Subgroups — C₄×C₇×#435 #13197702

Order 1792.

1282 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#435	C₂	1	2	yes	maximal
2	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
5	C₇×#1771	C₂	1	2	yes	maximal, complemented
6	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1753	C₂	1	2	yes	maximal, complemented
8	C₇×#1752	C₂	1	2	yes	maximal, complemented
9	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₄	1	2	yes	—
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
18	C₇×#435	C₄	1	16	yes	direct product factor
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₄×C₇×M₁₆	—	2	4	no	—
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₇×#97	C₂²	1	2	yes	—
25	C₂×C₇×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₇×C₈	—	2	4	no	—
27	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₄	1	2	yes	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
35	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₄³×C₇	C₂²	1	1	yes	characteristic
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₄×#435	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	—	2	4	no	—
50	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	complemented
51	C₂²×C₇×C₈	—	2	4	no	—
52	C₂²×C₇×C₈	—	2	4	no	—
53	C₂²×C₇×C₈	C₂×C₄	1	8	yes	complemented
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	2	yes	—
58	C₄×C₇×D₄	—	2	8	no	—
59	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇	—	2	2	no	—
67	C₂×C₄²×C₇	—	2	2	no	—
68	C₂×C₄²×C₇	—	2	2	no	—
69	C₂×C₄²×C₇	—	2	2	no	—
70	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
80	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
81	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
82	C₇×#97	—	2	4	no	—
83	C₇×#97	—	2	4	no	—
84	C₇×#97	C₂×C₄	1	8	yes	complemented
85	C₄×C₇×C₈	—	2	4	no	—
86	C₄×C₇×C₈	—	2	2	no	—
87	C₄×C₇×C₈	—	2	2	no	—
88	C₄×C₇×C₈	—	2	2	no	—
89	C₄×C₇×C₈	D₄	1	4	yes	complemented
90	C₇×#95	C₂×C₄	1	2	yes	—
91	C₇×#95	C₂×C₄	1	2	yes	—
92	C₇×#95	C₂×C₄	1	2	yes	—
93	C₂×#435	C₂×C₇	1	2	yes	—
94	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂²×C₄×C₈	C₂×C₇	1	1	yes	characteristic, complemented
96	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
97	#1771	C₂×C₇	1	2	yes	complemented
98	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
99	#1753	C₂×C₇	1	2	yes	complemented
100	#1752	C₂×C₇	1	2	yes	complemented
101	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
103	C₄×#97	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
105	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₇×D₄	—	2	4	no	—
107	C₂×C₇×D₄	C₄²	1	4	yes	—
108	C₂²×C₄×C₇	—	2	4	no	—
109	C₂²×C₄×C₇	—	2	4	no	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	4	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	M₁₆	1	8	yes	complemented
120	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
131	C₇×M₁₆	—	2	16	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	—	2	2	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	—	2	16	no	—
139	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
140	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
141	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
142	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
143	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
144	C₂×C₇×C₈	#41	1	4	yes	—
145	C₇×C₄⋊C₄	—	2	4	no	—
146	C₇×C₄⋊C₄	C₄²	1	4	yes	—
147	C₇×C₂²⋊C₄	—	2	4	no	—
148	C₇×C₂²⋊C₄	—	2	4	no	—
149	C₇×C₂²⋊C₄	C₄²	1	4	yes	—
150	C₇×C₂²⋊C₄	C₄²	1	4	yes	—
151	C₄²×C₇	—	2	4	no	—
152	C₄²×C₇	—	2	4	no	—
153	C₄²×C₇	—	2	4	no	—
154	C₄²×C₇	—	2	4	no	—
155	C₄²×C₇	—	2	1	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	2	1	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	C₂²×C₄	1	4	yes	—
161	C₄²×C₇	C₂×D₄	1	2	yes	—
162	C₄²×C₇	#41	1	2	yes	—
163	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
164	C₂³×C₈	C₂²×C₇	1	2	yes	—
165	C₂×C₄×D₄	C₄×C₇	1	2	yes	—
166	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
168	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
169	#435	C₄×C₇	1	16	yes	direct product factor
170	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
171	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
