Subgroups — #13074581

Order 1408.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#376	C₂	1	1	yes	maximal, characteristic
2	#10622542	C₂	1	3	yes	maximal
3	#10622541	C₂	1	3	yes	maximal
4	C₁₁⋊#401	C₂	1	2	yes	maximal
5	#10622271	C₂	1	6	yes	maximal
6	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₁	C₂²	1	3	yes	—
8	C₂×C₄⋊Dic₁₁	C₂²	1	3	yes	—
9	C₂×Dic₁₁⋊C₄	C₂²	1	6	yes	—
10	C₁₁×#95	C₂²	1	3	yes	—
11	C₁₁×#95	C₂²	1	1	yes	characteristic
12	C₁₁⋊#95	C₂²	1	6	yes	—
13	C₁₁⋊#95	C₂²	1	6	yes	—
14	C₁₁⋊#95	C₂²	1	6	yes	—
15	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
16	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
17	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₁	C₂³	1	2	yes	—
19	C₂²×Dic₁₁	C₂³	1	6	yes	—
20	C₂×Dic₂₂	—	2	6	no	—
21	C₄²×C₁₁	—	2	6	no	—
22	C₄⋊Dic₁₁	—	2	6	no	—
23	Dic₁₁⋊C₄	—	4	6	no	—
24	#2645	—	11	1	no	maximal, Sylow
25	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
26	C₂×C₄×C₁₁	—	2	3	no	—
27	C₂×C₄×C₁₁	—	2	3	no	—
28	C₂×C₄×C₁₁	—	2	3	no	—
29	C₂×C₄×C₁₁	—	2	6	no	—
30	C₂×C₄×C₁₁	—	2	3	no	—
31	C₂×C₄×C₁₁	#41	1	6	yes	—
32	C₂×Dic₁₁	—	2	6	no	—
33	C₂×Dic₁₁	—	2	6	no	—
34	C₂×Dic₁₁	—	2	6	no	—
35	C₂×Dic₁₁	—	2	6	no	—
36	Dic₂₂	—	4	4	no	—
37	#401	—	11	2	no	—
38	#400	—	11	6	no	—
39	#391	—	11	3	no	—
40	#389	—	11	3	no	—
41	#376	D₁₁	1	1	yes	characteristic
42	C₂²×C₁₁	C₂×#41	1	3	yes	—
43	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
44	C₂²×C₁₁	2₋¹⁺⁴	1	3	yes	—
45	C₄×C₁₁	—	4	3	no	—
46	C₄×C₁₁	—	4	3	no	—
47	C₄×C₁₁	#126	1	4	yes	—
48	Dic₁₁	—	4	2	no	—
49	Dic₁₁	—	4	6	no	—
50	C₂²×Q₈	—	11	1	no	—
51	C₂×C₄⋊C₄	—	11	3	no	—
52	C₂×C₄⋊C₄	—	11	6	no	—
53	C₂×C₄²	C₂×D₁₁	1	3	yes	—
54	#95	—	11	6	no	—
55	#95	—	11	6	no	—
56	#95	—	11	6	no	—
57	#95	C₂×D₁₁	1	3	yes	—
58	#95	C₂×D₁₁	1	1	yes	characteristic
59	C₂×C₁₁	C₂×#126	1	1	yes	characteristic
60	C₂×C₁₁	#541	1	3	yes	—
61	C₂×C₁₁	#542	1	3	yes	—
62	C₂×Q₈	—	22	6	no	—
63	C₂²×C₄	—	11	2	no	—
64	C₂²×C₄	—	11	6	no	—
65	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
66	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
67	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
68	C₄⋊C₄	—	22	6	no	—
69	C₄⋊C₄	—	44	6	no	—
70	C₄²	—	2	6	no	—
71	C₁₁	#2645	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂³×D₁₁	1	1	yes	characteristic
73	Q₈	—	44	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	22	6	no	—
80	C₂×C₄	—	22	6	no	—
81	C₂×C₄	—	22	6	no	—
82	C₂×C₄	—	22	6	no	—
83	C₂×C₄	#4339	1	6	yes	—
84	C₂²	C₂×#4339	1	3	yes	—
85	C₂²	#67042	1	1	yes	characteristic
86	C₂²	#67043	1	3	yes	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	44	2	no	—
90	C₄	—	44	6	no	—
91	C₄	#66929	1	4	yes	—
92	C₂	C₂×#66929	1	1	yes	characteristic
93	C₂	#10623049	1	3	yes	—
94	C₂	#10623065	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#376	C₂
hypercenter	#376	D₁₁
hypocenter	C₁₁	#2645
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
71. C₁₁	#2645	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#376	2
#10622542	2
#10622541	2
C₁₁⋊#401	2
#10622271	2
#2645	11