Subgroups — #13066758

Order 1408.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#504	C₂	1	1	yes	maximal, characteristic
2	#10622137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#131	C₄	1	1	yes	characteristic
5	C₁₁×M₃₂	—	2	1	no	—
6	C₁₁×M₃₂	C₄	1	1	yes	characteristic
7	C₂×C₁₁×C₁₆	—	2	1	no	—
8	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₁⋊C₃₂	—	2	1	no	—
10	C₁₁⋊C₃₂	—	2	1	no	—
11	C₁₁×#41	C₈	1	1	yes	characteristic
12	C₁₁×M₁₆	—	2	1	no	—
13	C₁₁×M₁₆	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₁	—	2	1	no	—
15	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₁₆	—	2	1	no	—
17	C₁₁×C₁₆	D₄	1	1	yes	characteristic
18	C₁₁×C₁₆	D₄	1	1	yes	characteristic
19	#1401	—	11	1	no	maximal, Sylow
20	Q₈×C₁₁	C₁₆	1	1	yes	characteristic
21	D₄×C₁₁	—	2	1	no	—
22	D₄×C₁₁	C₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₁	—	2	1	no	—
24	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
25	C₈×C₁₁	—	2	1	no	—
26	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₁	M₁₆	1	1	yes	characteristic
28	#504	D₁₁	1	1	yes	characteristic
29	M₆₄	—	11	1	no	—
30	C₂×C₃₂	—	11	1	no	—
31	C₂²×C₁₁	—	2	1	no	—
32	C₂²×C₁₁	M₃₂	1	1	yes	characteristic
33	C₄×C₁₁	—	2	1	no	—
34	C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
35	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
36	#131	Dic₁₁	1	1	yes	characteristic
37	M₃₂	—	2	1	no	—
38	M₃₂	Dic₁₁	1	1	yes	characteristic
39	C₂×C₁₆	—	2	1	no	—
40	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
41	C₃₂	—	22	1	no	—
42	C₃₂	—	22	1	no	—
43	C₂×C₁₁	—	2	1	no	—
44	C₂×C₁₁	—	4	1	no	—
45	C₂×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
46	#41	C₁₁⋊C₈	1	1	yes	characteristic
47	M₁₆	—	2	1	no	—
48	M₁₆	C₁₁⋊C₈	1	1	yes	characteristic
49	C₂×C₈	—	2	1	no	—
50	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
51	C₁₆	—	2	1	no	—
52	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
53	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
54	C₁₁	#1401	1	1	yes	characteristic, complemented, Sylow
55	Q₈	C₁₁⋊C₁₆	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	C₁₁⋊C₁₆	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	#4318	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#66876	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
67	C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₁₁×#504	C₂
socle	C₂×C₁₁	C₂²⋊C₁₆
prime radical	C₁₁×#41	C₈
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	#504	D₁₁
hypocenter	C₁₁	#1401
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
2. #10622137	C₂	semidirect
3. C₂×C₁₁⋊C₃₂	C₂	semidirect
54. C₁₁	#1401	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#504	2
#10622137	2
C₂×C₁₁⋊C₃₂	2
#1401	11