Group #44507564 — subgroups

Subgroups — #44507564

Order 30848.

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

normal subgroups only

This group has 216 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×C₄⋊#14515349	C₂	1	1	yes	maximal, characteristic
2	#29507563	C₂	1	1	yes	maximal, characteristic
3	#29507471	C₂	1	4	yes	maximal
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	#21440549	C₄	1	2	yes	—
9	#21440549	C₄	1	2	yes	—
10	C₂²×C₈×C₂₄₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₂₄₁	—	2	2	no	—
13	C₂²×Dic₂₄₁	C₂×C₄	1	4	yes	—
14	C₂×#14515349	—	2	2	no	—
15	C₂×#14515349	—	2	4	no	—
16	C₄×Dic₂₄₁	—	2	2	no	—
17	C₄×Dic₂₄₁	—	2	2	no	—
18	C₂²×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₂₄₁	—	2	2	no	—
22	C₂×C₈×C₂₄₁	—	2	4	no	—
23	C₄²×C₂₄₁	D₄	1	2	yes	—
24	C₄²×C₂₄₁	Q₈	1	2	yes	—
25	C₂×Dic₂₄₁	—	2	4	no	—
26	C₂×Dic₂₄₁	—	2	4	no	—
27	C₂×Dic₂₄₁	—	2	4	no	—
28	#14515349	—	4	2	no	—
29	C₂³×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₄₁	—	2	2	no	—
31	C₂×C₄×C₂₄₁	—	2	2	no	—
32	C₂×C₄×C₂₄₁	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₄₁	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₄₁	C₂×D₄	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	C₈×C₂₄₁	—	4	2	no	—
39	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₂₄₁	#117	1	2	yes	—
41	C₂²×C₂₄₁	#131	1	2	yes	—
42	C₂²×C₂₄₁	#131	1	2	yes	—
43	C₄×C₂₄₁	—	2	2	no	—
44	C₄×C₂₄₁	—	2	2	no	—
45	C₄×C₂₄₁	#124	1	1	yes	characteristic
46	C₄×C₂₄₁	#124	1	1	yes	characteristic
47	C₄×C₂₄₁	#125	1	2	yes	—
48	Dic₂₄₁	—	4	4	no	—
49	C₂×C₂₄₁	#382	1	1	yes	characteristic
50	C₂×C₂₄₁	#424	1	1	yes	characteristic
51	C₂×C₂₄₁	#424	1	1	yes	characteristic
52	C₂×C₂₄₁	#433	1	4	yes	—
53	C₂₄₁	#1832	1	1	yes	characteristic, complemented, Sylow
54	#1832	—	241	1	no	maximal, Sylow
55	C₂×C₄⋊C₈	—	241	1	no	—
56	C₂×C₄⋊C₈	D₂₄₁	1	1	yes	characteristic
57	#376	—	241	1	no	—
58	#336	—	241	4	no	—
59	C₂²×C₈	—	241	2	no	—
60	C₂²×C₈	C₂×D₂₄₁	1	2	yes	—
61	C₂×C₄²	—	241	2	no	—
62	C₂×C₄²	C₂×D₂₄₁	1	1	yes	characteristic
63	C₄⋊C₈	—	2	2	no	—
64	C₄⋊C₈	—	482	2	no	—
65	#95	—	241	2	no	—
66	#95	—	241	2	no	—
67	C₂²×C₄	—	241	4	no	—
68	C₂²×C₄	C₄×D₂₄₁	1	1	yes	characteristic
69	C₂²×C₄	C₄×D₂₄₁	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	4	no	—
73	C₂×C₈	—	482	2	no	—
74	C₂×C₈	—	482	4	no	—
75	C₄²	—	482	2	no	—
76	C₄²	—	482	2	no	—
77	C₄²	C₂²⋊D₂₄₁	1	2	yes	—
78	C₄²	Dic₄₈₂	1	2	yes	—
79	C₂³	C₂×C₄×D₂₄₁	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	482	4	no	—
83	C₂×C₄	—	482	4	no	—
84	C₂×C₄	—	482	4	no	—
85	C₂×C₄	#16838749	1	2	yes	—
86	C₂×C₄	#16838749	1	2	yes	—
87	C₂×C₄	C₂×C₂²⋊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	—	4	2	no	—
92	C₈	—	964	2	no	—
93	C₂²	C₂×#16838749	1	1	yes	characteristic
94	C₂²	#21440600	1	2	yes	—
95	C₂²	#21440648	1	2	yes	—
96	C₂²	#21440650	1	2	yes	—
97	C₄	—	2	2	no	—
98	C₄	—	2	2	no	—
99	C₄	—	964	4	no	—
100	C₄	#21440629	1	1	yes	characteristic
101	C₄	#21440631	1	1	yes	characteristic
102	C₄	#21440633	1	2	yes	—
103	C₂	#29507582	1	1	yes	characteristic
104	C₂	#29507743	1	1	yes	characteristic
105	C₂	#29507745	1	1	yes	characteristic
106	C₂	#29507777	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14515349

