Subgroups — C₇×#61341 #13238557

Order 1792.

1844 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3508	C₂	1	1	yes	maximal, characteristic
2	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3375	C₂	1	2	yes	maximal, complemented
4	C₇×#3371	C₂	1	4	yes	maximal, complemented
5	C₇×#3368	C₂	1	2	yes	maximal, complemented
6	C₇×#3368	C₂	1	4	yes	maximal, complemented
7	C₇×#3365	C₂	1	2	yes	maximal, complemented
8	C₇×#3362	C₂	1	2	yes	maximal, complemented
9	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3081	C₂	1	2	yes	maximal, complemented
12	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3043	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
20	C₇×#559	C₂²	1	2	yes	—
21	C₇×#559	C₂²	1	2	yes	—
22	C₇×Q₈²	—	2	1	no	—
23	C₇×Q₈²	C₂²	1	2	yes	complemented
24	C₇×#557	—	2	1	no	—
25	C₇×#557	—	2	2	no	—
26	C₇×#557	C₂²	1	2	yes	complemented
27	C₇×#557	C₂²	1	4	yes	complemented
28	C₇×#550	C₂²	1	2	yes	—
29	C₇×#550	C₂²	1	2	yes	—
30	C₇×#546	—	2	2	no	—
31	C₇×#546	—	2	2	no	—
32	C₇×#544	—	2	2	no	—
33	C₇×#544	C₂²	1	2	yes	—
34	C₇×#540	—	2	2	no	—
35	C₇×#535	C₂²	1	2	yes	—
36	C₇×#533	—	2	2	no	—
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₇×#532	—	2	1	no	—
40	C₇×#532	—	2	1	no	—
41	C₂×C₇×#127	C₂²	1	1	yes	characteristic
42	C₇×#519	C₂²	1	2	yes	—
43	C₇×#518	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
46	C₇×#490	C₂²	1	4	yes	—
47	C₇×#490	C₂²	1	4	yes	complemented
48	C₇×#489	C₂²	1	4	yes	complemented
49	C₇×#488	C₂²	1	4	yes	complemented
50	C₇×#486	C₂²	1	2	yes	—
51	C₇×#486	C₂²	1	2	yes	—
52	C₇×#486	C₂²	1	4	yes	complemented
53	C₇×#479	C₂²	1	2	yes	complemented
54	C₇×#478	C₂²	1	2	yes	complemented
55	C₇×#478	C₂²	1	4	yes	complemented
56	C₇×#478	C₂²	1	4	yes	complemented
57	C₇×#477	C₂²	1	1	yes	characteristic, complemented
58	C₇×#476	C₂²	1	1	yes	characteristic, complemented
59	C₇×#476	C₂²	1	4	yes	complemented
60	C₇×#475	C₂²	1	1	yes	characteristic, complemented
61	C₇×#474	C₂²	1	1	yes	characteristic, complemented
62	C₇×#474	C₂²	1	4	yes	complemented
63	C₇×#464	C₂²	1	4	yes	complemented
64	C₇×#464	C₂²	1	4	yes	complemented
65	C₇×#460	C₂²	1	2	yes	—
66	C₇×#460	C₂²	1	4	yes	—
67	C₇×#460	C₂²	1	2	yes	—
68	C₇×#460	C₂²	1	4	yes	complemented
69	C₇×#460	C₂²	1	4	yes	complemented
70	C₇×#446	C₂²	1	4	yes	complemented
71	C₇×#446	C₂²	1	2	yes	complemented
72	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
73	C₇×#441	C₂²	1	2	yes	complemented
74	C₇×#440	C₂²	1	2	yes	complemented
75	C₇×#440	C₂²	1	4	yes	complemented
76	C₇×#440	C₂²	1	4	yes	complemented
77	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
78	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
79	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
80	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₇×#427	C₂²	1	2	yes	—
83	C₇×#424	C₂²	1	2	yes	—
84	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₇×#419	C₂²	1	1	yes	characteristic
86	C₇×#418	C₂²	1	2	yes	—
87	C₇×#418	C₂²	1	2	yes	—
