Subgroups — #14641673

Order 2816.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066816	C₂	1	2	yes	maximal
2	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
4	#10622142	—	2	2	no	—
5	C₁₁×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
7	#66882	—	4	2	no	—
8	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
10	#7545	—	11	1	no	maximal, Sylow
11	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
12	C₄⋊Dic₁₁	—	8	2	no	—
13	C₁₁×C₁₆	C₄⋊C₄	1	1	yes	characteristic
14	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
15	C₂×C₆₄	D₁₁	1	1	yes	characteristic
16	#1423	—	11	2	no	—
17	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
18	C₂×Dic₁₁	—	16	2	no	—
19	C₈×C₁₁	#107	1	1	yes	characteristic
20	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
21	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
22	#366	—	22	2	no	—
23	C₆₄	Dic₁₁	1	2	yes	complemented
24	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
25	C₄×C₁₁	#366	1	1	yes	characteristic
26	C₄×C₁₁	Q₆₄	1	1	yes	characteristic
27	Dic₁₁	—	32	2	no	—
28	C₂×C₁₆	D₄₄	1	1	yes	characteristic
29	#107	—	44	2	no	—
30	C₃₂	Dic₂₂	1	1	yes	characteristic
31	C₃₂	C₂×Dic₁₁	1	1	yes	characteristic
32	C₂×C₁₁	#1423	1	1	yes	characteristic
33	C₂×C₁₁	D₆₄	1	1	yes	characteristic
34	C₂×C₁₁	Q₁₂₈	1	1	yes	characteristic
35	C₂×C₈	D₈₈	1	1	yes	characteristic
36	C₄⋊C₄	—	88	2	no	—
37	C₁₆	Dic₄₄	1	1	yes	characteristic
38	C₁₆	C₄⋊Dic₁₁	1	1	yes	characteristic
39	C₁₁	#7545	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	—	176	2	no	—
41	C₂×C₄	D₁₇₆	1	1	yes	characteristic
42	C₈	Dic₈₈	1	1	yes	characteristic
43	C₈	#66882	1	1	yes	characteristic
44	C₂²	D₃₅₂	1	1	yes	characteristic
45	C₄	—	352	2	no	—
46	C₄	Dic₁₇₆	1	1	yes	characteristic
47	C₄	#10622142	1	1	yes	characteristic
48	C₂	#13066816	1	1	yes	characteristic
49	C₂	D₇₀₄	1	1	yes	characteristic
50	C₂	Dic₃₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₅₂
commutator	C₁₁×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₂×C₁₁×C₆₄	C₂
socle, prime radical	C₂²×C₁₁	D₃₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	#7545
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
5. C₁₁×C₆₄	C₄	semidirect
23. C₆₄	Dic₁₁	semidirect
39. C₁₁	#7545	semidirect

Maximal subgroups

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

subgroup	index
#13066816	2
C₂×C₁₁×C₆₄	2
#7545	11