Subgroups — #13066756

Order 1408.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#10622137	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×C₁₁	C₄	1	1	yes	characteristic
4	C₁₁×M₃₂	—	2	2	no	—
5	C₂×C₁₁×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₁₁⋊C₃₂	—	2	2	no	—
8	C₂²×C₄×C₁₁	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₁	—	2	1	no	—
10	C₂×C₈×C₁₁	—	2	1	no	—
11	C₂×C₈×C₁₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₁₁×C₁₆	—	2	1	no	—
14	C₁₁×C₁₆	D₄	1	2	yes	—
15	#1400	—	11	1	no	maximal, Sylow
16	C₂³×C₁₁	C₁₆	1	1	yes	characteristic
17	C₂×C₄×C₁₁	—	2	1	no	—
18	C₂×C₄×C₁₁	—	2	1	no	—
19	C₂×C₄×C₁₁	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
21	C₈×C₁₁	—	2	1	no	—
22	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₁	M₁₆	1	1	yes	characteristic
24	C₂×M₃₂	D₁₁	1	1	yes	characteristic
25	M₆₄	—	11	2	no	—
26	C₂²×C₁₁	—	2	1	no	—
27	C₂²×C₁₁	—	4	1	no	—
28	C₂²×C₁₁	C₂×C₁₆	1	1	yes	characteristic
29	C₄×C₁₁	—	2	1	no	—
30	C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₁₁	M₃₂	1	1	yes	characteristic
32	C₂²×C₈	Dic₁₁	1	1	yes	characteristic
33	M₃₂	—	2	2	no	—
34	C₂×C₁₆	Dic₁₁	1	1	yes	characteristic
35	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
36	C₃₂	—	22	2	no	—
37	C₂×C₁₁	—	2	1	no	—
38	C₂×C₁₁	—	4	1	no	—
39	C₂×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
40	C₂²×C₄	C₁₁⋊C₈	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	C₁₁⋊C₈	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
45	C₁₆	—	2	1	no	—
46	C₁₆	C₂²⋊D₁₁	1	2	yes	—
47	C₁₁	#1400	1	1	yes	characteristic, complemented, Sylow
48	C₂³	C₁₁⋊C₁₆	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
52	C₂×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	#4318	1	1	yes	characteristic
55	C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#66876	1	1	yes	characteristic
61	C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊Dic₁₁
commutator	C₂²×C₁₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₂×C₁₁×M₃₂	C₂
socle	C₂×C₁₁	C₂²⋊C₁₆
prime radical	C₂³×C₁₁	C₁₆
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	C₂×M₃₂	D₁₁
hypocenter	C₁₁	#1400
LCS	G ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. #10622137	C₂	semidirect
47. C₁₁	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×M₃₂	2
#10622137	2
#1400	11