Subgroups — C₇×#60864 #13238080

Order 1792.

2036 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic
3	C₇×#3235	C₂	1	4	yes	maximal, complemented
4	C₇×#3234	C₂	1	4	yes	maximal, complemented
5	C₇×#3228	C₂	1	4	yes	maximal, complemented
6	C₇×#3227	C₂	1	2	yes	maximal, complemented
7	C₇×#3226	C₂	1	2	yes	maximal, complemented
8	C₇×#3165	C₂	1	2	yes	maximal, complemented
9	C₇×#3138	C₂	1	2	yes	maximal, complemented
10	C₇×#3094	C₂	1	4	yes	maximal, complemented
11	C₇×#3077	C₂	1	4	yes	maximal, complemented
12	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₇×#533	—	2	1	no	—
15	C₇×#533	—	2	1	no	—
16	C₇×#533	—	2	1	no	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	C₂²	1	2	yes	—
19	C₇×#533	C₂²	1	2	yes	—
20	C₇×#533	C₂²	1	2	yes	complemented
21	C₇×#533	C₂²	1	2	yes	complemented
22	C₇×#532	—	2	1	no	—
23	C₇×#532	—	2	1	no	—
24	C₇×#532	—	2	1	no	—
25	C₇×#532	—	2	1	no	—
26	C₇×#532	C₂²	1	2	yes	—
27	C₇×#532	C₂²	1	2	yes	—
28	C₇×#532	C₂²	1	2	yes	—
29	C₇×#532	C₂²	1	2	yes	—
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×#127	C₂²	1	1	yes	characteristic
34	C₂×C₇×#125	C₂²	1	2	yes	complemented
35	C₂×C₇×#124	—	2	1	no	—
36	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₇×#121	—	2	1	no	—
39	C₂×C₇×#121	C₂²	1	2	yes	—
40	C₂×C₄×C₇×Q₈	—	2	1	no	—
41	C₂×C₄×C₇×Q₈	—	2	1	no	—
42	C₂×C₄×C₇×D₄	—	2	1	no	—
43	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
44	C₂×C₇×#117	C₂²	1	2	yes	—
45	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
46	C₇×#501	C₂²	1	8	yes	complemented
47	C₇×#500	C₂²	1	4	yes	complemented
48	C₇×#498	C₂²	1	4	yes	complemented
49	C₇×#490	C₂²	1	8	yes	complemented
50	C₇×#486	C₂²	1	4	yes	complemented
51	C₇×#486	C₂²	1	4	yes	complemented
52	C₇×#482	C₂²	1	16	yes	complemented
53	C₇×#481	C₂²	1	8	yes	complemented
54	C₇×#480	C₂²	1	8	yes	complemented
55	C₇×#478	C₂²	1	16	yes	complemented
56	C₇×#476	C₂²	1	8	yes	complemented
57	C₇×#474	C₂²	1	8	yes	complemented
58	C₇×#432	C₂²	1	2	yes	complemented
59	C₇×#432	C₂²	1	2	yes	complemented
60	C₇×#431	C₂²	1	2	yes	complemented
61	C₇×#431	C₂²	1	2	yes	complemented
62	C₇×#428	C₂²	1	8	yes	—
63	C₇×#423	C₂²	1	2	yes	—
64	C₇×#418	C₂²	1	8	yes	—
65	C₇×#407	C₂²	1	2	yes	—
66	C₄×C₇×M₁₆	C₂²	1	2	yes	—
67	#60864	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₇×#41	—	2	2	no	—
69	C₂×C₇×#41	—	2	2	no	—
70	C₂×C₇×#41	—	2	2	no	—
71	C₂×C₇×#41	—	2	2	no	—
72	C₂×C₇×#41	—	4	8	no	—
73	C₂²×C₇×Q₈	—	2	1	no	—
74	C₂²×C₇×Q₈	—	2	1	no	—
75	C₂²×C₇×Q₈	—	2	1	no	—
76	C₂²×C₇×D₄	—	2	2	no	—
77	C₂²×C₇×D₄	—	2	1	no	—
78	C₂²×C₇×D₄	—	2	1	no	—
79	C₂²×C₇×D₄	C₂³	1	2	yes	—
80	C₂³×C₄×C₇	—	2	2	no	—
81	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₂×C₇×M₁₆	C₂³	1	4	yes	—
85	C₇×C₄⋊Q₈	—	2	1	no	—
86	C₇×C₄⋊Q₈	—	2	1	no	—
87	C₇×C₄⋊Q₈	—	2	1	no	—
88	C₇×C₄⋊Q₈	—	2	1	no	—
89	C₇×C₄⋊Q₈	—	2	1	no	—
90	C₇×C₄⋊Q₈	—	2	1	no	—
91	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
