Subgroups — #13357994

Order 1792.

860 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2290	C₂	1	1	yes	maximal, characteristic
2	C₂×#89772	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#89698	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729369	C₂	1	1	yes	maximal, characteristic
5	#11729368	C₂	1	1	yes	maximal, characteristic
6	#11729336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₂²⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	#11727239	C₂	1	1	yes	maximal, characteristic, complemented
9	#11727238	C₂	1	1	yes	maximal, characteristic, complemented
10	#11727206	C₂	1	1	yes	maximal, characteristic, complemented
11	#11727206	C₂	1	1	yes	maximal, characteristic, complemented
12	#11727205	C₂	1	1	yes	maximal, characteristic, complemented
13	#11727205	C₂	1	1	yes	maximal, characteristic, complemented
14	#11727190	C₂	1	1	yes	maximal, characteristic, complemented
15	#11727188	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
19	C₇×#388	C₄	1	1	yes	characteristic
20	C₇×#388	C₄	1	1	yes	characteristic
21	C₇×#387	C₄	1	1	yes	characteristic
22	C₇×#387	C₄	1	1	yes	characteristic
23	C₇×#386	C₄	1	1	yes	characteristic
24	C₇×#386	C₄	1	1	yes	characteristic
25	C₇×#385	C₄	1	1	yes	characteristic
26	C₇×#385	C₄	1	1	yes	characteristic
27	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₇×#376	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
39	#89772	—	2	4	no	—
40	#89698	—	2	4	no	—
41	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
47	C₂×#6377	C₂²	1	1	yes	characteristic
48	C₂×#6377	C₂²	1	1	yes	characteristic
49	C₂×#6377	C₂²	1	1	yes	characteristic
50	C₂×#6377	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
55	#89319	C₂²	1	1	yes	characteristic
56	#89319	C₂²	1	1	yes	characteristic
57	#89319	C₂²	1	1	yes	characteristic
58	#89319	C₂²	1	1	yes	characteristic
59	#89319	C₂²	1	1	yes	characteristic
60	#89319	C₂²	1	1	yes	characteristic
61	#21273	—	7	1	no	maximal, Sylow
62	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₄×C₇×D₄	—	2	2	no	—
68	C₄×C₇×D₄	—	2	2	no	—
69	C₇×#117	—	2	2	no	—
70	C₇×#117	—	2	2	no	—
71	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
79	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₇	—	2	2	no	—
85	C₂×C₄²×C₇	—	2	2	no	—
86	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
97	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
101	C₇×#95	C₂×C₄	1	1	yes	characteristic
102	C₇×#95	C₂×C₄	1	1	yes	characteristic
103	C₇×#95	C₂×C₄	1	1	yes	characteristic
104	C₇×#95	C₂×C₄	1	1	yes	characteristic
105	C₇×#95	C₂×C₄	1	1	yes	characteristic
106	C₇×#95	C₂×C₄	1	1	yes	characteristic
107	C₇×#95	C₂×C₄	1	1	yes	characteristic
108	C₇×#95	C₂×C₄	1	1	yes	characteristic
109	C₇×#95	C₂×C₄	1	1	yes	characteristic
110	C₇×#95	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
112	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
113	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
