Group #27196896 — subgroups

Subgroups — C₂×Dic₁₀₃⋊C₁₆ #27196896

Order 13184.

184 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₈×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀₃⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₀₃⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₀₃	C₄	1	1	yes	characteristic
7	C₂×C₁₀₃⋊C₁₆	—	2	2	no	—
8	C₂×C₁₀₃⋊C₁₆	C₂²	1	2	yes	—
9	C₈×Dic₁₀₃	C₄	1	2	yes	—
10	C₈×Dic₁₀₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₀₃	—	2	2	no	—
13	C₂×C₁₆×C₁₀₃	C₂²	1	2	yes	—
14	C₂²×Dic₁₀₃	C₈	1	1	yes	characteristic
15	C₂²×Dic₁₀₃	C₈	1	1	yes	characteristic
16	C₂×C₁₀₃⋊C₈	—	2	2	no	—
17	C₂×C₁₀₃⋊C₈	C₂×C₄	1	2	yes	—
18	C₄×Dic₁₀₃	C₈	1	2	yes	—
19	C₄×Dic₁₀₃	C₂×C₄	1	2	yes	—
20	C₁₀₃⋊C₁₆	—	2	2	no	—
21	C₂²×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₀₃	D₄	1	2	yes	—
24	C₂×C₈×C₁₀₃	Q₈	1	2	yes	—
25	C₂×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
26	C₁₆×C₁₀₃	—	2	2	no	—
27	C₂³×C₁₀₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₀₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₀₃	M₁₆	1	2	yes	—
31	C₂×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₁₀₃	—	2	2	no	—
33	C₂×Dic₁₀₃	C₁₆	1	4	yes	complemented
34	C₂×Dic₁₀₃	C₂×C₈	1	2	yes	—
35	C₂×Dic₁₀₃	C₂×C₈	1	2	yes	—
36	C₈×C₁₀₃	C₄⋊C₄	1	2	yes	—
37	C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
39	C₁₀₃⋊C₈	—	2	2	no	—
40	C₂²×C₁₀₃	C₄⋊C₈	1	2	yes	—
41	C₂²×C₁₀₃	C₂×C₁₆	1	2	yes	—
42	C₂²×C₁₀₃	M₃₂	1	2	yes	—
43	C₂²×C₁₀₃	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₁₀₃	C₄⋊C₈	1	2	yes	—
45	C₄×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₁₀₃	C₂×M₁₆	1	1	yes	characteristic
47	Dic₁₀₃	—	2	2	no	—
48	Dic₁₀₃	C₂×C₁₆	1	4	yes	complemented
49	C₂×C₁₀₃	C₄⋊C₁₆	1	4	yes	complemented
50	C₂×C₁₀₃	C₂×C₄⋊C₈	1	1	yes	characteristic
51	C₂×C₁₀₃	C₂²×C₁₆	1	1	yes	characteristic
52	C₂×C₁₀₃	C₂×M₃₂	1	1	yes	characteristic
53	C₂×C₄⋊C₁₆	—	103	1	no	maximal, Sylow
54	C₁₀₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₁₆	—	103	1	no	—
56	C₂²×C₁₆	D₁₀₃	1	1	yes	characteristic
57	C₂×C₄×C₈	—	103	1	no	—
58	C₄⋊C₁₆	—	103	4	no	—
59	C₂²×C₈	—	103	1	no	—
60	C₂²×C₈	C₂×D₁₀₃	1	1	yes	characteristic
61	C₂×C₄²	—	103	1	no	—
62	C₂×C₁₆	—	2	2	no	—
63	C₂×C₁₆	—	103	2	no	—
64	C₂×C₁₆	—	206	2	no	—
65	C₂×C₁₆	C₂×D₁₀₃	1	2	yes	—
66	C₄×C₈	—	103	2	no	—
67	C₄×C₈	—	103	2	no	—
68	C₂²×C₄	—	103	1	no	—
69	C₂²×C₄	—	103	1	no	—
70	C₂²×C₄	C₄×D₁₀₃	1	1	yes	characteristic
71	C₂×C₈	—	103	2	no	—
72	C₂×C₈	—	206	2	no	—
73	C₂×C₈	Dic₂₀₆	1	2	yes	—
74	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
75	C₂×C₈	C₂²⋊D₁₀₃	1	2	yes	—
76	C₂×C₈	C₂²×D₁₀₃	1	1	yes	characteristic
77	C₄²	—	103	2	no	—
78	C₄²	—	103	2	no	—
79	C₁₆	—	2	2	no	—
80	C₁₆	—	206	2	no	—
81	C₂³	C₈×D₁₀₃	1	1	yes	characteristic
82	C₂×C₄	—	103	4	no	—
83	C₂×C₄	—	103	2	no	—
84	C₂×C₄	—	103	2	no	—
85	C₂×C₄	—	206	2	no	—
86	C₂×C₄	Dic₁₀₃⋊C₄	1	2	yes	—
87	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
88	C₂×C₄	#13110088	1	2	yes	—
89	C₂×C₄	C₂×C₄×D₁₀₃	1	1	yes	characteristic
90	C₈	—	206	2	no	—
91	C₈	Dic₁₀₃⋊C₄	1	2	yes	—
92	C₈	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
93	C₈	C₂×Dic₂₀₆	1	1	yes	characteristic
94	C₂²	Dic₁₀₃⋊C₈	1	2	yes	—
95	C₂²	C₁₆×D₁₀₃	1	2	yes	—
96	C₂²	#15692960	1	2	yes	—
97	C₂²	C₂×C₈×D₁₀₃	1	1	yes	characteristic
98	C₄	—	103	4	no	—
99	C₄	—	206	2	no	—
100	C₄	Dic₁₀₃⋊C₈	1	2	yes	—
101	C₄	C₂×Dic₁₀₃⋊C₄	1	1	yes	characteristic
102	C₄	C₂×#13110088	1	1	yes	characteristic
103	C₂	Dic₁₀₃⋊C₁₆	1	4	yes	direct product factor
104	C₂	C₂×Dic₁₀₃⋊C₈	1	1	yes	characteristic
105	C₂	C₂×C₁₆×D₁₀₃	1	1	yes	characteristic
106	C₂	C₂×#15692960	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₀₃⋊C₁₆

