Subgroups — C₇×#21513 #13198729

Order 1792.

1120 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₇×#459	C₄	1	8	yes	complemented
25	C₇×#442	—	2	4	no	—
26	C₄×C₇×D₈	—	2	4	no	—
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₂×C₇×#106	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₇×#102	C₂²	1	1	yes	characteristic
37	C₂×C₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#390	C₂²	1	1	yes	characteristic
42	C₇×#390	C₂²	1	1	yes	characteristic
43	C₇×#386	—	2	1	no	—
44	C₇×#386	—	2	1	no	—
45	C₇×#386	—	2	1	no	—
46	C₇×#386	—	2	1	no	—
47	C₇×#382	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
53	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
54	C₇×#376	C₂²	1	1	yes	characteristic
55	C₂×C₇×#95	—	2	1	no	—
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	#21513	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×D₄	—	2	1	no	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	—	2	1	no	—
71	C₂³×C₄×C₇	—	2	1	no	—
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂×C₇×D₈	—	2	2	no	—
74	C₂×C₇×D₈	—	2	2	no	—
75	C₂×C₇×D₈	—	2	2	no	—
76	C₂×C₇×D₈	—	2	2	no	—
77	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
78	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₇×#127	—	2	2	no	—
84	C₇×#127	C₂×C₄	1	4	yes	complemented
85	C₄×C₇×D₄	—	2	2	no	—
86	C₄×C₇×D₄	—	2	2	no	—
87	C₄×C₇×D₄	—	2	2	no	—
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	—	2	2	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	C₂×C₄	1	4	yes	complemented
94	C₄×C₇×D₄	D₄	1	4	yes	complemented
95	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	—	2	1	no	—
111	C₂×C₄²×C₇	—	2	1	no	—
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#107	—	2	2	no	—
116	C₇×#106	—	2	2	no	—
117	C₇×C₄⋊C₈	—	2	2	no	—
118	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
119	C₇×#102	—	2	2	no	—
120	C₇×#102	—	2	2	no	—
121	C₇×#102	—	2	2	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#102	—	2	2	no	—
124	C₇×#102	—	2	2	no	—
125	C₇×#102	C₂×C₄	1	4	yes	complemented
126	C₇×#102	C₂×C₄	1	4	yes	complemented
127	C₇×#97	—	2	2	no	—
128	C₄×C₇×C₈	—	2	2	no	—
129	C₇×#95	—	2	1	no	—
130	C₇×#95	—	2	1	no	—
131	C₇×#95	—	2	1	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	D₄	1	1	yes	characteristic
135	C₇×#95	D₄	1	1	yes	characteristic
136	C₇×#95	D₄	1	1	yes	characteristic
137	C₇×#95	D₄	1	1	yes	characteristic
138	C₂×#459	C₂×C₇	1	1	yes	characteristic
139	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
141	#2328	C₂×C₇	1	1	yes	characteristic, complemented
142	#2275	C₂×C₇	1	1	yes	characteristic, complemented
143	#1982	C₂×C₇	1	1	yes	characteristic, complemented
144	#1949	C₂×C₇	1	1	yes	characteristic, complemented
145	#1926	C₂×C₇	1	1	yes	characteristic, complemented
146	#1925	C₂×C₇	1	1	yes	characteristic, complemented
147	#1879	C₂×C₇	1	1	yes	characteristic, complemented
148	#1879	C₂×C₇	1	1	yes	characteristic, complemented
149	#1804	C₂×C₇	1	1	yes	characteristic, complemented
150	#1768	C₂×C₇	1	1	yes	characteristic, complemented
151	#1762	C₂×C₇	1	1	yes	characteristic, complemented
152	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂⁴×C₇	—	2	1	no	—
