Subgroups — C₇×#22552 #13199768

Order 1792.

1280 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1923	C₂	1	2	yes	maximal, complemented
5	C₇×#1923	C₂	1	2	yes	maximal, complemented
6	C₇×#1850	C₂	1	2	yes	maximal, complemented
7	C₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1779	C₂	1	1	yes	maximal, characteristic
10	C₇×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₂²×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
15	C₂²×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
18	C₇×#431	—	2	4	no	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
21	C₂×C₇×C₂²⋊C₈	—	2	4	no	—
22	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
30	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
31	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
32	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
33	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
34	C₄×C₇×C₂²⋊C₄	C₄	1	1	yes	characteristic
35	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₇×#95	C₄	1	1	yes	characteristic
40	C₂×C₇×#95	C₄	1	1	yes	characteristic
41	C₇×#336	C₂²	1	2	yes	complemented
42	C₇×#336	C₂²	1	2	yes	complemented
43	C₇×#336	C₂²	1	2	yes	complemented
44	C₇×#336	C₂²	1	2	yes	complemented
45	#22552	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁵×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	—	2	2	no	—
48	C₂³×C₄×C₇	—	2	4	no	—
49	C₂³×C₄×C₇	—	2	2	no	—
50	C₂³×C₄×C₇	—	4	2	no	—
51	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂²×C₇×C₈	—	2	4	no	—
62	C₂²×C₇×C₈	—	2	4	no	—
63	C₂²×C₇×C₈	—	4	2	no	—
64	C₂²×C₇×C₈	C₂³	1	2	yes	—
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₂²×C₇×C₈	C₂³	1	2	yes	—
67	C₂²×C₇×C₈	C₂³	1	2	yes	—
68	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₇×C₂²⋊C₄	C₈	1	8	yes	complemented
70	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	—	2	2	no	—
79	C₂×C₄²×C₇	—	2	2	no	—
80	C₂×C₄²×C₇	—	4	2	no	—
81	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₇×C₄⋊C₈	—	2	4	no	—
90	C₇×C₄⋊C₈	—	4	2	no	—
91	C₇×C₂²⋊C₈	—	2	2	no	—
92	C₇×C₂²⋊C₈	—	2	2	no	—
93	C₇×C₂²⋊C₈	—	2	4	no	—
94	C₇×C₂²⋊C₈	—	2	2	no	—
95	C₇×C₂²⋊C₈	—	2	4	no	—
96	C₇×C₂²⋊C₈	—	4	2	no	—
97	C₇×C₂²⋊C₈	D₄	1	4	yes	—
98	C₄×C₇×C₈	—	2	4	no	—
99	C₄×C₇×C₈	—	4	2	no	—
100	C₇×#95	C₂×C₄	1	1	yes	characteristic
101	C₇×#95	C₂×C₄	1	1	yes	characteristic
102	C₇×#95	C₂×C₄	1	1	yes	characteristic
103	C₇×#95	C₂×C₄	1	1	yes	characteristic
104	C₇×#95	C₂×C₄	1	1	yes	characteristic
105	C₇×#95	C₂×C₄	1	1	yes	characteristic
106	C₇×#95	C₂×C₄	1	1	yes	characteristic
107	C₇×#95	C₂×C₄	1	1	yes	characteristic
108	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
110	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
111	#1923	C₂×C₇	1	2	yes	complemented
112	#1923	C₂×C₇	1	2	yes	complemented
113	#1850	C₂×C₇	1	2	yes	complemented
114	#1817	C₂×C₇	1	1	yes	characteristic, complemented
115	#1797	C₂×C₇	1	1	yes	characteristic, complemented
116	#1779	C₂×C₇	1	1	yes	characteristic
117	C₈×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
118	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
119	C₂⁴×C₇	—	2	2	no	—
120	C₂⁴×C₇	—	2	2	no	—
121	C₂⁴×C₇	—	2	2	no	—
122	C₂⁴×C₇	—	2	2	no	—
123	C₂⁴×C₇	—	4	1	no	—
124	C₂⁴×C₇	—	4	1	no	—
125	C₂⁴×C₇	C₂×C₈	1	4	yes	—
126	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
