Subgroups — #13375571

Order 1792.

788 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2396	C₂	1	1	yes	maximal, characteristic
2	C₂×#89796	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#89771	C₂	1	1	yes	maximal, characteristic
4	#11729388	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729336	C₂	1	1	yes	maximal, characteristic
6	#11727239	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727239	C₂	1	1	yes	maximal, characteristic, complemented
8	#11727239	C₂	1	1	yes	maximal, characteristic, complemented
9	#11727237	C₂	1	1	yes	maximal, characteristic, complemented
10	#11727236	C₂	1	1	yes	maximal, characteristic, complemented
11	#11727231	C₂	1	1	yes	maximal, characteristic, complemented
12	#11727204	C₂	1	1	yes	maximal, characteristic
13	#11727203	C₂	1	1	yes	maximal, characteristic
14	#11727202	C₂	1	1	yes	maximal, characteristic
15	#11727201	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₂²×#1136	C₂²	1	1	yes	characteristic
19	C₂³×C₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₇×#400	C₄	1	1	yes	characteristic
21	C₇×#399	C₄	1	1	yes	characteristic
22	C₇×#398	C₄	1	1	yes	characteristic
23	C₇×#398	C₄	1	1	yes	characteristic
24	C₇×#396	C₄	1	1	yes	characteristic
25	C₇×#396	C₄	1	1	yes	characteristic
26	C₇×#395	C₄	1	1	yes	characteristic
27	C₇×#393	C₄	1	1	yes	characteristic
28	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₂²⋊C₄	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	#89796	—	2	4	no	—
36	#89771	—	2	4	no	—
37	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
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×#6377	C₂²	1	1	yes	characteristic
46	C₂×#6377	C₂²	1	1	yes	characteristic
47	C₂×#6377	C₂²	1	1	yes	characteristic
48	C₂×#6377	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
51	#89319	C₂²	1	1	yes	characteristic
52	#89319	C₂²	1	1	yes	characteristic
53	#89319	C₂²	1	1	yes	characteristic
54	#89319	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	#22960	—	7	1	no	maximal, Sylow
62	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₄×C₇×Q₈	—	2	2	no	—
65	C₄×C₇×Q₈	—	2	2	no	—
66	C₇×#117	—	2	2	no	—
67	C₇×#117	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×C₄⋊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×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	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×#1136	—	2	2	no	—
92	C₂×#1136	—	2	2	no	—
93	C₂×#1136	—	4	1	no	—
94	C₂²×C₇⋊C₈	—	2	2	no	—
95	C₂²×C₇⋊C₈	—	2	2	no	—
96	C₂²×C₇⋊C₈	—	4	1	no	—
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	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇⋊C₈	C₂³	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	C₇×#95	C₂×C₄	1	1	yes	characteristic
112	C₇×#95	C₂×C₄	1	1	yes	characteristic
113	C₇×#95	C₂×C₄	1	1	yes	characteristic
114	C₇×#95	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
116	C₂²⋊(C₇⋊C₈)	Q₈	1	4	yes	complemented
117	C₄⋊(C₇⋊C₈)	—	2	2	no	—
118	C₄⋊(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)	—	4	1	no	—
123	C₄⋊(C₇⋊C₈)	—	4	1	no	—
124	C₄⋊(C₇⋊C₈)	D₄	1	4	yes	—
125	#6377	—	2	2	no	—
126	#6377	—	2	2	no	—
127	#6377	—	4	1	no	—
128	#6377	—	4	1	no	—
129	C₄×C₇⋊C₈	—	2	2	no	—
130	C₄×C₇⋊C₈	—	2	2	no	—
131	C₂×#446	—	7	1	no	—
132	C₂×#424	—	7	1	no	—
133	#2396	D₇	1	1	yes	characteristic
