Subgroups — C₇×#21492 #13198708

Order 1792.

1058 conjugacy classes of subgroups.

The subgroup lattice has 518 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, complemented
2	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2392	C₂	1	1	yes	maximal, characteristic
5	C₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1923	C₂	1	2	yes	maximal, complemented
8	C₇×#1869	C₂	1	2	yes	maximal, complemented
9	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1752	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₇×#435	—	2	8	no	—
19	C₇×C₈×D₄	—	2	4	no	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₇×#405	—	2	4	no	—
28	C₂×C₇×#97	C₂²	1	2	yes	—
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₂×C₇×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₇×#398	C₄	1	1	yes	characteristic
34	C₇×#397	C₄	1	1	yes	characteristic
35	C₇×#396	C₄	1	2	yes	—
36	C₇×#394	C₄	1	2	yes	—
37	C₇×#394	C₄	1	1	yes	characteristic
38	C₇×#392	C₄	1	1	yes	characteristic
39	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	#21492	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
49	C₂×C₇×M₁₆	—	2	2	no	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂×C₇×M₁₆	D₄	1	4	yes	complemented
52	C₂²×C₇×C₈	—	2	2	no	—
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	—	2	2	no	—
55	C₂²×C₇×C₈	—	2	4	no	—
56	C₂²×C₇×C₈	—	2	4	no	—
57	C₂²×C₇×C₈	—	2	4	no	—
58	C₂²×C₇×C₈	C₂³	1	2	yes	—
59	C₂²×C₇×C₈	C₂³	1	2	yes	—
60	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₄×C₇×D₄	—	2	4	no	—
65	C₄×C₇×D₄	—	2	4	no	—
66	C₄×C₇×D₄	—	2	2	no	—
67	C₄×C₇×D₄	—	2	2	no	—
68	C₇×#117	—	2	2	no	—
69	C₇×#117	—	2	2	no	—
70	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
85	C₇×C₄⋊C₈	—	2	4	no	—
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	2	no	—
88	C₇×C₂²⋊C₈	—	2	4	no	—
89	C₇×C₂²⋊C₈	—	2	4	no	—
90	C₇×C₂²⋊C₈	—	2	4	no	—
91	C₇×C₂²⋊C₈	—	2	4	no	—
92	C₇×#97	—	2	2	no	—
93	C₇×#97	—	2	4	no	—
94	C₇×#97	—	2	2	no	—
95	C₄×C₇×C₈	—	2	2	no	—
96	C₄×C₇×C₈	D₄	1	4	yes	complemented
97	C₇×#95	C₂×C₄	1	2	yes	—
98	C₇×#95	C₂×C₄	1	2	yes	—
99	C₇×#95	C₂×C₄	1	1	yes	characteristic
100	C₇×#95	C₂×C₄	1	1	yes	characteristic
101	C₂×#435	C₂×C₇	1	2	yes	complemented
102	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
103	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
104	#2392	C₂×C₇	1	1	yes	characteristic
105	#1955	C₂×C₇	1	1	yes	characteristic, complemented
106	#1940	C₂×C₇	1	1	yes	characteristic, complemented
107	#1923	C₂×C₇	1	2	yes	complemented
108	#1869	C₂×C₇	1	2	yes	complemented
109	#1798	C₂×C₇	1	1	yes	characteristic, complemented
110	#1770	C₂×C₇	1	1	yes	characteristic, complemented
111	#1752	C₂×C₇	1	2	yes	complemented
112	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
113	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
114	C₂×C₇×D₄	—	2	4	no	—
115	C₂×C₇×D₄	—	2	4	no	—
116	C₂×C₇×D₄	—	2	4	no	—
117	C₂×C₇×D₄	—	2	2	no	—
118	C₂×C₇×D₄	—	4	2	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	C₂²×C₄	1	2	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	2	yes	—
133	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇	#41	1	2	yes	—
139	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
140	C₇×M₁₆	—	2	8	no	—
141	C₂×C₇×C₈	—	2	8	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	1	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	—	4	8	no	—
155	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
156	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
157	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
159	C₂×C₇×C₈	#41	1	2	yes	—
160	C₂×C₇×C₈	#41	1	2	yes	—
161	C₇×C₄⋊C₄	—	2	2	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	4	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	4	2	no	—
166	C₇×C₂²⋊C₄	—	2	4	no	—
