Subgroups — #49147702

Order 36928.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#17987230	C₂	1	2	yes	maximal
2	C₄×C₈×C₅₇₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#17987230	—	2	2	no	—
4	C₂×C₈×C₅₇₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₅₇₇	C₄	1	1	yes	characteristic
6	C₄²×C₅₇₇	C₂²	1	1	yes	characteristic
7	#17987230	—	4	2	no	—
8	C₂×C₄×C₅₇₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅₇₇	D₄	1	1	yes	characteristic
10	C₂×C₄×C₅₇₇	Q₈	1	1	yes	characteristic
11	C₈×C₅₇₇	—	2	1	no	—
12	C₈×C₅₇₇	C₈	1	2	yes	complemented
13	C₂²×C₅₇₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₅₇₇	—	2	1	no	—
15	C₄×C₅₇₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₅₇₇	M₁₆	1	1	yes	characteristic
17	C₄×C₅₇₇	D₈	1	1	yes	characteristic
18	C₄×C₅₇₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₅₇₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₅₇₇	#107	1	1	yes	characteristic
21	C₂×C₅₇₇	#108	1	1	yes	characteristic
22	C₅₇₇	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	577	1	no	maximal, Sylow
24	C₄⋊C₈	—	577	2	no	—
25	C₄×C₈	D₅₇₇	1	1	yes	characteristic
26	C₂×C₈	—	1154	2	no	—
27	C₂×C₈	Dic₅₇₇	1	1	yes	characteristic
28	C₂×C₈	Dic₅₇₇	1	1	yes	characteristic
29	C₄²	C₂×D₅₇₇	1	1	yes	characteristic
30	C₂×C₄	C₂×Dic₅₇₇	1	1	yes	characteristic
31	C₂×C₄	D₂₃₀₈	1	1	yes	characteristic
32	C₂×C₄	Dic₁₁₅₄	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	2308	2	no	—
35	C₈	#17987230	1	2	yes	complemented
36	C₂²	C₄⋊Dic₅₇₇	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×#17987230	1	1	yes	characteristic
39	C₄	#22604402	1	1	yes	characteristic
40	C₄	D₄₆₁₆	1	1	yes	characteristic
41	C₄	Dic₂₃₀₈	1	1	yes	characteristic
42	C₂	C₄⋊#17987230	1	1	yes	characteristic
43	C₂	#32914598	1	1	yes	characteristic
44	C₂	#32914600	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₃₀₈
commutator	C₄×C₅₇₇	C₂×C₈
Frattini	C₄²	C₂×D₅₇₇
Fitting	C₄×C₈×C₅₇₇	C₂
socle, prime radical	C₂²×C₅₇₇	C₄⋊C₄
cosocle	C₄²×C₅₇₇	C₂²
hypercenter	C₄×C₈	D₅₇₇
hypocenter	C₅₇₇	#335
LCS	G ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
12. C₈×C₅₇₇	C₈	semidirect
22. C₅₇₇	#335	semidirect
35. C₈	#17987230	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#17987230	2
C₄×C₈×C₅₇₇	2
#335	577