Subgroups — #11928375

Order 1248.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	#10597728	C₂	1	2	yes	maximal
3	#88113	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₃×Dic₂₆	—	2	2	no	—
8	C₃⋊#1057	—	2	2	no	—
9	C₂×Dic₂₆	D₃	1	1	yes	characteristic
10	#6122	—	3	2	no	—
11	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₁₃	—	2	1	no	—
13	C₃×Dic₁₃	—	2	1	no	—
14	C₃×Dic₁₃	D₄	1	2	yes	—
15	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
16	C₂×Dic₁₃	Dic₃	1	1	yes	characteristic
17	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
18	Dic₂₆	—	2	2	no	—
19	#1057	—	6	2	no	—
20	#836	—	13	1	no	maximal, Hall
21	C₂×C₃×C₁₃	—	2	1	no	—
22	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
24	C₄×C₁₃	—	2	1	no	—
25	Dic₁₃	—	2	1	no	—
26	Dic₁₃	#67	1	2	yes	—
27	C₂×C₃×Q₈	—	13	1	no	—
28	#208	—	13	2	no	—
29	C₃×C₁₃	#101	1	1	yes	characteristic, complemented, Hall
30	#101	—	39	1	no	Sylow
31	C₂×C₁₃	—	2	1	no	—
32	C₂×C₁₃	#217	1	1	yes	characteristic
33	C₃×Q₈	—	26	2	no	—
34	C₂×C₃×C₄	—	13	1	no	—
35	C₂×C₃×C₄	—	13	1	no	—
36	C₂×C₃×C₄	#261	1	1	yes	characteristic
37	C₃⋊C₈	—	26	2	no	—
38	C₂×Q₈	—	13	1	no	—
39	M₁₆	—	39	2	no	—
40	C₁₃	#836	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₃	C₂×#261	1	1	yes	characteristic
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	13	2	no	—
44	C₃×C₄	—	26	1	no	—
45	Q₈	—	26	2	no	—
46	C₂×C₄	—	13	1	no	—
47	C₂×C₄	—	13	1	no	—
48	C₂×C₄	C₃⋊#261	1	1	yes	characteristic
49	C₈	—	78	2	no	—
50	C₂×C₃	—	2	1	no	—
51	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
52	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	13	2	no	—
55	C₄	—	26	1	no	—
56	C₃	#88113	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	2	1	no	—
58	C₂	#10597729	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597729
commutator, prime radical	C₂²×C₃×C₁₃	C₂×C₄
Frattini	C₂²	C₂×C₃⋊#261
Fitting	C₂×C₃×C₄×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂²⋊C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypercenter	C₂×C₄	C₃⋊#261
hypocenter	C₃×C₁₃	#101
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
29. C₃×C₁₃	#101	semidirect
40. C₁₃	#836	semidirect
56. C₃	#88113	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Dic₂₆	2
#10597728	2
#88113	3
#836	13