Subgroups — C₇×#22066 #13199282

Order 1792.

830 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2395	C₂	1	1	yes	maximal, characteristic
4	C₇×#1940	C₂	1	2	yes	maximal, complemented
5	C₇×#1924	C₂	1	2	yes	maximal, complemented
6	C₇×#1916	C₂	1	2	yes	maximal, complemented
7	C₇×#1870	C₂	1	1	yes	maximal, characteristic
8	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1850	C₂	1	2	yes	maximal, complemented
10	C₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₇×#117	C₂²	1	1	yes	characteristic
17	C₇×C₈×D₄	—	2	4	no	—
18	C₇×#424	—	2	4	no	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₇×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₇×#400	C₄	1	1	yes	characteristic
30	C₇×#399	C₄	1	1	yes	characteristic
31	C₇×#398	C₄	1	1	yes	characteristic
32	C₇×#397	C₄	1	2	yes	—
33	C₇×#397	C₄	1	1	yes	characteristic
34	C₇×#394	C₄	1	2	yes	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₇×C₂²⋊C₄	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	#22066	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₂×C₇×M₁₆	—	2	2	no	—
48	C₂×C₇×M₁₆	—	4	2	no	—
49	C₂²×C₇×C₈	—	2	2	no	—
50	C₂²×C₇×C₈	—	4	2	no	—
51	C₂²×C₇×C₈	—	4	2	no	—
52	C₂²×C₇×C₈	D₄	1	4	yes	—
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₄×C₇×D₄	—	2	2	no	—
60	C₄×C₇×D₄	—	2	2	no	—
61	C₇×#117	—	2	2	no	—
62	C₇×#117	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
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	2	yes	—
73	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₇×C₄⋊C₈	—	2	4	no	—
78	C₇×C₄⋊C₈	—	2	4	no	—
79	C₇×C₄⋊C₈	—	2	2	no	—
80	C₇×C₄⋊C₈	—	4	2	no	—
81	C₇×C₂²⋊C₈	—	2	2	no	—
82	C₇×C₂²⋊C₈	—	2	2	no	—
83	C₇×C₂²⋊C₈	—	2	2	no	—
84	C₇×C₂²⋊C₈	—	4	2	no	—
85	C₇×#97	—	4	2	no	—
86	C₄×C₇×C₈	—	2	2	no	—
87	C₇×#95	C₂×C₄	1	2	yes	—
88	C₇×#95	C₂×C₄	1	1	yes	characteristic
89	C₇×#95	C₂×C₄	1	2	yes	—
90	C₇×#95	C₂×C₄	1	1	yes	characteristic
91	C₇×#95	C₂×C₄	1	2	yes	—
92	C₇×#95	C₂×C₄	1	2	yes	—
93	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
94	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
95	#2395	C₂×C₇	1	1	yes	characteristic
96	#1940	C₂×C₇	1	2	yes	complemented
97	#1924	C₂×C₇	1	2	yes	complemented
98	#1916	C₂×C₇	1	2	yes	complemented
99	#1870	C₂×C₇	1	1	yes	characteristic
100	#1851	C₂×C₇	1	1	yes	characteristic, complemented
101	#1850	C₂×C₇	1	2	yes	complemented
102	#1818	C₂×C₇	1	1	yes	characteristic, complemented
103	#1752	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	2	no	—
107	C₂×C₇×D₄	—	2	2	no	—
108	C₂×C₇×D₄	—	2	2	no	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇	#41	1	2	yes	—
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₇×M₁₆	—	4	4	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	2	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	2	no	—
139	C₂×C₇×C₈	—	4	4	no	—
140	C₂×C₇×C₈	—	4	4	no	—
141	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	4	no	—
147	C₇×C₄⋊C₄	—	4	2	no	—
148	C₇×C₂²⋊C₄	—	2	4	no	—
149	C₇×C₂²⋊C₄	—	2	2	no	—
150	C₇×C₂²⋊C₄	—	2	4	no	—
151	C₇×C₂²⋊C₄	—	2	2	no	—
152	C₇×C₂²⋊C₄	—	4	2	no	—
153	C₇×C₂²⋊C₄	—	4	2	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	2	2	no	—
156	C₄²×C₇	—	2	2	no	—
157	C₄²×C₇	—	2	1	no	—
158	C₄²×C₇	—	2	2	no	—
159	C₄²×C₇	—	2	2	no	—
160	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
161	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
164	C₂×#117	C₂²×C₇	1	1	yes	characteristic
165	C₈×D₄	—	2	4	no	—
166	#424	—	2	4	no	—
167	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
168	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
169	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
171	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
175	C₂×#97	C₂²×C₇	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
177	#400	C₄×C₇	1	1	yes	characteristic
178	#399	C₄×C₇	1	1	yes	characteristic
179	#398	C₄×C₇	1	1	yes	characteristic
180	#397	C₄×C₇	1	2	yes	—
181	#397	C₄×C₇	1	1	yes	characteristic
182	#394	C₄×C₇	1	2	yes	—
183	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
184	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
185	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
186	#336	C₂²×C₇	1	2	yes	—
187	#336	C₂²×C₇	1	2	yes	—
188	#336	C₂²×C₇	1	2	yes	—
189	#336	C₂²×C₇	1	2	yes	—
190	#336	C₂²×C₇	1	2	yes	—
191	C₂³×C₇	—	2	1	no	—
192	C₂³×C₇	—	2	2	no	—
193	C₂³×C₇	—	2	2	no	—
194	C₂³×C₇	—	2	1	no	—
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	—	2	1	no	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	C₄×D₄	1	2	yes	—
200	C₂³×C₇	#131	1	2	yes	—
201	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
