Subgroups — #28412345

Order 14656.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14270087	C₂	1	2	yes	maximal
2	C₈×Dic₂₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14270087	—	2	2	no	—
4	C₂×#14270080	C₄	1	1	yes	characteristic
5	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₂₉	C₄	1	1	yes	characteristic
7	#14270087	—	4	2	no	—
8	C₂×Dic₂₂₉	D₄	1	1	yes	characteristic
9	C₂×Dic₂₂₉	Q₈	1	1	yes	characteristic
10	#14270080	C₈	1	2	yes	complemented
11	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₂₉	—	2	1	no	—
13	C₂²×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₂₂₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₂₂₉	M₁₆	1	1	yes	characteristic
16	Dic₂₂₉	—	2	1	no	—
17	Dic₂₂₉	D₈	1	1	yes	characteristic
18	Dic₂₂₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₂₂₉	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₂₂₉	#107	1	1	yes	characteristic
21	C₂×C₂₂₉	#108	1	1	yes	characteristic
22	C₂₂₉	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	229	1	no	maximal, Sylow
24	C₄⋊C₈	—	229	2	no	—
25	C₄×C₈	—	229	1	no	—
26	C₂×C₈	—	458	2	no	—
27	C₂×C₈	—	229	1	no	—
28	C₂×C₈	#11745021	1	1	yes	characteristic
29	C₄²	—	229	1	no	—
30	C₂×C₄	—	229	1	no	—
31	C₂×C₄	—	229	1	no	—
32	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	916	2	no	—
35	C₈	—	229	2	no	—
36	C₂²	C₄⋊#11745021	1	1	yes	characteristic
37	C₄	—	458	1	no	—
38	C₄	—	229	1	no	—
39	C₄	—	229	1	no	—
40	C₄	D₂₂₉⋊C₈	1	1	yes	characteristic
41	C₄	#16814675	1	1	yes	characteristic
42	C₂	#20301055	1	1	yes	characteristic
43	C₂	#20301057	1	1	yes	characteristic
44	C₂	#20301058	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#11745021
commutator	C₄×C₂₂₉	C₂×C₈
Frattini	C₂×C₄	C₂×#11745021
Fitting	C₂×C₈×C₂₂₉	C₄
socle, prime radical	C₂²×C₂₂₉	C₄⋊C₄
cosocle	C₄×Dic₂₂₉	C₂²
hypercenter	C₂×C₈	#11745021
hypocenter	C₂₂₉	#335
LCS	G ▷ C₄×C₂₂₉ ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #14270080	C₈	semidirect
22. C₂₂₉	#335	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14270087	2
C₈×Dic₂₂₉	2
#335	229