Subgroups — #45688296

Order 33344.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16861967	C₂	1	2	yes	maximal
2	C₈×Dic₅₂₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#16861967	—	2	2	no	—
4	C₂×#16861960	C₄	1	1	yes	characteristic
5	C₄×Dic₅₂₁	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₅₂₁	C₄	1	1	yes	characteristic
7	#16861967	—	4	2	no	—
8	C₂×Dic₅₂₁	D₄	1	1	yes	characteristic
9	C₂×Dic₅₂₁	Q₈	1	1	yes	characteristic
10	#16861960	C₈	1	2	yes	complemented
11	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₅₂₁	—	2	1	no	—
13	C₂²×C₅₂₁	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₅₂₁	C₂×C₈	1	1	yes	characteristic
15	C₄×C₅₂₁	M₁₆	1	1	yes	characteristic
16	Dic₅₂₁	—	2	1	no	—
17	Dic₅₂₁	D₈	1	1	yes	characteristic
18	Dic₅₂₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₅₂₁	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₅₂₁	#107	1	1	yes	characteristic
21	C₂×C₅₂₁	#108	1	1	yes	characteristic
22	C₅₂₁	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	521	1	no	maximal, Sylow
24	C₄⋊C₈	—	521	2	no	—
25	C₄×C₈	—	521	1	no	—
26	C₂×C₈	—	521	1	no	—
27	C₂×C₈	—	1042	2	no	—
28	C₂×C₈	#14523438	1	1	yes	characteristic
29	C₄²	—	521	1	no	—
30	C₂×C₄	—	521	1	no	—
31	C₂×C₄	—	521	1	no	—
32	C₂×C₄	C₂×#14523438	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	521	2	no	—
35	C₈	—	2084	2	no	—
36	C₂²	C₄⋊#14523438	1	1	yes	characteristic
37	C₄	—	521	1	no	—
38	C₄	—	521	1	no	—
39	C₄	—	1042	1	no	—
40	C₄	#22552372	1	1	yes	characteristic
41	C₄	#22552373	1	1	yes	characteristic
42	C₂	#30659775	1	1	yes	characteristic
43	C₂	#30659777	1	1	yes	characteristic
44	C₂	#30659778	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#14523438
commutator	C₄×C₅₂₁	C₂×C₈
Frattini	C₂×C₄	C₂×#14523438
Fitting	C₂×C₈×C₅₂₁	C₄
socle, prime radical	C₂²×C₅₂₁	C₄⋊C₄
cosocle	C₄×Dic₅₂₁	C₂²
hypercenter	C₂×C₈	#14523438
hypocenter	C₅₂₁	#335
LCS	G ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #16861960	C₈	semidirect
22. C₅₂₁	#335	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#16861967	2
C₈×Dic₅₂₁	2
#335	521