154	C₂⁴×C₇	—	2	1	no	—
155	C₂⁴×C₇	—	2	1	no	—
156	C₂×C₇×D₄	—	2	4	no	—
157	C₂×C₇×D₄	—	2	4	no	—
158	C₂×C₇×D₄	—	2	1	no	—
159	C₂×C₇×D₄	—	2	1	no	—
160	C₂×C₇×D₄	—	2	1	no	—
161	C₂×C₇×D₄	—	2	1	no	—
162	C₂×C₇×D₄	—	2	1	no	—
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	—	2	1	no	—
170	C₂×C₇×D₄	—	2	1	no	—
171	C₂×C₇×D₄	—	8	1	no	—
172	C₂×C₇×D₄	—	8	1	no	—
173	C₂×C₇×D₄	—	8	1	no	—
174	C₂×C₇×D₄	—	8	1	no	—
175	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
176	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
177	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
178	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
179	C₂×C₇×D₄	#41	1	2	yes	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	4	no	—
184	C₂²×C₄×C₇	—	2	4	no	—
185	C₂²×C₄×C₇	—	2	4	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	4	2	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	—	8	1	no	—
191	C₂²×C₄×C₇	—	8	1	no	—
192	C₂²×C₄×C₇	—	8	1	no	—
193	C₂²×C₄×C₇	—	8	1	no	—
194	C₂²×C₄×C₇	—	8	1	no	—
195	C₂²×C₄×C₇	—	8	1	no	—
196	C₂²×C₄×C₇	—	8	1	no	—
197	C₂²×C₄×C₇	—	8	1	no	—
198	C₂²×C₄×C₇	—	8	1	no	—
199	C₂²×C₄×C₇	—	8	1	no	—
200	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
207	C₇×D₈	—	2	8	no	—
208	C₇×D₈	—	2	8	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
220	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
230	C₇×C₄⋊C₄	#41	1	2	yes	—
231	C₇×C₂²⋊C₄	—	2	4	no	—
232	C₇×C₂²⋊C₄	—	2	4	no	—
233	C₇×C₂²⋊C₄	—	2	4	no	—
234	C₇×C₂²⋊C₄	—	4	2	no	—
235	C₇×C₂²⋊C₄	—	4	2	no	—
236	C₇×C₂²⋊C₄	—	8	1	no	—
237	C₇×C₂²⋊C₄	—	8	1	no	—
238	C₇×C₂²⋊C₄	—	8	1	no	—
239	C₇×C₂²⋊C₄	—	8	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	2	1	no	—
242	C₄²×C₇	—	8	1	no	—
243	C₄²×C₇	—	8	1	no	—
244	C₄²×C₇	—	8	1	no	—
245	C₄²×C₇	C₂²×C₄	1	2	yes	—
246	C₄²×C₇	C₂×D₄	1	2	yes	—
247	C₄²×C₇	#41	1	2	yes	—
248	C₄²×C₇	#41	1	2	yes	—
249	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
250	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
251	C₂×#127	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
257	#459	C₄×C₇	1	8	yes	complemented
258	#442	—	2	4	no	—
259	C₄×D₈	—	2	4	no	—
260	C₂×#107	C₂²×C₇	1	1	yes	characteristic
261	C₂×#106	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×#102	C₂²×C₇	1	1	yes	characteristic
265	C₂×#102	C₂²×C₇	1	1	yes	characteristic
266	C₂×#102	C₂²×C₇	1	1	yes	characteristic
267	C₂×#102	C₂²×C₇	1	1	yes	characteristic
268	C₂×#102	C₂²×C₇	1	1	yes	characteristic
269	C₂×#102	C₂²×C₇	1	1	yes	characteristic
270	C₂×#102	C₂²×C₇	1	1	yes	characteristic
271	C₂×#102	C₂²×C₇	1	1	yes	characteristic
272	C₂×#97	C₂²×C₇	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
274	#390	C₂²×C₇	1	1	yes	characteristic
275	#390	C₂²×C₇	1	1	yes	characteristic
276	#386	—	2	1	no	—
277	#386	—	2	1	no	—
278	#386	—	2	1	no	—
279	#386	—	2	1	no	—
280	#382	C₂²×C₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
282	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	—	2	1	no	—
285	C₄×C₂²⋊C₄	—	2	1	no	—
286	C₄×C₂²⋊C₄	—	2	1	no	—
287	#376	C₂²×C₇	1	1	yes	characteristic
288	C₂×#95	—	2	1	no	—
289	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic
