Group #16844435 — subgroups

Subgroups — #16844435

Order 3968.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₄⋊Q₈×D₃₁	C₂	1	1	yes	maximal, characteristic
2	#14521105	C₂	1	2	yes	maximal
3	#14520798	C₂	1	1	yes	maximal, characteristic, complemented
4	#14520797	C₂	1	2	yes	maximal, complemented
5	C₃₁×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×D₃₁	C₄	1	2	yes	—
7	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	#11758521	C₄	1	2	yes	—
9	C₄⋊C₄×D₃₁	—	2	2	no	—
10	#11758465	—	2	2	no	—
11	C₄²×D₃₁	C₂²	1	1	yes	characteristic
12	#11758446	C₂²	1	1	yes	characteristic
13	C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
14	(C₂×D₃₁)⋊C₈	—	2	2	no	—
15	#11758403	—	2	2	no	—
16	C₄⋊(C₃₁⋊C₈)	C₂²	1	2	yes	—
17	C₂×Q₈×C₃₁	C₂×C₄	1	2	yes	—
18	Q₈×D₃₁	—	4	4	no	—
19	C₂×C₄×D₃₁	—	2	2	no	—
20	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₃₁	D₄	1	2	yes	—
22	C₂×Dic₆₂	—	2	2	no	—
23	C₂×Dic₆₂	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₃₁	—	2	2	no	—
25	C₄⋊C₄×C₃₁	—	2	2	no	—
26	C₄²×C₃₁	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₃₁	—	2	2	no	—
28	Dic₃₁⋊C₄	—	2	4	no	—
29	C₄×Dic₃₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₃₁	D₄	1	2	yes	—
31	C₂×C₃₁⋊C₈	—	2	2	no	—
32	C₂²×D₃₁	C₂²⋊C₄	1	1	yes	characteristic
33	Q₈×C₃₁	—	4	2	no	—
34	C₂×C₄×C₃₁	—	2	2	no	—
35	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
37	C₂×Dic₃₁	—	2	2	no	—
38	C₂×Dic₃₁	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₃₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×D₃₁	—	2	2	no	—
41	C₄×D₃₁	—	2	2	no	—
42	C₄×D₃₁	—	2	2	no	—
43	C₄×D₃₁	—	4	4	no	—
44	Dic₆₂	—	4	4	no	—
45	Dic₆₂	—	4	2	no	—
46	C₈×C₃₁	—	4	2	no	—
47	C₃₁⋊C₈	—	4	2	no	—
48	#1558	—	31	1	no	maximal, Sylow
49	C₂²×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂×D₃₁	—	2	2	no	—
51	C₂×D₃₁	#100	1	2	yes	—
52	C₄×C₃₁	—	2	1	no	—
53	C₄×C₃₁	—	4	2	no	—
54	C₄×C₃₁	#137	1	2	yes	—
55	C₄×C₃₁	#137	1	2	yes	—
56	Dic₃₁	—	2	1	no	—
57	Dic₃₁	—	2	2	no	—
58	Dic₃₁	—	4	2	no	—
59	C₂×C₄⋊Q₈	—	31	1	no	—
60	#432	—	31	2	no	—
61	#333	—	31	1	no	—
62	#333	—	31	2	no	—
63	#333	D₃₁	1	1	yes	characteristic, complemented
64	C₂×C₃₁	C₂×#100	1	1	yes	characteristic
65	C₂×C₃₁	#419	1	2	yes	—
66	D₃₁	—	2	2	no	—
67	C₂²×Q₈	—	31	2	no	—
68	C₄⋊Q₈	—	31	2	no	—
69	C₄⋊Q₈	—	31	1	no	—
70	C₄⋊Q₈	—	62	2	no	—
71	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
72	C₂×C₄⋊C₄	—	62	2	no	—
73	C₂×C₄²	—	31	1	no	—
74	C₄⋊C₈	—	31	2	no	—
75	C₄⋊C₈	C₂×D₃₁	1	2	yes	—
76	C₂²⋊C₈	—	62	2	no	—
77	#97	—	62	2	no	—
78	C₃₁	#1558	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	31	2	no	—
80	C₂×Q₈	—	62	2	no	—
81	C₂×Q₈	—	124	4	no	—
82	C₂×Q₈	C₄×D₃₁	1	2	yes	—
83	C₂²×C₄	—	31	1	no	—
84	C₂²×C₄	—	31	2	no	—
85	C₂²×C₄	—	62	2	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	62	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	62	4	no	—
90	C₄⋊C₄	—	62	2	no	—
91	C₄²	—	31	1	no	—
92	C₄²	—	31	2	no	—
93	C₄²	C₂²×D₃₁	1	1	yes	characteristic
94	C₂³	—	31	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	124	2	no	—
97	Q₈	—	124	4	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	31	2	no	—
100	C₂×C₄	—	31	1	no	—
101	C₂×C₄	—	62	2	no	—
102	C₂×C₄	—	62	2	no	—
103	C₂×C₄	—	62	2	no	—
104	C₂×C₄	—	62	2	no	—
105	C₂×C₄	—	124	4	no	—
106	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
107	C₂×C₄	D₄×D₃₁	1	2	yes	—
108	C₈	—	4	2	no	—
109	C₈	—	124	2	no	—
110	C₂²	—	31	2	no	—
111	C₂²	—	62	2	no	—
112	C₂²	C₂²⋊C₄×D₃₁	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	4	2	no	—
115	C₄	—	62	1	no	—
116	C₄	—	62	2	no	—
117	C₄	—	124	2	no	—
118	C₄	#11758492	1	2	yes	—
119	C₄	#11758495	1	2	yes	—
120	C₂	—	62	2	no	—
121	C₂	#100×D₃₁	1	1	yes	characteristic
122	C₂	#14521056	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₃₁

