Subgroups — #43247529

Order 28352.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₅₄₄	C₂	1	1	yes	maximal, characteristic
2	#28381826	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₇₇₂	—	2	1	no	—
5	D₃₅₄₄	—	2	1	no	—
6	D₃₅₄₄	C₄	1	2	yes	—
7	C₄₄₃⋊C₁₆	—	2	1	no	—
8	M₁₆×C₄₄₃	—	2	1	no	—
9	C₂×C₈×C₄₄₃	C₂²	1	1	yes	characteristic
10	C₂²×D₄₄₃	—	4	1	no	—
11	D₁₇₇₂	—	2	2	no	—
12	D₁₇₇₂	—	4	1	no	—
13	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
14	C₈×C₄₄₃	—	4	1	no	—
15	C₈×C₄₄₃	C₂×C₄	1	1	yes	characteristic
16	C₈×C₄₄₃	D₄	1	1	yes	characteristic
17	C₂²×C₄₄₃	SD₁₆	1	1	yes	characteristic
18	C₂×D₄₄₃	—	4	2	no	—
19	C₂×D₄₄₃	—	8	2	no	—
20	C₄×C₄₄₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₄₃	D₈	1	1	yes	characteristic
22	C₂×C₄₄₃	—	2	1	no	—
23	C₂×C₄₄₃	#102	1	1	yes	characteristic
24	D₄₄₃	—	8	2	no	—
25	C₄₄₃	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	443	1	no	maximal, Sylow
27	C₂×D₈	—	443	1	no	—
28	M₃₂	—	443	1	no	—
29	#108	D₄₄₃	1	1	yes	characteristic, complemented
30	C₂×D₄	—	886	1	no	—
31	D₈	—	886	1	no	—
32	D₈	—	443	2	no	—
33	M₁₆	—	2	1	no	—
34	C₂×C₈	C₂×D₄₄₃	1	1	yes	characteristic
35	C₁₆	—	886	1	no	—
36	C₂³	—	1772	1	no	—
37	D₄	—	886	2	no	—
38	D₄	—	1772	1	no	—
39	C₂×C₄	C₂²⋊D₄₄₃	1	1	yes	characteristic
40	C₈	—	4	1	no	—
41	C₈	C₄×D₄₄₃	1	1	yes	characteristic
42	C₈	D₁₇₇₂	1	1	yes	characteristic
43	C₂²	—	3544	2	no	—
44	C₂²	—	1772	2	no	—
45	C₂²	#20296774	1	1	yes	characteristic
46	C₄	(C₂×D₄₄₃)⋊C₄	1	1	yes	characteristic
47	C₄	#20296772	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	3544	2	no	—
50	C₂	#28381806	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28381806
commutator	C₈×C₄₄₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₄₃
Fitting	#108×C₄₄₃	C₂
socle	C₂×C₄₄₃	#102
prime radical	C₂×D₃₅₄₄	C₂
cosocle	C₂×C₈×C₄₄₃	C₂²
hypercenter	#108	D₄₄₃
hypocenter	C₄₄₃	#361
LCS	G ▷ C₈×C₄₄₃ ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #28381826	C₂	semidirect
3. #108×C₄₄₃	C₂	semidirect
25. C₄₄₃	#361	semidirect
29. #108	D₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₅₄₄	2
#28381826	2
#108×C₄₄₃	2
#361	443