93	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×#127	—	2	1	no	—
98	C₇×#127	—	2	1	no	—
99	C₇×#127	C₂³	1	2	yes	—
100	C₇×#127	C₂³	1	2	yes	—
101	C₇×#125	—	2	2	no	—
102	C₇×#125	—	2	2	no	—
103	C₇×#125	C₂³	1	4	yes	—
104	C₇×#125	C₂³	1	4	yes	—
105	C₇×#124	—	2	2	no	—
106	C₇×#124	—	2	2	no	—
107	C₇×#124	—	2	2	no	—
108	C₇×#124	—	2	2	no	—
109	C₇×C₂²⋊Q₈	—	2	2	no	—
110	C₇×C₂²⋊Q₈	—	2	2	no	—
111	C₇×C₂²⋊Q₈	—	2	2	no	—
112	C₇×C₂²⋊Q₈	—	2	2	no	—
113	C₇×C₂²⋊Q₈	—	2	2	no	—
114	C₇×C₂²⋊Q₈	—	2	2	no	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	2	no	—
117	C₇×#121	—	2	2	no	—
118	C₇×#121	—	2	2	no	—
119	C₇×#121	—	2	2	no	—
120	C₇×#121	—	2	2	no	—
121	C₇×#121	—	2	2	no	—
122	C₇×#121	—	2	2	no	—
123	C₇×#121	C₂³	1	4	yes	—
124	C₇×#121	C₂³	1	4	yes	—
125	C₄×C₇×Q₈	—	2	2	no	—
126	C₄×C₇×Q₈	—	2	2	no	—
127	C₄×C₇×Q₈	—	2	2	no	—
128	C₄×C₇×Q₈	—	2	2	no	—
129	C₄×C₇×Q₈	—	2	2	no	—
130	C₄×C₇×Q₈	—	2	2	no	—
131	C₄×C₇×Q₈	—	2	2	no	—
132	C₄×C₇×Q₈	—	2	2	no	—
133	C₄×C₇×D₄	—	2	2	no	—
134	C₄×C₇×D₄	—	2	2	no	—
135	C₄×C₇×D₄	—	2	2	no	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	—	2	2	no	—
138	C₄×C₇×D₄	—	2	2	no	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₄×C₇×D₄	C₂³	1	4	yes	—
141	C₇×#117	—	2	2	no	—
142	C₇×#117	—	2	2	no	—
143	C₇×#117	C₂³	1	4	yes	—
144	C₇×#117	C₂³	1	4	yes	—
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	—	2	2	no	—
147	C₂×C₇×C₄⋊C₄	—	2	2	no	—
148	C₂×C₇×C₄⋊C₄	—	2	1	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
155	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
156	C₂×C₄²×C₇	—	2	2	no	—
157	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	16	yes	—
170	C₇×#106	C₂³	1	16	yes	—
171	C₇×C₄⋊C₈	C₂³	1	4	yes	—
172	C₇×C₄⋊C₈	C₂³	1	4	yes	—
173	C₇×#102	C₂³	1	16	yes	—
174	C₇×#102	C₂³	1	16	yes	—
175	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₇×#97	C₂³	1	4	yes	—
178	C₄×C₇×C₈	C₂³	1	4	yes	—
179	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
180	C₂×#532	C₂×C₇	1	1	yes	characteristic
181	#3235	C₂×C₇	1	4	yes	complemented
182	#3234	C₂×C₇	1	4	yes	complemented
183	#3228	C₂×C₇	1	4	yes	complemented
184	#3227	C₂×C₇	1	2	yes	complemented
185	#3226	C₂×C₇	1	2	yes	complemented
186	#3165	C₂×C₇	1	2	yes	complemented
187	#3138	C₂×C₇	1	2	yes	complemented
188	#3094	C₂×C₇	1	4	yes	complemented
189	#3077	C₂×C₇	1	4	yes	complemented
190	#2920	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂⁴×C₇	—	2	2	no	—
192	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
193	C₇×#41	—	4	8	no	—
194	C₇×#41	—	4	8	no	—
195	C₇×#41	—	4	8	no	—
196	C₇×#41	—	4	8	no	—
197	C₂×C₇×Q₈	—	2	2	no	—
198	C₂×C₇×Q₈	—	2	2	no	—
199	C₂×C₇×Q₈	—	2	2	no	—
200	C₂×C₇×Q₈	—	2	2	no	—
201	C₂×C₇×Q₈	—	2	2	no	—
202	C₂×C₇×Q₈	—	2	2	no	—
203	C₂×C₇×Q₈	—	4	4	no	—
204	C₂×C₇×Q₈	—	4	4	no	—
205	C₂×C₇×Q₈	—	4	4	no	—
206	C₂×C₇×D₄	—	2	4	no	—
207	C₂×C₇×D₄	—	2	4	no	—
208	C₂×C₇×D₄	—	2	2	no	—
