Subgroups — C₇×#61261 #13238477

Order 1792.

1782 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3493	C₂	1	2	yes	maximal, complemented
2	C₇×#3350	C₂	1	4	yes	maximal, complemented
3	C₇×#3348	C₂	1	4	yes	maximal, complemented
4	C₇×#3342	C₂	1	2	yes	maximal, complemented
5	C₇×#3341	C₂	1	2	yes	maximal, complemented
6	C₇×#3339	C₂	1	2	yes	maximal, complemented
7	C₇×#3336	C₂	1	2	yes	maximal, complemented
8	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3099	C₂	1	2	yes	maximal, complemented
10	C₇×#3093	C₂	1	2	yes	maximal, complemented
11	C₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#135	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
21	C₇×#556	—	2	2	no	—
22	C₇×#556	C₂²	1	4	yes	—
23	C₇×#555	—	2	2	no	—
24	C₇×#555	C₂²	1	4	yes	—
25	C₇×#553	—	2	2	no	—
26	C₇×#553	C₂²	1	4	yes	—
27	C₇×#552	—	2	2	no	—
28	C₇×#552	C₂²	1	4	yes	—
29	C₇×#544	C₂²	1	2	yes	—
30	C₇×#538	—	2	4	no	—
31	C₇×#537	C₂²	1	2	yes	—
32	C₇×#529	—	2	4	no	—
33	C₇×#525	C₂²	1	2	yes	—
34	C₇×#525	C₂²	1	1	yes	characteristic
35	C₇×#520	C₂²	1	2	yes	—
36	C₇×#520	C₂²	1	2	yes	—
37	C₂×C₇×#117	C₂²	1	2	yes	—
38	C₇×#501	C₂²	1	4	yes	complemented
39	C₇×#500	C₂²	1	2	yes	complemented
40	C₇×#499	C₂²	1	2	yes	complemented
41	C₇×#485	C₂²	1	4	yes	—
42	C₇×#485	C₂²	1	4	yes	—
43	C₇×#485	C₂²	1	4	yes	complemented
44	C₇×#483	C₂²	1	4	yes	complemented
45	C₇×#482	C₂²	1	4	yes	—
46	C₇×#482	C₂²	1	4	yes	—
47	C₇×#482	C₂²	1	4	yes	complemented
48	C₇×#481	C₂²	1	4	yes	complemented
49	C₇×#479	C₂²	1	4	yes	complemented
50	C₇×#478	C₂²	1	4	yes	complemented
51	C₇×#476	C₂²	1	4	yes	complemented
52	C₇×#475	C₂²	1	4	yes	complemented
53	C₇×#468	C₂²	1	4	yes	complemented
54	C₇×#467	C₂²	1	1	yes	characteristic
55	C₇×#467	C₂²	1	1	yes	characteristic
56	C₇×#467	C₂²	1	2	yes	complemented
57	C₇×#466	C₂²	1	1	yes	characteristic
58	C₇×#466	C₂²	1	1	yes	characteristic
59	C₇×#466	C₂²	1	2	yes	complemented
60	C₇×#465	C₂²	1	2	yes	—
61	C₇×#465	C₂²	1	2	yes	—
62	C₇×#440	C₂²	1	4	yes	complemented
63	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
64	C₄×C₇×D₈	C₂²	1	2	yes	complemented
65	C₇×#435	C₂²	1	2	yes	—
66	C₇×#435	C₂²	1	2	yes	—
67	C₇×C₈×D₄	C₂²	1	2	yes	—
68	C₇×C₈×D₄	C₂²	1	2	yes	—
69	C₇×#428	C₂²	1	2	yes	—
70	C₇×#428	C₂²	1	2	yes	—
71	C₇×#428	C₂²	1	4	yes	complemented
72	C₇×#427	C₂²	1	1	yes	characteristic
73	C₇×#427	C₂²	1	2	yes	—
74	C₇×#427	C₂²	1	2	yes	—
75	C₇×#427	C₂²	1	2	yes	—
76	C₇×#427	C₂²	1	2	yes	—
77	C₇×#427	C₂²	1	2	yes	complemented
78	C₂×C₇×#107	C₂²	1	1	yes	characteristic
79	C₂×C₇×#107	C₂²	1	1	yes	characteristic
80	C₂×C₇×#107	C₂²	1	2	yes	complemented
81	C₂×C₇×#106	C₂²	1	2	yes	—
82	C₇×#424	C₂²	1	1	yes	characteristic
83	C₇×#417	C₂²	1	2	yes	—
84	C₇×#417	C₂²	1	2	yes	—
85	C₇×#416	C₂²	1	2	yes	—
86	C₇×#408	C₂²	1	1	yes	characteristic
87	C₇×#407	C₂²	1	1	yes	characteristic
88	C₇×#405	C₂²	1	1	yes	characteristic
89	#61261	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂×C₇×#41	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₇×#135	—	2	4	no	—
94	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