88	C₇×#417	C₂²	1	1	yes	characteristic
89	C₇×#416	C₂²	1	2	yes	—
90	C₂×C₇×#102	C₂²	1	2	yes	—
91	C₇×#405	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	#61341	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	—	2	2	no	—
95	C₂×C₇×#41	—	2	2	no	—
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇×D₄	—	2	1	no	—
99	C₂²×C₇×D₄	—	2	1	no	—
100	C₂²×C₇×D₄	C₂³	1	2	yes	—
101	C₇×#137	—	2	4	no	—
102	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₇×SD₁₆	—	2	8	no	—
104	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	2	yes	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	—	2	4	no	—
112	C₇×C₄⋊Q₈	—	2	2	no	—
113	C₇×C₄⋊Q₈	—	2	4	no	—
114	C₇×C₄⋊Q₈	—	2	2	no	—
115	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₇×#127	—	2	1	no	—
121	C₇×#127	—	2	1	no	—
122	C₇×#127	C₂³	1	2	yes	—
123	C₇×#127	C₂³	1	4	yes	—
124	C₇×#127	C₂³	1	2	yes	—
125	C₇×#125	—	2	4	no	—
126	C₇×#125	—	2	4	no	—
127	C₇×#125	—	2	4	no	—
128	C₇×#125	—	2	2	no	—
129	C₇×#125	D₄	1	2	yes	—
130	C₇×#125	C₂³	1	4	yes	—
131	C₇×#125	C₂³	1	2	yes	—
132	C₇×#124	—	2	2	no	—
133	C₇×#124	—	2	2	no	—
134	C₇×#124	C₂³	1	4	yes	—
135	C₇×#123	—	2	4	no	—
136	C₇×#123	—	2	4	no	—
137	C₇×C₂²⋊Q₈	—	2	1	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	2	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	2	no	—
146	C₇×#121	—	2	4	no	—
147	C₇×#121	—	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	2	no	—
152	C₄×C₇×Q₈	—	2	4	no	—
153	C₄×C₇×Q₈	—	2	2	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	—	2	1	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
159	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
160	C₄×C₇×Q₈	C₂³	1	2	yes	—
161	C₄×C₇×Q₈	C₂³	1	2	yes	—
162	C₄×C₇×Q₈	C₂³	1	4	yes	—
163	C₄×C₇×Q₈	C₂³	1	4	yes	—
164	C₄×C₇×Q₈	C₂³	1	2	yes	—
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	1	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	—	2	2	no	—
171	C₄×C₇×D₄	—	2	2	no	—
172	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
173	C₄×C₇×D₄	C₂³	1	4	yes	—
174	C₄×C₇×D₄	C₂³	1	4	yes	—
175	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
176	C₇×#117	—	2	4	no	—
177	C₇×#117	—	2	1	no	—
178	C₇×#117	C₂³	1	1	yes	characteristic
179	C₇×#117	C₂³	1	2	yes	—
180	C₇×#117	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	—	2	1	no	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
184	C₂×C₄²×C₇	—	2	1	no	—
185	C₂×C₄²×C₇	—	2	1	no	—
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₇×#107	C₂³	1	2	yes	—
188	C₇×#107	C₂³	1	2	yes	—
189	C₇×#107	C₂³	1	2	yes	—
190	C₇×#106	C₂³	1	2	yes	—
191	C₇×#106	C₂³	1	2	yes	—
192	C₇×#106	C₂³	1	2	yes	—
193	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₇×C₄⋊C₈	C₂³	1	4	yes	—
195	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
196	C₇×C₄⋊C₈	C₂³	1	4	yes	—
197	C₇×C₄⋊C₈	C₂³	1	2	yes	—
198	C₇×#103	C₂³	1	2	yes	—
199	C₇×#103	C₂³	1	2	yes	—
200	C₇×#103	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#102	C₂³	1	4	yes	—
