Subgroups — #13066720

Order 1408.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#66883	C₂	1	2	yes	maximal
3	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
4	C₂×#4318	—	2	2	no	—
5	C₁₁×M₃₂	—	2	2	no	—
6	C₂×C₁₁×C₁₆	C₄	1	2	yes	—
7	#66883	—	2	2	no	—
8	#66883	C₄	1	4	yes	—
9	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₁	D₄	1	2	yes	—
13	C₂×C₈×C₁₁	Q₈	1	1	yes	characteristic
14	#4318	—	2	4	no	—
15	#4318	—	4	2	no	—
16	C₂×C₁₁⋊C₈	—	4	2	no	—
17	C₁₁×C₁₆	—	2	2	no	—
18	#1385	—	11	1	no	maximal, Sylow
19	C₂³×C₁₁	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
23	C₂×C₄×C₁₁	SD₁₆	1	2	yes	—
24	C₈×C₁₁	C₄²	1	1	yes	characteristic
25	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₁	C₄⋊C₄	1	2	yes	—
27	C₁₁⋊C₈	—	4	4	no	—
28	C₂×M₃₂	D₁₁	1	1	yes	characteristic
29	C₂×#108	—	11	2	no	—
30	C₂²×C₁₁	—	4	1	no	—
31	C₂²×C₁₁	#103	1	2	yes	—
32	C₂²×C₁₁	#107	1	1	yes	characteristic
33	C₄×C₁₁	#95	1	1	yes	characteristic
34	C₄×C₁₁	#102	1	2	yes	—
35	C₄×C₁₁	#106	1	1	yes	characteristic
36	C₂×M₁₆	—	22	2	no	—
37	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
38	M₃₂	—	2	2	no	—
39	C₂×C₁₆	Dic₁₁	1	2	yes	—
40	#108	—	11	4	no	—
41	#108	—	22	2	no	—
42	C₂×C₁₁	—	2	2	no	—
43	C₂×C₁₁	—	2	1	no	—
44	C₂×C₁₁	#340	1	1	yes	characteristic
45	C₂²×C₄	D₄₄	1	1	yes	characteristic
46	M₁₆	—	22	4	no	—
47	M₁₆	—	44	2	no	—
48	C₂×C₈	—	44	2	no	—
49	C₂×C₈	Dic₂₂	1	1	yes	characteristic
50	C₂×C₈	C₄×D₁₁	1	2	yes	—
51	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
53	C₁₆	—	2	2	no	—
54	C₁₁	#1385	1	1	yes	characteristic, complemented, Sylow
55	C₂³	Dic₄₄	1	1	yes	characteristic
56	C₂×C₄	#4314	1	2	yes	—
57	C₂×C₄	D₈₈	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
59	C₂×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
60	C₈	—	44	4	no	—
61	C₈	C₄×Dic₁₁	1	1	yes	characteristic
62	C₈	Dic₁₁⋊C₄	1	2	yes	—
63	C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
64	C₂²	—	4	1	no	—
65	C₂²	#66880	1	2	yes	—
66	C₂²	#66882	1	1	yes	characteristic
67	C₄	#66881	1	1	yes	characteristic
68	C₄	#66885	1	2	yes	—
69	C₄	C₁₁⋊#95	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	#10622189	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#66881
commutator	C₈×C₁₁	C₄²
Frattini	C₂²×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×M₃₂	C₂
socle	C₂×C₁₁	#340
prime radical	C₂³×C₁₁	Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂²
hypercenter	C₂×M₃₂	D₁₁
hypocenter	C₁₁	#1385
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
54. C₁₁	#1385	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×M₃₂	2
C₂×#66883	2
#1385	11