293	#336	C₂²×C₇	1	1	yes	characteristic
294	#336	C₂²×C₇	1	1	yes	characteristic
295	C₂³×C₇	—	2	2	no	—
296	C₂³×C₇	—	2	2	no	—
297	C₂³×C₇	—	2	2	no	—
298	C₂³×C₇	—	2	2	no	—
299	C₂³×C₇	—	2	2	no	—
300	C₂³×C₇	—	4	1	no	—
301	C₂³×C₇	—	4	1	no	—
302	C₂³×C₇	—	4	1	no	—
303	C₂³×C₇	—	4	1	no	—
304	C₂³×C₇	—	4	1	no	—
305	C₂³×C₇	—	4	1	no	—
306	C₂³×C₇	—	4	1	no	—
307	C₂³×C₇	—	4	1	no	—
308	C₂³×C₇	—	4	1	no	—
309	C₂³×C₇	—	4	1	no	—
310	C₂³×C₇	—	4	1	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	—	4	1	no	—
313	C₂³×C₇	—	4	1	no	—
314	C₂³×C₇	—	4	1	no	—
315	C₂³×C₇	—	4	1	no	—
316	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
317	C₇×D₄	—	2	2	no	—
318	C₇×D₄	—	2	2	no	—
319	C₇×D₄	—	2	2	no	—
320	C₇×D₄	—	2	2	no	—
321	C₇×D₄	—	2	2	no	—
322	C₇×D₄	—	2	2	no	—
323	C₇×D₄	—	2	2	no	—
324	C₇×D₄	—	4	1	no	—
325	C₇×D₄	—	4	1	no	—
326	C₇×D₄	—	4	1	no	—
327	C₇×D₄	—	4	1	no	—
328	C₇×D₄	—	8	4	no	—
329	C₇×D₄	—	8	4	no	—
330	C₇×D₄	C₄×D₄	1	4	yes	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	1	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	1	no	—
346	C₂×C₄×C₇	—	2	1	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	4	1	no	—
355	C₂×C₄×C₇	—	4	1	no	—
356	C₂×C₄×C₇	—	4	1	no	—
357	C₂×C₄×C₇	—	4	1	no	—
358	C₂×C₄×C₇	—	4	1	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	8	4	no	—
361	C₂×C₄×C₇	—	8	4	no	—
362	C₂×C₄×C₇	—	8	4	no	—
363	C₂×C₄×C₇	—	8	4	no	—
364	C₂×C₄×C₇	—	8	4	no	—
365	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
366	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
367	C₂×C₄×C₇	#121	1	2	yes	—
368	C₂×C₄×C₇	#121	1	2	yes	—
369	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
370	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
373	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
375	C₇×C₈	—	2	2	no	—
376	C₇×C₈	—	2	2	no	—
377	C₇×C₈	—	4	1	no	—
378	C₇×C₈	—	4	1	no	—
379	C₂²×D₄	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂×D₈	—	2	2	no	—
390	C₂×D₈	—	2	2	no	—
391	C₂×D₈	—	2	2	no	—
392	C₂×D₈	—	2	2	no	—
393	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
394	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
395	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
399	#127	—	2	2	no	—
400	#127	C₂×C₄×C₇	1	4	yes	complemented
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	C₂×C₄×C₇	1	4	yes	complemented
410	C₄×D₄	C₇×D₄	1	4	yes	complemented
411	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
431	#107	—	2	2	no	—
432	#106	—	2	2	no	—
433	C₄⋊C₈	—	2	2	no	—
434	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
435	#102	—	2	2	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	#102	—	2	2	no	—
439	#102	—	2	2	no	—
440	#102	—	2	2	no	—
441	#102	C₂×C₄×C₇	1	4	yes	complemented
442	#102	C₂×C₄×C₇	1	4	yes	complemented
443	#97	—	2	2	no	—
444	C₄×C₈	—	2	2	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	C₇×D₄	1	1	yes	characteristic
451	#95	C₇×D₄	1	1	yes	characteristic
452	#95	C₇×D₄	1	1	yes	characteristic
453	#95	C₇×D₄	1	1	yes	characteristic
454	C₂²×C₇	—	2	4	no	—
455	C₂²×C₇	—	4	2	no	—
456	C₂²×C₇	—	4	2	no	—
457	C₂²×C₇	—	4	2	no	—
458	C₂²×C₇	—	4	2	no	—