C₂

yes

maximal, characteristic

#14521105

C₂

yes

maximal

#14520798

C₂

yes

maximal, characteristic, complemented

#14520797

C₂

yes

maximal, complemented

C₃₁×#333

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₃₁

C₄

yes

—

C₃₁×C₄⋊Q₈

C₂²

yes

characteristic

#11758521

C₄

yes

—

C₄⋊C₄×D₃₁

—

#11758465

—

C₄²×D₃₁

C₂²

yes

characteristic

#11758446

C₂²

yes

characteristic

C₃₁×C₄⋊C₈

C₂²

yes

—

(C₂×D₃₁)⋊C₈

—

#11758403

—

C₄⋊(C₃₁⋊C₈)

C₂²

yes

—

C₂×Q₈×C₃₁

C₂×C₄

yes

—

Q₈×D₃₁

—

C₂×C₄×D₃₁

—

C₂×C₄×D₃₁

C₂×C₄

yes

characteristic

C₂×C₄×D₃₁

D₄

yes

—

C₂×Dic₆₂

—

C₂×Dic₆₂

C₂×C₄

yes

—

C₂×C₈×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂³

yes

characteristic

C₄⋊Dic₃₁

—

Dic₃₁⋊C₄

—

C₄×Dic₃₁

C₂×C₄

yes

characteristic

C₄×Dic₃₁

D₄

yes

—

C₂×C₃₁⋊C₈

—

C₂²×D₃₁

C₂²⋊C₄

yes

characteristic

Q₈×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

C₂²⋊C₄

yes

—

C₂×Dic₃₁

C₂²⋊C₄

yes

characteristic

C₄×D₃₁

—

C₄×D₃₁

—

C₄×D₃₁

—

C₄×D₃₁

—

Dic₆₂

—

Dic₆₂

—

C₈×C₃₁

—

C₃₁⋊C₈

—

#1558

—

maximal, Sylow

C₂²×C₃₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₃₁

—

C₂×D₃₁

#100

yes

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

#137

yes

—

C₄×C₃₁

#137

yes

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

—

C₂×C₄⋊Q₈

—

—

—

—

D₃₁

yes

characteristic, complemented

C₂×C₃₁

C₂×#100

yes

characteristic

C₂×C₃₁

#419

yes

—

D₃₁

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₃₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₃₁

yes

—

C₂²⋊C₈

—

#97

—

C₃₁

#1558

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

124

—

C₂×Q₈

C₄×D₃₁

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₃₁

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

124

—

Q₈

—

124

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

124

—

106

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

107

C₂×C₄

D₄×D₃₁

yes

—

108

C₈

—

109

C₈

—

124

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂²⋊C₄×D₃₁

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

124

—

118

C₄

#11758492

yes

—

119

C₄

#11758495

yes

—

120

C₂

—

121

C₂

#100×D₃₁

yes

characteristic

122

C₂

#14521056

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#333	C₂
socle	C₂²×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂²×D₃₁	C₂²⋊C₄
cosocle	C₄²×C₃₁	C₂³
hypercenter	#333	D₃₁
hypocenter	C₃₁	#1558
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₃₁

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₄²

C₂²×D₃₁

Fitting

C₃₁×#333

C₂

socle

C₂²×C₃₁

C₂×C₂²⋊C₄

prime radical

C₂²×D₃₁

C₂²⋊C₄

cosocle

C₄²×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂×C₄×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
3. #14520798	C₂	semidirect
4. #14520797	C₂	semidirect
5. C₃₁×#333	C₂	semidirect
63. #333	D₃₁	semidirect
78. C₃₁	#1558	semidirect

H ≅ G/N

type

3. #14520798

C₂

semidirect

4. #14520797

C₂

semidirect

5. C₃₁×#333

C₂

semidirect

63. #333

D₃₁

semidirect

78. C₃₁

#1558

semidirect

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

subgroup	index
C₄⋊Q₈×D₃₁	2
#14521105	2
#14520798	2
#14520797	2
C₃₁×#333	2
#1558	31

subgroup

index

C₄⋊Q₈×D₃₁

C₃₁×#333

Subgroups — #16844435

Conjugacy classes of subgroups

Complements

Maximal subgroups