Subgroups — C₂×C₇×#2965 #13237413

Order 1792.

2286 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#2965	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#446	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#435	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#431	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₇×M₁₆	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×#41	C₄	1	1	yes	characteristic
11	C₂²×C₇×M₁₆	C₂²	1	4	yes	—
12	C₂³×C₇×C₈	C₂²	1	2	yes	—
13	C₄×C₇×#41	C₄	1	8	yes	—
14	C₄×C₇×#41	C₂²	1	8	yes	—
15	C₂×C₄×C₇×Q₈	C₄	1	1	yes	characteristic
16	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₄	1	2	yes	—
18	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₄	1	2	yes	—
22	C₂×C₇×#117	C₄	1	1	yes	characteristic
23	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	2	yes	—
25	C₇×#446	C₂²	1	16	yes	complemented
26	C₇×#436	C₂²	1	16	yes	complemented
27	C₇×#435	C₂²	1	32	yes	complemented
28	C₇×#431	C₂²	1	16	yes	complemented
29	C₇×#431	C₂²	1	8	yes	complemented
30	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
31	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
32	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
34	C₄×C₇×M₁₆	C₂²	1	16	yes	complemented
35	C₂×C₇×#97	C₂²	1	4	yes	—
36	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	8	yes	complemented
41	C₂×#2965	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₇×#41	—	2	8	no	—
43	C₂×C₇×#41	C₂×C₄	1	8	yes	—
44	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
46	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₂×C₇×M₁₆	—	2	16	no	—
54	C₂×C₇×M₁₆	C₂³	1	16	yes	—
55	C₂²×C₇×C₈	—	2	8	no	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	4	yes	—
58	C₂²×C₇×C₈	C₂³	1	8	yes	—
59	C₂²×C₇×C₈	C₂³	1	2	yes	—
60	C₄×C₇×Q₈	C₂×C₄	1	8	yes	—
61	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
62	C₄×C₇×Q₈	C₂³	1	4	yes	—
63	C₄×C₇×D₄	C₂×C₄	1	16	yes	—
64	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
65	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
66	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
67	C₄×C₇×D₄	C₂³	1	8	yes	—
68	C₄×C₇×D₄	C₂³	1	4	yes	—
69	C₇×#117	C₂×C₄	1	16	yes	—
70	C₇×#117	C₂×C₄	1	8	yes	—
71	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂×C₄	1	8	yes	—
83	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
84	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₇	C₂³	1	4	yes	—
87	C₂×C₄²×C₇	C₂³	1	8	yes	—
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₇×C₄⋊C₈	C₂³	1	16	yes	—
90	C₇×C₄⋊C₈	C₂³	1	8	yes	—
91	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
92	C₇×C₂²⋊C₈	C₂³	1	16	yes	—
93	C₇×#97	C₂³	1	16	yes	—
94	C₄×C₇×C₈	C₂³	1	4	yes	—
95	C₄×C₇×C₈	C₂³	1	4	yes	—
96	C₄×C₇×C₈	C₂³	1	8	yes	—
97	C₄×C₇×C₈	C₂³	1	8	yes	—
98	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic
99	#2965	C₂×C₇	1	16	yes	direct product factor
100	C₂×#446	C₂×C₇	1	2	yes	complemented
101	C₂×#436	C₂×C₇	1	2	yes	complemented
102	C₂×#435	C₂×C₇	1	4	yes	complemented
103	C₂×#431	C₂×C₇	1	2	yes	complemented
104	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂×C₄×M₁₆	C₂×C₇	1	2	yes	complemented
106	C₂²×C₄×C₈	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₇×#41	—	2	32	no	—
110	C₂×C₇×Q₈	—	2	4	no	—
111	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
112	C₂×C₇×D₄	—	2	8	no	—
113	C₂×C₇×D₄	—	2	4	no	—
114	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
115	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	8	no	—
119	C₂²×C₄×C₇	—	2	4	no	—
120	C₂²×C₄×C₇	—	2	8	no	—
121	C₂²×C₄×C₇	M₁₆	1	8	yes	complemented
122	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
131	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
