Subgroups — C₇×#22627 #13199843

Order 1792.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₇×#1940	C₂	1	2	yes	maximal, complemented
3	C₇×#1917	C₂	1	2	yes	maximal, complemented
4	C₇×#1916	C₂	1	2	yes	maximal, complemented
5	C₇×#1797	C₂	1	1	yes	maximal, characteristic
6	C₇×#1797	C₂	1	1	yes	maximal, characteristic
7	C₇×#1797	C₂	1	1	yes	maximal, characteristic
8	C₇×#1771	C₂	1	2	yes	maximal, complemented
9	C₇×#1749	C₂	1	1	yes	maximal, characteristic
10	C₇×#1749	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂²×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#97	C₂²	1	2	yes	—
25	C₂×C₇×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
27	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
28	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
29	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
30	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₇×#95	C₄	1	1	yes	characteristic
36	C₂×C₇×#95	C₄	1	1	yes	characteristic
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#22627	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₂×C₇×C₄⋊C₄	—	2	4	no	—
56	C₂×C₇×C₄⋊C₄	—	2	4	no	—
57	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇	—	2	4	no	—
66	C₂×C₄²×C₇	—	4	2	no	—
67	C₂×C₄²×C₇	—	4	2	no	—
68	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊C₈	—	2	4	no	—
81	C₇×C₄⋊C₈	—	4	2	no	—
82	C₇×C₄⋊C₈	—	4	2	no	—
83	C₇×C₂²⋊C₈	—	2	2	no	—
84	C₇×C₂²⋊C₈	—	2	2	no	—
85	C₇×C₂²⋊C₈	—	2	2	no	—
86	C₇×C₂²⋊C₈	Q₈	1	4	yes	—
87	C₇×#97	—	2	4	no	—
88	C₇×#97	—	4	2	no	—
89	C₄×C₇×C₈	—	4	2	no	—
90	C₇×#95	C₂×C₄	1	1	yes	characteristic
91	C₇×#95	C₂×C₄	1	1	yes	characteristic
92	C₇×#95	C₂×C₄	1	1	yes	characteristic
93	C₇×#95	C₂×C₄	1	1	yes	characteristic
94	C₇×#95	C₂×C₄	1	1	yes	characteristic
95	C₇×#95	C₂×C₄	1	1	yes	characteristic
96	C₇×#95	C₂×C₄	1	1	yes	characteristic
97	C₇×#95	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
99	#1940	C₂×C₇	1	2	yes	complemented
100	#1917	C₂×C₇	1	2	yes	complemented
101	#1916	C₂×C₇	1	2	yes	complemented
102	#1797	C₂×C₇	1	1	yes	characteristic
103	#1797	C₂×C₇	1	1	yes	characteristic
104	#1797	C₂×C₇	1	1	yes	characteristic
105	#1771	C₂×C₇	1	2	yes	complemented
106	#1749	C₂×C₇	1	1	yes	characteristic
107	#1749	C₂×C₇	1	1	yes	characteristic
108	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
109	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	2	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	4	1	no	—
123	C₂²×C₄×C₇	—	4	1	no	—
124	C₂²×C₄×C₇	—	4	1	no	—
125	C₂²×C₄×C₇	—	4	1	no	—
126	C₂²×C₄×C₇	—	4	1	no	—
127	C₂²×C₄×C₇	—	4	1	no	—
128	C₂²×C₄×C₇	—	4	1	no	—
129	C₂²×C₄×C₇	M₁₆	1	4	yes	—
130	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
135	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₇	#41	1	2	yes	—
145	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	2	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	2	2	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	2	no	—
156	C₂×C₇×C₈	—	2	2	no	—
157	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
158	C₇×C₄⋊C₄	—	2	2	no	—
159	C₇×C₄⋊C₄	—	2	2	no	—
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	—	2	2	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	2	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	M₁₆	1	4	yes	—
166	C₄²×C₇	—	2	2	no	—
167	C₄²×C₇	—	2	2	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	2	2	no	—
170	C₄²×C₇	—	2	2	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	2	no	—
173	C₄²×C₇	—	4	1	no	—
174	C₄²×C₇	—	4	1	no	—
175	C₄²×C₇	—	4	1	no	—
176	C₄²×C₇	—	4	1	no	—
177	C₄²×C₇	#41	1	4	yes	—
178	C₂²×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
179	C₂²×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
180	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
181	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
182	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