134	#1984	—	7	1	no	—
135	#1940	—	7	1	no	—
136	#1940	—	7	1	no	—
137	#1940	—	7	1	no	—
138	#1917	—	7	1	no	—
139	#1916	—	7	1	no	—
140	#1851	—	7	1	no	—
141	#1850	—	7	1	no	—
142	#1770	—	7	1	no	—
143	#1753	—	7	1	no	—
144	#1752	—	7	1	no	—
145	#1750	—	7	1	no	—
146	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₇×Q₈	—	2	2	no	—
148	C₂×C₇×Q₈	—	2	2	no	—
149	C₂×C₇×Q₈	—	4	1	no	—
150	C₂²×C₄×C₇	—	2	1	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
168	C₂²×C₄×C₇	#41	1	2	yes	—
169	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
170	C₇×C₄⋊C₄	—	2	2	no	—
171	C₇×C₄⋊C₄	—	2	2	no	—
172	C₇×C₄⋊C₄	—	2	2	no	—
173	C₇×C₄⋊C₄	—	2	2	no	—
174	C₇×C₄⋊C₄	—	2	2	no	—
175	C₇×C₄⋊C₄	—	2	2	no	—
176	C₇×C₄⋊C₄	—	4	1	no	—
177	C₇×C₄⋊C₄	—	4	1	no	—
178	C₇×C₄⋊C₄	—	4	1	no	—
179	C₇×C₄⋊C₄	—	4	1	no	—
180	C₇×C₄⋊C₄	—	4	1	no	—
181	C₇×C₂²⋊C₄	—	2	2	no	—
182	C₇×C₂²⋊C₄	—	2	2	no	—
183	C₇×C₂²⋊C₄	—	2	2	no	—
184	C₇×C₂²⋊C₄	—	4	1	no	—
185	C₇×C₂²⋊C₄	—	4	1	no	—
186	C₇×C₂²⋊C₄	—	4	1	no	—
187	C₄²×C₇	—	2	1	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	—	2	1	no	—
190	C₄²×C₇	—	2	1	no	—
191	C₄²×C₇	—	2	1	no	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	—	2	1	no	—
194	C₄²×C₇	—	2	1	no	—
195	C₄²×C₇	—	2	1	no	—
196	C₄²×C₇	—	2	1	no	—
197	C₄²×C₇	C₂×D₄	1	2	yes	—
198	C₄²×C₇	#41	1	2	yes	—
199	#1136	—	4	4	no	—
200	C₂×C₇⋊C₈	—	2	1	no	—
201	C₂×C₇⋊C₈	—	2	1	no	—
202	C₂×C₇⋊C₈	—	2	1	no	—
203	C₂×C₇⋊C₈	—	2	1	no	—
204	C₂×C₇⋊C₈	—	2	1	no	—
205	C₂×C₇⋊C₈	—	2	1	no	—
206	C₂×C₇⋊C₈	—	2	1	no	—
207	C₂×C₇⋊C₈	—	2	1	no	—
208	C₂×C₇⋊C₈	—	2	1	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	—	2	1	no	—
220	C₂×C₇⋊C₈	—	4	4	no	—
221	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
222	C₂×C₇⋊C₈	C₂×D₄	1	2	yes	—
223	C₂×C₇⋊C₈	C₂×Q₈	1	2	yes	—
224	C₂×C₇⋊C₈	C₂×Q₈	1	2	yes	—
225	C₂²×M₁₆	—	7	1	no	—
226	C₂³×C₈	—	7	1	no	—
227	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
228	C₂×#117	C₂×D₇	1	1	yes	characteristic
229	#446	—	14	4	no	—
230	#424	—	14	4	no	—
231	C₂×C₄⋊C₈	—	7	1	no	—
232	C₂×C₄⋊C₈	—	7	1	no	—
233	C₂×C₄⋊C₈	—	7	1	no	—
234	C₂×C₄⋊C₈	—	7	1	no	—
235	C₂×C₄⋊C₈	—	7	1	no	—
236	C₂×C₄⋊C₈	—	7	1	no	—
237	C₂×C₄⋊C₈	—	7	1	no	—
238	C₂×C₄⋊C₈	—	7	1	no	—
239	C₂×C₂²⋊C₈	—	7	1	no	—
240	C₂×C₂²⋊C₈	—	7	1	no	—
241	C₂×#97	—	7	1	no	—
242	C₂×#97	—	7	1	no	—
243	C₂×#97	—	7	1	no	—
244	C₂×#97	—	7	1	no	—
245	C₂×C₄×C₈	—	7	1	no	—
246	C₂×C₄×C₈	—	7	1	no	—
247	#400	Dic₇	1	1	yes	characteristic
248	#399	Dic₇	1	1	yes	characteristic
249	#398	Dic₇	1	1	yes	characteristic
250	#398	Dic₇	1	1	yes	characteristic
251	#396	Dic₇	1	1	yes	characteristic
252	#396	Dic₇	1	1	yes	characteristic
253	#395	Dic₇	1	1	yes	characteristic
254	#393	Dic₇	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
260	#336	—	7	1	no	—
261	#336	—	7	1	no	—
262	#336	—	7	1	no	—
263	#336	—	7	1	no	—
264	#336	—	7	1	no	—
265	#336	—	7	1	no	—
266	#336	—	7	1	no	—
267	#336	—	7	1	no	—
268	#336	—	7	1	no	—
269	#336	—	7	1	no	—
270	C₂³×C₇	—	2	1	no	—
271	C₂³×C₇	—	2	1	no	—
272	C₂³×C₇	—	2	1	no	—
273	C₂³×C₇	—	2	1	no	—
274	C₂³×C₇	—	2	1	no	—
275	C₂³×C₇	—	2	1	no	—
276	C₂³×C₇	C₄×Q₈	1	2	yes	—
277	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
278	C₇×Q₈	—	4	4	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	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	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
