Subgroups — #14641587

Order 2816.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070909	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622514	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	#10622137	C₄	1	1	yes	characteristic
7	#10622085	—	2	1	no	—
8	D₁₁×C₃₂	—	2	1	no	—
9	C₁₁×C₆₄	—	2	1	no	—
10	C₁₁⋊C₆₄	—	2	1	no	—
11	#66954	C₈	1	1	yes	characteristic
12	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
13	#66876	C₈	1	1	yes	characteristic
14	#66862	—	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	#7514	—	11	1	no	maximal, Sylow
20	#4339	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
22	#4318	C₁₆	1	1	yes	characteristic
23	#4313	—	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	#2258	—	11	1	no	—
29	M₁₂₈	D₁₁	1	1	yes	characteristic, complemented
30	C₂×C₆₄	—	11	1	no	—
31	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
32	C₂²⋊D₁₁	—	2	1	no	—
33	D₄₄	C₃₂	1	1	yes	characteristic
34	C₄×D₁₁	—	2	1	no	—
35	Dic₂₂	C₃₂	1	1	yes	characteristic
36	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₈×C₁₁	M₃₂	1	1	yes	characteristic
38	C₁₁⋊C₈	—	2	1	no	—
39	#504	—	11	1	no	—
40	M₆₄	—	11	1	no	—
41	M₆₄	—	22	1	no	—
42	C₂×C₃₂	—	22	1	no	—
43	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
44	C₆₄	—	2	1	no	—
45	C₆₄	—	22	1	no	—
46	C₂²×C₁₁	M₆₄	1	1	yes	characteristic
47	C₂×D₁₁	—	2	1	no	—
48	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
49	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
50	Dic₁₁	—	2	1	no	—
51	#131	—	11	1	no	—
52	M₃₂	—	11	1	no	—
53	M₃₂	—	22	1	no	—
54	C₂×C₁₆	—	22	1	no	—
55	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
56	C₃₂	—	22	1	no	—
57	C₃₂	D₄₄	1	1	yes	characteristic
58	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	C₂²⋊C₃₂	1	1	yes	characteristic
61	D₁₁	—	4	1	no	—
62	#41	—	11	1	no	—
63	M₁₆	—	11	1	no	—
64	M₁₆	—	22	1	no	—
65	C₂×C₈	—	22	1	no	—
66	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
67	C₁₆	—	22	1	no	—
68	C₁₆	#4313	1	1	yes	characteristic
69	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
70	C₁₁	#7514	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	11	1	no	—
72	D₄	—	11	1	no	—
73	D₄	—	22	1	no	—
74	C₂×C₄	—	22	1	no	—
75	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
76	C₈	—	22	1	no	—
77	C₈	#66862	1	1	yes	characteristic
78	C₈	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
79	C₂²	—	22	1	no	—
80	C₂²	#10622085	1	1	yes	characteristic
81	C₄	—	22	1	no	—
82	C₄	D₁₁×C₃₂	1	1	yes	characteristic
83	C₄	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	44	1	no	—
86	C₂	(C₂×D₁₁)⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×M₁₂₈	C₂
socle	C₂×C₁₁	C₂²⋊C₃₂
prime radical	#4339	C₁₆
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₁
hypocenter	C₁₁	#7514
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁⋊C₆₄	C₂	semidirect
3. C₁₁×M₁₂₈	C₂	semidirect
29. M₁₂₈	D₁₁	semidirect
70. C₁₁	#7514	semidirect

Maximal subgroups

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

subgroup	index
#13070909	2
C₂×C₁₁⋊C₆₄	2
C₁₁×M₁₂₈	2
#7514	11