Subgroups — C₇×#61285 #13238501

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3506	C₂	1	1	yes	maximal, characteristic
3	C₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₇×#3351	C₂	1	4	yes	maximal, complemented
6	C₇×#3340	C₂	1	2	yes	maximal, complemented
7	C₇×#3337	C₂	1	4	yes	maximal, complemented
8	C₇×#3335	C₂	1	2	yes	maximal, complemented
9	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3097	C₂	1	2	yes	maximal, complemented
11	C₇×#3096	C₂	1	2	yes	maximal, complemented
12	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3057	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2912	C₂	1	2	yes	maximal, complemented
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	2	yes	—
20	C₇×#559	—	2	1	no	—
21	C₇×#559	—	2	2	no	—
22	C₇×#557	—	2	1	no	—
23	C₇×#556	—	2	1	no	—
24	C₇×#556	—	2	2	no	—
25	C₇×#556	C₂²	1	2	yes	complemented
26	C₇×#555	C₂²	1	2	yes	—
27	C₇×#554	C₂²	1	2	yes	complemented
28	C₇×#553	C₂²	1	4	yes	—
29	C₇×#552	C₂²	1	4	yes	complemented
30	C₇×#550	—	2	1	no	—
31	C₇×#547	C₂²	1	2	yes	—
32	C₇×#539	—	2	2	no	—
33	C₇×#538	—	2	2	no	—
34	C₇×#536	C₂²	1	2	yes	—
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×#529	—	2	2	no	—
40	C₇×#525	—	2	2	no	—
41	C₇×#520	C₂²	1	2	yes	—
42	C₇×#520	C₂²	1	2	yes	—
43	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₇×#500	C₂²	1	1	yes	characteristic, complemented
46	C₇×#500	C₂²	1	1	yes	characteristic, complemented
47	C₇×#499	C₂²	1	2	yes	complemented
48	C₇×#499	C₂²	1	2	yes	complemented
49	C₇×#498	C₂²	1	1	yes	characteristic, complemented
50	C₇×#498	C₂²	1	1	yes	characteristic, complemented
51	C₇×#485	C₂²	1	4	yes	complemented
52	C₇×#485	C₂²	1	4	yes	complemented
53	C₇×#484	C₂²	1	4	yes	complemented
54	C₇×#483	C₂²	1	4	yes	complemented
55	C₇×#482	C₂²	1	4	yes	—
56	C₇×#482	C₂²	1	4	yes	—
57	C₇×#481	C₂²	1	4	yes	—
58	C₇×#480	C₂²	1	4	yes	—
59	C₇×#479	C₂²	1	4	yes	complemented
60	C₇×#478	C₂²	1	4	yes	—
61	C₇×#477	C₂²	1	2	yes	complemented
62	C₇×#476	C₂²	1	2	yes	—
63	C₇×#475	C₂²	1	2	yes	complemented
64	C₇×#474	C₂²	1	2	yes	—
65	C₇×#468	C₂²	1	4	yes	—
66	C₇×#468	C₂²	1	4	yes	—
67	C₇×#465	C₂²	1	4	yes	—
68	C₇×#465	C₂²	1	4	yes	—
69	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
70	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
71	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
72	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
73	C₇×#436	C₂²	1	2	yes	complemented
74	C₇×#436	C₂²	1	2	yes	complemented
75	C₇×C₈×D₄	C₂²	1	2	yes	complemented
76	C₇×C₈×D₄	C₂²	1	2	yes	complemented
77	C₇×#428	C₂²	1	2	yes	—
78	C₇×#428	C₂²	1	2	yes	—
79	C₇×#428	C₂²	1	4	yes	complemented
80	C₇×#428	C₂²	1	4	yes	complemented
81	C₇×#427	C₂²	1	2	yes	—
82	C₇×#427	C₂²	1	2	yes	—
83	C₇×#427	C₂²	1	4	yes	complemented
84	C₂×C₇×#106	C₂²	1	1	yes	characteristic
85	C₂×C₇×#106	C₂²	1	4	yes	complemented
86	C₇×#423	C₂²	1	1	yes	characteristic
87	C₇×#419	C₂²	1	2	yes	—
88	C₇×#418	C₂²	1	2	yes	—
89	C₂×C₇×#103	C₂²	1	1	yes	characteristic
90	C₂×C₇×#102	C₂²	1	1	yes	characteristic
91	C₇×#408	C₂²	1	2	yes	—
92	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