167	C₇×C₂²⋊C₄	—	2	4	no	—
168	C₇×C₂²⋊C₄	—	2	2	no	—
169	C₇×C₂²⋊C₄	—	2	2	no	—
170	C₇×C₂²⋊C₄	—	2	4	no	—
171	C₇×C₂²⋊C₄	—	2	4	no	—
172	C₇×C₂²⋊C₄	—	4	2	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	2	2	no	—
175	C₄²×C₇	—	2	1	no	—
176	C₄²×C₇	—	2	2	no	—
177	C₄²×C₇	C₂×D₄	1	2	yes	—
178	C₄²×C₇	#41	1	2	yes	—
179	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
181	C₂³×C₈	C₂²×C₇	1	2	yes	—
182	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
183	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
184	C₂×#117	C₂²×C₇	1	1	yes	characteristic
185	#435	—	2	8	no	—
186	C₈×D₄	—	2	4	no	—
187	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
192	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
194	#405	—	2	4	no	—
195	C₂×#97	C₂²×C₇	1	1	yes	characteristic
196	C₂×#97	C₂²×C₇	1	1	yes	characteristic
197	C₂×#97	C₂²×C₇	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
200	#398	C₄×C₇	1	1	yes	characteristic
201	#397	C₄×C₇	1	1	yes	characteristic
202	#396	C₄×C₇	1	2	yes	—
203	#394	C₄×C₇	1	2	yes	—
204	#394	C₄×C₇	1	1	yes	characteristic
205	#392	C₄×C₇	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
207	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
208	#336	C₂²×C₇	1	2	yes	—
209	#336	C₂²×C₇	1	2	yes	—
210	#336	C₂²×C₇	1	2	yes	—
211	C₂³×C₇	—	2	1	no	—
212	C₂³×C₇	—	2	2	no	—
213	C₂³×C₇	—	2	2	no	—
214	C₂³×C₇	—	2	2	no	—
215	C₂³×C₇	—	2	1	no	—
216	C₂³×C₇	—	2	2	no	—
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	2	2	no	—
220	C₂³×C₇	—	2	2	no	—
221	C₂³×C₇	C₄×D₄	1	2	yes	—
222	C₂³×C₇	#131	1	4	yes	—
223	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
224	C₇×D₄	—	2	8	no	—
225	C₇×D₄	—	4	8	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	2	1	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	2	no	—
246	C₂×C₄×C₇	—	2	2	no	—
247	C₂×C₄×C₇	—	4	2	no	—
248	C₂×C₄×C₇	—	4	2	no	—
249	C₂×C₄×C₇	—	4	2	no	—
250	C₂×C₄×C₇	—	4	2	no	—
251	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
252	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
260	C₇×C₈	—	2	2	no	—
261	C₇×C₈	—	2	2	no	—
262	C₇×C₈	—	2	2	no	—
263	C₇×C₈	—	4	2	no	—
264	C₇×C₈	—	4	2	no	—
265	C₇×C₈	#121	1	4	yes	—
266	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
267	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
268	C₂³×C₄	C₂³×C₇	1	2	yes	—
269	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	C₇×D₄	1	4	yes	complemented
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	4	no	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	—	2	4	no	—
279	C₂²×C₈	C₂³×C₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	#117	—	2	2	no	—
290	#117	—	2	2	no	—
291	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
303	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₇	1	2	yes	—
305	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
306	C₄⋊C₈	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	C₂²⋊C₈	—	2	4	no	—
311	C₂²⋊C₈	—	2	4	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	#97	—	2	2	no	—
314	#97	—	2	4	no	—
315	#97	—	2	2	no	—
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	C₇×D₄	1	4	yes	complemented
318	#95	C₂×C₄×C₇	1	2	yes	—
319	#95	C₂×C₄×C₇	1	2	yes	—
320	#95	C₂×C₄×C₇	1	1	yes	characteristic
321	#95	C₂×C₄×C₇	1	1	yes	characteristic
322	C₂²×C₇	—	2	4	no	—
323	C₂²×C₇	—	2	4	no	—
324	C₂²×C₇	—	2	4	no	—
325	C₂²×C₇	—	2	4	no	—
326	C₂²×C₇	—	2	2	no	—
327	C₂²×C₇	—	4	1	no	—
328	C₂²×C₇	—	4	1	no	—
329	C₂²×C₇	—	4	2	no	—
330	C₂²×C₇	—	4	2	no	—
331	C₂²×C₇	—	4	2	no	—
332	C₂²×C₇	—	4	2	no	—
333	C₂²×C₇	—	4	2	no	—
334	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
336	C₂²×C₇	C₄×#41	1	1	yes	characteristic
337	C₂²×C₇	C₂×#131	1	2	yes	—
338	C₂²×C₇	#568	1	2	yes	—
339	C₄×C₇	—	2	2	no	—
340	C₄×C₇	—	2	2	no	—
341	C₄×C₇	—	2	2	no	—