202	C₇×D₄	—	2	8	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	4	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	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	—	2	2	no	—
217	C₂×C₄×C₇	—	2	2	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	—	2	2	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₇	#131	1	2	yes	—
230	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
233	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
234	C₇×C₈	—	2	2	no	—
235	C₇×C₈	—	2	2	no	—
236	C₇×C₈	—	4	1	no	—
237	C₇×C₈	—	4	2	no	—
238	C₇×C₈	—	4	1	no	—
239	C₇×C₈	—	4	2	no	—
240	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	4	2	no	—
247	C₂²×C₈	—	4	2	no	—
248	C₂²×C₈	C₇×D₄	1	4	yes	—
249	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₇	1	2	yes	—
251	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇	1	2	yes	—
253	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
270	C₂×C₄²	C₂³×C₇	1	2	yes	—
271	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₇	1	2	yes	—
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	4	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	4	2	no	—
281	#97	—	4	2	no	—
282	C₄×C₈	—	2	2	no	—
283	#95	C₂×C₄×C₇	1	2	yes	—
284	#95	C₂×C₄×C₇	1	1	yes	characteristic
285	#95	C₂×C₄×C₇	1	2	yes	—
286	#95	C₂×C₄×C₇	1	1	yes	characteristic
287	#95	C₂×C₄×C₇	1	2	yes	—
288	#95	C₂×C₄×C₇	1	2	yes	—
289	C₂²×C₇	—	2	2	no	—
290	C₂²×C₇	—	2	2	no	—
291	C₂²×C₇	—	2	2	no	—
292	C₂²×C₇	—	2	2	no	—
293	C₂²×C₇	—	2	4	no	—
294	C₂²×C₇	—	4	1	no	—
295	C₂²×C₇	—	4	1	no	—
296	C₂²×C₇	—	4	2	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₇	#520	1	2	yes	—
301	C₂²×C₇	C₂×#131	1	1	yes	characteristic
302	C₂²×C₇	C₂×#131	1	1	yes	characteristic
303	C₂²×C₇	#568	1	2	yes	—
304	C₄×C₇	—	2	2	no	—
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	4	1	no	—
307	C₄×C₇	—	4	2	no	—
308	C₄×C₇	—	4	1	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	4	2	no	—
311	C₄×C₇	—	4	2	no	—
312	C₄×C₇	#534	1	1	yes	characteristic
313	C₄×C₇	#536	1	1	yes	characteristic
314	C₄×C₇	#539	1	2	yes	—
315	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
316	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
327	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
331	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
335	C₂²×C₄	C₇×#41	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
337	M₁₆	—	4	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	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	—	4	4	no	—
351	C₂×C₈	—	4	4	no	—
352	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
353	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₂×C₇	—	4	2	no	—
372	C₂×C₇	—	4	2	no	—
373	C₂×C₇	#2322	1	1	yes	characteristic
374	C₂×C₇	#2929	1	1	yes	characteristic
375	C₂×C₇	#2932	1	1	yes	characteristic
376	C₂×C₇	#2992	1	2	yes	—
377	C₂×C₇	#2993	1	2	yes	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	C₄×C₇×D₄	1	2	yes	—
387	C₂³	C₇×#131	1	2	yes	—
388	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
389	D₄	—	2	8	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	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	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
416	C₂×C₄	C₇×#131	1	2	yes	—
417	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
419	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
421	C₈	—	2	2	no	—
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₇	#22066	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
439	C₂²	C₇×#520	1	2	yes	—
440	C₂²	C₂×C₇×#131	1	1	yes	characteristic
441	C₂²	C₂×C₇×#131	1	1	yes	characteristic
442	C₂²	C₇×#568	1	2	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	C₇×#534	1	1	yes	characteristic
452	C₄	C₇×#536	1	1	yes	characteristic
453	C₄	C₇×#539	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	C₇×#2322	1	1	yes	characteristic
457	C₂	C₇×#2929	1	1	yes	characteristic
458	C₂	C₇×#2932	1	1	yes	characteristic
459	C₂	C₇×#2992	1	2	yes	—
460	C₂	C₇×#2993	1	2	yes	—

	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×#1924	C₂	semidirect
6. C₇×#1916	C₂	semidirect
8. C₇×#1851	C₂	semidirect
9. C₇×#1850	C₂	semidirect
10. C₇×#1818	C₂	semidirect
11. C₇×#1752	C₂	semidirect
43. #22066	C₇	direct (N × H)
94. C₂×#424	C₂×C₇	semidirect
96. #1940	C₂×C₇	semidirect
97. #1924	C₂×C₇	semidirect
98. #1916	C₂×C₇	semidirect
100. #1851	C₂×C₇	semidirect
101. #1850	C₂×C₇	semidirect
102. #1818	C₂×C₇	semidirect
103. #1752	C₂×C₇	semidirect
427. C₇	#22066	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×C₈×D₄	2
C₂×C₇×#424	2
C₇×#2395	2
C₇×#1940	2
C₇×#1924	2
C₇×#1916	2
C₇×#1870	2
C₇×#1851	2
C₇×#1850	2
C₇×#1818	2
C₇×#1752	2
#22066	7

Subgroups — C7×#22066 #13199282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22066 #13199282