139	C₇×M₁₆	—	2	32	no	—
140	C₂×C₇×C₈	—	2	4	no	—
141	C₂×C₇×C₈	—	2	8	no	—
142	C₂×C₇×C₈	—	2	16	no	—
143	C₂×C₇×C₈	#41	1	8	yes	complemented
144	C₂×C₇×C₈	C₂⁴	1	4	yes	—
145	C₂×C₇×C₈	C₂⁴	1	8	yes	—
146	C₂×C₇×C₈	C₂⁴	1	4	yes	—
147	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
148	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
150	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
151	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
152	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
153	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
154	C₄²×C₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₇	C₂²×C₄	1	4	yes	—
156	C₄²×C₇	C₂²×C₄	1	8	yes	—
157	C₄²×C₇	C₂²×C₄	1	8	yes	—
158	C₄²×C₇	C₂²×C₄	1	4	yes	—
159	C₄²×C₇	C₂²×C₄	1	4	yes	—
160	C₄²×C₇	C₂²×C₄	1	2	yes	—
161	C₄²×C₇	C₂⁴	1	2	yes	—
162	C₄²×C₇	C₂⁴	1	2	yes	—
163	C₄²×C₇	C₂⁴	1	4	yes	—
164	C₂²×#41	C₄×C₇	1	1	yes	characteristic
165	C₂²×M₁₆	C₂²×C₇	1	4	yes	—
166	C₂³×C₈	C₂²×C₇	1	2	yes	—
167	C₄×#41	C₄×C₇	1	8	yes	—
168	C₄×#41	C₂²×C₇	1	8	yes	—
169	C₂×C₄×Q₈	C₄×C₇	1	1	yes	characteristic
170	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
171	C₂×C₄×D₄	C₄×C₇	1	2	yes	—
172	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
173	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
174	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
175	C₂×#117	C₄×C₇	1	2	yes	—
176	C₂×#117	C₄×C₇	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
178	C₂²×C₄²	C₂²×C₇	1	2	yes	—
179	#446	C₂²×C₇	1	16	yes	complemented
180	#436	C₂²×C₇	1	16	yes	complemented
181	#435	C₂²×C₇	1	32	yes	complemented
182	#431	C₂²×C₇	1	16	yes	complemented
183	#431	C₂²×C₇	1	8	yes	complemented
184	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
185	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
186	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
188	C₄×M₁₆	C₂²×C₇	1	16	yes	complemented
189	C₂×#97	C₂²×C₇	1	4	yes	—
190	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₇	1	8	yes	complemented
195	C₂³×C₇	—	2	2	no	—
196	C₂³×C₇	—	2	2	no	—
197	C₂³×C₇	—	2	4	no	—
198	C₂³×C₇	—	2	4	no	—
199	C₂³×C₇	—	2	4	no	—
200	C₂³×C₇	C₂×M₁₆	1	4	yes	—
201	C₂³×C₇	C₂³×C₄	1	4	yes	—
202	C₂³×C₇	C₂³×C₄	1	2	yes	—
203	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
204	C₇×Q₈	—	2	8	no	—
205	C₇×D₄	—	2	16	no	—
206	C₇×D₄	—	2	8	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	4	no	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	4	no	—
212	C₂×C₄×C₇	—	2	4	no	—
213	C₂×C₄×C₇	—	2	8	no	—
214	C₂×C₄×C₇	—	2	16	no	—
215	C₂×C₄×C₇	—	2	8	no	—
216	C₂×C₄×C₇	—	2	16	no	—
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	2	8	no	—
219	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
220	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
221	C₂×C₄×C₇	C₂×M₁₆	1	16	yes	complemented
222	C₂×C₄×C₇	#131	1	4	yes	—
223	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
225	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
227	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
228	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
230	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₇	C₂×#41	1	4	yes	—
233	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
234	C₇×C₈	—	2	4	no	—
235	C₇×C₈	—	2	8	no	—
236	C₇×C₈	C₂×#41	1	8	yes	complemented
237	C₂×#41	—	2	8	no	—
238	C₂×#41	C₂×C₄×C₇	1	8	yes	—
239	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
240	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
241	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
242	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
243	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
