Subgroups — #13066757

Order 1408.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622514	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622137	C₂	1	1	yes	maximal, characteristic, complemented
4	#66954	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	#66876	C₄	1	1	yes	characteristic
7	#66862	—	2	1	no	—
8	C₁₆×D₁₁	—	2	1	no	—
9	C₁₁×C₃₂	—	2	1	no	—
10	C₁₁⋊C₃₂	—	2	1	no	—
11	#4339	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	#4318	C₈	1	1	yes	characteristic
14	#4313	—	2	1	no	—
15	C₈×D₁₁	—	2	1	no	—
16	C₁₁×C₁₆	D₄	1	1	yes	characteristic
17	C₁₁×C₁₆	D₄	1	1	yes	characteristic
18	C₁₁⋊C₁₆	—	2	1	no	—
19	#1401	—	11	1	no	maximal, Sylow
20	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
21	C₂²⋊D₁₁	—	2	1	no	—
22	D₄₄	C₁₆	1	1	yes	characteristic
23	C₄×D₁₁	—	2	1	no	—
24	Dic₂₂	C₁₆	1	1	yes	characteristic
25	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₁	M₁₆	1	1	yes	characteristic
27	C₁₁⋊C₈	—	2	1	no	—
28	#504	—	11	1	no	—
29	M₆₄	—	11	1	no	—
30	C₂×C₃₂	D₁₁	1	1	yes	characteristic, complemented
31	C₂²×C₁₁	M₃₂	1	1	yes	characteristic
32	C₂×D₁₁	—	2	1	no	—
33	C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
35	Dic₁₁	—	2	1	no	—
36	#131	—	11	1	no	—
37	M₃₂	—	11	1	no	—
38	M₃₂	—	22	1	no	—
39	C₂×C₁₆	—	22	1	no	—
40	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
41	C₃₂	—	2	1	no	—
42	C₃₂	—	22	1	no	—
43	C₂×C₁₁	—	2	1	no	—
44	C₂×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
45	D₁₁	—	4	1	no	—
46	#41	—	11	1	no	—
47	M₁₆	—	11	1	no	—
48	M₁₆	—	22	1	no	—
49	C₂×C₈	—	22	1	no	—
50	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
51	C₁₆	—	22	1	no	—
52	C₁₆	D₄₄	1	1	yes	characteristic
53	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
54	C₁₁	#1401	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	11	1	no	—
56	D₄	—	11	1	no	—
57	D₄	—	22	1	no	—
58	C₂×C₄	—	22	1	no	—
59	C₂×C₄	C₈×D₁₁	1	1	yes	characteristic
60	C₈	—	22	1	no	—
61	C₈	#4313	1	1	yes	characteristic
62	C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
63	C₂²	—	22	1	no	—
64	C₂²	#66862	1	1	yes	characteristic
65	C₄	—	22	1	no	—
66	C₄	C₁₆×D₁₁	1	1	yes	characteristic
67	C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	44	1	no	—
70	C₂	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄₄
commutator	C₄×C₁₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₂×C₁₁×C₃₂	C₂
socle	C₂×C₁₁	C₂²⋊C₁₆
prime radical	#4339	C₈
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	C₂×C₃₂	D₁₁
hypocenter	C₁₁	#1401
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×C₃₂	C₂	semidirect
3. #10622137	C₂	semidirect
30. C₂×C₃₂	D₁₁	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
#10622514	2
C₂×C₁₁×C₃₂	2
#10622137	2
#1401	11