C₂

yes

maximal, characteristic

#29507563

C₂

yes

maximal, characteristic

#29507471

C₂

yes

maximal

C₂×C₄⋊C₈×C₂₄₁

C₂

yes

maximal, characteristic

C₂²×#14515349

C₂²

yes

—

C₂×C₄×Dic₂₄₁

C₂²

yes

—

C₄⋊#14515349

—

#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

—

C₄×Dic₂₄₁

—

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

—

#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

characteristic

C₂×C₄×C₂₄₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₄₁

#41

yes

—

C₂×C₄×C₂₄₁

#41

yes

—

C₈×C₂₄₁

—

C₂²×C₂₄₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₄₁

#117

yes

—

C₂²×C₂₄₁

#131

yes

—

C₂²×C₂₄₁

#131

yes

—

C₄×C₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

yes

C₄×C₂₄₁

yes

C₄×C₂₄₁

yes

—

Dic₂₄₁

—

C₂×C₂₄₁

yes

C₂×C₂₄₁

yes

C₂×C₂₄₁

yes

C₂×C₂₄₁

yes

—

C₂₄₁

#1832

yes

characteristic, complemented, Sylow

#1832

—

241

maximal, Sylow

C₂×C₄⋊C₈

—

241

—

C₂×C₄⋊C₈

D₂₄₁

yes

characteristic

#376

—

241

—

#336

—

241

—

C₂²×C₈

—

241

—

C₂²×C₈

C₂×D₂₄₁

yes

—

C₂×C₄²

—

241

—

C₂×C₄²

C₂×D₂₄₁

yes

characteristic

C₄⋊C₈

—

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

—

482

—

C₄²

—

482

—

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

—

482

—

C₂×C₄

#16838749

yes

—

C₂×C₄

#16838749

yes

—

C₂×C₄

C₂×C₂²⋊D₂₄₁

yes

characteristic

C₂×C₄

C₂×Dic₄₈₂

yes

characteristic

C₂×C₄

#16838769

yes

—

C₂×C₄

#16838771

yes

—

C₈

—

C₈

—

964

—

C₂²

C₂×#16838749

yes

characteristic

C₂²

#21440600

yes

—

C₂²

#21440648

yes

—

C₂²

#21440650

yes

—

C₄

—

C₄

—

C₄

—

964

—

100

C₄

#21440629

yes

characteristic

101

C₄

#21440631

yes

characteristic

102

C₄

#21440633

yes

—

103

C₂

#29507582

yes

characteristic

104

C₂

#29507743

yes

characteristic

105

C₂

#29507745

yes

characteristic

106

C₂

#29507777

yes

—

	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	#1832
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
53. C₂₄₁	#1832	semidirect

H ≅ G/N

type

53. C₂₄₁

#1832

semidirect

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

subgroup	index
C₂×C₄⋊#14515349	2
#29507563	2
#29507471	2
C₂×C₄⋊C₈×C₂₄₁	2
#1832	241

subgroup

index

C₂×C₄⋊C₈×C₂₄₁

241

Subgroups — #44507564

Conjugacy classes of subgroups

Complements

Maximal subgroups