127	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
128	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	—	2	2	no	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	1	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	2	2	no	—
139	C₂²×C₄×C₇	—	2	2	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	2	no	—
142	C₂²×C₄×C₇	—	2	2	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	2	no	—
146	C₂²×C₄×C₇	—	2	1	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	2	no	—
150	C₂²×C₄×C₇	—	4	1	no	—
151	C₂²×C₄×C₇	—	4	1	no	—
152	C₂²×C₄×C₇	—	4	1	no	—
153	C₂²×C₄×C₇	—	4	1	no	—
154	C₂²×C₄×C₇	—	4	1	no	—
155	C₂²×C₄×C₇	—	4	1	no	—
156	C₂²×C₄×C₇	—	4	1	no	—
157	C₂²×C₄×C₇	—	4	8	no	—
158	C₂²×C₄×C₇	—	4	8	no	—
159	C₂²×C₄×C₇	C₂×C₈	1	4	yes	complemented
160	C₂²×C₄×C₇	C₂×C₈	1	4	yes	complemented
161	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₇	#41	1	4	yes	—
174	C₂²×C₄×C₇	#41	1	2	yes	—
175	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
176	C₂×C₇×C₈	—	2	2	no	—
177	C₂×C₇×C₈	—	2	2	no	—
178	C₂×C₇×C₈	—	2	2	no	—
179	C₂×C₇×C₈	—	2	2	no	—
180	C₂×C₇×C₈	—	2	2	no	—
181	C₂×C₇×C₈	—	2	2	no	—
182	C₂×C₇×C₈	—	2	2	no	—
183	C₂×C₇×C₈	—	2	2	no	—
184	C₂×C₇×C₈	—	2	2	no	—
185	C₂×C₇×C₈	—	2	2	no	—
186	C₂×C₇×C₈	—	2	2	no	—
187	C₂×C₇×C₈	—	4	8	no	—
188	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
189	C₇×C₂²⋊C₄	—	2	2	no	—
190	C₇×C₂²⋊C₄	—	2	2	no	—
191	C₇×C₂²⋊C₄	—	2	2	no	—
192	C₇×C₂²⋊C₄	C₂×C₈	1	4	yes	—
193	C₇×C₂²⋊C₄	C₂×C₈	1	4	yes	—
194	C₇×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
195	C₇×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
196	C₇×C₂²⋊C₄	M₁₆	1	4	yes	—
197	C₄²×C₇	—	2	2	no	—
198	C₄²×C₇	—	2	2	no	—
199	C₄²×C₇	—	2	1	no	—
200	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	2	no	—
204	C₄²×C₇	—	2	2	no	—
205	C₄²×C₇	—	4	1	no	—
206	C₄²×C₇	—	4	1	no	—
207	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₇	1	2	yes	—
209	C₂²×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
210	C₂²×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
213	#431	—	2	4	no	—
214	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
215	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
216	C₂×C₂²⋊C₈	—	2	4	no	—
217	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
221	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
222	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
225	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
226	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
227	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
228	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
229	C₄×C₂²⋊C₄	C₄×C₇	1	1	yes	characteristic
230	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
231	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
232	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
234	C₂×#95	C₄×C₇	1	1	yes	characteristic
235	C₂×#95	C₄×C₇	1	1	yes	characteristic
236	#336	C₂²×C₇	1	2	yes	complemented
237	#336	C₂²×C₇	1	2	yes	complemented
238	#336	C₂²×C₇	1	2	yes	complemented
239	#336	C₂²×C₇	1	2	yes	complemented
240	C₂³×C₇	—	2	1	no	—
241	C₂³×C₇	—	2	1	no	—
242	C₂³×C₇	—	2	1	no	—
243	C₂³×C₇	—	2	1	no	—
244	C₂³×C₇	—	2	1	no	—
245	C₂³×C₇	—	2	1	no	—
246	C₂³×C₇	—	2	1	no	—
247	C₂³×C₇	—	2	1	no	—
248	C₂³×C₇	—	2	1	no	—
249	C₂³×C₇	—	2	1	no	—
250	C₂³×C₇	—	2	1	no	—
