Subgroups — #131⋊C₂₇ #11720116

Order 864.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41⋊C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₉×#131	C₃	1	1	yes	maximal, characteristic
3	Q₈⋊C₂₇	C₄	1	1	yes	characteristic
4	C₈×C₂₇	—	4	1	no	maximal
5	C₉×#41	C₂×C₃	1	1	yes	characteristic
6	C₉×M₁₆	—	3	1	no	—
7	C₂×C₈×C₉	—	3	1	no	—
8	C₄×C₂₇	—	4	1	no	—
9	C₃×#131	C₉	1	1	yes	characteristic
10	Q₈×C₉	C₃×C₄	1	1	yes	characteristic
11	D₄×C₉	—	3	1	no	—
12	C₂×C₄×C₉	—	3	1	no	—
13	C₈×C₉	—	3	1	no	—
14	C₈×C₉	A₄	1	1	yes	characteristic
15	C₂×C₂₇	—	4	1	no	—
16	C₃×#41	C₂×C₉	1	1	yes	characteristic
17	C₃×M₁₆	—	3	1	no	—
18	C₂×C₃×C₈	—	3	1	no	—
19	C₂²×C₉	—	3	1	no	—
20	C₄×C₉	—	3	1	no	—
21	C₄×C₉	C₂×A₄	1	1	yes	characteristic
22	#131	C₂₇	1	1	yes	characteristic, complemented, Sylow
23	C₂₇	—	4	1	no	Sylow
24	C₃×Q₈	C₄×C₉	1	1	yes	characteristic
25	C₃×D₄	—	3	1	no	—
26	C₂×C₃×C₄	—	3	1	no	—
27	C₃×C₈	—	3	1	no	—
28	C₃×C₈	C₂²⋊C₉	1	1	yes	characteristic
29	C₂×C₉	—	6	1	no	—
30	C₂×C₉	C₄×A₄	1	1	yes	characteristic
31	#41	C₂×C₂₇	1	1	yes	characteristic
32	M₁₆	—	3	1	no	—
33	C₂×C₈	—	3	1	no	—
34	C₂²×C₃	—	3	1	no	—
35	C₃×C₄	—	3	1	no	—
36	C₃×C₄	C₂×C₂²⋊C₉	1	1	yes	characteristic
37	C₉	#131⋊C₃	1	1	yes	characteristic
38	Q₈	C₄×C₂₇	1	1	yes	characteristic
39	D₄	—	3	1	no	—
40	C₂×C₄	—	3	1	no	—
41	C₈	—	3	1	no	—
42	C₈	C₂²⋊C₂₇	1	1	yes	characteristic
43	C₂×C₃	—	6	1	no	—
44	C₂×C₃	C₄×C₂²⋊C₉	1	1	yes	characteristic
45	C₂²	—	3	1	no	—
46	C₄	—	3	1	no	—
47	C₄	C₂×C₂²⋊C₂₇	1	1	yes	characteristic
48	C₃	#131⋊C₉	1	1	yes	characteristic
49	C₂	—	6	1	no	—
50	C₂	C₄×C₂²⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₉	A₄
commutator, hypocenter	Q₈	C₄×C₂₇
Frattini	C₄×C₉	C₂×A₄
Fitting	C₉×#131	C₃
socle	C₂×C₃	C₄×C₂²⋊C₉
prime radical	C₃×#41	C₂×C₉
cosocle	C₉×#41	C₂×C₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₈×C₉

Complements

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

N	H ≅ G/N	type
22. #131	C₂₇	semidirect

Maximal subgroups

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

subgroup	index
#41⋊C₂₇	2
C₉×#131	3
C₈×C₂₇	4

Subgroups — #131⋊C27 #11720116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #131⋊C₂₇ #11720116