204	C₇×#102	C₂³	1	4	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	2	yes	—
207	C₇×#102	C₂³	1	4	yes	—
208	C₇×#102	C₂³	1	4	yes	—
209	C₇×#102	C₂³	1	4	yes	—
210	C₇×#102	C₂³	1	4	yes	—
211	C₇×#102	C₂³	1	2	yes	—
212	C₇×#97	C₂³	1	4	yes	—
213	C₇×#97	C₂³	1	2	yes	—
214	C₄×C₇×C₈	C₂³	1	2	yes	—
215	C₄×C₇×C₈	C₂³	1	4	yes	—
216	#3508	C₂×C₇	1	1	yes	characteristic
217	#3502	C₂×C₇	1	1	yes	characteristic, complemented
218	#3375	C₂×C₇	1	2	yes	complemented
219	#3371	C₂×C₇	1	4	yes	complemented
220	#3368	C₂×C₇	1	2	yes	complemented
221	#3368	C₂×C₇	1	4	yes	complemented
222	#3365	C₂×C₇	1	2	yes	complemented
223	#3362	C₂×C₇	1	2	yes	complemented
224	#3138	C₂×C₇	1	1	yes	characteristic, complemented
225	#3136	C₂×C₇	1	2	yes	complemented
226	#3081	C₂×C₇	1	2	yes	complemented
227	#3076	C₂×C₇	1	1	yes	characteristic, complemented
228	#3043	C₂×C₇	1	2	yes	complemented
229	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
230	#2962	C₂×C₇	1	1	yes	characteristic, complemented
231	#2949	C₂×C₇	1	2	yes	complemented
232	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
233	C₂⁴×C₇	—	2	2	no	—
234	C₇×#41	—	2	2	no	—
235	C₇×#41	—	2	2	no	—
236	C₇×#41	—	8	4	no	—
237	C₇×#41	—	8	4	no	—
238	C₂×C₇×Q₈	—	2	1	no	—
239	C₂×C₇×Q₈	—	2	1	no	—
240	C₂×C₇×Q₈	—	2	1	no	—
241	C₂×C₇×Q₈	—	2	4	no	—
242	C₂×C₇×Q₈	—	2	2	no	—
243	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
244	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
245	C₂×C₇×Q₈	#41	1	4	yes	complemented
246	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
247	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
248	C₂×C₇×D₄	—	2	1	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	2	no	—
251	C₂×C₇×D₄	—	2	2	no	—
252	C₂×C₇×D₄	—	2	4	no	—
253	C₂×C₇×D₄	—	2	4	no	—
254	C₂×C₇×D₄	—	2	2	no	—
255	C₂×C₇×D₄	—	2	2	no	—
256	C₂×C₇×D₄	—	2	4	no	—
257	C₂×C₇×D₄	—	2	4	no	—
258	C₂×C₇×D₄	—	8	2	no	—
259	C₂×C₇×D₄	—	8	2	no	—
260	C₂×C₇×D₄	C₂⁴	1	4	yes	—
261	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₇	—	2	1	no	—
263	C₂²×C₄×C₇	—	2	1	no	—
264	C₂²×C₄×C₇	—	2	1	no	—
265	C₂²×C₄×C₇	—	2	1	no	—
266	C₂²×C₄×C₇	—	2	1	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	4	no	—
269	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₇×Q₁₆	—	2	4	no	—
273	C₇×SD₁₆	—	2	8	no	—
274	C₇×SD₁₆	—	2	8	no	—
275	C₇×SD₁₆	—	2	4	no	—
276	C₇×M₁₆	—	2	2	no	—
277	C₇×M₁₆	—	2	2	no	—
278	C₂×C₇×C₈	—	2	4	no	—
279	C₂×C₇×C₈	C₂⁴	1	2	yes	—
280	C₂×C₇×C₈	C₂⁴	1	2	yes	—
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₂×C₇×C₈	C₂⁴	1	2	yes	—
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	—	2	2	no	—
285	C₇×C₄⋊C₄	—	2	1	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	—	2	4	no	—
289	C₇×C₄⋊C₄	—	2	4	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
302	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
308	C₇×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
313	C₇×C₂²⋊C₄	—	2	1	no	—
314	C₇×C₂²⋊C₄	—	2	4	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
