Subgroups — C₇×#22652 #13199868

Order 1792.

964 conjugacy classes of subgroups.

The subgroup lattice has 458 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×C₇×#424	C₂	1	2	yes	maximal, complemented
3	C₇×#2293	C₂	1	1	yes	maximal, characteristic
4	C₇×#1940	C₂	1	2	yes	maximal, complemented
5	C₇×#1851	C₂	1	2	yes	maximal, complemented
6	C₇×#1850	C₂	1	2	yes	maximal, complemented
7	C₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1798	C₂	1	2	yes	maximal, complemented
9	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₇×C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₇×#117	C₂²	1	2	yes	—
14	C₇×#435	—	2	8	no	—
15	C₇×#424	—	2	8	no	—
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₇×#97	C₂²	1	2	yes	—
27	C₇×#390	C₄	1	1	yes	characteristic
28	C₇×#390	C₄	1	1	yes	characteristic
29	C₇×#389	C₄	1	1	yes	characteristic
30	C₇×#389	C₄	1	1	yes	characteristic
31	C₇×#388	C₄	1	2	yes	—
32	C₇×#388	C₄	1	2	yes	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₄³×C₇	C₂²	1	1	yes	characteristic
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	2	yes	—
39	#22652	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₇	C₂³	1	2	yes	—
42	C₂×C₇×M₁₆	—	2	4	no	—
43	C₂×C₇×M₁₆	—	2	4	no	—
44	C₂×C₇×M₁₆	—	4	2	no	—
45	C₂²×C₇×C₈	—	2	4	no	—
46	C₂²×C₇×C₈	—	2	4	no	—
47	C₂²×C₇×C₈	—	4	2	no	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₄×C₇×D₄	D₄	1	4	yes	—
53	C₄×C₇×D₄	Q₈	1	4	yes	—
54	C₇×#117	—	2	4	no	—
55	C₇×#117	—	2	4	no	—
56	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
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×C₂²⋊C₄	C₂×C₄	1	2	yes	—
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	2	yes	—
65	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×C₄⋊C₈	—	2	4	no	—
75	C₇×C₄⋊C₈	—	2	4	no	—
76	C₇×C₄⋊C₈	—	2	4	no	—
77	C₇×C₄⋊C₈	—	2	4	no	—
78	C₇×C₄⋊C₈	—	2	2	no	—
79	C₇×C₄⋊C₈	—	4	1	no	—
80	C₇×C₄⋊C₈	—	4	1	no	—
81	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
82	C₇×C₂²⋊C₈	—	2	4	no	—
83	C₇×C₂²⋊C₈	—	2	4	no	—
84	C₇×#97	—	2	4	no	—
85	C₇×#95	C₂×C₄	1	2	yes	—
86	C₇×#95	C₂×C₄	1	2	yes	—
87	C₇×#95	C₂×C₄	1	2	yes	—
88	C₂×#435	C₂×C₇	1	2	yes	—
89	C₂×#424	C₂×C₇	1	2	yes	complemented
90	#2293	C₂×C₇	1	1	yes	characteristic
91	#1940	C₂×C₇	1	2	yes	complemented
92	#1851	C₂×C₇	1	2	yes	complemented
93	#1850	C₂×C₇	1	2	yes	complemented
94	#1842	C₂×C₇	1	1	yes	characteristic, complemented
95	#1798	C₂×C₇	1	2	yes	complemented
96	#1767	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
98	C₂×C₇×D₄	—	4	1	no	—
99	C₂×C₇×D₄	—	4	1	no	—
100	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	2	no	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
117	C₇×M₁₆	—	4	8	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	2	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	2	2	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	2	2	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	4	8	no	—
130	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
131	C₇×C₄⋊C₄	—	2	4	no	—
132	C₇×C₄⋊C₄	—	2	4	no	—
133	C₇×C₄⋊C₄	—	4	1	no	—
134	C₇×C₄⋊C₄	—	4	1	no	—
135	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
136	C₇×C₂²⋊C₄	—	2	4	no	—
137	C₇×C₂²⋊C₄	—	2	4	no	—
138	C₇×C₂²⋊C₄	—	2	4	no	—
139	C₇×C₂²⋊C₄	—	4	2	no	—
140	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
141	C₄²×C₇	—	2	2	no	—
142	C₄²×C₇	—	2	2	no	—
143	C₄²×C₇	—	2	2	no	—
144	C₄²×C₇	—	2	1	no	—
145	C₄²×C₇	—	2	1	no	—
146	C₄²×C₇	—	4	1	no	—
147	C₄²×C₇	—	4	1	no	—
148	C₄²×C₇	—	4	1	no	—
149	C₄²×C₇	C₂×D₄	1	2	yes	—
150	C₄²×C₇	C₂×D₄	1	2	yes	—
151	C₄²×C₇	C₂×Q₈	1	2	yes	—
