Subgroups — #14515513

Order 1936.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757247	C₂	1	1	yes	maximal, characteristic, complemented
2	#11757245	C₂	1	1	yes	maximal, characteristic
3	#11757242	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₁₁	—	2	1	no	—
5	C₁₁⋊Dic₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×Dic₁₁	—	2	1	no	—
7	C₂×C₁₁²	D₄	1	1	yes	characteristic
8	C₁₁×D₁₁	—	4	1	no	—
9	C₁₁²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₂²⋊D₁₁	—	22	1	no	—
11	Dic₂₂	—	22	1	no	—
12	C₂²×C₁₁	—	22	1	no	—
13	C₂×D₁₁	—	2	1	no	—
14	C₄×C₁₁	—	22	1	no	—
15	Dic₁₁	—	2	1	no	—
16	Dic₁₁	—	22	1	no	—
17	Dic₁₁	—	22	1	no	—
18	Dic₁₁	—	44	2	no	—
19	C₂×C₁₁	—	2	1	no	—
20	C₂×C₁₁	—	2	1	no	—
21	C₂×C₁₁	—	4	2	no	—
22	C₂×C₁₁	—	44	1	no	—
23	D₁₁	—	4	1	no	—
24	SD₁₆	—	121	1	no	maximal, Sylow
25	C₁₁	—	2	1	no	—
26	C₁₁	—	2	1	no	—
27	C₁₁	—	4	2	no	—
28	Q₈	—	121	1	no	—
29	D₄	—	121	1	no	—
30	C₈	—	121	1	no	—
31	C₂²	—	22	1	no	—
32	C₄	—	22	1	no	—
33	C₄	—	121	1	no	—
34	C₂	—	44	1	no	—
35	C₂	#92150⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#92150⋊C₂
commutator, cosocle	C₁₁⋊Dic₁₁	C₂²
Fitting, socle	C₂×C₁₁²	D₄
prime radical	#11757245	C₂
hypocenter	C₁₁²	SD₁₆
LCS	G ▷ C₁₁⋊Dic₁₁ ▷ C₂×C₁₁² ▷ C₁₁²
UCS	C₁ ◁ C₂

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

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