317	C₄²×C₇	—	2	1	no	—
318	C₄²×C₇	—	2	1	no	—
319	C₄²×C₇	—	2	1	no	—
320	C₄²×C₇	—	2	2	no	—
321	C₄²×C₇	—	2	2	no	—
322	C₄²×C₇	—	2	4	no	—
323	C₄²×C₇	—	2	4	no	—
324	C₄²×C₇	—	2	2	no	—
325	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂⁴	1	1	yes	characteristic
328	C₄²×C₇	C₂⁴	1	4	yes	—
329	C₄²×C₇	C₂⁴	1	1	yes	characteristic
330	C₂×#137	C₂²×C₇	1	1	yes	characteristic
331	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
332	#559	C₂²×C₇	1	2	yes	—
333	#559	C₂²×C₇	1	2	yes	—
334	Q₈²	—	2	1	no	—
335	Q₈²	C₂²×C₇	1	2	yes	complemented
336	#557	—	2	1	no	—
337	#557	—	2	2	no	—
338	#557	C₂²×C₇	1	2	yes	complemented
339	#557	C₂²×C₇	1	4	yes	complemented
340	#550	C₂²×C₇	1	2	yes	—
341	#550	C₂²×C₇	1	2	yes	—
342	#546	—	2	2	no	—
343	#546	—	2	2	no	—
344	#544	—	2	2	no	—
345	#544	C₂²×C₇	1	2	yes	—
346	#540	—	2	2	no	—
347	#535	C₂²×C₇	1	2	yes	—
348	#533	—	2	2	no	—
349	#533	C₂²×C₇	1	1	yes	characteristic
350	#533	C₂²×C₇	1	1	yes	characteristic
351	#532	—	2	1	no	—
352	#532	—	2	1	no	—
353	C₂×#127	C₂²×C₇	1	1	yes	characteristic
354	#519	C₂²×C₇	1	2	yes	—
355	#518	C₂²×C₇	1	2	yes	—
356	C₄×#41	C₂²×C₇	1	1	yes	characteristic
357	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
358	#490	C₂²×C₇	1	4	yes	—
359	#490	C₂²×C₇	1	4	yes	complemented
360	#489	C₂²×C₇	1	4	yes	complemented
361	#488	C₂²×C₇	1	4	yes	complemented
362	#486	C₂²×C₇	1	2	yes	—
363	#486	C₂²×C₇	1	2	yes	—
364	#486	C₂²×C₇	1	4	yes	complemented
365	#479	C₂²×C₇	1	2	yes	complemented
366	#478	C₂²×C₇	1	2	yes	complemented
367	#478	C₂²×C₇	1	4	yes	complemented
368	#478	C₂²×C₇	1	4	yes	complemented
369	#477	C₂²×C₇	1	1	yes	characteristic, complemented
370	#476	C₂²×C₇	1	1	yes	characteristic, complemented
371	#476	C₂²×C₇	1	4	yes	complemented
372	#475	C₂²×C₇	1	1	yes	characteristic, complemented
373	#474	C₂²×C₇	1	1	yes	characteristic, complemented
374	#474	C₂²×C₇	1	4	yes	complemented
375	#464	C₂²×C₇	1	4	yes	complemented
376	#464	C₂²×C₇	1	4	yes	complemented
377	#460	C₂²×C₇	1	2	yes	—
378	#460	C₂²×C₇	1	4	yes	—
379	#460	C₂²×C₇	1	2	yes	—
380	#460	C₂²×C₇	1	4	yes	complemented
381	#460	C₂²×C₇	1	4	yes	complemented
382	#446	C₂²×C₇	1	4	yes	complemented
383	#446	C₂²×C₇	1	2	yes	complemented
384	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
385	#441	C₂²×C₇	1	2	yes	complemented
386	#440	C₂²×C₇	1	2	yes	complemented
387	#440	C₂²×C₇	1	4	yes	complemented
388	#440	C₂²×C₇	1	4	yes	complemented
389	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
390	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
391	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
392	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
393	#428	C₂²×C₇	1	1	yes	characteristic
394	#427	C₂²×C₇	1	2	yes	—
395	#424	C₂²×C₇	1	2	yes	—
396	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
397	#419	C₂²×C₇	1	1	yes	characteristic
398	#418	C₂²×C₇	1	2	yes	—
399	#418	C₂²×C₇	1	2	yes	—
400	#417	C₂²×C₇	1	1	yes	characteristic
401	#416	C₂²×C₇	1	2	yes	—
402	C₂×#102	C₂²×C₇	1	2	yes	—