152	C₄²×C₇	#41	1	2	yes	—
153	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
154	C₂³×C₈	C₂²×C₇	1	2	yes	—
155	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
156	C₂×#117	C₂²×C₇	1	2	yes	—
157	#435	—	2	8	no	—
158	#424	—	2	8	no	—
159	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
160	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
161	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
162	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
164	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
168	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
169	C₂×#97	C₂²×C₇	1	2	yes	—
170	#390	C₄×C₇	1	1	yes	characteristic
171	#390	C₄×C₇	1	1	yes	characteristic
172	#389	C₄×C₇	1	1	yes	characteristic
173	#389	C₄×C₇	1	1	yes	characteristic
174	#388	C₄×C₇	1	2	yes	—
175	#388	C₄×C₇	1	2	yes	—
176	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
177	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
178	C₄³	C₂²×C₇	1	1	yes	characteristic
179	#336	C₂²×C₇	1	2	yes	—
180	#336	C₂²×C₇	1	2	yes	—
181	#336	C₂²×C₇	1	2	yes	—
182	C₂³×C₇	—	2	2	no	—
183	C₂³×C₇	—	2	2	no	—
184	C₂³×C₇	—	2	2	no	—
185	C₂³×C₇	—	2	2	no	—
186	C₂³×C₇	—	2	2	no	—
187	C₂³×C₇	—	2	2	no	—
188	C₂³×C₇	C₂×C₄⋊C₄	1	4	yes	—
189	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
190	C₇×D₄	—	4	4	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	1	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	1	no	—
200	C₂×C₄×C₇	—	2	1	no	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	4	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	4	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	1	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
217	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
218	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
219	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₇	#131	1	2	yes	—
222	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
228	C₇×C₈	—	2	4	no	—
229	C₇×C₈	—	4	2	no	—
230	C₇×C₈	—	4	2	no	—
231	C₇×C₈	—	4	2	no	—
232	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₇	1	2	yes	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	—	4	2	no	—
237	C₂²×C₈	—	2	4	no	—
238	C₂²×C₈	—	2	4	no	—
239	C₂²×C₈	—	4	2	no	—
240	C₂²×C₈	C₂³×C₇	1	2	yes	—
241	C₂²×C₈	C₂³×C₇	1	2	yes	—
242	C₂²×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₇	1	2	yes	—
244	C₄×D₄	C₇×D₄	1	4	yes	—
245	C₄×D₄	C₇×Q₈	1	4	yes	—
246	#117	—	2	4	no	—
247	#117	—	2	4	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
258	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
260	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₇	1	2	yes	—
263	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
266	C₄⋊C₈	—	2	4	no	—
267	C₄⋊C₈	—	2	4	no	—
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	—	2	4	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	4	1	no	—
272	C₄⋊C₈	—	4	1	no	—
273	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	#97	—	2	4	no	—
277	#95	C₂×C₄×C₇	1	2	yes	—
278	#95	C₂×C₄×C₇	1	2	yes	—
279	#95	C₂×C₄×C₇	1	2	yes	—
280	C₂²×C₇	—	2	4	no	—
281	C₂²×C₇	—	2	4	no	—
282	C₂²×C₇	—	2	4	no	—
283	C₂²×C₇	—	4	2	no	—
284	C₂²×C₇	—	4	2	no	—
285	C₂²×C₇	—	4	2	no	—
286	C₂²×C₇	—	4	2	no	—
287	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
288	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂²×C₇	#520	1	1	yes	characteristic
290	C₂²×C₇	C₂×#131	1	1	yes	characteristic
291	C₂²×C₇	#568	1	1	yes	characteristic
292	C₂²×C₇	#568	1	1	yes	characteristic
293	C₂²×C₇	#568	1	1	yes	characteristic
