Group #44507563 — subgroups

Subgroups — #44507563

Order 30848.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×#21440571	C₂	1	2	yes	maximal
2	#29507563	C₂	1	1	yes	maximal, characteristic
3	#29507472	C₂	1	1	yes	maximal, characteristic
4	#29507471	C₂	1	2	yes	maximal
5	#336×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#14515349	C₂²	1	2	yes	—
7	C₂×C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
9	#21440571	—	2	4	no	—
10	#21440549	C₄	1	2	yes	—
11	#21440549	C₄	1	2	yes	—
12	C₂²×C₈×C₂₄₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
14	C₂²×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₂₄₁	C₂×C₄	1	2	yes	—
17	C₂×#14515349	—	2	2	no	—
18	C₂×#14515349	—	2	2	no	—
19	C₂×#14515349	—	2	2	no	—
20	C₄×Dic₂₄₁	—	2	2	no	—
21	C₄×Dic₂₄₁	D₄	1	2	yes	—
22	C₄×Dic₂₄₁	Q₈	1	2	yes	—
23	C₂²×C₄×C₂₄₁	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₂₄₁	—	2	2	no	—
26	C₂×C₈×C₂₄₁	—	2	2	no	—
27	C₂×C₈×C₂₄₁	—	2	2	no	—
28	C₄²×C₂₄₁	—	2	2	no	—
29	C₂×Dic₂₄₁	—	2	2	no	—
30	C₂×Dic₂₄₁	—	2	2	no	—
31	C₂×Dic₂₄₁	—	2	1	no	—
32	C₂×Dic₂₄₁	—	2	1	no	—
33	C₂×Dic₂₄₁	—	2	2	no	—
34	C₂×Dic₂₄₁	—	2	2	no	—
35	C₂×Dic₂₄₁	C₄⋊C₄	1	4	yes	—
36	#14515349	—	4	2	no	—
37	C₂³×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₄₁	—	2	2	no	—
39	C₂×C₄×C₂₄₁	—	2	2	no	—
40	C₂×C₄×C₂₄₁	—	2	2	no	—
41	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₂₄₁	#41	1	2	yes	—
44	C₂×C₄×C₂₄₁	#41	1	2	yes	—
45	C₈×C₂₄₁	—	4	2	no	—
46	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₂₄₁	#117	1	1	yes	characteristic
48	C₂²×C₂₄₁	#117	1	1	yes	characteristic
49	C₂²×C₂₄₁	#131	1	2	yes	—
50	C₂²×C₂₄₁	#131	1	2	yes	—
51	C₄×C₂₄₁	—	4	2	no	—
52	C₄×C₂₄₁	#124	1	2	yes	—
53	C₄×C₂₄₁	#125	1	2	yes	—
54	Dic₂₄₁	—	2	4	no	—
55	Dic₂₄₁	—	4	1	no	—
56	Dic₂₄₁	—	4	1	no	—
57	C₂×C₂₄₁	#382	1	1	yes	characteristic