93	#61285	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	C₂³	1	1	yes	characteristic
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	—	2	1	no	—
99	C₂×C₇×SD₁₆	—	2	4	no	—
100	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
102	C₇×#131	—	2	8	no	—
103	C₂×C₇×M₁₆	C₂³	1	4	yes	—
104	C₂×C₇×M₁₆	C₂³	1	2	yes	—
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	4	yes	—
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₇×#127	—	2	2	no	—
115	C₇×#127	D₄	1	1	yes	characteristic
116	C₇×#126	—	2	4	no	—
117	C₇×#126	—	2	4	no	—
118	C₇×#126	—	2	4	no	—
119	C₇×#125	—	2	2	no	—
120	C₇×#125	—	2	4	no	—
121	C₇×#125	C₂³	1	2	yes	—
122	C₇×#125	C₂³	1	2	yes	—
123	C₇×#124	—	2	2	no	—
124	C₇×#124	—	2	2	no	—
125	C₇×#124	—	2	2	no	—
126	C₇×#124	—	2	4	no	—
127	C₇×#124	D₄	1	2	yes	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×#123	—	2	4	no	—
132	C₇×C₂²⋊Q₈	—	2	1	no	—
133	C₇×C₂²⋊Q₈	—	2	1	no	—
134	C₇×C₂²⋊Q₈	—	2	1	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	2	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	4	no	—
142	C₇×#121	D₄	1	2	yes	—
143	C₇×#121	D₄	1	2	yes	—
144	C₇×#121	C₂³	1	4	yes	—
145	C₇×#121	C₂³	1	4	yes	—
146	C₇×#120	—	2	4	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	C₂³	1	2	yes	—
157	C₄×C₇×Q₈	C₂³	1	2	yes	—
158	C₄×C₇×D₄	—	2	4	no	—
159	C₄×C₇×D₄	—	2	4	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	4	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	—	2	1	no	—
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	2	yes	—
170	C₇×#117	—	2	2	no	—
171	C₇×#117	—	2	4	no	—
172	C₇×#117	C₂³	1	4	yes	—
173	C₇×#117	C₂³	1	4	yes	—
174	C₇×#117	C₂³	1	2	yes	—
175	C₇×#117	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	—	2	1	no	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₄²×C₇	—	2	1	no	—
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₇×#107	C₂³	1	2	yes	—
185	C₇×#107	C₂³	1	2	yes	—
186	C₇×#107	C₂³	1	4	yes	—
187	C₇×#107	C₂³	1	4	yes	—
188	C₇×#107	C₂³	1	2	yes	—
189	C₇×#107	C₂³	1	2	yes	—
190	C₇×#106	C₂³	1	4	yes	—
191	C₇×#106	C₂³	1	4	yes	—
192	C₇×#106	C₂³	1	2	yes	—
193	C₇×#106	C₂³	1	2	yes	—
194	C₇×#106	C₂³	1	2	yes	—
195	C₇×#106	C₂³	1	2	yes	—
196	C₇×#106	C₂³	1	2	yes	—
197	C₇×#106	C₂³	1	2	yes	—
198	C₇×C₄⋊C₈	C₂³	1	2	yes	—
199	C₇×C₄⋊C₈	C₂³	1	2	yes	—
200	C₇×#103	C₂³	1	4	yes	—
201	C₇×#103	C₂³	1	4	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#102	C₂³	1	4	yes	—
205	C₇×#102	C₂³	1	4	yes	—
206	C₇×#102	C₂³	1	2	yes	—
207	C₇×#102	C₂³	1	2	yes	—
208	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
211	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
212	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
213	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
214	#3507	C₂×C₇	1	1	yes	characteristic, complemented
215	#3506	C₂×C₇	1	1	yes	characteristic
216	#3357	C₂×C₇	1	2	yes	complemented
217	#3353	C₂×C₇	1	2	yes	complemented
218	#3351	C₂×C₇	1	4	yes	complemented
219	#3340	C₂×C₇	1	2	yes	complemented
220	#3337	C₂×C₇	1	4	yes	complemented
221	#3335	C₂×C₇	1	2	yes	complemented
222	#3160	C₂×C₇	1	1	yes	characteristic, complemented
223	#3097	C₂×C₇	1	2	yes	complemented
