Subgroups — #13070195

Order 1408.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#430	C₂	1	1	yes	maximal, characteristic
2	#10622732	C₂	1	1	yes	maximal, characteristic
3	C₁₁⋊#338	C₂	1	1	yes	maximal, characteristic
4	#10622196	C₂	1	2	yes	maximal
5	#10622194	C₂	1	2	yes	maximal
6	C₂×C₁₁×M₁₆	C₂²	1	2	yes	—
7	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
8	#66979	C₂²	1	1	yes	characteristic
9	C₂×#4318	C₂²	1	2	yes	—
10	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₁×#108	—	2	2	no	—
12	Dic₁₁⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
14	C₁₁×M₁₆	—	2	2	no	—
15	C₁₁×M₁₆	—	2	2	no	—
16	C₁₁×M₁₆	—	2	2	no	—
17	C₂×C₈×C₁₁	—	2	2	no	—
18	C₂×C₈×C₁₁	D₄	1	2	yes	—
19	C₂²⋊Dic₁₁	Q₈	1	2	yes	—
20	C₄⋊Dic₁₁	—	2	1	no	—
21	C₄×Dic₁₁	—	2	1	no	—
22	#4318	—	2	2	no	—
23	#4318	—	2	2	no	—
24	C₂×C₁₁⋊C₈	—	2	1	no	—
25	C₂×C₁₁⋊C₈	—	2	2	no	—
26	C₂×C₁₁⋊C₈	—	2	2	no	—
27	#2103	—	11	1	no	maximal, Sylow
28	C₂³×C₁₁	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₁	#41	1	2	yes	—
31	C₂×C₄×C₁₁	#41	1	2	yes	—
32	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
33	C₂×Dic₁₁	—	2	2	no	—
34	C₈×C₁₁	—	2	2	no	—
35	C₈×C₁₁	—	4	2	no	—
36	C₁₁⋊C₈	—	4	1	no	—
37	C₁₁⋊C₈	—	4	2	no	—
38	#430	D₁₁	1	1	yes	characteristic
39	#424	—	11	1	no	—
40	#344	—	11	2	no	—
41	#341	—	11	2	no	—
42	#338	—	11	1	no	—
43	C₂²×C₁₁	—	4	1	no	—
44	C₂²×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂²×C₁₁	#125	1	2	yes	—
46	C₄×C₁₁	#123	1	1	yes	characteristic
47	C₄×C₁₁	#124	1	1	yes	characteristic
48	C₄×C₁₁	#126	1	2	yes	—
49	Dic₁₁	—	4	2	no	—
50	C₂×M₁₆	—	11	2	no	—
51	C₂×M₁₆	C₂×D₁₁	1	2	yes	—
52	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
53	C₂²×C₈	—	11	1	no	—
54	#117	—	11	1	no	—
55	#108	—	2	2	no	—
56	C₄⋊C₈	—	22	2	no	—
57	C₂×C₁₁	—	2	1	no	—
58	C₂×C₁₁	—	2	2	no	—
59	C₂×C₁₁	#400	1	1	yes	characteristic
60	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
61	M₁₆	—	2	2	no	—
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	22	2	no	—
65	M₁₆	—	22	2	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	22	2	no	—
68	C₂×C₈	—	22	2	no	—
69	C₂×C₈	—	22	1	no	—
70	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
71	C₄⋊C₄	—	22	1	no	—
72	C₂²⋊C₄	—	11	2	no	—
73	C₄²	—	22	1	no	—
74	C₁₁	#2103	1	1	yes	characteristic, complemented, Sylow
75	C₂³	Q₈×D₁₁	1	1	yes	characteristic
76	C₂×C₄	—	22	2	no	—
77	C₂×C₄	#4339	1	2	yes	—
78	C₂×C₄	#4341	1	2	yes	—
79	C₂×C₄	#4343	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	2	no	—
83	C₈	—	44	2	no	—
84	C₈	—	44	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#66942	1	2	yes	—
87	C₂²	#66999	1	1	yes	characteristic
88	C₄	—	44	2	no	—
89	C₄	#66951	1	2	yes	—
90	C₄	#66982	1	1	yes	characteristic
91	C₄	#66989	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#10622595	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#66989
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#430	C₂
socle	C₂×C₁₁	#400
prime radical	C₂³×C₁₁	C₂×Q₈
hypercenter	#430	D₁₁
hypocenter	C₁₁	#2103
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

Complements

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

N	H ≅ G/N	type
74. C₁₁	#2103	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#430	2
#10622732	2
C₁₁⋊#338	2
#10622196	2
#10622194	2
#2103	11