342	C₄×C₇	—	4	1	no	—
343	C₄×C₇	—	4	1	no	—
344	C₄×C₇	—	4	2	no	—
345	C₄×C₇	—	4	2	no	—
346	C₄×C₇	—	4	2	no	—
347	C₄×C₇	C₂×#121	1	1	yes	characteristic
348	C₄×C₇	#525	1	1	yes	characteristic
349	C₄×C₇	#529	1	1	yes	characteristic
350	C₄×C₇	#532	1	1	yes	characteristic
351	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
352	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	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	C₂²×C₄×C₇	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
373	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
377	C₂²×C₄	C₇×#41	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
379	M₁₆	—	2	8	no	—
380	C₂×C₈	—	2	8	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	4	8	no	—
394	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
395	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
396	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
397	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
398	C₂×C₈	C₇×#41	1	2	yes	—
399	C₂×C₈	C₇×#41	1	2	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	2	no	—
416	C₄²	C₂×C₇×D₄	1	2	yes	—
417	C₄²	C₇×#41	1	2	yes	—
418	C₂×C₇	—	4	4	no	—
419	C₂×C₇	—	4	2	no	—
420	C₂×C₇	C₄×#121	1	1	yes	characteristic
421	C₂×C₇	#2929	1	1	yes	characteristic
422	C₂×C₇	#2932	1	1	yes	characteristic
423	C₂×C₇	#2933	1	2	yes	—
424	C₂×C₇	#2968	1	2	yes	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	C₄×C₇×D₄	1	2	yes	—
436	C₂³	C₇×#131	1	4	yes	—
437	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
438	D₄	—	2	8	no	—
439	D₄	—	4	8	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
466	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
467	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
468	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
470	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
471	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
472	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₈	C₇×#121	1	4	yes	—
480	C₇	#21492	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
494	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
495	C₂²	C₄×C₇×#41	1	1	yes	characteristic
496	C₂²	C₂×C₇×#131	1	2	yes	—
497	C₂²	C₇×#568	1	2	yes	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	C₂×C₇×#121	1	1	yes	characteristic
507	C₄	C₇×#525	1	1	yes	characteristic
508	C₄	C₇×#529	1	1	yes	characteristic
509	C₄	C₇×#532	1	1	yes	characteristic
510	C₂	—	4	4	no	—
511	C₂	—	4	2	no	—
512	C₂	C₄×C₇×#121	1	1	yes	characteristic
513	C₂	C₇×#2929	1	1	yes	characteristic
514	C₂	C₇×#2932	1	1	yes	characteristic
515	C₂	C₇×#2933	1	2	yes	—
516	C₂	C₇×#2968	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	C₇×#392	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×#435	C₂	semidirect
2. C₂×C₇×C₈×D₄	C₂	semidirect
3. C₂×C₇×#405	C₂	semidirect
5. C₇×#1955	C₂	semidirect
6. C₇×#1940	C₂	semidirect
7. C₇×#1923	C₂	semidirect
8. C₇×#1869	C₂	semidirect
9. C₇×#1798	C₂	semidirect
10. C₇×#1770	C₂	semidirect
11. C₇×#1752	C₂	semidirect
44. #21492	C₇	direct (N × H)
51. C₂×C₇×M₁₆	D₄	semidirect
96. C₄×C₇×C₈	D₄	semidirect
101. C₂×#435	C₂×C₇	semidirect
102. C₂×C₈×D₄	C₂×C₇	semidirect
103. C₂×#405	C₂×C₇	semidirect
105. #1955	C₂×C₇	semidirect
106. #1940	C₂×C₇	semidirect
107. #1923	C₂×C₇	semidirect
108. #1869	C₂×C₇	semidirect
109. #1798	C₂×C₇	semidirect
110. #1770	C₂×C₇	semidirect
111. #1752	C₂×C₇	semidirect
272. C₂×M₁₆	C₇×D₄	semidirect
317. C₄×C₈	C₇×D₄	semidirect
480. C₇	#21492	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×C₈×D₄	2
C₂×C₇×#405	2
C₇×#2392	2
C₇×#1955	2
C₇×#1940	2
C₇×#1923	2
C₇×#1869	2
C₇×#1798	2
C₇×#1770	2
C₇×#1752	2
#21492	7

Subgroups — C7×#21492 #13198708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21492 #13198708