Subgroups — C₇×#60860 #13238076

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3239	C₂	1	4	yes	maximal, complemented
4	C₇×#3238	C₂	1	4	yes	maximal, complemented
5	C₇×#3230	C₂	1	2	yes	maximal, complemented
6	C₇×#3229	C₂	1	2	yes	maximal, complemented
7	C₇×#3227	C₂	1	2	yes	maximal, complemented
8	C₇×#3226	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	2	yes	maximal, complemented
10	C₇×#3141	C₂	1	2	yes	maximal, complemented
11	C₇×#3092	C₂	1	4	yes	maximal, complemented
12	C₇×#3079	C₂	1	4	yes	maximal, complemented
13	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×C₇×Q₈	—	2	1	no	—
15	C₇×#533	C₂²	1	1	yes	characteristic
16	C₇×#533	C₂²	1	1	yes	characteristic
17	C₇×#533	C₂²	1	1	yes	characteristic
18	C₇×#532	C₂²	1	1	yes	characteristic
19	C₇×#532	C₂²	1	1	yes	characteristic
20	C₇×#532	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
26	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
27	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₇×#529	—	2	1	no	—
34	C₇×#529	—	2	1	no	—
35	C₇×#529	—	2	1	no	—
36	C₇×#529	—	2	1	no	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#525	—	2	1	no	—
40	C₇×#525	—	2	1	no	—
41	C₇×#525	C₂²	1	2	yes	—
42	C₄×C₇×#41	—	2	1	no	—
43	C₄×C₇×#41	—	2	1	no	—
44	C₄×C₇×#41	C₂²	1	2	yes	—
45	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
46	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
48	C₇×#501	C₂²	1	8	yes	complemented
49	C₇×#500	C₂²	1	4	yes	complemented
50	C₇×#498	C₂²	1	4	yes	complemented
51	C₇×#489	C₂²	1	8	yes	complemented
52	C₇×#487	C₂²	1	4	yes	complemented
53	C₇×#486	C₂²	1	4	yes	complemented
54	C₇×#484	C₂²	1	8	yes	—
55	C₇×#483	C₂²	1	8	yes	—
56	C₇×#481	C₂²	1	8	yes	—
57	C₇×#480	C₂²	1	8	yes	—
58	C₇×#477	C₂²	1	8	yes	complemented
59	C₇×#476	C₂²	1	8	yes	complemented
60	C₇×#475	C₂²	1	8	yes	complemented
61	C₇×#474	C₂²	1	8	yes	complemented
62	C₇×#432	C₂²	1	2	yes	—
63	C₇×#432	C₂²	1	2	yes	—
64	C₇×#431	C₂²	1	2	yes	—
65	C₇×#431	C₂²	1	2	yes	—
66	C₇×#428	C₂²	1	8	yes	—
67	C₇×#423	C₂²	1	2	yes	—
68	C₇×#417	C₂²	1	8	yes	—
69	C₇×#407	C₂²	1	2	yes	—
70	C₄×C₇×M₁₆	C₂²	1	2	yes	—
71	#60860	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₇×#41	—	2	1	no	—
73	C₂×C₇×#41	—	2	1	no	—
74	C₂×C₇×#41	C₂³	1	2	yes	—
75	C₂²×C₇×Q₈	—	2	2	no	—
76	C₂²×C₇×Q₈	—	2	2	no	—
77	C₂²×C₇×Q₈	—	2	2	no	—
78	C₂²×C₇×Q₈	—	2	2	no	—
79	C₂²×C₇×Q₈	—	2	2	no	—
80	C₂²×C₇×Q₈	—	2	2	no	—
81	C₂²×C₇×Q₈	—	4	8	no	—
82	C₂³×C₄×C₇	—	2	2	no	—
83	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
86	C₂×C₇×M₁₆	C₂³	1	4	yes	—
87	C₇×C₄⋊Q₈	—	2	2	no	—
88	C₇×C₄⋊Q₈	—	2	2	no	—
89	C₇×C₄⋊Q₈	—	2	2	no	—
90	C₇×C₄⋊Q₈	—	2	2	no	—
91	C₇×C₄⋊Q₈	—	2	2	no	—
92	C₇×C₄⋊Q₈	—	2	2	no	—
93	C₇×C₄⋊Q₈	—	2	2	no	—
94	C₇×C₄⋊Q₈	—	2	2	no	—
95	C₇×C₄⋊Q₈	—	2	2	no	—
96	C₇×C₄⋊Q₈	—	2	2	no	—
97	C₇×C₄⋊Q₈	—	2	2	no	—
98	C₇×C₄⋊Q₈	—	2	2	no	—
99	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
103	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₇×#127	C₂³	1	1	yes	characteristic
107	C₇×#126	—	2	2	no	—
108	C₇×#126	—	2	2	no	—
109	C₇×#125	—	2	1	no	—
110	C₇×#125	—	2	1	no	—
111	C₇×#125	C₂³	1	2	yes	—
112	C₇×#124	—	2	1	no	—
113	C₇×#124	—	2	1	no	—
114	C₇×#124	C₂³	1	2	yes	—
115	C₇×#123	—	2	2	no	—
116	C₇×#123	—	2	2	no	—
117	C₇×#123	—	2	2	no	—
118	C₇×C₂²⋊Q₈	—	2	1	no	—
119	C₇×C₂²⋊Q₈	—	2	1	no	—
120	C₇×C₂²⋊Q₈	—	2	1	no	—
121	C₇×C₂²⋊Q₈	—	2	1	no	—
122	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
