Group #28412554 — subgroups

Subgroups — C₂×D₂₂₉⋊M₁₆ #28412554

Order 14656.

298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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×#16814676	C₂	1	2	yes	maximal, complemented
2	D₂₂₉⋊M₁₆	C₂	1	8	yes	maximal, direct product factor
3	C₂×#16814675	C₂	1	2	yes	maximal, complemented
4	C₂×D₂₂₉⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×D₂₂₉	C₂	1	1	yes	maximal, characteristic
6	#16814676	C₂²	1	8	yes	complemented
7	#16814675	C₂²	1	8	yes	complemented
8	D₂₂₉⋊C₈	C₂²	1	8	yes	complemented
9	C₂×#14270087	C₂²	1	4	yes	complemented
10	C₂³×D₂₂₉	C₄	1	1	yes	characteristic
11	C₂²×Dic₂₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₂₂₉	C₄	1	4	yes	—
13	C₂×C₄×D₂₂₉	C₄	1	1	yes	characteristic
14	C₂×C₄×D₂₂₉	C₄	1	1	yes	characteristic
15	C₂×C₄×D₂₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₂₂₉	C₂²	1	4	yes	—
17	C₂×C₄×D₂₂₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₂₂₉	C₄	1	1	yes	characteristic
19	#14270087	C₂³	1	8	yes	complemented
20	C₂²×D₂₂₉	—	2	4	no	—
21	C₂²×D₂₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₂₂₉	C₂×C₄	1	4	yes	—
23	C₂²×D₂₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₂₂₉	C₂×C₄	1	2	yes	—
25	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₂₂₉	C₂³	1	1	yes	characteristic
27	C₂×Dic₂₂₉	C₂³	1	2	yes	—
28	C₄×D₂₂₉	C₂×C₄	1	4	yes	—
29	C₄×D₂₂₉	C₂×C₄	1	2	yes	—
30	C₄×D₂₂₉	C₂×C₄	1	2	yes	—
31	C₄×D₂₂₉	C₂×C₄	1	4	yes	—
32	C₄×D₂₂₉	C₂³	1	2	yes	—
33	C₄×D₂₂₉	C₂³	1	2	yes	—
34	C₂³×C₂₂₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₂₉	C₂×C₄	1	4	yes	—
36	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₂₂₉	—	2	2	no	—
39	C₂²×C₂₂₉	C₂²×C₄	1	2	yes	—
40	C₂²×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×D₂₂₉	—	2	2	no	—
42	C₂×D₂₂₉	—	2	8	no	—
43	C₂×D₂₂₉	M₁₆	1	4	yes	complemented
44	C₂×D₂₂₉	C₂²×C₄	1	2	yes	—
45	C₂×D₂₂₉	C₂²×C₄	1	2	yes	—
46	C₄×C₂₂₉	C₂²×C₄	1	2	yes	—
47	C₄×C₂₂₉	C₂²×C₄	1	2	yes	—
48	Dic₂₂₉	C₂²×C₄	1	1	yes	characteristic
49	Dic₂₂₉	C₂²×C₄	1	2	yes	—
50	Dic₂₂₉	C₂⁴	1	1	yes	characteristic
51	C₂×C₂₂₉	—	2	2	no	—
52	C₂×C₂₂₉	C₂×M₁₆	1	2	yes	complemented
53	C₂×C₂₂₉	C₂³×C₄	1	1	yes	characteristic
54	D₂₂₉	—	2	2	no	—
55	D₂₂₉	C₂×M₁₆	1	4	yes	complemented
56	C₂₂₉	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂²×M₁₆	—	229	1	no	maximal, Sylow
58	C₂³×C₄	—	229	1	no	—
59	C₂×M₁₆	—	229	2	no	—
60	C₂×M₁₆	—	229	8	no	—
61	C₂×M₁₆	—	229	2	no	—
62	C₂²×C₈	—	229	2	no	—
63	C₂⁴	—	229	1	no	—
64	C₂²×C₄	—	229	1	no	—
65	C₂²×C₄	—	229	4	no	—
66	C₂²×C₄	—	229	1	no	—
67	C₂²×C₄	—	229	1	no	—
68	C₂²×C₄	—	229	4	no	—
69	C₂²×C₄	—	229	1	no	—
70	C₂²×C₄	—	229	1	no	—
71	C₂²×C₄	#11745021	1	1	yes	characteristic
72	M₁₆	—	229	8	no	—
73	M₁₆	—	229	8	no	—
74	C₂×C₈	—	229	4	no	—
75	C₂×C₈	—	229	8	no	—
76	C₂³	—	458	4	no	—
77	C₂³	—	229	4	no	—
78	C₂³	—	229	1	no	—
79	C₂³	—	229	1	no	—
80	C₂³	C₂×#11745021	1	1	yes	characteristic
81	C₂×C₄	—	229	1	no	—
82	C₂×C₄	—	229	2	no	—
83	C₂×C₄	—	229	2	no	—
84	C₂×C₄	—	229	1	no	—
85	C₂×C₄	—	229	2	no	—
86	C₂×C₄	—	229	2	no	—
87	C₂×C₄	—	229	2	no	—
88	C₂×C₄	—	229	4	no	—
89	C₂×C₄	—	229	4	no	—
90	C₂×C₄	—	229	2	no	—
91	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
92	C₂×C₄	C₂×#11745021	1	4	yes	—
93	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
94	C₈	—	229	8	no	—
95	C₂²	—	2	2	no	—
96	C₂²	—	458	8	no	—
97	C₂²	—	458	2	no	—
98	C₂²	—	229	2	no	—
99	C₂²	—	229	4	no	—
100	C₂²	—	229	2	no	—
101	C₂²	C₂²×#11745021	1	2	yes	—
102	C₂²	C₂²×#11745021	1	1	yes	characteristic
103	C₄	—	229	1	no	—
104	C₄	—	229	1	no	—
105	C₄	—	229	2	no	—
106	C₄	C₂²×#11745021	1	2	yes	—
107	C₄	C₂²×#11745021	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	—	458	2	no	—
110	C₂	—	229	4	no	—
111	C₂	D₂₂₉⋊M₁₆	1	2	yes	direct product factor
112	C₂	C₂³×#11745021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16814676