172	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
173	C₄×M₁₆	—	2	4	no	—
174	C₂×#97	C₂²×C₇	1	2	yes	—
175	C₂×#97	C₂²×C₇	1	2	yes	—
176	C₂×#97	C₂²×C₇	1	2	yes	—
177	C₂×C₄×C₈	—	2	4	no	—
178	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
183	C₄×C₄⋊C₄	C₄×C₇	1	2	yes	—
184	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
185	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
186	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
187	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
188	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
189	C₄³	C₂²×C₇	1	1	yes	characteristic
190	#336	C₂²×C₇	1	2	yes	—
191	#336	C₂²×C₇	1	2	yes	—
192	#336	C₂²×C₇	1	2	yes	—
193	C₂³×C₇	—	2	1	no	—
194	C₂³×C₇	—	2	1	no	—
195	C₂³×C₇	—	2	2	no	—
196	C₂³×C₇	—	2	1	no	—
197	C₂³×C₇	—	2	1	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	2	2	no	—
200	C₂³×C₇	C₂×C₄²	1	2	yes	—
201	C₂³×C₇	C₂×C₄²	1	2	yes	—
202	C₂³×C₇	C₂×M₁₆	1	4	yes	—
203	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
204	C₇×D₄	—	2	8	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	2	4	no	—
217	C₂×C₄×C₇	—	2	16	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	4	8	no	—
225	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
226	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
227	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
228	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
229	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
230	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
231	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
232	C₂×C₄×C₇	#131	1	4	yes	—
233	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	2	yes	—
236	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
237	C₇×C₈	—	2	4	no	—
238	C₇×C₈	—	2	4	no	—
239	C₇×C₈	—	2	4	no	—
240	C₇×C₈	C₄×D₄	1	8	yes	complemented
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	C₂³×C₇	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
249	C₂²×C₈	—	2	4	no	—
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	C₂×C₄×C₇	1	8	yes	complemented
252	C₂²×C₈	C₂³×C₇	1	2	yes	—
253	C₂²×C₈	C₂³×C₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₇	1	2	yes	—
255	C₂²×C₈	C₂³×C₇	1	2	yes	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
269	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
270	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
271	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	C₄⋊C₈	C₂×C₄×C₇	1	8	yes	complemented
278	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	complemented
279	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	complemented
280	#97	—	2	4	no	—
281	#97	—	2	4	no	—
282	#97	C₂×C₄×C₇	1	8	yes	complemented
283	C₄×C₈	—	2	4	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	C₇×D₄	1	4	yes	complemented
288	#95	C₂×C₄×C₇	1	2	yes	—
289	#95	C₂×C₄×C₇	1	2	yes	—
290	#95	C₂×C₄×C₇	1	2	yes	—
291	C₂²×C₇	—	2	2	no	—
292	C₂²×C₇	—	2	4	no	—
293	C₂²×C₇	—	2	4	no	—
294	C₂²×C₇	—	2	2	no	—
295	C₂²×C₇	—	2	2	no	—
296	C₂²×C₇	—	2	2	no	—
297	C₂²×C₇	—	2	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	4	2	no	—
300	C₂²×C₇	C₄×M₁₆	1	4	yes	complemented
301	C₂²×C₇	C₂²×C₄²	1	1	yes	characteristic
302	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₇	C₄×#41	1	1	yes	characteristic
304	C₂²×C₇	C₂²×M₁₆	1	2	yes	—
305	C₂²×C₇	C₂×#131	1	2	yes	—
306	C₄×C₇	—	2	2	no	—
307	C₄×C₇	—	2	2	no	—
308	C₄×C₇	—	2	4	no	—
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	2	2	no	—
311	C₄×C₇	—	4	2	no	—
312	C₄×C₇	—	4	2	no	—
313	C₄×C₇	#435	1	8	yes	direct product factor
314	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
315	C₄×C₇	C₄×#41	1	2	yes	—
316	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
317	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	C₄²×C₇	1	4	yes	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	C₇×M₁₆	1	8	yes	complemented
332	C₂²×C₄	C₂²×C₄×C₇	1	2	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	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
343	M₁₆	—	2	16	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	16	no	—
351	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
352	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
