Group #44507580 — subgroups

Subgroups — #44507580

Order 30848.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×#21440553	C₂	1	1	yes	maximal, characteristic
2	#29507583	C₂	1	1	yes	maximal, characteristic
3	#29507479	C₂	1	4	yes	maximal
4	#384×C₂₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14515349	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₂₄₁	C₂²	1	2	yes	—
7	#21440553	C₄	1	4	yes	complemented
8	#21440549	—	2	2	no	—
9	C₂×C₄⋊C₄×C₂₄₁	—	2	2	no	—
10	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
12	C₂²×Dic₂₄₁	—	2	2	no	—
13	C₂×#14515349	—	2	2	no	—
14	C₂×#14515349	—	2	2	no	—
15	C₂×#14515349	C₂×C₄	1	4	yes	—
16	C₄⋊Dic₂₄₁	—	2	4	no	—
17	C₂²×C₄×C₂₄₁	—	2	2	no	—
18	C₂²×C₄×C₂₄₁	D₄	1	2	yes	—
19	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₄₁	—	2	4	no	—
21	C₄⋊C₄×C₂₄₁	—	4	4	no	—
22	C₄²×C₂₄₁	C₂×C₄	1	2	yes	—
23	C₄²×C₂₄₁	Q₈	1	2	yes	—
24	C₂×Dic₂₄₁	—	4	2	no	—
25	C₂×Dic₂₄₁	—	4	2	no	—
26	C₂×Dic₂₄₁	—	4	2	no	—
27	#14515349	—	2	4	no	—
28	C₂³×C₂₄₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₄₁	—	2	2	no	—
30	C₂×C₄×C₂₄₁	—	2	2	no	—
31	C₂×C₄×C₂₄₁	—	4	2	no	—
32	C₂×C₄×C₂₄₁	—	4	4	no	—
33	C₂×C₄×C₂₄₁	C₄⋊C₄	1	4	yes	—
34	C₂×C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₂₄₁	#41	1	2	yes	—
37	C₂×C₄×C₂₄₁	#41	1	2	yes	—
38	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₂₄₁	#124	1	1	yes	characteristic
40	C₂²×C₂₄₁	#124	1	1	yes	characteristic
41	C₂²×C₂₄₁	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²×C₂₄₁	#137	1	2	yes	—
43	C₄×C₂₄₁	—	2	4	no	—
44	C₄×C₂₄₁	—	8	2	no	—
45	C₄×C₂₄₁	#117	1	2	yes	—
46	C₄×C₂₄₁	#125	1	2	yes	—
47	Dic₂₄₁	—	8	2	no	—
48	C₂×C₂₄₁	#382	1	1	yes	characteristic
49	C₂×C₂₄₁	#428	1	2	yes	—
50	C₂×C₂₄₁	#489	1	2	yes	—
51	C₂×C₂₄₁	#490	1	1	yes	characteristic
52	C₂×C₂₄₁	#491	1	1	yes	characteristic
53	C₂₄₁	#1836	1	1	yes	characteristic, complemented, Sylow
54	#1836	—	241	1	no	maximal, Sylow
55	C₂×#97	—	241	1	no	—
56	#384	D₂₄₁	1	1	yes	characteristic
57	#382	—	241	1	no	—
58	#340	—	241	4	no	—
59	C₂²×C₈	—	241	2	no	—
60	C₂×C₄⋊C₄	—	2	2	no	—
61	C₂×C₄⋊C₄	—	241	2	no	—
62	C₂×C₄⋊C₄	C₂×D₂₄₁	1	2	yes	—
63	C₂×C₄²	C₂×D₂₄₁	1	1	yes	characteristic
64	#97	—	241	4	no	—
65	#95	—	482	2	no	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	482	2	no	—
68	C₂²×C₄	C₂²⋊D₂₄₁	1	2	yes	—
69	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
70	C₂×C₈	—	482	2	no	—
71	C₂×C₈	—	482	2	no	—
72	C₂×C₈	—	241	4	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄⋊C₄	—	482	4	no	—
76	C₄²	C₄×D₂₄₁	1	2	yes	—
77	C₄²	Dic₄₈₂	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	4	4	no	—
83	C₂×C₄	—	964	2	no	—
84	C₂×C₄	—	964	2	no	—
85	C₂×C₄	—	964	2	no	—
86	C₂×C₄	#16838749	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₂₄₁	1	1	yes	characteristic
88	C₂×C₄	C₂×Dic₄₈₂	1	1	yes	characteristic
89	C₂×C₄	#16838769	1	2	yes	—
90	C₂×C₄	#16838771	1	2	yes	—
91	C₈	—	482	4	no	—
92	C₂²	C₂×#16838749	1	1	yes	characteristic
93	C₂²	#21440629	1	1	yes	characteristic
94	C₂²	#21440631	1	1	yes	characteristic
95	C₂²	#21440668	1	2	yes	—
96	C₂²	#21440673	1	2	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	1928	2	no	—
100	C₄	#21440600	1	2	yes	—
101	C₄	#21440633	1	2	yes	—
102	C₂	#29507582	1	1	yes	characteristic
103	C₂	#29507757	1	2	yes	—
104	C₂	#29508079	1	2	yes	—
105	C₂	#29508081	1	1	yes	characteristic
106	C₂	#29508085	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#21440553