123	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
124	C₇×#121	—	2	1	no	—
125	C₇×#121	—	2	1	no	—
126	C₇×#121	—	2	1	no	—
127	C₇×#121	—	2	1	no	—
128	C₇×#121	C₂³	1	2	yes	—
129	C₇×#121	C₂³	1	2	yes	—
130	C₇×#120	—	2	2	no	—
131	C₄×C₇×Q₈	—	2	1	no	—
132	C₄×C₇×Q₈	—	2	1	no	—
133	C₄×C₇×Q₈	—	2	1	no	—
134	C₄×C₇×Q₈	—	2	1	no	—
135	C₄×C₇×Q₈	C₂³	1	2	yes	—
136	C₄×C₇×Q₈	C₂³	1	2	yes	—
137	C₄×C₇×D₄	—	2	2	no	—
138	C₄×C₇×D₄	—	2	2	no	—
139	C₄×C₇×D₄	—	2	2	no	—
140	C₄×C₇×D₄	—	2	2	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	—	2	2	no	—
143	C₄×C₇×D₄	—	2	1	no	—
144	C₄×C₇×D₄	—	2	1	no	—
145	C₄×C₇×D₄	—	2	1	no	—
146	C₄×C₇×D₄	—	2	1	no	—
147	C₄×C₇×D₄	C₂³	1	2	yes	—
148	C₄×C₇×D₄	C₂³	1	2	yes	—
149	C₇×#117	—	2	1	no	—
150	C₇×#117	—	2	1	no	—
151	C₇×#117	—	2	2	no	—
152	C₇×#117	—	2	2	no	—
153	C₇×#117	—	2	2	no	—
154	C₇×#117	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	—	2	2	no	—
156	C₂×C₇×C₄⋊C₄	—	2	2	no	—
157	C₂×C₇×C₄⋊C₄	—	2	2	no	—
158	C₂×C₇×C₄⋊C₄	—	2	2	no	—
159	C₂×C₇×C₄⋊C₄	—	2	2	no	—
160	C₂×C₇×C₄⋊C₄	—	2	2	no	—
161	C₂×C₇×C₄⋊C₄	—	2	2	no	—
162	C₂×C₇×C₄⋊C₄	—	2	2	no	—
163	C₂×C₇×C₄⋊C₄	—	2	2	no	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₄²×C₇	—	2	2	no	—
168	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
169	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
170	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
172	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
173	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₇×#107	C₂³	1	16	yes	—
181	C₇×#106	C₂³	1	16	yes	—
182	C₇×C₄⋊C₈	C₂³	1	4	yes	—
183	C₇×C₄⋊C₈	C₂³	1	4	yes	—
184	C₇×#103	C₂³	1	16	yes	—
185	C₇×#102	C₂³	1	16	yes	—
186	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₇×#97	C₂³	1	4	yes	—
189	C₄×C₇×C₈	C₂³	1	4	yes	—
190	#3444	C₂×C₇	1	1	yes	characteristic
191	C₂²×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
192	#3239	C₂×C₇	1	4	yes	complemented
193	#3238	C₂×C₇	1	4	yes	complemented
194	#3230	C₂×C₇	1	2	yes	complemented
195	#3229	C₂×C₇	1	2	yes	complemented
196	#3227	C₂×C₇	1	2	yes	complemented
197	#3226	C₂×C₇	1	2	yes	complemented
198	#3165	C₂×C₇	1	2	yes	complemented
199	#3141	C₂×C₇	1	2	yes	complemented
200	#3092	C₂×C₇	1	4	yes	complemented
201	#3079	C₂×C₇	1	4	yes	complemented
202	#2920	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
204	C₇×#41	—	2	8	no	—
205	C₇×#41	—	4	4	no	—
206	C₇×#41	—	4	4	no	—
207	C₂×C₇×Q₈	—	2	1	no	—
208	C₂×C₇×Q₈	—	2	1	no	—
209	C₂×C₇×Q₈	—	2	4	no	—
210	C₂×C₇×Q₈	—	2	4	no	—
211	C₂×C₇×Q₈	—	2	4	no	—
212	C₂×C₇×Q₈	—	2	4	no	—
213	C₂×C₇×Q₈	—	4	8	no	—
214	C₂×C₇×Q₈	—	4	8	no	—
215	C₂×C₇×Q₈	—	4	8	no	—
216	C₂×C₇×Q₈	—	4	8	no	—
217	C₂×C₇×Q₈	—	4	8	no	—
218	C₂×C₇×Q₈	—	4	8	no	—
219	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
220	C₂×C₇×D₄	—	2	2	no	—
221	C₂×C₇×D₄	—	2	2	no	—
222	C₂×C₇×D₄	—	2	2	no	—
223	C₂×C₇×D₄	—	2	1	no	—
224	C₂×C₇×D₄	—	2	1	no	—
225	C₂×C₇×D₄	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₇	—	2	4	no	—
227	C₂²×C₄×C₇	—	2	4	no	—
228	C₂²×C₄×C₇	—	2	4	no	—
229	C₂²×C₄×C₇	—	2	4	no	—
230	C₂²×C₄×C₇	—	2	4	no	—
231	C₂²×C₄×C₇	—	2	4	no	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	4	8	no	—
236	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₇×M₁₆	—	2	8	no	—
255	C₂×C₇×C₈	C₂⁴	1	8	yes	—
256	C₇×C₄⋊C₄	—	2	4	no	—
257	C₇×C₄⋊C₄	—	2	4	no	—
258	C₇×C₄⋊C₄	—	2	4	no	—
259	C₇×C₄⋊C₄	—	2	4	no	—
260	C₇×C₄⋊C₄	—	2	4	no	—