96	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
97	C₇×#131	—	2	4	no	—
98	C₂×C₇×M₁₆	C₂³	1	2	yes	—
99	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
101	C₂²×C₇×C₈	—	2	4	no	—
102	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×C₈	C₂³	1	2	yes	—
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₇×C₄⋊Q₈	—	2	2	no	—
110	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₇×#126	—	2	4	no	—
112	C₇×#126	—	2	4	no	—
113	C₇×#126	—	2	4	no	—
114	C₇×#126	—	2	4	no	—
115	C₇×#125	—	2	4	no	—
116	C₇×#125	—	2	2	no	—
117	C₇×#125	C₂³	1	4	yes	—
118	C₇×#124	—	2	4	no	—
119	C₇×#124	—	2	4	no	—
120	C₇×#124	—	2	4	no	—
121	C₇×#123	—	2	4	no	—
122	C₇×#123	—	2	2	no	—
123	C₇×#123	—	2	4	no	—
124	C₇×#123	D₄	1	2	yes	—
125	C₇×C₂²⋊Q₈	—	2	2	no	—
126	C₇×C₂²⋊Q₈	—	2	4	no	—
127	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
129	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₇×#121	—	2	4	no	—
133	C₇×#121	—	2	2	no	—
134	C₇×#121	—	2	4	no	—
135	C₇×#121	—	2	4	no	—
136	C₇×#121	D₄	1	1	yes	characteristic
137	C₇×#121	D₄	1	1	yes	characteristic
138	C₇×#121	C₂³	1	2	yes	—
139	C₇×#121	C₂³	1	2	yes	—
140	C₇×#121	C₂³	1	4	yes	—
141	C₇×#120	—	2	2	no	—
142	C₇×#120	D₄	1	2	yes	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	—	2	4	no	—
145	C₄×C₇×Q₈	C₂³	1	4	yes	—
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	—	2	4	no	—
151	C₄×C₇×D₄	—	2	4	no	—
152	C₄×C₇×D₄	C₂³	1	4	yes	—
153	C₄×C₇×D₄	C₂³	1	2	yes	—
154	C₄×C₇×D₄	C₂³	1	2	yes	—
155	C₇×#117	—	2	2	no	—
156	C₇×#117	—	2	2	no	—
157	C₇×#117	—	2	2	no	—
158	C₇×#117	—	2	4	no	—
159	C₇×#117	—	2	4	no	—
160	C₇×#117	C₂³	1	4	yes	—
161	C₇×#117	C₂³	1	4	yes	—
162	C₇×#117	C₂³	1	4	yes	—
163	C₇×#117	C₂³	1	2	yes	—
164	C₇×#117	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₄⋊C₄	—	2	2	no	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₄²×C₇	—	2	2	no	—
171	C₇×#107	C₂³	1	1	yes	characteristic
172	C₇×#107	C₂³	1	1	yes	characteristic
173	C₇×#107	C₂³	1	2	yes	—
174	C₇×#107	C₂³	1	2	yes	—
175	C₇×#107	C₂³	1	4	yes	—
176	C₇×#107	C₂³	1	4	yes	—
177	C₇×#107	C₂³	1	2	yes	—
178	C₇×#107	C₂³	1	2	yes	—
179	C₇×#106	C₂³	1	4	yes	—
180	C₇×#106	C₂³	1	4	yes	—
181	C₇×#106	C₂³	1	4	yes	—
182	C₇×#106	C₂³	1	4	yes	—
183	C₇×#106	C₂³	1	2	yes	—
184	C₇×C₄⋊C₈	C₂³	1	2	yes	—
185	C₇×C₄⋊C₈	C₂³	1	2	yes	—
186	C₇×#103	C₂³	1	2	yes	—
187	C₇×#103	C₂³	1	2	yes	—
188	C₇×#103	C₂³	1	4	yes	—
189	C₇×#103	C₂³	1	4	yes	—
190	C₇×#102	C₂³	1	2	yes	—
191	C₇×#102	C₂³	1	2	yes	—
192	C₇×#102	C₂³	1	4	yes	—
193	C₇×#102	C₂³	1	4	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
198	C₇×#97	C₂³	1	2	yes	—
199	C₄×C₇×C₈	C₂³	1	2	yes	—
200	#3493	C₂×C₇	1	2	yes	complemented
201	#3350	C₂×C₇	1	4	yes	complemented
202	#3348	C₂×C₇	1	4	yes	complemented
203	#3342	C₂×C₇	1	2	yes	complemented
204	#3341	C₂×C₇	1	2	yes	complemented
205	#3339	C₂×C₇	1	2	yes	complemented
206	#3336	C₂×C₇	1	2	yes	complemented
207	#3164	C₂×C₇	1	1	yes	characteristic, complemented
208	#3099	C₂×C₇	1	2	yes	complemented
209	#3093	C₂×C₇	1	2	yes	complemented
210	#3084	C₂×C₇	1	2	yes	complemented
211	#3061	C₂×C₇	1	1	yes	characteristic, complemented