209	C₂×C₇×D₄	—	2	2	no	—
210	C₂×C₇×D₄	—	2	2	no	—
211	C₂×C₇×D₄	—	2	2	no	—
212	C₂×C₇×D₄	—	2	2	no	—
213	C₂×C₇×D₄	—	2	8	no	—
214	C₂×C₇×D₄	—	4	4	no	—
215	C₂×C₇×D₄	—	4	4	no	—
216	C₂×C₇×D₄	—	4	8	no	—
217	C₂×C₇×D₄	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₇	—	2	4	no	—
219	C₂²×C₄×C₇	—	2	4	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	2	no	—
222	C₂²×C₄×C₇	—	2	2	no	—
223	C₂²×C₄×C₇	—	2	4	no	—
224	C₂²×C₄×C₇	—	2	4	no	—
225	C₂²×C₄×C₇	—	4	2	no	—
226	C₂²×C₄×C₇	—	4	8	no	—
227	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
245	C₇×M₁₆	—	2	8	no	—
246	C₂×C₇×C₈	C₂⁴	1	8	yes	—
247	C₇×C₄⋊C₄	—	2	2	no	—
248	C₇×C₄⋊C₄	—	2	2	no	—
249	C₇×C₄⋊C₄	—	2	4	no	—
250	C₇×C₄⋊C₄	—	2	4	no	—
251	C₇×C₄⋊C₄	—	2	4	no	—
252	C₇×C₄⋊C₄	—	2	4	no	—
253	C₇×C₄⋊C₄	—	2	2	no	—
254	C₇×C₄⋊C₄	—	2	2	no	—
255	C₇×C₄⋊C₄	—	2	2	no	—
256	C₇×C₄⋊C₄	—	2	2	no	—
257	C₇×C₄⋊C₄	—	2	2	no	—
258	C₇×C₄⋊C₄	—	2	2	no	—
259	C₇×C₄⋊C₄	—	2	2	no	—
260	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
261	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
262	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
263	C₇×C₂²⋊C₄	—	2	4	no	—
264	C₇×C₂²⋊C₄	—	2	4	no	—
265	C₇×C₂²⋊C₄	—	2	4	no	—
266	C₇×C₂²⋊C₄	—	2	4	no	—
267	C₇×C₂²⋊C₄	—	2	4	no	—
268	C₇×C₂²⋊C₄	—	2	4	no	—
269	C₄²×C₇	—	2	4	no	—
270	C₄²×C₇	—	2	4	no	—
271	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₇	C₂⁴	1	1	yes	characteristic
284	C₄²×C₇	C₂⁴	1	1	yes	characteristic
285	C₄²×C₇	C₂⁴	1	1	yes	characteristic
286	C₄²×C₇	C₂⁴	1	1	yes	characteristic
287	C₂²×#41	—	2	1	no	—
288	#533	—	2	1	no	—
289	#533	—	2	1	no	—
290	#533	—	2	1	no	—
291	#533	—	2	1	no	—
292	#533	C₂²×C₇	1	2	yes	—
293	#533	C₂²×C₇	1	2	yes	—
294	#533	C₂²×C₇	1	2	yes	complemented
295	#533	C₂²×C₇	1	2	yes	complemented
296	#532	—	2	1	no	—
297	#532	—	2	1	no	—
298	#532	—	2	1	no	—
299	#532	—	2	1	no	—
300	#532	C₂²×C₇	1	2	yes	—
301	#532	C₂²×C₇	1	2	yes	—
302	#532	C₂²×C₇	1	2	yes	—
303	#532	C₂²×C₇	1	2	yes	—
304	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
305	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
306	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
307	C₂×#127	C₂²×C₇	1	1	yes	characteristic
308	C₂×#125	C₂²×C₇	1	2	yes	complemented
309	C₂×#124	—	2	1	no	—
310	C₂×C₂²⋊Q₈	—	2	1	no	—
311	C₂×C₂²⋊Q₈	—	2	1	no	—
312	C₂×#121	—	2	1	no	—
313	C₂×#121	C₂²×C₇	1	2	yes	—
314	C₂×C₄×Q₈	—	2	1	no	—
315	C₂×C₄×Q₈	—	2	1	no	—
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
318	C₂×#117	C₂²×C₇	1	2	yes	—
319	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
320	#501	C₂²×C₇	1	8	yes	complemented
321	#500	C₂²×C₇	1	4	yes	complemented
322	#498	C₂²×C₇	1	4	yes	complemented
323	#490	C₂²×C₇	1	8	yes	complemented
324	#486	C₂²×C₇	1	4	yes	complemented
325	#486	C₂²×C₇	1	4	yes	complemented
326	#482	C₂²×C₇	1	16	yes	complemented
327	#481	C₂²×C₇	1	8	yes	complemented
328	#480	C₂²×C₇	1	8	yes	complemented
