Group #21462196 — subgroups

Subgroups — D₄×#11758187 #21462196

Order 7808.

174 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11758187	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11758187	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11758187	C₂	1	2	yes	maximal, complemented
4	C₄×#11758187	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#92418	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758187	—	2	4	no	—
7	C₂×#11758187	C₂²	1	2	yes	—
8	C₂×#11758187	C₂²	1	1	yes	characteristic
9	C₂×#11758187	C₂²	1	1	yes	characteristic
10	C₂²×#92418	C₂²	1	2	yes	—
11	C₄⋊#92418	C₄	1	1	yes	characteristic
12	C₂²⋊#92418	C₄	1	2	yes	—
13	C₄×#92418	C₂²	1	1	yes	characteristic
14	C₄×D₄×C₆₁	C₄	1	1	yes	characteristic
15	C₂×D₄×C₆₁	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
17	C₄⋊C₄×C₆₁	C₈	1	1	yes	characteristic
18	C₂²⋊C₄×C₆₁	C₈	1	2	yes	—
19	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×#92418	—	2	2	no	—
21	C₂×#92418	—	2	2	no	—
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂×C₄	1	2	yes	—
24	C₂×#92418	C₂³	1	1	yes	characteristic
25	#11758187	—	2	2	no	—
26	#11758187	—	2	1	no	—
27	#11758187	D₄	1	2	yes	direct product factor
28	C₂³×C₆₁	C₂×C₈	1	2	yes	—
29	D₄×C₆₁	C₁₆	1	4	yes	complemented
30	C₂×C₄×C₆₁	—	2	2	no	—
31	C₂×C₄×C₆₁	—	2	2	no	—
32	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	#92418	—	2	2	no	—
37	#92418	—	2	1	no	—
38	#92418	C₂×D₄	1	1	yes	characteristic
39	#92418	#41	1	1	yes	characteristic
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	—	2	2	no	—
42	C₂²×C₆₁	C₂×C₁₆	1	4	yes	complemented
43	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	C₂×C₁₆	1	2	yes	complemented
47	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
48	C₄×C₆₁	#131	1	1	yes	characteristic
49	D₄×C₁₆	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	2	4	no	—
51	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
52	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
53	C₂×C₆₁	#504	1	1	yes	characteristic
54	C₂²×C₁₆	—	61	2	no	—
55	C₈×D₄	—	61	1	no	—
56	C₄⋊C₁₆	—	61	1	no	—
57	C₂²⋊C₁₆	—	61	2	no	—
58	C₄×C₁₆	—	61	1	no	—
59	C₆₁	D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	61	2	no	—
61	C₄×D₄	#6923	1	1	yes	characteristic
62	C₂×C₁₆	—	61	1	no	—
63	C₂×C₁₆	—	61	1	no	—
64	C₂×C₁₆	—	61	2	no	—
65	C₂×C₁₆	—	122	4	no	—
66	C₄⋊C₈	—	61	1	no	—
67	C₂²⋊C₈	—	61	2	no	—
68	C₄×C₈	—	61	1	no	—
69	C₂×D₄	#92420	1	1	yes	characteristic
70	C₂²×C₄	C₂×#6923	1	2	yes	—
71	C₂×C₈	—	61	1	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	61	2	no	—
74	C₂×C₈	—	122	2	no	—
75	C₂×C₈	—	122	2	no	—
76	C₄⋊C₄	#92420	1	1	yes	characteristic
77	C₂²⋊C₄	#92420	1	2	yes	—
78	C₄²	C₂×#6923	1	1	yes	characteristic
79	C₁₆	—	61	2	no	—
80	C₁₆	—	122	1	no	—
81	C₁₆	—	122	2	no	—
82	C₂³	C₂×#92420	1	2	yes	—
83	D₄	#11758187	1	4	yes	direct product factor
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	C₂×#92420	1	1	yes	characteristic
87	C₂×C₄	C₂×#92420	1	2	yes	—
88	C₂×C₄	C₂×#92420	1	1	yes	characteristic
89	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
90	C₈	—	61	1	no	—
91	C₈	—	61	1	no	—
92	C₈	—	122	2	no	—
93	C₈	—	122	1	no	—
94	C₂²	—	2	2	no	—
95	C₂²	—	2	2	no	—
96	C₂²	C₂×#11758187	1	4	yes	complemented
97	C₂²	C₂²×#92420	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	1	no	—
100	C₄	C₂×#11758187	1	2	yes	complemented
101	C₄	D₄×#6923	1	1	yes	characteristic
102	C₄	#14519864	1	1	yes	characteristic
103	C₂	—	2	4	no	—
104	C₂	D₄×#92420	1	1	yes	characteristic
105	C₂	C₂²×#11758187	1	1	yes	characteristic
106	C₂	#16840820	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11758187

