Subgroups — C₇×#61219 #13238435

Order 1792.

2102 conjugacy classes of subgroups.

The subgroup lattice has 806 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×#3496	C₂	1	1	yes	maximal, characteristic
3	C₇×#3315	C₂	1	4	yes	maximal, complemented
4	C₇×#3314	C₂	1	4	yes	maximal, complemented
5	C₇×#3311	C₂	1	4	yes	maximal, complemented
6	C₇×#3310	C₂	1	4	yes	maximal, complemented
7	C₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3098	C₂	1	2	yes	maximal, complemented
9	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3063	C₂	1	2	yes	maximal, complemented
11	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3009	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2897	C₂	1	2	yes	maximal, complemented
16	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂×C₇×#137	C₂²	1	2	yes	complemented
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	2	yes	complemented
20	C₇×#559	—	2	1	no	—
21	C₇×#557	—	2	1	no	—
22	C₇×#556	—	2	2	no	—
23	C₇×#556	C₂²	1	2	yes	complemented
24	C₇×#554	C₂²	1	2	yes	complemented
25	C₇×#552	C₂²	1	4	yes	complemented
26	C₇×#547	—	2	1	no	—
27	C₇×#547	C₂²	1	2	yes	—
28	C₇×#546	—	2	2	no	—
29	C₇×#546	C₂²	1	4	yes	—
30	C₇×D₄²	—	2	1	no	—
31	C₇×D₄²	C₂²	1	2	yes	—
32	C₇×#539	—	2	2	no	—
33	C₇×#537	C₂²	1	2	yes	—
34	C₇×#536	C₂²	1	2	yes	complemented
35	C₇×#534	—	2	2	no	—
36	C₇×#533	C₂²	1	1	yes	characteristic, complemented
37	C₇×#532	C₂²	1	1	yes	characteristic
38	C₇×#532	C₂²	1	1	yes	characteristic
39	C₇×#529	—	2	2	no	—
40	C₂×C₇×#121	—	2	2	no	—
41	C₇×#520	C₂²	1	2	yes	complemented
42	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₇×#491	C₂²	1	2	yes	complemented
45	C₇×#490	C₂²	1	2	yes	complemented
46	C₇×#489	C₂²	1	2	yes	complemented
47	C₇×#489	C₂²	1	2	yes	complemented
48	C₇×#485	C₂²	1	4	yes	complemented
49	C₇×#484	C₂²	1	4	yes	complemented
50	C₇×#482	C₂²	1	4	yes	complemented
51	C₇×#480	C₂²	1	4	yes	complemented
52	C₇×#478	C₂²	1	4	yes	complemented
53	C₇×#476	C₂²	1	2	yes	complemented
54	C₇×#474	C₂²	1	2	yes	complemented
55	C₇×#470	C₂²	1	4	yes	complemented
56	C₇×#468	C₂²	1	4	yes	complemented
57	C₇×#467	C₂²	1	4	yes	complemented
58	C₇×#465	C₂²	1	4	yes	complemented
59	C₇×#464	C₂²	1	4	yes	complemented
60	C₇×#462	C₂²	1	2	yes	complemented
61	C₇×#460	C₂²	1	2	yes	complemented
62	C₇×#452	C₂²	1	4	yes	complemented
63	C₇×#452	C₂²	1	4	yes	complemented
64	C₇×#450	C₂²	1	4	yes	complemented
65	C₇×#450	C₂²	1	4	yes	complemented
66	C₇×#440	C₂²	1	4	yes	complemented
67	C₇×#440	C₂²	1	4	yes	complemented
68	C₇×#435	C₂²	1	4	yes	complemented
69	C₇×#435	C₂²	1	4	yes	complemented
70	C₇×#428	C₂²	1	2	yes	complemented
71	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
72	C₇×#423	C₂²	1	1	yes	characteristic, complemented
73	C₇×#418	C₂²	1	2	yes	—
74	C₇×#418	C₂²	1	4	yes	complemented
75	C₇×#417	C₂²	1	2	yes	complemented
76	C₇×#417	C₂²	1	4	yes	complemented
77	C₇×#416	C₂²	1	2	yes	complemented
78	C₇×#416	C₂²	1	4	yes	complemented
79	C₇×#416	C₂²	1	2	yes	complemented