329	#478	C₂²×C₇	1	16	yes	complemented
330	#476	C₂²×C₇	1	8	yes	complemented
331	#474	C₂²×C₇	1	8	yes	complemented
332	#432	C₂²×C₇	1	2	yes	complemented
333	#432	C₂²×C₇	1	2	yes	complemented
334	#431	C₂²×C₇	1	2	yes	complemented
335	#431	C₂²×C₇	1	2	yes	complemented
336	#428	C₂²×C₇	1	8	yes	—
337	#423	C₂²×C₇	1	2	yes	—
338	#418	C₂²×C₇	1	8	yes	—
339	#407	C₂²×C₇	1	2	yes	—
340	C₄×M₁₆	C₂²×C₇	1	2	yes	—
341	C₂³×C₇	—	2	2	no	—
342	C₂³×C₇	—	2	2	no	—
343	C₂³×C₇	—	2	4	no	—
344	C₂³×C₇	—	4	1	no	—
345	C₂³×C₇	—	4	4	no	—
346	C₂³×C₇	—	4	4	no	—
347	C₂³×C₇	—	4	4	no	—
348	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
349	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
351	C₇×Q₈	—	4	4	no	—
352	C₇×Q₈	—	4	4	no	—
353	C₇×Q₈	—	4	4	no	—
354	C₇×Q₈	—	4	4	no	—
355	C₇×Q₈	—	4	4	no	—
356	C₇×Q₈	—	4	4	no	—
357	C₇×D₄	—	2	8	no	—
358	C₇×D₄	—	4	4	no	—
359	C₇×D₄	—	4	4	no	—
360	C₇×D₄	—	4	8	no	—
361	C₇×D₄	—	4	8	no	—
362	C₇×D₄	—	4	4	no	—
363	C₇×D₄	—	4	4	no	—
364	C₇×D₄	—	4	4	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	no	—
377	C₂×C₄×C₇	—	2	2	no	—
378	C₂×C₄×C₇	—	2	4	no	—
379	C₂×C₄×C₇	—	2	4	no	—
380	C₂×C₄×C₇	—	2	4	no	—
381	C₂×C₄×C₇	—	4	1	no	—
382	C₂×C₄×C₇	—	4	1	no	—
383	C₂×C₄×C₇	—	4	1	no	—
384	C₂×C₄×C₇	—	4	8	no	—
385	C₂×C₄×C₇	—	4	4	no	—
386	C₂×C₄×C₇	—	4	4	no	—
387	C₂×C₄×C₇	—	4	4	no	—
388	C₂×C₄×C₇	—	4	8	no	—
389	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
390	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
402	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
403	C₇×C₈	—	2	8	no	—
404	C₂×#41	—	2	2	no	—
405	C₂×#41	—	2	2	no	—
406	C₂×#41	—	2	2	no	—
407	C₂×#41	—	2	2	no	—
408	C₂×#41	—	4	8	no	—
409	C₂²×Q₈	—	2	1	no	—
410	C₂²×Q₈	—	2	1	no	—
411	C₂²×Q₈	—	2	1	no	—
412	C₂²×D₄	—	2	2	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	C₂³×C₇	1	2	yes	—
416	C₂³×C₄	—	2	2	no	—
417	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
418	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂×M₁₆	C₂³×C₇	1	4	yes	—
421	C₄⋊Q₈	—	2	1	no	—
422	C₄⋊Q₈	—	2	1	no	—
423	C₄⋊Q₈	—	2	1	no	—
424	C₄⋊Q₈	—	2	1	no	—
425	C₄⋊Q₈	—	2	1	no	—
426	C₄⋊Q₈	—	2	1	no	—
427	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
428	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
429	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
430	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
431	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
432	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
433	#127	—	2	1	no	—
434	#127	—	2	1	no	—
435	#127	C₂³×C₇	1	2	yes	—
436	#127	C₂³×C₇	1	2	yes	—
437	#125	—	2	2	no	—
438	#125	—	2	2	no	—
439	#125	C₂³×C₇	1	4	yes	—
440	#125	C₂³×C₇	1	4	yes	—
441	#124	—	2	2	no	—
442	#124	—	2	2	no	—
443	#124	—	2	2	no	—
444	#124	—	2	2	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	#121	—	2	2	no	—
454	#121	—	2	2	no	—
455	#121	—	2	2	no	—
