Subgroups — C₇×#61258 #13238474

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3492	C₂	1	2	yes	maximal, complemented
2	C₇×#3346	C₂	1	4	yes	maximal, complemented
3	C₇×#3343	C₂	1	4	yes	maximal, complemented
4	C₇×#3339	C₂	1	2	yes	maximal, complemented
5	C₇×#3338	C₂	1	2	yes	maximal, complemented
6	C₇×#3336	C₂	1	2	yes	maximal, complemented
7	C₇×#3334	C₂	1	2	yes	maximal, complemented
8	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3098	C₂	1	2	yes	maximal, complemented
10	C₇×#3092	C₂	1	2	yes	maximal, complemented
11	C₇×#3083	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	C₂²×C₇×#107	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×#554	—	2	2	no	—
22	C₇×#554	C₂²	1	4	yes	—
23	C₇×#553	—	2	2	no	—
24	C₇×#553	C₂²	1	4	yes	—
25	C₇×#552	—	2	2	no	—
26	C₇×#552	C₂²	1	4	yes	—
27	C₇×#547	—	2	2	no	—
28	C₇×#547	C₂²	1	4	yes	—
29	C₇×#544	C₂²	1	2	yes	—
30	C₇×#539	—	2	4	no	—
31	C₇×#537	C₂²	1	2	yes	—
32	C₇×#525	—	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	C₂²×C₇×C₄⋊C₄	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	complemented
42	C₇×#484	C₂²	1	4	yes	—
43	C₇×#484	C₂²	1	4	yes	complemented
44	C₇×#483	C₂²	1	4	yes	—
45	C₇×#482	C₂²	1	4	yes	complemented
46	C₇×#481	C₂²	1	4	yes	—
47	C₇×#480	C₂²	1	4	yes	—
48	C₇×#480	C₂²	1	4	yes	complemented
49	C₇×#479	C₂²	1	4	yes	complemented
50	C₇×#478	C₂²	1	4	yes	complemented
51	C₇×#477	C₂²	1	4	yes	complemented
52	C₇×#474	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	complemented
74	C₂×C₇×#107	C₂²	1	1	yes	characteristic
75	C₂×C₇×#107	C₂²	1	1	yes	characteristic
76	C₂×C₇×#107	C₂²	1	2	yes	—
77	C₂×C₇×#107	C₂²	1	2	yes	—
78	C₂×C₇×#107	C₂²	1	2	yes	—
79	C₂×C₇×#107	C₂²	1	2	yes	—
80	C₂×C₇×#107	C₂²	1	2	yes	—
81	C₂×C₇×#107	C₂²	1	2	yes	complemented
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	#61258	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	4	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂×C₇×#41	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇	—	2	2	no	—
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₇×#135	—	2	4	no	—
96	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
98	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
99	C₇×#131	—	2	4	no	—
100	C₂×C₇×M₁₆	C₂³	1	2	yes	—
101	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
103	C₂²×C₇×C₈	—	2	4	no	—
104	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	2	yes	—
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₇×C₄⋊Q₈	—	2	2	no	—
112	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₇×#126	—	2	4	no	—
114	C₇×#126	—	2	4	no	—
115	C₇×#125	—	2	4	no	—
116	C₇×#125	—	2	4	no	—
117	C₇×#125	—	2	2	no	—
118	C₇×#125	C₂³	1	4	yes	—
119	C₇×#123	—	2	4	no	—
120	C₇×#123	—	2	2	no	—
121	C₇×#123	—	2	4	no	—
122	C₇×#123	—	2	4	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	—	2	4	no	—
128	C₇×C₂²⋊Q₈	—	2	4	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₇×#121	—	2	4	no	—
136	C₇×#121	—	2	4	no	—
137	C₇×#121	—	2	2	no	—
138	C₇×#121	D₄	1	1	yes	characteristic
139	C₇×#121	D₄	1	1	yes	characteristic
140	C₇×#121	C₂³	1	2	yes	—
141	C₇×#121	C₂³	1	2	yes	—
142	C₇×#121	C₂³	1	4	yes	—
143	C₇×#120	—	2	2	no	—
144	C₇×#120	D₄	1	2	yes	—
145	C₄×C₇×Q₈	—	2	2	no	—
