Group #16847516 — subgroups

Subgroups — #16847516

Order 3968.

138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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	#14521003	C₂	1	1	yes	maximal, characteristic
2	Dic₃₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₃₁)⋊C₁₆	C₂	1	2	yes	maximal
4	#14520825	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#92469	C₄	1	1	yes	characteristic
7	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
8	#11758449	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₃₁	C₂²	1	2	yes	—
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	#11758403	C₄	1	1	yes	characteristic
12	C₈×Dic₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁⋊C₁₆	C₂²	1	2	yes	—
14	#11758391	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
18	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
19	(C₂×D₃₁)⋊C₄	C₈	1	2	yes	—
20	Dic₃₁⋊C₄	C₈	1	2	yes	—
21	C₄×Dic₃₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃₁⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃₁⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#92469	—	2	2	no	—
25	C₈×D₃₁	—	2	2	no	—
26	C₁₆×C₃₁	—	2	2	no	—
27	C₃₁⋊C₁₆	—	2	2	no	—
28	C₂²×D₃₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₁	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₃₁	C₂×C₈	1	2	yes	—
32	C₂×Dic₃₁	C₂×C₈	1	1	yes	characteristic
33	C₄×D₃₁	—	2	1	no	—
34	C₄×D₃₁	—	2	1	no	—
35	C₈×C₃₁	M₁₆	1	2	yes	—
36	C₈×C₃₁	#41	1	2	yes	—
37	C₃₁⋊C₈	—	2	1	no	—
38	C₃₁⋊C₈	—	2	1	no	—
39	#2164	—	31	1	no	maximal, Sylow
40	C₂²×C₃₁	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₃₁	—	2	1	no	—
42	C₂×D₃₁	—	2	2	no	—
43	C₄×C₃₁	—	2	2	no	—
44	C₄×C₃₁	#117	1	1	yes	characteristic
45	C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
46	Dic₃₁	—	2	1	no	—
47	Dic₃₁	—	2	2	no	—
48	#405	—	31	1	no	—
49	C₄⋊C₁₆	—	31	2	no	—
50	C₂²⋊C₁₆	—	31	2	no	—
51	#346	—	31	1	no	—
52	C₄×C₁₆	D₃₁	1	1	yes	characteristic, complemented
53	C₂×C₃₁	#431	1	1	yes	characteristic
54	C₂×C₃₁	#504	1	2	yes	—
55	D₃₁	—	4	1	no	—
56	C₂×M₁₆	—	31	1	no	—
57	C₂²×C₈	—	31	1	no	—
58	#117	—	31	1	no	—
59	C₂×C₁₆	—	31	2	no	—
60	C₂×C₁₆	C₂×D₃₁	1	2	yes	—
61	#97	—	31	1	no	—
62	#97	—	31	1	no	—
63	C₄×C₈	—	31	1	no	—
64	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
65	C₃₁	#2164	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	31	1	no	—
67	M₁₆	—	62	2	no	—
68	C₂×C₈	—	31	1	no	—
69	C₂×C₈	—	31	1	no	—
70	C₂×C₈	—	62	2	no	—
71	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
73	C₄⋊C₄	—	31	2	no	—
74	C₂²⋊C₄	—	31	2	no	—
75	C₄²	—	31	1	no	—
76	C₄²	C₄×D₃₁	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	62	2	no	—
79	C₂³	—	31	1	no	—
80	C₂×C₄	—	31	2	no	—
81	C₂×C₄	—	31	1	no	—
82	C₂×C₄	—	62	1	no	—
83	C₂×C₄	—	62	1	no	—
84	C₂×C₄	C₈×D₃₁	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
86	C₈	—	62	1	no	—
87	C₈	—	62	1	no	—
88	C₈	#92469	1	2	yes	—
89	C₈	#92495	1	2	yes	—
90	C₂²	—	62	1	no	—
91	C₂²	—	62	2	no	—
92	C₂²	C₂×C₈×D₃₁	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	62	1	no	—
95	C₄	—	62	2	no	—
96	C₄	#11758449	1	1	yes	characteristic
97	C₄	C₂×#92469	1	1	yes	characteristic
98	C₂	—	124	1	no	—
99	C₂	#14521100	1	1	yes	characteristic
100	C₂	#14521465	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14521003

