Subgroups — #11928139

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	#88067	—	3	1	no	maximal, Hall
5	C₃×D₄×C₁₃	—	2	1	no	—
6	Dic₇₈	—	2	1	no	—
7	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×D₈	D₃	1	1	yes	characteristic
9	Dic₅₂	—	3	1	no	—
10	#6090	—	3	1	no	—
11	C₂²×C₃×C₁₃	—	4	1	no	—
12	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
13	Dic₃₉	—	4	1	no	—
14	D₄×C₁₃	—	2	1	no	—
15	Dic₂₆	—	6	1	no	—
16	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
17	#827	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	—	8	1	no	—
19	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
20	C₂²×C₁₃	—	4	1	no	—
21	C₄×C₁₃	#67	1	1	yes	characteristic
22	Dic₁₃	—	12	1	no	—
23	C₃×D₈	D₁₃	1	1	yes	characteristic
24	Dic₁₂	—	13	1	no	—
25	C₃⋊C₁₆	—	13	1	no	—
26	C₃×C₁₃	SD₃₂	1	1	yes	characteristic, complemented, Hall
27	SD₃₂	—	39	1	no	Sylow
28	C₂×C₁₃	—	8	1	no	—
29	C₂×C₁₃	#213	1	1	yes	characteristic
30	C₃×D₄	—	2	1	no	—
31	Dic₆	—	26	1	no	—
32	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
33	Q₁₆	—	39	1	no	—
34	D₈	D₃₉	1	1	yes	characteristic
35	C₁₆	—	39	1	no	—
36	C₁₃	#827	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	4	1	no	—
38	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
39	Dic₃	—	52	1	no	—
40	Q₈	—	78	1	no	—
41	D₄	—	2	1	no	—
42	C₈	C₂×D₃₉	1	1	yes	characteristic
43	C₂×C₃	—	8	1	no	—
44	C₂×C₃	#6104	1	1	yes	characteristic
45	C₂²	—	4	1	no	—
46	C₄	—	156	1	no	—
47	C₄	#64625	1	1	yes	characteristic
48	C₃	#88067	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	8	1	no	—
50	C₂	#10597667	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597667
commutator, cosocle	C₃×C₈×C₁₃	C₂²
Frattini	C₈	C₂×D₃₉
Fitting, prime radical	C₃×C₁₃×D₈	C₂
socle	C₂×C₃×C₁₃	D₈
hypercenter	D₈	D₃₉
hypocenter	C₃×C₁₃	SD₃₂
LCS	G ▷ C₃×C₈×C₁₃ ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
2. Dic₁₅₆	C₂	semidirect
3. C₃⋊#6090	C₂	semidirect
26. C₃×C₁₃	SD₃₂	semidirect
36. C₁₃	#827	semidirect
48. C₃	#88067	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×D₈	2
Dic₁₅₆	2
C₃⋊#6090	2
#88067	3
#827	13