Group #25096985 — subgroups

Subgroups — #25096985

Order 11008.

1118 conjugacy classes of subgroups; only the 571 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 571 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×#14582923	C₂	1	6	yes	maximal
2	#19134749	C₂	1	8	yes	maximal, complemented
3	C₂×C₄₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10621877	C₂²	1	4	yes	—
5	#14582923	—	2	24	no	—
6	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	24	yes	—
7	C₂²×C₄²×C₄₃	C₂²	1	3	yes	—
8	C₄₃×#376	C₄	1	4	yes	—
9	C₄₃×#376	C₂²	1	4	yes	—
10	C₂×#95×C₄₃	C₄	1	4	yes	—
11	C₂×#10621877	—	2	24	no	—
12	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
13	C₄⋊(C₄₃⋊C₈)	—	2	48	no	—
14	C₂³×C₄×C₄₃	C₂×C₄	1	6	yes	—
15	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₄₃	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₄₃	D₄	1	12	yes	—
18	C₂×C₄²×C₄₃	Q₈	1	12	yes	—
19	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
20	#95×C₄₃	C₂×C₄	1	16	yes	—
21	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	—	4	12	no	—
23	C₂²×C₄×C₄₃	C₄⋊C₄	1	24	yes	—
24	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
25	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
27	C₂²×C₄×C₄₃	C₂×Q₈	1	6	yes	—
28	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
29	C₄²×C₄₃	C₄⋊C₄	1	24	yes	—
30	C₄²×C₄₃	C₂×D₄	1	12	yes	—
31	C₄²×C₄₃	C₂×Q₈	1	12	yes	—
32	#10621877	—	4	16	no	—
33	C₂×C₄₃⋊C₈	—	2	24	no	—
34	C₂³×C₄₃	—	2	4	no	—
35	C₂³×C₄₃	C₂×C₄⋊C₄	1	6	yes	—
36	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	24	no	—
38	C₂×C₄×C₄₃	—	4	24	no	—
39	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	24	yes	—
40	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	6	yes	—
41	C₂×C₄×C₄₃	#127	1	4	yes	—
42	C₂×C₄×C₄₃	C₄⋊Q₈	1	12	yes	—
43	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
44	C₂×C₄×C₄₃	C₂²×Q₈	1	3	yes	—
45	C₄₃⋊C₈	—	4	8	no	—
46	#20792	—	43	1	no	maximal, Sylow
47	C₂²×C₄₃	—	2	12	no	—
48	C₂²×C₄₃	#384	1	4	yes	—
49	C₂²×C₄₃	C₂²×C₄⋊C₄	1	3	yes	—
50	C₂²×C₄₃	#568	1	4	yes	—
51	C₄×C₄₃	—	2	24	no	—
52	C₄×C₄₃	#384	1	4	yes	—
53	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
54	C₄×C₄₃	C₂×C₄⋊Q₈	1	3	yes	—
55	C₂×#423	—	43	6	no	—
56	C₂×#376	D₄₃	1	1	yes	characteristic
57	#1843	—	43	8	no	—
58	C₂×C₄₃	—	2	4	no	—
59	C₂×C₄₃	C₂×#384	1	1	yes	characteristic
60	C₂×C₄₃	#2905	1	6	yes	—
61	C₂²×M₁₆	—	43	4	no	—
62	C₂²×C₄²	C₂×D₄₃	1	3	yes	—
63	#423	—	86	24	no	—
64	C₂×C₄⋊C₈	—	43	24	no	—
65	#376	Dic₄₃	1	4	yes	—
66	#376	C₂×D₄₃	1	4	yes	—
67	C₂×#95	Dic₄₃	1	4	yes	—
68	C₄₃	#20792	1	1	yes	characteristic, complemented, Sylow
69	C₂³×C₄	C₂×Dic₄₃	1	6	yes	—
70	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
71	C₂×M₁₆	—	86	24	no	—
72	C₂²×C₈	—	43	8	no	—
73	C₂×C₄²	Dic₈₆	1	12	yes	—
74	C₂×C₄²	D₁₇₂	1	12	yes	—
75	C₂×C₄²	C₂×Dic₄₃	1	6	yes	—
76	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
77	C₄⋊C₈	—	86	48	no	—
78	#95	C₂×Dic₄₃	1	16	yes	—
79	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
80	C₂²×C₄	—	4	12	no	—
81	C₂²×C₄	C₄⋊Dic₄₃	1	24	yes	—
82	C₂²×C₄	C₂×Dic₈₆	1	6	yes	—
83	C₂²×C₄	C₂×D₁₇₂	1	6	yes	—
84	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
85	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
86	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
87	M₁₆	—	172	16	no	—
88	C₂×C₈	—	86	24	no	—
89	C₄²	C₄⋊Dic₄₃	1	24	yes	—
90	C₄²	C₂×Dic₈₆	1	12	yes	—
91	C₄²	C₂×D₁₇₂	1	12	yes	—
92	C₂³	—	2	4	no	—
93	C₂³	C₂×C₄⋊Dic₄₃	1	6	yes	—
94	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
95	C₂×C₄	—	2	24	no	—
96	C₂×C₄	—	4	24	no	—
97	C₂×C₄	C₂×C₄⋊Dic₄₃	1	24	yes	—
98	C₂×C₄	C₂×C₄⋊Dic₄₃	1	6	yes	—
99	C₂×C₄	#13063322	1	4	yes	—
100	C₂×C₄	#13063325	1	12	yes	—
101	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
102	C₂×C₄	C₂²×Dic₈₆	1	3	yes	—
103	C₈	—	172	8	no	—
104	C₂²	—	2	12	no	—
105	C₂²	#14582769	1	4	yes	—
106	C₂²	C₂²×C₄⋊Dic₄₃	1	3	yes	—
107	C₂²	#14583666	1	4	yes	—
108	C₄	—	2	24	no	—
109	C₄	#14582769	1	4	yes	—
110	C₄	C₂×#13063322	1	1	yes	characteristic
111	C₄	C₂×#13063325	1	3	yes	—
112	C₂	—	2	4	no	—
113	C₂	C₂×#14582769	1	1	yes	characteristic
114	C₂	#19143159	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582923