212	#3050	C₂×C₇	1	1	yes	characteristic, complemented
213	#2951	C₂×C₇	1	1	yes	characteristic, complemented
214	#2929	C₂×C₇	1	1	yes	characteristic, complemented
215	#2913	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
217	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
218	C₇×#41	—	2	2	no	—
219	C₇×#41	—	2	2	no	—
220	C₇×#41	—	2	4	no	—
221	C₇×#41	—	2	4	no	—
222	C₂×C₇×Q₈	—	2	4	no	—
223	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
225	C₂×C₇×D₄	—	2	2	no	—
226	C₂×C₇×D₄	—	2	2	no	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
230	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
231	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
232	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
233	C₂×C₇×D₄	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	2	no	—
237	C₂²×C₄×C₇	—	2	2	no	—
238	C₂²×C₄×C₇	—	2	4	no	—
239	C₂²×C₄×C₇	—	2	2	no	—
240	C₂²×C₄×C₇	—	2	4	no	—
241	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
248	C₇×Q₁₆	—	2	2	no	—
249	C₇×SD₁₆	—	2	4	no	—
250	C₇×D₈	—	2	2	no	—
251	C₇×M₁₆	—	2	2	no	—
252	C₇×M₁₆	—	2	2	no	—
253	C₇×M₁₆	—	2	4	no	—
254	C₂×C₇×C₈	—	2	2	no	—
255	C₂×C₇×C₈	—	2	2	no	—
256	C₂×C₇×C₈	—	2	2	no	—
257	C₂×C₇×C₈	—	2	2	no	—
258	C₂×C₇×C₈	—	2	2	no	—
259	C₂×C₇×C₈	—	2	4	no	—
260	C₂×C₇×C₈	#41	1	4	yes	—
261	C₂×C₇×C₈	C₂⁴	1	2	yes	—
262	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
263	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
264	C₂×C₇×C₈	C₂⁴	1	2	yes	—
265	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
267	C₇×C₄⋊C₄	—	2	2	no	—
268	C₇×C₄⋊C₄	—	2	4	no	—
269	C₇×C₄⋊C₄	—	2	2	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	4	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	—	2	4	no	—
277	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
279	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₇×C₂²⋊C₄	—	2	4	no	—
286	C₇×C₂²⋊C₄	—	2	4	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	2	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	2	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	—	2	4	no	—
303	C₄²×C₇	—	2	4	no	—
304	C₄²×C₇	—	2	4	no	—
305	C₄²×C₇	—	2	2	no	—
306	C₄²×C₇	C₂⁴	1	2	yes	—
307	C₂×#135	C₂²×C₇	1	1	yes	characteristic
308	C₂×#131	C₂²×C₇	1	1	yes	characteristic
309	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
310	#556	—	2	2	no	—
311	#556	C₂²×C₇	1	4	yes	—
312	#555	—	2	2	no	—
313	#555	C₂²×C₇	1	4	yes	—
314	#553	—	2	2	no	—
315	#553	C₂²×C₇	1	4	yes	—
316	#552	—	2	2	no	—
317	#552	C₂²×C₇	1	4	yes	—
318	#544	C₂²×C₇	1	2	yes	—
319	#538	—	2	4	no	—
320	#537	C₂²×C₇	1	2	yes	—
321	#529	—	2	4	no	—
322	#525	C₂²×C₇	1	2	yes	—
323	#525	C₂²×C₇	1	1	yes	characteristic
324	#520	C₂²×C₇	1	2	yes	—
325	#520	C₂²×C₇	1	2	yes	—
326	C₂×#117	C₂²×C₇	1	2	yes	—
327	#501	C₂²×C₇	1	4	yes	complemented
328	#500	C₂²×C₇	1	2	yes	complemented
329	#499	C₂²×C₇	1	2	yes	complemented
330	#485	C₂²×C₇	1	4	yes	—
331	#485	C₂²×C₇	1	4	yes	—
332	#485	C₂²×C₇	1	4	yes	complemented
333	#483	C₂²×C₇	1	4	yes	complemented
334	#482	C₂²×C₇	1	4	yes	—
335	#482	C₂²×C₇	1	4	yes	—
336	#482	C₂²×C₇	1	4	yes	complemented
