Subgroups — #14641583

Order 2816.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622085	C₂	1	1	yes	maximal, characteristic
2	#13066827	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₁₁	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
7	#10622085	—	2	1	no	—
8	#10622085	—	2	1	no	—
9	C₁₁×C₆₄	—	2	1	no	—
10	C₁₁⋊C₆₄	—	2	1	no	—
11	C₂×C₈×D₁₁	C₈	1	1	yes	characteristic
12	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
14	C₁₆×D₁₁	—	2	1	no	—
15	C₁₆×D₁₁	—	2	1	no	—
16	C₁₁×C₃₂	D₄	1	1	yes	characteristic
17	C₁₁×C₃₂	D₄	1	1	yes	characteristic
18	C₁₁⋊C₃₂	—	2	1	no	—
19	#7513	—	11	1	no	maximal, Sylow
20	C₂×C₄×D₁₁	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
22	C₂×C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
23	C₈×D₁₁	—	2	1	no	—
24	C₈×D₁₁	—	2	1	no	—
25	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
27	C₁₁⋊C₁₆	—	2	1	no	—
28	C₂×M₆₄	—	11	1	no	—
29	M₁₂₈	—	11	1	no	—
30	M₁₂₈	D₁₁	1	1	yes	characteristic, complemented
31	C₂²×D₁₁	C₃₂	1	1	yes	characteristic
32	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
33	C₂×Dic₁₁	C₃₂	1	1	yes	characteristic
34	C₄×D₁₁	—	2	1	no	—
35	C₄×D₁₁	—	2	1	no	—
36	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₈×C₁₁	M₃₂	1	1	yes	characteristic
38	C₁₁⋊C₈	—	2	1	no	—
39	C₂²×C₁₆	—	11	1	no	—
40	M₆₄	—	22	1	no	—
41	M₆₄	—	22	1	no	—
42	C₂×C₃₂	—	11	1	no	—
43	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
44	C₆₄	—	2	1	no	—
45	C₆₄	—	22	1	no	—
46	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
47	C₂×D₁₁	—	2	1	no	—
48	C₂×D₁₁	—	4	1	no	—
49	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
50	C₄×C₁₁	M₆₄	1	1	yes	characteristic
51	Dic₁₁	—	2	1	no	—
52	C₂²×C₈	—	11	1	no	—
53	C₂×C₁₆	—	11	1	no	—
54	C₂×C₁₆	—	22	1	no	—
55	C₂×C₁₆	—	22	1	no	—
56	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
57	C₃₂	—	22	1	no	—
58	C₃₂	D₄₄	1	1	yes	characteristic
59	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
60	C₂×C₁₁	—	2	1	no	—
61	C₂×C₁₁	C₂²⋊C₃₂	1	1	yes	characteristic
62	D₁₁	—	4	1	no	—
63	C₂²×C₄	—	11	1	no	—
64	C₂×C₈	—	11	1	no	—
65	C₂×C₈	—	22	1	no	—
66	C₂×C₈	—	22	1	no	—
67	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
68	C₁₆	—	22	1	no	—
69	C₁₆	#4313	1	1	yes	characteristic
70	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
71	C₁₁	#7513	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	11	1	no	—
73	C₂×C₄	—	11	1	no	—
74	C₂×C₄	—	22	1	no	—
75	C₂×C₄	—	22	1	no	—
76	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
77	C₈	—	22	1	no	—
78	C₈	#66862	1	1	yes	characteristic
79	C₈	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
80	C₂²	—	22	1	no	—
81	C₂²	—	44	1	no	—
82	C₂²	D₁₁×C₃₂	1	1	yes	characteristic
83	C₄	—	22	1	no	—
84	C₄	#10622085	1	1	yes	characteristic
85	C₄	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	44	1	no	—
88	C₂	(C₂×D₁₁)⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	(C₂×D₁₁)⋊C₄
commutator	C₂²×C₁₁	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×M₁₂₈	C₂
socle	C₂×C₁₁	C₂²⋊C₃₂
prime radical	C₂²×D₁₁	C₃₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₁
hypocenter	C₁₁	#7513
LCS	G ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #13066827	C₂	semidirect
3. C₁₁×M₁₂₈	C₂	semidirect
30. M₁₂₈	D₁₁	semidirect
71. C₁₁	#7513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622085	2
#13066827	2
C₁₁×M₁₂₈	2
#7513	11