Subgroups — #46780905

Order 33664.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682328	C₂	1	1	yes	maximal, characteristic
2	#30681733	C₂	1	1	yes	maximal, characteristic, complemented
3	#355×C₂₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16862363	—	2	1	no	—
5	C₂×#16862361	—	2	1	no	—
6	#22554467	C₄	1	1	yes	characteristic, complemented
7	#22554385	—	2	1	no	—
8	#22554381	C₄	1	1	yes	characteristic, complemented
9	#124×C₂₆₃	C₂²	1	1	yes	characteristic
10	#101×C₂₆₃	—	2	1	no	—
11	C₂×D₁₀₅₂	—	2	1	no	—
12	C₂×D₁₀₅₂	—	4	1	no	—
13	#16862363	—	4	2	no	—
14	#16862361	—	4	2	no	—
15	C₂×C₂₆₃⋊C₈	—	2	1	no	—
16	C₂²⋊Dic₂₆₃	—	4	1	no	—
17	C₂×Q₈×C₂₆₃	D₄	1	1	yes	characteristic
18	C₂×D₄×C₂₆₃	D₄	1	1	yes	characteristic
19	M₁₆×C₂₆₃	—	4	1	no	—
20	C₂²⋊C₄×C₂₆₃	—	4	1	no	—
21	C₄²×C₂₆₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₂₆₃	—	4	1	no	—
23	D₁₀₅₂	—	4	1	no	—
24	D₁₀₅₂	—	4	1	no	—
25	D₁₀₅₂	—	8	2	no	—
26	C₂×Dic₂₆₃	—	8	1	no	—
27	C₂₆₃⋊C₈	—	2	2	no	—
28	C₂³×C₂₆₃	—	2	1	no	—
29	Q₈×C₂₆₃	—	4	1	no	—
30	D₄×C₂₆₃	—	4	1	no	—
31	C₂×C₄×C₂₆₃	—	2	1	no	—
32	C₂×C₄×C₂₆₃	—	2	1	no	—
33	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₈×C₂₆₃	—	8	1	no	—
35	C₂²×C₂₆₃	—	4	1	no	—
36	C₂²×C₂₆₃	—	8	1	no	—
37	C₂²×C₂₆₃	#99	1	1	yes	characteristic
38	C₂×D₂₆₃	—	8	2	no	—
39	C₂×D₂₆₃	—	8	1	no	—
40	C₄×C₂₆₃	—	2	1	no	—
41	C₄×C₂₆₃	—	4	1	no	—
42	C₄×C₂₆₃	—	4	1	no	—
43	Dic₂₆₃	—	16	1	no	—
44	C₂×C₂₆₃	—	2	1	no	—
45	C₂×C₂₆₃	—	8	1	no	—
46	C₂×C₂₆₃	#353	1	1	yes	characteristic
47	D₂₆₃	—	16	1	no	—
48	C₂₆₃	#1406	1	1	yes	characteristic, complemented, Sylow
49	#1406	—	263	1	no	maximal, Sylow
50	#496	—	263	1	no	—
51	#355	D₂₆₃	1	1	yes	characteristic, complemented
52	#354	—	263	1	no	—
53	C₂×SD₁₆	—	526	1	no	—
54	C₂×D₈	—	526	1	no	—
55	#127	—	263	1	no	—
56	#124	C₂×D₂₆₃	1	1	yes	characteristic
57	#101	—	2	1	no	—
58	#99	—	526	1	no	—
59	#97	—	263	1	no	—
60	C₂×Q₈	C₂²⋊D₂₆₃	1	1	yes	characteristic
61	C₂×D₄	—	526	1	no	—
62	C₂×D₄	—	1052	1	no	—
63	C₂×D₄	D₁₀₅₂	1	1	yes	characteristic
64	SD₁₆	—	1052	2	no	—
65	D₈	—	1052	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	526	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	1052	1	no	—
70	C₄²	C₄×D₂₆₃	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	1052	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	1052	1	no	—
76	D₄	—	1052	1	no	—
77	D₄	—	2104	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	2104	1	no	—
81	C₂×C₄	(C₂×D₂₆₃)⋊C₄	1	1	yes	characteristic
82	C₈	—	8	1	no	—
83	C₈	—	526	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	2104	2	no	—
87	C₂²	—	2104	1	no	—
88	C₂²	#22554384	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	4208	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	4208	1	no	—
96	C₂	#30681730	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30681730
commutator	C₄²×C₂₆₃	C₂×C₄
Frattini	#124	C₂×D₂₆₃
Fitting	#355×C₂₆₃	C₂
socle	C₂×C₂₆₃	#353
prime radical	#30682328	C₂
cosocle	#124×C₂₆₃	C₂²
hypercenter	#355	D₂₆₃
hypocenter	C₂₆₃	#1406
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂×C₄×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
2. #30681733	C₂	semidirect
3. #355×C₂₆₃	C₂	semidirect
6. #22554467	C₄	semidirect
8. #22554381	C₄	semidirect
48. C₂₆₃	#1406	semidirect
51. #355	D₂₆₃	semidirect

Maximal subgroups

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

subgroup	index
#30682328	2
#30681733	2
#355×C₂₆₃	2
#1406	263