337	#481	C₂²×C₇	1	4	yes	complemented
338	#479	C₂²×C₇	1	4	yes	complemented
339	#478	C₂²×C₇	1	4	yes	complemented
340	#476	C₂²×C₇	1	4	yes	complemented
341	#475	C₂²×C₇	1	4	yes	complemented
342	#468	C₂²×C₇	1	4	yes	complemented
343	#467	C₂²×C₇	1	1	yes	characteristic
344	#467	C₂²×C₇	1	1	yes	characteristic
345	#467	C₂²×C₇	1	2	yes	complemented
346	#466	C₂²×C₇	1	1	yes	characteristic
347	#466	C₂²×C₇	1	1	yes	characteristic
348	#466	C₂²×C₇	1	2	yes	complemented
349	#465	C₂²×C₇	1	2	yes	—
350	#465	C₂²×C₇	1	2	yes	—
351	#440	C₂²×C₇	1	4	yes	complemented
352	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
353	C₄×D₈	C₂²×C₇	1	2	yes	complemented
354	#435	C₂²×C₇	1	2	yes	—
355	#435	C₂²×C₇	1	2	yes	—
356	C₈×D₄	C₂²×C₇	1	2	yes	—
357	C₈×D₄	C₂²×C₇	1	2	yes	—
358	#428	C₂²×C₇	1	2	yes	—
359	#428	C₂²×C₇	1	2	yes	—
360	#428	C₂²×C₇	1	4	yes	complemented
361	#427	C₂²×C₇	1	2	yes	—
362	#427	C₂²×C₇	1	2	yes	—
363	#427	C₂²×C₇	1	2	yes	—
364	#427	C₂²×C₇	1	2	yes	—
365	#427	C₂²×C₇	1	1	yes	characteristic
366	#427	C₂²×C₇	1	2	yes	complemented
367	C₂×#107	C₂²×C₇	1	1	yes	characteristic
368	C₂×#107	C₂²×C₇	1	1	yes	characteristic
369	C₂×#107	C₂²×C₇	1	2	yes	complemented
370	C₂×#106	C₂²×C₇	1	2	yes	—
371	#424	C₂²×C₇	1	1	yes	characteristic
372	#417	C₂²×C₇	1	2	yes	—
373	#417	C₂²×C₇	1	2	yes	—
374	#416	C₂²×C₇	1	2	yes	—
375	#408	C₂²×C₇	1	1	yes	characteristic
376	#407	C₂²×C₇	1	1	yes	characteristic
377	#405	C₂²×C₇	1	1	yes	characteristic
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	4	1	no	—
381	C₂³×C₇	—	4	1	no	—
382	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
384	C₂³×C₇	C₂²×D₄	1	2	yes	—
385	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₇×Q₈	—	2	2	no	—
387	C₇×Q₈	—	2	2	no	—
388	C₇×Q₈	—	2	2	no	—
389	C₇×Q₈	—	8	4	no	—
390	C₇×D₄	—	2	4	no	—
391	C₇×D₄	—	2	2	no	—
392	C₇×D₄	—	2	2	no	—
393	C₇×D₄	—	2	2	no	—
394	C₇×D₄	—	4	2	no	—
395	C₇×D₄	—	4	2	no	—
396	C₇×D₄	—	4	4	no	—
397	C₇×D₄	—	8	2	no	—
398	C₇×D₄	—	8	4	no	—
399	C₇×D₄	—	8	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	1	no	—
404	C₂×C₄×C₇	—	2	1	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	1	no	—
407	C₂×C₄×C₇	—	2	1	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	4	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	4	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	4	4	no	—
415	C₂×C₄×C₇	—	8	4	no	—
416	C₂×C₄×C₇	—	8	2	no	—
417	C₂×C₄×C₇	—	8	4	no	—
418	C₂×C₄×C₇	—	8	2	no	—
419	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂×#41	1	2	yes	—
426	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
427	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
428	C₇×C₈	—	2	1	no	—
429	C₇×C₈	—	2	1	no	—
430	C₇×C₈	—	2	2	no	—
431	C₇×C₈	—	2	2	no	—
432	C₇×C₈	C₂×#41	1	2	yes	—
433	C₇×C₈	C₂×#41	1	2	yes	—
434	C₂×#41	C₂³×C₇	1	2	yes	—
435	C₂×#41	C₂³×C₇	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
437	#135	—	2	4	no	—
438	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
439	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
440	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
441	#131	—	2	4	no	—