146	C₄×C₇×Q₈	C₂³	1	4	yes	—
147	C₄×C₇×D₄	—	2	4	no	—
148	C₄×C₇×D₄	—	2	2	no	—
149	C₄×C₇×D₄	—	2	4	no	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	4	no	—
153	C₄×C₇×D₄	—	2	4	no	—
154	C₄×C₇×D₄	C₂³	1	4	yes	—
155	C₄×C₇×D₄	C₂³	1	2	yes	—
156	C₄×C₇×D₄	C₂³	1	2	yes	—
157	C₇×#117	—	2	2	no	—
158	C₇×#117	—	2	4	no	—
159	C₇×#117	C₂³	1	4	yes	—
160	C₇×#117	C₂³	1	2	yes	—
161	C₇×#117	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	—	2	2	no	—
163	C₂×C₇×C₄⋊C₄	—	2	2	no	—
164	C₂×C₇×C₄⋊C₄	—	2	2	no	—
165	C₂×C₇×C₄⋊C₄	—	2	2	no	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
178	C₇×#107	C₂³	1	4	yes	—
179	C₇×#107	C₂³	1	2	yes	—
180	C₇×#107	C₂³	1	2	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	#3492	C₂×C₇	1	2	yes	complemented
201	#3346	C₂×C₇	1	4	yes	complemented
202	#3343	C₂×C₇	1	4	yes	complemented
203	#3339	C₂×C₇	1	2	yes	complemented
204	#3338	C₂×C₇	1	2	yes	complemented
205	#3336	C₂×C₇	1	2	yes	complemented
206	#3334	C₂×C₇	1	2	yes	complemented
207	#3164	C₂×C₇	1	1	yes	characteristic, complemented
208	#3098	C₂×C₇	1	2	yes	complemented
209	#3092	C₂×C₇	1	2	yes	complemented
210	#3083	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	C₂²×#107	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	C₇×#41	—	8	8	no	—
223	C₂×C₇×Q₈	—	2	4	no	—
224	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
225	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
226	C₂×C₇×D₄	—	2	2	no	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
231	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
232	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
233	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
234	C₂×C₇×D₄	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	2	no	—
237	C₂²×C₄×C₇	—	2	4	no	—
238	C₂²×C₄×C₇	—	2	2	no	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	2	no	—
241	C₂²×C₄×C₇	—	2	4	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	8	4	no	—
245	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₇×Q₁₆	—	2	2	no	—
253	C₇×SD₁₆	—	2	4	no	—
254	C₇×D₈	—	2	2	no	—
255	C₇×M₁₆	—	2	2	no	—
256	C₇×M₁₆	—	2	2	no	—
257	C₇×M₁₆	—	2	4	no	—
258	C₂×C₇×C₈	—	2	2	no	—
259	C₂×C₇×C₈	—	2	2	no	—
260	C₂×C₇×C₈	—	2	2	no	—
261	C₂×C₇×C₈	—	2	2	no	—
262	C₂×C₇×C₈	—	2	2	no	—
263	C₂×C₇×C₈	—	2	4	no	—
264	C₂×C₇×C₈	#41	1	4	yes	complemented
265	C₂×C₇×C₈	C₂⁴	1	2	yes	—
266	C₂×C₇×C₈	C₂⁴	1	2	yes	—
267	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
270	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	4	no	—
277	C₇×C₄⋊C₄	—	2	4	no	—
278	C₇×C₄⋊C₄	—	2	4	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	2	no	—
283	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
284	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
285	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
286	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
287	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	2	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	2	no	—
299	C₇×C₂²⋊C₄	—	2	2	no	—
300	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
301	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
302	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
303	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