251	C₂³×C₇	—	2	1	no	—
252	C₂³×C₇	—	2	1	no	—
253	C₂³×C₇	—	2	1	no	—
254	C₂³×C₇	—	2	8	no	—
255	C₂³×C₇	—	2	8	no	—
256	C₂³×C₇	—	4	4	no	—
257	C₂³×C₇	—	4	4	no	—
258	C₂³×C₇	—	4	4	no	—
259	C₂³×C₇	—	4	4	no	—
260	C₂³×C₇	—	4	4	no	—
261	C₂³×C₇	#117	1	2	yes	—
262	C₂³×C₇	C₄×D₄	1	2	yes	—
263	C₂³×C₇	C₂²×C₈	1	2	yes	—
264	C₂³×C₇	C₂²×C₈	1	2	yes	—
265	C₂³×C₇	C₂²×C₈	1	2	yes	—
266	C₂³×C₇	C₂×M₁₆	1	2	yes	—
267	C₂³×C₇	#131	1	2	yes	—
268	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₇	—	2	1	no	—
270	C₂×C₄×C₇	—	2	1	no	—
271	C₂×C₄×C₇	—	2	1	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	8	no	—
286	C₂×C₄×C₇	—	2	4	no	—
287	C₂×C₄×C₇	—	2	4	no	—
288	C₂×C₄×C₇	—	2	4	no	—
289	C₂×C₄×C₇	—	2	4	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	4	4	no	—
300	C₂×C₄×C₇	—	4	4	no	—
301	C₂×C₄×C₇	—	4	4	no	—
302	C₂×C₄×C₇	—	4	4	no	—
303	C₂×C₄×C₇	—	4	4	no	—
304	C₂×C₄×C₇	—	4	4	no	—
305	C₂×C₄×C₇	—	4	2	no	—
306	C₂×C₄×C₇	—	4	2	no	—
307	C₂×C₄×C₇	#117	1	2	yes	—
308	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
309	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
310	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
311	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
312	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
313	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
314	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
315	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₇	C₂×#41	1	2	yes	—
317	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
319	C₇×C₈	—	2	4	no	—
320	C₇×C₈	—	4	2	no	—
321	C₇×C₈	—	4	2	no	—
322	C₇×C₈	—	4	2	no	—
323	C₂⁵	C₂×C₄×C₇	1	1	yes	characteristic
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	—	2	4	no	—
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	—	4	2	no	—
328	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
329	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
330	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
331	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
332	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
333	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
334	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
338	C₂²×C₈	—	2	4	no	—
339	C₂²×C₈	—	2	4	no	—
340	C₂²×C₈	—	4	2	no	—
341	C₂²×C₈	C₂³×C₇	1	2	yes	—
342	C₂²×C₈	C₂³×C₇	1	2	yes	—
343	C₂²×C₈	C₂³×C₇	1	2	yes	—
344	C₂²×C₈	C₂³×C₇	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	C₇×C₈	1	8	yes	complemented
347	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	—	4	2	no	—
358	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
359	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
360	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
361	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
366	C₄⋊C₈	—	2	4	no	—
367	C₄⋊C₈	—	4	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	C₂²⋊C₈	—	2	2	no	—
370	C₂²⋊C₈	—	2	4	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	2	4	no	—
373	C₂²⋊C₈	—	4	2	no	—
374	C₂²⋊C₈	C₇×D₄	1	4	yes	—
375	C₄×C₈	—	2	4	no	—
376	C₄×C₈	—	4	2	no	—
377	#95	C₂×C₄×C₇	1	1	yes	characteristic
378	#95	C₂×C₄×C₇	1	1	yes	characteristic
379	#95	C₂×C₄×C₇	1	1	yes	characteristic
380	#95	C₂×C₄×C₇	1	1	yes	characteristic
381	#95	C₂×C₄×C₇	1	1	yes	characteristic
382	#95	C₂×C₄×C₇	1	1	yes	characteristic
383	#95	C₂×C₄×C₇	1	1	yes	characteristic
