Group #27195892 — subgroups

Subgroups — #27195892

Order 13184.

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

normal subgroups only

This group has 208 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×#15692957	C₂	1	1	yes	maximal, characteristic
2	#20267829	C₂	1	1	yes	maximal, characteristic
3	#20267817	C₂	1	2	yes	maximal
4	#20267551	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#13110089	C₂²	1	2	yes	—
7	#15692980	C₂²	1	2	yes	—
8	#15692957	—	2	2	no	—
9	#15692955	C₄	1	2	yes	complemented
10	#15692953	C₄	1	2	yes	complemented
11	Dic₁₀₃⋊C₈	—	2	4	no	—
12	C₂²×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₁₀₃	—	2	2	no	—
16	#13110089	—	2	2	no	—
17	#13110089	—	2	2	no	—
18	C₂×C₁₀₃⋊C₈	—	2	2	no	—
19	C₄⋊Dic₁₀₃	C₂×C₄	1	4	yes	—
20	C₂²⋊Dic₁₀₃	—	2	2	no	—
21	C₄×Dic₁₀₃	—	2	2	no	—
22	C₂²×C₄×C₁₀₃	—	2	1	no	—
23	C₂²×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₀₃	—	2	1	no	—
25	C₂×C₈×C₁₀₃	—	2	1	no	—
26	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₀₃	D₄	1	2	yes	—
29	C₂×C₈×C₁₀₃	D₄	1	2	yes	—
30	C₂×C₈×C₁₀₃	Q₈	1	2	yes	—
31	C₄²×C₁₀₃	—	2	1	no	—
32	C₄²×C₁₀₃	Q₈	1	2	yes	—
33	C₂³×C₁₀₃	#41	1	1	yes	characteristic
34	C₂×C₄×C₁₀₃	—	2	4	no	—
35	C₂×C₄×C₁₀₃	—	2	2	no	—
36	C₂×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₀₃	#41	1	1	yes	characteristic
42	C₂×Dic₁₀₃	—	2	4	no	—
43	C₈×C₁₀₃	—	2	2	no	—
44	C₈×C₁₀₃	C₄⋊C₄	1	2	yes	—
45	C₈×C₁₀₃	C₄⋊C₄	1	2	yes	—
46	C₁₀₃⋊C₈	—	4	2	no	—
47	C₂²×C₁₀₃	—	2	2	no	—
48	C₂²×C₁₀₃	C₄×D₄	1	1	yes	characteristic
49	C₂²×C₁₀₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₁₀₃	#125	1	1	yes	characteristic
51	C₄×C₁₀₃	—	2	4	no	—
52	C₄×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₁₀₃	C₄×Q₈	1	1	yes	characteristic
54	C₄×C₁₀₃	#121	1	1	yes	characteristic
55	C₄×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₁₀₃	—	4	4	no	—
57	C₂×C₁₀₃	—	2	1	no	—
58	C₂×C₁₀₃	—	2	1	no	—
59	C₂×C₁₀₃	#389	1	1	yes	characteristic
60	C₂×C₁₀₃	#443	1	2	yes	—
61	#1945	—	103	1	no	maximal, Sylow
62	C₁₀₃	#1945	1	1	yes	characteristic, complemented, Sylow
63	C₂×#108	—	103	1	no	—
64	#427	—	103	1	no	—
65	#424	—	103	2	no	—
66	C₂×C₄×C₈	D₁₀₃	1	1	yes	characteristic
67	#339	—	103	2	no	—
68	C₂×M₁₆	—	103	2	no	—
69	C₂²×C₈	C₂×D₁₀₃	1	1	yes	characteristic
70	C₂²×C₈	C₂×D₁₀₃	1	1	yes	characteristic
71	#117	—	103	2	no	—
72	C₂×C₄²	C₂×D₁₀₃	1	1	yes	characteristic
73	#108	—	206	2	no	—
74	#107	—	103	2	no	—
75	#106	—	103	2	no	—
76	C₄⋊C₈	—	206	4	no	—
77	C₄×C₈	—	2	2	no	—
78	C₂²×C₄	—	2	1	no	—
79	C₂²×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
80	M₁₆	—	206	2	no	—
81	M₁₆	—	206	2	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	206	2	no	—
85	C₂×C₈	Dic₂₀₆	1	2	yes	—
86	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
87	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
88	C₂×C₈	D₄₁₂	1	2	yes	—
89	C₂×C₈	C₂²⋊D₁₀₃	1	2	yes	—
90	C₄⋊C₄	—	103	4	no	—
91	C₂²⋊C₄	—	206	2	no	—
92	C₄²	—	2	1	no	—
93	C₄²	—	206	2	no	—
94	C₄²	Dic₂₀₆	1	2	yes	—
95	C₂³	#13110105	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	206	4	no	—
99	C₂×C₄	C₂×C₄×D₁₀₃	1	1	yes	characteristic
100	C₂×C₄	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
101	C₂×C₄	C₂×D₄₁₂	1	1	yes	characteristic
102	C₂×C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
103	C₂×C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
104	C₂×C₄	#13110105	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	412	2	no	—
107	C₈	Dic₁₀₃⋊C₄	1	2	yes	—
108	C₈	Dic₁₀₃⋊C₄	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	C₄×D₄₁₂	1	1	yes	characteristic
111	C₂²	#15693000	1	1	yes	characteristic
112	C₂²	#15693013	1	1	yes	characteristic
113	C₄	—	2	4	no	—
114	C₄	—	412	4	no	—
115	C₄	C₂×Dic₁₀₃⋊C₄	1	1	yes	characteristic
116	C₄	C₄×Dic₂₀₆	1	1	yes	characteristic
117	C₄	#15692995	1	1	yes	characteristic
118	C₄	#15693021	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#20267689	1	1	yes	characteristic
122	C₂	#20267909	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15692957

