Subgroups — C₇×#34634 #13211850

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 422 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	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic
3	C₇×#2629	C₂	1	4	yes	maximal, complemented
4	C₇×#2628	C₂	1	4	yes	maximal, complemented
5	C₇×#2627	C₂	1	4	yes	maximal, complemented
6	C₇×#2626	C₂	1	4	yes	maximal
7	C₇×#2396	C₂	1	8	yes	maximal, complemented
8	C₇×#2296	C₂	1	2	yes	maximal, complemented
9	C₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2280	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
12	C₇×#533	—	2	8	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
14	C₂×C₇×#125	C₂²	1	2	yes	complemented
15	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
16	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
17	C₂×C₇×#117	—	2	8	no	—
18	C₂×C₇×#117	C₂²	1	4	yes	—
19	C₂×C₇×#117	C₂²	1	2	yes	—
20	C₂×C₇×#117	C₂²	1	2	yes	—
21	C₂×C₇×#117	C₂²	1	2	yes	—
22	C₂×C₇×#117	C₂²	1	2	yes	—
23	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
27	C₇×#400	C₂²	1	8	yes	complemented
28	C₇×#399	C₂²	1	8	yes	—
29	C₇×#398	C₂²	1	16	yes	complemented
30	C₇×#396	C₂²	1	16	yes	—
31	C₇×#395	C₂²	1	8	yes	complemented
32	C₇×#393	C₂²	1	8	yes	—
33	C₇×#389	C₂²	1	8	yes	complemented
34	C₇×#385	C₂²	1	8	yes	—
35	C₇×#384	C₂²	1	2	yes	complemented
36	C₇×#382	C₂²	1	2	yes	complemented
37	C₇×#381	C₂²	1	4	yes	—
38	C₇×#380	C₂²	1	8	yes	—
39	C₇×#380	C₂²	1	4	yes	—
40	C₇×#379	C₂²	1	4	yes	—
41	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
42	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
44	#34634	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁵×C₇	C₂³	1	1	yes	characteristic
46	C₂²×C₇×Q₈	C₂³	1	4	yes	—
47	C₂³×C₄×C₇	—	2	4	no	—
48	C₂³×C₄×C₇	—	2	4	no	—
49	C₂³×C₄×C₇	Q₈	1	8	yes	complemented
50	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
56	C₇×C₄⋊Q₈	—	2	8	no	—
57	C₇×#125	—	2	8	no	—
58	C₇×C₂²⋊Q₈	—	2	16	no	—
59	C₄×C₇×Q₈	—	2	16	no	—
60	C₇×#117	—	2	8	no	—
61	C₇×#117	—	2	8	no	—
62	C₇×#117	—	2	16	no	—
63	C₇×#117	—	2	8	no	—
64	C₇×#117	—	2	8	no	—
65	C₂×C₇×C₄⋊C₄	—	2	8	no	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
74	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
75	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
77	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
78	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
79	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
80	C₂×C₄²×C₇	—	2	4	no	—
81	C₂×C₄²×C₇	D₄	1	8	yes	—
82	C₂×C₄²×C₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₇	C₂³	1	4	yes	—
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	2	yes	—
89	C₇×#95	C₂³	1	16	yes	—
90	C₇×#95	C₂³	1	8	yes	—
91	C₇×#95	C₂³	1	16	yes	—
92	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂²×#117	C₂×C₇	1	1	yes	characteristic
94	#2629	C₂×C₇	1	4	yes	complemented
95	#2628	C₂×C₇	1	4	yes	complemented
96	#2627	C₂×C₇	1	4	yes	complemented
97	#2626	C₂×C₇	1	4	yes	—
98	#2396	C₂×C₇	1	8	yes	complemented
99	#2296	C₂×C₇	1	2	yes	complemented
100	#2285	C₂×C₇	1	1	yes	characteristic, complemented
101	#2280	C₂×C₇	1	2	yes	—
102	C₂⁴×C₇	—	2	2	no	—
103	C₂⁴×C₇	—	2	2	no	—
104	C₂⁴×C₇	—	4	4	no	—
105	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
106	C₂⁴×C₇	C₂⁴	1	2	yes	—
107	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₇×Q₈	—	2	8	no	—