C₂

yes

maximal, complemented

D₂₂₉⋊M₁₆

C₂

yes

maximal, direct product factor

C₂×#16814675

C₂

yes

maximal, complemented

C₂×D₂₂₉⋊C₈

C₂

yes

maximal, complemented

C₂²×C₄×D₂₂₉

C₂

yes

maximal, characteristic

#16814676

C₂²

yes

complemented

#16814675

C₂²

yes

complemented

D₂₂₉⋊C₈

C₂²

yes

complemented

C₂×#14270087

C₂²

yes

complemented

C₂³×D₂₂₉

C₄

yes

characteristic

C₂²×Dic₂₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₂₉

C₄

yes

—

C₂×C₄×D₂₂₉

C₄

yes

characteristic

C₂×C₄×D₂₂₉

C₄

yes

characteristic

C₂×C₄×D₂₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₂₉

C₂²

yes

—

C₂×C₄×D₂₂₉

C₂²

yes

characteristic

C₂²×C₄×C₂₂₉

C₄

yes

characteristic

#14270087

C₂³

yes

complemented

C₂²×D₂₂₉

—

C₂²×D₂₂₉

C₂×C₄

yes

characteristic

C₂²×D₂₂₉

C₂×C₄

yes

—

C₂²×D₂₂₉

C₂×C₄

yes

characteristic

C₂×Dic₂₂₉

C₂×C₄

yes

—

C₂×Dic₂₂₉

C₂×C₄

yes

characteristic

C₂×Dic₂₂₉

C₂³

yes

characteristic

C₂×Dic₂₂₉

C₂³

yes

—

C₄×D₂₂₉

C₂×C₄

yes

—

C₄×D₂₂₉

C₂×C₄

yes

—

C₄×D₂₂₉

C₂×C₄

yes

—

C₄×D₂₂₉

C₂×C₄

yes

—

C₄×D₂₂₉

C₂³

yes

—

C₄×D₂₂₉

C₂³

yes

—

C₂³×C₂₂₉

C₂×C₄

yes

characteristic

C₂×C₄×C₂₂₉

C₂×C₄

yes

—

C₂×C₄×C₂₂₉

C₂×C₄

yes

characteristic

C₂×C₄×C₂₂₉

C₂×C₄

yes

characteristic

C₂²×C₂₂₉

—

C₂²×C₂₂₉

C₂²×C₄

yes

—

C₂²×C₂₂₉

C₂²×C₄

yes

characteristic

C₂×D₂₂₉

—

C₂×D₂₂₉

—

C₂×D₂₂₉

M₁₆

yes

complemented

C₂×D₂₂₉

C₂²×C₄

yes

—

C₂×D₂₂₉

C₂²×C₄

yes

—

C₄×C₂₂₉

C₂²×C₄

yes

—

C₄×C₂₂₉

C₂²×C₄

yes

—

Dic₂₂₉

C₂²×C₄

yes

characteristic

Dic₂₂₉

C₂²×C₄

yes

—

Dic₂₂₉

C₂⁴

yes

characteristic

C₂×C₂₂₉

—

C₂×C₂₂₉

C₂×M₁₆

yes

complemented

C₂×C₂₂₉

C₂³×C₄

yes

characteristic

D₂₂₉

—

D₂₂₉

C₂×M₁₆

yes

complemented

C₂₂₉

C₂²×M₁₆

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

229

maximal, Sylow

C₂³×C₄

—

229

—

C₂×M₁₆

—

229

—

C₂×M₁₆

—

229

—

C₂×M₁₆

—

229

—

C₂²×C₈

—

229

—

C₂⁴

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

—

229

—

C₂²×C₄

#11745021

yes

characteristic

M₁₆

—

229

—

M₁₆

—

229

—

C₂×C₈

—

229

—

C₂×C₈

—

229

—

C₂³

—

458

—

C₂³

—

229

—

C₂³

—

229

—

C₂³

—

229

—

C₂³

C₂×#11745021

yes

characteristic

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

—

229

—

C₂×C₄

C₂×#11745021

yes

characteristic

C₂×C₄

C₂×#11745021

yes

—

C₂×C₄

C₂×#11745021

yes

characteristic

C₈

—

229

