Group #16844849 — subgroups

Subgroups — #16844849

Order 3968.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14521779	C₂	1	1	yes	maximal, characteristic
2	#14521341	C₂	1	2	yes	maximal
3	#14520798	C₂	1	1	yes	maximal, characteristic
4	#14520781	C₂	1	2	yes	maximal
5	C₃₁×#494	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₃₁	—	2	2	no	—
7	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	#11758521	—	2	2	no	—
10	#11758465	—	2	2	no	—
11	#11758464	—	2	2	no	—
12	C₄×Dic₆₂	C₂²	1	2	yes	—
13	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
14	#11758398	—	2	2	no	—
15	#11758395	—	2	2	no	—
16	C₄⋊(C₃₁⋊C₈)	C₂²	1	2	yes	—
17	C₂×Q₈×C₃₁	—	2	1	no	—
18	C₂×Q₈×C₃₁	D₄	1	2	yes	—
19	C₂×Dic₆₂	—	2	2	no	—
20	C₂×Dic₆₂	D₄	1	2	yes	—
21	Q₁₆×C₃₁	—	4	4	no	—
22	C₂×C₈×C₃₁	—	2	1	no	—
23	C₄⋊C₄×C₃₁	—	2	2	no	—
24	C₄⋊C₄×C₃₁	—	2	2	no	—
25	C₄²×C₃₁	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₃₁	D₄	1	2	yes	—
27	Dic₃₁⋊C₄	—	2	4	no	—
28	Dic₃₁⋊C₄	—	2	2	no	—
29	C₄×Dic₃₁	—	2	2	no	—
30	C₄×Dic₃₁	—	2	2	no	—
31	C₂×C₃₁⋊C₈	—	2	2	no	—
32	Q₈×C₃₁	—	4	2	no	—
33	Q₈×C₃₁	—	4	2	no	—
34	C₂×C₄×C₃₁	—	2	2	no	—
35	C₂×C₄×C₃₁	—	4	1	no	—
36	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₃₁	—	2	2	no	—
39	C₂×Dic₃₁	—	2	2	no	—
40	Dic₆₂	—	2	2	no	—
41	Dic₆₂	—	8	2	no	—
42	Dic₆₂	Q₁₆	1	4	yes	complemented
43	C₈×C₃₁	—	2	2	no	—
44	C₃₁⋊C₈	—	4	2	no	—
45	#1633	—	31	1	no	maximal, Sylow
46	C₂²×C₃₁	#120	1	1	yes	characteristic
47	C₄×C₃₁	—	2	1	no	—
48	C₄×C₃₁	—	4	2	no	—
49	C₄×C₃₁	—	8	1	no	—
50	C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
51	C₄×C₃₁	#137	1	2	yes	—
52	Dic₃₁	—	2	4	no	—
53	Dic₃₁	—	4	2	no	—
54	Q₈²	—	31	1	no	—
55	#494	D₃₁	1	1	yes	characteristic
56	#477	—	31	2	no	—
57	#333	—	31	1	no	—
58	Q₈⋊C₈	—	31	2	no	—
59	C₂×C₃₁	#451	1	2	yes	—
60	C₂×C₃₁	#453	1	1	yes	characteristic
61	C₂×Q₁₆	—	2	2	no	—
62	C₄⋊Q₈	—	62	2	no	—
63	C₄⋊Q₈	—	62	2	no	—
64	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
65	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
66	C₄×Q₈	—	31	2	no	—
67	C₄×Q₈	—	62	2	no	—
68	#107	—	62	2	no	—
69	C₄⋊C₈	—	31	2	no	—
70	#103	—	62	2	no	—
71	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
72	C₃₁	#1633	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	31	2	no	—
75	C₂×Q₈	—	62	2	no	—
76	C₂×Q₈	C₂²⋊D₃₁	1	2	yes	—
77	Q₁₆	—	4	4	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	62	2	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	31	2	no	—
83	C₄⋊C₄	—	62	4	no	—
84	C₄⋊C₄	—	62	2	no	—
85	C₄²	—	62	2	no	—
86	C₄²	—	62	2	no	—
87	C₄²	C₂²×D₃₁	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	31	4	no	—
91	Q₈	—	62	2	no	—
92	Q₈	—	248	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	62	2	no	—
96	C₂×C₄	—	62	2	no	—
97	C₂×C₄	D₄×D₃₁	1	2	yes	—
98	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	124	2	no	—
101	C₂²	#11758514	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	4	2	no	—
104	C₄	—	8	1	no	—
105	C₄	—	62	4	no	—
106	C₄	—	124	2	no	—
107	C₄	Q₁₆×D₃₁	1	2	yes	—
108	C₄	#11758495	1	2	yes	—
109	C₂	#14521203	1	2	yes	—
110	C₂	#14521216	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14521779

