Group #14521769 — subgroups

Subgroups — #14521769

Order 1984.

212 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	#11758513	C₂	1	2	yes	maximal
3	#11758503	C₂	1	2	yes	maximal, complemented
4	#11758501	C₂	1	2	yes	maximal, complemented
5	#11758464	C₂	1	2	yes	maximal, complemented
6	#11758456	C₂	1	4	yes	maximal, complemented
7	#11758446	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×Dic₆₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₃₁	C₂²	1	2	yes	—
11	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
12	C₂×Dic₆₂	C₂²	1	2	yes	—
13	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₄²×C₃₁	C₂²	1	1	yes	characteristic
16	C₂²⋊Dic₃₁	C₂²	1	4	yes	—
17	C₂²⋊Dic₃₁	C₂²	1	4	yes	—
18	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
19	C₄⋊Dic₃₁	C₂²	1	2	yes	—
20	C₄⋊Dic₃₁	C₂²	1	2	yes	—
21	Dic₃₁⋊C₄	C₂²	1	2	yes	—
22	Dic₃₁⋊C₄	C₂²	1	4	yes	—
23	C₄×Dic₃₁	C₂²	1	2	yes	—
24	C₄×Dic₃₁	C₂²	1	4	yes	—
25	C₂³×C₃₁	C₂³	1	2	yes	—
26	D₄×C₃₁	—	2	2	no	—
27	C₂×C₄×C₃₁	—	2	4	no	—
28	C₂×C₄×C₃₁	C₂³	1	2	yes	—
29	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
32	C₂×Dic₃₁	C₂³	1	2	yes	—
33	C₂×Dic₃₁	C₂³	1	2	yes	—
34	C₂×Dic₃₁	C₂³	1	4	yes	—
35	Dic₆₂	—	2	4	no	—
36	Dic₆₂	—	2	2	no	—
37	C₂²×C₃₁	—	2	2	no	—
38	C₂²×C₃₁	—	2	2	no	—
39	C₂²×C₃₁	—	2	2	no	—
40	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
41	C₄×C₃₁	—	2	2	no	—
42	C₄×C₃₁	—	2	1	no	—
43	C₄×C₃₁	#41	1	2	yes	—
44	C₄×C₃₁	#41	1	2	yes	—
45	Dic₃₁	—	2	4	no	—
46	Dic₃₁	—	2	2	no	—
47	Dic₃₁	—	2	2	no	—
48	#556	—	31	1	no	maximal, Sylow
49	C₂×C₃₁	—	4	2	no	—
50	C₂×C₃₁	C₂×#41	1	1	yes	characteristic
51	C₂×C₃₁	C₂×#41	1	1	yes	characteristic
52	C₂×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
53	C₄⋊Q₈	—	31	1	no	—
54	#126	—	31	4	no	—
55	#124	—	31	2	no	—
56	C₂²⋊Q₈	—	31	2	no	—
57	C₄×Q₈	—	31	2	no	—
58	C₄×Q₈	—	31	1	no	—
59	C₄×D₄	D₃₁	1	1	yes	characteristic
60	#117	—	31	2	no	—
61	C₃₁	#556	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	31	1	no	—
63	C₂×Q₈	—	31	2	no	—
64	C₂×D₄	C₂×D₃₁	1	1	yes	characteristic
65	C₂²×C₄	C₂×D₃₁	1	2	yes	—
66	C₄⋊C₄	—	31	4	no	—
67	C₄⋊C₄	—	31	2	no	—
68	C₄⋊C₄	—	31	1	no	—
69	C₄⋊C₄	—	31	2	no	—
70	C₄⋊C₄	—	31	2	no	—
71	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
72	C₂²⋊C₄	—	31	4	no	—
73	C₂²⋊C₄	—	31	4	no	—
74	C₂²⋊C₄	C₂×D₃₁	1	2	yes	—
75	C₄²	—	31	4	no	—
76	C₄²	—	31	2	no	—
77	C₄²	C₂×D₃₁	1	1	yes	characteristic
78	C₂³	C₂²×D₃₁	1	2	yes	—
79	Q₈	—	62	4	no	—
80	Q₈	—	62	2	no	—
81	D₄	—	2	2	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	31	2	no	—
84	C₂×C₄	—	31	4	no	—
85	C₂×C₄	—	31	2	no	—
86	C₂×C₄	C₂²×D₃₁	1	2	yes	—
87	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
88	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
89	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	—	2	2	no	—
92	C₂²	—	2	2	no	—
93	C₂²	C₂³×D₃₁	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	2	1	no	—
96	C₄	—	62	4	no	—
97	C₄	—	62	2	no	—
98	C₄	—	62	2	no	—
99	C₄	#92495	1	2	yes	—
100	C₄	#92497	1	2	yes	—
101	C₂	—	4	2	no	—
102	C₂	C₂×#92495	1	1	yes	characteristic
103	C₂	C₂×#92497	1	1	yes	characteristic
104	C₂	#11758567	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₄×C₃₁

