Group #16844790 — subgroups

Subgroups — #16844790

Order 3968.

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

normal subgroups only

This group has 228 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, complemented
2	#14521423	C₂	1	1	yes	maximal, characteristic
3	#14521250	C₂	1	2	yes	maximal
4	#14520779	C₂	1	2	yes	maximal, complemented
5	C₃₁×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	#11758521	—	2	2	no	—
8	C₂×#92481	—	2	2	no	—
9	C₂×#92470	—	2	2	no	—
10	#11758465	—	2	2	no	—
11	#11758464	—	2	2	no	—
12	#11758451	C₂²	1	1	yes	characteristic
13	C₄×Dic₆₂	C₂²	1	2	yes	—
14	C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	#11758409	—	2	2	no	—
16	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₃₁	D₄	1	2	yes	—
18	C₂×D₁₂₄	—	2	2	no	—
19	C₂×D₁₂₄	—	2	1	no	—
20	C₂×Dic₆₂	—	2	2	no	—
21	C₂×Dic₆₂	D₄	1	2	yes	—
22	C₂×C₈×C₃₁	—	2	2	no	—
23	C₄⋊C₄×C₃₁	—	2	2	no	—
24	C₄²×C₃₁	C₂³	1	1	yes	characteristic
25	#92481	—	4	4	no	—
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	1	no	—
32	#92470	—	4	4	no	—
33	C₂²×D₃₁	—	4	1	no	—
34	Q₈×C₃₁	—	4	2	no	—
35	C₂×C₄×C₃₁	—	2	2	no	—
36	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
38	C₂×Dic₃₁	—	2	2	no	—
39	C₂×Dic₃₁	—	2	2	no	—
40	D₁₂₄	—	4	2	no	—
41	D₁₂₄	—	4	2	no	—
42	D₁₂₄	—	4	2	no	—
43	Dic₆₂	—	2	2	no	—
44	Dic₆₂	—	8	2	no	—
45	Dic₆₂	SD₁₆	1	4	yes	complemented
46	C₈×C₃₁	—	4	2	no	—
47	C₃₁⋊C₈	—	2	2	no	—
48	#1623	—	31	1	no	maximal, Sylow
49	C₂²×C₃₁	#120	1	1	yes	characteristic
50	C₂×D₃₁	—	8	2	no	—
51	C₂×D₃₁	—	8	1	no	—
52	C₄×C₃₁	—	2	1	no	—
53	C₄×C₃₁	—	4	2	no	—
54	C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
55	C₄×C₃₁	#137	1	2	yes	—
56	Dic₃₁	—	2	4	no	—
57	Dic₃₁	—	4	2	no	—
58	Q₈²	—	31	1	no	—
59	#492	—	31	1	no	—
60	#460	—	31	2	no	—
61	#333	D₃₁	1	1	yes	characteristic, complemented
62	Q₈⋊C₈	—	31	2	no	—
63	C₂×C₃₁	#448	1	2	yes	—
64	C₂×C₃₁	#453	1	1	yes	characteristic
65	D₃₁	—	16	1	no	—
66	C₂×SD₁₆	—	62	2	no	—
67	C₂×SD₁₆	—	62	2	no	—
68	C₄⋊Q₈	—	62	2	no	—
69	C₄⋊Q₈	—	62	2	no	—
70	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
71	#127	—	31	1	no	—
72	C₄×Q₈	—	31	2	no	—
73	C₄×Q₈	—	62	2	no	—
74	C₄⋊C₈	C₂×D₃₁	1	2	yes	—
75	#102	—	62	2	no	—
76	C₄×C₈	—	31	1	no	—
77	C₃₁	#1623	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₈	—	31	2	no	—
79	C₂×Q₈	—	62	2	no	—
80	C₂×Q₈	D₁₂₄	1	2	yes	—
81	C₂×D₄	—	62	1	no	—
82	C₂×D₄	—	62	2	no	—
83	SD₁₆	—	124	4	no	—
84	SD₁₆	—	124	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	62	1	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	31	2	no	—
89	C₄⋊C₄	—	62	4	no	—
90	C₄⋊C₄	—	62	2	no	—
91	C₄²	—	62	2	no	—
92	C₄²	—	62	2	no	—
93	C₄²	C₂²×D₃₁	1	1	yes	characteristic
94	C₂³	—	124	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	31	4	no	—
97	Q₈	—	62	2	no	—
98	Q₈	—	248	2	no	—
99	D₄	—	124	2	no	—
100	D₄	—	124	2	no	—
101	D₄	—	124	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	62	2	no	—
104	C₂×C₄	—	62	2	no	—
105	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
106	C₂×C₄	D₄×D₃₁	1	2	yes	—
107	C₈	—	4	2	no	—
108	C₈	—	62	2	no	—
109	C₂²	—	248	2	no	—
110	C₂²	—	248	1	no	—
111	C₂²	#11758459	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	62	4	no	—
115	C₄	—	124	2	no	—
116	C₄	SD₁₆×D₃₁	1	2	yes	—
117	C₄	#11758495	1	2	yes	—
118	C₂	—	496	1	no	—
119	C₂	#14521189	1	2	yes	—
120	C₂	#14521219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14521779

