Group #16844620 — subgroups

Subgroups — #16844620

Order 3968.

148 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14521180	C₂	1	2	yes	maximal
2	#14520800	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal
4	#14520770	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₃₁	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₃₁	C₂²	1	2	yes	—
8	C₃₁×#107	C₄	1	1	yes	characteristic
9	C₃₁×#103	C₄	1	2	yes	—
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₄⋊(C₃₁⋊C₈)	—	2	2	no	—
12	C₄⋊(C₃₁⋊C₈)	C₂²	1	2	yes	—
13	#11758391	—	2	2	no	—
14	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₃₁	C₂×C₄	1	2	yes	—
17	Q₁₆×C₃₁	—	2	2	no	—
18	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₃₁	—	2	2	no	—
21	C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
22	C₄²×C₃₁	—	2	2	no	—
23	C₄²×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×C₃₁⋊C₈	—	2	2	no	—
25	C₂×C₃₁⋊C₈	—	2	1	no	—
26	C₂×C₃₁⋊C₈	D₄	1	2	yes	—
27	Q₈×C₃₁	—	2	2	no	—
28	Q₈×C₃₁	—	2	2	no	—
29	C₂×C₄×C₃₁	—	2	2	no	—
30	C₂×C₄×C₃₁	—	2	2	no	—
31	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₃₁	#41	1	1	yes	characteristic
34	C₈×C₃₁	—	2	1	no	—
35	C₈×C₃₁	M₁₆	1	2	yes	—
36	C₃₁⋊C₈	—	2	2	no	—
37	C₃₁⋊C₈	—	4	1	no	—
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	—	4	2	no	—
43	C₄×C₃₁	—	4	2	no	—
44	C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₃₁	#131	1	1	yes	characteristic
46	C₄×C₃₁	#137	1	2	yes	—
47	#446	—	31	2	no	—
48	C₄×Q₁₆	D₃₁	1	1	yes	characteristic
49	#334	—	31	1	no	—
50	Q₈⋊C₈	—	31	2	no	—
51	#322	—	31	1	no	—
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	Dic₃₁	1	1	yes	characteristic
56	C₄×Q₈	C₂×D₃₁	1	2	yes	—
57	#107	Dic₃₁	1	1	yes	characteristic
58	C₄⋊C₈	—	31	2	no	—
59	C₄⋊C₈	—	62	2	no	—
60	#103	Dic₃₁	1	2	yes	—
61	#97	—	62	2	no	—
62	C₄×C₈	—	31	1	no	—
63	C₄×C₈	—	31	1	no	—
64	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
65	C₃₁	#1593	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	C₂×Dic₃₁	1	2	yes	—
67	Q₁₆	—	2	2	no	—
68	C₂×C₈	—	31	2	no	—
69	C₂×C₈	—	62	2	no	—
70	C₂×C₈	—	62	1	no	—
71	C₂×C₈	C₂×Dic₃₁	1	1	yes	characteristic
72	C₂×C₈	C₂×Dic₃₁	1	1	yes	characteristic
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	C₂×Dic₃₁	1	2	yes	—
75	C₄²	—	2	2	no	—
76	C₄²	C₂²×D₃₁	1	1	yes	characteristic
77	Q₈	—	2	2	no	—
78	Q₈	—	2	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
82	C₂×C₄	#92497	1	1	yes	characteristic
83	C₂×C₄	C₂²×Dic₃₁	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	62	2	no	—
86	C₈	—	124	1	no	—
87	C₈	—	124	2	no	—
88	C₈	#92474	1	2	yes	—
89	C₂²	D₄×Dic₃₁	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	4	2	no	—
92	C₄	—	4	2	no	—
93	C₄	#11758495	1	2	yes	—
94	C₄	C₂×#92474	1	1	yes	characteristic
95	C₄	#11758525	1	1	yes	characteristic
96	C₂	#14521127	1	1	yes	characteristic
97	C₂	#14521156	1	1	yes	characteristic
98	C₂	#14521171	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14521180

C₂

yes

maximal

#14520800

C₂

yes

maximal, characteristic

Q₈⋊(C₃₁⋊C₈)

C₂

yes

maximal

#14520770

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₃₁

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₃₁

C₄

yes

characteristic

C₄×Q₈×C₃₁

C₂²

yes

—

C₃₁×#107

C₄

yes

characteristic

C₃₁×#103

C₄

yes

—

C₄×C₈×C₃₁

C₂²

yes

characteristic

C₄⋊(C₃₁⋊C₈)

—

C₄⋊(C₃₁⋊C₈)

C₂²

yes

—

#11758391

—

C₄×C₃₁⋊C₈

C₂²

yes

characteristic

C₄×C₃₁⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₃₁

C₂×C₄

yes

—

Q₁₆×C₃₁

—

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₂×C₈×C₃₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

C₂×C₄

yes

—

C₄²×C₃₁

—

C₄²×C₃₁

C₂³

yes

characteristic

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

D₄

yes

—

Q₈×C₃₁

—

Q₈×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

#41

yes

characteristic

C₈×C₃₁

—

C₈×C₃₁

M₁₆

yes

—

C₃₁⋊C₈

—

C₃₁⋊C₈

—

C₃₁⋊C₈

—

#1593

—

maximal, Sylow

C₂²×C₃₁

C₄×D₄

yes

characteristic

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

C₂×M₁₆

yes

C₄×C₃₁

yes

C₄×C₃₁

yes

—

#446

—

C₄×Q₁₆

D₃₁

yes

characteristic

#334

—

Q₈⋊C₈

—

#322

—

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂×Q₁₆

Dic₃₁

yes

characteristic

C₄×Q₈

C₂×D₃₁

yes

—

#107

Dic₃₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#103

Dic₃₁

yes

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₃₁

yes

characteristic

C₃₁

#1593

yes

characteristic, complemented, Sylow

C₂×Q₈

C₂×Dic₃₁

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₃₁

yes

characteristic

C₂×C₈

C₂×Dic₃₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₃₁

yes

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₃₁

yes

characteristic

C₂×C₄

#92497

yes

characteristic

C₂×C₄

C₂²×Dic₃₁

yes

characteristic

C₈

—

C₈

—

C₈

—

124

—

C₈

—

124

—

C₈

#92474

yes

—

C₂²

D₄×Dic₃₁

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#11758495

yes

—

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	D₄×D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₄²	C₂²×D₃₁
Fitting	C₄×Q₁₆×C₃₁	C₂
socle, prime radical	C₂²×C₃₁	C₄×D₄
cosocle	C₄²×C₃₁	C₂³
hypercenter	C₄×Q₁₆	D₃₁
hypocenter	C₃₁	#1593
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

subgroup

G/H

center

C₂×C₄

D₄×D₃₁

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₄²

C₂²×D₃₁

Fitting

C₄×Q₁₆×C₃₁

C₂

socle, prime radical

C₂²×C₃₁

C₄×D₄

cosocle

C₄²×C₃₁

C₂³

hypercenter

C₄×Q₁₆

D₃₁

hypocenter

C₃₁

#1593

LCS

G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

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
#14521180	2
#14520800	2
Q₈⋊(C₃₁⋊C₈)	2
#14520770	2
C₄×Q₁₆×C₃₁	2
#1593	31

subgroup

index

Q₈⋊(C₃₁⋊C₈)

C₄×Q₁₆×C₃₁

Subgroups — #16844620

Conjugacy classes of subgroups

Complements

Maximal subgroups