403	#405	C₂²×C₇	1	2	yes	—
404	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
405	C₂³×C₇	—	2	4	no	—
406	C₂³×C₇	—	2	1	no	—
407	C₂³×C₇	—	4	4	no	—
408	C₂³×C₇	—	8	2	no	—
409	C₂³×C₇	—	8	2	no	—
410	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₇×Q₈	—	2	4	no	—
412	C₇×Q₈	—	2	4	no	—
413	C₇×Q₈	—	2	2	no	—
414	C₇×Q₈	—	2	1	no	—
415	C₇×Q₈	—	2	1	no	—
416	C₇×Q₈	—	4	2	no	—
417	C₇×Q₈	—	4	2	no	—
418	C₇×Q₈	—	8	1	no	—
419	C₇×Q₈	—	8	4	no	—
420	C₇×Q₈	C₂×#41	1	4	yes	—
421	C₇×D₄	—	2	4	no	—
422	C₇×D₄	—	2	1	no	—
423	C₇×D₄	—	2	4	no	—
424	C₇×D₄	—	2	1	no	—
425	C₇×D₄	—	4	4	no	—
426	C₇×D₄	—	4	2	no	—
427	C₇×D₄	—	4	4	no	—
428	C₇×D₄	—	4	4	no	—
429	C₇×D₄	—	8	2	no	—
430	C₇×D₄	—	8	2	no	—
431	C₇×D₄	—	8	4	no	—
432	C₇×D₄	—	8	4	no	—
433	C₂×C₄×C₇	—	2	4	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	1	no	—
439	C₂×C₄×C₇	—	2	1	no	—
440	C₂×C₄×C₇	—	2	1	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	4	1	no	—
443	C₂×C₄×C₇	—	4	2	no	—
444	C₂×C₄×C₇	—	4	2	no	—
445	C₂×C₄×C₇	—	4	2	no	—
446	C₂×C₄×C₇	—	8	4	no	—
447	C₂×C₄×C₇	—	8	4	no	—
448	C₂×C₄×C₇	—	8	1	no	—
449	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
452	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
453	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇	C₂×#41	1	2	yes	—
457	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
458	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
459	C₇×C₈	—	2	2	no	—
460	C₇×C₈	—	2	2	no	—
461	C₇×C₈	—	2	2	no	—
462	C₇×C₈	—	2	2	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	C₂³×C₇	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂³×C₇	1	2	yes	—
470	#137	—	2	4	no	—
471	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
472	C₂×SD₁₆	—	2	8	no	—
473	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
476	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
477	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₇	1	2	yes	—
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	—	2	4	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	4	no	—
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
485	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
486	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
489	#127	—	2	1	no	—
490	#127	—	2	1	no	—
491	#127	C₂³×C₇	1	2	yes	—
492	#127	C₂³×C₇	1	2	yes	—
493	#127	C₂³×C₇	1	4	yes	—
494	#125	—	2	4	no	—
495	#125	—	2	4	no	—
496	#125	—	2	4	no	—
497	#125	—	2	2	no	—
498	#125	C₇×D₄	1	2	yes	—
499	#125	C₂³×C₇	1	2	yes	—
500	#125	C₂³×C₇	1	4	yes	—
501	#124	—	2	2	no	—
502	#124	—	2	2	no	—
503	#124	C₂³×C₇	1	4	yes	—
504	#123	—	2	4	no	—
505	#123	—	2	4	no	—
506	C₂²⋊Q₈	—	2	1	no	—
507	C₂²⋊Q₈	—	2	1	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
510	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	4	no	—
516	#121	—	2	4	no	—
517	#120	—	2	4	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	4	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	C₂³×C₇	1	2	yes	—
528	C₄×Q₈	C₂³×C₇	1	2	yes	—