304	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
305	C₄²×C₇	—	2	4	no	—
306	C₄²×C₇	—	2	4	no	—
307	C₄²×C₇	—	2	2	no	—
308	C₄²×C₇	C₂⁴	1	2	yes	—
309	C₂×#135	C₂²×C₇	1	1	yes	characteristic
310	C₂×#131	C₂²×C₇	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
312	#554	—	2	2	no	—
313	#554	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	#547	—	2	2	no	—
319	#547	C₂²×C₇	1	4	yes	—
320	#544	C₂²×C₇	1	2	yes	—
321	#539	—	2	4	no	—
322	#537	C₂²×C₇	1	2	yes	—
323	#525	—	2	4	no	—
324	#525	C₂²×C₇	1	2	yes	—
325	#525	C₂²×C₇	1	1	yes	characteristic
326	#520	C₂²×C₇	1	2	yes	—
327	#520	C₂²×C₇	1	2	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
329	#501	C₂²×C₇	1	4	yes	complemented
330	#500	C₂²×C₇	1	2	yes	complemented
331	#499	C₂²×C₇	1	2	yes	complemented
332	#485	C₂²×C₇	1	4	yes	complemented
333	#484	C₂²×C₇	1	4	yes	—
334	#484	C₂²×C₇	1	4	yes	complemented
335	#483	C₂²×C₇	1	4	yes	—
336	#482	C₂²×C₇	1	4	yes	complemented
337	#481	C₂²×C₇	1	4	yes	—
338	#480	C₂²×C₇	1	4	yes	—
339	#480	C₂²×C₇	1	4	yes	complemented
340	#479	C₂²×C₇	1	4	yes	complemented
341	#478	C₂²×C₇	1	4	yes	complemented
342	#477	C₂²×C₇	1	4	yes	complemented
343	#474	C₂²×C₇	1	4	yes	complemented
344	#468	C₂²×C₇	1	4	yes	complemented
345	#467	C₂²×C₇	1	1	yes	characteristic
346	#467	C₂²×C₇	1	1	yes	characteristic
347	#467	C₂²×C₇	1	2	yes	complemented
348	#466	C₂²×C₇	1	1	yes	characteristic
349	#466	C₂²×C₇	1	1	yes	characteristic
350	#466	C₂²×C₇	1	2	yes	complemented
351	#465	C₂²×C₇	1	2	yes	—
352	#465	C₂²×C₇	1	2	yes	—
353	#440	C₂²×C₇	1	4	yes	complemented
354	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
355	C₄×D₈	C₂²×C₇	1	2	yes	complemented
356	#435	C₂²×C₇	1	2	yes	—
357	#435	C₂²×C₇	1	2	yes	—
358	C₈×D₄	C₂²×C₇	1	2	yes	—
359	C₈×D₄	C₂²×C₇	1	2	yes	—
360	#428	C₂²×C₇	1	2	yes	—
361	#428	C₂²×C₇	1	2	yes	—
362	#428	C₂²×C₇	1	4	yes	complemented
363	#427	C₂²×C₇	1	1	yes	characteristic
364	#427	C₂²×C₇	1	2	yes	complemented
365	C₂×#107	C₂²×C₇	1	2	yes	—
366	C₂×#107	C₂²×C₇	1	2	yes	—
367	C₂×#107	C₂²×C₇	1	2	yes	—
368	C₂×#107	C₂²×C₇	1	2	yes	—
369	C₂×#107	C₂²×C₇	1	2	yes	—
370	C₂×#107	C₂²×C₇	1	1	yes	characteristic
371	C₂×#107	C₂²×C₇	1	1	yes	characteristic
372	C₂×#107	C₂²×C₇	1	2	yes	complemented
373	#424	C₂²×C₇	1	1	yes	characteristic
374	#417	C₂²×C₇	1	2	yes	—
375	#417	C₂²×C₇	1	2	yes	—
376	#416	C₂²×C₇	1	2	yes	—
377	#408	C₂²×C₇	1	1	yes	characteristic
378	#407	C₂²×C₇	1	1	yes	characteristic
379	#405	C₂²×C₇	1	1	yes	characteristic
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	2	2	no	—
382	C₂³×C₇	—	2	2	no	—
383	C₂³×C₇	—	2	2	no	—
384	C₂³×C₇	C₂²×D₄	1	2	yes	—
385	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
388	C₇×Q₈	—	2	2	no	—
389	C₇×Q₈	—	2	2	no	—
390	C₇×Q₈	—	2	2	no	—
391	C₇×Q₈	—	8	4	no	—
392	C₇×D₄	—	2	4	no	—
393	C₇×D₄	—	2	4	no	—
394	C₇×D₄	—	2	4	no	—
395	C₇×D₄	—	2	2	no	—
396	C₇×D₄	—	2	2	no	—
397	C₇×D₄	—	2	2	no	—
398	C₇×D₄	—	4	4	no	—
399	C₇×D₄	—	4	4	no	—
400	C₇×D₄	—	4	4	no	—
401	C₇×D₄	—	8	4	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	1	no	—
406	C₂×C₄×C₇	—	2	1	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	1	no	—
409	C₂×C₄×C₇	—	2	1	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	4	8	no	—
417	C₂×C₄×C₇	—	4	4	no	—
418	C₂×C₄×C₇	—	8	4	no	—
