Subgroups — #13066532

Order 1408.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₁₆	C₄	1	2	yes	—
5	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₁⋊C₁₆	C₄	1	2	yes	—
7	C₄×C₁₁⋊C₈	C₄	1	2	yes	—
8	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₁⋊C₈	C₈	1	4	yes	—
12	C₁₁×C₁₆	C₈	1	4	yes	complemented
13	C₁₁⋊C₁₆	C₈	1	4	yes	complemented
14	#1311	—	11	1	no	maximal, Sylow
15	C₂×C₄×C₁₁	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₁₁	C₂×C₈	1	2	yes	—
17	C₈×C₁₁	C₂×C₈	1	2	yes	—
18	C₈×C₁₁	C₂×C₈	1	2	yes	—
19	C₁₁⋊C₈	—	2	4	no	—
20	C₄×C₁₆	—	11	1	no	—
21	C₄×C₁₆	D₁₁	1	1	yes	characteristic
22	C₈²	—	11	1	no	—
23	C₂²×C₁₁	C₄×C₈	1	1	yes	characteristic
24	C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
25	C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
26	C₄×C₁₁	M₃₂	1	4	yes	—
27	C₂×C₁₆	—	11	2	no	—
28	C₂×C₁₆	Dic₁₁	1	2	yes	—
29	C₄×C₈	—	11	2	no	—
30	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
31	C₂×C₁₁	C₈²	1	1	yes	characteristic
32	C₂×C₁₁	#346	1	2	yes	—
33	C₂×C₈	—	11	4	no	—
34	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
35	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
36	C₄²	C₄×D₁₁	1	1	yes	characteristic
37	C₁₆	—	11	4	no	—
38	C₁₆	C₁₁⋊C₈	1	4	yes	complemented
39	C₁₁	#1311	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	C₈×D₁₁	1	2	yes	—
41	C₂×C₄	C₄×Dic₁₁	1	1	yes	characteristic
42	C₈	—	22	4	no	—
43	C₈	C₈×D₁₁	1	2	yes	—
44	C₈	C₂×C₁₁⋊C₈	1	2	yes	—
45	C₂²	C₈×Dic₁₁	1	1	yes	characteristic
46	C₄	#66862	1	4	yes	—
47	C₄	C₄×C₁₁⋊C₈	1	1	yes	characteristic
48	C₄	C₈×Dic₁₁	1	1	yes	characteristic
49	C₂	C₈×C₁₁⋊C₈	1	1	yes	characteristic
50	C₂	#10622140	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₁₁
commutator	C₂×C₁₁	C₈²
Fitting	C₄×C₁₁×C₁₆	C₂
socle, prime radical	C₂²×C₁₁	C₄×C₈
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	C₄×C₁₆	D₁₁
hypocenter	C₁₁	#1311
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₁×C₁₆	C₈	semidirect
13. C₁₁⋊C₁₆	C₈	semidirect
38. C₁₆	C₁₁⋊C₈	semidirect
39. C₁₁	#1311	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁×C₁₆	2
C₄×C₁₁⋊C₁₆	2
C₈×C₁₁⋊C₈	2
#1311	11