80	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₇×#102	C₂²	1	1	yes	characteristic
82	C₂×C₇×#102	C₂²	1	4	yes	complemented
83	C₇×#408	C₂²	1	2	yes	complemented
84	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
85	#61219	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₇×H(5,𝔽₂)	—	2	8	no	—
87	C₇×H(5,𝔽₂)	—	4	4	no	—
88	C₂×C₇×#41	—	2	2	no	—
89	C₂×C₇×#41	C₂³	1	2	yes	—
90	C₂×C₇×#41	C₂³	1	4	yes	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
93	C₂²×C₇×D₄	—	2	4	no	—
94	C₂²×C₇×D₄	—	2	2	no	—
95	C₂²×C₇×D₄	—	2	2	no	—
96	C₂²×C₇×D₄	C₂³	1	4	yes	—
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	—	2	1	no	—
99	C₇×#137	—	4	4	no	—
100	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₇×SD₁₆	—	2	4	no	—
102	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
104	C₇×#131	—	4	4	no	—
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	4	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	4	yes	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₇×#127	D₄	1	1	yes	characteristic
116	C₇×#127	C₂³	1	1	yes	characteristic
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×#124	—	2	2	no	—
123	C₇×#124	—	2	2	no	—
124	C₇×#124	D₄	1	2	yes	—
125	C₇×#124	C₂³	1	2	yes	—
126	C₇×#123	—	2	4	no	—
127	C₇×#123	—	2	4	no	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×C₂²⋊Q₈	—	2	2	no	—
131	C₇×C₂²⋊Q₈	—	2	1	no	—
132	C₇×C₂²⋊Q₈	—	2	1	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₇×#121	—	2	4	no	—
138	C₇×#121	—	2	2	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	1	no	—
141	C₇×#121	—	2	1	no	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	4	no	—
144	C₇×#121	D₄	1	2	yes	—
145	C₇×#121	D₄	1	2	yes	—
146	C₇×#121	C₂³	1	4	yes	—
147	C₇×#120	—	2	4	no	—
148	C₇×#120	—	2	4	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	2	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	C₂³	1	2	yes	—
156	C₄×C₇×Q₈	C₂³	1	2	yes	—
157	C₄×C₇×D₄	—	2	4	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	—	2	1	no	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	2	yes	—
166	C₄×C₇×D₄	C₂³	1	2	yes	—
167	C₄×C₇×D₄	C₂³	1	2	yes	—
168	C₇×#117	—	2	4	no	—
169	C₇×#117	C₂³	1	4	yes	—
170	C₇×#117	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	—	2	1	no	—
172	C₂×C₇×C₄⋊C₄	—	2	2	no	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
178	C₂×C₄²×C₇	—	2	1	no	—
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₇×#107	C₂³	1	4	yes	—
181	C₇×#107	C₂³	1	4	yes	—
182	C₇×#106	C₂³	1	4	yes	—
183	C₇×C₄⋊C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊C₈	C₂³	1	2	yes	—
185	C₇×#103	C₂³	1	2	yes	—
186	C₇×#103	C₂³	1	4	yes	—
187	C₇×#103	C₂³	1	2	yes	—
188	C₇×#103	C₂³	1	2	yes	—
189	C₇×#103	C₂³	1	4	yes	—
190	C₇×#103	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×#102	C₂³	1	2	yes	—
195	C₇×#102	C₂³	1	4	yes	—
196	C₇×#102	C₂³	1	2	yes	—
197	C₇×#102	C₂³	1	2	yes	—
198	C₇×#102	C₂³	1	4	yes	—
199	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