224	#3096	C₂×C₇	1	2	yes	complemented
225	#3078	C₂×C₇	1	1	yes	characteristic, complemented
226	#3077	C₂×C₇	1	1	yes	characteristic, complemented
227	#3057	C₂×C₇	1	2	yes	complemented
228	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
229	#2931	C₂×C₇	1	1	yes	characteristic, complemented
230	#2912	C₂×C₇	1	2	yes	complemented
231	C₂⁴×C₇	—	2	1	no	—
232	C₇×#41	—	2	4	no	—
233	C₇×#41	—	2	4	no	—
234	C₇×#41	—	8	4	no	—
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	1	no	—
239	C₂×C₇×Q₈	—	2	1	no	—
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	2	2	no	—
242	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
243	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
244	C₂×C₇×D₄	—	2	4	no	—
245	C₂×C₇×D₄	—	2	4	no	—
246	C₂×C₇×D₄	—	2	1	no	—
247	C₂×C₇×D₄	—	2	2	no	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
250	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
251	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
252	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
253	C₂×C₇×D₄	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇	—	2	1	no	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	4	no	—
258	C₂²×C₄×C₇	—	2	4	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	8	2	no	—
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₇×SD₁₆	—	2	4	no	—
267	C₇×SD₁₆	—	2	4	no	—
268	C₇×M₁₆	—	2	4	no	—
269	C₇×M₁₆	—	2	8	no	—
270	C₂×C₇×C₈	—	2	2	no	—
271	C₂×C₇×C₈	—	2	8	no	—
272	C₂×C₇×C₈	#41	1	4	yes	complemented
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	C₂⁴	1	4	yes	—
276	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
277	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
278	C₇×C₄⋊C₄	—	2	2	no	—
279	C₇×C₄⋊C₄	—	2	2	no	—
280	C₇×C₄⋊C₄	—	2	1	no	—
281	C₇×C₄⋊C₄	—	2	1	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	1	no	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	1	no	—
291	C₇×C₄⋊C₄	—	2	2	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
295	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	2	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	2	no	—
309	C₇×C₂²⋊C₄	—	2	2	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	4	no	—
312	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
313	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
314	C₄²×C₇	—	2	2	no	—
315	C₄²×C₇	—	2	2	no	—
316	C₄²×C₇	—	2	4	no	—
317	C₄²×C₇	—	2	4	no	—
318	C₄²×C₇	—	2	2	no	—
319	C₄²×C₇	—	2	2	no	—
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	1	yes	characteristic
324	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
325	C₂×#131	C₂²×C₇	1	2	yes	—
326	#559	—	2	1	no	—
327	#559	—	2	2	no	—
328	#557	—	2	1	no	—
329	#556	—	2	1	no	—
330	#556	—	2	2	no	—
331	#556	C₂²×C₇	1	2	yes	complemented
332	#555	C₂²×C₇	1	2	yes	—
333	#554	C₂²×C₇	1	2	yes	complemented
334	#553	C₂²×C₇	1	4	yes	—
335	#552	C₂²×C₇	1	4	yes	complemented
336	#550	—	2	1	no	—
337	#547	C₂²×C₇	1	2	yes	—
338	#539	—	2	2	no	—
339	#538	—	2	2	no	—
340	#536	C₂²×C₇	1	2	yes	—
341	#535	C₂²×C₇	1	2	yes	—
342	#533	C₂²×C₇	1	1	yes	characteristic
343	#533	C₂²×C₇	1	1	yes	characteristic
