Group #24905573 — subgroups

Subgroups — #24905573

Order 10624.

136 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14581732	C₂	1	1	yes	maximal, characteristic
2	C₂×#14581726	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₈₃	—	2	1	no	—
5	#14581732	—	2	1	no	—
6	#14581732	C₄	1	2	yes	complemented
7	C₂×C₈₃⋊C₁₆	—	2	1	no	—
8	#14581726	—	2	1	no	—
9	#14581726	C₄	1	2	yes	—
10	C₂×M₁₆×C₈₃	—	2	1	no	—
11	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
12	#108×C₈₃	—	2	1	no	—
13	#108×C₈₃	C₄	1	2	yes	complemented
14	C₂²×Dic₈₃	—	4	1	no	—
15	C₄⋊Dic₈₃	—	2	2	no	—
16	C₄⋊Dic₈₃	—	4	1	no	—
17	C₈₃⋊C₁₆	—	2	2	no	—
18	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
19	M₁₆×C₈₃	—	2	2	no	—
20	M₁₆×C₈₃	—	4	1	no	—
21	C₂×C₈×C₈₃	—	4	1	no	—
22	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₈₃	Q₈	1	1	yes	characteristic
28	C₂³×C₈₃	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₈₃	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₈₃	—	4	2	no	—
36	C₂×Dic₈₃	—	8	2	no	—
37	C₈×C₈₃	—	4	2	no	—
38	C₈×C₈₃	C₄²	1	1	yes	characteristic
39	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₈₃	—	2	1	no	—
43	C₂²×C₈₃	—	2	1	no	—
44	C₂²×C₈₃	#102	1	1	yes	characteristic
45	C₂²×C₈₃	#103	1	1	yes	characteristic
46	C₂²×C₈₃	#106	1	1	yes	characteristic
47	C₄×C₈₃	#95	1	1	yes	characteristic
48	C₄×C₈₃	#102	1	1	yes	characteristic
49	C₄×C₈₃	#103	1	1	yes	characteristic
50	C₄×C₈₃	#107	1	1	yes	characteristic
51	Dic₈₃	—	8	2	no	—
52	C₂×C₈₃	—	2	1	no	—
53	C₂×C₈₃	—	2	1	no	—
54	C₂×C₈₃	#340	1	1	yes	characteristic
55	C₂×C₈₃	#361	1	1	yes	characteristic
56	C₂×C₈₃	#362	1	1	yes	characteristic
57	#1387	—	83	1	no	maximal, Sylow
58	C₈₃	#1387	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₃₂	—	83	1	no	—
60	C₂×#108	D₈₃	1	1	yes	characteristic
61	C₂×#107	—	83	1	no	—
62	C₂×M₁₆	—	2	1	no	—
63	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	166	1	no	—
65	M₃₂	—	83	2	no	—
66	M₃₂	—	166	1	no	—
67	C₂×C₁₆	—	166	1	no	—
68	#108	—	2	1	no	—
69	#108	Dic₈₃	1	2	yes	complemented
70	#107	—	83	2	no	—
71	#107	—	166	1	no	—
72	C₂²×C₄	—	332	1	no	—
73	C₂²×C₄	C₂²⋊D₈₃	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	4	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	Dic₁₆₆	1	1	yes	characteristic
78	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
79	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
80	C₂×C₈	D₃₃₂	1	1	yes	characteristic
81	C₂×C₈	C₂×Dic₈₃	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
83	C₄⋊C₄	—	332	1	no	—
84	C₄⋊C₄	—	166	2	no	—
85	C₁₆	—	166	2	no	—
86	C₂³	#13050577	1	1	yes	characteristic
87	C₂×C₄	—	332	2	no	—
88	C₂×C₄	—	664	2	no	—
89	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
91	C₂×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
92	C₂×C₄	#13050575	1	1	yes	characteristic
93	C₂×C₄	#13050578	1	1	yes	characteristic
94	C₂×C₄	#13050580	1	1	yes	characteristic
95	C₈	—	4	2	no	—
96	C₈	C₄×Dic₈₃	1	1	yes	characteristic
97	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
98	C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
99	C₈	C₄⋊Dic₈₃	1	1	yes	characteristic
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	#14581712	1	1	yes	characteristic
103	C₂²	#14581716	1	1	yes	characteristic
104	C₂²	#14581723	1	1	yes	characteristic
105	C₄	—	664	2	no	—
106	C₄	C₈₃⋊#95	1	1	yes	characteristic
107	C₄	#14581713	1	1	yes	characteristic
108	C₄	#14581715	1	1	yes	characteristic
109	C₄	#14581725	1	1	yes	characteristic
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#19127463	1	1	yes	characteristic
113	C₂	#19127513	1	1	yes	characteristic
114	C₂	#19127516	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14581732