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	C₂³×C₇	1	4	yes	—
460	#121	C₂³×C₇	1	4	yes	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	—	2	2	no	—
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	C₂³×C₇	1	4	yes	—
476	C₄×D₄	C₂³×C₇	1	4	yes	—
477	#117	—	2	2	no	—
478	#117	—	2	2	no	—
479	#117	C₂³×C₇	1	4	yes	—
480	#117	C₂³×C₇	1	4	yes	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	2	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
489	C₂×C₂²⋊C₄	—	2	2	no	—
490	C₂×C₂²⋊C₄	—	2	2	no	—
491	C₂×C₂²⋊C₄	—	2	2	no	—
492	C₂×C₄²	—	2	2	no	—
493	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
494	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
495	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
496	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
497	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
498	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
505	#107	C₂³×C₇	1	16	yes	—
506	#106	C₂³×C₇	1	16	yes	—
507	C₄⋊C₈	C₂³×C₇	1	4	yes	—
508	C₄⋊C₈	C₂³×C₇	1	4	yes	—
509	#102	C₂³×C₇	1	16	yes	—
510	#102	C₂³×C₇	1	16	yes	—
511	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
512	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
513	#97	C₂³×C₇	1	4	yes	—
514	C₄×C₈	C₂³×C₇	1	4	yes	—
515	C₂²×C₇	—	2	1	no	—
516	C₂²×C₇	—	2	1	no	—
517	C₂²×C₇	—	2	1	no	—
518	C₂²×C₇	—	2	1	no	—
519	C₂²×C₇	—	2	1	no	—
520	C₂²×C₇	—	2	1	no	—
521	C₂²×C₇	—	2	1	no	—
522	C₂²×C₇	—	4	4	no	—
523	C₂²×C₇	—	4	4	no	—
524	C₂²×C₇	—	4	4	no	—
525	C₂²×C₇	—	4	4	no	—
526	C₂²×C₇	—	8	8	no	—
527	C₂²×C₇	#536	1	2	yes	—
528	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
529	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
530	C₄×C₇	—	2	1	no	—
531	C₄×C₇	—	2	1	no	—
532	C₄×C₇	—	2	1	no	—
533	C₄×C₇	—	2	1	no	—
534	C₄×C₇	—	2	1	no	—
535	C₄×C₇	—	2	1	no	—
536	C₄×C₇	—	2	1	no	—
537	C₄×C₇	—	4	4	no	—
538	C₄×C₇	—	4	4	no	—
539	C₄×C₇	—	4	4	no	—
540	C₄×C₇	#536	1	2	yes	—
541	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
542	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
543	C₄×C₇	#575	1	2	yes	—
544	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
547	#41	—	4	8	no	—
548	#41	—	4	8	no	—
549	#41	—	4	8	no	—
550	#41	—	4	8	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	4	no	—
558	C₂×Q₈	—	4	4	no	—
559	C₂×Q₈	—	4	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	8	no	—
571	C₂×D₄	C₂⁴×C₇	1	4	yes	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	8	no	—
581	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
582	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
583	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
584	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
585	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
586	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
587	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