114	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
115	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
116	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
117	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
118	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
119	C₄⋊(C₇⋊C₈)	—	2	2	no	—
120	C₄⋊(C₇⋊C₈)	—	2	2	no	—
121	C₄⋊(C₇⋊C₈)	—	2	2	no	—
122	C₄⋊(C₇⋊C₈)	—	2	2	no	—
123	C₄⋊(C₇⋊C₈)	—	2	2	no	—
124	C₄⋊(C₇⋊C₈)	—	2	2	no	—
125	#6377	—	2	2	no	—
126	#6377	—	2	2	no	—
127	#6377	—	2	2	no	—
128	#6377	D₄	1	4	yes	complemented
129	C₄×C₇⋊C₈	—	2	2	no	—
130	C₄×C₇⋊C₈	—	2	2	no	—
131	C₄×C₇⋊C₈	—	2	2	no	—
132	C₄×C₇⋊C₈	—	2	2	no	—
133	C₂×#433	—	7	1	no	—
134	C₂×#432	—	7	1	no	—
135	#2290	D₇	1	1	yes	characteristic
136	#1955	—	7	1	no	—
137	#1954	—	7	1	no	—
138	#1940	—	7	1	no	—
139	#1939	—	7	1	no	—
140	#1924	—	7	1	no	—
141	#1924	—	7	1	no	—
142	#1923	—	7	1	no	—
143	#1923	—	7	1	no	—
144	#1768	—	7	1	no	—
145	#1750	—	7	1	no	—
146	C₄×C₂²⋊C₈	—	7	1	no	—
147	#1726	—	7	1	no	—
148	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
149	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇×D₄	—	2	2	no	—
151	C₂×C₇×D₄	—	2	2	no	—
152	C₂×C₇×D₄	—	4	1	no	—
153	C₂²×C₄×C₇	—	2	2	no	—
154	C₂²×C₄×C₇	—	2	2	no	—
155	C₂²×C₄×C₇	—	2	2	no	—
156	C₂²×C₄×C₇	—	2	2	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	4	1	no	—
170	C₂²×C₄×C₇	—	4	1	no	—
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
184	C₇×C₄⋊C₄	—	2	2	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	4	1	no	—
189	C₇×C₂²⋊C₄	—	2	2	no	—
190	C₇×C₂²⋊C₄	—	2	2	no	—
191	C₇×C₂²⋊C₄	—	2	2	no	—
192	C₇×C₂²⋊C₄	—	2	2	no	—
193	C₇×C₂²⋊C₄	—	2	2	no	—
194	C₇×C₂²⋊C₄	—	2	2	no	—
195	C₇×C₂²⋊C₄	—	4	1	no	—
196	C₇×C₂²⋊C₄	—	4	1	no	—
197	C₄²×C₇	—	2	2	no	—
198	C₄²×C₇	—	2	2	no	—
199	C₄²×C₇	—	2	1	no	—
200	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	1	no	—
204	C₄²×C₇	—	2	1	no	—
205	C₄²×C₇	C₂×D₄	1	2	yes	—
206	C₄²×C₇	#41	1	2	yes	—
207	C₄²×C₇	#41	1	2	yes	—
208	C₄²×C₇	#41	1	2	yes	—
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	—	2	1	no	—
220	C₂×C₇⋊C₈	—	2	1	no	—
221	C₂×C₇⋊C₈	—	2	1	no	—
222	C₂×C₇⋊C₈	—	2	1	no	—
223	C₂×C₇⋊C₈	—	2	1	no	—
224	C₂×C₇⋊C₈	—	2	1	no	—
225	C₂×C₇⋊C₈	—	2	1	no	—
226	C₂×C₇⋊C₈	—	2	1	no	—
227	C₂×C₇⋊C₈	—	2	1	no	—
228	C₂×C₇⋊C₈	—	2	1	no	—
229	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
230	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
231	C₂×C₇⋊C₈	#41	1	2	yes	—
232	C₂×C₇⋊C₈	#41	1	2	yes	—
233	C₂×C₄×D₄	C₂×D₇	1	1	yes	characteristic
234	C₂×#117	C₂×D₇	1	1	yes	characteristic
235	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
236	#433	—	14	4	no	—
237	#432	—	14	4	no	—
238	C₂×C₄⋊C₈	—	7	1	no	—
239	C₂×C₄⋊C₈	—	7	1	no	—
240	C₂×C₄⋊C₈	—	7	1	no	—
241	C₂×C₄⋊C₈	—	7	1	no	—
242	C₂×C₄⋊C₈	—	7	1	no	—
243	C₂×C₄⋊C₈	—	7	1	no	—
244	C₂×C₂²⋊C₈	—	7	1	no	—
245	C₂×C₂²⋊C₈	—	7	1	no	—
246	C₂×C₂²⋊C₈	—	7	1	no	—
247	C₂×C₂²⋊C₈	—	7	1	no	—
248	C₂×C₂²⋊C₈	—	7	1	no	—
249	C₂×C₂²⋊C₈	—	7	1	no	—
250	C₂×C₂²⋊C₈	—	7	1	no	—
