Group #44507581 — subgroups

Subgroups — #44507581

Order 30848.

188 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 81 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	#29507740	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₂₄₁	C₂	1	1	yes	maximal, characteristic
3	#29507482	C₂	1	1	yes	maximal, characteristic
4	#29507481	C₂	1	2	yes	maximal
5	#341×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#16838754	C₂²	1	2	yes	—
7	C₂²×#14515349	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
9	#21440571	—	2	4	no	—
10	C₈×Dic₂₄₁	C₄	1	2	yes	—
11	C₈×Dic₂₄₁	C₄	1	2	yes	—
12	C₂×M₁₆×C₂₄₁	C₂²	1	2	yes	—
13	C₂²×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
14	C₂²×Dic₂₄₁	Q₈	1	2	yes	—
15	#16838754	—	2	2	no	—
16	#16838754	—	2	2	no	—
17	C₂×#14515349	—	2	2	no	—
18	C₂×#14515349	—	2	2	no	—
19	C₂×#14515349	C₂×C₄	1	2	yes	—
20	C₄×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₂₄₁	D₄	1	2	yes	—
23	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
24	M₁₆×C₂₄₁	—	2	2	no	—
25	M₁₆×C₂₄₁	—	2	2	no	—
26	C₂×C₈×C₂₄₁	—	2	2	no	—
27	C₂×C₈×C₂₄₁	—	2	2	no	—
28	C₂×C₈×C₂₄₁	C₂×C₄	1	2	yes	—
29	C₂×Dic₂₄₁	—	2	4	no	—
30	C₂×Dic₂₄₁	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₂₄₁	C₄⋊C₄	1	2	yes	—
32	#14515349	—	2	2	no	—
33	#14515349	—	4	2	no	—
34	C₂³×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₄₁	#41	1	2	yes	—
38	C₂×C₄×C₂₄₁	#41	1	2	yes	—
39	C₈×C₂₄₁	—	2	2	no	—
40	C₈×C₂₄₁	—	4	2	no	—
41	C₂²×C₂₄₁	—	2	2	no	—
42	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₂₄₁	#125	1	2	yes	—
44	C₄×C₂₄₁	#117	1	1	yes	characteristic
45	C₄×C₂₄₁	#117	1	1	yes	characteristic
46	C₄×C₂₄₁	#124	1	2	yes	—
47	Dic₂₄₁	—	2	2	no	—
48	Dic₂₄₁	#108	1	4	yes	—
49	C₂×C₂₄₁	—	2	2	no	—
50	C₂×C₂₄₁	#382	1	1	yes	characteristic
51	C₂×C₂₄₁	C₂×#108	1	2	yes	—
52	C₂₄₁	#1837	1	1	yes	characteristic, complemented, Sylow
53	#1837	—	241	1	no	maximal, Sylow
54	#423	—	241	2	no	—
55	C₂×C₄×C₈	—	241	1	no	—
56	#341	—	241	2	no	—
57	#341	—	241	1	no	—
58	#341	D₂₄₁	1	1	yes	characteristic
59	C₂×M₁₆	—	241	2	no	—
60	C₂×M₁₆	C₂×D₂₄₁	1	2	yes	—
61	C₂²×C₈	—	241	1	no	—
62	C₂²×C₈	C₂×D₂₄₁	1	1	yes	characteristic
63	C₂×C₄²	—	241	1	no	—
64	C₄⋊C₈	—	482	4	no	—
65	C₄×C₈	—	241	2	no	—
66	C₄×C₈	—	241	2	no	—
67	C₂²×C₄	—	241	2	no	—
68	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	482	2	no	—
72	M₁₆	—	482	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	482	2	no	—
76	C₂×C₈	—	482	2	no	—
77	C₂×C₈	—	241	2	no	—
78	C₂×C₈	C₄×D₂₄₁	1	2	yes	—
79	C₄²	—	241	1	no	—
80	C₄²	—	241	1	no	—
81	C₄²	—	241	2	no	—
82	C₂³	Q₈×D₂₄₁	1	1	yes	characteristic
83	C₂×C₄	—	482	4	no	—
84	C₂×C₄	—	241	2	no	—
85	C₂×C₄	—	241	2	no	—
86	C₂×C₄	C₂×C₄×D₂₄₁	1	1	yes	characteristic
87	C₂×C₄	D₄×D₂₄₁	1	1	yes	characteristic
88	C₂×C₄	#16838769	1	2	yes	—
89	C₂×C₄	#16838770	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	964	2	no	—
93	C₈	—	482	2	no	—
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊C₄×D₂₄₁	1	1	yes	characteristic
96	C₂²	#21440632	1	2	yes	—
97	C₄	—	482	2	no	—
98	C₄	—	241	4	no	—
99	C₄	#21440598	1	1	yes	characteristic
100	C₄	#21440599	1	1	yes	characteristic
101	C₄	#21440628	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	#29507581	1	1	yes	characteristic
104	C₂	#108×D₂₄₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#29507740

