Subgroups — C₇×#25963 #13203179

Order 1792.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#103	C₂	1	1	yes	maximal, characteristic
3	C₇×#2440	C₂	1	1	yes	maximal, characteristic
4	C₇×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2024	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1852	C₂	1	1	yes	maximal, characteristic
12	C₇×#1850	C₂	1	1	yes	maximal, characteristic
13	C₇×#1808	C₂	1	1	yes	maximal, characteristic
14	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1787	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₇×#477	—	2	4	no	—
24	C₂×C₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₇×#107	C₂²	1	1	yes	characteristic
26	C₂×C₇×#107	C₂²	1	1	yes	characteristic
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	—	2	4	no	—
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#103	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₇×#398	—	2	1	no	—
41	C₇×#395	—	2	1	no	—
42	C₇×#391	—	2	1	no	—
43	C₇×#391	—	2	1	no	—
44	C₇×#391	C₂²	1	1	yes	characteristic
45	C₇×#391	C₂²	1	1	yes	characteristic
46	C₇×#389	C₂²	1	1	yes	characteristic
47	C₇×#389	C₂²	1	1	yes	characteristic
48	C₇×#385	—	2	1	no	—
49	C₇×#384	C₂²	1	1	yes	characteristic
50	C₇×#380	—	2	1	no	—
51	C₇×#380	C₂²	1	1	yes	characteristic
52	C₇×#380	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	#25963	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×Q₈	—	2	1	no	—
63	C₂²×C₇×Q₈	—	2	1	no	—
64	C₂²×C₇×Q₈	—	2	2	no	—
65	C₂²×C₇×Q₈	—	2	2	no	—
66	C₂²×C₇×Q₈	—	2	2	no	—
67	C₂²×C₇×Q₈	—	4	1	no	—
68	C₂²×C₇×Q₈	—	4	1	no	—
69	C₂²×C₇×Q₈	Q₈	1	4	yes	complemented
70	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	—	2	2	no	—
76	C₂²×C₇×C₈	—	2	2	no	—
77	C₂²×C₇×C₈	—	4	1	no	—
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	C₇×C₄⋊Q₈	—	2	2	no	—
83	C₇×C₄⋊Q₈	—	4	1	no	—
84	C₇×C₂²⋊Q₈	—	4	4	no	—
85	C₄×C₇×Q₈	—	2	2	no	—
86	C₄×C₇×Q₈	—	2	2	no	—
87	C₄×C₇×Q₈	—	4	1	no	—
88	C₄×C₇×Q₈	—	4	1	no	—
89	C₂×C₇×C₄⋊C₄	—	2	2	no	—
90	C₂×C₇×C₄⋊C₄	—	2	1	no	—
91	C₂×C₇×C₄⋊C₄	—	2	1	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	4	1	no	—
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	—	2	1	no	—
111	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₇×#107	—	2	2	no	—
114	C₇×#107	—	2	2	no	—
115	C₇×#107	—	4	1	no	—
116	C₇×#107	—	4	1	no	—
117	C₇×C₄⋊C₈	—	2	2	no	—
118	C₇×C₄⋊C₈	—	4	1	no	—
119	C₇×#103	—	2	2	no	—
120	C₇×#103	—	2	2	no	—
121	C₇×#103	—	2	2	no	—
122	C₇×#103	—	2	2	no	—
123	C₇×#103	—	2	2	no	—
124	C₇×#103	—	4	1	no	—
125	C₇×#103	—	4	1	no	—
126	C₇×#103	D₄	1	4	yes	—
127	C₇×C₂²⋊C₈	—	2	2	no	—
128	C₇×#95	—	2	1	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	—	2	1	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	D₄	1	1	yes	characteristic
137	C₇×#95	D₄	1	1	yes	characteristic
138	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂²×#103	C₂×C₇	1	1	yes	characteristic
140	#2440	C₂×C₇	1	1	yes	characteristic
141	Q₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
142	#2095	C₂×C₇	1	1	yes	characteristic, complemented
143	#2068	C₂×C₇	1	1	yes	characteristic, complemented
144	#2068	C₂×C₇	1	1	yes	characteristic, complemented
145	#2024	C₂×C₇	1	1	yes	characteristic, complemented
146	#1863	C₂×C₇	1	1	yes	characteristic, complemented
147	#1863	C₂×C₇	1	1	yes	characteristic, complemented
148	#1852	C₂×C₇	1	1	yes	characteristic
149	#1850	C₂×C₇	1	1	yes	characteristic
150	#1808	C₂×C₇	1	1	yes	characteristic
151	#1803	C₂×C₇	1	1	yes	characteristic, complemented
152	#1787	C₂×C₇	1	1	yes	characteristic