419	C₂×C₄×C₇	—	8	2	no	—
420	C₂×C₄×C₇	—	8	4	no	—
421	C₂×C₄×C₇	—	8	2	no	—
422	C₂×C₄×C₇	—	8	4	no	—
423	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
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	C₂×#41	1	2	yes	—
430	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
431	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
432	C₇×C₈	—	2	1	no	—
433	C₇×C₈	—	2	1	no	—
434	C₇×C₈	—	2	2	no	—
435	C₇×C₈	—	2	2	no	—
436	C₇×C₈	C₂×#41	1	2	yes	—
437	C₇×C₈	C₂×#41	1	2	yes	—
438	C₂×#41	—	2	4	no	—
439	C₂×#41	C₂³×C₇	1	2	yes	—
440	C₂×#41	C₂³×C₇	1	1	yes	characteristic
441	C₂³×C₄	—	2	2	no	—
442	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
443	#135	—	2	4	no	—
444	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
445	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
446	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
447	#131	—	2	4	no	—
448	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
449	C₂×M₁₆	C₂³×C₇	1	2	yes	—
450	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
451	C₂²×C₈	—	2	4	no	—
452	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₇	1	2	yes	—
458	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
459	C₄⋊Q₈	—	2	2	no	—
460	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
461	#126	—	2	4	no	—
462	#126	—	2	4	no	—
463	#125	—	2	4	no	—
464	#125	—	2	4	no	—
465	#125	—	2	2	no	—
466	#125	C₂³×C₇	1	4	yes	—
467	#123	—	2	4	no	—
468	#123	—	2	2	no	—
469	#123	—	2	4	no	—
470	#123	—	2	4	no	—
471	#123	—	2	4	no	—
472	#123	C₇×D₄	1	2	yes	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	4	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
479	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
480	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
481	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
482	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
483	#121	—	2	4	no	—
484	#121	—	2	4	no	—
485	#121	—	2	2	no	—
486	#121	C₇×D₄	1	1	yes	characteristic
487	#121	C₇×D₄	1	1	yes	characteristic
488	#121	C₂³×C₇	1	2	yes	—
489	#121	C₂³×C₇	1	2	yes	—
490	#121	C₂³×C₇	1	4	yes	—
491	#120	—	2	2	no	—
492	#120	C₇×D₄	1	2	yes	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	C₂³×C₇	1	4	yes	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	C₂³×C₇	1	4	yes	—
503	C₄×D₄	C₂³×C₇	1	2	yes	—
504	C₄×D₄	C₂³×C₇	1	2	yes	—
505	#117	—	2	2	no	—
506	#117	—	2	4	no	—
507	#117	C₂³×C₇	1	2	yes	—
508	#117	C₂³×C₇	1	4	yes	—
509	#117	C₂³×C₇	1	1	yes	characteristic
510	C₂×C₄⋊C₄	—	2	2	no	—
511	C₂×C₄⋊C₄	—	2	2	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
519	#107	C₂³×C₇	1	2	yes	—
520	#107	C₂³×C₇	1	2	yes	—
521	#107	C₂³×C₇	1	2	yes	—
522	#107	C₂³×C₇	1	2	yes	—
523	#107	C₂³×C₇	1	4	yes	—
524	#107	C₂³×C₇	1	4	yes	—
525	#107	C₂³×C₇	1	1	yes	characteristic
526	#107	C₂³×C₇	1	4	yes	—
527	#107	C₂³×C₇	1	1	yes	characteristic
528	#107	C₂³×C₇	1	4	yes	—
529	#106	C₂³×C₇	1	2	yes	—
530	#106	C₂³×C₇	1	4	yes	—
531	#106	C₂³×C₇	1	4	yes	—
532	C₄⋊C₈	C₂³×C₇	1	2	yes	—
533	C₄⋊C₈	C₂³×C₇	1	2	yes	—
534	#103	C₂³×C₇	1	2	yes	—
535	#103	C₂³×C₇	1	2	yes	—
536	#103	C₂³×C₇	1	4	yes	—
537	#103	C₂³×C₇	1	4	yes	—
538	#102	C₂³×C₇	1	2	yes	—
539	#102	C₂³×C₇	1	2	yes	—
540	#102	C₂³×C₇	1	4	yes	—
541	#102	C₂³×C₇	1	4	yes	—