109	C₂×C₇×Q₈	—	4	8	no	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	32	no	—
113	C₂²×C₄×C₇	—	2	4	no	—
114	C₂²×C₄×C₇	—	2	4	no	—
115	C₂²×C₄×C₇	—	2	4	no	—
116	C₂²×C₄×C₇	—	2	4	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	4	4	no	—
119	C₂²×C₄×C₇	—	4	4	no	—
120	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
123	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
124	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
125	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₇	#41	1	4	yes	—
127	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
135	C₇×C₄⋊C₄	—	2	8	no	—
136	C₇×C₄⋊C₄	—	2	8	no	—
137	C₇×C₄⋊C₄	—	2	8	no	—
138	C₇×C₄⋊C₄	—	2	16	no	—
139	C₇×C₄⋊C₄	—	2	8	no	—
140	C₇×C₄⋊C₄	—	2	8	no	—
141	C₇×C₄⋊C₄	—	4	8	no	—
142	C₇×C₄⋊C₄	—	4	16	no	—
143	C₇×C₂²⋊C₄	—	2	8	no	—
144	C₇×C₂²⋊C₄	—	2	8	no	—
145	C₇×C₂²⋊C₄	—	2	8	no	—
146	C₇×C₂²⋊C₄	—	2	8	no	—
147	C₇×C₂²⋊C₄	—	4	16	no	—
148	C₄²×C₇	—	2	4	no	—
149	C₄²×C₇	—	2	4	no	—
150	C₄²×C₇	—	2	8	no	—
151	C₄²×C₇	—	2	8	no	—
152	C₄²×C₇	C₂×D₄	1	8	yes	—
153	C₄²×C₇	C₂×D₄	1	4	yes	—
154	C₄²×C₇	C₂×D₄	1	4	yes	—
155	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
156	#533	—	2	8	no	—
157	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
158	C₂×#125	C₂²×C₇	1	2	yes	complemented
159	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
160	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
161	C₂×#117	—	2	8	no	—
162	C₂×#117	C₂²×C₇	1	2	yes	—
163	C₂×#117	C₂²×C₇	1	2	yes	—
164	C₂×#117	C₂²×C₇	1	4	yes	—
165	C₂×#117	C₂²×C₇	1	2	yes	—
166	C₂×#117	C₂²×C₇	1	2	yes	—
167	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
168	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
169	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
170	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
171	#400	C₂²×C₇	1	8	yes	complemented
172	#399	C₂²×C₇	1	8	yes	—
173	#398	C₂²×C₇	1	16	yes	complemented
174	#396	C₂²×C₇	1	16	yes	—
175	#395	C₂²×C₇	1	8	yes	complemented
176	#393	C₂²×C₇	1	8	yes	—
177	#389	C₂²×C₇	1	8	yes	complemented
178	#385	C₂²×C₇	1	8	yes	—
179	#384	C₂²×C₇	1	2	yes	complemented
180	#382	C₂²×C₇	1	2	yes	complemented
181	#381	C₂²×C₇	1	4	yes	—
182	#380	C₂²×C₇	1	4	yes	—
183	#380	C₂²×C₇	1	8	yes	—
184	#379	C₂²×C₇	1	4	yes	—
185	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
186	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
187	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
188	C₂³×C₇	—	2	4	no	—
189	C₂³×C₇	—	2	8	no	—
190	C₂³×C₇	—	2	2	no	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	2	8	no	—
193	C₂³×C₇	—	4	8	no	—
194	C₂³×C₇	—	4	8	no	—
195	C₂³×C₇	—	4	8	no	—
196	C₂³×C₇	C₂²×D₄	1	2	yes	—
197	C₂³×C₇	C₂²×Q₈	1	4	yes	—
198	C₂³×C₇	C₂²×Q₈	1	2	yes	—
199	C₂³×C₇	C₂×#41	1	2	yes	—
200	C₂³×C₇	C₂⁵	1	1	yes	characteristic
201	C₇×Q₈	—	4	16	no	—
202	C₂×C₄×C₇	—	2	8	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	4	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	16	no	—
208	C₂×C₄×C₇	—	2	16	no	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	8	no	—
211	C₂×C₄×C₇	—	2	8	no	—
212	C₂×C₄×C₇	—	2	16	no	—
213	C₂×C₄×C₇	—	2	16	no	—
214	C₂×C₄×C₇	—	2	8	no	—
215	C₂×C₄×C₇	—	4	8	no	—
216	C₂×C₄×C₇	—	4	8	no	—
217	C₂×C₄×C₇	C₂²⋊Q₈	1	16	yes	—
218	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
223	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
