Subgroups — #11928146

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#10597662	C₂	1	2	yes	maximal, complemented
3	#88073	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₄	1	2	yes	—
5	C₃×D₄×C₁₃	—	2	2	no	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₃⋊#1055	—	2	2	no	—
8	C₂×D₄×C₁₃	D₃	1	1	yes	characteristic
9	#6099	—	3	2	no	—
10	C₂²×C₃×C₁₃	—	2	2	no	—
11	C₂²×C₃×C₁₃	—	4	2	no	—
12	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₁₃	D₄	1	2	yes	—
14	C₂³×C₁₃	Dic₃	1	2	yes	—
15	D₄×C₁₃	—	2	2	no	—
16	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
17	#1055	—	6	2	no	—
18	#833	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	—	2	1	no	—
20	C₂×C₃×C₁₃	—	4	2	no	—
21	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂²×C₁₃	—	2	2	no	—
23	C₂²×C₁₃	—	4	2	no	—
24	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
25	C₄×C₁₃	#67	1	2	yes	—
26	C₂×C₃×D₄	D₁₃	1	1	yes	characteristic
27	#208	—	13	2	no	—
28	C₃×C₁₃	#100	1	1	yes	characteristic, complemented, Hall
29	#100	—	39	1	no	Sylow
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	—	4	2	no	—
32	C₂×C₁₃	#217	1	1	yes	characteristic
33	C₂³×C₃	Dic₁₃	1	2	yes	—
34	C₃×D₄	—	2	2	no	—
35	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
36	C₃⋊C₈	—	26	2	no	—
37	C₂×D₄	D₃₉	1	1	yes	characteristic
38	M₁₆	—	39	2	no	—
39	C₁₃	#833	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₃	—	2	2	no	—
41	C₂²×C₃	—	4	2	no	—
42	C₂²×C₃	C₂×Dic₁₃	1	1	yes	characteristic
43	C₃×C₄	C₂²⋊D₁₃	1	2	yes	—
44	C₂³	Dic₃₉	1	2	yes	—
45	D₄	—	2	2	no	—
46	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
47	C₈	—	78	2	no	—
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	4	2	no	—
50	C₂×C₃	C₂²⋊Dic₁₃	1	1	yes	characteristic
51	C₂²	—	2	2	no	—
52	C₂²	—	4	2	no	—
53	C₂²	C₂×Dic₃₉	1	1	yes	characteristic
54	C₄	#64625	1	2	yes	—
55	C₃	#88073	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	4	2	no	—
58	C₂	#10597671	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597671
commutator	C₂²×C₃×C₁₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₃₉
Fitting, prime radical	C₂×C₃×D₄×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂²⋊C₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	C₂×D₄	D₃₉
hypocenter	C₃×C₁₃	#100
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. #10597662	C₂	semidirect
28. C₃×C₁₃	#100	semidirect
39. C₁₃	#833	semidirect
55. C₃	#88073	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₃	2
#10597662	2
#88073	3
#833	13