153	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₇×Q₈	—	2	4	no	—
155	C₂×C₇×Q₈	—	2	1	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	2	1	no	—
158	C₂×C₇×Q₈	—	2	1	no	—
159	C₂×C₇×Q₈	—	2	8	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	4	2	no	—
165	C₂×C₇×Q₈	—	4	2	no	—
166	C₂×C₇×Q₈	—	4	2	no	—
167	C₂×C₇×Q₈	—	4	4	no	—
168	C₂×C₇×Q₈	—	4	4	no	—
169	C₂×C₇×Q₈	—	4	4	no	—
170	C₂×C₇×Q₈	—	4	2	no	—
171	C₂×C₇×Q₈	—	8	1	no	—
172	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
173	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
174	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
175	C₂×C₇×Q₈	#41	1	2	yes	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	4	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	—	4	2	no	—
191	C₂²×C₄×C₇	—	4	2	no	—
192	C₂²×C₄×C₇	—	4	2	no	—
193	C₂²×C₄×C₇	—	8	1	no	—
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
200	C₂²×C₄×C₇	#41	1	2	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
214	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
215	C₇×C₄⋊C₄	—	2	1	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	—	4	2	no	—
229	C₇×C₄⋊C₄	—	4	2	no	—
230	C₇×C₄⋊C₄	—	4	2	no	—
231	C₇×C₄⋊C₄	—	4	2	no	—
232	C₇×C₄⋊C₄	—	4	2	no	—
233	C₇×C₄⋊C₄	—	8	1	no	—
234	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
235	C₇×C₂²⋊C₄	—	2	2	no	—
236	C₇×C₂²⋊C₄	—	4	2	no	—
237	C₇×C₂²⋊C₄	—	4	2	no	—
238	C₇×C₂²⋊C₄	Q₁₆	1	4	yes	—
239	C₄²×C₇	—	2	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	2	1	no	—
242	C₄²×C₇	—	2	1	no	—
243	C₄²×C₇	—	4	2	no	—
244	C₄²×C₇	—	4	2	no	—
245	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	#477	—	2	4	no	—
253	C₂×#107	C₂²×C₇	1	1	yes	characteristic
254	C₂×#107	C₂²×C₇	1	1	yes	characteristic
255	C₂×#107	C₂²×C₇	1	1	yes	characteristic
256	C₂×#107	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×#103	—	2	4	no	—
260	C₂×#103	C₂²×C₇	1	1	yes	characteristic
261	C₂×#103	C₂²×C₇	1	1	yes	characteristic
262	C₂×#103	C₂²×C₇	1	1	yes	characteristic
263	C₂×#103	C₂²×C₇	1	1	yes	characteristic
264	C₂×#103	C₂²×C₇	1	1	yes	characteristic
265	C₂×#103	C₂²×C₇	1	1	yes	characteristic
266	C₂×#103	C₂²×C₇	1	1	yes	characteristic
267	C₂×#103	C₂²×C₇	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
269	#398	—	2	1	no	—
270	#395	—	2	1	no	—
271	#391	—	2	1	no	—
272	#391	—	2	1	no	—
273	#391	C₂²×C₇	1	1	yes	characteristic
274	#391	C₂²×C₇	1	1	yes	characteristic
275	#389	C₂²×C₇	1	1	yes	characteristic
276	#389	C₂²×C₇	1	1	yes	characteristic
277	#385	—	2	1	no	—
278	#384	C₂²×C₇	1	1	yes	characteristic
279	#380	—	2	1	no	—
280	#380	C₂²×C₇	1	1	yes	characteristic
281	#380	C₂²×C₇	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	—	2	1	no	—
283	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
284	#340	C₂²×C₇	1	1	yes	characteristic
285	#340	C₂²×C₇	1	1	yes	characteristic
286	#340	C₂²×C₇	1	1	yes	characteristic
287	#340	C₂²×C₇	1	1	yes	characteristic
288	#336	C₂²×C₇	1	1	yes	characteristic
289	#336	C₂²×C₇	1	1	yes	characteristic
290	C₂³×C₇	—	2	1	no	—
291	C₂³×C₇	—	2	1	no	—
292	C₂³×C₇	—	2	1	no	—
293	C₂³×C₇	—	2	1	no	—
294	C₂³×C₇	C₂²⋊Q₈	1	2	yes	—
295	C₂³×C₇	C₂×Q₁₆	1	2	yes	—
296	C₂³×C₇	AGL(1,ℤ/8)	1	2	yes	—
297	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
298	C₇×Q₈	—	2	2	no	—
299	C₇×Q₈	—	2	2	no	—
300	C₇×Q₈	—	2	2	no	—
301	C₇×Q₈	—	2	2	no	—
302	C₇×Q₈	—	2	2	no	—
303	C₇×Q₈	—	4	8	no	—
304	C₇×Q₈	—	4	1	no	—
305	C₇×Q₈	—	4	1	no	—
306	C₇×Q₈	—	8	4	no	—
307	C₇×Q₈	C₂²⋊Q₈	1	4	yes	complemented
