Group #27193237 — subgroups

Subgroups — #27193237

Order 13184.

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

normal subgroups only

This group has 128 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	C₂²×C₁₀₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#15692957	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13110089	—	2	1	no	—
5	C₂×C₁₀₃⋊C₁₆	—	2	1	no	—
6	C₂×C₁₀₃⋊C₁₆	—	2	1	no	—
7	C₂×C₁₀₃⋊C₁₆	C₄	1	2	yes	—
8	#15692957	—	2	1	no	—
9	#15692957	C₄	1	2	yes	—
10	C₂×M₁₆×C₁₀₃	—	2	1	no	—
11	C₂²×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	#108×C₁₀₃	—	2	1	no	—
13	#108×C₁₀₃	C₄	1	2	yes	—
14	#13110089	—	2	2	no	—
15	#13110089	—	4	1	no	—
16	C₂×C₁₀₃⋊C₈	—	4	1	no	—
17	C₁₀₃⋊C₁₆	—	2	2	no	—
18	C₂²×C₄×C₁₀₃	D₄	1	1	yes	characteristic
19	M₁₆×C₁₀₃	—	2	2	no	—
20	M₁₆×C₁₀₃	—	4	1	no	—
21	C₂×C₈×C₁₀₃	—	4	1	no	—
22	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₁₀₃	Q₈	1	1	yes	characteristic
28	C₂³×C₁₀₃	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
35	C₈×C₁₀₃	—	4	2	no	—
36	C₈×C₁₀₃	C₄²	1	1	yes	characteristic
37	C₈×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₈×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
40	C₁₀₃⋊C₈	—	4	2	no	—
41	C₂²×C₁₀₃	—	2	2	no	—
42	C₂²×C₁₀₃	#103	1	1	yes	characteristic
43	C₂²×C₁₀₃	#103	1	1	yes	characteristic
44	C₂²×C₁₀₃	#107	1	1	yes	characteristic
45	C₄×C₁₀₃	#95	1	1	yes	characteristic
46	C₄×C₁₀₃	#102	1	1	yes	characteristic
47	C₄×C₁₀₃	#102	1	1	yes	characteristic
48	C₄×C₁₀₃	#106	1	1	yes	characteristic
49	C₂×C₁₀₃	—	2	1	no	—
50	C₂×C₁₀₃	—	2	1	no	—
51	C₂×C₁₀₃	#340	1	1	yes	characteristic
52	C₂×C₁₀₃	#368	1	2	yes	—
53	#1381	—	103	1	no	maximal, Sylow
54	C₁₀₃	#1381	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₁₆	—	103	1	no	—
56	C₂×#108	—	103	1	no	—
57	C₂×#108	D₁₀₃	1	1	yes	characteristic
58	C₂×M₁₆	—	2	1	no	—
59	C₂×M₁₆	—	206	1	no	—
60	C₂²×C₈	C₂×D₁₀₃	1	1	yes	characteristic
61	C₂×C₁₆	—	103	2	no	—
62	C₂×C₁₆	—	206	1	no	—
63	C₂×C₁₆	—	206	1	no	—
64	#108	—	2	1	no	—
65	#108	—	103	2	no	—
66	#108	—	206	1	no	—
67	#108	Dic₁₀₃	1	2	yes	—
68	C₂²×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	4	1	no	—
71	M₁₆	—	412	1	no	—
72	M₁₆	—	206	2	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	—	412	1	no	—
75	C₂×C₈	Dic₂₀₆	1	1	yes	characteristic
76	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
77	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
78	C₂×C₈	D₄₁₂	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₁₀₃	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
81	C₁₆	—	206	2	no	—
82	C₂³	#13110095	1	1	yes	characteristic
83	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
84	C₂×C₄	C₂²⋊Dic₁₀₃	1	1	yes	characteristic
85	C₂×C₄	Dic₁₀₃⋊C₄	1	1	yes	characteristic
86	C₂×C₄	#13110090	1	1	yes	characteristic
87	C₂×C₄	#13110092	1	1	yes	characteristic
88	C₂×C₄	#13110093	1	1	yes	characteristic
89	C₈	—	4	2	no	—
90	C₈	—	412	2	no	—
91	C₈	C₄×Dic₁₀₃	1	1	yes	characteristic
92	C₈	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
93	C₈	Dic₁₀₃⋊C₄	1	1	yes	characteristic
94	C₈	C₄⋊Dic₁₀₃	1	1	yes	characteristic
95	C₂²	—	2	2	no	—
96	C₂²	#15692944	1	1	yes	characteristic
97	C₂²	#15692945	1	1	yes	characteristic
98	C₂²	#15692954	1	1	yes	characteristic
99	C₄	C₁₀₃⋊#95	1	1	yes	characteristic
100	C₄	#15692941	1	1	yes	characteristic
101	C₄	#15692942	1	1	yes	characteristic
102	C₄	#15692952	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#20267553	1	1	yes	characteristic
106	C₂	#20267620	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₀₃⋊C₁₆

