Group #44506583 — subgroups

Subgroups — #44506583

Order 30848.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508447	C₂	1	1	yes	maximal, characteristic
2	#29508009	C₂	1	2	yes	maximal
3	#29507466	C₂	1	1	yes	maximal, characteristic
4	#29507449	C₂	1	2	yes	maximal
5	#494×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	#21440641	—	2	2	no	—
7	#21440640	—	2	2	no	—
8	C₄×Dic₄₈₂	C₂²	1	2	yes	—
9	#21440607	—	2	2	no	—
10	#21440575	—	2	2	no	—
11	C₄⋊#14515349	C₂²	1	2	yes	—
12	#21440565	—	2	2	no	—
13	C₂×Q₁₆×C₂₄₁	—	2	2	no	—
14	C₄⋊Q₈×C₂₄₁	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₂₄₁	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₈₂	—	2	2	no	—
18	C₂×Dic₄₈₂	D₄	1	2	yes	—
19	C₂×#14515349	—	2	2	no	—
20	C₄⋊Dic₂₄₁	D₄	1	2	yes	—
21	#16838749	—	2	4	no	—
22	#16838749	—	2	2	no	—
23	C₄×Dic₂₄₁	—	2	2	no	—
24	C₄×Dic₂₄₁	—	2	2	no	—
25	C₂×Q₈×C₂₄₁	—	2	1	no	—
26	C₂×Q₈×C₂₄₁	D₄	1	2	yes	—
27	Q₁₆×C₂₄₁	—	4	4	no	—
28	C₂×C₈×C₂₄₁	—	2	1	no	—
29	C₄⋊C₄×C₂₄₁	—	2	2	no	—
30	C₄⋊C₄×C₂₄₁	—	2	2	no	—
31	C₄²×C₂₄₁	C₂³	1	1	yes	characteristic
32	Dic₄₈₂	—	2	2	no	—
33	Dic₄₈₂	—	8	2	no	—
34	Dic₄₈₂	Q₁₆	1	4	yes	complemented
35	C₂×Dic₂₄₁	—	2	2	no	—
36	C₂×Dic₂₄₁	—	2	2	no	—
37	#14515349	—	4	2	no	—
38	Q₈×C₂₄₁	—	4	2	no	—
39	Q₈×C₂₄₁	—	4	2	no	—
40	C₂×C₄×C₂₄₁	—	2	2	no	—
41	C₂×C₄×C₂₄₁	—	4	1	no	—
42	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
44	C₈×C₂₄₁	—	2	2	no	—
45	C₂²×C₂₄₁	#120	1	1	yes	characteristic
46	C₄×C₂₄₁	—	2	1	no	—
47	C₄×C₂₄₁	—	4	2	no	—
48	C₄×C₂₄₁	—	8	1	no	—
49	C₄×C₂₄₁	C₂×Q₁₆	1	2	yes	—
50	C₄×C₂₄₁	#137	1	2	yes	—
51	Dic₂₄₁	—	2	4	no	—
52	Dic₂₄₁	—	4	2	no	—
53	C₂×C₂₄₁	#451	1	2	yes	—
54	C₂×C₂₄₁	#453	1	1	yes	characteristic
55	C₂₄₁	#1633	1	1	yes	characteristic, complemented, Sylow
56	#1633	—	241	1	no	maximal, Sylow
57	Q₈²	—	241	1	no	—
58	#494	D₂₄₁	1	1	yes	characteristic
59	#477	—	241	2	no	—
60	#333	—	241	1	no	—
61	Q₈⋊C₈	—	241	2	no	—
62	C₂×Q₁₆	—	2	2	no	—
63	C₄⋊Q₈	—	482	2	no	—
64	C₄⋊Q₈	—	482	2	no	—
65	C₄⋊Q₈	C₂×D₂₄₁	1	1	yes	characteristic
66	C₄⋊Q₈	C₂×D₂₄₁	1	1	yes	characteristic
67	C₄×Q₈	—	482	2	no	—
68	C₄×Q₈	—	241	2	no	—
69	#107	—	482	2	no	—
70	C₄⋊C₈	—	241	2	no	—
71	#103	—	482	2	no	—
72	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	482	2	no	—
75	C₂×Q₈	—	241	2	no	—
76	C₂×Q₈	C₂²⋊D₂₄₁	1	2	yes	—
77	Q₁₆	—	4	4	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	482	2	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	482	4	no	—
83	C₄⋊C₄	—	482	2	no	—
84	C₄⋊C₄	—	241	2	no	—
85	C₄²	—	482	2	no	—
86	C₄²	—	482	2	no	—
87	C₄²	C₂²×D₂₄₁	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	1928	2	no	—
91	Q₈	—	482	2	no	—
92	Q₈	—	241	4	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	482	2	no	—
96	C₂×C₄	—	482	2	no	—
97	C₂×C₄	D₄×D₂₄₁	1	2	yes	—
98	C₂×C₄	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	964	2	no	—
101	C₂²	#21440610	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	4	2	no	—
104	C₄	—	8	1	no	—
105	C₄	—	964	2	no	—
106	C₄	—	482	4	no	—
107	C₄	Q₁₆×D₂₄₁	1	2	yes	—
108	C₄	#21440674	1	2	yes	—
109	C₂	#29507871	1	2	yes	—
110	C₂	#29507884	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#29508447

