Subgroups — #11928129

Order 1248.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₉	C₂	1	2	yes	maximal
3	#88058	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×Dic₃₉	—	2	2	no	—
6	C₃×C₈×C₁₃	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic
8	C₄⋊Dic₁₃	—	3	2	no	—
9	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
10	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₃	Q₈	1	1	yes	characteristic
12	Dic₃₉	—	4	2	no	—
13	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
14	C₂×Dic₁₃	—	6	2	no	—
15	C₈×C₁₃	Dic₃	1	2	yes	complemented
16	#818	—	13	1	no	maximal, Hall
17	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
19	C₂×C₃×C₁₃	Q₁₆	1	1	yes	characteristic
20	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
21	C₄×C₁₃	Dic₆	1	1	yes	characteristic
22	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
23	Dic₁₃	—	12	2	no	—
24	C₂×C₃×C₈	D₁₃	1	1	yes	characteristic
25	C₄⋊Dic₃	—	13	2	no	—
26	C₃×C₁₃	#107	1	1	yes	characteristic, complemented, Hall
27	#107	—	39	1	no	Sylow
28	C₂×C₁₃	D₂₄	1	1	yes	characteristic
29	C₂×C₁₃	Dic₁₂	1	1	yes	characteristic
30	C₂×C₁₃	C₄⋊Dic₃	1	1	yes	characteristic
31	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
32	C₂×Dic₃	—	26	2	no	—
33	C₃×C₈	Dic₁₃	1	2	yes	complemented
34	C₂×C₈	D₃₉	1	1	yes	characteristic
35	C₄⋊C₄	—	39	2	no	—
36	C₁₃	#818	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	D₅₂	1	1	yes	characteristic
38	C₃×C₄	Dic₂₆	1	1	yes	characteristic
39	C₃×C₄	C₂×Dic₁₃	1	1	yes	characteristic
40	Dic₃	—	52	2	no	—
41	C₂×C₄	—	78	2	no	—
42	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
43	C₈	Dic₃₉	1	2	yes	complemented
44	C₂×C₃	D₁₀₄	1	1	yes	characteristic
45	C₂×C₃	Dic₅₂	1	1	yes	characteristic
46	C₂×C₃	C₄⋊Dic₁₃	1	1	yes	characteristic
47	C₂²	D₁₅₆	1	1	yes	characteristic
48	C₄	—	156	2	no	—
49	C₄	Dic₇₈	1	1	yes	characteristic
50	C₄	C₂×Dic₃₉	1	1	yes	characteristic
51	C₃	#88058	1	1	yes	characteristic, complemented, Sylow
52	C₂	D₃₁₂	1	1	yes	characteristic
53	C₂	Dic₁₅₆	1	1	yes	characteristic
54	C₂	C₄⋊Dic₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₅₆
commutator	C₃×C₄×C₁₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₃₉
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	D₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	C₂×C₈	D₃₉
hypocenter	C₃×C₁₃	#107
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. C₃×C₈×C₁₃	C₄	semidirect
15. C₈×C₁₃	Dic₃	semidirect
26. C₃×C₁₃	#107	semidirect
33. C₃×C₈	Dic₁₃	semidirect
36. C₁₃	#818	semidirect
43. C₈	Dic₃₉	semidirect
51. C₃	#88058	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₈×C₁₃	2
C₄⋊Dic₃₉	2
#88058	3
#818	13