58	C₂×C₂₄₁	#424	1	2	yes	—
59	C₂×C₂₄₁	#433	1	2	yes	—
60	C₂×C₂₄₁	#433	1	1	yes	characteristic
61	C₂×C₂₄₁	#433	1	1	yes	characteristic
62	C₂₄₁	#1832	1	1	yes	characteristic, complemented, Sylow
63	#1832	—	241	1	no	maximal, Sylow
64	C₂×C₄⋊C₈	—	241	2	no	—
65	#376	—	241	1	no	—
66	#336	—	241	2	no	—
67	#336	—	241	1	no	—
68	#336	D₂₄₁	1	1	yes	characteristic
69	C₂²×C₈	—	241	2	no	—
70	C₂²×C₈	C₂×D₂₄₁	1	2	yes	—
71	C₂×C₄²	—	241	1	no	—
72	C₂×C₄²	—	241	1	no	—
73	C₂×C₄²	C₂×D₂₄₁	1	1	yes	characteristic
74	C₄⋊C₈	—	482	4	no	—
75	#95	—	241	2	no	—
76	#95	—	241	2	no	—
77	C₂²×C₄	—	241	1	no	—
78	C₂²×C₄	—	241	1	no	—
79	C₂²×C₄	—	241	2	no	—
80	C₂²×C₄	C₄×D₂₄₁	1	2	yes	—
81	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	482	2	no	—
86	C₂×C₈	—	482	2	no	—
87	C₂×C₈	—	482	2	no	—
88	C₄²	—	2	2	no	—
89	C₄²	—	482	2	no	—
90	C₄²	—	241	2	no	—
91	C₄²	—	241	2	no	—
92	C₂³	C₂×C₄×D₂₄₁	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	482	1	no	—
97	C₂×C₄	—	482	1	no	—
98	C₂×C₄	—	482	2	no	—
99	C₂×C₄	—	482	2	no	—
100	C₂×C₄	—	482	2	no	—
101	C₂×C₄	—	482	2	no	—
102	C₂×C₄	—	241	4	no	—
103	C₂×C₄	D₄×D₂₄₁	1	1	yes	characteristic
104	C₂×C₄	Q₈×D₂₄₁	1	1	yes	characteristic
105	C₂×C₄	#16838769	1	2	yes	—
106	C₂×C₄	#16838770	1	2	yes	—
107	C₈	—	4	2	no	—
108	C₈	—	964	2	no	—
109	C₂²	C₄⋊C₄×D₂₄₁	1	1	yes	characteristic
110	C₂²	#21440598	1	1	yes	characteristic
111	C₂²	#21440599	1	1	yes	characteristic
112	C₂²	#21440648	1	2	yes	—
113	C₂²	#21440650	1	2	yes	—
114	C₄	—	4	2	no	—
115	C₄	—	964	1	no	—
116	C₄	—	964	1	no	—
117	C₄	—	482	4	no	—
118	C₄	#21440628	1	2	yes	—
119	C₄	#21440632	1	2	yes	—
120	C₂	#29507581	1	1	yes	characteristic
121	C₂	#29507742	1	2	yes	—
122	C₂	#29507775	1	2	yes	—
123	C₂	#29507776	1	1	yes	characteristic
124	C₂	#29507779	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#21440571

