Subgroups — C₇×#34982 #13212198

Order 1792.

4046 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#2848	C₂	1	4	yes	maximal, complemented
4	C₇×#2626	C₂	1	4	yes	maximal, complemented
5	C₇×#2437	C₂	1	16	yes	maximal, complemented
6	C₇×#2315	C₂	1	2	yes	maximal, complemented
7	C₇×#2315	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#379	C₂	1	2	yes	maximal
9	C₂⁶×C₇	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
11	C₇×#543	—	2	8	no	—
12	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
13	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
14	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
15	C₂²×C₇×C₂²⋊C₄	—	2	8	no	—
16	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
17	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
22	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₇×#399	C₂²	1	8	yes	complemented
24	C₇×#396	C₂²	1	16	yes	complemented
25	C₇×#393	C₂²	1	8	yes	complemented
26	C₇×#385	C₂²	1	8	yes	complemented
27	C₇×#385	C₂²	1	8	yes	complemented
28	C₇×#385	C₂²	1	16	yes	complemented
29	C₇×#385	C₂²	1	8	yes	complemented
30	C₇×#380	C₂²	1	8	yes	complemented
31	C₇×#380	C₂²	1	8	yes	complemented
32	C₇×#380	C₂²	1	4	yes	complemented
33	C₇×#379	C₂²	1	8	yes	—
34	C₇×#379	C₂²	1	4	yes	—
35	C₇×#379	C₂²	1	4	yes	—
36	#34982	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁵×C₇	—	2	4	no	—
38	C₂⁵×C₇	—	2	4	no	—
39	C₂⁵×C₇	—	4	8	no	—
40	C₂⁵×C₇	Q₈	1	8	yes	complemented
41	C₂⁵×C₇	C₂³	1	1	yes	characteristic
42	C₂⁵×C₇	C₂³	1	4	yes	—
43	C₂⁵×C₇	C₂³	1	1	yes	characteristic
44	C₂⁵×C₇	C₂³	1	1	yes	characteristic
45	C₂²×C₇×Q₈	C₂³	1	4	yes	complemented
46	C₂³×C₄×C₇	—	2	8	no	—
47	C₂³×C₄×C₇	—	4	8	no	—
48	C₂³×C₄×C₇	C₂³	1	8	yes	—
49	C₂³×C₄×C₇	C₂³	1	4	yes	—
50	C₂³×C₄×C₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₇×C₂²⋊Q₈	—	2	16	no	—
54	C₇×C₂²⋊Q₈	—	2	32	no	—
55	C₇×C₂²⋊Q₈	—	4	16	no	—
56	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
57	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
58	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
59	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
60	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
61	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
62	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
63	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
64	C₂×C₇×C₂²⋊C₄	—	2	32	no	—
65	C₂×C₇×C₂²⋊C₄	—	4	16	no	—
66	C₂×C₇×C₂²⋊C₄	D₄	1	8	yes	—
67	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
68	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
69	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
70	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
71	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
72	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
73	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
75	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₇×#95	C₂³	1	16	yes	complemented
77	C₇×#95	C₂³	1	8	yes	complemented
78	C₂×#543	C₂×C₇	1	1	yes	characteristic, complemented
