Group #44507598 — subgroups

Subgroups — #44507598

Order 30848.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₄⋊#14515349	C₂	1	1	yes	maximal, characteristic
2	C₂×#21440571	C₂	1	4	yes	maximal
3	#29507563	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₈×C₂₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14515349	C₂²	1	2	yes	—
6	C₂×C₄×Dic₂₄₁	C₂²	1	2	yes	—
7	C₄⋊#14515349	—	2	2	no	—
8	#21440571	—	2	8	no	—
9	#21440549	C₄	1	2	yes	—
10	#21440549	C₄	1	2	yes	—
11	C₂²×C₈×C₂₄₁	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₂₄₁	—	2	2	no	—
14	C₂²×Dic₂₄₁	C₂×C₄	1	4	yes	—
15	C₂×#14515349	—	2	4	no	—
16	C₂×#14515349	—	2	2	no	—
17	C₄×Dic₂₄₁	D₄	1	4	yes	—
18	C₄×Dic₂₄₁	Q₈	1	4	yes	—
19	C₂²×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₂₄₁	—	2	4	no	—
23	C₂×C₈×C₂₄₁	—	2	2	no	—
24	C₄²×C₂₄₁	D₄	1	2	yes	—
25	C₄²×C₂₄₁	Q₈	1	2	yes	—
26	C₂×Dic₂₄₁	—	2	4	no	—
27	C₂×Dic₂₄₁	—	2	4	no	—
28	C₂×Dic₂₄₁	C₄⋊C₄	1	8	yes	—
29	#14515349	—	4	2	no	—
30	C₂³×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₄₁	—	2	2	no	—
32	C₂×C₄×C₂₄₁	—	2	2	no	—
33	C₂×C₄×C₂₄₁	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₄₁	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₄₁	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₂₄₁	—	4	2	no	—
40	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	2	yes	—
41	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₂₄₁	#131	1	2	yes	—
43	C₂²×C₂₄₁	#131	1	2	yes	—
44	C₄×C₂₄₁	—	2	2	no	—
45	C₄×C₂₄₁	—	2	2	no	—
46	C₄×C₂₄₁	#127	1	1	yes	characteristic
47	C₄×C₂₄₁	C₄⋊Q₈	1	1	yes	characteristic
48	C₄×C₂₄₁	C₄⋊Q₈	1	2	yes	—
49	Dic₂₄₁	—	2	8	no	—
50	C₂×C₂₄₁	#384	1	1	yes	characteristic
51	C₂×C₂₄₁	#424	1	4	yes	—
52	C₂×C₂₄₁	#424	1	1	yes	characteristic
53	C₂×C₂₄₁	#424	1	1	yes	characteristic
54	C₂₄₁	#1843	1	1	yes	characteristic, complemented, Sylow
55	#1843	—	241	1	no	maximal, Sylow
56	C₂×C₄⋊C₈	—	241	4	no	—
57	C₂×C₄⋊C₈	—	241	1	no	—
58	C₂×C₄⋊C₈	D₂₄₁	1	1	yes	characteristic
59	#376	—	241	1	no	—
60	C₂²×C₈	—	241	2	no	—
61	C₂²×C₈	C₂×D₂₄₁	1	2	yes	—
62	C₂×C₄²	—	241	2	no	—
63	C₂×C₄²	C₂×D₂₄₁	1	1	yes	characteristic
64	C₄⋊C₈	—	2	2	no	—
65	C₄⋊C₈	—	482	8	no	—
66	C₄⋊C₈	—	482	2	no	—
67	#95	—	241	2	no	—
68	#95	—	241	2	no	—
69	C₂²×C₄	—	241	4	no	—
70	C₂²×C₄	C₄×D₂₄₁	1	1	yes	characteristic
71	C₂²×C₄	C₄×D₂₄₁	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	482	4	no	—
76	C₂×C₈	—	482	2	no	—
77	C₄²	—	241	4	no	—
78	C₄²	—	241	4	no	—
79	C₄²	C₂²⋊D₂₄₁	1	2	yes	—
80	C₄²	Dic₄₈₂	1	2	yes	—
81	C₂³	C₂×C₄×D₂₄₁	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	482	4	no	—
85	C₂×C₄	—	482	4	no	—
86	C₂×C₄	—	241	8	no	—
87	C₂×C₄	#16838749	1	2	yes	—
88	C₂×C₄	#16838749	1	2	yes	—
89	C₂×C₄	D₄×D₂₄₁	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
91	C₂×C₄	Q₈×D₂₄₁	1	2	yes	—
92	C₂×C₄	C₂×Dic₄₈₂	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	—	964	2	no	—
95	C₂²	C₄⋊C₄×D₂₄₁	1	2	yes	—
96	C₂²	C₂×#16838749	1	1	yes	characteristic
97	C₂²	#21440648	1	2	yes	—
98	C₂²	#21440650	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	2	2	no	—
101	C₄	—	482	8	no	—
102	C₄	#21440638	1	1	yes	characteristic
103	C₄	#21440640	1	1	yes	characteristic
104	C₄	#21440641	1	2	yes	—
105	C₂	#29507586	1	1	yes	characteristic
106	C₂	#29507742	1	4	yes	—
107	C₂	#29507743	1	1	yes	characteristic
108	C₂	#29507745	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14515349