261	C₇×C₄⋊C₄	—	2	4	no	—
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	1	no	—
264	C₇×C₄⋊C₄	—	2	1	no	—
265	C₇×C₄⋊C₄	—	2	1	no	—
266	C₇×C₄⋊C₄	—	2	1	no	—
267	C₇×C₄⋊C₄	—	2	2	no	—
268	C₇×C₄⋊C₄	—	2	2	no	—
269	C₇×C₄⋊C₄	—	2	2	no	—
270	C₇×C₄⋊C₄	—	2	2	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
274	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
275	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₇×C₂²⋊C₄	—	2	2	no	—
277	C₇×C₂²⋊C₄	—	2	2	no	—
278	C₇×C₂²⋊C₄	—	2	2	no	—
279	C₇×C₂²⋊C₄	—	2	2	no	—
280	C₇×C₂²⋊C₄	—	2	2	no	—
281	C₇×C₂²⋊C₄	—	2	2	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	2	no	—
284	C₇×C₂²⋊C₄	—	2	2	no	—
285	C₄²×C₇	—	2	2	no	—
286	C₄²×C₇	—	2	2	no	—
287	C₄²×C₇	—	2	2	no	—
288	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
293	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
294	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
295	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₇	C₂⁴	1	1	yes	characteristic
301	C₄²×C₇	C₂⁴	1	1	yes	characteristic
302	C₄²×C₇	C₂⁴	1	1	yes	characteristic
303	C₄²×C₇	C₂⁴	1	1	yes	characteristic
304	C₂³×Q₈	—	2	1	no	—
305	#533	C₂²×C₇	1	1	yes	characteristic
306	#533	C₂²×C₇	1	1	yes	characteristic
307	#533	C₂²×C₇	1	1	yes	characteristic
308	#532	C₂²×C₇	1	1	yes	characteristic
309	#532	C₂²×C₇	1	1	yes	characteristic
310	#532	C₂²×C₇	1	1	yes	characteristic
311	C₂×C₄⋊Q₈	—	2	1	no	—
312	C₂×C₄⋊Q₈	—	2	1	no	—
313	C₂×C₄⋊Q₈	—	2	1	no	—
314	C₂×C₄⋊Q₈	—	2	1	no	—
315	C₂×C₄⋊Q₈	—	2	1	no	—
316	C₂×C₄⋊Q₈	—	2	1	no	—
317	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
318	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
319	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
320	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
321	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
322	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
323	#529	—	2	1	no	—
324	#529	—	2	1	no	—
325	#529	—	2	1	no	—
326	#529	—	2	1	no	—
327	#529	C₂²×C₇	1	2	yes	—
328	#529	C₂²×C₇	1	2	yes	—
329	#525	—	2	1	no	—
330	#525	—	2	1	no	—
331	#525	C₂²×C₇	1	2	yes	—
332	C₄×#41	—	2	1	no	—
333	C₄×#41	—	2	1	no	—
334	C₄×#41	C₂²×C₇	1	2	yes	—
335	C₂²×C₄⋊C₄	—	2	1	no	—
336	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
337	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
338	#501	C₂²×C₇	1	8	yes	complemented
339	#500	C₂²×C₇	1	4	yes	complemented
340	#498	C₂²×C₇	1	4	yes	complemented
341	#489	C₂²×C₇	1	8	yes	complemented
342	#487	C₂²×C₇	1	4	yes	complemented
343	#486	C₂²×C₇	1	4	yes	complemented
344	#484	C₂²×C₇	1	8	yes	—
345	#483	C₂²×C₇	1	8	yes	—
346	#481	C₂²×C₇	1	8	yes	—
347	#480	C₂²×C₇	1	8	yes	—
348	#477	C₂²×C₇	1	8	yes	complemented
349	#476	C₂²×C₇	1	8	yes	complemented
350	#475	C₂²×C₇	1	8	yes	complemented
351	#474	C₂²×C₇	1	8	yes	complemented
352	#432	C₂²×C₇	1	2	yes	—
353	#432	C₂²×C₇	1	2	yes	—
354	#431	C₂²×C₇	1	2	yes	—
355	#431	C₂²×C₇	1	2	yes	—
356	#428	C₂²×C₇	1	8	yes	—
357	#423	C₂²×C₇	1	2	yes	—
358	#417	C₂²×C₇	1	8	yes	—
359	#407	C₂²×C₇	1	2	yes	—
360	C₄×M₁₆	C₂²×C₇	1	2	yes	—
361	C₂³×C₇	—	2	2	no	—
362	C₂³×C₇	—	2	2	no	—
363	C₂³×C₇	—	2	2	no	—
364	C₂³×C₇	—	2	2	no	—
365	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
366	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
368	C₇×Q₈	—	2	4	no	—
369	C₇×Q₈	—	4	8	no	—
370	C₇×Q₈	—	4	8	no	—
371	C₇×Q₈	—	4	8	no	—
372	C₇×Q₈	—	4	8	no	—
373	C₇×Q₈	—	4	2	no	—