251	C₂×C₂²⋊C₈	—	7	1	no	—
252	C₂×#97	—	7	1	no	—
253	C₂×#97	—	7	1	no	—
254	C₂×#97	—	7	1	no	—
255	C₂×#97	—	7	1	no	—
256	C₂×C₄×C₈	—	7	1	no	—
257	C₂×C₄×C₈	—	7	1	no	—
258	C₂×C₄×C₈	—	7	1	no	—
259	C₂×C₄×C₈	—	7	1	no	—
260	#388	Dic₇	1	1	yes	characteristic
261	#388	Dic₇	1	1	yes	characteristic
262	#387	Dic₇	1	1	yes	characteristic
263	#387	Dic₇	1	1	yes	characteristic
264	#386	Dic₇	1	1	yes	characteristic
265	#386	Dic₇	1	1	yes	characteristic
266	#385	Dic₇	1	1	yes	characteristic
267	#385	Dic₇	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
269	C₄×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
270	C₄×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
271	#376	C₂×D₇	1	1	yes	characteristic
272	#336	—	7	1	no	—
273	#336	—	7	1	no	—
274	#336	—	7	1	no	—
275	#336	—	7	1	no	—
276	#336	—	7	1	no	—
277	#336	—	7	1	no	—
278	C₂³×C₇	—	2	1	no	—
279	C₂³×C₇	—	2	1	no	—
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	—	2	1	no	—
282	C₂³×C₇	—	2	1	no	—
283	C₂³×C₇	—	2	1	no	—
284	C₂³×C₇	—	2	1	no	—
285	C₂³×C₇	—	2	1	no	—
286	C₂³×C₇	—	2	1	no	—
287	C₂³×C₇	—	2	1	no	—
288	C₂³×C₇	—	2	1	no	—
289	C₂³×C₇	—	2	1	no	—
290	C₂³×C₇	—	2	1	no	—
291	C₂³×C₇	#131	1	2	yes	—
292	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
293	C₇×D₄	—	4	4	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	1	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	1	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	2	1	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	1	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	4	4	no	—
326	C₂×C₄×C₇	—	4	4	no	—
327	C₂×C₄×C₇	—	4	1	no	—
328	C₂×C₄×C₇	—	4	1	no	—
329	C₂×C₄×C₇	—	4	1	no	—
330	C₂×C₄×C₇	—	4	1	no	—
331	C₂×C₄×C₇	—	4	1	no	—
332	C₂×C₄×C₇	—	4	1	no	—
333	C₂×C₄×C₇	—	4	1	no	—
334	C₂×C₄×C₇	—	4	1	no	—
335	C₂×C₄×C₇	#117	1	2	yes	—
336	C₂×C₄×C₇	#117	1	2	yes	—
337	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
338	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
339	C₂×C₄×C₇	#131	1	2	yes	—
340	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
346	C₇⋊C₈	—	2	2	no	—
347	C₇⋊C₈	—	2	2	no	—
348	C₇⋊C₈	—	2	2	no	—
349	C₇⋊C₈	—	2	2	no	—
350	C₇⋊C₈	—	4	1	no	—
351	C₇⋊C₈	—	4	1	no	—
352	C₇⋊C₈	—	4	1	no	—
353	C₇⋊C₈	—	4	1	no	—
354	C₂²×D₄	C₂×Dic₇	1	1	yes	characteristic
355	C₂³×C₄	C₂×Dic₇	1	1	yes	characteristic
356	C₂³×C₄	C₂×Dic₇	1	1	yes	characteristic
357	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
358	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
359	C₂²×C₈	—	7	1	no	—
360	C₂²×C₈	—	7	1	no	—
361	C₂²×C₈	—	7	1	no	—
362	C₂²×C₈	—	7	1	no	—
363	C₂²×C₈	—	7	1	no	—
364	C₂²×C₈	—	7	1	no	—
365	C₂²×C₈	—	7	1	no	—
366	C₂²×C₈	—	7	1	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	#117	—	2	2	no	—
370	#117	—	2	2	no	—
371	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
387	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
388	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
391	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
