Subgroups — #11928148

Order 1248.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#10597662	C₂	1	2	yes	maximal
3	#88076	—	3	1	no	maximal, Hall
4	C₃×Q₈×C₁₃	—	2	2	no	—
5	C₂×C₃×C₄×C₁₃	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₃⋊#1055	—	2	2	no	—
8	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic
9	#6099	—	3	2	no	—
10	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₃	—	2	2	no	—
12	C₃×C₄×C₁₃	D₄	1	2	yes	—
13	Q₈×C₁₃	—	2	2	no	—
14	C₂×C₄×C₁₃	Dic₃	1	2	yes	—
15	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
16	#1055	—	6	2	no	—
17	#836	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	—	2	1	no	—
19	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
21	C₄×C₁₃	—	2	2	no	—
22	C₄×C₁₃	#67	1	2	yes	—
23	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic
24	#208	—	13	2	no	—
25	C₃×C₁₃	#101	1	1	yes	characteristic, complemented, Hall
26	#101	—	39	1	no	Sylow
27	C₂×C₁₃	—	2	1	no	—
28	C₂×C₁₃	#217	1	1	yes	characteristic
29	C₃×Q₈	—	2	2	no	—
30	C₂×C₃×C₄	Dic₁₃	1	2	yes	—
31	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
32	C₃⋊C₈	—	26	2	no	—
33	C₂×Q₈	D₃₉	1	1	yes	characteristic
34	M₁₆	—	39	2	no	—
35	C₁₃	#836	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₃	C₂×Dic₁₃	1	1	yes	characteristic
37	C₃×C₄	—	2	2	no	—
38	C₃×C₄	C₂²⋊D₁₃	1	2	yes	—
39	Q₈	—	2	2	no	—
40	C₂×C₄	Dic₃₉	1	2	yes	—
41	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
42	C₈	—	78	2	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	C₂²⋊Dic₁₃	1	1	yes	characteristic
45	C₂²	C₂×Dic₃₉	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	#64625	1	2	yes	—
48	C₃	#88076	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	2	1	no	—
50	C₂	#10597671	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597671
commutator, prime radical	C₂²×C₃×C₁₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₃₉
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂²⋊C₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	C₂×Q₈	D₃₉
hypocenter	C₃×C₁₃	#101
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
25. C₃×C₁₃	#101	semidirect
35. C₁₃	#836	semidirect
48. C₃	#88076	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₃	2
#10597662	2
#88076	3
#836	13