C₂

yes

maximal, characteristic

C₂×#21440571

C₂

yes

maximal

#29507563

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₂₄₁

C₂

yes

maximal, characteristic

C₂²×#14515349

C₂²

yes

—

C₂×C₄×Dic₂₄₁

C₂²

yes

—

C₄⋊#14515349

—

#21440571

—

#21440549

C₄

yes

—

#21440549

C₄

yes

—

C₂²×C₈×C₂₄₁

C₂²

yes

—

C₂×C₄²×C₂₄₁

C₂²

yes

characteristic

C₄⋊C₈×C₂₄₁

—

C₂²×Dic₂₄₁

C₂×C₄

yes

—

C₂×#14515349

—

C₂×#14515349

—

C₄×Dic₂₄₁

D₄

yes

—

C₄×Dic₂₄₁

Q₈

yes

—

C₂²×C₄×C₂₄₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₄₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₄₁

C₂³

yes

characteristic

C₂×C₈×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₄²×C₂₄₁

D₄

yes

—

C₄²×C₂₄₁

Q₈

yes

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

C₄⋊C₄

yes

—

#14515349

—

C₂³×C₂₄₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₄₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₄₁

C₂×Q₈

yes

—

C₂×C₄×C₂₄₁

C₂×Q₈

yes

characteristic

C₈×C₂₄₁

—

C₂²×C₂₄₁

C₂×C₄⋊C₄

yes

—

C₂²×C₂₄₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₄₁

#131

yes

—

C₂²×C₂₄₁

#131

yes

—

C₄×C₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

#127

yes

characteristic

C₄×C₂₄₁

C₄⋊Q₈

yes

characteristic

C₄×C₂₄₁

C₄⋊Q₈

yes

—

Dic₂₄₁

—

C₂×C₂₄₁

#384

yes

characteristic

C₂×C₂₄₁

#424

yes

—

C₂×C₂₄₁

yes

C₂×C₂₄₁

yes

C₂₄₁

yes

characteristic, complemented, Sylow

#1843

—

241

maximal, Sylow

C₂×C₄⋊C₈

—

241

—

C₂×C₄⋊C₈

—

241

—

C₂×C₄⋊C₈

D₂₄₁

yes

characteristic

#376

—

241

—

C₂²×C₈

—

241

—

C₂²×C₈

C₂×D₂₄₁

yes

—

C₂×C₄²

—

241

—

C₂×C₄²

C₂×D₂₄₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

482

—

C₄⋊C₈

—

482

—

#95

—

241

—

#95

—

241

—

C₂²×C₄

—

241

—

C₂²×C₄

C₄×D₂₄₁

yes

characteristic

C₂²×C₄

C₄×D₂₄₁

yes

characteristic

C₂²×C₄

C₂²×D₂₄₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

482

—

C₂×C₈

—

482

—

C₄²

—

241

—

C₄²

—

241

—

C₄²

C₂²⋊D₂₄₁

yes

—

C₄²

Dic₄₈₂

yes

—

C₂³

C₂×C₄×D₂₄₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

482

—

C₂×C₄

—

482

—

C₂×C₄

—

241

—

C₂×C₄

#16838749

yes

—

C₂×C₄

#16838749

yes

—

C₂×C₄

D₄×D₂₄₁

yes

—

C₂×C₄

C₂×C₂²⋊D₂₄₁

yes

characteristic

C₂×C₄

Q₈×D₂₄₁

yes

—

C₂×C₄

C₂×Dic₄₈₂

yes

characteristic

C₈

—

C₈

—

964

—

C₂²

C₄⋊C₄×D₂₄₁

yes

—

C₂²

C₂×#16838749

yes

characteristic

C₂²

#21440648

yes

—

C₂²

#21440650

yes

—

C₄

—

100

C₄

—

101

C₄

—

482

—

102

C₄

#21440638

yes

characteristic

103

C₄

#21440640

yes

characteristic

104

C₄

#21440641

yes

—

105

C₂

#29507586

yes

characteristic

106

C₂

#29507742

yes

—

107

C₂

#29507743

yes

characteristic

108

C₂

#29507745

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₄₁
commutator, socle, prime radical	C₂³×C₂₄₁	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₂₄₁	C₂
cosocle	C₂²×C₄×C₂₄₁	C₂³
hypercenter	C₂×C₄⋊C₈	D₂₄₁
hypocenter	C₂₄₁	#1843
LCS	G ▷ C₂³×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₄₁

commutator, socle, prime radical

C₂³×C₂₄₁

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₂₄₁

C₂

cosocle

C₂²×C₄×C₂₄₁

C₂³

hypercenter

C₂×C₄⋊C₈

D₂₄₁

C₂₄₁

G ▷ C₂³×C₂₄₁ ▷ C₂₄₁

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
54. C₂₄₁	#1843	semidirect

H ≅ G/N

type

54. C₂₄₁

#1843

semidirect

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

subgroup	index
C₂×C₄⋊#14515349	2
C₂×#21440571	2
#29507563	2
C₂×C₄⋊C₈×C₂₄₁	2
#1843	241

subgroup

index

C₂×C₄⋊C₈×C₂₄₁

241

Subgroups — #44507598

Conjugacy classes of subgroups

Complements

Maximal subgroups