C₂

yes

maximal, characteristic

#20267829

C₂

yes

maximal, characteristic

#20267817

C₂

yes

maximal

#20267551

C₂

yes

maximal

C₂×C₄×C₈×C₁₀₃

C₂

yes

maximal, characteristic

C₂×#13110089

C₂²

yes

—

#15692980

C₂²

yes

—

#15692957

—

#15692955

C₄

yes

complemented

#15692953

C₄

yes

complemented

Dic₁₀₃⋊C₈

—

C₂²×C₈×C₁₀₃

C₂²

yes

characteristic

C₂²×C₈×C₁₀₃

C₂²

yes

characteristic

C₂×C₄²×C₁₀₃

C₂²

yes

characteristic

C₄×C₈×C₁₀₃

—

#13110089

—

#13110089

—

C₂×C₁₀₃⋊C₈

—

C₄⋊Dic₁₀₃

C₂×C₄

yes

—

C₂²⋊Dic₁₀₃

—

C₄×Dic₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

C₂³

yes

characteristic

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

D₄

yes

—

C₂×C₈×C₁₀₃

D₄

yes

—

C₂×C₈×C₁₀₃

Q₈

yes

—

C₄²×C₁₀₃

—

C₄²×C₁₀₃

Q₈

yes

—

C₂³×C₁₀₃

#41

yes

characteristic

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₀₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₀₃