459	C₂²×C₇	—	4	2	no	—
460	C₂²×C₇	—	4	2	no	—
461	C₂²×C₇	—	4	2	no	—
462	C₂²×C₇	—	4	2	no	—
463	C₂²×C₇	—	4	2	no	—
464	C₂²×C₇	—	4	2	no	—
465	C₂²×C₇	—	4	2	no	—
466	C₂²×C₇	—	4	2	no	—
467	C₂²×C₇	—	8	1	no	—
468	C₂²×C₇	—	8	1	no	—
469	C₂²×C₇	—	8	1	no	—
470	C₂²×C₇	—	8	1	no	—
471	C₂²×C₇	—	8	1	no	—
472	C₂²×C₇	—	8	1	no	—
473	C₂²×C₇	—	8	1	no	—
474	C₂²×C₇	—	8	1	no	—
475	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
476	C₂²×C₇	C₂×#121	1	1	yes	characteristic
477	C₂²×C₇	#525	1	1	yes	characteristic
478	C₂²×C₇	#576	1	1	yes	characteristic
479	C₂²×C₇	#576	1	1	yes	characteristic
480	C₂²×C₇	#576	1	1	yes	characteristic
481	C₂²×C₇	#577	1	1	yes	characteristic
482	C₄×C₇	—	2	2	no	—
483	C₄×C₇	—	2	2	no	—
484	C₄×C₇	—	2	2	no	—
485	C₄×C₇	—	2	2	no	—
486	C₄×C₇	—	4	1	no	—
487	C₄×C₇	—	4	1	no	—
488	C₄×C₇	—	4	2	no	—
489	C₄×C₇	—	4	2	no	—
490	C₄×C₇	—	4	2	no	—
491	C₄×C₇	—	8	1	no	—
492	C₄×C₇	—	8	1	no	—
493	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
494	C₄×C₇	C₄×#41	1	1	yes	characteristic
495	C₄×C₇	#529	1	1	yes	characteristic
496	C₄×C₇	#532	1	1	yes	characteristic
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	1	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	8	1	no	—
516	C₂×D₄	—	8	1	no	—
517	C₂×D₄	—	8	1	no	—
518	C₂×D₄	—	8	1	no	—
519	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
521	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
522	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
523	C₂×D₄	C₇×#41	1	2	yes	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	—	8	1	no	—
536	C₂²×C₄	—	8	1	no	—
537	C₂²×C₄	—	8	1	no	—
538	C₂²×C₄	—	8	1	no	—
539	C₂²×C₄	—	8	1	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	—	8	1	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
551	D₈	—	2	8	no	—
552	D₈	—	2	8	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
564	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
573	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
574	C₄⋊C₄	C₇×#41	1	2	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	8	1	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	8	1	no	—
587	C₄²	—	8	1	no	—
588	C₄²	—	8	1	no	—
589	C₄²	C₂²×C₄×C₇	1	2	yes	—
590	C₄²	C₂×C₇×D₄	1	2	yes	—
591	C₄²	C₇×#41	1	2	yes	—
592	C₄²	C₇×#41	1	2	yes	—
593	C₂×C₇	—	4	4	no	—
594	C₂×C₇	—	8	2	no	—
595	C₂×C₇	—	8	2	no	—
596	C₂×C₇	C₄×#121	1	1	yes	characteristic
597	C₂×C₇	#2946	1	1	yes	characteristic
598	C₂×C₇	#2948	1	1	yes	characteristic
599	C₂×C₇	#3041	1	1	yes	characteristic
600	C₂×C₇	#3045	1	1	yes	characteristic
601	C₂×C₇	#3119	1	1	yes	characteristic
602	C₂×C₇	#3122	1	1	yes	characteristic
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	2	no	—
630	D₄	—	2	2	no	—
631	D₄	—	2	2	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	8	4	no	—
637	D₄	—	8	4	no	—
638	D₄	C₄×C₇×D₄	1	4	yes	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	—	8	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	—	8	4	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
674	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
675	C₂×C₄	C₇×#121	1	2	yes	—
676	C₂×C₄	C₇×#121	1	2	yes	—