320	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
321	C₂×C₄×C₇	#131	1	2	yes	—
322	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
324	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
328	C₇⋊C₈	—	2	2	no	—
329	C₇⋊C₈	—	2	2	no	—
330	C₇⋊C₈	—	2	2	no	—
331	C₇⋊C₈	—	2	2	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₇⋊C₈	—	4	1	no	—
335	C₇⋊C₈	—	4	1	no	—
336	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
337	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
338	C₂×M₁₆	—	14	2	no	—
339	C₂×M₁₆	—	14	2	no	—
340	C₂×M₁₆	—	28	1	no	—
341	C₂²×C₈	—	7	1	no	—
342	C₂²×C₈	—	7	1	no	—
343	C₂²×C₈	—	7	1	no	—
344	C₂²×C₈	—	7	1	no	—
345	C₂²×C₈	—	7	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	7	1	no	—
348	C₂²×C₈	—	7	1	no	—
349	C₂²×C₈	—	14	2	no	—
350	C₂²×C₈	—	14	2	no	—
351	C₂²×C₈	—	28	1	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	C₂×Dic₇	1	1	yes	characteristic
373	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
374	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
376	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
379	C₄⋊C₈	—	7	4	no	—
380	C₄⋊C₈	—	14	2	no	—
381	C₄⋊C₈	—	14	2	no	—
382	C₄⋊C₈	—	14	2	no	—
383	C₄⋊C₈	—	14	2	no	—
384	C₄⋊C₈	—	14	2	no	—
385	C₄⋊C₈	—	28	1	no	—
386	C₄⋊C₈	—	28	1	no	—
387	C₂²⋊C₈	—	7	4	no	—
388	C₂²⋊C₈	—	14	2	no	—
389	#97	—	14	2	no	—
390	#97	—	14	2	no	—
391	#97	—	28	1	no	—
392	#97	—	28	1	no	—
393	C₄×C₈	—	14	2	no	—
394	C₄×C₈	—	14	2	no	—
395	#95	C₂×Dic₇	1	1	yes	characteristic
396	#95	C₂×Dic₇	1	1	yes	characteristic
397	#95	C₂×Dic₇	1	1	yes	characteristic
398	#95	C₂×Dic₇	1	1	yes	characteristic
399	#95	C₂×Dic₇	1	1	yes	characteristic
400	#95	C₂×Dic₇	1	1	yes	characteristic
401	#95	C₂×Dic₇	1	1	yes	characteristic
402	#95	C₂×Dic₇	1	1	yes	characteristic
403	#95	C₂×Dic₇	1	1	yes	characteristic
404	#95	C₂×Dic₇	1	1	yes	characteristic
405	C₂²×C₇	—	2	2	no	—
406	C₂²×C₇	—	2	2	no	—
407	C₂²×C₇	—	2	2	no	—
408	C₂²×C₇	—	4	1	no	—
409	C₂²×C₇	—	4	1	no	—
410	C₂²×C₇	—	4	1	no	—
411	C₂²×C₇	—	4	1	no	—
412	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
413	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
414	C₂²×C₇	#520	1	1	yes	characteristic
415	C₂²×C₇	C₂×#131	1	1	yes	characteristic
416	C₂²×C₇	#568	1	1	yes	characteristic
417	C₂²×C₇	#568	1	1	yes	characteristic
418	C₂²×C₇	#568	1	1	yes	characteristic
419	C₄×C₇	—	2	2	no	—
420	C₄×C₇	—	2	2	no	—
421	C₄×C₇	—	2	2	no	—
422	C₄×C₇	—	2	2	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	—	4	1	no	—
426	C₄×C₇	—	4	1	no	—
427	C₄×C₇	—	4	1	no	—
428	C₄×C₇	—	4	1	no	—
429	C₄×C₇	—	4	1	no	—
430	C₄×C₇	—	4	1	no	—
431	C₄×C₇	—	4	1	no	—
432	C₄×C₇	#546	1	1	yes	characteristic
433	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
434	C₄×C₇	#552	1	1	yes	characteristic
435	C₄×C₇	#554	1	1	yes	characteristic
436	C₂⁴	C₂²×Dic₇	1	1	yes	characteristic
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	4	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	Q₈×D₇	1	2	yes	—
445	C₂²×C₄	#1161	1	2	yes	—
446	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
447	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
448	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
449	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
459	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
460	M₁₆	—	28	4	no	—
461	C₂×C₈	—	7	2	no	—