C₂

yes

maximal

#29507563

C₂

yes

maximal, characteristic

#29507472

C₂

yes

maximal, characteristic

#29507471

C₂

yes

maximal

#336×C₂₄₁

C₂

yes

maximal, characteristic

C₂²×#14515349

C₂²

yes

—

C₂×C₄×Dic₂₄₁

C₂²

yes

characteristic

C₂×C₄×Dic₂₄₁

C₂²

yes

characteristic

#21440571

—

#21440549

C₄

yes

—

#21440549

C₄

yes

—

C₂²×C₈×C₂₄₁

C₂²

yes

—

C₂×C₄²×C₂₄₁

C₂²

yes

characteristic

C₂²×Dic₂₄₁

C₂×C₄

yes

characteristic

C₂²×Dic₂₄₁

C₂×C₄

yes

characteristic

C₂²×Dic₂₄₁

C₂×C₄

yes

—

C₂×#14515349

—

C₂×#14515349

—

C₂×#14515349

—

C₄×Dic₂₄₁

—

C₄×Dic₂₄₁

D₄

yes

—

C₄×Dic₂₄₁

Q₈

yes

—

C₂²×C₄×C₂₄₁

C₂×C₄

yes

—

C₂²×C₄×C₂₄₁

C₂³

yes

characteristic

C₂×C₈×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₄²×C₂₄₁

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

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

—

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

C₂²×C₂₄₁

yes

C₂²×C₂₄₁

yes

C₂²×C₂₄₁

yes

—

C₂²×C₂₄₁

#131

yes

—

C₄×C₂₄₁

—

C₄×C₂₄₁

#124

yes

—

C₄×C₂₄₁

#125

yes

—

Dic₂₄₁

—

Dic₂₄₁

—

Dic₂₄₁

—

C₂×C₂₄₁

#382

yes

characteristic

C₂×C₂₄₁

#424

yes

—

C₂×C₂₄₁

#433

yes

—

C₂×C₂₄₁

yes

C₂×C₂₄₁

yes

C₂₄₁

yes

characteristic, complemented, Sylow

#1832

—

241

maximal, Sylow

C₂×C₄⋊C₈

—

241

—

#376

—

241

—

#336

—

241

—

#336

—

241

—

#336

D₂₄₁

yes

characteristic

C₂²×C₈

—

241

—

C₂²×C₈

C₂×D₂₄₁

yes

—

C₂×C₄²

—

241

—

C₂×C₄²

—

241

—

C₂×C₄²

C₂×D₂₄₁

yes

characteristic

C₄⋊C₈

—

482

—

#95

—

241

—

#95

—

241

—

C₂²×C₄

—

241

—

C₂²×C₄

—

241

—

C₂²×C₄

—

241

—

C₂²×C₄

C₄×D₂₄₁

yes

—

C₂²×C₄

C₂²×D₂₄₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

482

—

C₂×C₈

—

482

—

C₂×C₈

—

482

—

C₄²

—

C₄²

—

482

—

C₄²

—

241

—

C₄²

—

241

—

C₂³

C₂×C₄×D₂₄₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

482

—

C₂×C₄

—

482

—

C₂×C₄

—

482

—

C₂×C₄

—

482

—

100

C₂×C₄

—

482

—

101

C₂×C₄

—

482

—

102

C₂×C₄

—

241

—

103

C₂×C₄

D₄×D₂₄₁

yes

characteristic

104

C₂×C₄

Q₈×D₂₄₁

yes

characteristic

105

C₂×C₄

#16838769

yes

—

106

C₂×C₄

#16838770

yes

—

107

C₈

—

108

C₈

—

964

—

109

C₂²

C₄⋊C₄×D₂₄₁

yes

characteristic

110

C₂²

#21440598

yes

characteristic

111

C₂²

#21440599

yes

characteristic

112

C₂²

#21440648

yes

—

113

C₂²

#21440650

yes

—

114

C₄

—

115

C₄

—

964

—

116

C₄

—

964

—

117

C₄

—

482

—

118

C₄

#21440628

yes

—

119

C₄

#21440632

yes

—

120

C₂

#29507581

yes

characteristic

121

C₂

#29507742

yes

—

122

C₂

#29507775

yes

—

123

C₂

#29507776

yes

characteristic

124

C₂

#29507779

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₄₁
commutator, socle, prime radical	C₂³×C₂₄₁	C₂²×C₄
Fitting	#336×C₂₄₁	C₂
cosocle	C₂²×C₄×C₂₄₁	C₂³
hypercenter	#336	D₂₄₁
hypocenter	C₂₄₁	#1832
LCS	G ▷ C₂³×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₄₁

commutator, socle, prime radical

C₂³×C₂₄₁

C₂²×C₄

Fitting

#336×C₂₄₁

C₂

cosocle

C₂²×C₄×C₂₄₁

C₂³

D₂₄₁

C₂₄₁

G ▷ C₂³×C₂₄₁ ▷ C₂₄₁

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
62. C₂₄₁	#1832	semidirect

H ≅ G/N

type

62. C₂₄₁

#1832

semidirect

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

subgroup	index
C₂×#21440571	2
#29507563	2
#29507472	2
#29507471	2
#336×C₂₄₁	2
#1832	241

subgroup

index

#336×C₂₄₁

241

Subgroups — #44507563

Conjugacy classes of subgroups

Complements

Maximal subgroups