Subgroups — #13066809

Order 1408.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	#10622144	C₂	1	1	yes	maximal, characteristic
3	#10622137	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×Q₁₆	—	2	1	no	—
5	C₁₁×Q₃₂	—	2	1	no	—
6	C₁₁×Q₃₂	C₄	1	2	yes	—
7	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	#66883	—	2	1	no	—
9	C₁₁⋊C₃₂	—	2	1	no	—
10	C₂×Q₈×C₁₁	—	4	1	no	—
11	C₁₁×Q₁₆	—	2	2	no	—
12	C₁₁×Q₁₆	—	4	1	no	—
13	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
14	#4318	—	4	1	no	—
15	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₁₆	D₄	1	1	yes	characteristic
17	#1420	—	11	1	no	maximal, Sylow
18	Q₈×C₁₁	—	4	2	no	—
19	Q₈×C₁₁	—	8	1	no	—
20	C₂×C₄×C₁₁	—	8	1	no	—
21	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
22	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
24	C₁₁⋊C₈	—	8	1	no	—
25	C₂×Q₃₂	D₁₁	1	1	yes	characteristic
26	M₆₄	—	11	1	no	—
27	#368	—	11	1	no	—
28	C₂²×C₁₁	SD₃₂	1	1	yes	characteristic
29	C₄×C₁₁	—	8	2	no	—
30	C₄×C₁₁	#102	1	1	yes	characteristic
31	C₄×C₁₁	D₁₆	1	1	yes	characteristic
32	C₂×Q₁₆	—	2	1	no	—
33	Q₃₂	—	2	1	no	—
34	Q₃₂	Dic₁₁	1	2	yes	—
35	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
36	#108	—	22	1	no	—
37	C₃₂	—	22	1	no	—
38	C₂×C₁₁	—	2	1	no	—
39	C₂×C₁₁	#357	1	1	yes	characteristic
40	C₂×Q₈	—	4	1	no	—
41	Q₁₆	—	2	2	no	—
42	Q₁₆	—	4	1	no	—
43	M₁₆	—	44	1	no	—
44	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
45	C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
46	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
47	C₁₁	#1420	1	1	yes	characteristic, complemented, Sylow
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#4323	1	1	yes	characteristic
52	C₈	—	88	1	no	—
53	C₈	#4324	1	1	yes	characteristic
54	C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
55	C₂²	#66891	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#66890	1	1	yes	characteristic
58	C₄	#66896	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#10622200	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10622200
commutator	C₁₁×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₂×C₁₁×Q₃₂	C₂
socle	C₂×C₁₁	#357
prime radical	C₂²×C₁₁	SD₃₂
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	C₂×Q₃₂	D₁₁
hypocenter	C₁₁	#1420
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
47. C₁₁	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×Q₃₂	2
#10622144	2
#10622137	2
#1420	11