C₂

yes

maximal, characteristic

C₂×C₈×Dic₁₀₃

C₂

yes

maximal, characteristic

Dic₁₀₃⋊C₁₆

C₂

yes

maximal, direct product factor

C₂²×C₁₆×C₁₀₃

C₂

yes

maximal, characteristic

C₂²×C₁₀₃⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₁₀₃

C₄

yes

characteristic

C₂×C₁₀₃⋊C₁₆

—

C₂×C₁₀₃⋊C₁₆

C₂²

yes

—

C₈×Dic₁₀₃

C₄

yes

—

C₈×Dic₁₀₃

C₂²

yes

—

C₂²×C₈×C₁₀₃

C₂²

yes

characteristic

C₂×C₁₆×C₁₀₃

—

C₂×C₁₆×C₁₀₃

C₂²

yes

—

C₂²×Dic₁₀₃

C₈

yes

characteristic

C₂²×Dic₁₀₃

C₈

yes

characteristic

C₂×C₁₀₃⋊C₈

—

C₂×C₁₀₃⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₀₃

C₈

yes

—

C₄×Dic₁₀₃

C₂×C₄

yes

—

C₁₀₃⋊C₁₆

—

C₂²×C₄×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₀₃

D₄

yes

—

C₂×C₈×C₁₀₃

Q₈

yes

—

C₂×C₈×C₁₀₃

C₂³

yes

characteristic

C₁₆×C₁₀₃

—

C₂³×C₁₀₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₀₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₀₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₀₃