353	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
354	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
355	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
356	C₂×C₈	C₇×#41	1	4	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	C₄²×C₇	1	4	yes	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	C₄²×C₇	1	4	yes	—
362	C₂²⋊C₄	C₄²×C₇	1	4	yes	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	C₂²×C₄×C₇	1	4	yes	—
373	C₄²	C₂×C₇×D₄	1	2	yes	—
374	C₄²	C₇×#41	1	2	yes	—
375	C₂×C₇	—	2	4	no	—
376	C₂×C₇	—	4	2	no	—
377	C₂×C₇	C₄²×D₄	1	1	yes	characteristic
378	C₂×C₇	C₂×C₄×M₁₆	1	1	yes	characteristic
379	C₂×C₇	C₄×#131	1	1	yes	characteristic
380	C₂×C₇	C₂×#435	1	2	yes	—
381	C₂×C₇	#2965	1	2	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	C₂×C₄²×C₇	1	2	yes	—
390	C₂³	C₂×C₄²×C₇	1	2	yes	—
391	C₂³	C₂×C₇×M₁₆	1	4	yes	—
392	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
393	D₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
415	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
416	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
417	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
418	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
419	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
420	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
421	C₂×C₄	C₇×#131	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
423	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
424	C₂×C₄	C₂×C₇×#41	1	2	yes	—
425	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	—	2	4	no	—
428	C₈	—	2	4	no	—
429	C₈	C₄×C₇×D₄	1	8	yes	complemented
430	C₇	C₄×#435	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	C₄×C₇×M₁₆	1	4	yes	complemented
441	C₂²	C₂²×C₄²×C₇	1	1	yes	characteristic
442	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
443	C₂²	C₄×C₇×#41	1	1	yes	characteristic
444	C₂²	C₂²×C₇×M₁₆	1	2	yes	—
445	C₂²	C₂×C₇×#131	1	2	yes	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	C₇×#435	1	8	yes	direct product factor
454	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
455	C₄	C₄×C₇×#41	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	C₄²×C₇×D₄	1	1	yes	characteristic
459	C₂	C₂×C₄×C₇×M₁₆	1	1	yes	characteristic
460	C₂	C₄×C₇×#131	1	1	yes	characteristic
461	C₂	C₂×C₇×#435	1	2	yes	—
462	C₂	C₇×#2965	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₇	C₂³
commutator	C₂²	C₂²×C₄²×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×D₄	C₂×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. C₂×C₄×C₇×M₁₆	C₂	semidirect
3. C₂²×C₄×C₇×C₈	C₂	semidirect
5. C₇×#1771	C₂	semidirect
6. C₄×C₇×C₄⋊C₈	C₂	semidirect
7. C₇×#1753	C₂	semidirect
8. C₇×#1752	C₂	semidirect
9. C₄×C₇×C₂²⋊C₈	C₂	semidirect
10. C₄×C₇×C₂²⋊C₈	C₂	semidirect
11. C₄×C₇×#97	C₂	semidirect
18. C₇×#435	C₄	direct (N × H)
42. C₄×#435	C₇	direct (N × H)
50. C₂×C₇×M₁₆	C₂×C₄	semidirect
53. C₂²×C₇×C₈	C₂×C₄	semidirect
79. C₇×C₄⋊C₈	C₂×C₄	semidirect
80. C₇×C₂²⋊C₈	C₂×C₄	semidirect
81. C₇×C₂²⋊C₈	C₂×C₄	semidirect
84. C₇×#97	C₂×C₄	semidirect
89. C₄×C₇×C₈	D₄	semidirect
94. C₂×C₄×M₁₆	C₂×C₇	semidirect
95. C₂²×C₄×C₈	C₂×C₇	semidirect
97. #1771	C₂×C₇	semidirect
98. C₄×C₄⋊C₈	C₂×C₇	semidirect
99. #1753	C₂×C₇	semidirect
100. #1752	C₂×C₇	semidirect
101. C₄×C₂²⋊C₈	C₂×C₇	semidirect
102. C₄×C₂²⋊C₈	C₂×C₇	semidirect
103. C₄×#97	C₂×C₇	semidirect
119. C₂²×C₄×C₇	M₁₆	semidirect
169. #435	C₄×C₇	direct (N × H)
240. C₇×C₈	C₄×D₄	semidirect
248. C₂×M₁₆	C₂×C₄×C₇	semidirect
251. C₂²×C₈	C₂×C₄×C₇	semidirect
277. C₄⋊C₈	C₂×C₄×C₇	semidirect
278. C₂²⋊C₈	C₂×C₄×C₇	semidirect
279. C₂²⋊C₈	C₂×C₄×C₇	semidirect
282. #97	C₂×C₄×C₇	semidirect
287. C₄×C₈	C₇×D₄	semidirect
300. C₂²×C₇	C₄×M₁₆	semidirect
313. C₄×C₇	#435	direct (N × H)
331. C₂²×C₄	C₇×M₁₆	semidirect
429. C₈	C₄×C₇×D₄	semidirect
430. C₇	C₄×#435	direct (N × H)
440. C₂²	C₄×C₇×M₁₆	semidirect
453. C₄	C₇×#435	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×#435	2
C₂×C₄×C₇×M₁₆	2
C₂²×C₄×C₇×C₈	2
C₄²×C₇×D₄	2
C₇×#1771	2
C₄×C₇×C₄⋊C₈	2
C₇×#1753	2
C₇×#1752	2
C₄×C₇×C₂²⋊C₈	2
C₄×C₇×#97	2
C₄×#435	7

Subgroups — C4×C7×#435 #13197702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#435 #13197702