201	C₇×#97	C₂³	1	2	yes	—
202	C₇×#97	C₂³	1	2	yes	—
203	#3507	C₂×C₇	1	1	yes	characteristic, complemented
204	#3496	C₂×C₇	1	1	yes	characteristic
205	#3315	C₂×C₇	1	4	yes	complemented
206	#3314	C₂×C₇	1	4	yes	complemented
207	#3311	C₂×C₇	1	4	yes	complemented
208	#3310	C₂×C₇	1	4	yes	complemented
209	#3135	C₂×C₇	1	1	yes	characteristic, complemented
210	#3098	C₂×C₇	1	2	yes	complemented
211	#3077	C₂×C₇	1	1	yes	characteristic, complemented
212	#3063	C₂×C₇	1	2	yes	complemented
213	#3037	C₂×C₇	1	1	yes	characteristic, complemented
214	#3009	C₂×C₇	1	2	yes	complemented
215	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
216	#2932	C₂×C₇	1	1	yes	characteristic, complemented
217	#2897	C₂×C₇	1	2	yes	complemented
218	C₂⁴×C₇	—	2	1	no	—
219	C₂⁴×C₇	—	2	4	no	—
220	C₇×#41	—	2	4	no	—
221	C₇×#41	—	2	4	no	—
222	C₇×#41	—	2	8	no	—
223	C₇×#41	—	2	4	no	—
224	C₇×#41	—	2	4	no	—
225	C₇×#41	—	4	4	no	—
226	C₇×#41	—	4	8	no	—
227	C₂×C₇×Q₈	—	2	1	no	—
228	C₂×C₇×Q₈	—	2	1	no	—
229	C₂×C₇×Q₈	—	2	1	no	—
230	C₂×C₇×Q₈	—	2	2	no	—
231	C₂×C₇×Q₈	—	2	2	no	—
232	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
233	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
234	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
235	C₂×C₇×D₄	—	2	8	no	—
236	C₂×C₇×D₄	—	2	4	no	—
237	C₂×C₇×D₄	—	2	2	no	—
238	C₂×C₇×D₄	—	2	4	no	—
239	C₂×C₇×D₄	—	2	1	no	—
240	C₂×C₇×D₄	—	2	1	no	—
241	C₂×C₇×D₄	—	2	4	no	—
242	C₂×C₇×D₄	—	2	1	no	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	4	4	no	—
245	C₂×C₇×D₄	—	4	8	no	—
246	C₂×C₇×D₄	—	4	16	no	—
247	C₂×C₇×D₄	—	8	4	no	—
248	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
249	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
250	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
251	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
252	C₂×C₇×D₄	#41	1	4	yes	—
253	C₂×C₇×D₄	C₂⁴	1	2	yes	—
254	C₂×C₇×D₄	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	4	no	—
259	C₂²×C₄×C₇	—	2	4	no	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	8	2	no	—
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₇×Q₁₆	—	4	4	no	—
269	C₇×SD₁₆	—	2	8	no	—
270	C₇×SD₁₆	—	4	4	no	—
271	C₇×M₁₆	—	2	4	no	—
272	C₇×M₁₆	—	4	4	no	—
273	C₂×C₇×C₈	—	2	2	no	—
274	C₂×C₇×C₈	—	2	2	no	—
275	C₂×C₇×C₈	—	4	4	no	—
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₂×C₇×C₈	C₂⁴	1	4	yes	—
279	C₇×C₄⋊C₄	—	2	1	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	2	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	1	no	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	4	no	—
288	C₇×C₄⋊C₄	—	2	1	no	—
289	C₇×C₄⋊C₄	—	2	1	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	4	no	—
293	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
294	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
295	C₇×C₄⋊C₄	C₂⁴	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×C₂²⋊C₄	—	2	4	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	—	2	2	no	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	2	no	—