79	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
80	#2848	C₂×C₇	1	4	yes	complemented
81	#2626	C₂×C₇	1	4	yes	complemented
82	#2437	C₂×C₇	1	16	yes	complemented
83	#2315	C₂×C₇	1	2	yes	complemented
84	#2315	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂×#379	C₂×C₇	1	2	yes	—
86	C₂⁴×C₇	—	2	2	no	—
87	C₂⁴×C₇	—	2	2	no	—
88	C₂⁴×C₇	—	2	8	no	—
89	C₂⁴×C₇	—	2	32	no	—
90	C₂⁴×C₇	—	2	8	no	—
91	C₂⁴×C₇	—	2	2	no	—
92	C₂⁴×C₇	—	2	8	no	—
93	C₂⁴×C₇	—	2	2	no	—
94	C₂⁴×C₇	—	2	16	no	—
95	C₂⁴×C₇	—	4	32	no	—
96	C₂⁴×C₇	—	4	4	no	—
97	C₂⁴×C₇	—	4	8	no	—
98	C₂⁴×C₇	—	4	4	no	—
99	C₂⁴×C₇	—	4	32	no	—
100	C₂⁴×C₇	—	4	32	no	—
101	C₂⁴×C₇	C₂×D₄	1	4	yes	—
102	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
103	C₂⁴×C₇	C₂×Q₈	1	16	yes	—
104	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
105	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
106	C₂⁴×C₇	#41	1	4	yes	—
107	C₂⁴×C₇	C₂⁴	1	2	yes	—
108	C₂⁴×C₇	C₂⁴	1	2	yes	—
109	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
110	C₂⁴×C₇	C₂⁴	1	2	yes	—
111	C₂×C₇×Q₈	—	2	8	no	—
112	C₂×C₇×Q₈	—	4	8	no	—
113	C₂²×C₄×C₇	—	2	4	no	—
114	C₂²×C₄×C₇	—	2	16	no	—
115	C₂²×C₄×C₇	—	2	8	no	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	16	no	—
118	C₂²×C₄×C₇	—	4	4	no	—
119	C₂²×C₄×C₇	—	4	8	no	—
120	C₂²×C₄×C₇	—	4	4	no	—
121	C₂²×C₄×C₇	—	4	8	no	—
122	C₂²×C₄×C₇	—	4	8	no	—
123	C₂²×C₄×C₇	—	4	32	no	—
124	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
125	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
126	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
129	C₇×C₄⋊C₄	—	2	8	no	—
130	C₇×C₄⋊C₄	—	2	16	no	—
131	C₇×C₄⋊C₄	—	4	8	no	—
132	C₇×C₄⋊C₄	—	4	16	no	—
133	C₇×C₂²⋊C₄	—	2	8	no	—
134	C₇×C₂²⋊C₄	—	2	8	no	—
135	C₇×C₂²⋊C₄	—	2	8	no	—
136	C₇×C₂²⋊C₄	—	2	8	no	—
137	C₇×C₂²⋊C₄	—	2	8	no	—
138	C₇×C₂²⋊C₄	—	2	32	no	—
139	C₇×C₂²⋊C₄	—	2	16	no	—
140	C₇×C₂²⋊C₄	—	4	16	no	—
141	C₇×C₂²⋊C₄	C₂×D₄	1	16	yes	—
142	C₂⁶	C₂²×C₇	1	1	yes	characteristic
143	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
144	#543	—	2	8	no	—
145	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
146	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
147	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
148	C₂²×C₂²⋊C₄	—	2	8	no	—
149	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
150	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
151	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
152	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
153	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
154	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
155	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
156	#399	C₂²×C₇	1	8	yes	complemented
157	#396	C₂²×C₇	1	16	yes	complemented
158	#393	C₂²×C₇	1	8	yes	complemented
159	#385	C₂²×C₇	1	8	yes	complemented
160	#385	C₂²×C₇	1	8	yes	complemented
161	#385	C₂²×C₇	1	8	yes	complemented
162	#385	C₂²×C₇	1	16	yes	complemented
163	#380	C₂²×C₇	1	4	yes	complemented
164	#380	C₂²×C₇	1	8	yes	complemented
