Subgroups — C₁₁×#1417 #13064255

Order 1408.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#508	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#135	—	2	1	no	—
5	C₁₁×Q₃₂	C₄	1	1	yes	characteristic
6	C₁₁×SD₃₂	—	2	1	no	—
7	C₁₁×D₁₆	C₄	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₁×#108	—	2	1	no	—
10	C₁₁×C₃₂	—	2	1	no	—
11	C₁₁×#41	—	4	1	no	—
12	C₁₁×Q₁₆	—	2	1	no	—
13	C₁₁×SD₁₆	—	4	1	no	—
14	C₁₁×D₈	—	2	1	no	—
15	C₁₁×M₁₆	—	4	1	no	—
16	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₁₁×C₁₆	D₄	1	1	yes	characteristic
19	#1417	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	Q₈×C₁₁	—	4	1	no	—
21	D₄×C₁₁	—	4	1	no	—
22	D₄×C₁₁	—	8	1	no	—
23	C₂×C₄×C₁₁	—	8	1	no	—
24	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
25	C₈×C₁₁	—	8	1	no	—
26	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
28	#508	C₂×C₁₁	1	1	yes	characteristic
29	C₂×C₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
30	#368	C₂×C₁₁	1	1	yes	characteristic, complemented
31	C₂²×C₁₁	—	8	1	no	—
32	C₂²×C₁₁	SD₃₂	1	1	yes	characteristic
33	C₄×C₁₁	—	8	1	no	—
34	C₄×C₁₁	#102	1	1	yes	characteristic
35	C₄×C₁₁	D₁₆	1	1	yes	characteristic
36	#135	—	2	1	no	—
37	Q₃₂	C₄×C₁₁	1	1	yes	characteristic
38	SD₃₂	—	2	1	no	—
39	D₁₆	C₄×C₁₁	1	1	yes	characteristic
40	C₂×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
41	#108	—	2	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×C₁₁	—	2	1	no	—
44	C₂×C₁₁	—	16	1	no	—
45	C₂×C₁₁	#357	1	1	yes	characteristic
46	#41	—	4	1	no	—
47	Q₁₆	—	2	1	no	—
48	SD₁₆	—	4	1	no	—
49	D₈	—	2	1	no	—
50	M₁₆	—	4	1	no	—
51	C₂×C₈	D₄×C₁₁	1	1	yes	characteristic
52	C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
53	C₁₆	D₄×C₁₁	1	1	yes	characteristic
54	C₁₁	#1417	1	1	yes	characteristic, direct product factor, Sylow
55	Q₈	—	4	1	no	—
56	D₄	—	4	1	no	—
57	D₄	—	8	1	no	—
58	C₂×C₄	—	8	1	no	—
59	C₂×C₄	C₁₁×D₈	1	1	yes	characteristic
60	C₈	—	8	1	no	—
61	C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
62	C₈	C₁₁×SD₁₆	1	1	yes	characteristic
63	C₂²	—	8	1	no	—
64	C₂²	C₁₁×SD₃₂	1	1	yes	characteristic
65	C₄	—	8	1	no	—
66	C₄	C₁₁×#102	1	1	yes	characteristic
67	C₄	C₁₁×D₁₆	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	C₁₁×#357	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	D₁₆
commutator	C₁₆	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₁
socle	C₂×C₁₁	#357
prime radical	C₁₁×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×C₃₂	C₂	semidirect
3. C₁₁×#368	C₂	semidirect
19. #1417	C₁₁	direct (N × H)
29. C₂×C₃₂	C₂×C₁₁	semidirect
30. #368	C₂×C₁₁	semidirect
54. C₁₁	#1417	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#508	2
C₂×C₁₁×C₃₂	2
C₁₁×#368	2
#1417	11

Subgroups — C11×#1417 #13064255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1417 #13064255