309	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
310	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
311	C₄²×C₇	—	2	2	no	—
312	C₄²×C₇	—	2	2	no	—
313	C₄²×C₇	—	2	4	no	—
314	C₄²×C₇	—	2	2	no	—
315	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₇	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇	C₂⁴	1	1	yes	characteristic
319	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
320	C₂×#137	C₂²×C₇	1	2	yes	complemented
321	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
322	C₂×#131	C₂²×C₇	1	2	yes	complemented
323	#559	—	2	1	no	—
324	#557	—	2	1	no	—
325	#556	—	2	2	no	—
326	#556	C₂²×C₇	1	2	yes	complemented
327	#554	C₂²×C₇	1	2	yes	complemented
328	#552	C₂²×C₇	1	4	yes	complemented
329	#547	—	2	1	no	—
330	#547	C₂²×C₇	1	2	yes	—
331	#546	—	2	2	no	—
332	#546	C₂²×C₇	1	4	yes	—
333	D₄²	—	2	1	no	—
334	D₄²	C₂²×C₇	1	2	yes	—
335	#539	—	2	2	no	—
336	#537	C₂²×C₇	1	2	yes	—
337	#536	C₂²×C₇	1	2	yes	complemented
338	#534	—	2	2	no	—
339	#533	C₂²×C₇	1	1	yes	characteristic, complemented
340	#532	C₂²×C₇	1	1	yes	characteristic
341	#532	C₂²×C₇	1	1	yes	characteristic
342	#529	—	2	2	no	—
343	C₂×#121	—	2	2	no	—
344	#520	C₂²×C₇	1	2	yes	complemented
345	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
346	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
347	#491	C₂²×C₇	1	2	yes	complemented
348	#490	C₂²×C₇	1	2	yes	complemented
349	#489	C₂²×C₇	1	2	yes	complemented
350	#489	C₂²×C₇	1	2	yes	complemented
351	#485	C₂²×C₇	1	4	yes	complemented
352	#484	C₂²×C₇	1	4	yes	complemented
353	#482	C₂²×C₇	1	4	yes	complemented
354	#480	C₂²×C₇	1	4	yes	complemented
355	#478	C₂²×C₇	1	4	yes	complemented
356	#476	C₂²×C₇	1	2	yes	complemented
357	#474	C₂²×C₇	1	2	yes	complemented
358	#470	C₂²×C₇	1	4	yes	complemented
359	#468	C₂²×C₇	1	4	yes	complemented
360	#467	C₂²×C₇	1	4	yes	complemented
361	#465	C₂²×C₇	1	4	yes	complemented
362	#464	C₂²×C₇	1	4	yes	complemented
363	#462	C₂²×C₇	1	2	yes	complemented
364	#460	C₂²×C₇	1	2	yes	complemented
365	#452	C₂²×C₇	1	4	yes	complemented
366	#452	C₂²×C₇	1	4	yes	complemented
367	#450	C₂²×C₇	1	4	yes	complemented
368	#450	C₂²×C₇	1	4	yes	complemented
369	#440	C₂²×C₇	1	4	yes	complemented
370	#440	C₂²×C₇	1	4	yes	complemented
371	#435	C₂²×C₇	1	4	yes	complemented
372	#435	C₂²×C₇	1	4	yes	complemented
373	#428	C₂²×C₇	1	2	yes	complemented
374	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
375	#423	C₂²×C₇	1	1	yes	characteristic, complemented
376	#418	C₂²×C₇	1	2	yes	—
377	#418	C₂²×C₇	1	4	yes	complemented
378	#417	C₂²×C₇	1	2	yes	complemented
379	#417	C₂²×C₇	1	4	yes	complemented
380	#416	C₂²×C₇	1	2	yes	complemented
381	#416	C₂²×C₇	1	2	yes	complemented
382	#416	C₂²×C₇	1	4	yes	complemented
383	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
384	C₂×#102	C₂²×C₇	1	1	yes	characteristic
385	C₂×#102	C₂²×C₇	1	4	yes	complemented
386	#408	C₂²×C₇	1	2	yes	complemented
387	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