—

C₂²

—

C₂²

—

458

—

C₂²

—

458

—

C₂²

—

229

—

C₂²

—

229

—

100

C₂²

—

229

—

101

C₂²

C₂²×#11745021

yes

—

102

C₂²

C₂²×#11745021

yes

characteristic

103

C₄

—

229

—

104

C₄

—

229

—

105

C₄

—

229

—

106

C₄

C₂²×#11745021

yes

—

107

C₄

C₂²×#11745021

yes

—

108

C₂

—

109

C₂

—

458

—

110

C₂

—

229

—

111

C₂

D₂₂₉⋊M₁₆

yes

direct product factor

112

C₂

C₂³×#11745021

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11745021
commutator	C₂×C₂₂₉	C₂³×C₄
Frattini	C₂	C₂³×#11745021
Fitting	C₂²×C₄×C₂₂₉	C₄
socle	C₂²×C₂₂₉	C₂²×C₄
prime radical	C₂³×D₂₂₉	C₄
cosocle	Dic₂₂₉	C₂⁴
hypercenter	C₂²×C₄	#11745021
hypocenter	C₂₂₉	C₂²×M₁₆
LCS	G ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

subgroup

G/H

center

C₂×C₄

C₂×#11745021

commutator

C₂×C₂₂₉

C₂³×C₄

Frattini

C₂

C₂³×#11745021

Fitting

C₂²×C₄×C₂₂₉

C₄

socle

C₂²×C₂₂₉

C₂²×C₄

prime radical

C₂³×D₂₂₉

C₄

cosocle

Dic₂₂₉

C₂⁴

hypercenter

C₂²×C₄

#11745021

hypocenter

C₂₂₉

C₂²×M₁₆

LCS

G ▷ C₂×C₂₂₉ ▷ C₂₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄

N	H ≅ G/N	type
1. C₂×#16814676	C₂	semidirect
2. D₂₂₉⋊M₁₆	C₂	direct (N × H)
3. C₂×#16814675	C₂	semidirect
4. C₂×D₂₂₉⋊C₈	C₂	semidirect
6. #16814676	C₂²	semidirect
7. #16814675	C₂²	semidirect
8. D₂₂₉⋊C₈	C₂²	semidirect
9. C₂×#14270087	C₂²	semidirect
19. #14270087	C₂³	semidirect
43. C₂×D₂₂₉	M₁₆	semidirect
52. C₂×C₂₂₉	C₂×M₁₆	semidirect
55. D₂₂₉	C₂×M₁₆	semidirect
56. C₂₂₉	C₂²×M₁₆	semidirect
111. C₂	D₂₂₉⋊M₁₆	direct (N × H)

H ≅ G/N

type

1. C₂×#16814676

C₂

semidirect

2. D₂₂₉⋊M₁₆

C₂

direct (N × H)

3. C₂×#16814675

C₂

semidirect

4. C₂×D₂₂₉⋊C₈

C₂

semidirect

6. #16814676

C₂²

semidirect

7. #16814675

C₂²

semidirect

8. D₂₂₉⋊C₈

C₂²

semidirect

9. C₂×#14270087

C₂²

semidirect

19. #14270087

C₂³

semidirect

43. C₂×D₂₂₉

M₁₆

semidirect

52. C₂×C₂₂₉

C₂×M₁₆

semidirect

55. D₂₂₉

C₂×M₁₆

semidirect

56. C₂₂₉

C₂²×M₁₆

semidirect

111. C₂

D₂₂₉⋊M₁₆

direct (N × H)

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

subgroup	index
C₂×#16814676	2
D₂₂₉⋊M₁₆	2
C₂×#16814675	2
C₂×D₂₂₉⋊C₈	2
C₂²×C₄×D₂₂₉	2
C₂²×M₁₆	229

subgroup

index

C₂×#16814676

D₂₂₉⋊M₁₆

C₂×#16814675

C₂×D₂₂₉⋊C₈

C₂²×C₄×D₂₂₉

C₂²×M₁₆

229

Subgroups — C₂×D₂₂₉⋊M₁₆ #28412554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×D229⋊M16 #28412554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₂₂₉⋊M₁₆ #28412554