C₂

yes

maximal, characteristic

C₂×#15692957

C₂

yes

maximal, characteristic

C₂×#108×C₁₀₃

C₂

yes

maximal, characteristic

C₂×#13110089

—

C₂×C₁₀₃⋊C₁₆

—

C₂×C₁₀₃⋊C₁₆

—

C₂×C₁₀₃⋊C₁₆

C₄

yes

—

#15692957

—

#15692957

C₄

yes

—

C₂×M₁₆×C₁₀₃

—

C₂²×C₈×C₁₀₃

C₂²

yes

characteristic

#108×C₁₀₃

—

#108×C₁₀₃

C₄

yes

—

#13110089

—

#13110089

—

C₂×C₁₀₃⋊C₈

—

C₁₀₃⋊C₁₆

—

C₂²×C₄×C₁₀₃

D₄

yes

characteristic

M₁₆×C₁₀₃

—

M₁₆×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

D₄

yes

characteristic

C₂×C₈×C₁₀₃

D₄

yes

characteristic

C₂×C₈×C₁₀₃

Q₈

yes

characteristic

C₂³×C₁₀₃

Q₁₆

yes

characteristic

C₂×C₄×C₁₀₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₀₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₀₃

D₈

yes

characteristic

C₂×C₄×C₁₀₃

SD₁₆

yes

characteristic

C₂×C₄×C₁₀₃

SD₁₆

yes

characteristic

C₈×C₁₀₃

—

C₈×C₁₀₃

C₄²

yes

characteristic

C₈×C₁₀₃

C₂²⋊C₄

yes

characteristic

C₈×C₁₀₃

C₄⋊C₄

yes

characteristic

C₈×C₁₀₃

C₄⋊C₄

yes

characteristic

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

yes

C₂²×C₁₀₃

yes

C₂²×C₁₀₃

yes

C₄×C₁₀₃

yes

C₄×C₁₀₃

yes

C₄×C₁₀₃

yes

C₄×C₁₀₃

yes

C₂×C₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

#340

yes

characteristic

C₂×C₁₀₃

#368

yes

—

#1381

—

103

maximal, Sylow

C₁₀₃

#1381

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

103

—

C₂×#108

—

103

—

C₂×#108

D₁₀₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

206

—

C₂²×C₈

C₂×D₁₀₃

yes

characteristic

C₂×C₁₆

—

103

—

C₂×C₁₆

—

206

—

C₂×C₁₆

—

206

—

#108

—

#108

—

103

—

#108

—

206

—

#108

Dic₁₀₃

yes

—

C₂²×C₄

C₂²⋊D₁₀₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

412

—

M₁₆

—

206

—

C₂×C₈

—

C₂×C₈

—

412

—

C₂×C₈

Dic₂₀₆

yes

characteristic

C₂×C₈

C₄×D₁₀₃

yes

characteristic

C₂×C₈

C₄×D₁₀₃

yes

characteristic

C₂×C₈

D₄₁₂

yes

characteristic

C₂×C₈

C₂×Dic₁₀₃

yes

characteristic

C₂×C₈

C₂²⋊D₁₀₃

yes

characteristic

C₁₆

—

206

—

C₂³

#13110095

yes

characteristic

C₂×C₄

(C₂×D₁₀₃)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₁₀₃

yes

characteristic

C₂×C₄

Dic₁₀₃⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

412

—

C₈

C₄×Dic₁₀₃

yes

characteristic

C₈

(C₂×D₁₀₃)⋊C₄

yes

characteristic

C₈

Dic₁₀₃⋊C₄

yes

characteristic

C₈

C₄⋊Dic₁₀₃

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

C₁₀₃⋊#95

yes

characteristic

100

C₄

#15692941

yes

characteristic

101

C₄

#15692942

yes

characteristic

102

C₄

#15692952

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#20267553

yes

characteristic

106

C₂

#20267620

yes

—

	subgroup	G/H
center	C₂×C₄	#13110090
commutator	C₈×C₁₀₃	C₄²
Frattini	C₂²×C₈	C₂×D₁₀₃
Fitting	C₂×#108×C₁₀₃	C₂
socle	C₂²×C₁₀₃	#107
prime radical	C₂³×C₁₀₃	Q₁₆
cosocle	C₂²×C₈×C₁₀₃	C₂²
hypercenter	C₂×#108	D₁₀₃
hypocenter	C₁₀₃	#1381
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

#13110090

commutator

C₈×C₁₀₃

C₄²

Frattini

C₂²×C₈

C₂×D₁₀₃

Fitting

C₂×#108×C₁₀₃

C₂

socle

C₂²×C₁₀₃

#107

prime radical

C₂³×C₁₀₃

Q₁₆

cosocle

C₂²×C₈×C₁₀₃

C₂²

D₁₀₃

C₁₀₃

G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
54. C₁₀₃	#1381	semidirect

H ≅ G/N

type

54. C₁₀₃

#1381

semidirect

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

subgroup	index
C₂²×C₁₀₃⋊C₁₆	2
C₂×#15692957	2
C₂×#108×C₁₀₃	2
#1381	103

subgroup

index

C₂²×C₁₀₃⋊C₁₆

C₂×#15692957

C₂×#108×C₁₀₃

#1381

103

Subgroups — #27193237

Conjugacy classes of subgroups

Complements

Maximal subgroups