388	C₂³×C₇	—	2	2	no	—
389	C₂³×C₇	—	2	4	no	—
390	C₂³×C₇	—	2	2	no	—
391	C₂³×C₇	—	4	8	no	—
392	C₂³×C₇	—	8	1	no	—
393	C₂³×C₇	—	8	1	no	—
394	C₂³×C₇	—	8	4	no	—
395	C₂³×C₇	—	8	4	no	—
396	C₂³×C₇	C₂²×D₄	1	4	yes	—
397	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
398	C₇×Q₈	—	2	4	no	—
399	C₇×Q₈	—	2	2	no	—
400	C₇×Q₈	—	2	2	no	—
401	C₇×Q₈	—	2	2	no	—
402	C₇×Q₈	—	2	2	no	—
403	C₇×Q₈	—	4	2	no	—
404	C₇×Q₈	—	4	2	no	—
405	C₇×Q₈	—	8	1	no	—
406	C₇×D₄	—	2	8	no	—
407	C₇×D₄	—	2	4	no	—
408	C₇×D₄	—	2	4	no	—
409	C₇×D₄	—	2	2	no	—
410	C₇×D₄	—	2	2	no	—
411	C₇×D₄	—	2	2	no	—
412	C₇×D₄	—	4	2	no	—
413	C₇×D₄	—	4	2	no	—
414	C₇×D₄	—	4	8	no	—
415	C₇×D₄	—	4	2	no	—
416	C₇×D₄	—	4	8	no	—
417	C₇×D₄	—	4	4	no	—
418	C₇×D₄	—	8	1	no	—
419	C₇×D₄	—	8	4	no	—
420	C₇×D₄	C₂×#41	1	4	yes	—
421	C₂×C₄×C₇	—	2	4	no	—
422	C₂×C₄×C₇	—	2	4	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
430	C₂×C₄×C₇	—	4	1	no	—
431	C₂×C₄×C₇	—	4	8	no	—
432	C₂×C₄×C₇	—	4	4	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	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
446	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
447	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
448	C₇×C₈	—	2	2	no	—
449	C₇×C₈	—	2	2	no	—
450	C₇×C₈	—	2	4	no	—
451	H(5,𝔽₂)	—	2	8	no	—
452	H(5,𝔽₂)	—	4	4	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	C₂³×C₇	1	2	yes	—
455	C₂×#41	C₂³×C₇	1	4	yes	—
456	C₂×#41	C₂³×C₇	1	2	yes	—
457	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
458	C₂²×D₄	—	2	4	no	—
459	C₂²×D₄	—	2	2	no	—
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	C₂³×C₇	1	4	yes	—
462	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
463	C₂³×C₄	—	2	1	no	—
464	#137	—	4	4	no	—
465	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
466	C₂×SD₁₆	—	2	4	no	—
467	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
468	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
469	#131	—	4	4	no	—
470	C₂×M₁₆	C₂³×C₇	1	2	yes	—
471	C₂×M₁₆	C₂³×C₇	1	4	yes	—
472	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₇	1	4	yes	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
480	#127	C₇×D₄	1	1	yes	characteristic
481	#127	C₂³×C₇	1	1	yes	characteristic
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#125	—	2	2	no	—
485	#125	—	2	4	no	—
486	#125	C₂³×C₇	1	2	yes	—
487	#124	—	2	2	no	—
488	#124	—	2	2	no	—
489	#124	C₇×D₄	1	2	yes	—
490	#124	C₂³×C₇	1	2	yes	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	1	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
501	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
502	#121	—	2	4	no	—
503	#121	—	2	2	no	—
504	#121	—	2	2	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	2	no	—
508	#121	—	2	4	no	—
509	#121	C₇×D₄	1	2	yes	—
510	#121	C₇×D₄	1	2	yes	—
511	#121	C₂³×C₇	1	4	yes	—
512	#120	—	2	4	no	—
513	#120	—	2	4	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	C₂³×C₇	1	2	yes	—
521	C₄×Q₈	C₂³×C₇	1	2	yes	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	C₂³×C₇	1	2	yes	—
