Subgroups — #14670187

Order 2816.

370 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	6	yes	maximal
2	C₁₁×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#97	C₄	1	3	yes	—
4	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
5	C₁₁×#376	C₄	1	1	yes	characteristic
6	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	—
7	C₄⋊(C₁₁⋊C₁₆)	—	2	12	no	—
8	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
11	C₁₁×#97	—	2	6	no	—
12	C₄×C₈×C₁₁	D₄	1	6	yes	—
13	C₄×C₈×C₁₁	Q₈	1	6	yes	—
14	C₁₁×#95	C₈	1	4	yes	—
15	C₂×C₁₁⋊C₁₆	—	2	12	no	—
16	#12899	—	11	1	no	maximal, Sylow
17	C₂²×C₄×C₁₁	C₂×C₈	1	6	yes	—
18	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	—	2	6	no	—
20	C₂×C₈×C₁₁	C₄⋊C₄	1	6	yes	—
21	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
22	C₂×C₈×C₁₁	C₂×Q₈	1	3	yes	—
23	C₄²×C₁₁	C₄⋊C₄	1	6	yes	—
24	C₄²×C₁₁	M₁₆	1	6	yes	—
25	C₁₁⋊C₁₆	—	4	4	no	—
26	C₂×C₄⋊C₁₆	—	11	6	no	—
27	#1726	D₁₁	1	1	yes	characteristic
28	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₁	—	2	12	no	—
30	C₂×C₄×C₁₁	C₄⋊C₈	1	12	yes	—
31	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₁₁	C₂×M₁₆	1	3	yes	—
33	C₈×C₁₁	—	2	6	no	—
34	C₈×C₁₁	#127	1	1	yes	characteristic
35	C₈×C₁₁	C₄⋊Q₈	1	3	yes	—
36	C₂²×C₁₆	—	11	4	no	—
37	C₂×#97	Dic₁₁	1	3	yes	—
38	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
39	#376	Dic₁₁	1	1	yes	characteristic
40	C₄⋊C₁₆	—	22	12	no	—
41	C₂²×C₁₁	C₂×C₄⋊C₈	1	3	yes	—
42	C₂²×C₁₁	#504	1	4	yes	—
43	C₄×C₁₁	—	2	12	no	—
44	C₄×C₁₁	#384	1	1	yes	characteristic
45	C₄×C₁₁	#423	1	3	yes	—
46	C₂²×C₈	C₂×Dic₁₁	1	3	yes	—
47	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
48	C₂×C₄²	C₂×Dic₁₁	1	3	yes	—
49	C₂×C₁₆	—	22	12	no	—
50	#97	—	2	6	no	—
51	C₄×C₈	Dic₂₂	1	6	yes	—
52	C₄×C₈	D₄₄	1	6	yes	—
53	#95	C₁₁⋊C₈	1	4	yes	—
54	C₂×C₁₁	#1842	1	1	yes	characteristic
55	C₂×C₁₁	#2151	1	6	yes	—
56	C₂²×C₄	C₂×C₁₁⋊C₈	1	6	yes	—
57	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
58	C₂×C₈	—	2	6	no	—
59	C₂×C₈	C₄⋊Dic₁₁	1	6	yes	—
60	C₂×C₈	C₂×Dic₂₂	1	3	yes	—
61	C₂×C₈	C₂×D₄₄	1	3	yes	—
62	C₄²	#4318	1	6	yes	—
63	C₄²	C₄⋊Dic₁₁	1	6	yes	—
64	C₁₆	—	44	4	no	—
65	C₁₁	#12899	1	1	yes	characteristic, complemented, Sylow
66	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	12	yes	—
69	C₂×C₄	C₂×#4318	1	3	yes	—
70	C₂×C₄	C₂×C₄⋊Dic₁₁	1	3	yes	—
71	C₈	—	2	6	no	—
72	C₈	#66922	1	3	yes	—
73	C₈	#66927	1	1	yes	characteristic
74	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	3	yes	—
75	C₂²	#10622753	1	4	yes	—
76	C₄	—	2	12	no	—
77	C₄	#10622537	1	3	yes	—
78	C₄	#10622548	1	1	yes	characteristic
79	C₂	#13068768	1	1	yes	characteristic
80	C₂	#13070375	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₁
commutator, socle, prime radical	C₂³×C₁₁	C₂²×C₈
Fitting	C₁₁×#1726	C₂
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1726	D₁₁
hypocenter	C₁₁	#12899
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
65. C₁₁	#12899	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₁₁⋊C₁₆)	2
C₁₁×#1726	2
#12899	11