Subgroups — #13077003

Order 1408.

400 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
2	#10622549	C₂	1	2	yes	maximal
3	#10622546	C₂	1	8	yes	maximal
4	#10622541	C₂	1	4	yes	maximal
5	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₁	C₂²	1	4	yes	—
7	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
9	C₂×Dic₁₁⋊C₄	C₂²	1	8	yes	—
10	C₁₁⋊#95	C₂²	1	8	yes	—
11	C₁₁⋊#95	C₂²	1	8	yes	—
12	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
13	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
14	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₁₁	C₂³	1	8	yes	—
16	C₄²×C₁₁	—	2	8	no	—
17	C₄²×C₁₁	—	2	4	no	—
18	C₄²×C₁₁	Q₈	1	4	yes	—
19	C₄⋊Dic₁₁	—	2	8	no	—
20	Dic₁₁⋊C₄	—	2	16	no	—
21	#2864	—	11	1	no	maximal, Sylow
22	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
23	C₂×C₄×C₁₁	—	2	4	no	—
24	C₂×C₄×C₁₁	—	2	4	no	—
25	C₂×C₄×C₁₁	—	2	4	no	—
26	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
27	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
28	C₂×C₄×C₁₁	#41	1	8	yes	—
29	C₂×C₄×C₁₁	#41	1	4	yes	—
30	C₂×Dic₁₁	—	2	16	no	—
31	C₂×Dic₁₁	—	2	8	no	—
32	#389	—	11	4	no	—
33	#387	—	11	8	no	—
34	#382	—	11	2	no	—
35	C₄³	D₁₁	1	1	yes	characteristic
36	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
37	C₂²×C₁₁	C₂×#41	1	2	yes	—
38	C₂²×C₁₁	C₂×#41	1	4	yes	—
39	C₄×C₁₁	—	2	8	no	—
40	C₄×C₁₁	—	2	4	no	—
41	C₄×C₁₁	#125	1	4	yes	—
42	Dic₁₁	—	4	8	no	—
43	C₂×C₄⋊C₄	—	11	4	no	—
44	C₂×C₄⋊C₄	—	11	8	no	—
45	C₂×C₄²	C₂×D₁₁	1	4	yes	—
46	C₂×C₄²	C₂×D₁₁	1	2	yes	—
47	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
48	#95	—	11	8	no	—
49	#95	—	11	8	no	—
50	C₂×C₁₁	C₂×#125	1	1	yes	characteristic
51	C₂×C₁₁	#529	1	4	yes	—
52	C₂×C₁₁	#533	1	2	yes	—
53	C₂²×C₄	—	11	8	no	—
54	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
55	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
56	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
57	C₄⋊C₄	—	22	16	no	—
58	C₄⋊C₄	—	22	8	no	—
59	C₄²	—	2	8	no	—
60	C₄²	—	2	4	no	—
61	C₄²	Dic₂₂	1	4	yes	—
62	C₁₁	#2864	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂³×D₁₁	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	22	8	no	—
68	C₂×C₄	—	22	16	no	—
69	C₂×C₄	C₂×Dic₂₂	1	4	yes	—
70	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
71	C₂×C₄	#4339	1	8	yes	—
72	C₂×C₄	#4339	1	4	yes	—
73	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
74	C₂²	C₂×#4339	1	2	yes	—
75	C₂²	C₂×#4339	1	4	yes	—
76	C₄	—	2	4	no	—
77	C₄	—	2	8	no	—
78	C₄	—	44	8	no	—
79	C₄	#66923	1	4	yes	—
80	C₂	C₂×#66923	1	1	yes	characteristic
81	C₂	#10623001	1	2	yes	—
82	C₂	#10623010	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₄³×C₁₁	C₂
hypercenter	C₄³	D₁₁
hypocenter	C₁₁	#2864
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
62. C₁₁	#2864	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
#10622549	2
#10622546	2
#10622541	2
#2864	11