185	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
186	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
187	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
190	C₂×#97	C₂²×C₇	1	2	yes	—
191	C₂×#97	C₂²×C₇	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
193	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
194	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
195	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
196	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
197	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
199	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
201	C₂×#95	C₄×C₇	1	1	yes	characteristic
202	C₂×#95	C₄×C₇	1	1	yes	characteristic
203	#336	C₂²×C₇	1	2	yes	—
204	#336	C₂²×C₇	1	2	yes	—
205	#336	C₂²×C₇	1	2	yes	—
206	#336	C₂²×C₇	1	2	yes	—
207	#336	C₂²×C₇	1	2	yes	—
208	#336	C₂²×C₇	1	2	yes	—
209	C₂³×C₇	—	2	1	no	—
210	C₂³×C₇	—	2	1	no	—
211	C₂³×C₇	—	2	1	no	—
212	C₂³×C₇	—	2	1	no	—
213	C₂³×C₇	C₄×Q₈	1	2	yes	—
214	C₂³×C₇	C₂×M₁₆	1	2	yes	—
215	C₂³×C₇	#131	1	2	yes	—
216	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₇	—	2	8	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	1	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	2	4	no	—
235	C₂×C₄×C₇	—	2	4	no	—
236	C₂×C₄×C₇	—	2	1	no	—
237	C₂×C₄×C₇	—	2	1	no	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	1	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	1	no	—
242	C₂×C₄×C₇	—	2	1	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	1	no	—
245	C₂×C₄×C₇	—	2	1	no	—
246	C₂×C₄×C₇	—	2	1	no	—
247	C₂×C₄×C₇	—	2	1	no	—
248	C₂×C₄×C₇	—	2	1	no	—
249	C₂×C₄×C₇	—	2	1	no	—
250	C₂×C₄×C₇	—	2	1	no	—
251	C₂×C₄×C₇	—	4	4	no	—
252	C₂×C₄×C₇	—	4	4	no	—
253	C₂×C₄×C₇	—	4	4	no	—
254	C₂×C₄×C₇	—	4	4	no	—
255	C₂×C₄×C₇	—	4	4	no	—
256	C₂×C₄×C₇	#117	1	2	yes	—
257	C₂×C₄×C₇	#117	1	2	yes	—
258	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
259	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
260	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
261	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
262	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
263	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
264	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂×#41	1	2	yes	—
267	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
268	C₇×C₈	—	2	4	no	—
269	C₇×C₈	—	4	2	no	—
270	C₇×C₈	—	4	2	no	—
271	C₇×C₈	—	4	2	no	—
272	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
273	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
274	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
276	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₇	1	2	yes	—
282	C₂²×C₈	C₂³×C₇	1	2	yes	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	4	no	—
285	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	—	4	2	no	—
295	C₂×C₄²	—	4	2	no	—
296	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
297	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
298	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
299	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
300	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
301	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
308	C₄⋊C₈	—	2	4	no	—
309	C₄⋊C₈	—	4	2	no	—
310	C₄⋊C₈	—	4	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	C₇×Q₈	1	4	yes	—
315	#97	—	2	4	no	—
316	#97	—	4	2	no	—
317	C₄×C₈	—	4	2	no	—
318	#95	C₂×C₄×C₇	1	1	yes	characteristic
319	#95	C₂×C₄×C₇	1	1	yes	characteristic
320	#95	C₂×C₄×C₇	1	1	yes	characteristic
321	#95	C₂×C₄×C₇	1	1	yes	characteristic
322	#95	C₂×C₄×C₇	1	1	yes	characteristic
323	#95	C₂×C₄×C₇	1	1	yes	characteristic
324	#95	C₂×C₄×C₇	1	1	yes	characteristic
325	#95	C₂×C₄×C₇	1	1	yes	characteristic
326	C₂²×C₇	—	2	2	no	—
327	C₂²×C₇	—	2	2	no	—
328	C₂²×C₇	—	2	2	no	—
329	C₂²×C₇	—	2	2	no	—
330	C₂²×C₇	—	2	2	no	—
