Subgroups — #13066665

Order 1408.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#10622096	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×Q₁₆	—	2	1	no	—
5	C₂×C₁₁×Q₁₆	C₄	1	2	yes	—
6	C₁₁×C₄⋊Q₈	—	2	1	no	—
7	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁⋊C₁₆	—	2	1	no	—
9	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
10	C₂×Q₈×C₁₁	—	2	2	no	—
11	C₁₁×Q₁₆	—	4	1	no	—
12	C₁₁×Q₁₆	—	4	1	no	—
13	C₁₁×Q₁₆	—	4	2	no	—
14	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₁₁×C₄⋊C₄	—	4	1	no	—
17	C₁₁×C₄⋊C₄	—	4	1	no	—
18	C₄²×C₁₁	D₄	1	1	yes	characteristic
19	C₂×C₁₁⋊C₈	—	4	1	no	—
20	C₁₁⋊C₁₆	—	4	1	no	—
21	#1362	—	11	1	no	maximal, Sylow
22	Q₈×C₁₁	—	4	2	no	—
23	Q₈×C₁₁	—	4	2	no	—
24	C₂×C₄×C₁₁	—	4	2	no	—
25	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
28	C₈×C₁₁	—	2	1	no	—
29	C₈×C₁₁	D₈	1	1	yes	characteristic
30	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
31	C₁₁⋊C₈	—	8	1	no	—
32	#494	D₁₁	1	1	yes	characteristic
33	C₄⋊C₁₆	—	11	1	no	—
34	#335	—	11	1	no	—
35	C₂²×C₁₁	#102	1	1	yes	characteristic
36	C₄×C₁₁	—	2	1	no	—
37	C₄×C₁₁	—	8	2	no	—
38	C₄×C₁₁	#100	1	1	yes	characteristic
39	C₄×C₁₁	#102	1	1	yes	characteristic
40	C₄×C₁₁	SD₃₂	1	1	yes	characteristic
41	C₄×C₁₁	Q₃₂	1	1	yes	characteristic
42	C₂×Q₁₆	—	2	1	no	—
43	C₂×Q₁₆	Dic₁₁	1	2	yes	—
44	C₄⋊Q₈	—	2	1	no	—
45	C₂×C₁₆	—	22	1	no	—
46	C₄⋊C₈	—	22	1	no	—
47	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
48	C₂×C₁₁	#331	1	1	yes	characteristic
49	C₂×C₁₁	#358	1	1	yes	characteristic
50	C₂×C₁₁	#362	1	1	yes	characteristic
51	C₂×Q₈	—	2	2	no	—
52	Q₁₆	—	4	2	no	—
53	Q₁₆	—	4	1	no	—
54	Q₁₆	—	4	1	no	—
55	C₂×C₈	—	44	1	no	—
56	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₄⋊C₄	—	4	1	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
61	C₁₆	—	44	1	no	—
62	C₁₁	#1362	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	4	2	no	—
64	Q₈	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	#4323	1	1	yes	characteristic
67	C₂×C₄	#4324	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	88	1	no	—
71	C₈	#4323	1	1	yes	characteristic
72	C₈	#4324	1	1	yes	characteristic
73	C₂²	#66896	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	8	2	no	—
76	C₄	#66892	1	1	yes	characteristic
77	C₄	#66893	1	1	yes	characteristic
78	C₄	#66896	1	1	yes	characteristic
79	C₄	#66897	1	1	yes	characteristic
80	C₂	#10622182	1	1	yes	characteristic
81	C₂	#10622202	1	1	yes	characteristic
82	C₂	#10622203	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#66896
commutator	C₂×C₈×C₁₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₁₁×#494	C₂
socle, prime radical	C₂²×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	#494	D₁₁
hypocenter	C₁₁	#1362
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
62. C₁₁	#1362	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#494	2
C₄⋊(C₁₁⋊C₁₆)	2
#10622096	2
#1362	11