529	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
530	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
531	C₄×Q₈	C₂³×C₇	1	4	yes	—
532	C₄×Q₈	C₂³×C₇	1	4	yes	—
533	C₄×Q₈	C₂³×C₇	1	2	yes	—
534	C₄×Q₈	C₂³×C₇	1	2	yes	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
542	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
543	C₄×D₄	C₂³×C₇	1	4	yes	—
544	C₄×D₄	C₂³×C₇	1	4	yes	—
545	#117	—	2	4	no	—
546	#117	—	2	1	no	—
547	#117	C₂³×C₇	1	1	yes	characteristic
548	#117	C₂³×C₇	1	2	yes	—
549	#117	C₂³×C₇	1	2	yes	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₄²	—	2	1	no	—
554	C₂×C₄²	—	2	1	no	—
555	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
556	#107	C₂³×C₇	1	2	yes	—
557	#107	C₂³×C₇	1	2	yes	—
558	#107	C₂³×C₇	1	2	yes	—
559	#106	C₂³×C₇	1	2	yes	—
560	#106	C₂³×C₇	1	2	yes	—
561	#106	C₂³×C₇	1	2	yes	—
562	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
563	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
564	C₄⋊C₈	C₂³×C₇	1	2	yes	—
565	C₄⋊C₈	C₂³×C₇	1	4	yes	—
566	C₄⋊C₈	C₂³×C₇	1	4	yes	—
567	#103	C₂³×C₇	1	2	yes	—
568	#103	C₂³×C₇	1	2	yes	—
569	#103	C₂³×C₇	1	2	yes	—
570	#103	C₂³×C₇	1	2	yes	—
571	#103	C₂³×C₇	1	2	yes	—
572	#102	C₂³×C₇	1	4	yes	—
573	#102	C₂³×C₇	1	4	yes	—
574	#102	C₂³×C₇	1	2	yes	—
575	#102	C₂³×C₇	1	2	yes	—
576	#102	C₂³×C₇	1	2	yes	—
577	#102	C₂³×C₇	1	4	yes	—
578	#102	C₂³×C₇	1	4	yes	—
579	#102	C₂³×C₇	1	4	yes	—
580	#102	C₂³×C₇	1	4	yes	—
581	#97	C₂³×C₇	1	2	yes	—
582	#97	C₂³×C₇	1	4	yes	—
583	C₄×C₈	C₂³×C₇	1	2	yes	—
584	C₄×C₈	C₂³×C₇	1	4	yes	—
585	C₂²×C₇	—	2	1	no	—
586	C₂²×C₇	—	2	1	no	—
587	C₂²×C₇	—	4	1	no	—
588	C₂²×C₇	—	4	4	no	—
589	C₂²×C₇	—	4	1	no	—
590	C₂²×C₇	—	4	4	no	—
591	C₂²×C₇	—	4	1	no	—
592	C₂²×C₇	—	4	4	no	—
593	C₂²×C₇	—	16	4	no	—
594	C₂²×C₇	#548	1	2	yes	—
595	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
596	C₄×C₇	—	2	1	no	—
597	C₄×C₇	—	2	1	no	—
598	C₄×C₇	—	2	4	no	—
599	C₄×C₇	—	2	4	no	—
600	C₄×C₇	—	2	1	no	—
601	C₄×C₇	—	2	4	no	—
602	C₄×C₇	—	4	1	no	—
603	C₄×C₇	—	4	2	no	—
604	C₄×C₇	—	4	2	no	—
605	C₄×C₇	—	4	1	no	—
606	C₄×C₇	—	4	1	no	—
607	C₄×C₇	—	4	2	no	—
608	C₄×C₇	#548	1	2	yes	—
609	C₄×C₇	#577	1	2	yes	—
610	C₄×C₇	C₂²×#41	1	1	yes	characteristic
611	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
612	C₂⁴	—	2	2	no	—
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	#41	—	8	4	no	—
616	#41	—	8	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
623	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
624	C₂×Q₈	C₇×#41	1	4	yes	complemented
625	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
626	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	8	2	no	—
638	C₂×D₄	—	8	2	no	—
639	C₂×D₄	C₂⁴×C₇	1	4	yes	—
640	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
649	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
651	Q₁₆	—	2	4	no	—
652	SD₁₆	—	2	8	no	—
653	SD₁₆	—	2	8	no	—
654	SD₁₆	—	2	4	no	—
655	M₁₆	—	2	2	no	—
656	M₁₆	—	2	2	no	—
657	C₂×C₈	—	2	4	no	—
658	C₂×C₈	C₂⁴×C₇	1	2	yes	—