462	C₂×C₈	—	7	2	no	—
463	C₂×C₈	—	7	2	no	—
464	C₂×C₈	—	7	2	no	—
465	C₂×C₈	—	14	1	no	—
466	C₂×C₈	—	14	1	no	—
467	C₂×C₈	—	14	1	no	—
468	C₂×C₈	—	14	1	no	—
469	C₂×C₈	—	14	1	no	—
470	C₂×C₈	—	14	1	no	—
471	C₂×C₈	—	14	1	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	1	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	14	1	no	—
476	C₂×C₈	—	14	1	no	—
477	C₂×C₈	—	14	1	no	—
478	C₂×C₈	—	14	1	no	—
479	C₂×C₈	—	14	1	no	—
480	C₂×C₈	—	14	1	no	—
481	C₂×C₈	—	14	1	no	—
482	C₂×C₈	—	14	1	no	—
483	C₂×C₈	—	14	1	no	—
484	C₂×C₈	—	14	1	no	—
485	C₂×C₈	—	28	4	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	D₄×D₇	1	2	yes	—
514	C₄²	#1159	1	2	yes	—
515	C₂×C₇	—	4	2	no	—
516	C₂×C₇	#2360	1	1	yes	characteristic
517	C₂×C₇	#2932	1	1	yes	characteristic
518	C₂×C₇	#2933	1	1	yes	characteristic
519	C₂×C₇	#2961	1	1	yes	characteristic
520	C₂×C₇	#2962	1	1	yes	characteristic
521	C₂×C₇	#2993	1	1	yes	characteristic
522	C₂×C₇	#2995	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	Q₈×Dic₇	1	2	yes	—
530	C₂³	C₂³×Dic₇	1	1	yes	characteristic
531	Q₈	—	4	4	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	D₄×Dic₇	1	2	yes	—
572	C₂×C₄	D₄×Dic₇	1	2	yes	—
573	C₂×C₄	Q₈×Dic₇	1	2	yes	—
574	C₂×C₄	#6511	1	2	yes	—
575	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
576	C₂×C₄	C₂×#1159	1	1	yes	characteristic
577	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
578	C₂×C₄	C₂×#1161	1	1	yes	characteristic
579	C₂×C₄	#6553	1	1	yes	characteristic
580	C₂×C₄	#6554	1	1	yes	characteristic
581	C₈	—	14	2	no	—
582	C₈	—	14	2	no	—
583	C₈	—	14	2	no	—
584	C₈	—	14	2	no	—
585	C₈	—	28	1	no	—
586	C₈	—	28	1	no	—
587	C₈	—	28	1	no	—
588	C₈	—	28	1	no	—
589	C₇	#22960	1	1	yes	characteristic, complemented, Sylow
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
598	C₂²	C₂×Q₈×Dic₇	1	1	yes	characteristic
599	C₂²	C₂×#6511	1	1	yes	characteristic
600	C₂²	#90510	1	1	yes	characteristic
601	C₂²	#90510	1	1	yes	characteristic
602	C₂²	#90510	1	1	yes	characteristic
603	C₂²	#90518	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	#90321	1	1	yes	characteristic
618	C₄	#90323	1	1	yes	characteristic
619	C₄	#90326	1	1	yes	characteristic
620	C₄	#90333	1	1	yes	characteristic
621	C₂	—	4	2	no	—
622	C₂	#11740192	1	1	yes	characteristic
623	C₂	#11740363	1	1	yes	characteristic
624	C₂	#11740576	1	1	yes	characteristic
625	C₂	#11740578	1	1	yes	characteristic
626	C₂	#11740721	1	1	yes	characteristic
627	C₂	#11740774	1	1	yes	characteristic
628	C₂	#11740775	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇
commutator, socle	C₂³×C₇	C₂³×C₄
Fitting	C₇×#2396	C₂
prime radical	C₂⁴×C₇	C₂²×C₄
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	#2396	D₇
hypocenter	C₇	#22960
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
2. C₂×#89796	C₂	semidirect
4. #11729388	C₂	semidirect
6. #11727239	C₂	semidirect
7. #11727239	C₂	semidirect
8. #11727239	C₂	semidirect
9. #11727237	C₂	semidirect
10. #11727236	C₂	semidirect
11. #11727231	C₂	semidirect
116. C₂²⋊(C₇⋊C₈)	Q₈	semidirect
589. C₇	#22960	semidirect

Maximal subgroups

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

subgroup	index
C₇×#2396	2
C₂×#89796	2
C₂×#89771	2
#11729388	2
#11729336	2
#11727239	2
#11727237	2
#11727236	2
#11727231	2
#11727204	2
#11727203	2
#11727202	2
#11727201	2
#22960	7