165	#380	C₂²×C₇	1	8	yes	complemented
166	#379	C₂²×C₇	1	4	yes	—
167	#379	C₂²×C₇	1	4	yes	—
168	#379	C₂²×C₇	1	8	yes	—
169	C₂³×C₇	—	2	16	no	—
170	C₂³×C₇	—	2	16	no	—
171	C₂³×C₇	—	2	8	no	—
172	C₂³×C₇	—	2	16	no	—
173	C₂³×C₇	—	2	2	no	—
174	C₂³×C₇	—	2	2	no	—
175	C₂³×C₇	—	2	4	no	—
176	C₂³×C₇	—	2	4	no	—
177	C₂³×C₇	—	2	8	no	—
178	C₂³×C₇	—	2	32	no	—
179	C₂³×C₇	—	2	8	no	—
180	C₂³×C₇	—	2	32	no	—
181	C₂³×C₇	—	2	2	no	—
182	C₂³×C₇	—	2	2	no	—
183	C₂³×C₇	—	2	8	no	—
184	C₂³×C₇	—	4	8	no	—
185	C₂³×C₇	—	4	8	no	—
186	C₂³×C₇	—	4	16	no	—
187	C₂³×C₇	—	4	8	no	—
188	C₂³×C₇	—	4	8	no	—
189	C₂³×C₇	—	4	32	no	—
190	C₂³×C₇	—	4	32	no	—
191	C₂³×C₇	—	4	128	no	—
192	C₂³×C₇	—	4	8	no	—
193	C₂³×C₇	—	4	8	no	—
194	C₂³×C₇	C₂²⋊Q₈	1	16	yes	complemented
195	C₂³×C₇	C₂²×D₄	1	4	yes	—
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	C₂²×Q₈	1	4	yes	—
200	C₂³×C₇	C₂²×Q₈	1	4	yes	—
201	C₂³×C₇	C₂×#41	1	2	yes	—
202	C₂³×C₇	C₂×#41	1	4	yes	—
203	C₂³×C₇	H(5,𝔽₂)	1	8	yes	—
204	C₂³×C₇	C₂⁵	1	1	yes	characteristic
205	C₇×Q₈	—	8	8	no	—
206	C₂×C₄×C₇	—	2	8	no	—
207	C₂×C₄×C₇	—	2	4	no	—
208	C₂×C₄×C₇	—	2	8	no	—
209	C₂×C₄×C₇	—	2	8	no	—
210	C₂×C₄×C₇	—	2	16	no	—
211	C₂×C₄×C₇	—	2	16	no	—
212	C₂×C₄×C₇	—	2	8	no	—
213	C₂×C₄×C₇	—	4	8	no	—
214	C₂×C₄×C₇	—	4	32	no	—
215	C₂×C₄×C₇	—	4	8	no	—
216	C₂×C₄×C₇	—	8	8	no	—
217	C₂×C₄×C₇	—	8	8	no	—
218	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
219	C₂⁵	—	2	4	no	—
220	C₂⁵	—	2	4	no	—
221	C₂⁵	—	4	8	no	—
222	C₂⁵	C₇×Q₈	1	8	yes	complemented
223	C₂⁵	C₂³×C₇	1	1	yes	characteristic
224	C₂⁵	C₂³×C₇	1	4	yes	—
225	C₂⁵	C₂³×C₇	1	1	yes	characteristic
226	C₂⁵	C₂³×C₇	1	1	yes	characteristic
227	C₂²×Q₈	C₂³×C₇	1	4	yes	complemented
228	C₂³×C₄	—	2	8	no	—
229	C₂³×C₄	—	4	8	no	—
230	C₂³×C₄	C₂³×C₇	1	8	yes	—
231	C₂³×C₄	C₂³×C₇	1	4	yes	—
232	C₂³×C₄	C₂³×C₇	1	4	yes	—
233	C₂³×C₄	C₂³×C₇	1	2	yes	—
234	C₂³×C₄	C₂³×C₇	1	2	yes	—
235	C₂²⋊Q₈	—	2	16	no	—
236	C₂²⋊Q₈	—	2	32	no	—
237	C₂²⋊Q₈	—	4	16	no	—
238	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
239	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
240	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
241	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	8	no	—
244	C₂×C₂²⋊C₄	—	2	8	no	—
245	C₂×C₂²⋊C₄	—	2	8	no	—
246	C₂×C₂²⋊C₄	—	2	32	no	—
247	C₂×C₂²⋊C₄	—	4	16	no	—
248	C₂×C₂²⋊C₄	C₇×D₄	1	8	yes	—
249	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
251	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
258	#95	C₂³×C₇	1	16	yes	complemented
259	#95	C₂³×C₇	1	8	yes	complemented
260	C₂²×C₇	—	2	32	no	—
261	C₂²×C₇	—	2	4	no	—
262	C₂²×C₇	—	2	4	no	—
263	C₂²×C₇	—	2	4	no	—
264	C₂²×C₇	—	2	8	no	—
265	C₂²×C₇	—	2	4	no	—
266	C₂²×C₇	—	2	8	no	—
267	C₂²×C₇	—	2	8	no	—
268	C₂²×C₇	—	2	8	no	—
269	C₂²×C₇	—	2	4	no	—
270	C₂²×C₇	—	2	8	no	—
271	C₂²×C₇	—	2	4	no	—
272	C₂²×C₇	—	2	8	no	—
273	C₂²×C₇	—	4	16	no	—
274	C₂²×C₇	—	4	64	no	—
275	C₂²×C₇	—	4	16	no	—
276	C₂²×C₇	—	4	4	no	—
277	C₂²×C₇	—	4	4	no	—
278	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
279	C₂²×C₇	C₂×C₂²⋊Q₈	1	8	yes	—
280	C₂²×C₇	#543	1	8	yes	complemented
