Subgroups — #11928115

Order 1248.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1055	C₂	1	2	yes	maximal
3	#88043	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	2	yes	—
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₃⋊#1055	C₄	1	4	yes	complemented
7	C₄²×C₁₃	D₃	1	1	yes	characteristic
8	C₂×#1055	—	3	2	no	—
9	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₃×C₄×C₁₃	—	2	2	no	—
11	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₃	Dic₃	1	2	yes	—
13	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
14	#1055	—	3	4	no	—
15	#803	—	13	1	no	maximal, Hall
16	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
17	C₂×C₃×C₁₃	M₁₆	1	2	yes	—
18	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
19	C₄×C₁₃	—	2	2	no	—
20	C₄×C₁₃	C₄×D₃	1	2	yes	—
21	C₃×C₄²	D₁₃	1	1	yes	characteristic
22	C₂×C₃⋊C₈	—	13	2	no	—
23	C₃×C₁₃	#97	1	1	yes	characteristic, complemented, Hall
24	#97	—	39	1	no	Sylow
25	C₂×C₁₃	#208	1	2	yes	—
26	C₂×C₁₃	C₄×Dic₃	1	1	yes	characteristic
27	C₂×C₃×C₄	Dic₁₃	1	2	yes	—
28	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
29	C₃⋊C₈	—	13	4	no	—
30	C₂×C₈	—	39	2	no	—
31	C₄²	D₃₉	1	1	yes	characteristic
32	C₁₃	#803	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	C₂×Dic₁₃	1	1	yes	characteristic
34	C₃×C₄	—	2	2	no	—
35	C₃×C₄	C₄×D₁₃	1	2	yes	—
36	C₂×C₄	Dic₃₉	1	2	yes	—
37	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
38	C₈	—	39	4	no	—
39	C₂×C₃	#6099	1	2	yes	—
40	C₂×C₃	C₄×Dic₁₃	1	1	yes	characteristic
41	C₂²	C₂×Dic₃₉	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₄×D₃₉	1	2	yes	—
44	C₃	#88043	1	1	yes	characteristic, complemented, Sylow
45	C₂	#10597662	1	2	yes	—
46	C₂	C₄×Dic₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃₉
commutator	C₂×C₃×C₁₃	C₄²
Fitting	C₃×C₄²×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂×C₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	C₄²	D₃₉
hypocenter	C₃×C₁₃	#97
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₃⋊#1055	C₄	semidirect
23. C₃×C₁₃	#97	semidirect
32. C₁₃	#803	semidirect
44. C₃	#88043	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₃	2
C₂×C₃⋊#1055	2
#88043	3
#803	13