542	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
544	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
545	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
546	#97	C₂³×C₇	1	2	yes	—
547	C₄×C₈	C₂³×C₇	1	2	yes	—
548	C₂²×C₇	—	2	8	no	—
549	C₂²×C₇	—	2	1	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	1	no	—
555	C₂²×C₇	—	2	2	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	2	2	no	—
558	C₂²×C₇	—	4	2	no	—
559	C₂²×C₇	—	4	2	no	—
560	C₂²×C₇	—	4	2	no	—
561	C₂²×C₇	#547	1	2	yes	—
562	C₂²×C₇	#576	1	2	yes	—
563	C₂²×C₇	#578	1	2	yes	—
564	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₇	—	2	1	no	—
566	C₄×C₇	—	2	1	no	—
567	C₄×C₇	—	2	2	no	—
568	C₄×C₇	—	2	2	no	—
569	C₄×C₇	—	2	2	no	—
570	C₄×C₇	—	4	2	no	—
571	C₄×C₇	—	4	4	no	—
572	C₄×C₇	—	4	4	no	—
573	C₄×C₇	—	4	2	no	—
574	C₄×C₇	—	4	2	no	—
575	C₄×C₇	#547	1	2	yes	—
576	C₄×C₇	C₂²×#41	1	1	yes	characteristic
577	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
578	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
579	#41	—	2	2	no	—
580	#41	—	2	2	no	—
581	#41	—	2	4	no	—
582	#41	—	2	4	no	—
583	#41	—	8	8	no	—
584	C₂×Q₈	—	2	4	no	—
585	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
586	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
592	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
593	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
594	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
595	C₂×D₄	C₂⁴×C₇	1	2	yes	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	8	4	no	—
606	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
607	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
608	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
613	Q₁₆	—	2	2	no	—
614	SD₁₆	—	2	4	no	—
615	D₈	—	2	2	no	—
616	M₁₆	—	2	2	no	—
617	M₁₆	—	2	2	no	—
618	M₁₆	—	2	4	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	4	no	—
625	C₂×C₈	C₇×#41	1	4	yes	complemented
626	C₂×C₈	C₂⁴×C₇	1	2	yes	—
627	C₂×C₈	C₂⁴×C₇	1	2	yes	—
628	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
645	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
646	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
647	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
649	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
651	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	2	no	—
669	C₄²	C₂⁴×C₇	1	2	yes	—
670	C₂×C₇	—	2	2	no	—
671	C₂×C₇	—	2	2	no	—
672	C₂×C₇	—	2	2	no	—
673	C₂×C₇	—	4	2	no	—
674	C₂×C₇	—	8	2	no	—
675	C₂×C₇	C₂×#547	1	1	yes	characteristic
676	C₂×C₇	C₂×#576	1	1	yes	characteristic
677	C₂×C₇	C₂×#578	1	1	yes	characteristic
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	C₂²×C₇×D₄	1	2	yes	—
683	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
684	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
685	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	8	4	no	—
690	D₄	—	2	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	8	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
722	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
723	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
724	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
725	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂×C₇×#41	1	2	yes	—