C₂

yes

maximal, characteristic

#29507583

C₂

yes

maximal, characteristic

#29507479

C₂

yes

maximal

#384×C₂₄₁

C₂

yes

maximal, characteristic

C₂²×#14515349

C₂²

yes

—

C₂×C₄⋊Dic₂₄₁

C₂²

yes

—

#21440553

C₄

yes

complemented

#21440549

—

C₂×C₄⋊C₄×C₂₄₁

—

C₂×C₄⋊C₄×C₂₄₁

C₂²

yes

—

C₂×C₄²×C₂₄₁

C₂²

yes

characteristic

C₂²×Dic₂₄₁

—

C₂×#14515349

—

C₂×#14515349

—

C₂×#14515349

C₂×C₄

yes

—

C₄⋊Dic₂₄₁

—

C₂²×C₄×C₂₄₁

—

C₂²×C₄×C₂₄₁

D₄

yes

—

C₂²×C₄×C₂₄₁

C₂³

yes

characteristic

C₄⋊C₄×C₂₄₁

—

C₄⋊C₄×C₂₄₁

—

C₄²×C₂₄₁

C₂×C₄

yes

—

C₄²×C₂₄₁

Q₈

yes

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

#14515349

—

C₂³×C₂₄₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₄₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₄₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₄₁

#41

yes

—

C₂×C₄×C₂₄₁

#41

yes

—

C₂²×C₂₄₁

C₂×C₄⋊C₄

yes

C₂²×C₂₄₁

yes

C₂²×C₂₄₁

yes

C₂²×C₂₄₁

yes

—

C₂²×C₂₄₁

#137

yes

—

C₄×C₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

#117

yes

—

C₄×C₂₄₁

#125

yes

—

Dic₂₄₁

—

C₂×C₂₄₁

#382

yes

characteristic

C₂×C₂₄₁

#428

yes

—

C₂×C₂₄₁

#489

yes

—

C₂×C₂₄₁

yes

C₂×C₂₄₁

yes

C₂₄₁

yes

characteristic, complemented, Sylow

#1836

—

241

maximal, Sylow

C₂×#97

—

241

—

#384

D₂₄₁

yes

characteristic

#382

—

241

—

#340

—

241

—

C₂²×C₈

—

241

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

241

—

C₂×C₄⋊C₄

C₂×D₂₄₁

yes

—

C₂×C₄²

C₂×D₂₄₁

yes

characteristic

#97

—

241

—

#95

—

482

—

C₂²×C₄

—

C₂²×C₄

—

482

—

C₂²×C₄

C₂²⋊D₂₄₁

yes

—

C₂²×C₄

C₂²×D₂₄₁

yes

characteristic

C₂×C₈

—

482

—

C₂×C₈

—

482

—

C₂×C₈

—

241

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

482

—

C₄²

C₄×D₂₄₁

yes

—

C₄²

Dic₄₈₂

yes

—

C₂³

C₂×C₂²⋊D₂₄₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

964

—

C₂×C₄

—

964

—

C₂×C₄

—

964

—

C₂×C₄

#16838749

yes

—

C₂×C₄

C₂×C₄×D₂₄₁

yes

characteristic

C₂×C₄

C₂×Dic₄₈₂

yes

characteristic

C₂×C₄

#16838769

yes

—

C₂×C₄

#16838771

yes

—

C₈

—

482

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#21440673

yes

—

C₄

—

C₄

—

C₄

—

1928

—

100

C₄

#21440600

yes

—

101

C₄

#21440633

yes

—

102

C₂

#29507582

yes

characteristic

103

C₂

#29507757

yes

—

104

C₂

#29508079

yes

—

105

C₂

#29508081

yes

characteristic

106

C₂

#29508085

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₄₁
commutator	C₂×C₄×C₂₄₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₄₁
Fitting	#384×C₂₄₁	C₂
socle, prime radical	C₂³×C₂₄₁	C₂×D₄
cosocle	C₂²×C₄×C₂₄₁	C₂³
hypercenter	#384	D₂₄₁
hypocenter	C₂₄₁	#1836
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₄₁

commutator

C₂×C₄×C₂₄₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₄₁

Fitting

#384×C₂₄₁

C₂

socle, prime radical

C₂³×C₂₄₁

C₂×D₄

cosocle

C₂²×C₄×C₂₄₁

C₂³

D₂₄₁

C₂₄₁

G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
7. #21440553	C₄	semidirect
53. C₂₄₁	#1836	semidirect

H ≅ G/N

type

7. #21440553

C₄

semidirect

53. C₂₄₁

#1836

semidirect

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

subgroup	index
C₂×#21440553	2
#29507583	2
#29507479	2
#384×C₂₄₁	2
#1836	241

subgroup

index

#384×C₂₄₁

241

Subgroups — #44507580

Conjugacy classes of subgroups

Complements

Maximal subgroups