308	C₂×C₄×C₇	—	2	2	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	2	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	2	2	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	2	no	—
318	C₂×C₄×C₇	—	2	2	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	2	no	—
321	C₂×C₄×C₇	—	2	2	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	2	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	2	1	no	—
329	C₂×C₄×C₇	—	4	8	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	—	4	1	no	—
336	C₂×C₄×C₇	—	4	1	no	—
337	C₂×C₄×C₇	—	4	1	no	—
338	C₂×C₄×C₇	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	8	4	no	—
350	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
351	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
352	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
353	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
355	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
359	C₇×C₈	—	2	2	no	—
360	C₇×C₈	—	4	1	no	—
361	C₇×C₈	—	4	1	no	—
362	C₇×C₈	—	4	1	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×Q₈	—	2	2	no	—
366	C₂²×Q₈	—	2	2	no	—
367	C₂²×Q₈	—	2	2	no	—
368	C₂²×Q₈	—	4	1	no	—
369	C₂²×Q₈	—	4	1	no	—
370	C₂²×Q₈	C₇×Q₈	1	4	yes	complemented
371	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
372	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
376	C₂²×C₈	—	2	2	no	—
377	C₂²×C₈	—	2	2	no	—
378	C₂²×C₈	—	4	1	no	—
379	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	C₄⋊Q₈	—	2	2	no	—
384	C₄⋊Q₈	—	4	1	no	—
385	C₂²⋊Q₈	—	4	4	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	4	1	no	—
389	C₄×Q₈	—	4	1	no	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	4	1	no	—
400	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
414	#107	—	2	2	no	—
415	#107	—	2	2	no	—
416	#107	—	4	1	no	—
417	#107	—	4	1	no	—
418	C₄⋊C₈	—	2	2	no	—
419	C₄⋊C₈	—	4	1	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#103	—	2	2	no	—
425	#103	—	4	1	no	—
426	#103	—	4	1	no	—
427	#103	C₇×D₄	1	4	yes	—
428	C₂²⋊C₈	—	2	2	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	C₇×D₄	1	1	yes	characteristic
438	#95	C₇×D₄	1	1	yes	characteristic
439	C₂²×C₇	—	2	2	no	—
440	C₂²×C₇	—	2	2	no	—
441	C₂²×C₇	—	2	2	no	—
442	C₂²×C₇	—	2	2	no	—
443	C₂²×C₇	—	2	2	no	—
444	C₂²×C₇	—	2	2	no	—
445	C₂²×C₇	#477	1	4	yes	complemented
446	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
447	C₂²×C₇	D₄²	1	1	yes	characteristic
448	C₂²×C₇	#546	1	1	yes	characteristic
449	C₂²×C₇	C₂²×Q₁₆	1	1	yes	characteristic
450	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²×C₇	#577	1	1	yes	characteristic
452	C₂²×C₇	#578	1	1	yes	characteristic
453	C₄×C₇	—	2	2	no	—
454	C₄×C₇	—	2	4	no	—
455	C₄×C₇	—	2	2	no	—
456	C₄×C₇	—	2	2	no	—
457	C₄×C₇	—	4	2	no	—
458	C₄×C₇	—	4	1	no	—
459	C₄×C₇	—	4	2	no	—
460	C₄×C₇	—	4	1	no	—
461	C₄×C₇	—	8	1	no	—
462	C₄×C₇	—	8	1	no	—
463	C₄×C₇	—	8	1	no	—
464	C₄×C₇	—	8	1	no	—
465	C₄×C₇	—	8	1	no	—
466	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
467	C₄×C₇	#543	1	1	yes	characteristic
468	C₄×C₇	#546	1	1	yes	characteristic
469	C₄×C₇	#551	1	1	yes	characteristic
470	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	8	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	4	2	no	—
482	C₂×Q₈	—	4	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	—	4	4	no	—
485	C₂×Q₈	—	4	4	no	—
486	C₂×Q₈	—	4	4	no	—
487	C₂×Q₈	—	4	2	no	—
488	C₂×Q₈	—	8	1	no	—
489	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
490	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
491	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
492	C₂×Q₈	C₇×#41	1	2	yes	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	8	1	no	—