659	C₂×C₈	C₂⁴×C₇	1	2	yes	—
660	C₂×C₈	C₂⁴×C₇	1	2	yes	—
661	C₂×C₈	C₂⁴×C₇	1	2	yes	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
677	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
678	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
679	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
680	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
681	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
682	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
686	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	2	no	—
704	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
705	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
706	C₄²	C₂⁴×C₇	1	1	yes	characteristic
707	C₄²	C₂⁴×C₇	1	4	yes	—
708	C₄²	C₂⁴×C₇	1	1	yes	characteristic
709	C₂×C₇	—	2	2	no	—
710	C₂×C₇	—	8	1	no	—
711	C₂×C₇	—	8	4	no	—
712	C₂×C₇	C₂×#548	1	1	yes	characteristic
713	C₂×C₇	C₂×#577	1	1	yes	characteristic
714	C₂×C₇	#3585	1	1	yes	characteristic
715	C₂³	—	2	4	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	4	4	no	—
718	C₂³	—	8	2	no	—
719	C₂³	—	8	2	no	—
720	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
721	Q₈	—	2	2	no	—
722	Q₈	—	2	4	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	4	2	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	8	1	no	—
729	Q₈	—	8	4	no	—
730	Q₈	C₂×C₇×#41	1	4	yes	—
731	D₄	—	2	4	no	—
732	D₄	—	2	1	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	1	no	—
735	D₄	—	4	4	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	8	2	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	4	no	—
742	D₄	—	8	4	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	1	no	—
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	4	yes	—
762	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
763	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
764	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
766	C₂×C₄	C₂×C₇×#41	1	2	yes	—
767	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
768	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
769	C₈	—	2	2	no	—
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₇	#61341	1	1	yes	characteristic, direct product factor, Sylow
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	16	4	no	—
783	C₂²	C₇×#548	1	2	yes	—
784	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
785	C₄	—	2	1	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	C₇×#548	1	2	yes	—
798	C₄	C₇×#577	1	2	yes	—
799	C₄	C₂²×C₇×#41	1	1	yes	characteristic
800	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	8	4	no	—
803	C₂	—	8	1	no	—
804	C₂	C₂×C₇×#548	1	1	yes	characteristic
805	C₂	C₂×C₇×#577	1	1	yes	characteristic
806	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3502	C₂	semidirect
3. C₇×#3375	C₂	semidirect
4. C₇×#3371	C₂	semidirect
5. C₇×#3368	C₂	semidirect
6. C₇×#3368	C₂	semidirect
7. C₇×#3365	C₂	semidirect
8. C₇×#3362	C₂	semidirect
9. C₇×#3138	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3081	C₂	semidirect