588	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
589	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
590	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
591	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
593	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
594	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
599	M₁₆	—	2	8	no	—
600	C₂×C₈	C₂⁴×C₇	1	8	yes	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
615	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
616	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
626	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
627	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
628	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
629	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
630	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
631	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
632	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
633	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
634	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
635	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
636	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
637	C₄²	C₂⁴×C₇	1	1	yes	characteristic
638	C₄²	C₂⁴×C₇	1	1	yes	characteristic
639	C₄²	C₂⁴×C₇	1	1	yes	characteristic
640	C₄²	C₂⁴×C₇	1	1	yes	characteristic
641	C₂×C₇	—	2	2	no	—
642	C₂×C₇	—	2	2	no	—
643	C₂×C₇	—	4	1	no	—
644	C₂×C₇	—	8	4	no	—
645	C₂×C₇	C₂×#536	1	1	yes	characteristic
646	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
647	C₂×C₇	C₂×#575	1	1	yes	characteristic
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
656	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
657	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
658	Q₈	—	4	4	no	—
659	Q₈	—	4	4	no	—
660	Q₈	—	4	4	no	—
661	Q₈	—	4	4	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	4	4	no	—
664	D₄	—	2	8	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	8	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
697	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
698	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
699	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
700	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
701	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
702	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
703	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
706	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
707	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
708	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
709	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
710	C₈	—	2	8	no	—
711	C₇	#60864	1	1	yes	characteristic, direct product factor, Sylow
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	8	8	no	—