442	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
443	C₂×M₁₆	C₂³×C₇	1	2	yes	—
444	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
445	C₂²×C₈	—	2	4	no	—
446	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₇	1	2	yes	—
452	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
453	C₄⋊Q₈	—	2	2	no	—
454	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
455	#126	—	2	4	no	—
456	#126	—	2	4	no	—
457	#126	—	2	4	no	—
458	#126	—	2	4	no	—
459	#125	—	2	4	no	—
460	#125	—	2	2	no	—
461	#125	C₂³×C₇	1	4	yes	—
462	#124	—	2	4	no	—
463	#124	—	2	4	no	—
464	#124	—	2	4	no	—
465	#123	—	2	4	no	—
466	#123	—	2	2	no	—
467	#123	—	2	4	no	—
468	#123	C₇×D₄	1	2	yes	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
472	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
473	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
474	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
475	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
476	#121	—	2	4	no	—
477	#121	—	2	2	no	—
478	#121	—	2	4	no	—
479	#121	—	2	4	no	—
480	#121	C₇×D₄	1	1	yes	characteristic
481	#121	C₇×D₄	1	1	yes	characteristic
482	#121	C₂³×C₇	1	2	yes	—
483	#121	C₂³×C₇	1	2	yes	—
484	#121	C₂³×C₇	1	4	yes	—
485	#120	—	2	2	no	—
486	#120	C₇×D₄	1	2	yes	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	C₂³×C₇	1	4	yes	—
490	C₄×D₄	—	2	4	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	C₂³×C₇	1	4	yes	—
497	C₄×D₄	C₂³×C₇	1	2	yes	—
498	C₄×D₄	C₂³×C₇	1	2	yes	—
499	#117	—	2	2	no	—
500	#117	—	2	2	no	—
501	#117	—	2	2	no	—
502	#117	—	2	4	no	—
503	#117	—	2	4	no	—
504	#117	C₂³×C₇	1	4	yes	—
505	#117	C₂³×C₇	1	4	yes	—
506	#117	C₂³×C₇	1	2	yes	—
507	#117	C₂³×C₇	1	4	yes	—
508	#117	C₂³×C₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₄²	—	2	2	no	—
515	#107	C₂³×C₇	1	2	yes	—
516	#107	C₂³×C₇	1	2	yes	—
517	#107	C₂³×C₇	1	2	yes	—
518	#107	C₂³×C₇	1	2	yes	—
519	#107	C₂³×C₇	1	1	yes	characteristic
520	#107	C₂³×C₇	1	4	yes	—
521	#107	C₂³×C₇	1	1	yes	characteristic
522	#107	C₂³×C₇	1	4	yes	—
523	#106	C₂³×C₇	1	4	yes	—
524	#106	C₂³×C₇	1	4	yes	—
525	#106	C₂³×C₇	1	2	yes	—
526	#106	C₂³×C₇	1	4	yes	—
527	#106	C₂³×C₇	1	4	yes	—
528	C₄⋊C₈	C₂³×C₇	1	2	yes	—
529	C₄⋊C₈	C₂³×C₇	1	2	yes	—
530	#103	C₂³×C₇	1	2	yes	—
531	#103	C₂³×C₇	1	2	yes	—
532	#103	C₂³×C₇	1	4	yes	—
533	#103	C₂³×C₇	1	4	yes	—
534	#102	C₂³×C₇	1	2	yes	—
535	#102	C₂³×C₇	1	2	yes	—
536	#102	C₂³×C₇	1	4	yes	—
537	#102	C₂³×C₇	1	4	yes	—
538	C₂²⋊C₈	C₂³×C₇	1	2	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	C₄×C₈	C₂³×C₇	1	2	yes	—
544	C₂²×C₇	—	2	1	no	—
545	C₂²×C₇	—	2	1	no	—
546	C₂²×C₇	—	2	2	no	—
547	C₂²×C₇	—	2	1	no	—
548	C₂²×C₇	—	2	1	no	—
549	C₂²×C₇	—	2	2	no	—
550	C₂²×C₇	—	2	1	no	—
551	C₂²×C₇	—	2	1	no	—
552	C₂²×C₇	—	2	1	no	—
553	C₂²×C₇	—	2	1	no	—
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	4	4	no	—
556	C₂²×C₇	—	4	2	no	—
557	C₂²×C₇	—	4	2	no	—
558	C₂²×C₇	—	4	2	no	—
559	C₂²×C₇	#547	1	2	yes	—
560	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₇	—	2	2	no	—
562	C₄×C₇	—	2	2	no	—
563	C₄×C₇	—	2	1	no	—
564	C₄×C₇	—	2	1	no	—
565	C₄×C₇	—	2	2	no	—
566	C₄×C₇	—	4	4	no	—