344	#532	C₂²×C₇	1	1	yes	characteristic
345	#529	—	2	2	no	—
346	#525	—	2	2	no	—
347	#520	C₂²×C₇	1	2	yes	—
348	#520	C₂²×C₇	1	2	yes	—
349	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
351	#500	C₂²×C₇	1	1	yes	characteristic, complemented
352	#500	C₂²×C₇	1	1	yes	characteristic, complemented
353	#499	C₂²×C₇	1	2	yes	complemented
354	#499	C₂²×C₇	1	2	yes	complemented
355	#498	C₂²×C₇	1	1	yes	characteristic, complemented
356	#498	C₂²×C₇	1	1	yes	characteristic, complemented
357	#485	C₂²×C₇	1	4	yes	complemented
358	#485	C₂²×C₇	1	4	yes	complemented
359	#484	C₂²×C₇	1	4	yes	complemented
360	#483	C₂²×C₇	1	4	yes	complemented
361	#482	C₂²×C₇	1	4	yes	—
362	#482	C₂²×C₇	1	4	yes	—
363	#481	C₂²×C₇	1	4	yes	—
364	#480	C₂²×C₇	1	4	yes	—
365	#479	C₂²×C₇	1	4	yes	complemented
366	#478	C₂²×C₇	1	4	yes	—
367	#477	C₂²×C₇	1	2	yes	complemented
368	#476	C₂²×C₇	1	2	yes	—
369	#475	C₂²×C₇	1	2	yes	complemented
370	#474	C₂²×C₇	1	2	yes	—
371	#468	C₂²×C₇	1	4	yes	—
372	#468	C₂²×C₇	1	4	yes	—
373	#465	C₂²×C₇	1	4	yes	—
374	#465	C₂²×C₇	1	4	yes	—
375	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
376	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
377	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
378	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
379	#436	C₂²×C₇	1	2	yes	complemented
380	#436	C₂²×C₇	1	2	yes	complemented
381	C₈×D₄	C₂²×C₇	1	2	yes	complemented
382	C₈×D₄	C₂²×C₇	1	2	yes	complemented
383	#428	C₂²×C₇	1	2	yes	—
384	#428	C₂²×C₇	1	2	yes	—
385	#428	C₂²×C₇	1	4	yes	complemented
386	#428	C₂²×C₇	1	4	yes	complemented
387	#427	C₂²×C₇	1	2	yes	—
388	#427	C₂²×C₇	1	2	yes	—
389	#427	C₂²×C₇	1	4	yes	complemented
390	C₂×#106	C₂²×C₇	1	1	yes	characteristic
391	C₂×#106	C₂²×C₇	1	4	yes	complemented
392	#423	C₂²×C₇	1	1	yes	characteristic
393	#419	C₂²×C₇	1	2	yes	—
394	#418	C₂²×C₇	1	2	yes	—
395	C₂×#103	C₂²×C₇	1	1	yes	characteristic
396	C₂×#102	C₂²×C₇	1	1	yes	characteristic
397	#408	C₂²×C₇	1	2	yes	—
398	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
399	C₂³×C₇	—	2	2	no	—
400	C₂³×C₇	—	4	2	no	—
401	C₂³×C₇	—	8	1	no	—
402	C₂³×C₇	—	8	1	no	—
403	C₂³×C₇	C₂²×D₄	1	4	yes	—
404	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
405	C₇×Q₈	—	2	4	no	—
406	C₇×Q₈	—	2	2	no	—
407	C₇×Q₈	—	2	2	no	—
408	C₇×Q₈	—	4	2	no	—
409	C₇×Q₈	—	4	2	no	—
410	C₇×Q₈	—	4	2	no	—
411	C₇×Q₈	—	8	1	no	—
412	C₇×Q₈	—	8	1	no	—
413	C₇×D₄	—	2	8	no	—
414	C₇×D₄	—	2	4	no	—
415	C₇×D₄	—	2	4	no	—
416	C₇×D₄	—	2	2	no	—
417	C₇×D₄	—	2	2	no	—
418	C₇×D₄	—	4	2	no	—
419	C₇×D₄	—	4	2	no	—
420	C₇×D₄	—	8	4	no	—
421	C₇×D₄	—	8	4	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	4	no	—
424	C₂×C₄×C₇	—	2	4	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	4	1	no	—
433	C₂×C₄×C₇	—	4	2	no	—
434	C₂×C₄×C₇	—	4	4	no	—
435	C₂×C₄×C₇	—	8	2	no	—
436	C₂×C₄×C₇	—	8	1	no	—
437	C₂×C₄×C₇	—	8	4	no	—
438	C₂×C₄×C₇	—	8	1	no	—
439	C₂×C₄×C₇	—	8	4	no	—
440	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
442	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇	C₂×#41	1	2	yes	—
447	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