384	#95	C₂×C₄×C₇	1	1	yes	characteristic
385	C₂²×C₇	—	2	2	no	—
386	C₂²×C₇	—	2	2	no	—
387	C₂²×C₇	—	2	2	no	—
388	C₂²×C₇	—	2	2	no	—
389	C₂²×C₇	—	2	2	no	—
390	C₂²×C₇	—	2	2	no	—
391	C₂²×C₇	—	2	2	no	—
392	C₂²×C₇	—	2	2	no	—
393	C₂²×C₇	—	2	2	no	—
394	C₂²×C₇	—	2	2	no	—
395	C₂²×C₇	—	2	2	no	—
396	C₂²×C₇	—	2	2	no	—
397	C₂²×C₇	—	2	2	no	—
398	C₂²×C₇	—	2	2	no	—
399	C₂²×C₇	—	2	2	no	—
400	C₂²×C₇	—	4	16	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	—	4	1	no	—
404	C₂²×C₇	—	4	1	no	—
405	C₂²×C₇	#431	1	4	yes	complemented
406	C₂²×C₇	C₈×D₄	1	4	yes	—
407	C₂²×C₇	C₂×#117	1	1	yes	characteristic
408	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
409	C₂²×C₇	#518	1	1	yes	characteristic
410	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
411	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
412	C₂²×C₇	C₂×#131	1	1	yes	characteristic
413	C₂²×C₇	#568	1	1	yes	characteristic
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	2	2	no	—
416	C₄×C₇	—	2	2	no	—
417	C₄×C₇	—	2	2	no	—
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	2	2	no	—
420	C₄×C₇	—	2	2	no	—
421	C₄×C₇	—	2	2	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	#546	1	2	yes	—
426	C₄×C₇	#551	1	2	yes	—
427	C₂⁴	—	2	2	no	—
428	C₂⁴	—	2	2	no	—
429	C₂⁴	—	2	2	no	—
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	4	1	no	—
432	C₂⁴	—	4	1	no	—
433	C₂⁴	C₂×C₇×C₈	1	4	yes	—
434	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
435	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
436	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	8	no	—
466	C₂²×C₄	—	4	8	no	—
467	C₂²×C₄	C₂×C₇×C₈	1	4	yes	complemented
468	C₂²×C₄	C₂×C₇×C₈	1	4	yes	complemented
469	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
474	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
481	C₂²×C₄	C₇×#41	1	4	yes	—
482	C₂²×C₄	C₇×#41	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	4	8	no	—
496	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	C₂×C₇×C₈	1	4	yes	—
501	C₂²⋊C₄	C₂×C₇×C₈	1	4	yes	—
502	C₂²⋊C₄	C₂×C₇×C₈	1	4	yes	complemented
503	C₂²⋊C₄	C₂×C₇×C₈	1	4	yes	complemented
504	C₂²⋊C₄	C₇×M₁₆	1	4	yes	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	1	no	—
515	C₂×C₇	—	2	4	no	—
516	C₂×C₇	—	2	4	no	—
517	C₂×C₇	—	4	2	no	—
518	C₂×C₇	#2342	1	1	yes	characteristic
519	C₂×C₇	C₂×#431	1	1	yes	characteristic
520	C₂×C₇	#2924	1	1	yes	characteristic
521	C₂×C₇	C₂×C₈×D₄	1	1	yes	characteristic
522	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
523	C₂×C₇	#2972	1	1	yes	characteristic
524	C₂×C₇	#2974	1	1	yes	characteristic
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	8	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	4	4	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	4	no	—
546	C₂³	C₇×#117	1	2	yes	—
547	C₂³	C₄×C₇×D₄	1	2	yes	—
548	C₂³	C₂²×C₇×C₈	1	2	yes	—
549	C₂³	C₂²×C₇×C₈	1	2	yes	—
550	C₂³	C₂²×C₇×C₈	1	2	yes	—
551	C₂³	C₂×C₇×M₁₆	1	2	yes	—
552	C₂³	C₇×#131	1	2	yes	—
553	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	C₇×#117	1	2	yes	—
593	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
594	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
595	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
596	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
597	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