567	C₄×C₇	—	4	2	no	—
568	C₄×C₇	—	4	4	no	—
569	C₄×C₇	—	4	2	no	—
570	C₄×C₇	—	4	2	no	—
571	C₄×C₇	#547	1	2	yes	—
572	C₄×C₇	C₂²×#41	1	1	yes	characteristic
573	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
574	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	4	no	—
578	#41	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
581	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
587	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
588	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
589	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
590	C₂×D₄	C₂⁴×C₇	1	2	yes	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
599	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
600	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
605	Q₁₆	—	2	2	no	—
606	SD₁₆	—	2	4	no	—
607	D₈	—	2	2	no	—
608	M₁₆	—	2	2	no	—
609	M₁₆	—	2	2	no	—
610	M₁₆	—	2	4	no	—
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	—	2	4	no	—
617	C₂×C₈	C₇×#41	1	4	yes	—
618	C₂×C₈	C₂⁴×C₇	1	2	yes	—
619	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₇	1	2	yes	—
622	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
623	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
635	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
636	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
637	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
639	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
641	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
642	C₂²⋊C₄	—	2	4	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	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
654	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
655	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
656	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
657	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	2	no	—
663	C₄²	C₂⁴×C₇	1	2	yes	—
664	C₂×C₇	—	2	2	no	—
665	C₂×C₇	—	4	2	no	—
666	C₂×C₇	—	4	1	no	—
667	C₂×C₇	—	4	1	no	—
668	C₂×C₇	—	8	2	no	—
669	C₂×C₇	C₂×#547	1	1	yes	characteristic
670	C₂×C₇	#3584	1	1	yes	characteristic
671	C₂×C₇	#3584	1	1	yes	characteristic
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
677	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
678	C₂³	C₂²×C₇×D₄	1	2	yes	—
679	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	8	4	no	—
684	D₄	—	2	4	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	4	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	2	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	—	8	2	no	—
713	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
714	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
715	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
716	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
717	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
718	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
719	C₂×C₄	C₂×C₇×#41	1	2	yes	—
720	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
721	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
722	C₈	—	2	1	no	—