728	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
729	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
730	C₈	—	2	1	no	—
731	C₈	—	2	1	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	2	no	—
734	C₈	C₂×C₇×#41	1	2	yes	—
735	C₈	C₂×C₇×#41	1	2	yes	—
736	C₇	#61258	1	1	yes	characteristic, direct product factor, Sylow
737	C₂²	—	2	8	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
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	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₇×#547	1	2	yes	—
751	C₂²	C₇×#576	1	2	yes	—
752	C₂²	C₇×#578	1	2	yes	—
753	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₇×#547	1	2	yes	—
765	C₄	C₂²×C₇×#41	1	1	yes	characteristic
766	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
767	C₂	—	2	2	no	—
768	C₂	—	2	2	no	—
769	C₂	—	2	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₇×#547	1	1	yes	characteristic
773	C₂	C₂×C₇×#576	1	1	yes	characteristic
774	C₂	C₂×C₇×#578	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×#3492	C₂	semidirect
2. C₇×#3346	C₂	semidirect
3. C₇×#3343	C₂	semidirect
4. C₇×#3339	C₂	semidirect
5. C₇×#3338	C₂	semidirect
6. C₇×#3336	C₂	semidirect
7. C₇×#3334	C₂	semidirect
8. C₇×#3164	C₂	semidirect
9. C₇×#3098	C₂	semidirect
10. C₇×#3092	C₂	semidirect
11. C₇×#3083	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. C₂²×C₇×#107	C₂	semidirect
38. C₇×#501	C₂²	semidirect
39. C₇×#500	C₂²	semidirect
40. C₇×#499	C₂²	semidirect
41. C₇×#485	C₂²	semidirect
43. C₇×#484	C₂²	semidirect
45. C₇×#482	C₂²	semidirect
48. C₇×#480	C₂²	semidirect
49. C₇×#479	C₂²	semidirect
50. C₇×#478	C₂²	semidirect
51. C₇×#477	C₂²	semidirect
52. C₇×#474	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
73. C₇×#427	C₂²	semidirect
81. C₂×C₇×#107	C₂²	semidirect
89. #61258	C₇	direct (N × H)
200. #3492	C₂×C₇	semidirect
201. #3346	C₂×C₇	semidirect
202. #3343	C₂×C₇	semidirect
203. #3339	C₂×C₇	semidirect
204. #3338	C₂×C₇	semidirect
205. #3336	C₂×C₇	semidirect
206. #3334	C₂×C₇	semidirect
207. #3164	C₂×C₇	semidirect
208. #3098	C₂×C₇	semidirect
209. #3092	C₂×C₇	semidirect
210. #3083	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. C₂²×#107	C₂×C₇	semidirect
264. C₂×C₇×C₈	#41	semidirect
329. #501	C₂²×C₇	semidirect
330. #500	C₂²×C₇	semidirect
331. #499	C₂²×C₇	semidirect
332. #485	C₂²×C₇	semidirect
334. #484	C₂²×C₇	semidirect
336. #482	C₂²×C₇	semidirect
339. #480	C₂²×C₇	semidirect
340. #479	C₂²×C₇	semidirect
341. #478	C₂²×C₇	semidirect
342. #477	C₂²×C₇	semidirect
343. #474	C₂²×C₇	semidirect
344. #468	C₂²×C₇	semidirect
347. #467	C₂²×C₇	semidirect
350. #466	C₂²×C₇	semidirect
353. #440	C₂²×C₇	semidirect
354. C₄×Q₁₆	C₂²×C₇	semidirect
355. C₄×D₈	C₂²×C₇	semidirect
362. #428	C₂²×C₇	semidirect
364. #427	C₂²×C₇	semidirect
372. C₂×#107	C₂²×C₇	semidirect
625. C₂×C₈	C₇×#41	semidirect
736. C₇	#61258	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×#3492	2
C₇×#3346	2
C₇×#3343	2
C₇×#3339	2
C₇×#3338	2
C₇×#3336	2
C₇×#3334	2
C₇×#3164	2
C₇×#3098	2
C₇×#3092	2
C₇×#3083	2
C₇×#3061	2
C₇×#3050	2
C₇×#2951	2
C₇×#2929	2
C₇×#2913	2
C₂²×C₇×#107	2
#61258	7

Subgroups — C7×#61258 #13238474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61258 #13238474