C₂

yes

maximal, characteristic

Dic₃₁⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₃₁)⋊C₁₆

C₂

yes

maximal

#14520825

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₃₁

C₂

yes

maximal, characteristic, complemented

C₂×#92469

C₄

yes

characteristic

C₂×C₈×D₃₁

C₂²

yes

characteristic

#11758449

C₄

yes

characteristic

C₂×C₁₆×C₃₁

C₂²

yes

—

C₄×C₈×C₃₁

C₂²

yes

characteristic

#11758403

C₄

yes

characteristic

C₈×Dic₃₁

C₂²

yes

characteristic

C₂×C₃₁⋊C₁₆

C₂²

yes

—

#11758391

C₄

yes

characteristic

C₂×C₄×D₃₁

C₂×C₄

yes

characteristic

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₂×C₈×C₃₁

C₂³

yes

characteristic

C₄²×C₃₁

C₂×C₄

yes

characteristic

(C₂×D₃₁)⋊C₄

C₈

yes

—

Dic₃₁⋊C₄

C₈

yes

—

C₄×Dic₃₁

C₂×C₄

yes

characteristic

C₂×C₃₁⋊C₈

C₂×C₄

yes

characteristic

C₂×C₃₁⋊C₈

C₂×C₄

yes

characteristic

#92469

—

C₈×D₃₁

—

C₁₆×C₃₁

—

C₃₁⋊C₁₆

—

C₂²×D₃₁

C₂×C₈

yes

characteristic

C₂×C₄×C₃₁

C₂×C₈

yes

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×Dic₃₁

C₂×C₈

yes

—

C₂×Dic₃₁

C₂×C₈

yes

characteristic

C₄×D₃₁

—

C₄×D₃₁

—

C₈×C₃₁

M₁₆

yes

—

C₈×C₃₁

#41

yes

—

C₃₁⋊C₈

—

C₃₁⋊C₈

—

#2164

—

maximal, Sylow

C₂²×C₃₁

C₂²×C₈

yes

characteristic

C₂×D₃₁

—

C₂×D₃₁

—

C₄×C₃₁

—

C₄×C₃₁

#117

yes

characteristic

C₄×C₃₁

C₂×M₁₆

yes

characteristic

Dic₃₁

—

Dic₃₁

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

D₃₁

yes

characteristic, complemented

C₂×C₃₁

#431

yes

characteristic

C₂×C₃₁

#504

yes

—

D₃₁

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₃₁

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₃₁

yes

characteristic

C₃₁

#2164

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₁

yes

characteristic

C₂×C₈

C₂²×D₃₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₃₁

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₃₁

yes

—

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₈

—

C₈

—

C₈

#92469

yes

—

C₈

#92495

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₃₁

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

124

—

C₂

#14521100

yes

characteristic

100

C₂

#14521465

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₃₁
commutator, socle	C₂²×C₃₁	C₂²×C₈
Fitting	C₄×C₁₆×C₃₁	C₂
prime radical	C₂²×D₃₁	C₂×C₈
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	C₄×C₁₆	D₃₁
hypocenter	C₃₁	#2164
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₃₁

commutator, socle

C₂²×C₃₁

C₂²×C₈

Fitting

C₄×C₁₆×C₃₁

C₂

prime radical

C₂²×D₃₁

C₂×C₈

cosocle

C₂×C₈×C₃₁

C₂³

hypercenter

C₄×C₁₆

D₃₁

C₃₁

G ▷ C₂²×C₃₁ ▷ C₃₁

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. Dic₃₁⋊C₁₆	C₂	semidirect
4. #14520825	C₂	semidirect
5. C₄×C₁₆×C₃₁	C₂	semidirect
52. C₄×C₁₆	D₃₁	semidirect
65. C₃₁	#2164	semidirect

H ≅ G/N

type

2. Dic₃₁⋊C₁₆

C₂

semidirect

4. #14520825

C₂

semidirect

5. C₄×C₁₆×C₃₁

C₂

semidirect

52. C₄×C₁₆

D₃₁

semidirect

65. C₃₁

#2164

semidirect

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

subgroup	index
#14521003	2
Dic₃₁⋊C₁₆	2
(C₂×D₃₁)⋊C₁₆	2
#14520825	2
C₄×C₁₆×C₃₁	2
#2164	31

subgroup

index

#14521003

Dic₃₁⋊C₁₆

(C₂×D₃₁)⋊C₁₆

#14520825

C₄×C₁₆×C₃₁

#2164

Subgroups — #16847516

Conjugacy classes of subgroups

Complements

Maximal subgroups