C₂

yes

maximal, characteristic

#11758513

C₂

yes

maximal

#11758503

C₂

yes

maximal, complemented

#11758501

C₂

yes

maximal, complemented

#11758464

C₂

yes

maximal, complemented

#11758456

C₂

yes

maximal, complemented

#11758446

C₂

yes

maximal, characteristic, complemented

C₄×Dic₆₂

C₂

yes

maximal, characteristic, complemented

C₂×D₄×C₃₁

C₂²

yes

characteristic

C₂²×C₄×C₃₁

C₂²

yes

—

C₂×Dic₆₂

C₂²

yes

characteristic

C₂×Dic₆₂

C₂²

yes

—

C₄⋊C₄×C₃₁

C₂²

yes

characteristic

C₂²⋊C₄×C₃₁

C₂²

yes

—

C₄²×C₃₁

C₂²

yes

characteristic

C₂²⋊Dic₃₁

C₂²

yes

—

C₂²⋊Dic₃₁

C₂²

yes

—

C₄⋊Dic₃₁

C₂²

yes

characteristic

C₄⋊Dic₃₁

C₂²

yes

—

C₄⋊Dic₃₁

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

—

C₄×Dic₃₁

C₂²

yes

—

C₄×Dic₃₁

C₂²

yes

—

C₂³×C₃₁

C₂³

yes

—

D₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂³

yes

—

C₂×C₄×C₃₁

C₂³

yes

characteristic

C₂×C₄×C₃₁

C₂³

yes

characteristic

C₂×C₄×C₃₁

C₂³

yes

characteristic

C₂×Dic₃₁

C₂³

yes

—

C₂×Dic₃₁

C₂³

yes

—

C₂×Dic₃₁

C₂³

yes

—

Dic₆₂

—

Dic₆₂

—

C₂²×C₃₁

—

C₂²×C₃₁

—

C₂²×C₃₁

—

C₂²×C₃₁

C₂⁴

yes

characteristic

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

#41

yes

—

C₄×C₃₁

#41

yes

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

—

#556

—

maximal, Sylow

C₂×C₃₁

—

C₂×C₃₁

C₂×#41

yes

characteristic

C₂×C₃₁

C₂×#41

yes

characteristic

C₂×C₃₁

2₋¹⁺⁴

yes

characteristic

C₄⋊Q₈

—

#126

—

#124

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×D₄

D₃₁

yes

characteristic

#117

—

C₃₁

#556

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

C₂×D₃₁

yes

characteristic

C₂²×C₄

C₂×D₃₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₃₁

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₃₁

yes

—

C₄²

—

C₄²

—

C₄²

C₂×D₃₁

yes

characteristic

C₂³

C₂²×D₃₁

yes

—

Q₈

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₃₁

yes

—

C₂×C₄

C₂²×D₃₁

yes

characteristic

C₂×C₄

C₂²×D₃₁

yes

characteristic

C₂×C₄

C₂²×D₃₁

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂³×D₃₁

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#92495

yes

—

100

C₄

#92497

yes

—

101

C₂

—

102

C₂

C₂×#92495

yes

characteristic

103

C₂

C₂×#92497

yes

characteristic

104

C₂

#11758567

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁴
Fitting	C₄×D₄×C₃₁	C₂
prime radical	C₂×D₄×C₃₁	C₂²
hypercenter	C₄×D₄	D₃₁
hypocenter	C₃₁	#556
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄×D₄

subgroup

G/H

center, Frattini

C₂²

C₂³×D₃₁

commutator, socle, cosocle

C₂²×C₃₁

C₂⁴

Fitting

C₄×D₄×C₃₁

C₂

prime radical

C₂×D₄×C₃₁

C₂²

hypercenter

C₄×D₄

D₃₁

C₃₁

G ▷ C₂²×C₃₁ ▷ C₃₁

C₁ ◁ C₂² ◁ C₄×D₄

N	H ≅ G/N	type
3. #11758503	C₂	semidirect
4. #11758501	C₂	semidirect
5. #11758464	C₂	semidirect
6. #11758456	C₂	semidirect
7. #11758446	C₂	semidirect
8. C₄×Dic₆₂	C₂	semidirect
61. C₃₁	#556	semidirect

H ≅ G/N

type

3. #11758503

C₂

semidirect

4. #11758501

C₂

semidirect

5. #11758464

C₂

semidirect

6. #11758456

C₂

semidirect

7. #11758446

C₂

semidirect

8. C₄×Dic₆₂

C₂

semidirect

61. C₃₁

#556

semidirect

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

subgroup	index
C₄×D₄×C₃₁	2
#11758513	2
#11758503	2
#11758501	2
#11758464	2
#11758456	2
#11758446	2
C₄×Dic₆₂	2
#556	31

subgroup

index

C₄×D₄×C₃₁

C₄×Dic₆₂

Subgroups — #14521769

Conjugacy classes of subgroups

Complements

Maximal subgroups