374	C₇×Q₈	—	4	2	no	—
375	C₇×D₄	—	2	4	no	—
376	C₇×D₄	—	4	4	no	—
377	C₇×D₄	—	4	4	no	—
378	C₇×D₄	—	4	4	no	—
379	C₇×D₄	—	4	2	no	—
380	C₇×D₄	—	4	2	no	—
381	C₂×C₄×C₇	—	2	2	no	—
382	C₂×C₄×C₇	—	2	2	no	—
383	C₂×C₄×C₇	—	2	2	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	2	2	no	—
387	C₂×C₄×C₇	—	2	2	no	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	2	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	8	no	—
400	C₂×C₄×C₇	—	4	8	no	—
401	C₂×C₄×C₇	—	4	8	no	—
402	C₂×C₄×C₇	—	4	8	no	—
403	C₂×C₄×C₇	—	4	4	no	—
404	C₂×C₄×C₇	—	4	4	no	—
405	C₂×C₄×C₇	—	4	4	no	—
406	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
407	C₂×C₄×C₇	#137	1	4	yes	—
408	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
420	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
421	C₇×C₈	—	2	8	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	C₂³×C₇	1	2	yes	—
425	C₂²×Q₈	—	2	2	no	—
426	C₂²×Q₈	—	2	2	no	—
427	C₂²×Q₈	—	2	2	no	—
428	C₂²×Q₈	—	2	2	no	—
429	C₂²×Q₈	—	2	2	no	—
430	C₂²×Q₈	—	2	2	no	—
431	C₂²×Q₈	—	4	8	no	—
432	C₂³×C₄	—	2	2	no	—
433	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
434	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
436	C₂×M₁₆	C₂³×C₇	1	4	yes	—
437	C₄⋊Q₈	—	2	2	no	—
438	C₄⋊Q₈	—	2	2	no	—
439	C₄⋊Q₈	—	2	2	no	—
440	C₄⋊Q₈	—	2	2	no	—
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	—	2	2	no	—
445	C₄⋊Q₈	—	2	2	no	—
446	C₄⋊Q₈	—	2	2	no	—
447	C₄⋊Q₈	—	2	2	no	—
448	C₄⋊Q₈	—	2	2	no	—
449	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
451	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
452	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
453	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
454	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
456	#127	C₂³×C₇	1	1	yes	characteristic
457	#126	—	2	2	no	—
458	#126	—	2	2	no	—
459	#125	—	2	1	no	—
460	#125	—	2	1	no	—
461	#125	C₂³×C₇	1	2	yes	—
462	#124	—	2	1	no	—
463	#124	—	2	1	no	—
464	#124	C₂³×C₇	1	2	yes	—
465	#123	—	2	2	no	—
466	#123	—	2	2	no	—
467	#123	—	2	2	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
473	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
474	#121	—	2	1	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	C₂³×C₇	1	2	yes	—
479	#121	C₂³×C₇	1	2	yes	—
480	#120	—	2	2	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	C₂³×C₇	1	2	yes	—
486	C₄×Q₈	C₂³×C₇	1	2	yes	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	C₂³×C₇	1	2	yes	—
498	C₄×D₄	C₂³×C₇	1	2	yes	—
499	#117	—	2	1	no	—
500	#117	—	2	1	no	—
501	#117	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	—	2	2	no	—
504	#117	C₂³×C₇	1	2	yes	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
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	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
517	C₂×C₄²	—	2	2	no	—
518	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
519	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
520	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
521	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
522	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
523	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
530	#107	C₂³×C₇	1	16	yes	—
531	#106	C₂³×C₇	1	16	yes	—
532	C₄⋊C₈	C₂³×C₇	1	4	yes	—
533	C₄⋊C₈	C₂³×C₇	1	4	yes	—
534	#103	C₂³×C₇	1	16	yes	—
535	#102	C₂³×C₇	1	16	yes	—
536	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