724	C₂²	C₇×#536	1	2	yes	—
725	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
726	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	4	no	—
737	C₄	C₇×#536	1	2	yes	—
738	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
739	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
740	C₄	C₇×#575	1	2	yes	—
741	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	8	4	no	—
746	C₂	C₂×C₇×#536	1	1	yes	characteristic
747	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
748	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#532	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
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#3235	C₂	semidirect
4. C₇×#3234	C₂	semidirect
5. C₇×#3228	C₂	semidirect
6. C₇×#3227	C₂	semidirect
7. C₇×#3226	C₂	semidirect
8. C₇×#3165	C₂	semidirect
9. C₇×#3138	C₂	semidirect
10. C₇×#3094	C₂	semidirect
11. C₇×#3077	C₂	semidirect
12. C₇×#2920	C₂	semidirect
20. C₇×#533	C₂²	semidirect
21. C₇×#533	C₂²	semidirect
31. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₇×#125	C₂²	semidirect
46. C₇×#501	C₂²	semidirect
47. C₇×#500	C₂²	semidirect
48. C₇×#498	C₂²	semidirect
49. C₇×#490	C₂²	semidirect
50. C₇×#486	C₂²	semidirect
51. C₇×#486	C₂²	semidirect
52. C₇×#482	C₂²	semidirect
53. C₇×#481	C₂²	semidirect
54. C₇×#480	C₂²	semidirect
55. C₇×#478	C₂²	semidirect
56. C₇×#476	C₂²	semidirect
57. C₇×#474	C₂²	semidirect
58. C₇×#432	C₂²	semidirect
59. C₇×#432	C₂²	semidirect
60. C₇×#431	C₂²	semidirect
61. C₇×#431	C₂²	semidirect
67. #60864	C₇	direct (N × H)
179. C₂×#533	C₂×C₇	semidirect
181. #3235	C₂×C₇	semidirect
182. #3234	C₂×C₇	semidirect
183. #3228	C₂×C₇	semidirect
184. #3227	C₂×C₇	semidirect
185. #3226	C₂×C₇	semidirect
186. #3165	C₂×C₇	semidirect
187. #3138	C₂×C₇	semidirect
188. #3094	C₂×C₇	semidirect
189. #3077	C₂×C₇	semidirect
190. #2920	C₂×C₇	semidirect
294. #533	C₂²×C₇	semidirect
295. #533	C₂²×C₇	semidirect
305. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
306. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
308. C₂×#125	C₂²×C₇	semidirect
320. #501	C₂²×C₇	semidirect
321. #500	C₂²×C₇	semidirect
322. #498	C₂²×C₇	semidirect
323. #490	C₂²×C₇	semidirect
324. #486	C₂²×C₇	semidirect
325. #486	C₂²×C₇	semidirect
326. #482	C₂²×C₇	semidirect
327. #481	C₂²×C₇	semidirect
328. #480	C₂²×C₇	semidirect
329. #478	C₂²×C₇	semidirect
330. #476	C₂²×C₇	semidirect
331. #474	C₂²×C₇	semidirect
332. #432	C₂²×C₇	semidirect
333. #432	C₂²×C₇	semidirect
334. #431	C₂²×C₇	semidirect
335. #431	C₂²×C₇	semidirect
711. C₇	#60864	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#533	2
C₂×C₇×#532	2
C₇×#3235	2
C₇×#3234	2
C₇×#3228	2
C₇×#3227	2
C₇×#3226	2
C₇×#3165	2
C₇×#3138	2
C₇×#3094	2
C₇×#3077	2
C₇×#2920	2
#60864	7

Subgroups — C7×#60864 #13238080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60864 #13238080