448	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
449	C₇×C₈	—	2	4	no	—
450	C₇×C₈	—	2	1	no	—
451	C₇×C₈	—	2	1	no	—
452	C₇×C₈	C₂×#41	1	2	yes	—
453	C₇×C₈	C₂×#41	1	2	yes	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	C₂³×C₇	1	2	yes	—
456	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂×SD₁₆	—	2	4	no	—
460	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
461	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
462	#131	—	2	8	no	—
463	C₂×M₁₆	C₂³×C₇	1	2	yes	—
464	C₂×M₁₆	C₂³×C₇	1	4	yes	—
465	C₂²×C₈	C₂³×C₇	1	4	yes	—
466	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
468	C₄⋊Q₈	—	2	2	no	—
469	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
472	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
473	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
474	#127	—	2	2	no	—
475	#127	C₇×D₄	1	1	yes	characteristic
476	#126	—	2	4	no	—
477	#126	—	2	4	no	—
478	#126	—	2	4	no	—
479	#125	—	2	2	no	—
480	#125	—	2	4	no	—
481	#125	C₂³×C₇	1	2	yes	—
482	#125	C₂³×C₇	1	2	yes	—
483	#124	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	—	2	4	no	—
487	#124	C₇×D₄	1	2	yes	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
499	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
500	#121	—	2	2	no	—
501	#121	—	2	4	no	—
502	#121	C₇×D₄	1	2	yes	—
503	#121	C₇×D₄	1	2	yes	—
504	#121	C₂³×C₇	1	4	yes	—
505	#121	C₂³×C₇	1	4	yes	—
506	#120	—	2	4	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	1	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	C₂³×C₇	1	2	yes	—
517	C₄×Q₈	C₂³×C₇	1	2	yes	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	C₂³×C₇	1	2	yes	—
527	C₄×D₄	C₂³×C₇	1	2	yes	—
528	C₄×D₄	C₂³×C₇	1	2	yes	—
529	C₄×D₄	C₂³×C₇	1	2	yes	—
530	#117	—	2	2	no	—
531	#117	—	2	4	no	—
532	#117	C₂³×C₇	1	2	yes	—
533	#117	C₂³×C₇	1	2	yes	—
534	#117	C₂³×C₇	1	4	yes	—
535	#117	C₂³×C₇	1	4	yes	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₄²	—	2	1	no	—
543	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
544	#107	C₂³×C₇	1	2	yes	—
545	#107	C₂³×C₇	1	2	yes	—
546	#107	C₂³×C₇	1	2	yes	—
547	#107	C₂³×C₇	1	2	yes	—
548	#107	C₂³×C₇	1	4	yes	—
549	#107	C₂³×C₇	1	4	yes	—
550	#106	C₂³×C₇	1	2	yes	—
551	#106	C₂³×C₇	1	2	yes	—
552	#106	C₂³×C₇	1	2	yes	—
553	#106	C₂³×C₇	1	4	yes	—
554	#106	C₂³×C₇	1	4	yes	—
555	#106	C₂³×C₇	1	2	yes	—
556	#106	C₂³×C₇	1	2	yes	—
557	#106	C₂³×C₇	1	2	yes	—
558	C₄⋊C₈	C₂³×C₇	1	2	yes	—
559	C₄⋊C₈	C₂³×C₇	1	2	yes	—
560	#103	C₂³×C₇	1	2	yes	—
561	#103	C₂³×C₇	1	2	yes	—
562	#103	C₂³×C₇	1	4	yes	—
563	#103	C₂³×C₇	1	4	yes	—
564	#102	C₂³×C₇	1	2	yes	—
565	#102	C₂³×C₇	1	2	yes	—
566	#102	C₂³×C₇	1	4	yes	—
567	#102	C₂³×C₇	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
570	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
574	C₂²×C₇	—	2	1	no	—
575	C₂²×C₇	—	2	1	no	—
576	C₂²×C₇	—	2	4	no	—
577	C₂²×C₇	—	2	4	no	—
578	C₂²×C₇	—	2	4	no	—
579	C₂²×C₇	—	4	2	no	—
580	C₂²×C₇	—	4	2	no	—
581	C₂²×C₇	—	4	2	no	—
582	C₂²×C₇	—	8	4	no	—
583	C₂²×C₇	#547	1	2	yes	—
584	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₇	—	2	1	no	—
586	C₄×C₇	—	2	1	no	—
587	C₄×C₇	—	2	4	no	—
588	C₄×C₇	—	2	1	no	—
589	C₄×C₇	—	4	2	no	—