537	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
538	#97	C₂³×C₇	1	4	yes	—
539	C₄×C₈	C₂³×C₇	1	4	yes	—
540	C₂²×C₇	—	2	8	no	—
541	C₂²×C₇	—	2	1	no	—
542	C₂²×C₇	—	2	1	no	—
543	C₂²×C₇	—	2	1	no	—
544	C₂²×C₇	—	2	1	no	—
545	C₂²×C₇	—	2	1	no	—
546	C₂²×C₇	—	2	1	no	—
547	C₂²×C₇	—	4	2	no	—
548	C₂²×C₇	—	4	2	no	—
549	C₂²×C₇	—	4	2	no	—
550	C₂²×C₇	#536	1	2	yes	—
551	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
552	C₂²×C₇	C₂×#137	1	2	yes	—
553	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₇	—	2	1	no	—
555	C₄×C₇	—	2	1	no	—
556	C₄×C₇	—	2	1	no	—
557	C₄×C₇	—	2	1	no	—
558	C₄×C₇	—	2	1	no	—
559	C₄×C₇	—	2	1	no	—
560	C₄×C₇	—	4	2	no	—
561	C₄×C₇	—	4	8	no	—
562	C₄×C₇	—	4	2	no	—
563	C₄×C₇	—	4	2	no	—
564	C₄×C₇	#536	1	2	yes	—
565	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
566	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
567	C₄×C₇	C₂×#137	1	2	yes	—
568	C₄×C₇	C₂×#137	1	2	yes	—
569	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
570	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
571	#41	—	2	8	no	—
572	#41	—	4	4	no	—
573	#41	—	4	4	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	4	8	no	—
581	C₂×Q₈	—	4	8	no	—
582	C₂×Q₈	—	4	8	no	—
583	C₂×Q₈	—	4	8	no	—
584	C₂×Q₈	—	4	8	no	—
585	C₂×Q₈	—	4	8	no	—
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	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	C₂⁴×C₇	1	2	yes	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	4	8	no	—
603	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
604	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
605	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
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	C₂×C₇×D₄	1	1	yes	characteristic
610	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
612	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
615	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
617	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
621	M₁₆	—	2	8	no	—
622	C₂×C₈	C₂⁴×C₇	1	8	yes	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
641	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
656	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
657	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
658	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
659	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
660	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
661	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
662	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
663	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
664	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
665	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
666	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
667	C₄²	C₂⁴×C₇	1	1	yes	characteristic
668	C₄²	C₂⁴×C₇	1	1	yes	characteristic
669	C₄²	C₂⁴×C₇	1	1	yes	characteristic
670	C₄²	C₂⁴×C₇	1	1	yes	characteristic
671	C₂×C₇	—	2	2	no	—
672	C₂×C₇	—	2	2	no	—
673	C₂×C₇	—	2	2	no	—
674	C₂×C₇	—	8	2	no	—
675	C₂×C₇	C₂×#536	1	1	yes	characteristic
676	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
677	C₂×C₇	C₂²×#137	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	1	yes	characteristic
683	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
684	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
685	Q₈	—	2	4	no	—