392	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
393	C₄⋊C₈	—	14	2	no	—
394	C₄⋊C₈	—	14	2	no	—
395	C₄⋊C₈	—	14	2	no	—
396	C₄⋊C₈	—	14	2	no	—
397	C₄⋊C₈	—	14	2	no	—
398	C₄⋊C₈	—	14	2	no	—
399	C₂²⋊C₈	—	14	2	no	—
400	C₂²⋊C₈	—	14	2	no	—
401	C₂²⋊C₈	—	14	2	no	—
402	C₂²⋊C₈	—	14	2	no	—
403	C₂²⋊C₈	—	14	2	no	—
404	C₂²⋊C₈	—	14	2	no	—
405	C₂²⋊C₈	—	14	2	no	—
406	C₂²⋊C₈	—	14	2	no	—
407	#97	—	7	4	no	—
408	#97	—	14	2	no	—
409	#97	—	14	2	no	—
410	#97	—	14	2	no	—
411	C₄×C₈	—	14	2	no	—
412	C₄×C₈	—	14	2	no	—
413	C₄×C₈	—	14	2	no	—
414	C₄×C₈	—	14	2	no	—
415	#95	C₂×Dic₇	1	1	yes	characteristic
416	#95	C₂×Dic₇	1	1	yes	characteristic
417	#95	C₂×Dic₇	1	1	yes	characteristic
418	#95	C₂×Dic₇	1	1	yes	characteristic
419	#95	C₂×Dic₇	1	1	yes	characteristic
420	#95	C₂×Dic₇	1	1	yes	characteristic
421	#95	C₂×Dic₇	1	1	yes	characteristic
422	#95	C₂×Dic₇	1	1	yes	characteristic
423	#95	C₂×Dic₇	1	1	yes	characteristic
424	#95	C₂×Dic₇	1	1	yes	characteristic
425	C₂²×C₇	—	2	2	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	2	no	—
428	C₂²×C₇	—	4	1	no	—
429	C₂²×C₇	—	4	1	no	—
430	C₂²×C₇	—	4	1	no	—
431	C₂²×C₇	—	4	1	no	—
432	C₂²×C₇	—	4	1	no	—
433	C₂²×C₇	—	4	1	no	—
434	C₂²×C₇	—	4	1	no	—
435	C₂²×C₇	—	4	1	no	—
436	C₂²×C₇	—	4	1	no	—
437	C₂²×C₇	—	4	1	no	—
438	C₂²×C₇	—	4	1	no	—
439	C₂²×C₇	C₂×#117	1	1	yes	characteristic
440	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
441	C₂²×C₇	C₄×#41	1	1	yes	characteristic
442	C₂²×C₇	C₂×#131	1	1	yes	characteristic
443	C₂²×C₇	C₂×#131	1	1	yes	characteristic
444	C₂²×C₇	#568	1	1	yes	characteristic
445	C₂²×C₇	#568	1	1	yes	characteristic
446	C₄×C₇	—	2	2	no	—
447	C₄×C₇	—	2	2	no	—
448	C₄×C₇	—	2	2	no	—
449	C₄×C₇	—	2	2	no	—
450	C₄×C₇	—	2	2	no	—
451	C₄×C₇	—	4	1	no	—
452	C₄×C₇	—	4	1	no	—
453	C₄×C₇	—	4	1	no	—
454	C₄×C₇	—	4	1	no	—
455	C₄×C₇	—	4	1	no	—
456	C₄×C₇	—	4	1	no	—
457	C₄×C₇	—	4	1	no	—
458	C₄×C₇	#529	1	1	yes	characteristic
459	C₄×C₇	#529	1	1	yes	characteristic
460	C₄×C₇	#532	1	1	yes	characteristic
461	C₄×C₇	#532	1	1	yes	characteristic
462	C₂⁴	C₂²×Dic₇	1	1	yes	characteristic
463	C₂⁴	C₂²×Dic₇	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
495	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
496	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
497	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
498	C₂×C₈	—	7	2	no	—
499	C₂×C₈	—	7	2	no	—
500	C₂×C₈	—	7	2	no	—
501	C₂×C₈	—	7	2	no	—
502	C₂×C₈	—	14	1	no	—
503	C₂×C₈	—	14	1	no	—
504	C₂×C₈	—	14	1	no	—
505	C₂×C₈	—	14	1	no	—
506	C₂×C₈	—	14	1	no	—
507	C₂×C₈	—	14	1	no	—
508	C₂×C₈	—	14	1	no	—
509	C₂×C₈	—	14	1	no	—
510	C₂×C₈	—	14	1	no	—
511	C₂×C₈	—	14	1	no	—
512	C₂×C₈	—	14	1	no	—
513	C₂×C₈	—	14	1	no	—
514	C₂×C₈	—	14	1	no	—
515	C₂×C₈	—	14	1	no	—
516	C₂×C₈	—	14	1	no	—
517	C₂×C₈	—	14	1	no	—
518	C₂×C₈	—	14	1	no	—
519	C₂×C₈	—	14	1	no	—
520	C₂×C₈	—	14	1	no	—
521	C₂×C₈	—	14	1	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	#1157	1	2	yes	—
544	C₄²	#1157	1	2	yes	—
545	C₄²	D₄×D₇	1	2	yes	—