244	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
245	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₇	1	2	yes	—
248	C₂×M₁₆	—	2	16	no	—
249	C₂×M₁₆	C₂³×C₇	1	16	yes	—
250	C₂²×C₈	—	2	8	no	—
251	C₂²×C₈	C₂³×C₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₇	1	8	yes	—
253	C₂²×C₈	C₂³×C₇	1	4	yes	—
254	C₂²×C₈	C₂³×C₇	1	2	yes	—
255	C₄×Q₈	C₂×C₄×C₇	1	8	yes	—
256	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
257	C₄×Q₈	C₂³×C₇	1	4	yes	—
258	C₄×D₄	C₂×C₄×C₇	1	16	yes	—
259	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
260	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
261	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
262	C₄×D₄	C₂³×C₇	1	8	yes	—
263	C₄×D₄	C₂³×C₇	1	4	yes	—
264	#117	C₂×C₄×C₇	1	16	yes	—
265	#117	C₂×C₄×C₇	1	8	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
273	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
275	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
276	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
277	C₂×C₄²	C₂×C₄×C₇	1	8	yes	—
278	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
279	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₇	1	2	yes	—
281	C₂×C₄²	C₂³×C₇	1	4	yes	—
282	C₂×C₄²	C₂³×C₇	1	8	yes	—
283	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₇	1	16	yes	—
285	C₄⋊C₈	C₂³×C₇	1	8	yes	—
286	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
287	C₂²⋊C₈	C₂³×C₇	1	16	yes	—
288	#97	C₂³×C₇	1	16	yes	—
289	C₄×C₈	C₂³×C₇	1	4	yes	—
290	C₄×C₈	C₂³×C₇	1	4	yes	—
291	C₄×C₈	C₂³×C₇	1	8	yes	—
292	C₄×C₈	C₂³×C₇	1	8	yes	—
293	C₂²×C₇	—	2	2	no	—
294	C₂²×C₇	—	2	8	no	—
295	C₂²×C₇	—	2	2	no	—
296	C₂²×C₇	—	2	4	no	—
297	C₂²×C₇	—	2	4	no	—
298	C₂²×C₇	—	2	4	no	—
299	C₂²×C₇	—	4	8	no	—
300	C₂²×C₇	C₄×#41	1	2	yes	—
301	C₂²×C₇	C₂²×M₁₆	1	4	yes	—
302	C₂²×C₇	C₂²×M₁₆	1	2	yes	—
303	C₂²×C₇	C₂×#131	1	2	yes	—
304	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	2	4	no	—
307	C₄×C₇	—	2	4	no	—
308	C₄×C₇	—	2	2	no	—
309	C₄×C₇	—	2	4	no	—
310	C₄×C₇	C₄×#41	1	2	yes	—
311	C₄×C₇	C₂²×M₁₆	1	4	yes	—
312	C₄×C₇	C₂²×M₁₆	1	4	yes	—
313	C₄×C₇	C₂×#131	1	4	yes	—
314	C₄×C₇	C₂²×#41	1	2	yes	—
315	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
316	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
317	#41	—	2	32	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
323	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	C₇×M₁₆	1	8	yes	complemented
330	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
333	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
338	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
339	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
343	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
346	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
347	M₁₆	—	2	32	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	8	no	—
350	C₂×C₈	—	2	16	no	—
351	C₂×C₈	C₇×#41	1	8	yes	complemented
352	C₂×C₈	C₂⁴×C₇	1	4	yes	—
353	C₂×C₈	C₂⁴×C₇	1	8	yes	—
354	C₂×C₈	C₂⁴×C₇	1	4	yes	—
355	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
356	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
357	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
358	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
359	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
360	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
361	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
362	C₄²	C₂²×C₄×C₇	1	2	yes	—
363	C₄²	C₂²×C₄×C₇	1	4	yes	—
364	C₄²	C₂²×C₄×C₇	1	8	yes	—
365	C₄²	C₂²×C₄×C₇	1	8	yes	—
366	C₄²	C₂²×C₄×C₇	1	4	yes	—
367	C₄²	C₂²×C₄×C₇	1	4	yes	—
368	C₄²	C₂²×C₄×C₇	1	2	yes	—
369	C₄²	C₂⁴×C₇	1	2	yes	—
370	C₄²	C₂⁴×C₇	1	2	yes	—