#41

yes

characteristic

C₂×Dic₁₀₃

—

C₈×C₁₀₃

—

C₈×C₁₀₃

C₄⋊C₄

yes

—

C₈×C₁₀₃

C₄⋊C₄

yes

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₄×D₄

yes

characteristic

C₂²×C₁₀₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₀₃

#125

yes

characteristic

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₀₃

C₄×Q₈

yes

characteristic

C₄×C₁₀₃

#121

yes

characteristic

C₄×C₁₀₃

C₄⋊Q₈

yes

characteristic

Dic₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

#389

yes

characteristic

C₂×C₁₀₃

#443

yes

—

#1945

—

103

maximal, Sylow

C₁₀₃

#1945

yes

characteristic, complemented, Sylow

C₂×#108

—

103

—

#427

—

103

—

#424

—

103

—

C₂×C₄×C₈

D₁₀₃

yes

characteristic

#339

—

103

—

C₂×M₁₆

—

103

—

C₂²×C₈

C₂×D₁₀₃

yes

characteristic

C₂²×C₈

C₂×D₁₀₃

yes

characteristic

#117

—

103

—

C₂×C₄²

C₂×D₁₀₃

yes

characteristic

#108

—

206

—

#107

—

103

—

#106

—

103

—

C₄⋊C₈

—

206

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₀₃

yes

characteristic

M₁₆

—

206

—

M₁₆

—

206

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

206

—

C₂×C₈

Dic₂₀₆

yes

—

C₂×C₈

C₄×D₁₀₃

yes

characteristic

C₂×C₈

C₄×D₁₀₃

yes

characteristic

C₂×C₈

D₄₁₂

yes

—

C₂×C₈

C₂²⋊D₁₀₃

yes

—

C₄⋊C₄

—

103

—

C₂²⋊C₄

—

206

—

C₄²

—

C₄²

—

206

—

C₄²

Dic₂₀₆

yes

—

C₂³

#13110105

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

206

—

C₂×C₄

C₂×C₄×D₁₀₃

yes

characteristic

100

C₂×C₄

C₂×C₂²⋊D₁₀₃

yes

characteristic

101

C₂×C₄

C₂×D₄₁₂

yes

characteristic

102

C₂×C₄

C₂×Dic₂₀₆

yes

characteristic

103

C₂×C₄

C₂×Dic₂₀₆

yes

characteristic

104

C₂×C₄

#13110105

yes

characteristic

105

C₈

—

106

C₈

—

412

—

107

C₈

Dic₁₀₃⋊C₄

yes

—

108

C₈

Dic₁₀₃⋊C₄

yes

—

109

C₂²

—

110

C₂²

C₄×D₄₁₂

yes

characteristic

111

C₂²

#15693000

yes

characteristic

112

C₂²

#15693013

yes

characteristic

113

C₄

—

114

C₄

—

412

—

115

C₄

C₂×Dic₁₀₃⋊C₄

yes

characteristic

116

C₄

C₄×Dic₂₀₆

yes

characteristic

117

C₄

#15692995

yes

characteristic

118

C₄

#15693021

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#20267689

yes

characteristic

122

C₂

#20267909

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₀₃
Fitting	C₂×C₄×C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₄×D₄
prime radical	C₂³×C₁₀₃	#41
cosocle	C₂²×C₄×C₁₀₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₀₃
hypocenter	C₁₀₃	#1945
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×D₄₁₂

commutator

C₂×C₄×C₁₀₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₀₃

Fitting

C₂×C₄×C₈×C₁₀₃

C₂

socle

C₂²×C₁₀₃

C₄×D₄

prime radical

C₂³×C₁₀₃

#41

cosocle

C₂²×C₄×C₁₀₃

C₂³

hypercenter

C₂×C₄×C₈

D₁₀₃

hypocenter

C₁₀₃

#1945

LCS

G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. #15692955	C₄	semidirect
10. #15692953	C₄	semidirect
62. C₁₀₃	#1945	semidirect

H ≅ G/N

type

9. #15692955

C₄

semidirect

10. #15692953

C₄

semidirect

62. C₁₀₃

#1945

semidirect

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

subgroup	index
C₂×#15692957	2
#20267829	2
#20267817	2
#20267551	2
C₂×C₄×C₈×C₁₀₃	2
#1945	103

subgroup

index

C₂×C₄×C₈×C₁₀₃

103

Subgroups — #27195892

Conjugacy classes of subgroups

Complements

Maximal subgroups