12. C₇×#3076	C₂	semidirect
13. C₇×#3043	C₂	semidirect
14. C₂×C₇×#460	C₂	semidirect
15. C₇×#2962	C₂	semidirect
16. C₇×#2949	C₂	semidirect
17. C₄×C₇×#137	C₂	semidirect
23. C₇×Q₈²	C₂²	semidirect
26. C₇×#557	C₂²	semidirect
27. C₇×#557	C₂²	semidirect
47. C₇×#490	C₂²	semidirect
48. C₇×#489	C₂²	semidirect
49. C₇×#488	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#479	C₂²	semidirect
54. C₇×#478	C₂²	semidirect
55. C₇×#478	C₂²	semidirect
56. C₇×#478	C₂²	semidirect
57. C₇×#477	C₂²	semidirect
58. C₇×#476	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
61. C₇×#474	C₂²	semidirect
62. C₇×#474	C₂²	semidirect
63. C₇×#464	C₂²	semidirect
64. C₇×#464	C₂²	semidirect
68. C₇×#460	C₂²	semidirect
69. C₇×#460	C₂²	semidirect
70. C₇×#446	C₂²	semidirect
71. C₇×#446	C₂²	semidirect
72. C₇×C₈×Q₈	C₂²	semidirect
73. C₇×#441	C₂²	semidirect
74. C₇×#440	C₂²	semidirect
75. C₇×#440	C₂²	semidirect
76. C₇×#440	C₂²	semidirect
77. C₄×C₇×Q₁₆	C₂²	semidirect
78. C₄×C₇×SD₁₆	C₂²	semidirect
79. C₄×C₇×SD₁₆	C₂²	semidirect
80. C₄×C₇×SD₁₆	C₂²	semidirect
93. #61341	C₇	direct (N × H)
217. #3502	C₂×C₇	semidirect
218. #3375	C₂×C₇	semidirect
219. #3371	C₂×C₇	semidirect
220. #3368	C₂×C₇	semidirect
221. #3368	C₂×C₇	semidirect
222. #3365	C₂×C₇	semidirect
223. #3362	C₂×C₇	semidirect
224. #3138	C₂×C₇	semidirect
225. #3136	C₂×C₇	semidirect
226. #3081	C₂×C₇	semidirect
227. #3076	C₂×C₇	semidirect
228. #3043	C₂×C₇	semidirect
229. C₂×#460	C₂×C₇	semidirect
230. #2962	C₂×C₇	semidirect
231. #2949	C₂×C₇	semidirect
232. C₄×#137	C₂×C₇	semidirect
245. C₂×C₇×Q₈	#41	semidirect
335. Q₈²	C₂²×C₇	semidirect
338. #557	C₂²×C₇	semidirect
339. #557	C₂²×C₇	semidirect
359. #490	C₂²×C₇	semidirect
360. #489	C₂²×C₇	semidirect
361. #488	C₂²×C₇	semidirect
364. #486	C₂²×C₇	semidirect
365. #479	C₂²×C₇	semidirect
366. #478	C₂²×C₇	semidirect
367. #478	C₂²×C₇	semidirect
368. #478	C₂²×C₇	semidirect
369. #477	C₂²×C₇	semidirect
370. #476	C₂²×C₇	semidirect
371. #476	C₂²×C₇	semidirect
372. #475	C₂²×C₇	semidirect
373. #474	C₂²×C₇	semidirect
374. #474	C₂²×C₇	semidirect
375. #464	C₂²×C₇	semidirect
376. #464	C₂²×C₇	semidirect
380. #460	C₂²×C₇	semidirect
381. #460	C₂²×C₇	semidirect
382. #446	C₂²×C₇	semidirect
383. #446	C₂²×C₇	semidirect
384. C₈×Q₈	C₂²×C₇	semidirect
385. #441	C₂²×C₇	semidirect
386. #440	C₂²×C₇	semidirect
387. #440	C₂²×C₇	semidirect
388. #440	C₂²×C₇	semidirect
389. C₄×Q₁₆	C₂²×C₇	semidirect
390. C₄×SD₁₆	C₂²×C₇	semidirect
391. C₄×SD₁₆	C₂²×C₇	semidirect
392. C₄×SD₁₆	C₂²×C₇	semidirect
624. C₂×Q₈	C₇×#41	semidirect
773. C₇	#61341	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×#3508	2
C₇×#3502	2
C₇×#3375	2
C₇×#3371	2
C₇×#3368	2
C₇×#3365	2
C₇×#3362	2
C₇×#3138	2
C₇×#3136	2
C₇×#3081	2
C₇×#3076	2
C₇×#3043	2
C₂×C₇×#460	2
C₇×#2962	2
C₇×#2949	2
C₄×C₇×#137	2
#61341	7

Subgroups — C7×#61341 #13238557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61341 #13238557