Subgroups — C₇×#23054 #13200270

Order 1792.

824 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1924	C₂	1	2	yes	maximal
7	C₇×#1924	C₂	1	2	yes	maximal
8	C₇×#1916	C₂	1	2	yes	maximal, complemented
9	C₇×#1771	C₂	1	2	yes	maximal, complemented
10	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
15	C₇×#446	—	2	4	no	—
16	C₇×#431	—	2	4	no	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	2	yes	—
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	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₇×#391	C₄	1	1	yes	characteristic
30	C₇×#389	C₄	1	1	yes	characteristic
31	C₇×#387	C₄	1	2	yes	—
32	C₇×#385	C₄	1	2	yes	—
33	C₇×#380	C₄	1	1	yes	characteristic
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#23054	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	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	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₇×C₂²⋊Q₈	—	2	4	no	—
55	C₄×C₇×Q₈	—	2	2	no	—
56	C₄×C₇×Q₈	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
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	2	yes	—
63	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₇	—	2	2	no	—
66	C₂×C₄²×C₇	—	2	2	no	—
67	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₇×C₄⋊C₈	—	2	4	no	—
74	C₇×C₄⋊C₈	—	2	4	no	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×C₄⋊C₈	D₄	1	4	yes	—
77	C₇×C₂²⋊C₈	—	2	4	no	—
78	C₇×C₂²⋊C₈	—	2	2	no	—
79	C₇×C₂²⋊C₈	—	2	2	no	—
80	C₇×#97	—	2	4	no	—
81	C₇×#97	—	2	4	no	—
82	C₄×C₇×C₈	—	2	4	no	—
83	C₄×C₇×C₈	—	2	2	no	—
84	C₄×C₇×C₈	—	2	2	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	C₇×#95	C₂×C₄	1	2	yes	—
89	C₇×#95	C₂×C₄	1	2	yes	—
90	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂×#431	C₂×C₇	1	1	yes	characteristic
92	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
93	#1984	C₂×C₇	1	1	yes	characteristic, complemented
94	#1939	C₂×C₇	1	1	yes	characteristic, complemented
95	#1924	C₂×C₇	1	2	yes	—
96	#1924	C₂×C₇	1	2	yes	—
97	#1916	C₂×C₇	1	2	yes	complemented
98	#1771	C₂×C₇	1	2	yes	complemented
99	#1770	C₂×C₇	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
101	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₇×Q₈	—	2	2	no	—
103	C₂×C₇×Q₈	—	2	2	no	—
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂²×C₄×C₇	—	2	2	no	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	2	2	no	—
109	C₂²×C₄×C₇	—	2	1	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	1	no	—
115	C₂²×C₄×C₇	—	4	1	no	—
116	C₂²×C₄×C₇	M₁₆	1	4	yes	—
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	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	C₂⁴	1	1	yes	characteristic
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
143	C₂×C₇×C₈	#41	1	2	yes	—
144	C₂×C₇×C₈	#41	1	2	yes	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	4	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	4	no	—
149	C₇×C₄⋊C₄	—	2	4	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₂²⋊C₄	—	2	4	no	—
152	C₇×C₂²⋊C₄	—	4	2	no	—
153	C₄²×C₇	—	2	2	no	—
154	C₄²×C₇	—	2	2	no	—
155	C₄²×C₇	—	2	1	no	—
156	C₄²×C₇	—	2	2	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	2	2	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	—	2	2	no	—
161	C₄²×C₇	C₂×D₄	1	2	yes	—
162	C₄²×C₇	#41	1	2	yes	—
163	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
164	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
165	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
166	#446	—	2	4	no	—
167	#431	—	2	4	no	—
168	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
170	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
173	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
175	C₂×#97	C₂²×C₇	1	2	yes	—
176	C₂×#97	C₂²×C₇	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
178	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
180	#391	C₄×C₇	1	1	yes	characteristic
181	#389	C₄×C₇	1	1	yes	characteristic
182	#387	C₄×C₇	1	2	yes	—
183	#385	C₄×C₇	1	2	yes	—
184	#380	C₄×C₇	1	1	yes	characteristic
185	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
186	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
188	#336	C₂²×C₇	1	1	yes	characteristic
189	#336	C₂²×C₇	1	2	yes	—
190	#336	C₂²×C₇	1	2	yes	—
191	#336	C₂²×C₇	1	2	yes	—
192	#336	C₂²×C₇	1	2	yes	—
193	#336	C₂²×C₇	1	1	yes	characteristic
194	C₂³×C₇	—	2	1	no	—
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	—	2	1	no	—
197	C₂³×C₇	—	2	1	no	—
198	C₂³×C₇	—	2	1	no	—
199	C₂³×C₇	—	2	1	no	—
200	C₂³×C₇	C₂×M₁₆	1	2	yes	—
201	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
202	C₇×Q₈	—	4	4	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	1	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	8	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	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	4	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	1	no	—
228	C₂×C₄×C₇	—	4	1	no	—
229	C₂×C₄×C₇	—	4	1	no	—
230	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
233	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
234	C₂×C₄×C₇	#131	1	2	yes	—
235	C₂×C₄×C₇	#131	1	2	yes	—
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