331	C₂²×C₇	—	2	2	no	—
332	C₂²×C₇	#446	1	4	yes	—
333	C₂²×C₇	C₂×#117	1	1	yes	characteristic
334	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
335	C₂²×C₇	#518	1	1	yes	characteristic
336	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
337	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
338	C₂²×C₇	C₂×#131	1	1	yes	characteristic
339	C₂²×C₇	#568	1	1	yes	characteristic
340	C₄×C₇	—	2	2	no	—
341	C₄×C₇	—	2	2	no	—
342	C₄×C₇	—	2	2	no	—
343	C₄×C₇	—	2	2	no	—
344	C₄×C₇	—	2	2	no	—
345	C₄×C₇	—	2	2	no	—
346	C₄×C₇	—	2	2	no	—
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	4	1	no	—
349	C₄×C₇	—	4	1	no	—
350	C₄×C₇	—	4	1	no	—
351	C₄×C₇	—	4	1	no	—
352	C₄×C₇	—	4	1	no	—
353	C₄×C₇	#553	1	2	yes	—
354	C₄×C₇	#554	1	2	yes	—
355	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	C₇×M₁₆	1	4	yes	—
376	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
377	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
390	C₂²×C₄	C₇×#41	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	C₇×M₁₆	1	4	yes	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	4	1	no	—
420	C₄²	—	4	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	4	1	no	—
423	C₄²	C₇×#41	1	4	yes	—
424	C₂×C₇	—	2	4	no	—
425	C₂×C₇	#2345	1	1	yes	characteristic
426	C₂×C₇	#2920	1	1	yes	characteristic
427	C₂×C₇	#2924	1	1	yes	characteristic
428	C₂×C₇	C₂×#446	1	1	yes	characteristic
429	C₂×C₇	Q₈×M₁₆	1	1	yes	characteristic
430	C₂×C₇	#2973	1	1	yes	characteristic
431	C₂×C₇	#2974	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	C₄×C₇×Q₈	1	2	yes	—
437	C₂³	C₂×C₇×M₁₆	1	2	yes	—
438	C₂³	C₇×#131	1	2	yes	—
439	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	C₇×#117	1	2	yes	—
480	C₂×C₄	C₇×#117	1	2	yes	—
481	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
482	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
483	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
484	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
485	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
486	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
487	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
488	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
489	C₂×C₄	C₂×C₇×#41	1	2	yes	—
490	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
491	C₈	—	2	4	no	—
492	C₈	—	4	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₇	#22627	1	1	yes	characteristic, direct product factor, Sylow
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	C₇×#446	1	4	yes	—
503	C₂²	C₂×C₇×#117	1	1	yes	characteristic
504	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
505	C₂²	C₇×#518	1	1	yes	characteristic
506	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
507	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
508	C₂²	C₂×C₇×#131	1	1	yes	characteristic
509	C₂²	C₇×#568	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	C₇×#553	1	2	yes	—
524	C₄	C₇×#554	1	2	yes	—
525	C₂	—	2	4	no	—
526	C₂	C₇×#2345	1	1	yes	characteristic
527	C₂	C₇×#2920	1	1	yes	characteristic
528	C₂	C₇×#2924	1	1	yes	characteristic
529	C₂	C₂×C₇×#446	1	1	yes	characteristic
530	C₂	C₇×Q₈×M₁₆	1	1	yes	characteristic
531	C₂	C₇×#2973	1	1	yes	characteristic
532	C₂	C₇×#2974	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂⁴×C₇	C₂²×C₄
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
2. C₇×#1940	C₂	semidirect
3. C₇×#1917	C₂	semidirect
4. C₇×#1916	C₂	semidirect
8. C₇×#1771	C₂	semidirect
43. #22627	C₇	direct (N × H)
99. #1940	C₂×C₇	semidirect
100. #1917	C₂×C₇	semidirect
101. #1916	C₂×C₇	semidirect
105. #1771	C₂×C₇	semidirect
495. C₇	#22627	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×C₄⋊C₄	2
C₇×#1940	2
C₇×#1917	2
C₇×#1916	2
C₇×#1797	2
C₇×#1771	2
C₇×#1749	2
C₄×C₇×C₂²⋊C₈	2
#22627	7

Subgroups — C7×#22627 #13199843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22627 #13199843