224	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
225	C₂×C₄×C₇	C₂×#41	1	2	yes	—
226	C₂×C₄×C₇	C₂×#41	1	2	yes	—
227	C₂⁵	C₂³×C₇	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₇	1	4	yes	—
229	C₂³×C₄	—	2	4	no	—
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	C₇×Q₈	1	8	yes	complemented
232	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₇	1	2	yes	—
234	C₂³×C₄	C₂³×C₇	1	2	yes	—
235	C₂³×C₄	C₂³×C₇	1	2	yes	—
236	C₂³×C₄	C₂³×C₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	8	no	—
239	#125	—	2	8	no	—
240	C₂²⋊Q₈	—	2	16	no	—
241	C₄×Q₈	—	2	16	no	—
242	#117	—	2	8	no	—
243	#117	—	2	8	no	—
244	#117	—	2	16	no	—
245	#117	—	2	8	no	—
246	#117	—	2	8	no	—
247	C₂×C₄⋊C₄	—	2	8	no	—
248	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
249	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
250	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
251	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
252	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
253	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
255	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
256	C₂×C₂²⋊C₄	—	2	8	no	—
257	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	C₇×D₄	1	8	yes	—
264	C₂×C₄²	C₂³×C₇	1	2	yes	—
265	C₂×C₄²	C₂³×C₇	1	2	yes	—
266	C₂×C₄²	C₂³×C₇	1	4	yes	—
267	C₂×C₄²	C₂³×C₇	1	4	yes	—
268	C₂×C₄²	C₂³×C₇	1	2	yes	—
269	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
271	#95	C₂³×C₇	1	16	yes	—
272	#95	C₂³×C₇	1	8	yes	—
273	#95	C₂³×C₇	1	16	yes	—
274	C₂²×C₇	—	2	4	no	—
275	C₂²×C₇	—	2	4	no	—
276	C₂²×C₇	—	2	4	no	—
277	C₂²×C₇	—	2	4	no	—
278	C₂²×C₇	—	2	8	no	—
279	C₂²×C₇	—	4	16	no	—
280	C₂²×C₇	—	4	4	no	—
281	C₂²×C₇	—	4	4	no	—
282	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
283	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
284	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
285	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
286	C₂²×C₇	#585	1	4	yes	—
287	C₄×C₇	—	2	4	no	—
288	C₄×C₇	—	2	4	no	—
289	C₄×C₇	—	2	4	no	—
290	C₄×C₇	—	4	4	no	—
291	C₄×C₇	—	4	8	no	—
292	C₄×C₇	—	4	8	no	—
293	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
294	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	4	4	no	—
298	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
299	C₂⁴	C₂⁴×C₇	1	2	yes	—
300	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
301	C₂×Q₈	—	2	8	no	—
302	C₂×Q₈	—	4	8	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	32	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
314	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
315	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
316	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
317	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
318	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
319	C₂²×C₄	C₇×#41	1	4	yes	—
320	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
321	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
323	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	16	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	—	4	16	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	4	16	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	8	no	—
344	C₄²	—	2	8	no	—
345	C₄²	C₂×C₇×D₄	1	8	yes	—
346	C₄²	C₂×C₇×D₄	1	4	yes	—
347	C₄²	C₂×C₇×D₄	1	4	yes	—
348	C₂×C₇	—	2	4	no	—
349	C₂×C₇	—	4	4	no	—