C₂

yes

maximal, characteristic

C₂×#14581726

C₂

yes

maximal, characteristic

C₂×#108×C₈₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₈₃

—

#14581732

—

#14581732

C₄

yes

complemented

C₂×C₈₃⋊C₁₆

—

#14581726

—

#14581726

C₄

yes

—

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

C₂²

yes

characteristic

#108×C₈₃

—

#108×C₈₃

C₄

yes

complemented

C₂²×Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

D₄

yes

characteristic

M₁₆×C₈₃

—

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

Q₈

yes

characteristic

C₂³×C₈₃

SD₁₆

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

D₈

yes

characteristic

C₂×C₄×C₈₃

SD₁₆

yes

characteristic

C₂×C₄×C₈₃

Q₁₆

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

—

C₈×C₈₃

C₄²

yes

characteristic

C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₈×C₈₃

C₄⋊C₄

yes

characteristic

C₈×C₈₃

C₄⋊C₄

yes

characteristic

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₄×C₈₃

yes

C₄×C₈₃

yes

C₄×C₈₃

yes

C₄×C₈₃

yes

Dic₈₃

—

C₂×C₈₃

—

C₂×C₈₃

—

C₂×C₈₃

yes

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

D₈₃

yes

characteristic

C₂×#107

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₈₃

yes

characteristic

C₂×C₄⋊C₄

—

166

—

M₃₂

—

M₃₂

—

166

—

C₂×C₁₆

—

166

—

#108

—

#108

Dic₈₃

yes

complemented

#107

—

#107

—

166

—

C₂²×C₄

—

332

—

C₂²×C₄

C₂²⋊D₈₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₆₆

yes

characteristic

C₂×C₈

C₄×D₈₃

yes

characteristic

C₂×C₈

C₄×D₈₃

yes

characteristic

C₂×C₈

D₃₃₂

yes

characteristic

C₂×C₈

C₂×Dic₈₃

yes

characteristic

C₂×C₈

C₂²⋊D₈₃

yes

characteristic

C₄⋊C₄

—

332

—

C₄⋊C₄

—

166

—

C₁₆

—

166

—

C₂³

#13050577

yes

characteristic

C₂×C₄

—

332

—

C₂×C₄

—

664

—

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₈₃

yes

characteristic

C₂×C₄

Dic₈₃⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

C₄×Dic₈₃

yes

characteristic

C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

C₈

Dic₈₃⋊C₄

yes

characteristic

C₈

C₄⋊Dic₈₃

yes

characteristic

100

C₂²

—

101

C₂²

—

102

C₂²

#14581712

yes

characteristic

103

C₂²

#14581716

yes

characteristic

104

C₂²

#14581723

yes

characteristic

105

C₄

—

664

—

106

C₄

C₈₃⋊#95

yes

characteristic

107

C₄

#14581713

yes

characteristic

108

C₄

#14581715

yes

characteristic

109

C₄

#14581725

yes

characteristic

110

C₂

—

111

C₂

—

112

C₂

#19127463

yes

characteristic

113

C₂

#19127513

yes

characteristic

114

C₂

#19127516

yes

characteristic

	subgroup	G/H
center	C₂²	#14581712
commutator	C₈×C₈₃	C₄²
Frattini	C₂²×C₈	C₂×D₈₃
Fitting	C₂×#108×C₈₃	C₂
socle	C₂²×C₈₃	#102
prime radical	C₂³×C₈₃	SD₁₆
cosocle	C₂²×C₈×C₈₃	C₂²
hypercenter	C₂×#108	D₈₃
hypocenter	C₈₃	#1387
LCS	G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₂²

#14581712

commutator

C₈×C₈₃

C₄²

Frattini

C₂²×C₈

C₂×D₈₃

Fitting

C₂×#108×C₈₃

C₂

socle

C₂²×C₈₃

#102

prime radical

C₂³×C₈₃

SD₁₆

cosocle

C₂²×C₈×C₈₃

C₂²

D₈₃

C₈₃

G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
6. #14581732	C₄	semidirect
13. #108×C₈₃	C₄	semidirect
58. C₈₃	#1387	semidirect
69. #108	Dic₈₃	semidirect

H ≅ G/N

type

6. #14581732

C₄

semidirect

13. #108×C₈₃

C₄

semidirect

58. C₈₃

#1387

semidirect

69. #108

Dic₈₃

semidirect

Subgroups — #24905573

Conjugacy classes of subgroups

Complements