Subgroups — #13077005

Order 1408.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#10622553	C₂	1	7	yes	maximal
3	#10622546	C₂	1	7	yes	maximal, complemented
4	C₂×C₄²×C₁₁	C₂²	1	7	yes	—
5	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	7	yes	—
6	C₂×Dic₁₁⋊C₄	C₂²	1	7	yes	—
7	C₁₁⋊#95	C₂²	1	14	yes	—
8	C₂³×D₁₁	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₁₁	C₂³	1	7	yes	—
10	C₂²×Dic₁₁	C₂³	1	7	yes	—
11	C₄²×C₁₁	—	2	14	no	—
12	(C₂×D₁₁)⋊C₄	—	2	14	no	—
13	Dic₁₁⋊C₄	—	2	14	no	—
14	#2865	—	11	1	no	maximal, Sylow
15	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
16	C₂²×D₁₁	—	2	7	no	—
17	C₂×C₄×C₁₁	—	2	14	no	—
18	C₂×C₄×C₁₁	#41	1	14	yes	—
19	C₂×Dic₁₁	—	2	14	no	—
20	C₂×Dic₁₁	—	2	7	no	—
21	#388	—	11	7	no	—
22	#387	—	11	7	no	—
23	C₄³	D₁₁	1	1	yes	characteristic, complemented
24	C₂²×C₁₁	C₂×#41	1	7	yes	—
25	C₂×D₁₁	—	4	7	no	—
26	C₄×C₁₁	—	2	14	no	—
27	Dic₁₁	—	4	7	no	—
28	C₂×C₄⋊C₄	—	11	7	no	—
29	C₂×C₂²⋊C₄	—	11	7	no	—
30	C₂×C₄²	C₂×D₁₁	1	7	yes	—
31	#95	—	11	14	no	—
32	C₂×C₁₁	#529	1	7	yes	—
33	D₁₁	—	8	1	no	—
34	C₂⁴	—	11	1	no	—
35	C₂²×C₄	—	11	7	no	—
36	C₂²×C₄	C₂²×D₁₁	1	7	yes	—
37	C₄⋊C₄	—	22	14	no	—
38	C₂²⋊C₄	—	22	14	no	—
39	C₄²	—	2	14	no	—
40	C₁₁	#2865	1	1	yes	characteristic, complemented, Sylow
41	C₂³	—	22	7	no	—
42	C₂³	C₂³×D₁₁	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	22	7	no	—
45	C₂×C₄	—	22	14	no	—
46	C₂×C₄	#4339	1	14	yes	—
47	C₂²	—	44	7	no	—
48	C₂²	C₂×#4339	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	44	7	no	—
51	C₂	—	88	1	no	—
52	C₂	#10623010	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₄³×C₁₁	C₂
prime radical	C₂³×D₁₁	C₂³
hypercenter	C₄³	D₁₁
hypocenter	C₁₁	#2865
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
1. C₄³×C₁₁	C₂	semidirect
3. #10622546	C₂	semidirect
23. C₄³	D₁₁	semidirect
40. C₁₁	#2865	semidirect

Maximal subgroups

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

subgroup	index
C₄³×C₁₁	2
#10622553	2
#10622546	2
#2865	11