C₂

yes

maximal

#19134749

C₂

yes

maximal, complemented

C₂×C₄₃×#376

C₂

yes

maximal, characteristic

C₂²×#10621877

C₂²

yes

—

#14582923

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂²×C₄²×C₄₃

C₂²

yes

—

C₄₃×#376

C₄

yes

—

C₄₃×#376

C₂²

yes

—

C₂×#95×C₄₃

C₄

yes

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

C₂³

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂×C₄

yes

—

C₂³×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

Q₈

yes

—

C₂×C₄²×C₄₃

C₂³

yes

—

#95×C₄₃

C₂×C₄

yes

—

C₂⁴×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×Q₈

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₄²×C₄₃

C₄⋊C₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×C₄⋊C₄

yes

—

C₂³×C₄₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

#127

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²×D₄

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₄₃⋊C₈

—

#20792

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#384

yes

—

C₂²×C₄₃

C₂²×C₄⋊C₄

yes

—

C₂²×C₄₃

#568

yes

—

C₄×C₄₃

—

C₄×C₄₃

#384

yes

—

C₄×C₄₃

C₂×#127

yes

characteristic

C₄×C₄₃

C₂×C₄⋊Q₈

yes

—

C₂×#423

—

C₂×#376

D₄₃

yes

characteristic

#1843

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#384

yes

characteristic

C₂×C₄₃

#2905

yes

—

C₂²×M₁₆

—

C₂²×C₄²

C₂×D₄₃

yes

—

#423

—

C₂×C₄⋊C₈

—

#376

Dic₄₃

yes

—

#376

C₂×D₄₃

yes

—

C₂×#95

Dic₄₃

yes

—

C₄₃

#20792

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×Dic₄₃

yes

—

C₂³×C₄

C₂²×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

Dic₈₆

yes

—

C₂×C₄²

D₁₇₂

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

—

C₄⋊C₈

—

#95

C₂×Dic₄₃

yes

—

C₂⁴

C₂²×Dic₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄⋊Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₈₆

yes

—

C₂²×C₄

C₂×D₁₇₂

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂²×C₄

C₂³×D₄₃

yes

characteristic

M₁₆

—

172

—

C₂×C₈

—

C₄²

C₄⋊Dic₄₃

yes

—

C₄²

C₂×Dic₈₆

yes

—

C₄²

C₂×D₁₇₂

yes

—

C₂³

—

C₂³

C₂×C₄⋊Dic₄₃

yes

—

C₂³

C₂³×Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

—

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

—

C₂×C₄

#13063322

yes

—

100

C₂×C₄

#13063325

yes

—

101

C₂×C₄

C₂²×D₁₇₂

yes

—

102

C₂×C₄

C₂²×Dic₈₆

yes

—

103

C₈

—

172

—

104

C₂²

—

105

C₂²

#14582769

yes

—

106

C₂²

C₂²×C₄⋊Dic₄₃

yes

—

107

C₂²

#14583666

yes

—

108

C₄

—

109

C₄

#14582769

yes

—

110

C₄

C₂×#13063322

yes

characteristic

111

C₄

C₂×#13063325

yes

—

112

C₂

—

113

C₂

C₂×#14582769

yes

characteristic

114

C₂

#19143159

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₂×C₄₃×#376	C₂
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#376	D₄₃
hypocenter	C₄₃	#20792
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂³×C₄

Fitting

C₂×C₄₃×#376

C₂

prime radical

C₂⁴×C₄₃

C₂²×C₄

cosocle

C₂²×C₄×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ C₂×#376

N	H ≅ G/N	type
2. #19134749	C₂	semidirect
68. C₄₃	#20792	semidirect

H ≅ G/N

type

2. #19134749

C₂

semidirect

68. C₄₃

#20792

semidirect

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

subgroup	index
C₂×#14582923	2
#19134749	2
C₂×C₄₃×#376	2
#20792	43

subgroup

index

C₂×#14582923

#19134749

C₂×C₄₃×#376

#20792

Subgroups — #25096985

Conjugacy classes of subgroups

Complements

Maximal subgroups