C₂

yes

maximal, characteristic

#29508009

C₂

yes

maximal

#29507466

C₂

yes

maximal, characteristic

#29507449

C₂

yes

maximal

#494×C₂₄₁

C₂

yes

maximal, characteristic

#21440641

—

#21440640

—

C₄×Dic₄₈₂

C₂²

yes

—

#21440607

—

#21440575

—

C₄⋊#14515349

C₂²

yes

—

#21440565

—

C₂×Q₁₆×C₂₄₁

—

C₄⋊Q₈×C₂₄₁

C₂²

yes

characteristic

C₄⋊Q₈×C₂₄₁

C₂²

yes

characteristic

C₄×C₈×C₂₄₁

C₂²

yes

characteristic

C₂×Dic₄₈₂

—

C₂×Dic₄₈₂

D₄

yes

—

C₂×#14515349

—

C₄⋊Dic₂₄₁

D₄

yes

—

#16838749

—

#16838749

—

C₄×Dic₂₄₁

—

C₄×Dic₂₄₁

—

C₂×Q₈×C₂₄₁

—

C₂×Q₈×C₂₄₁

D₄

yes

—

Q₁₆×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₄⋊C₄×C₂₄₁

—

C₄⋊C₄×C₂₄₁

—

C₄²×C₂₄₁

C₂³

yes

characteristic

Dic₄₈₂

—

Dic₄₈₂

—

Dic₄₈₂

Q₁₆

yes

complemented

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

#14515349

—

Q₈×C₂₄₁

—

Q₈×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

characteristic

C₈×C₂₄₁

—

C₂²×C₂₄₁

#120

yes

characteristic

C₄×C₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

C₂×Q₁₆

yes

—

C₄×C₂₄₁

#137

yes

—

Dic₂₄₁

—

Dic₂₄₁

—

C₂×C₂₄₁

#451

yes

—

C₂×C₂₄₁

#453

yes

characteristic

C₂₄₁

#1633

yes

characteristic, complemented, Sylow

#1633

—

241

maximal, Sylow

Q₈²

—

241

—

#494

D₂₄₁

yes

characteristic

#477

—

241

—

#333

—

241

—

Q₈⋊C₈

—

241

—

C₂×Q₁₆

—

C₄⋊Q₈

—

482

—

C₄⋊Q₈

—

482

—

C₄⋊Q₈

C₂×D₂₄₁

yes

characteristic

C₄⋊Q₈

C₂×D₂₄₁

yes

characteristic

C₄×Q₈

—

482

—

C₄×Q₈

—

241

—

#107

—

482

—

C₄⋊C₈

—

241

—

#103

—

482

—

C₄×C₈

C₂×D₂₄₁

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

482

—

C₂×Q₈

—

241

—

C₂×Q₈

C₂²⋊D₂₄₁

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

482

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

241

—

C₄²

—

482

—

C₄²

—

482

—

C₄²

C₂²×D₂₄₁

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

1928

—

Q₈

—

482

—

Q₈

—

241

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

482

—

C₂×C₄

—

482

—

C₂×C₄

D₄×D₂₄₁

yes

—

C₂×C₄

C₂×C₂²⋊D₂₄₁

yes

characteristic

C₈

—

100

C₈

—

964

—

101

C₂²

#21440610

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

964

—

106

C₄

—

482

—

107

C₄

Q₁₆×D₂₄₁

yes

—

108

C₄

#21440674

yes

—

109

C₂

#29507871

yes

—

110

C₂

#29507884

yes

characteristic

	subgroup	G/H
center	C₂²	#21440610
commutator, cosocle	C₄²×C₂₄₁	C₂³
Frattini	C₄²	C₂²×D₂₄₁
Fitting	#494×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	#120
hypercenter	#494	D₂₄₁
hypocenter	C₂₄₁	#1633
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#21440610

commutator, cosocle

C₄²×C₂₄₁

C₂³

Frattini

C₄²

C₂²×D₂₄₁

Fitting

#494×C₂₄₁

C₂

C₂²×C₂₄₁

D₂₄₁

C₂₄₁

G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
34. Dic₄₈₂	Q₁₆	semidirect
55. C₂₄₁	#1633	semidirect

H ≅ G/N

type

34. Dic₄₈₂

Q₁₆

semidirect

55. C₂₄₁

#1633

semidirect

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

subgroup	index
#29508447	2
#29508009	2
#29507466	2
#29507449	2
#494×C₂₄₁	2
#1633	241

subgroup

index

#494×C₂₄₁

241

Subgroups — #44506583

Conjugacy classes of subgroups

Complements

Maximal subgroups