590	C₄×C₇	—	4	2	no	—
591	C₄×C₇	—	4	2	no	—
592	C₄×C₇	—	4	2	no	—
593	C₄×C₇	—	4	2	no	—
594	C₄×C₇	—	4	2	no	—
595	C₄×C₇	—	4	2	no	—
596	C₄×C₇	#547	1	2	yes	—
597	C₄×C₇	#577	1	2	yes	—
598	C₄×C₇	C₂²×#41	1	1	yes	characteristic
599	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
600	C₂⁴	—	2	1	no	—
601	#41	—	2	4	no	—
602	#41	—	2	4	no	—
603	#41	—	8	4	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
619	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
620	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
621	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
622	C₂×D₄	C₂⁴×C₇	1	2	yes	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	8	2	no	—
631	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
632	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	2	4	no	—
637	M₁₆	—	2	4	no	—
638	M₁₆	—	2	8	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	2	8	no	—
641	C₂×C₈	C₇×#41	1	4	yes	complemented
642	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
643	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
644	C₂×C₈	C₂⁴×C₇	1	4	yes	—
645	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
646	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
664	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
682	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	2	no	—
689	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
690	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
691	C₄²	C₂⁴×C₇	1	1	yes	characteristic
692	C₄²	C₂⁴×C₇	1	1	yes	characteristic
693	C₂×C₇	—	2	2	no	—
694	C₂×C₇	—	4	4	no	—
695	C₂×C₇	—	8	2	no	—
696	C₂×C₇	C₂×#547	1	1	yes	characteristic
697	C₂×C₇	C₂×#577	1	1	yes	characteristic
698	C₂×C₇	#3584	1	1	yes	characteristic
699	C₂³	—	2	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	—	8	1	no	—
702	C₂³	—	8	1	no	—
703	C₂³	C₂²×C₇×D₄	1	4	yes	—
704	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
705	Q₈	—	2	4	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	8	1	no	—
712	Q₈	—	8	1	no	—
713	D₄	—	2	8	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	4	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	8	4	no	—
721	D₄	—	8	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	8	2	no	—
736	C₂×C₄	—	8	1	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
741	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
742	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
743	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
744	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
745	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
746	C₂×C₄	C₂×C₇×#41	1	2	yes	—
747	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
748	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
749	C₈	—	2	4	no	—
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	C₂×C₇×#41	1	2	yes	—
753	C₈	C₂×C₇×#41	1	2	yes	—
754	C₇	#61285	1	1	yes	characteristic, direct product factor, Sylow
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	8	4	no	—
764	C₂²	C₇×#547	1	2	yes	—
765	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₇×#547	1	2	yes	—