530	C₄×D₄	C₂³×C₇	1	2	yes	—
531	C₄×D₄	C₂³×C₇	1	2	yes	—
532	C₄×D₄	C₂³×C₇	1	2	yes	—
533	#117	—	2	4	no	—
534	#117	C₂³×C₇	1	2	yes	—
535	#117	C₂³×C₇	1	4	yes	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
545	#107	C₂³×C₇	1	4	yes	—
546	#107	C₂³×C₇	1	4	yes	—
547	#106	C₂³×C₇	1	4	yes	—
548	C₄⋊C₈	C₂³×C₇	1	2	yes	—
549	C₄⋊C₈	C₂³×C₇	1	2	yes	—
550	#103	C₂³×C₇	1	4	yes	—
551	#103	C₂³×C₇	1	2	yes	—
552	#103	C₂³×C₇	1	4	yes	—
553	#103	C₂³×C₇	1	2	yes	—
554	#103	C₂³×C₇	1	2	yes	—
555	#103	C₂³×C₇	1	2	yes	—
556	#102	C₂³×C₇	1	4	yes	—
557	#102	C₂³×C₇	1	2	yes	—
558	#102	C₂³×C₇	1	4	yes	—
559	#102	C₂³×C₇	1	4	yes	—
560	#102	C₂³×C₇	1	4	yes	—
561	#102	C₂³×C₇	1	2	yes	—
562	#102	C₂³×C₇	1	2	yes	—
563	#102	C₂³×C₇	1	2	yes	—
564	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
565	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
566	#97	C₂³×C₇	1	2	yes	—
567	#97	C₂³×C₇	1	2	yes	—
568	C₂²×C₇	—	2	1	no	—
569	C₂²×C₇	—	2	1	no	—
570	C₂²×C₇	—	2	4	no	—
571	C₂²×C₇	—	2	4	no	—
572	C₂²×C₇	—	2	4	no	—
573	C₂²×C₇	—	2	4	no	—
574	C₂²×C₇	—	4	2	no	—
575	C₂²×C₇	—	4	2	no	—
576	C₂²×C₇	—	4	2	no	—
577	C₂²×C₇	—	4	2	no	—
578	C₂²×C₇	—	4	2	no	—
579	C₂²×C₇	—	8	4	no	—
580	C₂²×C₇	—	16	8	no	—
581	C₂²×C₇	#546	1	2	yes	—
582	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₇	—	2	1	no	—
584	C₄×C₇	—	2	1	no	—
585	C₄×C₇	—	2	1	no	—
586	C₄×C₇	—	2	1	no	—
587	C₄×C₇	—	2	4	no	—
588	C₄×C₇	—	4	2	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	#546	1	2	yes	—
595	C₄×C₇	C₂²×#41	1	1	yes	characteristic
596	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	4	no	—
599	#41	—	2	4	no	—
600	#41	—	2	4	no	—
601	#41	—	2	8	no	—
602	#41	—	2	4	no	—
603	#41	—	2	4	no	—
604	#41	—	4	4	no	—
605	#41	—	4	8	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×Q₈	C₂⁴×C₇	1	2	yes	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	8	no	—
625	C₂×D₄	—	4	16	no	—
626	C₂×D₄	—	8	4	no	—
627	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
628	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
629	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
630	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
631	C₂×D₄	C₇×#41	1	4	yes	—
632	C₂×D₄	C₂⁴×C₇	1	2	yes	—
633	C₂×D₄	C₂⁴×C₇	1	2	yes	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	8	2	no	—
643	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
644	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
647	Q₁₆	—	4	4	no	—
648	SD₁₆	—	2	8	no	—
649	SD₁₆	—	4	4	no	—
650	M₁₆	—	2	4	no	—
651	M₁₆	—	4	4	no	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	4	4	no	—
655	C₂×C₈	C₂⁴×C₇	1	2	yes	—
656	C₂×C₈	C₂⁴×C₇	1	2	yes	—
657	C₂×C₈	C₂⁴×C₇	1	4	yes	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
673	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
689	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	2	no	—
694	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
695	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
696	C₄²	C₂⁴×C₇	1	1	yes	characteristic