371	C₄²	C₂⁴×C₇	1	4	yes	—
372	C₂×C₇	—	2	4	no	—
373	C₂×C₇	—	4	4	no	—
374	C₂×C₇	#2965	1	4	yes	direct product factor
375	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
376	C₂×C₇	C₂³×M₁₆	1	1	yes	characteristic
377	C₂×C₇	C₂²×#131	1	1	yes	characteristic
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	C₂×C₇×M₁₆	1	4	yes	—
384	C₂³	C₂³×C₄×C₇	1	4	yes	—
385	C₂³	C₂³×C₄×C₇	1	2	yes	—
386	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
387	Q₈	—	2	8	no	—
388	D₄	—	2	16	no	—
389	D₄	—	2	8	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	16	no	—
402	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
403	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
404	C₂×C₄	C₂×C₇×M₁₆	1	16	yes	complemented
405	C₂×C₄	C₇×#131	1	4	yes	—
406	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
407	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
408	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
409	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
410	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
411	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
413	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
414	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
415	C₂×C₄	C₂×C₇×#41	1	4	yes	—
416	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	2	8	no	—
419	C₈	C₂×C₇×#41	1	8	yes	complemented
420	C₇	C₂×#2965	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	2	2	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	4	8	no	—
428	C₂²	C₄×C₇×#41	1	2	yes	—
429	C₂²	C₂²×C₇×M₁₆	1	4	yes	—
430	C₂²	C₂²×C₇×M₁₆	1	2	yes	—
431	C₂²	C₂×C₇×#131	1	2	yes	—
432	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	C₄×C₇×#41	1	2	yes	—
439	C₄	C₂²×C₇×M₁₆	1	4	yes	—
440	C₄	C₂²×C₇×M₁₆	1	4	yes	—
441	C₄	C₂×C₇×#131	1	4	yes	—
442	C₄	C₂²×C₇×#41	1	2	yes	—
443	C₂	—	2	4	no	—
444	C₂	—	4	4	no	—
445	C₂	C₇×#2965	1	4	yes	direct product factor
446	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
447	C₂	C₂³×C₇×M₁₆	1	1	yes	characteristic
448	C₂	C₂²×C₇×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×#41	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2965	C₂	direct (N × H)
3. C₂×C₇×#446	C₂	semidirect
4. C₂×C₇×#436	C₂	semidirect
5. C₂×C₇×#435	C₂	semidirect
6. C₂×C₇×#431	C₂	semidirect
7. C₂×C₇×#431	C₂	semidirect
8. C₂×C₄×C₇×M₁₆	C₂	semidirect
9. C₂²×C₄×C₇×C₈	C₂	semidirect
25. C₇×#446	C₂²	semidirect
26. C₇×#436	C₂²	semidirect
27. C₇×#435	C₂²	semidirect
28. C₇×#431	C₂²	semidirect
29. C₇×#431	C₂²	semidirect
34. C₄×C₇×M₁₆	C₂²	semidirect
40. C₂×C₄×C₇×C₈	C₂²	semidirect
41. C₂×#2965	C₇	direct (N × H)
99. #2965	C₂×C₇	direct (N × H)
100. C₂×#446	C₂×C₇	semidirect
101. C₂×#436	C₂×C₇	semidirect
102. C₂×#435	C₂×C₇	semidirect
103. C₂×#431	C₂×C₇	semidirect
104. C₂×#431	C₂×C₇	semidirect
105. C₂×C₄×M₁₆	C₂×C₇	semidirect
106. C₂²×C₄×C₈	C₂×C₇	semidirect
121. C₂²×C₄×C₇	M₁₆	semidirect
143. C₂×C₇×C₈	#41	semidirect
179. #446	C₂²×C₇	semidirect
180. #436	C₂²×C₇	semidirect
181. #435	C₂²×C₇	semidirect
182. #431	C₂²×C₇	semidirect
183. #431	C₂²×C₇	semidirect
188. C₄×M₁₆	C₂²×C₇	semidirect
194. C₂×C₄×C₈	C₂²×C₇	semidirect
221. C₂×C₄×C₇	C₂×M₁₆	semidirect
236. C₇×C₈	C₂×#41	semidirect
329. C₂²×C₄	C₇×M₁₆	semidirect
351. C₂×C₈	C₇×#41	semidirect
374. C₂×C₇	#2965	direct (N × H)
404. C₂×C₄	C₂×C₇×M₁₆	semidirect
419. C₈	C₂×C₇×#41	semidirect
420. C₇	C₂×#2965	direct (N × H)
445. C₂	C₇×#2965	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×C₄×C₇×#41	2
C₇×#2965	2
C₂×C₇×#446	2
C₂×C₇×#436	2
C₂×C₇×#435	2
C₂×C₇×#431	2
C₂×C₄×C₇×M₁₆	2
C₂²×C₄×C₇×C₈	2
C₂×#2965	7

Subgroups — C2×C7×#2965 #13237413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2965 #13237413