281	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
282	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
283	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
284	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
285	C₄×C₇	—	2	8	no	—
286	C₄×C₇	—	4	4	no	—
287	C₄×C₇	—	4	8	no	—
288	C₄×C₇	—	4	8	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	—	2	8	no	—
292	C₂⁴	—	2	32	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	2	16	no	—
298	C₂⁴	—	4	32	no	—
299	C₂⁴	—	4	4	no	—
300	C₂⁴	—	4	8	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	—	4	32	no	—
303	C₂⁴	—	4	32	no	—
304	C₂⁴	C₂×C₇×D₄	1	4	yes	—
305	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
306	C₂⁴	C₂×C₇×Q₈	1	16	yes	—
307	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
308	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
309	C₂⁴	C₇×#41	1	4	yes	—
310	C₂⁴	C₂⁴×C₇	1	2	yes	—
311	C₂⁴	C₂⁴×C₇	1	2	yes	—
312	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
313	C₂⁴	C₂⁴×C₇	1	2	yes	—
314	C₂×Q₈	—	2	8	no	—
315	C₂×Q₈	—	4	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	16	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	16	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	—	4	8	no	—
326	C₂²×C₄	—	4	32	no	—
327	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
328	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
329	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	16	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	—	2	8	no	—
341	C₂²⋊C₄	—	2	32	no	—
342	C₂²⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	4	16	no	—
344	C₂²⋊C₄	C₂×C₇×D₄	1	16	yes	—
345	C₂×C₇	—	2	4	no	—
346	C₂×C₇	—	2	8	no	—
347	C₂×C₇	—	2	8	no	—
348	C₂×C₇	—	4	4	no	—
349	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
350	C₂×C₇	C₂×#543	1	2	yes	—
351	C₂×C₇	#3484	1	2	yes	—
352	C₂×C₇	#3490	1	2	yes	—
353	C₂³	—	2	16	no	—
354	C₂³	—	2	16	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	16	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	32	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	2	32	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	16	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	32	no	—
374	C₂³	—	4	32	no	—
375	C₂³	—	4	128	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	8	no	—
378	C₂³	C₇×C₂²⋊Q₈	1	16	yes	complemented
379	C₂³	C₂²×C₇×D₄	1	4	yes	—
380	C₂³	C₂²×C₇×D₄	1	2	yes	—
381	C₂³	C₂²×C₇×Q₈	1	4	yes	—
382	C₂³	C₂²×C₇×Q₈	1	2	yes	—
383	C₂³	C₂²×C₇×Q₈	1	4	yes	—
384	C₂³	C₂²×C₇×Q₈	1	4	yes	—
385	C₂³	C₂×C₇×#41	1	2	yes	—
386	C₂³	C₂×C₇×#41	1	4	yes	—
387	C₂³	C₇×H(5,𝔽₂)	1	8	yes	—
388	C₂³	C₂⁵×C₇	1	1	yes	characteristic
389	Q₈	—	8	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	16	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	32	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	8	8	no	—
401	C₂×C₄	—	8	8	no	—
402	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
403	C₇	#34982	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	32	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	16	no	—
