Subgroups — #11928141

Order 1248.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅₆	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#6090	C₂	1	1	yes	maximal, characteristic
4	#88069	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₃	—	2	1	no	—
6	Dic₇₈	—	2	1	no	—
7	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×Q₁₆	D₃	1	1	yes	characteristic
9	Dic₅₂	—	3	1	no	—
10	#6090	—	3	1	no	—
11	C₃×C₄×C₁₃	—	4	1	no	—
12	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
13	Dic₃₉	—	4	1	no	—
14	Q₈×C₁₃	—	2	1	no	—
15	Dic₂₆	—	6	1	no	—
16	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
17	#829	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
19	C₄×C₁₃	—	4	1	no	—
20	C₄×C₁₃	#67	1	1	yes	characteristic
21	Dic₁₃	—	12	1	no	—
22	C₃×Q₁₆	D₁₃	1	1	yes	characteristic
23	Dic₁₂	—	13	1	no	—
24	C₃⋊C₁₆	—	13	1	no	—
25	C₃×C₁₃	Q₃₂	1	1	yes	characteristic, complemented, Hall
26	Q₃₂	—	39	1	no	Sylow
27	C₂×C₁₃	#213	1	1	yes	characteristic
28	C₃×Q₈	—	2	1	no	—
29	Dic₆	—	26	1	no	—
30	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
31	Q₁₆	—	39	1	no	—
32	Q₁₆	D₃₉	1	1	yes	characteristic
33	C₁₆	—	39	1	no	—
34	C₁₃	#829	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₄	—	4	1	no	—
36	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
37	Dic₃	—	52	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	78	1	no	—
40	C₈	C₂×D₃₉	1	1	yes	characteristic
41	C₂×C₃	#6104	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	—	156	1	no	—
44	C₄	#64625	1	1	yes	characteristic
45	C₃	#88069	1	1	yes	characteristic, complemented, Sylow
46	C₂	#10597667	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597667
commutator, cosocle	C₃×C₈×C₁₃	C₂²
Frattini	C₈	C₂×D₃₉
Fitting	C₃×C₁₃×Q₁₆	C₂
socle, prime radical	C₂×C₃×C₁₃	D₈
hypercenter	Q₁₆	D₃₉
hypocenter	C₃×C₁₃	Q₃₂
LCS	G ▷ C₃×C₈×C₁₃ ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
25. C₃×C₁₃	Q₃₂	semidirect
34. C₁₃	#829	semidirect
45. C₃	#88069	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×Q₁₆	2
Dic₁₅₆	2
C₃⋊#6090	2
#88069	3
#829	13