Subgroups — #14674793

Order 2816.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070891	C₂	1	2	yes	maximal
2	#13066816	C₂	1	4	yes	maximal
3	C₄×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
4	#10622295	—	2	2	no	—
5	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
6	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	#10622142	—	2	2	no	—
8	#10622142	C₂²	1	4	yes	—
9	#66922	—	4	2	no	—
10	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
11	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
12	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
13	#66882	—	2	4	no	—
14	#66882	—	4	2	no	—
15	C₁₁×C₃₂	Q₈	1	4	yes	complemented
16	#13731	—	11	1	no	maximal, Sylow
17	C₂×Dic₂₂	—	8	2	no	—
18	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
19	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
20	C₄²×C₁₁	D₈	1	1	yes	characteristic
21	C₄⋊Dic₁₁	—	4	4	no	—
22	C₄⋊Dic₁₁	—	8	2	no	—
23	C₁₁×C₁₆	Q₁₆	1	2	yes	—
24	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
25	#2252	—	11	2	no	—
26	#1423	—	11	4	no	—
27	C₄×C₃₂	D₁₁	1	1	yes	characteristic
28	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
30	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
31	C₂×Dic₁₁	—	8	4	no	—
32	Dic₂₂	—	16	4	no	—
33	C₈×C₁₁	Q₃₂	1	2	yes	—
34	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
35	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
36	#500	—	22	2	no	—
37	C₂×C₃₂	C₂×D₁₁	1	2	yes	—
38	#366	—	11	4	no	—
39	#366	—	22	2	no	—
40	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
41	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
42	C₄×C₁₁	D₃₂	1	2	yes	—
43	C₄×C₁₁	Q₆₄	1	2	yes	—
44	C₄×C₁₁	#500	1	1	yes	characteristic
45	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
46	Dic₁₁	—	16	4	no	—
47	C₄⋊Q₈	—	44	2	no	—
48	C₂×C₁₆	D₄₄	1	1	yes	characteristic
49	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
50	#107	—	22	4	no	—
51	#107	—	44	2	no	—
52	C₄×C₈	D₄₄	1	1	yes	characteristic
53	C₃₂	Dic₂₂	1	4	yes	complemented
54	C₂×C₁₁	#2252	1	1	yes	characteristic
55	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
56	C₂×C₁₁	C₂×Q₆₄	1	1	yes	characteristic
57	C₂×Q₈	—	88	2	no	—
58	C₂×C₈	D₈₈	1	1	yes	characteristic
59	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
60	C₄⋊C₄	—	44	4	no	—
61	C₄⋊C₄	—	88	2	no	—
62	C₄²	D₈₈	1	1	yes	characteristic
63	C₁₆	Dic₄₄	1	2	yes	—
64	C₁₆	C₂×Dic₂₂	1	2	yes	—
65	C₁₁	#13731	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	176	4	no	—
67	C₂×C₄	—	88	4	no	—
68	C₂×C₄	D₁₇₆	1	1	yes	characteristic
69	C₂×C₄	D₁₇₆	1	1	yes	characteristic
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	—	176	4	no	—
76	C₄	D₃₅₂	1	2	yes	—
77	C₄	Dic₁₇₆	1	2	yes	—
78	C₄	#10622295	1	1	yes	characteristic
79	C₄	C₂×Dic₈₈	1	1	yes	characteristic
80	C₂	#13070891	1	1	yes	characteristic
81	C₂	C₂×D₃₅₂	1	1	yes	characteristic
82	C₂	C₂×Dic₁₇₆	1	1	yes	characteristic

	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	#13731
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
15. C₁₁×C₃₂	Q₈	semidirect
53. C₃₂	Dic₂₂	semidirect
65. C₁₁	#13731	semidirect

Maximal subgroups

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

subgroup	index
#13070891	2
#13066816	2
C₄×C₁₁×C₃₂	2
#13731	11