Subgroups — #46782381

Order 33664.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682334	C₂	1	2	yes	maximal
2	#30682318	C₂	1	1	yes	maximal, characteristic
3	#30682288	C₂	1	2	yes	maximal
4	#30681659	C₂	1	1	yes	maximal, characteristic
5	#498×C₂₆₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₀₅₂	—	2	2	no	—
7	#22554470	C₂²	1	1	yes	characteristic
8	#22554470	C₂²	1	1	yes	characteristic
9	#22554401	—	2	4	no	—
10	#22554394	—	2	4	no	—
11	C₄×C₂₆₃⋊C₈	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₂₆₃	C₂²	1	2	yes	—
13	#106×C₂₆₃	—	2	2	no	—
14	C₄×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₂₆	—	2	1	no	—
16	C₂×Dic₅₂₆	—	2	1	no	—
17	Dic₁₀₅₂	—	4	4	no	—
18	C₂×C₂₆₃⋊C₈	D₄	1	4	yes	—
19	C₄⋊Dic₂₆₃	—	2	2	no	—
20	C₄⋊Dic₂₆₃	—	2	2	no	—
21	C₂×Q₈×C₂₆₃	—	2	2	no	—
22	C₂×C₈×C₂₆₃	D₄	1	2	yes	—
23	C₄⋊C₄×C₂₆₃	—	2	2	no	—
24	C₄⋊C₄×C₂₆₃	—	2	2	no	—
25	C₄²×C₂₆₃	C₂³	1	1	yes	characteristic
26	Dic₅₂₆	—	4	2	no	—
27	Dic₅₂₆	—	4	2	no	—
28	C₂×Dic₂₆₃	—	4	1	no	—
29	C₂×Dic₂₆₃	—	4	1	no	—
30	C₂₆₃⋊C₈	—	2	4	no	—
31	Q₈×C₂₆₃	—	4	4	no	—
32	C₂×C₄×C₂₆₃	—	4	2	no	—
33	C₂×C₄×C₂₆₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
35	C₈×C₂₆₃	SD₁₆	1	4	yes	—
36	C₂²×C₂₆₃	#127	1	1	yes	characteristic
37	C₄×C₂₆₃	—	8	2	no	—
38	C₄×C₂₆₃	C₂×SD₁₆	1	2	yes	—
39	C₄×C₂₆₃	#137	1	4	yes	—
40	Dic₂₆₃	—	8	1	no	—
41	Dic₂₆₃	—	8	1	no	—
42	C₂×C₂₆₃	#492	1	1	yes	characteristic
43	C₂×C₂₆₃	#497	1	2	yes	—
44	C₂₆₃	#1716	1	1	yes	characteristic, complemented, Sylow
45	#1716	—	263	1	no	maximal, Sylow
46	#498	—	263	2	no	—
47	#498	D₂₆₃	1	1	yes	characteristic
48	#494	—	263	1	no	—
49	#487	—	263	2	no	—
50	#322	—	263	1	no	—
51	C₂×Q₁₆	—	526	2	no	—
52	C₄⋊Q₈	—	263	1	no	—
53	C₄⋊Q₈	—	263	1	no	—
54	C₄⋊Q₈	C₂×D₂₆₃	1	2	yes	—
55	#106	—	2	2	no	—
56	#106	—	526	4	no	—
57	#103	—	526	4	no	—
58	C₄×C₈	—	263	2	no	—
59	C₄×C₈	C₂×D₂₆₃	1	1	yes	characteristic
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	526	1	no	—
62	C₂×Q₈	—	526	1	no	—
63	Q₁₆	—	1052	4	no	—
64	C₂×C₈	—	263	4	no	—
65	C₂×C₈	C₂²⋊D₂₆₃	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	526	2	no	—
69	C₄⋊C₄	—	526	2	no	—
70	C₄²	C₂²×D₂₆₃	1	1	yes	characteristic
71	Q₈	—	4	4	no	—
72	Q₈	—	1052	2	no	—
73	Q₈	—	1052	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	1052	1	no	—
76	C₂×C₄	—	1052	1	no	—
77	C₂×C₄	D₄×D₂₆₃	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₂₆₃	1	1	yes	characteristic
79	C₈	—	526	4	no	—
80	C₈	#16862363	1	4	yes	—
81	C₂²	#22554466	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	2104	1	no	—
84	C₄	—	2104	1	no	—
85	C₄	C₂×#16862363	1	2	yes	—
86	C₄	#22554499	1	4	yes	—
87	C₂	#30682312	1	1	yes	characteristic
88	C₂	#30682329	1	2	yes	—

	subgroup	G/H
center	C₂²	#22554466
commutator, cosocle	C₄²×C₂₆₃	C₂³
Frattini	C₄²	C₂²×D₂₆₃
Fitting	#498×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	#127
hypercenter	#498	D₂₆₃
hypocenter	C₂₆₃	#1716
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
44. C₂₆₃	#1716	semidirect

Maximal subgroups

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

subgroup	index
#30682334	2
#30682318	2
#30682288	2
#30681659	2
#498×C₂₆₃	2
#1716	263