Subgroups — #14674797

Order 2816.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070895	C₂	1	2	yes	maximal
2	#13066818	C₂	1	2	yes	maximal
3	#13066816	C₂	1	2	yes	maximal
4	C₄×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
5	#10622296	—	2	2	no	—
6	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	#10622143	—	2	2	no	—
10	#10622142	C₂²	1	4	yes	—
11	#66923	—	4	2	no	—
12	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
14	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
15	#66882	—	2	4	no	—
16	#66881	—	4	2	no	—
17	C₁₁×C₃₂	Q₈	1	2	yes	—
18	C₁₁×C₃₂	Q₈	1	2	yes	—
19	#13732	—	11	1	no	maximal, Sylow
20	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
21	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
22	C₄²×C₁₁	D₈	1	1	yes	characteristic
23	C₄⋊Dic₁₁	—	4	4	no	—
24	Dic₁₁⋊C₄	—	8	4	no	—
25	C₁₁×C₁₆	Q₁₆	1	2	yes	—
26	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
27	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
28	#2253	—	11	2	no	—
29	#1424	—	11	2	no	—
30	#1423	—	11	2	no	—
31	C₄×C₃₂	D₁₁	1	1	yes	characteristic
32	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
33	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
34	C₂×Dic₁₁	—	8	4	no	—
35	C₈×C₁₁	Q₃₂	1	2	yes	—
36	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
37	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
38	#499	—	22	2	no	—
39	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
40	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
41	#367	—	22	2	no	—
42	#366	—	11	4	no	—
43	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
44	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
45	C₄×C₁₁	—	2	2	no	—
46	C₄×C₁₁	#500	1	1	yes	characteristic
47	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
48	Dic₁₁	—	16	4	no	—
49	#125	—	44	2	no	—
50	C₂×C₁₆	D₄₄	1	1	yes	characteristic
51	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
52	#107	—	22	4	no	—
53	#106	—	44	2	no	—
54	C₄×C₈	D₄₄	1	1	yes	characteristic
55	C₃₂	Dic₂₂	1	2	yes	—
56	C₃₂	Dic₂₂	1	2	yes	—
57	C₂×C₁₁	#2252	1	1	yes	characteristic
58	C₂×C₁₁	#2262	1	2	yes	—
59	C₂×C₈	D₈₈	1	1	yes	characteristic
60	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
61	C₄⋊C₄	—	44	4	no	—
62	C₄⋊C₄	—	88	4	no	—
63	C₄²	D₈₈	1	1	yes	characteristic
64	C₁₆	Dic₄₄	1	2	yes	—
65	C₁₆	C₂×Dic₂₂	1	1	yes	characteristic
66	C₁₆	C₂×Dic₂₂	1	1	yes	characteristic
67	C₁₁	#13732	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₄	—	88	4	no	—
69	C₂×C₄	D₁₇₆	1	2	yes	—
70	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
71	C₈	Dic₈₈	1	2	yes	—
72	C₈	#66922	1	1	yes	characteristic
73	C₈	C₂×Dic₄₄	1	1	yes	characteristic
74	C₂²	C₂×D₁₇₆	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	176	4	no	—
77	C₄	#10622295	1	1	yes	characteristic
78	C₄	C₂×Dic₈₈	1	1	yes	characteristic
79	C₂	#13070891	1	1	yes	characteristic
80	C₂	#13070925	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₆
commutator, cosocle	C₂×C₁₁×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₄×C₁₁×C₃₂	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₁₆
hypercenter	C₄×C₃₂	D₁₁
hypocenter	C₁₁	#13732
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
67. C₁₁	#13732	semidirect

Maximal subgroups

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

subgroup	index
#13070895	2
#13066818	2
#13066816	2
C₄×C₁₁×C₃₂	2
#13732	11