C₂

yes

maximal, characteristic, complemented

#14521423

C₂

yes

maximal, characteristic

#14521250

C₂

yes

maximal

#14520779

C₂

yes

maximal, complemented

C₃₁×#333

C₂

yes

maximal, characteristic, complemented

C₃₁×C₄⋊Q₈

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₆₂

C₂²

yes

—

C₃₁×C₄⋊C₈

C₂²

yes

—

#11758409

—

C₄×C₃₁⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₃₁

D₄

yes

—

C₂×D₁₂₄

—

C₂×D₁₂₄

—

C₂×Dic₆₂

—

C₂×Dic₆₂

D₄

yes

—

C₂×C₈×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂³

yes

characteristic

#92481

—

C₄⋊Dic₃₁

D₄

yes

—

Dic₃₁⋊C₄

—

Dic₃₁⋊C₄

—

C₄×Dic₃₁

—

C₄×Dic₃₁

—

C₂×C₃₁⋊C₈

—

#92470

—

C₂²×D₃₁

—

Q₈×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

D₁₂₄

—

D₁₂₄

—

D₁₂₄

—

Dic₆₂

—

Dic₆₂

—

Dic₆₂

SD₁₆

yes

complemented

C₈×C₃₁

—

C₃₁⋊C₈

—

—

C₂²×C₃₁

yes

C₂×D₃₁

—

C₂×D₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

C₂×SD₁₆

yes

—

C₄×C₃₁

#137

yes

—

Dic₃₁

—

Dic₃₁

—

Q₈²

—

#492

—

#460

—

#333

D₃₁

yes

characteristic, complemented

Q₈⋊C₈

—

C₂×C₃₁

#448

yes

—

C₂×C₃₁

#453

yes

characteristic

D₃₁

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₃₁

yes

characteristic

#127

—

C₄×Q₈

—

C₄×Q₈

—

C₄⋊C₈

C₂×D₃₁

yes

—

#102

—

C₄×C₈

—

C₃₁

#1623

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₁₂₄

yes

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

124

—

SD₁₆

—

124

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

C₂³

—

124

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

248

—

D₄

—

124

—

100

D₄

—

124

—

101

D₄

—

124

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×D₁₂₄

yes

characteristic

106

C₂×C₄

D₄×D₃₁

yes

—

107

C₈

—

108

C₈

—

109

C₂²

—

248

—

110

C₂²

—

248

—

111

C₂²

#11758459

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

124

—

116

C₄

SD₁₆×D₃₁

yes

—

117

C₄

#11758495

yes

—

118

C₂

—

496

—

119

C₂

#14521189

yes

—

120

C₂

#14521219

yes

characteristic

	subgroup	G/H
center	C₂²	#11758459
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#333	C₂
socle	C₂²×C₃₁	#120
prime radical	#11758451	C₂²
hypercenter	#333	D₃₁
hypocenter	C₃₁	#1623
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#11758459

commutator, cosocle

C₄²×C₃₁

C₂³

Frattini

C₄²

C₂²×D₃₁

Fitting

C₃₁×#333

C₂

C₂²×C₃₁

C₂²

D₃₁

C₃₁

G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #14521779	C₂	semidirect
4. #14520779	C₂	semidirect
5. C₃₁×#333	C₂	semidirect
45. Dic₆₂	SD₁₆	semidirect
61. #333	D₃₁	semidirect
77. C₃₁	#1623	semidirect

H ≅ G/N

type

1. #14521779

C₂

semidirect

4. #14520779

C₂

semidirect

5. C₃₁×#333

C₂

semidirect

45. Dic₆₂

SD₁₆

semidirect

61. #333

D₃₁

semidirect

77. C₃₁

#1623

semidirect

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

subgroup	index
#14521779	2
#14521423	2
#14521250	2
#14520779	2
C₃₁×#333	2
#1623	31

subgroup

index

C₃₁×#333

Subgroups — #16844790

Conjugacy classes of subgroups

Complements

Maximal subgroups