C₂

yes

maximal, complemented

C₄⋊#11758187

C₂

yes

maximal, characteristic, complemented

C₂²⋊#11758187

C₂

yes

maximal, complemented

C₄×#11758187

C₂

yes

maximal, characteristic, complemented

D₄×#92418

C₂

yes

maximal, characteristic

C₂×#11758187

—

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

C₂²×#92418

C₂²

yes

—

C₄⋊#92418

C₄

yes

characteristic

C₂²⋊#92418

C₄

yes

—

C₄×#92418

C₂²

yes

characteristic

C₄×D₄×C₆₁

C₄

yes

characteristic

C₂×D₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₄⋊C₄×C₆₁

C₈

yes

characteristic

C₂²⋊C₄×C₆₁

C₈

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂³

yes

—

—

D₄

yes

direct product factor

C₂³×C₆₁

C₂×C₈

yes

—

D₄×C₆₁

C₁₆

yes

complemented

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

—

—

C₂×D₄

yes

yes

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₁₆

yes

complemented

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₁₆

yes

complemented

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

D₄×C₁₆

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₈×D₄

yes

characteristic

C₂×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×C₆₁

#504

yes

characteristic

C₂²×C₁₆

—

C₈×D₄

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₆₁

D₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄×D₄

#6923

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₂×D₄

#92420

yes

characteristic

C₂²×C₄

C₂×#6923

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

#92420

yes

characteristic

C₂²⋊C₄

#92420

yes

—

C₄²

C₂×#6923

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

C₂×#92420

yes

—

D₄

#11758187

yes

direct product factor

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#92420

yes

characteristic

C₂×C₄

C₂×#92420

yes

—

C₂×C₄

C₂×#92420

yes

characteristic

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

—

122

—

C₂²

—

C₂²

—

C₂²

C₂×#11758187

yes

complemented

C₂²

C₂²×#92420

yes

characteristic

C₄

—

C₄

—

100

C₄

C₂×#11758187

yes

complemented

101

C₄

D₄×#6923

yes

characteristic

102

C₄

#14519864

yes

characteristic

103

C₂

—

104

C₂

D₄×#92420

yes

characteristic

105

C₂

C₂²×#11758187

yes

characteristic

106

C₂

#16840820

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator	C₂×C₆₁	C₂²×C₁₆
Fitting	C₄×D₄×C₆₁	C₄
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	C₄×D₄	#6923
hypocenter	C₆₁	D₄×C₁₆
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator

C₂×C₆₁

C₂²×C₁₆

Fitting

C₄×D₄×C₆₁

C₄

socle

C₂²×C₆₁

C₂²×C₈

hypercenter

C₄×D₄

#6923

hypocenter

C₆₁

D₄×C₁₆

LCS

G ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄×D₄

N	H ≅ G/N	type
1. C₂²×#11758187	C₂	semidirect
2. C₄⋊#11758187	C₂	semidirect
3. C₂²⋊#11758187	C₂	semidirect
4. C₄×#11758187	C₂	semidirect
27. #11758187	D₄	direct (N × H)
29. D₄×C₆₁	C₁₆	semidirect
42. C₂²×C₆₁	C₂×C₁₆	semidirect
46. C₄×C₆₁	C₂×C₁₆	semidirect
59. C₆₁	D₄×C₁₆	semidirect
83. D₄	#11758187	direct (N × H)
96. C₂²	C₂×#11758187	semidirect
100. C₄	C₂×#11758187	semidirect

H ≅ G/N

type

1. C₂²×#11758187

C₂

semidirect

2. C₄⋊#11758187

C₂

semidirect

3. C₂²⋊#11758187

C₂

semidirect

4. C₄×#11758187

C₂

semidirect

27. #11758187

D₄

direct (N × H)

29. D₄×C₆₁

C₁₆

semidirect

42. C₂²×C₆₁

C₂×C₁₆

semidirect

46. C₄×C₆₁

C₂×C₁₆

semidirect

59. C₆₁

D₄×C₁₆

semidirect

83. D₄

#11758187

direct (N × H)

96. C₂²

C₂×#11758187

semidirect

100. C₄

C₂×#11758187

semidirect

Subgroups — D₄×#11758187 #21462196

Conjugacy classes of subgroups

Complements

Subgroups — D4×#11758187 #21462196

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#11758187 #21462196