Subgroups — #31824075

Order 17984.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582879	C₂	1	1	yes	maximal, characteristic, complemented
2	#22582872	C₂	1	4	yes	maximal
3	#22582871	C₂	1	1	yes	maximal, characteristic, complemented
4	#22582869	C₂	1	4	yes	maximal, complemented
5	#22582858	C₂	1	2	yes	maximal
6	C₄×Dic₅₆₂	C₂	1	2	yes	maximal, complemented
7	#117×C₂₈₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₅₆₂	C₂²	1	2	yes	—
9	C₄⋊Dic₂₈₁	C₂²	1	2	yes	—
10	C₄⋊Dic₂₈₁	C₂²	1	4	yes	—
11	#17985117	C₂²	1	4	yes	—
12	#17985117	C₂²	1	4	yes	—
13	#17985117	C₂²	1	4	yes	—
14	C₂²⋊Dic₂₈₁	C₂²	1	4	yes	—
15	C₄×Dic₂₈₁	C₂²	1	4	yes	—
16	C₂²×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₂₈₁	C₂²	1	2	yes	—
18	C₂²⋊C₄×C₂₈₁	C₂²	1	2	yes	—
19	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
20	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
21	Dic₅₆₂	—	2	4	no	—
22	C₂×Dic₂₈₁	C₂³	1	4	yes	—
23	C₂×Dic₂₈₁	C₂³	1	4	yes	—
24	C₂³×C₂₈₁	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₂₈₁	—	2	2	no	—
26	C₂×C₄×C₂₈₁	C₂³	1	2	yes	—
27	C₂×C₄×C₂₈₁	C₂³	1	2	yes	—
28	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
29	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
30	C₂²×C₂₈₁	—	2	1	no	—
31	C₂²×C₂₈₁	—	2	2	no	—
32	C₂²×C₂₈₁	C₂⁴	1	1	yes	characteristic
33	C₄×C₂₈₁	—	2	1	no	—
34	C₄×C₂₈₁	—	2	2	no	—
35	C₄×C₂₈₁	—	2	2	no	—
36	C₄×C₂₈₁	#41	1	2	yes	—
37	Dic₂₈₁	—	2	4	no	—
38	Dic₂₈₁	—	2	4	no	—
39	C₂×C₂₈₁	—	4	1	no	—
40	C₂×C₂₈₁	C₂×#41	1	1	yes	characteristic
41	C₂×C₂₈₁	2₋¹⁺⁴	1	2	yes	—
42	C₂₈₁	#541	1	1	yes	characteristic, complemented, Sylow
43	#541	—	281	1	no	maximal, Sylow
44	C₄⋊Q₈	—	281	1	no	—
45	#126	—	281	4	no	—
46	#125	—	281	4	no	—
47	#125	—	281	1	no	—
48	C₂²⋊Q₈	—	281	2	no	—
49	C₄×Q₈	—	281	2	no	—
50	#117	D₂₈₁	1	1	yes	characteristic
51	C₂×Q₈	—	281	2	no	—
52	C₂²×C₄	C₂×D₂₈₁	1	1	yes	characteristic
53	C₄⋊C₄	—	281	4	no	—
54	C₄⋊C₄	—	281	4	no	—
55	C₄⋊C₄	—	281	4	no	—
56	C₄⋊C₄	—	281	2	no	—
57	C₄⋊C₄	—	281	4	no	—
58	C₄⋊C₄	C₂×D₂₈₁	1	2	yes	—
59	C₂²⋊C₄	—	281	4	no	—
60	C₂²⋊C₄	C₂×D₂₈₁	1	2	yes	—
61	C₄²	—	281	4	no	—
62	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
63	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
64	C₂³	C₂²×D₂₈₁	1	1	yes	characteristic
65	Q₈	—	562	4	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	281	4	no	—
68	C₂×C₄	—	281	4	no	—
69	C₂×C₄	C₂²×D₂₈₁	1	2	yes	—
70	C₂×C₄	C₂²×D₂₈₁	1	2	yes	—
71	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
73	C₂²	—	2	1	no	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂³×D₂₈₁	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	2	no	—
78	C₄	—	2	2	no	—
79	C₄	—	562	4	no	—
80	C₄	—	562	4	no	—
81	C₄	#17985138	1	2	yes	—
82	C₂	—	4	1	no	—
83	C₂	C₂×#17985138	1	1	yes	characteristic
84	C₂	#22582926	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₈₁
commutator, socle, cosocle	C₂²×C₂₈₁	C₂⁴
Fitting	#117×C₂₈₁	C₂
prime radical	C₂³×C₂₈₁	C₂³
hypercenter	#117	D₂₈₁
hypocenter	C₂₈₁	#541
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ #117

Complements

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

N	H ≅ G/N	type
1. #22582879	C₂	semidirect
3. #22582871	C₂	semidirect
4. #22582869	C₂	semidirect
6. C₄×Dic₅₆₂	C₂	semidirect
42. C₂₈₁	#541	semidirect

Maximal subgroups

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

subgroup	index
#22582879	2
#22582872	2
#22582871	2
#22582869	2
#22582858	2
C₄×Dic₅₆₂	2
#117×C₂₈₁	2
#541	281