C₂

yes

maximal, characteristic

#14521341

C₂

yes

maximal

#14520798

C₂

yes

maximal, characteristic

#14520781

C₂

yes

maximal

C₃₁×#494

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₃₁

—

C₃₁×C₄⋊Q₈

C₂²

yes

characteristic

C₃₁×C₄⋊Q₈

C₂²

yes

—

—

—

C₄×Dic₆₂

C₂²

yes

—

C₄×C₈×C₃₁

C₂²

yes

characteristic

#11758398

—

#11758395

—

C₄⋊(C₃₁⋊C₈)

C₂²

yes

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

D₄

yes

—

C₂×Dic₆₂

—

C₂×Dic₆₂

D₄

yes

—

Q₁₆×C₃₁

—

C₂×C₈×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂³

yes

characteristic

C₄⋊Dic₃₁

D₄

yes

—

Dic₃₁⋊C₄

—

Dic₃₁⋊C₄

—

C₄×Dic₃₁

—

C₄×Dic₃₁

—

C₂×C₃₁⋊C₈

—

Q₈×C₃₁

—

Q₈×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂×D₄

yes

—

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×Dic₃₁

—

C₂×Dic₃₁

—

Dic₆₂

—

Dic₆₂

—

Dic₆₂

Q₁₆

yes

complemented

C₈×C₃₁

—

C₃₁⋊C₈

—

—

C₂²×C₃₁

yes

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

C₂×Q₁₆

yes

—

C₄×C₃₁

#137

yes

—

Dic₃₁

—

Dic₃₁

—

Q₈²

—

#494

D₃₁

yes

characteristic

#477

—

#333

—

Q₈⋊C₈

—

C₂×C₃₁

#451

yes

—

C₂×C₃₁

#453

yes

characteristic

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₃₁

yes

characteristic

C₄⋊Q₈

C₂×D₃₁

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

C₂×D₃₁

yes

characteristic

C₃₁

#1633

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₃₁

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

248

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₃₁

yes

—

C₂×C₄

C₂×C₂²⋊D₃₁

yes

characteristic

C₈

—

100

C₈

—

124

—

101

C₂²

#11758514

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

124

—

107

C₄

Q₁₆×D₃₁

yes

—

108

C₄

#11758495

yes

—

109

C₂

#14521203

yes

—

110

C₂

#14521216

yes

characteristic

	subgroup	G/H
center	C₂²	#11758514
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#494	C₂
socle, prime radical	C₂²×C₃₁	#120
hypercenter	#494	D₃₁
hypocenter	C₃₁	#1633
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#11758514

commutator, cosocle

C₄²×C₃₁

C₂³

Frattini

C₄²

C₂²×D₃₁

Fitting

C₃₁×#494

C₂

C₂²×C₃₁

D₃₁

C₃₁

G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
42. Dic₆₂	Q₁₆	semidirect
72. C₃₁	#1633	semidirect

H ≅ G/N

type

42. Dic₆₂

Q₁₆

semidirect

72. C₃₁

#1633

semidirect

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

subgroup	index
#14521779	2
#14521341	2
#14520798	2
#14520781	2
C₃₁×#494	2
#1633	31

subgroup

index

C₃₁×#494

Subgroups — #16844849

Conjugacy classes of subgroups

Complements

Maximal subgroups