C₂

yes

maximal

C₂×C₈×Dic₂₄₁

C₂

yes

maximal, characteristic

#29507482

C₂

yes

maximal, characteristic

#29507481

C₂

yes

maximal

#341×C₂₄₁

C₂

yes

maximal, characteristic

C₂×#16838754

C₂²

yes

—

C₂²×#14515349

C₂²

yes

characteristic

C₂×C₄×Dic₂₄₁

C₂²

yes

characteristic

#21440571

—

C₈×Dic₂₄₁

C₄

yes

—

C₈×Dic₂₄₁

C₄

yes

—

C₂×M₁₆×C₂₄₁

C₂²

yes

—

C₂²×C₈×C₂₄₁

C₂²

yes

characteristic

C₂²×Dic₂₄₁

Q₈

yes

—

—

—

—

—

C₂×C₄

yes

—

C₄×Dic₂₄₁

C₂×C₄

yes

characteristic

C₄×Dic₂₄₁

C₂×C₄

yes

characteristic

C₄×Dic₂₄₁

D₄

yes

—

C₂²×C₄×C₂₄₁

C₂³

yes

characteristic

M₁₆×C₂₄₁

—

M₁₆×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₂×C₈×C₂₄₁

C₂×C₄

yes

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

C₄⋊C₄

yes

—

C₂×Dic₂₄₁

C₄⋊C₄

yes

—

#14515349

—

#14515349

—

C₂³×C₂₄₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₄₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₄₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₄₁

#41

yes

—

C₂×C₄×C₂₄₁

#41

yes

—

C₈×C₂₄₁

—

C₈×C₂₄₁

—

C₂²×C₂₄₁

—

C₂²×C₂₄₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₄₁

#125

yes

—

C₄×C₂₄₁

yes

C₄×C₂₄₁

yes

C₄×C₂₄₁

yes

—

Dic₂₄₁

—

Dic₂₄₁

#108

yes

—

C₂×C₂₄₁

—

C₂×C₂₄₁

#382

yes

characteristic

C₂×C₂₄₁

C₂×#108

yes

—

C₂₄₁

#1837

yes

characteristic, complemented, Sylow

#1837

—

241

maximal, Sylow

#423

—

241

—

C₂×C₄×C₈

—

241

—

#341

—

241

—

#341

—

241

—

#341

D₂₄₁

yes

characteristic

C₂×M₁₆

—

241

—

C₂×M₁₆

C₂×D₂₄₁

yes

—

C₂²×C₈

—

241

—

C₂²×C₈

C₂×D₂₄₁

yes

characteristic

C₂×C₄²

—

241

—

C₄⋊C₈

—

482

—

C₄×C₈

—

241

—

C₄×C₈

—

241

—

C₂²×C₄

—

241

—

C₂²×C₄

C₂²×D₂₄₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

482

—

M₁₆

—

482

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

482

—

C₂×C₈

—

482

—

C₂×C₈

—

241

—

C₂×C₈

C₄×D₂₄₁

yes

—

C₄²

—

241

—

C₄²

—

241

—

C₄²

—

241

—

C₂³

Q₈×D₂₄₁

yes

characteristic

C₂×C₄

—

482

—

C₂×C₄

—

241

—

C₂×C₄

—

241

—

C₂×C₄

C₂×C₄×D₂₄₁

yes

characteristic

C₂×C₄

D₄×D₂₄₁

yes

characteristic

C₂×C₄

#16838769

yes

—

C₂×C₄

#16838770

yes

—

C₈

—

C₈

—

C₈

—

964

—

C₈

—

482

—

C₂²

—

C₂²

C₄⋊C₄×D₂₄₁

yes

characteristic

C₂²

#21440632

yes

—

C₄

—

482

—

C₄

—

241

—

C₄

#21440598

yes

characteristic

100

C₄

#21440599

yes

characteristic

101

C₄

#21440628

yes

—

102

C₂

—

103

C₂

#29507581

yes

characteristic

104

C₂

#108×D₂₄₁

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₄₁
commutator	C₂×C₄×C₂₄₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₄₁
Fitting	#341×C₂₄₁	C₂
socle	C₂²×C₂₄₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₄₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₄₁	C₂³
hypercenter	#341	D₂₄₁
hypocenter	C₂₄₁	#1837
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₂₄₁

commutator

C₂×C₄×C₂₄₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₄₁

Fitting

#341×C₂₄₁

C₂

socle

C₂²×C₂₄₁

C₂×C₄⋊C₄

prime radical

C₂³×C₂₄₁

C₂×Q₈

cosocle

C₂²×C₄×C₂₄₁

C₂³

D₂₄₁

C₂₄₁

G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
52. C₂₄₁	#1837	semidirect

H ≅ G/N

type

52. C₂₄₁

#1837

semidirect

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

subgroup	index
#29507740	2
C₂×C₈×Dic₂₄₁	2
#29507482	2
#29507481	2
#341×C₂₄₁	2
#1837	241

subgroup

index

C₂×C₈×Dic₂₄₁

#341×C₂₄₁

241

Subgroups — #44507581

Conjugacy classes of subgroups

Complements

Maximal subgroups