778	C₄	C₇×#577	1	2	yes	—
779	C₄	C₂²×C₇×#41	1	1	yes	characteristic
780	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
781	C₂	—	2	2	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×C₇×#547	1	1	yes	characteristic
785	C₂	C₂×C₇×#577	1	1	yes	characteristic
786	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3507	C₂	semidirect
3. C₇×#3357	C₂	semidirect
4. C₇×#3353	C₂	semidirect
5. C₇×#3351	C₂	semidirect
6. C₇×#3340	C₂	semidirect
7. C₇×#3337	C₂	semidirect
8. C₇×#3335	C₂	semidirect
9. C₇×#3160	C₂	semidirect
10. C₇×#3097	C₂	semidirect
11. C₇×#3096	C₂	semidirect
12. C₇×#3078	C₂	semidirect
13. C₇×#3077	C₂	semidirect
14. C₇×#3057	C₂	semidirect
15. C₂×C₄×C₇×SD₁₆	C₂	semidirect
16. C₇×#2931	C₂	semidirect
17. C₇×#2912	C₂	semidirect
25. C₇×#556	C₂²	semidirect
27. C₇×#554	C₂²	semidirect
29. C₇×#552	C₂²	semidirect
45. C₇×#500	C₂²	semidirect
46. C₇×#500	C₂²	semidirect
47. C₇×#499	C₂²	semidirect
48. C₇×#499	C₂²	semidirect
49. C₇×#498	C₂²	semidirect
50. C₇×#498	C₂²	semidirect
51. C₇×#485	C₂²	semidirect
52. C₇×#485	C₂²	semidirect
53. C₇×#484	C₂²	semidirect
54. C₇×#483	C₂²	semidirect
59. C₇×#479	C₂²	semidirect
61. C₇×#477	C₂²	semidirect
63. C₇×#475	C₂²	semidirect
73. C₇×#436	C₂²	semidirect
74. C₇×#436	C₂²	semidirect
75. C₇×C₈×D₄	C₂²	semidirect
76. C₇×C₈×D₄	C₂²	semidirect
79. C₇×#428	C₂²	semidirect
80. C₇×#428	C₂²	semidirect
83. C₇×#427	C₂²	semidirect
85. C₂×C₇×#106	C₂²	semidirect
93. #61285	C₇	direct (N × H)
214. #3507	C₂×C₇	semidirect
216. #3357	C₂×C₇	semidirect
217. #3353	C₂×C₇	semidirect
218. #3351	C₂×C₇	semidirect
219. #3340	C₂×C₇	semidirect
220. #3337	C₂×C₇	semidirect
221. #3335	C₂×C₇	semidirect
222. #3160	C₂×C₇	semidirect
223. #3097	C₂×C₇	semidirect
224. #3096	C₂×C₇	semidirect
225. #3078	C₂×C₇	semidirect
226. #3077	C₂×C₇	semidirect
227. #3057	C₂×C₇	semidirect
228. C₂×C₄×SD₁₆	C₂×C₇	semidirect
229. #2931	C₂×C₇	semidirect
230. #2912	C₂×C₇	semidirect
272. C₂×C₇×C₈	#41	semidirect
331. #556	C₂²×C₇	semidirect
333. #554	C₂²×C₇	semidirect
335. #552	C₂²×C₇	semidirect
351. #500	C₂²×C₇	semidirect
352. #500	C₂²×C₇	semidirect
353. #499	C₂²×C₇	semidirect
354. #499	C₂²×C₇	semidirect
355. #498	C₂²×C₇	semidirect
356. #498	C₂²×C₇	semidirect
357. #485	C₂²×C₇	semidirect
358. #485	C₂²×C₇	semidirect
359. #484	C₂²×C₇	semidirect
360. #483	C₂²×C₇	semidirect
365. #479	C₂²×C₇	semidirect
367. #477	C₂²×C₇	semidirect
369. #475	C₂²×C₇	semidirect
379. #436	C₂²×C₇	semidirect
380. #436	C₂²×C₇	semidirect
381. C₈×D₄	C₂²×C₇	semidirect
382. C₈×D₄	C₂²×C₇	semidirect
385. #428	C₂²×C₇	semidirect
386. #428	C₂²×C₇	semidirect
389. #427	C₂²×C₇	semidirect
391. C₂×#106	C₂²×C₇	semidirect
641. C₂×C₈	C₇×#41	semidirect
754. C₇	#61285	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×#3507	2
C₇×#3506	2
C₇×#3357	2
C₇×#3353	2
C₇×#3351	2
C₇×#3340	2
C₇×#3337	2
C₇×#3335	2
C₇×#3160	2
C₇×#3097	2
C₇×#3096	2
C₇×#3078	2
C₇×#3077	2
C₇×#3057	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2931	2
C₇×#2912	2
#61285	7

Subgroups — C7×#61285 #13238501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61285 #13238501