677	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
678	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
680	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
681	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
682	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
683	C₈	—	2	2	no	—
684	C₈	—	2	2	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₇	#21513	1	1	yes	characteristic, direct product factor, Sylow
688	C₂²	—	2	4	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
710	C₂²	C₂×C₇×#121	1	1	yes	characteristic
711	C₂²	C₇×#525	1	1	yes	characteristic
712	C₂²	C₇×#576	1	1	yes	characteristic
713	C₂²	C₇×#576	1	1	yes	characteristic
714	C₂²	C₇×#576	1	1	yes	characteristic
715	C₂²	C₇×#577	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	8	1	no	—
726	C₄	—	8	1	no	—
727	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
728	C₄	C₄×C₇×#41	1	1	yes	characteristic
729	C₄	C₇×#529	1	1	yes	characteristic
730	C₄	C₇×#532	1	1	yes	characteristic
731	C₂	—	4	4	no	—
732	C₂	—	8	2	no	—
733	C₂	—	8	2	no	—
734	C₂	C₄×C₇×#121	1	1	yes	characteristic
735	C₂	C₇×#2946	1	1	yes	characteristic
736	C₂	C₇×#2948	1	1	yes	characteristic
737	C₂	C₇×#3041	1	1	yes	characteristic
738	C₂	C₇×#3045	1	1	yes	characteristic
739	C₂	C₇×#3119	1	1	yes	characteristic
740	C₂	C₇×#3122	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₇×#376 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₇×#442	C₂	semidirect
3. C₂×C₄×C₇×D₈	C₂	semidirect
4. C₇×#2328	C₂	semidirect
5. C₇×#2275	C₂	semidirect
6. C₇×#1982	C₂	semidirect
7. C₇×#1949	C₂	semidirect
8. C₇×#1926	C₂	semidirect
9. C₇×#1925	C₂	semidirect
10. C₇×#1879	C₂	semidirect
11. C₇×#1879	C₂	semidirect
12. C₇×#1804	C₂	semidirect
13. C₇×#1768	C₂	semidirect
14. C₇×#1762	C₂	semidirect
15. C₄×C₇×#102	C₂	semidirect
24. C₇×#459	C₄	semidirect
62. #21513	C₇	direct (N × H)
77. C₂×C₇×D₈	C₂×C₄	semidirect
78. C₂×C₇×D₈	C₂×C₄	semidirect
84. C₇×#127	C₂×C₄	semidirect
93. C₄×C₇×D₄	C₂×C₄	semidirect
94. C₄×C₇×D₄	D₄	semidirect
118. C₇×C₄⋊C₈	C₂×C₄	semidirect
125. C₇×#102	C₂×C₄	semidirect
126. C₇×#102	C₂×C₄	semidirect
139. C₂×#442	C₂×C₇	semidirect
140. C₂×C₄×D₈	C₂×C₇	semidirect
141. #2328	C₂×C₇	semidirect
142. #2275	C₂×C₇	semidirect
143. #1982	C₂×C₇	semidirect
144. #1949	C₂×C₇	semidirect
145. #1926	C₂×C₇	semidirect
146. #1925	C₂×C₇	semidirect
147. #1879	C₂×C₇	semidirect
148. #1879	C₂×C₇	semidirect
149. #1804	C₂×C₇	semidirect
150. #1768	C₂×C₇	semidirect
151. #1762	C₂×C₇	semidirect
152. C₄×#102	C₂×C₇	semidirect
257. #459	C₄×C₇	semidirect
393. C₂×D₈	C₂×C₄×C₇	semidirect
394. C₂×D₈	C₂×C₄×C₇	semidirect
400. #127	C₂×C₄×C₇	semidirect
409. C₄×D₄	C₂×C₄×C₇	semidirect
410. C₄×D₄	C₇×D₄	semidirect
434. C₄⋊C₈	C₂×C₄×C₇	semidirect
441. #102	C₂×C₄×C₇	semidirect
442. #102	C₂×C₄×C₇	semidirect
687. C₇	#21513	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×#459	2
C₂×C₇×#442	2
C₂×C₄×C₇×D₈	2
C₇×#2328	2
C₇×#2275	2
C₇×#1982	2
C₇×#1949	2
C₇×#1926	2
C₇×#1925	2
C₇×#1879	2
C₇×#1804	2
C₇×#1768	2
C₇×#1762	2
C₄×C₇×#102	2
#21513	7

Subgroups — C7×#21513 #13198729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21513 #13198729