697	C₄²	C₂⁴×C₇	1	1	yes	characteristic
698	C₂×C₇	—	2	2	no	—
699	C₂×C₇	—	4	4	no	—
700	C₂×C₇	—	4	4	no	—
701	C₂×C₇	—	8	2	no	—
702	C₂×C₇	C₂×#546	1	1	yes	characteristic
703	C₂×C₇	#3585	1	1	yes	characteristic
704	C₂×C₇	#3586	1	1	yes	characteristic
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	8	1	no	—
710	C₂³	—	8	1	no	—
711	C₂³	—	8	4	no	—
712	C₂³	—	8	4	no	—
713	C₂³	C₂²×C₇×D₄	1	4	yes	—
714	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
715	Q₈	—	2	4	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	8	1	no	—
723	D₄	—	2	8	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	8	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	1	no	—
736	D₄	—	8	4	no	—
737	D₄	C₂×C₇×#41	1	4	yes	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	8	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	—	8	4	no	—
755	C₂×C₄	—	8	1	no	—
756	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
757	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
758	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
759	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
760	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
762	C₂×C₄	C₂×C₇×#41	1	2	yes	—
763	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
764	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	2	4	no	—
768	C₇	#61219	1	1	yes	characteristic, direct product factor, Sylow
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	8	4	no	—
781	C₂²	—	16	8	no	—
782	C₂²	C₇×#546	1	2	yes	—
783	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	4	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	C₇×#546	1	2	yes	—
796	C₄	C₂²×C₇×#41	1	1	yes	characteristic
797	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂	—	2	2	no	—
799	C₂	—	4	4	no	—
800	C₂	—	4	4	no	—
801	C₂	—	8	2	no	—
802	C₂	C₂×C₇×#546	1	1	yes	characteristic
803	C₂	C₇×#3585	1	1	yes	characteristic
804	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3496	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×#3315	C₂	semidirect
4. C₇×#3314	C₂	semidirect
5. C₇×#3311	C₂	semidirect
6. C₇×#3310	C₂	semidirect
7. C₇×#3135	C₂	semidirect
8. C₇×#3098	C₂	semidirect
9. C₇×#3077	C₂	semidirect
10. C₇×#3063	C₂	semidirect
11. C₇×#3037	C₂	semidirect
12. C₇×#3009	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₇×#2932	C₂	semidirect
15. C₇×#2897	C₂	semidirect
17. C₂×C₇×#137	C₂²	semidirect
19. C₂×C₇×#131	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#554	C₂²	semidirect
25. C₇×#552	C₂²	semidirect
34. C₇×#536	C₂²	semidirect
36. C₇×#533	C₂²	semidirect
41. C₇×#520	C₂²	semidirect
42. C₂×C₄×C₇×Q₈	C₂²	semidirect
44. C₇×#491	C₂²	semidirect
45. C₇×#490	C₂²	semidirect
46. C₇×#489	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#485	C₂²	semidirect
49. C₇×#484	C₂²	semidirect
50. C₇×#482	C₂²	semidirect
51. C₇×#480	C₂²	semidirect
52. C₇×#478	C₂²	semidirect
53. C₇×#476	C₂²	semidirect
54. C₇×#474	C₂²	semidirect