511	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
517	C₂²×C₄	C₇×#41	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	4	4	no	—
531	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	8	1	no	—
551	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	C₇×Q₁₆	1	4	yes	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	4	2	no	—
561	C₄²	—	4	2	no	—
562	C₂×C₇	—	2	4	no	—
563	C₂×C₇	#2437	1	1	yes	characteristic
564	C₂×C₇	C₂×#477	1	1	yes	characteristic
565	C₂×C₇	#3082	1	1	yes	characteristic
566	C₂×C₇	#3265	1	1	yes	characteristic
567	C₂×C₇	D₄×Q₁₆	1	1	yes	characteristic
568	C₂×C₇	#3299	1	1	yes	characteristic
569	C₂×C₇	#3308	1	1	yes	characteristic
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	C₇×C₂²⋊Q₈	1	2	yes	—
575	C₂³	C₂×C₇×Q₁₆	1	2	yes	—
576	C₂³	C₇×AGL(1,ℤ/8)	1	2	yes	—
577	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	8	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	8	4	no	—
587	Q₈	C₇×C₂²⋊Q₈	1	4	yes	complemented
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	8	4	no	—
630	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
631	C₂×C₄	C₂×C₇×Q₁₆	1	2	yes	—
632	C₂×C₄	C₂×C₇×Q₁₆	1	2	yes	—
633	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
634	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
635	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
636	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
637	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
639	C₈	—	2	2	no	—
640	C₈	—	4	1	no	—
641	C₈	—	4	1	no	—
642	C₈	—	4	1	no	—
643	C₇	#25963	1	1	yes	characteristic, direct product factor, Sylow
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	C₇×#477	1	4	yes	complemented
651	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
652	C₂²	C₇×D₄²	1	1	yes	characteristic
653	C₂²	C₇×#546	1	1	yes	characteristic
654	C₂²	C₂²×C₇×Q₁₆	1	1	yes	characteristic
655	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
656	C₂²	C₇×#577	1	1	yes	characteristic
657	C₂²	C₇×#578	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
672	C₄	C₇×#543	1	1	yes	characteristic
673	C₄	C₇×#546	1	1	yes	characteristic
674	C₄	C₇×#551	1	1	yes	characteristic
675	C₂	—	2	4	no	—
676	C₂	C₇×#2437	1	1	yes	characteristic
677	C₂	C₂×C₇×#477	1	1	yes	characteristic
678	C₂	C₇×#3082	1	1	yes	characteristic
679	C₂	C₇×#3265	1	1	yes	characteristic
680	C₂	C₇×D₄×Q₁₆	1	1	yes	characteristic
681	C₂	C₇×#3299	1	1	yes	characteristic
682	C₂	C₇×#3308	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#477	C₂	semidirect
5. C₇×#2095	C₂	semidirect
6. C₇×#2068	C₂	semidirect
7. C₇×#2068	C₂	semidirect
8. C₇×#2024	C₂	semidirect
9. C₇×#1863	C₂	semidirect
10. C₇×#1863	C₂	semidirect
14. C₇×#1803	C₂	semidirect
61. #25963	C₇	direct (N × H)
69. C₂²×C₇×Q₈	Q₈	semidirect
138. C₂×#477	C₂×C₇	semidirect
142. #2095	C₂×C₇	semidirect
143. #2068	C₂×C₇	semidirect
144. #2068	C₂×C₇	semidirect
145. #2024	C₂×C₇	semidirect
146. #1863	C₂×C₇	semidirect
147. #1863	C₂×C₇	semidirect
151. #1803	C₂×C₇	semidirect
307. C₇×Q₈	C₂²⋊Q₈	semidirect
370. C₂²×Q₈	C₇×Q₈	semidirect
445. C₂²×C₇	#477	semidirect
587. Q₈	C₇×C₂²⋊Q₈	semidirect
643. C₇	#25963	direct (N × H)
650. C₂²	C₇×#477	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#477	2
C₂²×C₇×#103	2
C₇×#2440	2
C₇×Q₈×C₂²⋊C₄	2
C₇×#2095	2
C₇×#2068	2
C₇×#2024	2
C₇×#1863	2
C₇×#1852	2
C₇×#1850	2
C₇×#1808	2
C₇×#1803	2
C₇×#1787	2
#25963	7

Subgroups — C7×#25963 #13203179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#25963 #13203179