294	C₄×C₇	—	2	4	no	—
295	C₄×C₇	—	2	2	no	—
296	C₄×C₇	—	2	2	no	—
297	C₄×C₇	—	2	2	no	—
298	C₄×C₇	—	2	2	no	—
299	C₄×C₇	—	2	2	no	—
300	C₄×C₇	—	4	2	no	—
301	C₄×C₇	—	4	2	no	—
302	C₄×C₇	—	4	1	no	—
303	C₄×C₇	D₄²	1	1	yes	characteristic
304	C₄×C₇	#547	1	1	yes	characteristic
305	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
306	C₄×C₇	#554	1	1	yes	characteristic
307	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
317	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
318	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
320	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
325	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
327	M₁₆	—	4	8	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	8	no	—
340	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	C₂×C₇×D₄	1	2	yes	—
360	C₄²	C₂×C₇×D₄	1	2	yes	—
361	C₄²	C₂×C₇×Q₈	1	2	yes	—
362	C₄²	C₇×#41	1	2	yes	—
363	C₂×C₇	—	4	4	no	—
364	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
365	C₂×C₇	#2905	1	1	yes	characteristic
366	C₂×C₇	#2906	1	1	yes	characteristic
367	C₂×C₇	#2932	1	1	yes	characteristic
368	C₂×C₇	#2935	1	1	yes	characteristic
369	C₂×C₇	#2992	1	1	yes	characteristic
370	C₂×C₇	#2995	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
378	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
379	D₄	—	4	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
406	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
407	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
408	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
409	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
410	C₂×C₄	C₇×#131	1	2	yes	—
411	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
414	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
415	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₇	#22652	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
430	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
431	C₂²	C₇×#520	1	1	yes	characteristic
432	C₂²	C₂×C₇×#131	1	1	yes	characteristic
433	C₂²	C₇×#568	1	1	yes	characteristic
434	C₂²	C₇×#568	1	1	yes	characteristic
435	C₂²	C₇×#568	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	1	no	—
445	C₄	C₇×D₄²	1	1	yes	characteristic
446	C₄	C₇×#547	1	1	yes	characteristic
447	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
448	C₄	C₇×#554	1	1	yes	characteristic
449	C₂	—	4	4	no	—
450	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
451	C₂	C₇×#2905	1	1	yes	characteristic
452	C₂	C₇×#2906	1	1	yes	characteristic
453	C₂	C₇×#2932	1	1	yes	characteristic
454	C₂	C₇×#2935	1	1	yes	characteristic
455	C₂	C₇×#2992	1	1	yes	characteristic
456	C₂	C₇×#2995	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	C₂²×C₇×D₄	C₂×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. C₂×C₇×#424	C₂	semidirect
4. C₇×#1940	C₂	semidirect
5. C₇×#1851	C₂	semidirect
6. C₇×#1850	C₂	semidirect
7. C₇×#1842	C₂	semidirect
8. C₇×#1798	C₂	semidirect
9. C₇×#1767	C₂	semidirect
39. #22652	C₇	direct (N × H)
81. C₇×C₄⋊C₈	D₄	semidirect
89. C₂×#424	C₂×C₇	semidirect
91. #1940	C₂×C₇	semidirect
92. #1851	C₂×C₇	semidirect
93. #1850	C₂×C₇	semidirect
94. #1842	C₂×C₇	semidirect
95. #1798	C₂×C₇	semidirect
96. #1767	C₂×C₇	semidirect
273. C₄⋊C₈	C₇×D₄	semidirect
421. C₇	#22652	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×C₇×#424	2
C₇×#2293	2
C₇×#1940	2
C₇×#1851	2
C₇×#1850	2
C₇×#1842	2
C₇×#1798	2
C₇×#1767	2
#22652	7

Subgroups — C7×#22652 #13199868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22652 #13199868