241	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
242	C₇×C₈	—	2	4	no	—
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	—	2	2	no	—
245	C₇×C₈	—	4	1	no	—
246	C₇×C₈	—	4	2	no	—
247	C₇×C₈	—	4	1	no	—
248	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
249	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₇	1	2	yes	—
256	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
258	C₂²⋊Q₈	—	2	4	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×Q₈	—	2	2	no	—
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×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
272	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₇	1	2	yes	—
274	C₂×C₄²	C₂³×C₇	1	2	yes	—
275	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	C₄⋊C₈	—	2	4	no	—
278	C₄⋊C₈	—	2	4	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	C₇×D₄	1	4	yes	—
281	C₂²⋊C₈	—	2	4	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	#97	—	2	4	no	—
285	#97	—	2	4	no	—
286	C₄×C₈	—	2	4	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	C₂×C₄×C₇	1	2	yes	—
290	#95	C₂×C₄×C₇	1	2	yes	—
291	#95	C₂×C₄×C₇	1	2	yes	—
292	#95	C₂×C₄×C₇	1	2	yes	—
293	#95	C₂×C₄×C₇	1	2	yes	—
294	C₂²×C₇	—	2	2	no	—
295	C₂²×C₇	—	2	2	no	—
296	C₂²×C₇	—	2	2	no	—
297	C₂²×C₇	—	4	1	no	—
298	C₂²×C₇	—	4	1	no	—
299	C₂²×C₇	—	4	1	no	—
300	C₂²×C₇	—	4	1	no	—
301	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₇	C₄×#41	1	1	yes	characteristic
303	C₂²×C₇	#519	1	1	yes	characteristic
304	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
305	C₂²×C₇	C₂×#131	1	1	yes	characteristic
306	C₂²×C₇	C₂×#131	1	1	yes	characteristic
307	C₂²×C₇	#568	1	1	yes	characteristic
308	C₄×C₇	—	2	2	no	—
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	2	2	no	—
311	C₄×C₇	—	4	1	no	—
312	C₄×C₇	—	4	2	no	—
313	C₄×C₇	—	4	2	no	—
314	C₄×C₇	—	4	2	no	—
315	C₄×C₇	—	4	2	no	—
316	C₄×C₇	#435	1	4	yes	—
317	C₄×C₇	#547	1	1	yes	characteristic
318	C₄×C₇	#548	1	1	yes	characteristic
319	C₄×C₇	#552	1	1	yes	characteristic
320	C₄×C₇	#556	1	1	yes	characteristic
321	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	C₇×M₁₆	1	4	yes	—
337	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
363	C₂×C₈	C₇×#41	1	2	yes	—
364	C₂×C₈	C₇×#41	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	C₂×C₇×D₄	1	2	yes	—
382	C₄²	C₇×#41	1	2	yes	—
383	C₂×C₇	—	4	2	no	—
384	C₂×C₇	#2362	1	1	yes	characteristic
385	C₂×C₇	C₂×#435	1	1	yes	characteristic
386	C₂×C₇	#2933	1	1	yes	characteristic
387	C₂×C₇	#2965	1	1	yes	characteristic
388	C₂×C₇	#2969	1	1	yes	characteristic
389	C₂×C₇	#2983	1	1	yes	characteristic
390	C₂×C₇	#2986	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	C₂×C₇×M₁₆	1	2	yes	—
398	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
399	Q₈	—	4	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	1	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	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
428	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
429	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
430	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
431	C₂×C₄	C₇×#131	1	2	yes	—
432	C₂×C₄	C₇×#131	1	2	yes	—
433	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
434	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
437	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
439	C₈	—	2	4	no	—
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	—	4	1	no	—
443	C₈	—	4	2	no	—
444	C₈	—	4	1	no	—
445	C₇	#23054	1	1	yes	characteristic, direct product factor, Sylow
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
454	C₂²	C₄×C₇×#41	1	1	yes	characteristic
455	C₂²	C₇×#519	1	1	yes	characteristic
456	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
457	C₂²	C₂×C₇×#131	1	1	yes	characteristic
458	C₂²	C₂×C₇×#131	1	1	yes	characteristic
459	C₂²	C₇×#568	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	1	no	—
468	C₄	C₇×#435	1	4	yes	—
469	C₄	C₇×#547	1	1	yes	characteristic
470	C₄	C₇×#548	1	1	yes	characteristic
471	C₄	C₇×#552	1	1	yes	characteristic
472	C₄	C₇×#556	1	1	yes	characteristic
473	C₂	—	4	2	no	—
474	C₂	C₇×#2362	1	1	yes	characteristic
475	C₂	C₂×C₇×#435	1	1	yes	characteristic
476	C₂	C₇×#2933	1	1	yes	characteristic
477	C₂	C₇×#2965	1	1	yes	characteristic
478	C₂	C₇×#2969	1	1	yes	characteristic
479	C₂	C₇×#2983	1	1	yes	characteristic
480	C₂	C₇×#2986	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
1. C₂×C₇×#446	C₂	semidirect
4. C₇×#1984	C₂	semidirect
5. C₇×#1939	C₂	semidirect
8. C₇×#1916	C₂	semidirect
9. C₇×#1771	C₂	semidirect
10. C₇×#1770	C₂	semidirect
43. #23054	C₇	direct (N × H)
90. C₂×#446	C₂×C₇	semidirect
93. #1984	C₂×C₇	semidirect
94. #1939	C₂×C₇	semidirect
97. #1916	C₂×C₇	semidirect
98. #1771	C₂×C₇	semidirect
99. #1770	C₂×C₇	semidirect
445. C₇	#23054	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×#446	2
C₂×C₇×#431	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#1984	2
C₇×#1939	2
C₇×#1924	2
C₇×#1916	2
C₇×#1771	2
C₇×#1770	2
C₄×C₇×C₂²⋊C₈	2
#23054	7

Subgroups — C7×#23054 #13200270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23054 #13200270