55. C₇×#470	C₂²	semidirect
56. C₇×#468	C₂²	semidirect
57. C₇×#467	C₂²	semidirect
58. C₇×#465	C₂²	semidirect
59. C₇×#464	C₂²	semidirect
60. C₇×#462	C₂²	semidirect
61. C₇×#460	C₂²	semidirect
62. C₇×#452	C₂²	semidirect
63. C₇×#452	C₂²	semidirect
64. C₇×#450	C₂²	semidirect
65. C₇×#450	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₇×#440	C₂²	semidirect
68. C₇×#435	C₂²	semidirect
69. C₇×#435	C₂²	semidirect
70. C₇×#428	C₂²	semidirect
71. C₂×C₇×#107	C₂²	semidirect
72. C₇×#423	C₂²	semidirect
74. C₇×#418	C₂²	semidirect
75. C₇×#417	C₂²	semidirect
76. C₇×#417	C₂²	semidirect
77. C₇×#416	C₂²	semidirect
78. C₇×#416	C₂²	semidirect
79. C₇×#416	C₂²	semidirect
80. C₂×C₇×#103	C₂²	semidirect
82. C₂×C₇×#102	C₂²	semidirect
83. C₇×#408	C₂²	semidirect
84. C₂×C₇×#97	C₂²	semidirect
85. #61219	C₇	direct (N × H)
203. #3507	C₂×C₇	semidirect
205. #3315	C₂×C₇	semidirect
206. #3314	C₂×C₇	semidirect
207. #3311	C₂×C₇	semidirect
208. #3310	C₂×C₇	semidirect
209. #3135	C₂×C₇	semidirect
210. #3098	C₂×C₇	semidirect
211. #3077	C₂×C₇	semidirect
212. #3063	C₂×C₇	semidirect
213. #3037	C₂×C₇	semidirect
214. #3009	C₂×C₇	semidirect
215. C₂×#440	C₂×C₇	semidirect
216. #2932	C₂×C₇	semidirect
217. #2897	C₂×C₇	semidirect
320. C₂×#137	C₂²×C₇	semidirect
322. C₂×#131	C₂²×C₇	semidirect
326. #556	C₂²×C₇	semidirect
327. #554	C₂²×C₇	semidirect
328. #552	C₂²×C₇	semidirect
337. #536	C₂²×C₇	semidirect
339. #533	C₂²×C₇	semidirect
344. #520	C₂²×C₇	semidirect
345. C₂×C₄×Q₈	C₂²×C₇	semidirect
347. #491	C₂²×C₇	semidirect
348. #490	C₂²×C₇	semidirect
349. #489	C₂²×C₇	semidirect
350. #489	C₂²×C₇	semidirect
351. #485	C₂²×C₇	semidirect
352. #484	C₂²×C₇	semidirect
353. #482	C₂²×C₇	semidirect
354. #480	C₂²×C₇	semidirect
355. #478	C₂²×C₇	semidirect
356. #476	C₂²×C₇	semidirect
357. #474	C₂²×C₇	semidirect
358. #470	C₂²×C₇	semidirect
359. #468	C₂²×C₇	semidirect
360. #467	C₂²×C₇	semidirect
361. #465	C₂²×C₇	semidirect
362. #464	C₂²×C₇	semidirect
363. #462	C₂²×C₇	semidirect
364. #460	C₂²×C₇	semidirect
365. #452	C₂²×C₇	semidirect
366. #452	C₂²×C₇	semidirect
367. #450	C₂²×C₇	semidirect
368. #450	C₂²×C₇	semidirect
369. #440	C₂²×C₇	semidirect
370. #440	C₂²×C₇	semidirect
371. #435	C₂²×C₇	semidirect
372. #435	C₂²×C₇	semidirect
373. #428	C₂²×C₇	semidirect
374. C₂×#107	C₂²×C₇	semidirect
375. #423	C₂²×C₇	semidirect
377. #418	C₂²×C₇	semidirect
378. #417	C₂²×C₇	semidirect
379. #417	C₂²×C₇	semidirect
380. #416	C₂²×C₇	semidirect
381. #416	C₂²×C₇	semidirect
382. #416	C₂²×C₇	semidirect
383. C₂×#103	C₂²×C₇	semidirect
385. C₂×#102	C₂²×C₇	semidirect
386. #408	C₂²×C₇	semidirect
387. C₂×#97	C₂²×C₇	semidirect
768. C₇	#61219	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×#3496	2
C₇×#3315	2
C₇×#3314	2
C₇×#3311	2
C₇×#3310	2
C₇×#3135	2
C₇×#3098	2
C₇×#3077	2
C₇×#3063	2
C₇×#3037	2
C₇×#3009	2
C₂×C₇×#440	2
C₇×#2932	2
C₇×#2897	2
#61219	7

Subgroups — C7×#61219 #13238435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61219 #13238435