350	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂×C₇	#3449	1	2	yes	—
352	C₂×C₇	#3455	1	2	yes	—
353	C₂×C₇	#3458	1	2	yes	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	4	8	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	C₂²×C₇×D₄	1	2	yes	—
363	C₂³	C₂²×C₇×Q₈	1	4	yes	—
364	C₂³	C₂²×C₇×Q₈	1	2	yes	—
365	C₂³	C₂×C₇×#41	1	2	yes	—
366	C₂³	C₂⁵×C₇	1	1	yes	characteristic
367	Q₈	—	4	16	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	16	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	16	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	C₇×C₂²⋊Q₈	1	16	yes	—
384	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
385	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
386	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
387	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
388	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
389	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
390	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
391	C₂×C₄	C₂×C₇×#41	1	2	yes	—
392	C₂×C₄	C₂×C₇×#41	1	2	yes	—
393	C₇	#34634	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	16	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
403	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
404	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
405	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
406	C₂²	C₇×#585	1	4	yes	—
407	C₄	—	2	4	no	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	4	8	no	—
413	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
414	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
415	C₂	—	2	4	no	—
416	C₂	—	4	4	no	—
417	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
418	C₂	C₇×#3449	1	2	yes	—
419	C₂	C₇×#3455	1	2	yes	—
420	C₂	C₇×#3458	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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×#2629	C₂	semidirect
4. C₇×#2628	C₂	semidirect
5. C₇×#2627	C₂	semidirect
7. C₇×#2396	C₂	semidirect
8. C₇×#2296	C₂	semidirect
9. C₇×#2285	C₂	semidirect
13. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
14. C₂×C₇×#125	C₂²	semidirect
16. C₂×C₄×C₇×Q₈	C₂²	semidirect
27. C₇×#400	C₂²	semidirect
29. C₇×#398	C₂²	semidirect
31. C₇×#395	C₂²	semidirect
33. C₇×#389	C₂²	semidirect
35. C₇×#384	C₂²	semidirect
36. C₇×#382	C₂²	semidirect
41. C₄×C₇×C₄⋊C₄	C₂²	semidirect
42. C₄×C₇×C₄⋊C₄	C₂²	semidirect
44. #34634	C₇	direct (N × H)
49. C₂³×C₄×C₇	Q₈	semidirect
92. C₂×#533	C₂×C₇	semidirect
94. #2629	C₂×C₇	semidirect
95. #2628	C₂×C₇	semidirect
96. #2627	C₂×C₇	semidirect
98. #2396	C₂×C₇	semidirect
99. #2296	C₂×C₇	semidirect
100. #2285	C₂×C₇	semidirect
157. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
158. C₂×#125	C₂²×C₇	semidirect
160. C₂×C₄×Q₈	C₂²×C₇	semidirect
171. #400	C₂²×C₇	semidirect
173. #398	C₂²×C₇	semidirect
175. #395	C₂²×C₇	semidirect
177. #389	C₂²×C₇	semidirect
179. #384	C₂²×C₇	semidirect
180. #382	C₂²×C₇	semidirect
185. C₄×C₄⋊C₄	C₂²×C₇	semidirect
186. C₄×C₄⋊C₄	C₂²×C₇	semidirect
231. C₂³×C₄	C₇×Q₈	semidirect
393. C₇	#34634	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
C₂²×C₇×#117	2
C₇×#2629	2
C₇×#2628	2
C₇×#2627	2
C₇×#2626	2
C₇×#2396	2
C₇×#2296	2
C₇×#2285	2
C₇×#2280	2
#34634	7

Subgroups — C7×#34634 #13211850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34634 #13211850