Group #27194473 — subgroups

Subgroups — #27194473

Order 13184.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₁₀₃⋊#564	C₂	1	1	yes	maximal, characteristic
2	#20268200	C₂	1	2	yes	maximal
3	#20268161	C₂	1	1	yes	maximal, characteristic
4	#20267532	C₂	1	2	yes	maximal
5	#330×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	#15693021	C₂²	1	1	yes	characteristic
7	#15693013	C₂²	1	2	yes	—
8	#15693012	—	2	2	no	—
9	#15693011	—	2	2	no	—
10	#15693011	—	2	2	no	—
11	#15692955	—	2	2	no	—
12	#15692953	—	2	2	no	—
13	#15692944	—	2	2	no	—
14	#15692932	C₂²	1	1	yes	characteristic
15	#125×C₁₀₃	C₂²	1	1	yes	characteristic
16	#97×C₁₀₃	C₂²	1	2	yes	—
17	C₂×Dic₂₀₆	—	2	1	no	—
18	C₂×C₁₀₃⋊C₈	—	2	1	no	—
19	C₄⋊Dic₁₀₃	—	2	2	no	—
20	C₄⋊Dic₁₀₃	—	2	2	no	—
21	C₄⋊Dic₁₀₃	D₄	1	2	yes	—
22	C₄⋊Dic₁₀₃	D₄	1	2	yes	—
23	Dic₁₀₃⋊C₄	—	2	2	no	—
24	Dic₁₀₃⋊C₄	—	2	2	no	—
25	Dic₁₀₃⋊C₄	—	2	2	no	—
26	Dic₁₀₃⋊C₄	—	2	2	no	—
27	C₄×Dic₁₀₃	—	2	2	no	—
28	C₂×C₈×C₁₀₃	—	2	2	no	—
29	C₄⋊C₄×C₁₀₃	—	2	2	no	—
30	C₄⋊C₄×C₁₀₃	D₄	1	2	yes	—
31	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
32	C₂×C₄×C₁₀₃	—	2	2	no	—
33	C₂×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₁₀₃	—	2	2	no	—
36	C₂×Dic₁₀₃	—	2	2	no	—
37	C₂×Dic₁₀₃	—	4	1	no	—
38	Dic₂₀₆	—	4	2	no	—
39	C₈×C₁₀₃	—	2	4	no	—
40	C₁₀₃⋊C₈	—	4	1	no	—
41	C₂²×C₁₀₃	#120	1	1	yes	characteristic
42	C₄×C₁₀₃	—	2	1	no	—
43	C₄×C₁₀₃	—	2	2	no	—
44	C₄×C₁₀₃	—	4	2	no	—
45	Dic₁₀₃	—	4	2	no	—
46	Dic₁₀₃	—	4	2	no	—
47	Dic₁₀₃	—	8	1	no	—
48	C₂×C₁₀₃	#454	1	1	yes	characteristic
49	C₂×C₁₀₃	#456	1	2	yes	—
50	#1663	—	103	1	no	maximal, Sylow
51	C₁₀₃	#1663	1	1	yes	characteristic, complemented, Sylow
52	#564	—	103	1	no	—
53	#501	—	103	2	no	—
54	#491	—	103	1	no	—
55	#330	—	103	2	no	—
56	#330	D₁₀₃	1	1	yes	characteristic
57	C₄⋊Q₈	—	103	1	no	—
58	#125	—	103	2	no	—
59	#125	—	206	2	no	—
60	#125	—	206	2	no	—
61	#125	—	206	2	no	—
62	#125	C₂×D₁₀₃	1	1	yes	characteristic
63	#107	—	206	2	no	—
64	#106	—	206	2	no	—
65	#103	—	206	2	no	—
66	#97	—	103	1	no	—
67	#97	C₂×D₁₀₃	1	2	yes	—
68	C₂×Q₈	—	206	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	206	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	103	2	no	—
73	C₄⋊C₄	—	103	2	no	—
74	C₄⋊C₄	—	206	2	no	—
75	C₄⋊C₄	—	206	2	no	—
76	C₄⋊C₄	—	206	2	no	—
77	C₄⋊C₄	—	206	2	no	—
78	C₄⋊C₄	—	206	2	no	—
79	C₄⋊C₄	—	206	2	no	—
80	C₄⋊C₄	D₄₁₂	1	2	yes	—
81	C₄²	—	206	2	no	—
82	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
83	Q₈	—	412	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	412	1	no	—
86	C₂×C₄	—	206	2	no	—
87	C₂×C₄	—	206	2	no	—
88	C₂×C₄	D₄×D₁₀₃	1	2	yes	—
89	C₂×C₄	C₂×D₄₁₂	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	412	1	no	—
92	C₂²	#15692991	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	824	1	no	—
97	C₄	—	412	2	no	—
98	C₄	—	412	2	no	—
99	C₂	#20267966	1	1	yes	characteristic
100	C₂	#20267975	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₃⋊#564