598	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
599	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
600	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
601	C₂×C₄	C₂×C₇×#41	1	2	yes	—
602	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
603	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
604	C₈	—	2	4	no	—
605	C₈	—	4	2	no	—
606	C₈	—	4	2	no	—
607	C₈	—	4	2	no	—
608	C₇	#22552	1	1	yes	characteristic, direct product factor, Sylow
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	16	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	C₇×#431	1	4	yes	complemented
630	C₂²	C₇×C₈×D₄	1	4	yes	—
631	C₂²	C₂×C₇×#117	1	1	yes	characteristic
632	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
633	C₂²	C₇×#518	1	1	yes	characteristic
634	C₂²	C₂³×C₇×C₈	1	1	yes	characteristic
635	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
636	C₂²	C₂×C₇×#131	1	1	yes	characteristic
637	C₂²	C₇×#568	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	C₇×#546	1	2	yes	—
650	C₄	C₇×#551	1	2	yes	—
651	C₂	—	2	4	no	—
652	C₂	—	2	4	no	—
653	C₂	—	4	2	no	—
654	C₂	C₇×#2342	1	1	yes	characteristic
655	C₂	C₂×C₇×#431	1	1	yes	characteristic
656	C₂	C₇×#2924	1	1	yes	characteristic
657	C₂	C₂×C₇×C₈×D₄	1	1	yes	characteristic
658	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
659	C₂	C₇×#2972	1	1	yes	characteristic
660	C₂	C₇×#2974	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂²	C₂³×C₇×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂⁵×C₇	C₂×C₄
LCS	G ▷ C₂² ▷ 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×#431	C₂	semidirect
4. C₇×#1923	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₇×#1850	C₂	semidirect
7. C₇×#1817	C₂	semidirect
8. C₇×#1797	C₂	semidirect
10. C₇×C₈×C₂²⋊C₄	C₂	semidirect
11. C₄×C₇×C₂²⋊C₈	C₂	semidirect
19. C₂×C₇×C₄⋊C₈	C₂²	semidirect
20. C₂×C₇×C₄⋊C₈	C₂²	semidirect
29. C₂×C₄×C₇×C₈	C₂²	semidirect
30. C₂×C₄×C₇×C₈	C₂²	semidirect
41. C₇×#336	C₂²	semidirect
42. C₇×#336	C₂²	semidirect
43. C₇×#336	C₂²	semidirect
44. C₇×#336	C₂²	semidirect
45. #22552	C₇	direct (N × H)
69. C₂×C₇×C₂²⋊C₄	C₈	semidirect
108. C₂×#431	C₂×C₇	semidirect
111. #1923	C₂×C₇	semidirect
112. #1923	C₂×C₇	semidirect
113. #1850	C₂×C₇	semidirect
114. #1817	C₂×C₇	semidirect
115. #1797	C₂×C₇	semidirect
117. C₈×C₂²⋊C₄	C₂×C₇	semidirect
118. C₄×C₂²⋊C₈	C₂×C₇	semidirect
159. C₂²×C₄×C₇	C₂×C₈	semidirect
160. C₂²×C₄×C₇	C₂×C₈	semidirect
194. C₇×C₂²⋊C₄	C₂×C₈	semidirect
195. C₇×C₂²⋊C₄	C₂×C₈	semidirect
214. C₂×C₄⋊C₈	C₂²×C₇	semidirect
215. C₂×C₄⋊C₈	C₂²×C₇	semidirect
224. C₂×C₄×C₈	C₂²×C₇	semidirect
225. C₂×C₄×C₈	C₂²×C₇	semidirect
236. #336	C₂²×C₇	semidirect
237. #336	C₂²×C₇	semidirect
238. #336	C₂²×C₇	semidirect
239. #336	C₂²×C₇	semidirect
346. C₂×C₂²⋊C₄	C₇×C₈	semidirect
405. C₂²×C₇	#431	semidirect
467. C₂²×C₄	C₂×C₇×C₈	semidirect
468. C₂²×C₄	C₂×C₇×C₈	semidirect
502. C₂²⋊C₄	C₂×C₇×C₈	semidirect
503. C₂²⋊C₄	C₂×C₇×C₈	semidirect
608. C₇	#22552	direct (N × H)
629. C₂²	C₇×#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#431	2
C₂²×C₇×C₂²⋊C₈	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₇×#1923	2
C₇×#1850	2
C₇×#1817	2
C₇×#1797	2
C₇×#1779	2
C₇×C₈×C₂²⋊C₄	2
C₄×C₇×C₂²⋊C₈	2
#22552	7

Subgroups — C7×#22552 #13199768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22552 #13199768