686	Q₈	—	4	8	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	2	no	—
692	D₄	—	2	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	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	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	8	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
724	C₂×C₄	C₇×#137	1	4	yes	—
725	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
729	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
730	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
731	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
732	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
733	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
734	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
735	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
736	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
737	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
738	C₈	—	2	8	no	—
739	C₇	#60860	1	1	yes	characteristic, direct product factor, Sylow
740	C₂²	—	2	8	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₇×#536	1	2	yes	—
751	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
752	C₂²	C₂×C₇×#137	1	2	yes	—
753	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	4	8	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₇×#536	1	2	yes	—
765	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
766	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
767	C₄	C₂×C₇×#137	1	2	yes	—
768	C₄	C₂×C₇×#137	1	2	yes	—
769	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
770	C₂	—	2	2	no	—
771	C₂	—	2	2	no	—
772	C₂	—	2	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₂×C₇×#536	1	1	yes	characteristic
775	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
776	C₂	C₂²×C₇×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₇×C₄⋊Q₈	C₂	semidirect
3. C₇×#3239	C₂	semidirect
4. C₇×#3238	C₂	semidirect
5. C₇×#3230	C₂	semidirect
6. C₇×#3229	C₂	semidirect
7. C₇×#3227	C₂	semidirect
8. C₇×#3226	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3141	C₂	semidirect
11. C₇×#3092	C₂	semidirect
12. C₇×#3079	C₂	semidirect
13. C₇×#2920	C₂	semidirect
48. C₇×#501	C₂²	semidirect
49. C₇×#500	C₂²	semidirect
50. C₇×#498	C₂²	semidirect
51. C₇×#489	C₂²	semidirect
52. C₇×#487	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
61. C₇×#474	C₂²	semidirect
71. #60860	C₇	direct (N × H)
191. C₂²×C₄⋊Q₈	C₂×C₇	semidirect
192. #3239	C₂×C₇	semidirect
193. #3238	C₂×C₇	semidirect
194. #3230	C₂×C₇	semidirect
195. #3229	C₂×C₇	semidirect
196. #3227	C₂×C₇	semidirect
197. #3226	C₂×C₇	semidirect
198. #3165	C₂×C₇	semidirect
199. #3141	C₂×C₇	semidirect
200. #3092	C₂×C₇	semidirect
201. #3079	C₂×C₇	semidirect
202. #2920	C₂×C₇	semidirect
338. #501	C₂²×C₇	semidirect
339. #500	C₂²×C₇	semidirect
340. #498	C₂²×C₇	semidirect
341. #489	C₂²×C₇	semidirect
342. #487	C₂²×C₇	semidirect
343. #486	C₂²×C₇	semidirect
348. #477	C₂²×C₇	semidirect
349. #476	C₂²×C₇	semidirect
350. #475	C₂²×C₇	semidirect
351. #474	C₂²×C₇	semidirect
739. C₇	#60860	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×#3444	2
C₂²×C₇×C₄⋊Q₈	2
C₇×#3239	2
C₇×#3238	2
C₇×#3230	2
C₇×#3229	2
C₇×#3227	2
C₇×#3226	2
C₇×#3165	2
C₇×#3141	2
C₇×#3092	2
C₇×#3079	2
C₇×#2920	2
#60860	7

Subgroups — C7×#60860 #13238076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60860 #13238076