C₂

yes

maximal, characteristic

#20268200

C₂

yes

maximal

#20268161

C₂

yes

maximal, characteristic

#20267532

C₂

yes

maximal

#330×C₁₀₃

C₂

yes

maximal, characteristic

#15693021

C₂²

yes

characteristic

#15693013

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₁₀₃

C₂²

yes

characteristic

#97×C₁₀₃

C₂²

yes

—

C₂×Dic₂₀₆

—

C₂×C₁₀₃⋊C₈

—

C₄⋊Dic₁₀₃

—

C₄⋊Dic₁₀₃

—

C₄⋊Dic₁₀₃

D₄

yes

—

C₄⋊Dic₁₀₃

D₄

yes

—

Dic₁₀₃⋊C₄

—

Dic₁₀₃⋊C₄

—

Dic₁₀₃⋊C₄

—

Dic₁₀₃⋊C₄

—

C₄×Dic₁₀₃

—

C₂×C₈×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

D₄

yes

—

C₄²×C₁₀₃

C₂³

yes

characteristic

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂×D₄

yes

—

C₂×C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

Dic₂₀₆

—

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

#120

yes

characteristic

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

—

C₂×C₁₀₃

#454

yes

characteristic

C₂×C₁₀₃

#456

yes

—

#1663

—

103

maximal, Sylow

C₁₀₃

#1663

yes

characteristic, complemented, Sylow

#564

—

103

—

#501

—

103

—

#491

—

103

—

#330

—

103

—

#330

D₁₀₃

yes

characteristic

C₄⋊Q₈

—

103

—

#125

—

103

—

#125

—

206

—

#125

—

206

—

#125

—

206

—

#125

C₂×D₁₀₃

yes

characteristic

#107

—

206

—

#106

—

206

—

#103

—

206

—

#97

—

103

—

#97

C₂×D₁₀₃

yes

—

C₂×Q₈

—

206

—

C₂×C₈

—

C₂×C₈

—

206

—

C₄⋊C₄

—

C₄⋊C₄

—

103

—

C₄⋊C₄

—

103

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄⋊C₄

—

206

—

C₄⋊C₄

D₄₁₂

yes

—

C₄²

—

206

—

C₄²

C₂²×D₁₀₃

yes

characteristic

Q₈

—

412

—

C₂×C₄

—

C₂×C₄

—

412

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

D₄×D₁₀₃

yes

—

C₂×C₄

C₂×D₄₁₂

yes

characteristic

C₈

—

C₈

—

412

—

C₂²

#15692991

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

824

—

C₄

—

412

—

C₄

—

412

—

C₂

#20267966

yes

characteristic

100

C₂

#20267975

yes

—

	subgroup	G/H
center	C₂²	#15692991
commutator, cosocle	C₄²×C₁₀₃	C₂³
Frattini	C₄²	C₂²×D₁₀₃
Fitting	#330×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	#120
hypercenter	#330	D₁₀₃
hypocenter	C₁₀₃	#1663
LCS	G ▷ C₄²×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#15692991

commutator, cosocle

C₄²×C₁₀₃

C₂³

Frattini

C₄²

C₂²×D₁₀₃

Fitting

#330×C₁₀₃

C₂

C₂²×C₁₀₃

D₁₀₃

C₁₀₃

G ▷ C₄²×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
51. C₁₀₃	#1663	semidirect

H ≅ G/N

type

51. C₁₀₃

#1663

semidirect

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

subgroup	index
C₁₀₃⋊#564	2
#20268200	2
#20268161	2
#20267532	2
#330×C₁₀₃	2
#1663	103

subgroup

index

C₁₀₃⋊#564

#330×C₁₀₃

103

Subgroups — #27194473

Conjugacy classes of subgroups

Complements

Maximal subgroups