418	C₂²	—	4	64	no	—
419	C₂²	—	4	16	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
423	C₂²	C₂×C₇×C₂²⋊Q₈	1	8	yes	—
424	C₂²	C₇×#543	1	8	yes	complemented
425	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
426	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
427	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
428	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
429	C₄	—	2	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	8	no	—
432	C₄	—	4	8	no	—
433	C₂	—	2	4	no	—
434	C₂	—	2	8	no	—
435	C₂	—	2	8	no	—
436	C₂	—	4	4	no	—
437	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂	C₂×C₇×#543	1	2	yes	—
439	C₂	C₇×#3484	1	2	yes	—
440	C₂	C₇×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁶×C₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#543	C₂	semidirect
3. C₇×#2848	C₂	semidirect
4. C₇×#2626	C₂	semidirect
5. C₇×#2437	C₂	semidirect
6. C₇×#2315	C₂	semidirect
7. C₇×#2315	C₂	semidirect
12. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
13. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
14. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
23. C₇×#399	C₂²	semidirect
24. C₇×#396	C₂²	semidirect
25. C₇×#393	C₂²	semidirect
26. C₇×#385	C₂²	semidirect
27. C₇×#385	C₂²	semidirect
28. C₇×#385	C₂²	semidirect
29. C₇×#385	C₂²	semidirect
30. C₇×#380	C₂²	semidirect
31. C₇×#380	C₂²	semidirect
32. C₇×#380	C₂²	semidirect
36. #34982	C₇	direct (N × H)
40. C₂⁵×C₇	Q₈	semidirect
45. C₂²×C₇×Q₈	C₂³	semidirect
56. C₂×C₇×C₄⋊C₄	C₂³	semidirect
57. C₂×C₇×C₄⋊C₄	C₂³	semidirect
58. C₂×C₇×C₄⋊C₄	C₂³	semidirect
59. C₂×C₇×C₄⋊C₄	C₂³	semidirect
76. C₇×#95	C₂³	semidirect
77. C₇×#95	C₂³	semidirect
78. C₂×#543	C₂×C₇	semidirect
80. #2848	C₂×C₇	semidirect
81. #2626	C₂×C₇	semidirect
82. #2437	C₂×C₇	semidirect
83. #2315	C₂×C₇	semidirect
84. #2315	C₂×C₇	semidirect
145. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
146. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
147. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
156. #399	C₂²×C₇	semidirect
157. #396	C₂²×C₇	semidirect
158. #393	C₂²×C₇	semidirect
159. #385	C₂²×C₇	semidirect
160. #385	C₂²×C₇	semidirect
161. #385	C₂²×C₇	semidirect
162. #385	C₂²×C₇	semidirect
163. #380	C₂²×C₇	semidirect
164. #380	C₂²×C₇	semidirect
165. #380	C₂²×C₇	semidirect
194. C₂³×C₇	C₂²⋊Q₈	semidirect
222. C₂⁵	C₇×Q₈	semidirect
227. C₂²×Q₈	C₂³×C₇	semidirect
238. C₂×C₄⋊C₄	C₂³×C₇	semidirect
239. C₂×C₄⋊C₄	C₂³×C₇	semidirect
240. C₂×C₄⋊C₄	C₂³×C₇	semidirect
241. C₂×C₄⋊C₄	C₂³×C₇	semidirect
258. #95	C₂³×C₇	semidirect
259. #95	C₂³×C₇	semidirect
280. C₂²×C₇	#543	semidirect
378. C₂³	C₇×C₂²⋊Q₈	semidirect
403. C₇	#34982	direct (N × H)
424. C₂²	C₇×#543	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#543	2
C₂³×C₇×C₂²⋊C₄	2
C₇×#2848	2
C₇×#2626	2
C₇×#2437	2
C₇×#2315	2
C₂×C₇×#379	2
#34982	7

Subgroups — C7×#34982 #13212198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34982 #13212198