Subgroups — #43248534

Order 28352.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381933	C₂	1	2	yes	maximal, complemented
2	#28381919	C₂	1	6	yes	maximal, complemented
3	#28381908	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₁₇₇₂	C₂	1	3	yes	maximal, complemented
5	#131×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20296787	C₂²	1	6	yes	—
7	#20296786	—	2	6	no	—
8	C₂×Dic₈₈₆	C₂²	1	6	yes	—
9	Q₈×D₄₄₃	—	2	2	no	—
10	Dic₁₇₇₂	C₂²	1	3	yes	—
11	Dic₁₇₇₂	C₂²	1	6	yes	—
12	#20296776	C₂²	1	6	yes	—
13	D₃₅₄₄	C₂²	1	1	yes	characteristic
14	#41×C₄₄₃	C₂²	1	1	yes	characteristic
15	M₁₆×C₄₄₃	C₂²	1	3	yes	—
16	C₂×C₈×C₄₄₃	C₂²	1	3	yes	—
17	Dic₈₈₆	—	2	6	no	—
18	Dic₈₈₆	C₂³	1	6	yes	—
19	D₁₇₇₂	C₂³	1	2	yes	—
20	C₂²⋊D₄₄₃	—	2	6	no	—
21	C₂×Dic₄₄₃	—	2	6	no	—
22	C₄×D₄₄₃	—	2	6	no	—
23	Q₈×C₄₄₃	D₄	1	1	yes	characteristic
24	D₄×C₄₄₃	D₄	1	3	yes	—
25	C₂×C₄×C₄₄₃	C₂³	1	3	yes	—
26	C₈×C₄₄₃	C₂³	1	1	yes	characteristic
27	C₈×C₄₄₃	C₂³	1	3	yes	—
28	C₂²×C₄₄₃	C₂×D₄	1	3	yes	—
29	C₂×D₄₄₃	—	2	2	no	—
30	C₄×C₄₄₃	C₂×D₄	1	3	yes	—
31	C₄×C₄₄₃	C₂⁴	1	1	yes	characteristic
32	Dic₄₄₃	—	2	6	no	—
33	C₂×C₄₄₃	—	2	3	no	—
34	C₂×C₄₄₃	C₂²×D₄	1	1	yes	characteristic
35	D₄₄₃	—	4	2	no	—
36	C₄₄₃	#578	1	1	yes	characteristic, complemented, Sylow
37	#578	—	443	1	no	maximal, Sylow
38	2₋¹⁺⁴	—	443	2	no	—
39	#137	—	443	6	no	—
40	#135	—	443	3	no	—
41	C₂×Q₁₆	—	443	3	no	—
42	#131	D₄₄₃	1	1	yes	characteristic, complemented
43	#41	—	886	6	no	—
44	#41	—	443	6	no	—
45	#41	C₂×D₄₄₃	1	1	yes	characteristic
46	C₂×Q₈	—	886	2	no	—
47	C₂×Q₈	—	443	6	no	—
48	Q₁₆	—	443	3	no	—
49	Q₁₆	—	443	6	no	—
50	SD₁₆	—	443	6	no	—
51	D₈	—	443	1	no	—
52	M₁₆	C₂×D₄₄₃	1	3	yes	—
53	C₂×C₈	C₂×D₄₄₃	1	3	yes	—
54	Q₈	—	886	6	no	—
55	Q₈	—	443	6	no	—
56	Q₈	D₁₇₇₂	1	1	yes	characteristic
57	D₄	—	886	6	no	—
58	D₄	—	443	2	no	—
59	D₄	D₁₇₇₂	1	3	yes	—
60	C₂×C₄	—	886	6	no	—
61	C₂×C₄	—	886	6	no	—
62	C₂×C₄	C₂²×D₄₄₃	1	3	yes	—
63	C₈	C₂²×D₄₄₃	1	1	yes	characteristic
64	C₈	C₂²×D₄₄₃	1	3	yes	—
65	C₂²	—	886	2	no	—
66	C₂²	C₂×D₁₇₇₂	1	3	yes	—
67	C₄	—	886	6	no	—
68	C₄	C₂×D₁₇₇₂	1	3	yes	—
69	C₄	C₂³×D₄₄₃	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	1772	2	no	—
72	C₂	C₂²×D₁₇₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₇₇₂
commutator, cosocle	C₄×C₄₄₃	C₂⁴
Frattini	C₄	C₂³×D₄₄₃
Fitting	#131×C₄₄₃	C₂
socle	C₂×C₄₄₃	C₂²×D₄
hypercenter	#131	D₄₄₃
hypocenter	C₄₄₃	#578
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #28381933	C₂	semidirect
2. #28381919	C₂	semidirect
3. #28381908	C₂	semidirect
4. C₂×Dic₁₇₇₂	C₂	semidirect
5. #131×C₄₄₃	C₂	semidirect
36. C₄₄₃	#578	semidirect
42. #131	D₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
#28381933	2
#28381919	2
#28381908	2
C₂×Dic₁₇₇₂	2
#131×C₄₄₃	2
#578	443