	semidirect
89. #61480	C₇	direct (N × H)
199. #3519	C₂×C₇	semidirect
200. #3391	C₂×C₇	semidirect
201. #3380	C₂×C₇	semidirect
202. #3366	C₂×C₇	semidirect
203. #3341	C₂×C₇	semidirect
204. #3339	C₂×C₇	semidirect
205. #3325	C₂×C₇	semidirect
206. #3318	C₂×C₇	semidirect
207. D₄×D₈	C₂×C₇	semidirect
208. D₄×D₈	C₂×C₇	semidirect
209. #3176	C₂×C₇	semidirect
210. #3169	C₂×C₇	semidirect
211. #3122	C₂×C₇	semidirect
212. #3109	C₂×C₇	semidirect
213. #2966	C₂×C₇	semidirect
214. #2948	C₂×C₇	semidirect
215. C₂×C₄×D₈	C₂×C₇	semidirect
261. C₇×D₈	#41	semidirect
309. #555	C₂²×C₇	semidirect
310. #554	C₂²×C₇	semidirect
312. #553	C₂²×C₇	semidirect
313. #550	C₂²×C₇	semidirect
316. D₄²	C₂²×C₇	semidirect
317. D₄²	C₂²×C₇	semidirect
318. #540	C₂²×C₇	semidirect
320. #532	C₂²×C₇	semidirect
324. #518	C₂²×C₇	semidirect
325. C₂×C₄×D₄	C₂²×C₇	semidirect
326. #500	C₂²×C₇	semidirect
327. #499	C₂²×C₇	semidirect
328. #493	C₂²×C₇	semidirect
329. #493	C₂²×C₇	semidirect
330. #490	C₂²×C₇	semidirect
331. #486	C₂²×C₇	semidirect
332. #482	C₂²×C₇	semidirect
333. #482	C₂²×C₇	semidirect
334. #481	C₂²×C₇	semidirect
335. #478	C₂²×C₇	semidirect
336. #478	C₂²×C₇	semidirect
337. #476	C₂²×C₇	semidirect
338. #476	C₂²×C₇	semidirect
339. #469	C₂²×C₇	semidirect
340. #466	C₂²×C₇	semidirect
341. #466	C₂²×C₇	semidirect
342. #466	C₂²×C₇	semidirect
343. #466	C₂²×C₇	semidirect
344. #459	C₂²×C₇	semidirect
345. #459	C₂²×C₇	semidirect
346. #459	C₂²×C₇	semidirect
347. #459	C₂²×C₇	semidirect
348. #447	C₂²×C₇	semidirect
349. #447	C₂²×C₇	semidirect
350. #447	C₂²×C₇	semidirect
351. #446	C₂²×C₇	semidirect
352. C₈×Q₈	C₂²×C₇	semidirect
353. #442	C₂²×C₇	semidirect
354. #442	C₂²×C₇	semidirect
355. #442	C₂²×C₇	semidirect
359. C₄×D₈	C₂²×C₇	semidirect
360. C₄×D₈	C₂²×C₇	semidirect
361. C₄×D₈	C₂²×C₇	semidirect
362. C₄×D₈	C₂²×C₇	semidirect
363. C₄×D₈	C₂²×C₇	semidirect
364. C₄×D₈	C₂²×C₇	semidirect
365. C₄×D₈	C₂²×C₇	semidirect
366. #436	C₂²×C₇	semidirect
367. #435	C₂²×C₇	semidirect
368. C₈×D₄	C₂²×C₇	semidirect
369. C₈×D₄	C₂²×C₇	semidirect
370. #433	C₂²×C₇	semidirect
371. #432	C₂²×C₇	semidirect
372. #427	C₂²×C₇	semidirect
373. C₂×#107	C₂²×C₇	semidirect
374. #418	C₂²×C₇	semidirect
375. C₂×#102	C₂²×C₇	semidirect
376. #405	C₂²×C₇	semidirect
377. C₂×C₄×C₈	C₂²×C₇	semidirect
625. D₈	C₇×#41	semidirect
741. C₇	#61480	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×#3519	2
C₇×#3391	2
C₇×#3380	2
C₇×#3366	2
C₇×#3341	2
C₇×#3339	2
C₇×#3325	2
C₇×#3318	2
C₇×D₄×D₈	2
C₇×#3176	2
C₇×#3169	2
C₇×#3122	2
C₇×#3109	2
C₇×#2966	2
C₇×#2948	2
C₂×C₄×C₇×D₈	2
#61480	7

Subgroups — C7×#61480 #13238696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61480 #13238696