546	C₄²	#1159	1	2	yes	—
547	C₂×C₇	—	4	2	no	—
548	C₂×C₇	—	8	1	no	—
549	C₂×C₇	#2293	1	1	yes	characteristic
550	C₂×C₇	#2924	1	1	yes	characteristic
551	C₂×C₇	#2925	1	1	yes	characteristic
552	C₂×C₇	#2933	1	1	yes	characteristic
553	C₂×C₇	#2933	1	1	yes	characteristic
554	C₂×C₇	#2966	1	1	yes	characteristic
555	C₂×C₇	#2967	1	1	yes	characteristic
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	#6511	1	2	yes	—
570	C₂³	C₂³×Dic₇	1	1	yes	characteristic
571	D₄	—	4	4	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	#6489	1	2	yes	—
614	C₂×C₄	#6489	1	2	yes	—
615	C₂×C₄	D₄×Dic₇	1	2	yes	—
616	C₂×C₄	D₄×Dic₇	1	2	yes	—
617	C₂×C₄	#6511	1	2	yes	—
618	C₂×C₄	C₂×#1157	1	1	yes	characteristic
619	C₂×C₄	C₂×#1157	1	1	yes	characteristic
620	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
621	C₂×C₄	C₂×#1159	1	1	yes	characteristic
622	C₂×C₄	D₇×#41	1	1	yes	characteristic
623	C₂×C₄	D₇×#41	1	1	yes	characteristic
624	C₈	—	14	2	no	—
625	C₈	—	14	2	no	—
626	C₈	—	14	2	no	—
627	C₈	—	14	2	no	—
628	C₈	—	28	1	no	—
629	C₈	—	28	1	no	—
630	C₈	—	28	1	no	—
631	C₈	—	28	1	no	—
632	C₇	#21273	1	1	yes	characteristic, complemented, Sylow
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	C₂×#6489	1	1	yes	characteristic
648	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
649	C₂²	C₂×#6511	1	1	yes	characteristic
650	C₂²	C₂×#6511	1	1	yes	characteristic
651	C₂²	#90510	1	1	yes	characteristic
652	C₂²	#90510	1	1	yes	characteristic
653	C₂²	#41×Dic₇	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	#90239	1	1	yes	characteristic
667	C₄	#90239	1	1	yes	characteristic
668	C₄	#90248	1	1	yes	characteristic
669	C₄	#90248	1	1	yes	characteristic
670	C₂	—	4	2	no	—
671	C₂	—	8	1	no	—
672	C₂	#11739655	1	1	yes	characteristic
673	C₂	#11739764	1	1	yes	characteristic
674	C₂	#11739960	1	1	yes	characteristic
675	C₂	#11740363	1	1	yes	characteristic
676	C₂	#11740363	1	1	yes	characteristic
677	C₂	#11740571	1	1	yes	characteristic
678	C₂	#11740572	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇
commutator, socle	C₂³×C₇	C₂³×C₄
Fitting	C₇×#2290	C₂
prime radical	C₂²×C₇×D₄	C₂×C₄
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	#2290	D₇
hypocenter	C₇	#21273
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2290

Complements

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

N	H ≅ G/N	type
2. C₂×#89772	C₂	semidirect
3. C₂×#89698	C₂	semidirect
6. #11729336	C₂	semidirect
7. C₄×C₂²⋊(C₇⋊C₈)	C₂	semidirect
8. #11727239	C₂	semidirect
9. #11727238	C₂	semidirect
10. #11727206	C₂	semidirect
11. #11727206	C₂	semidirect
12. #11727205	C₂	semidirect
13. #11727205	C₂	semidirect
14. #11727190	C₂	semidirect
15. #11727188	C₂	semidirect
128. #6377	D₄	semidirect
632. C₇	#21273	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#2290	2
C₂×#89772	2
C₂×#89698	2
#11729369	2
#11729368	2
#11729336	2
C₄×C₂²⋊(C₇⋊C₈)	2
#11727239	2
#11727238	2
#11727206	2
#11727205	2
#11727190	2
#11727188	2
#21273	7