M₁₆

yes

—

C₂×C₄×C₁₀₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

C₁₆

yes

complemented

C₂×Dic₁₀₃

C₂×C₈

yes

—

C₂×Dic₁₀₃

C₂×C₈

yes

—

C₈×C₁₀₃

C₄⋊C₄

yes

—

C₈×C₁₀₃

C₂×D₄

yes

characteristic

C₈×C₁₀₃

C₂×Q₈

yes

characteristic

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

C₄⋊C₈

yes

—

C₂²×C₁₀₃

C₂×C₁₆

yes

—

C₂²×C₁₀₃

M₃₂

yes

—

C₂²×C₁₀₃

C₂²×C₈

yes

characteristic

C₄×C₁₀₃

C₄⋊C₈

yes

—

C₄×C₁₀₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₀₃

C₂×M₁₆

yes

characteristic

Dic₁₀₃

—

Dic₁₀₃

C₂×C₁₆

yes

complemented

C₂×C₁₀₃

C₄⋊C₁₆

yes

complemented

C₂×C₁₀₃

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₀₃

C₂²×C₁₆

yes

characteristic

C₂×C₁₀₃

C₂×M₃₂

yes

characteristic

C₂×C₄⋊C₁₆

—

103

maximal, Sylow

C₁₀₃

C₂×C₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

103

—

C₂²×C₁₆

D₁₀₃

yes

characteristic

C₂×C₄×C₈

—

103

—

C₄⋊C₁₆

—

103

—

C₂²×C₈

—

103

—

C₂²×C₈

C₂×D₁₀₃

yes

characteristic

C₂×C₄²

—

103

—

C₂×C₁₆

—

C₂×C₁₆

—

103

—

C₂×C₁₆

—

206

—

C₂×C₁₆

C₂×D₁₀₃

yes

—

C₄×C₈

—

103

—

C₄×C₈

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

C₄×D₁₀₃

yes

characteristic

C₂×C₈

—

103

—

C₂×C₈

—

206

—

C₂×C₈

Dic₂₀₆

yes

—

C₂×C₈

C₄×D₁₀₃

yes

characteristic

C₂×C₈

C₂²⋊D₁₀₃

yes

—

C₂×C₈

C₂²×D₁₀₃

yes

characteristic

C₄²

—

103

—

C₄²

—

103

—

C₁₆

—

C₁₆

—

206

—

C₂³

C₈×D₁₀₃

yes

characteristic

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

Dic₁₀₃⋊C₄

yes

—

C₂×C₄

C₈×D₁₀₃

yes

characteristic

C₂×C₄

#13110088

yes

—

C₂×C₄

C₂×C₄×D₁₀₃

yes

characteristic

C₈

—

206

—

C₈

Dic₁₀₃⋊C₄

yes

—

C₈

C₂×C₂²⋊D₁₀₃

yes

characteristic

C₈

C₂×Dic₂₀₆

yes

characteristic

C₂²

Dic₁₀₃⋊C₈

yes

—

C₂²

C₁₆×D₁₀₃

yes

—

C₂²

#15692960

yes

—

C₂²

C₂×C₈×D₁₀₃

yes

characteristic

C₄

—

103

—

C₄

—

206

—

100

C₄

Dic₁₀₃⋊C₈

yes

—

101

C₄

C₂×Dic₁₀₃⋊C₄

yes

characteristic

102

C₄

C₂×#13110088

yes

characteristic

103

C₂

Dic₁₀₃⋊C₁₆

yes

direct product factor

104

C₂

C₂×Dic₁₀₃⋊C₈

yes

characteristic

105

C₂

C₂×C₁₆×D₁₀₃

yes

characteristic

106

C₂

C₂×#15692960

yes

characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₀₃
commutator	C₂×C₁₀₃	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₁₀₃
Fitting	C₂²×C₁₆×C₁₀₃	C₂
socle, prime radical	C₂³×C₁₀₃	C₂×C₈
cosocle	C₂×C₈×C₁₀₃	C₂³
hypercenter	C₂²×C₁₆	D₁₀₃
hypocenter	C₁₀₃	C₂×C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂²×C₈

C₂×D₁₀₃

commutator

C₂×C₁₀₃

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₁₀₃

Fitting

C₂²×C₁₆×C₁₀₃

C₂

socle, prime radical

C₂³×C₁₀₃

C₂×C₈

cosocle

C₂×C₈×C₁₀₃

C₂³

hypercenter

C₂²×C₁₆

D₁₀₃

hypocenter

C₁₀₃

C₂×C₄⋊C₁₆

LCS

G ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
3. Dic₁₀₃⋊C₁₆	C₂	direct (N × H)
33. C₂×Dic₁₀₃	C₁₆	semidirect
48. Dic₁₀₃	C₂×C₁₆	semidirect
49. C₂×C₁₀₃	C₄⋊C₁₆	semidirect
54. C₁₀₃	C₂×C₄⋊C₁₆	semidirect
103. C₂	Dic₁₀₃⋊C₁₆	direct (N × H)

H ≅ G/N

type

3. Dic₁₀₃⋊C₁₆

C₂

direct (N × H)

33. C₂×Dic₁₀₃

C₁₆

semidirect

48. Dic₁₀₃

C₂×C₁₆

semidirect

49. C₂×C₁₀₃

C₄⋊C₁₆

semidirect

54. C₁₀₃

C₂×C₄⋊C₁₆

semidirect

103. C₂

Dic₁₀₃⋊C₁₆

direct (N × H)

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

subgroup	index
C₂²×C₁₀₃⋊C₁₆	2
C₂×C₈×Dic₁₀₃	2
Dic₁₀₃⋊C₁₆	2
C₂²×C₁₆×C₁₀₃	2
C₂×C₄⋊C₁₆	103

subgroup

index

C₂²×C₁₀₃⋊C₁₆

C₂×C₈×Dic₁₀₃

Dic₁₀₃⋊C₁₆

C₂²×C₁₆×C₁₀₃

C₂×C₄⋊C₁₆

103

Subgroups — C₂×Dic₁₀₃⋊C₁₆ #27196896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×Dic103⋊C16 #27196896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₁₀₃⋊C₁₆ #27196896