Group #16844621 — subgroups

Subgroups — #16844621

Order 3968.

148 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14521179	C₂	1	2	yes	maximal
2	C₄×Dic₁₂₄	C₂	1	1	yes	maximal, characteristic
3	#14520800	C₂	1	1	yes	maximal, characteristic
4	#14520781	C₂	1	2	yes	maximal
5	C₃₁×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₂₄	C₄	1	1	yes	characteristic
7	C₄×Dic₆₂	C₂²	1	2	yes	—
8	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	#11758406	C₄	1	1	yes	characteristic
12	#11758404	C₄	1	2	yes	—
13	#11758403	—	2	2	no	—
14	Dic₃₁⋊C₈	—	2	2	no	—
15	C₄⋊(C₃₁⋊C₈)	C₂²	1	2	yes	—
16	C₂×Dic₆₂	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₃₁	—	2	1	no	—
18	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₃₁	D₄	1	2	yes	—
21	C₄²×C₃₁	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₃₁	C₂×C₄	1	2	yes	—
23	Dic₃₁⋊C₄	—	2	2	no	—
24	C₄×Dic₃₁	—	2	2	no	—
25	C₂×C₃₁⋊C₈	—	2	2	no	—
26	Dic₁₂₄	—	2	2	no	—
27	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₃₁	#41	1	1	yes	characteristic
30	C₂×Dic₃₁	—	2	2	no	—
31	C₂×Dic₃₁	—	2	2	no	—
32	Dic₆₂	—	2	2	no	—
33	Dic₆₂	—	2	2	no	—
34	C₈×C₃₁	—	2	1	no	—
35	C₈×C₃₁	—	2	2	no	—
36	C₈×C₃₁	—	4	1	no	—
37	C₈×C₃₁	M₁₆	1	2	yes	—
38	C₃₁⋊C₈	—	4	2	no	—
39	#1593	—	31	1	no	maximal, Sylow
40	C₂²×C₃₁	C₄×D₄	1	1	yes	characteristic
41	C₄×C₃₁	—	2	1	no	—
42	C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
43	C₄×C₃₁	#131	1	1	yes	characteristic
44	C₄×C₃₁	#137	1	2	yes	—
45	Dic₃₁	—	4	2	no	—
46	Dic₃₁	—	4	2	no	—
47	#446	—	31	2	no	—
48	C₄×Q₁₆	—	31	1	no	—
49	#334	—	31	1	no	—
50	Q₈⋊C₈	—	31	2	no	—
51	#322	D₃₁	1	1	yes	characteristic
52	C₂×C₃₁	#436	1	1	yes	characteristic
53	C₂×C₃₁	#441	1	1	yes	characteristic
54	C₂×C₃₁	#444	1	1	yes	characteristic
55	C₂×Q₁₆	—	31	1	no	—
56	C₄×Q₈	—	31	2	no	—
57	#107	—	31	1	no	—
58	C₄⋊C₈	—	31	2	no	—
59	C₄⋊C₈	—	62	2	no	—
60	#103	—	31	2	no	—
61	#97	—	62	2	no	—
62	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
63	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
64	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
65	C₃₁	#1593	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	—	31	2	no	—
67	Q₁₆	—	62	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	62	2	no	—
70	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
71	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
72	C₂×C₈	D₁₂₄	1	2	yes	—
73	C₄⋊C₄	—	31	2	no	—
74	C₄⋊C₄	—	62	2	no	—
75	C₄²	—	62	2	no	—
76	C₄²	C₂²×D₃₁	1	1	yes	characteristic
77	Q₈	—	62	2	no	—
78	Q₈	—	62	2	no	—
79	C₂×C₄	—	62	2	no	—
80	C₂×C₄	—	62	2	no	—
81	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
83	C₂×C₄	#92495	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	124	2	no	—
88	C₈	#92469	1	2	yes	—
89	C₂²	C₄×D₁₂₄	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	124	2	no	—
92	C₄	—	124	2	no	—
93	C₄	C₂×#92469	1	1	yes	characteristic
94	C₄	#11758478	1	1	yes	characteristic
95	C₄	#11758486	1	2	yes	—
96	C₂	#14521128	1	1	yes	characteristic
97	C₂	#14521157	1	1	yes	characteristic
98	C₂	#14521172	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14521179

C₂

yes

maximal

C₄×Dic₁₂₄

C₂

yes

maximal, characteristic

#14520800

C₂

yes

maximal, characteristic

#14520781

C₂

yes

maximal

C₃₁×#322

C₂

yes

maximal, characteristic

C₂×Dic₁₂₄

C₄

yes

characteristic

C₄×Dic₆₂

C₂²

yes

—

C₄×C₈×C₃₁

C₂²

yes

characteristic

C₄×C₈×C₃₁

C₂²

yes

characteristic

C₄×C₈×C₃₁

C₂²

yes

characteristic

#11758406

C₄

yes

characteristic

#11758404

C₄

yes

—

#11758403

—

Dic₃₁⋊C₈

—

C₄⋊(C₃₁⋊C₈)

C₂²

yes

—

C₂×Dic₆₂

C₂×C₄

yes

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₂×C₈×C₃₁

D₄

yes

—

C₄²×C₃₁

C₂³

yes

characteristic

C₄⋊Dic₃₁

C₂×C₄

yes

—

Dic₃₁⋊C₄

—

C₄×Dic₃₁

—

C₂×C₃₁⋊C₈

—

Dic₁₂₄

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

#41

yes

characteristic

C₂×Dic₃₁

—

C₂×Dic₃₁

—

Dic₆₂

—

Dic₆₂

—

C₈×C₃₁

—

C₈×C₃₁

—

C₈×C₃₁

—

C₈×C₃₁

M₁₆

yes

—

C₃₁⋊C₈

—

#1593

—

maximal, Sylow

C₂²×C₃₁

C₄×D₄

yes

characteristic

C₄×C₃₁

—

C₄×C₃₁

C₂×M₁₆

yes

C₄×C₃₁

yes

C₄×C₃₁

yes

—

Dic₃₁

—

Dic₃₁

—

#446

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₃₁

yes

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₂×D₃₁

yes

characteristic

C₄×C₈

C₂×D₃₁

yes

characteristic

C₄×C₈

C₂×D₃₁

yes

characteristic

C₃₁

#1593

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₁

yes

characteristic

C₂×C₈

C₄×D₃₁

yes

characteristic

C₂×C₈

D₁₂₄

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

C₂×D₁₂₄

yes

characteristic

C₂×C₄

#92495

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

124

—

C₈

#92469

yes

—

C₂²

C₄×D₁₂₄

yes

characteristic

C₄

—

C₄

—

124

—

C₄

—

124

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₁₂₄
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#322	C₂
socle, prime radical	C₂²×C₃₁	C₄×D₄
cosocle	C₄²×C₃₁	C₂³
hypercenter	#322	D₃₁
hypocenter	C₃₁	#1593
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₁₂₄

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₄²

C₂²×D₃₁

Fitting

C₃₁×#322

C₂

socle, prime radical

C₂²×C₃₁

C₄×D₄

cosocle

C₄²×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
65. C₃₁	#1593	semidirect

H ≅ G/N

type

65. C₃₁

#1593

semidirect

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

subgroup	index
#14521179	2
C₄×Dic₁₂₄	2
#14520800	2
#14520781	2
C₃₁×#322	2
#1593	31

subgroup

index

C₄×Dic₁₂₄

C₃₁×#322

Subgroups — #16844621

Conjugacy classes of subgroups

Complements

Maximal subgroups