723	C₈	—	2	1	no	—
724	C₈	—	2	2	no	—
725	C₈	—	2	2	no	—
726	C₈	C₂×C₇×#41	1	2	yes	—
727	C₈	C₂×C₇×#41	1	2	yes	—
728	C₇	#61261	1	1	yes	characteristic, direct product factor, Sylow
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	C₇×#547	1	2	yes	—
745	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	C₇×#547	1	2	yes	—
757	C₄	C₂²×C₇×#41	1	1	yes	characteristic
758	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×C₇×#547	1	1	yes	characteristic
765	C₂	C₇×#3584	1	1	yes	characteristic
766	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3493	C₂	semidirect
2. C₇×#3350	C₂	semidirect
3. C₇×#3348	C₂	semidirect
4. C₇×#3342	C₂	semidirect
5. C₇×#3341	C₂	semidirect
6. C₇×#3339	C₂	semidirect
7. C₇×#3336	C₂	semidirect
8. C₇×#3164	C₂	semidirect
9. C₇×#3099	C₂	semidirect
10. C₇×#3093	C₂	semidirect
11. C₇×#3084	C₂	semidirect
12. C₇×#3061	C₂	semidirect
13. C₇×#3050	C₂	semidirect
14. C₇×#2951	C₂	semidirect
15. C₇×#2929	C₂	semidirect
16. C₇×#2913	C₂	semidirect
17. C₂×C₇×#427	C₂	semidirect
38. C₇×#501	C₂²	semidirect
39. C₇×#500	C₂²	semidirect
40. C₇×#499	C₂²	semidirect
43. C₇×#485	C₂²	semidirect
44. C₇×#483	C₂²	semidirect
47. C₇×#482	C₂²	semidirect
48. C₇×#481	C₂²	semidirect
49. C₇×#479	C₂²	semidirect
50. C₇×#478	C₂²	semidirect
51. C₇×#476	C₂²	semidirect
52. C₇×#475	C₂²	semidirect
53. C₇×#468	C₂²	semidirect
56. C₇×#467	C₂²	semidirect
59. C₇×#466	C₂²	semidirect
62. C₇×#440	C₂²	semidirect
63. C₄×C₇×Q₁₆	C₂²	semidirect
64. C₄×C₇×D₈	C₂²	semidirect
71. C₇×#428	C₂²	semidirect
77. C₇×#427	C₂²	semidirect
80. C₂×C₇×#107	C₂²	semidirect
89. #61261	C₇	direct (N × H)
200. #3493	C₂×C₇	semidirect
201. #3350	C₂×C₇	semidirect
202. #3348	C₂×C₇	semidirect
203. #3342	C₂×C₇	semidirect
204. #3341	C₂×C₇	semidirect
205. #3339	C₂×C₇	semidirect
206. #3336	C₂×C₇	semidirect
207. #3164	C₂×C₇	semidirect
208. #3099	C₂×C₇	semidirect
209. #3093	C₂×C₇	semidirect
210. #3084	C₂×C₇	semidirect
211. #3061	C₂×C₇	semidirect
212. #3050	C₂×C₇	semidirect
213. #2951	C₂×C₇	semidirect
214. #2929	C₂×C₇	semidirect
215. #2913	C₂×C₇	semidirect
216. C₂×#427	C₂×C₇	semidirect
327. #501	C₂²×C₇	semidirect
328. #500	C₂²×C₇	semidirect
329. #499	C₂²×C₇	semidirect
332. #485	C₂²×C₇	semidirect
333. #483	C₂²×C₇	semidirect
336. #482	C₂²×C₇	semidirect
337. #481	C₂²×C₇	semidirect
338. #479	C₂²×C₇	semidirect
339. #478	C₂²×C₇	semidirect
340. #476	C₂²×C₇	semidirect
341. #475	C₂²×C₇	semidirect
342. #468	C₂²×C₇	semidirect
345. #467	C₂²×C₇	semidirect
348. #466	C₂²×C₇	semidirect
351. #440	C₂²×C₇	semidirect
352. C₄×Q₁₆	C₂²×C₇	semidirect
353. C₄×D₈	C₂²×C₇	semidirect
360. #428	C₂²×C₇	semidirect
366. #427	C₂²×C₇	semidirect
369. C₂×#107	C₂²×C₇	semidirect
728. C₇	#61261	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×#3493	2
C₇×#3350	2
C₇×#3348	2
C₇×#3342	2
C₇×#3341	2
C₇×#3339	2
C₇×#3336	2
C₇×#3164	2
C₇×#3099	2
C₇×#3093	2
C₇×#3084	2
C₇×#3061	2
C₇×#3050	2
C₇×#2951	2
C₇×#2929	2
C₇×#2913	2
C₂×C₇×#427	2
#61261	7

Subgroups — C7×#61261 #13238477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61261 #13238477