Group #14571993 — subgroups

Subgroups — #14571993

Order 2432.

752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 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	C₂×#10597320	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597393	C₂	1	4	yes	maximal, complemented
3	#11926445	C₂	1	8	yes	maximal, complemented
4	C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂²×D₇₆	C₂²	1	2	yes	—
8	C₂²×D₇₆	C₂²	1	4	yes	—
9	C₁₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	#10597393	—	2	16	no	—
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	16	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
16	#10597320	—	2	4	no	—
17	C₂³×D₁₉	C₂³	1	4	yes	—
18	C₂×Q₈×C₁₉	—	2	8	no	—
19	C₂×Q₈×C₁₉	—	2	4	no	—
20	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
23	C₂²×Dic₁₉	C₂³	1	4	yes	—
24	C₂×D₇₆	—	2	8	no	—
25	C₂×D₇₆	—	2	8	no	—
26	C₂×D₇₆	—	2	4	no	—
27	C₂×D₇₆	—	2	16	no	—
28	C₄⋊C₄×C₁₉	—	2	8	no	—
29	C₄²×C₁₉	D₄	1	4	yes	—
30	(C₂×D₁₉)⋊C₄	—	2	32	no	—
31	C₄×Dic₁₉	—	2	8	no	—
32	C₄×Dic₁₉	D₄	1	8	yes	complemented
33	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
34	C₂²×D₁₉	—	2	8	no	—
35	C₂²×D₁₉	—	2	4	no	—
36	C₂²×D₁₉	—	2	16	no	—
37	Q₈×C₁₉	—	4	8	no	—
38	C₂×C₄×C₁₉	—	2	8	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	#41	1	8	yes	—
44	C₂×Dic₁₉	—	2	8	no	—
45	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
46	D₇₆	—	4	16	no	—
47	D₇₆	—	4	8	no	—
48	#2858	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
50	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
51	C₂²×C₁₉	C₂×#41	1	4	yes	—
52	C₂×D₁₉	—	4	8	no	—
53	C₂×D₁₉	—	4	4	no	—
54	C₂×D₁₉	—	4	16	no	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	#124	1	8	yes	complemented
57	C₄×C₁₉	#127	1	4	yes	—
58	Dic₁₉	—	2	8	no	—
59	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic, complemented
60	C₂×#127	—	19	1	no	—
61	C₂×#124	—	19	4	no	—
62	#390	—	19	8	no	—
63	C₄³	—	19	1	no	—
64	C₂×C₁₉	C₂×#124	1	2	yes	—
65	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
66	C₂×C₁₉	#532	1	4	yes	—
67	D₁₉	—	8	4	no	—
68	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
69	C₂²×D₄	—	19	2	no	—
70	C₂²×D₄	—	19	4	no	—
71	C₄⋊Q₈	—	2	4	no	—
72	#127	—	38	4	no	—
73	#124	—	38	16	no	—
74	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
75	C₂×C₂²⋊C₄	—	19	16	no	—
76	C₂×C₄²	—	19	2	no	—
77	C₂×C₄²	—	19	4	no	—
78	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
79	C₁₉	#2858	1	1	yes	characteristic, complemented, Sylow
80	C₂⁴	—	19	4	no	—
81	C₂×Q₈	—	2	8	no	—
82	C₂×Q₈	—	2	4	no	—
83	C₂×D₄	—	38	8	no	—
84	C₂×D₄	—	38	16	no	—
85	C₂×D₄	—	38	4	no	—
86	C₂×D₄	—	38	8	no	—
87	C₂²×C₄	—	19	4	no	—
88	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
89	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
90	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
91	C₄⋊C₄	—	2	8	no	—
92	C₂²⋊C₄	—	38	32	no	—
93	C₄²	—	19	8	no	—
94	C₄²	—	38	8	no	—
95	C₄²	C₂²⋊D₁₉	1	4	yes	—
96	C₂³	—	38	8	no	—
97	C₂³	—	38	16	no	—
98	C₂³	—	38	4	no	—
99	C₂³	C₂³×D₁₉	1	1	yes	characteristic
100	Q₈	—	4	8	no	—
101	D₄	—	76	8	no	—
102	D₄	—	76	16	no	—
103	C₂×C₄	—	2	8	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	19	8	no	—
106	C₂×C₄	—	38	8	no	—
107	C₂×C₄	D₄×D₁₉	1	4	yes	—
108	C₂×C₄	#64545	1	8	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
111	C₂²	—	76	8	no	—
112	C₂²	—	76	4	no	—
113	C₂²	—	76	16	no	—
114	C₂²	C₂×D₄×D₁₉	1	2	yes	—
115	C₂²	C₂×#64545	1	4	yes	—
116	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
117	C₄	—	4	4	no	—
118	C₄	—	38	8	no	—
119	C₄	#10597386	1	4	yes	—
120	C₄	#10597393	1	8	yes	complemented
121	C₂	—	152	4	no	—
122	C₂	C₂×#10597393	1	2	yes	—
123	C₂	C₂×#10597386	1	1	yes	characteristic
124	C₂	#11927095	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

C₂×#10597393

C₂

yes

maximal, complemented

#11926445

C₂

yes

maximal, complemented

C₄²×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597393

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597320

—

C₂³×D₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

complemented

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

D₇₆

—

#2858

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

complemented

C₄×C₁₉

#127

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic, complemented

C₂×#127

—

C₂×#124

—

#390

—

C₄³

—

C₂×C₁₉

C₂×#124

yes

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#532

yes

—

D₁₉

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂²×D₄

—

C₂²×D₄

—

C₄⋊Q₈

—

#127

—

#124

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₁₉

#2858

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₉

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

D₄×D₁₉

yes

—

108

C₂×C₄

#64545

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

110

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂×D₄×D₁₉

yes

—

115

C₂²

C₂×#64545

yes

—

116

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

#10597386

yes

—

120

C₄

#10597393

yes

complemented

121

C₂

—

152

—

122

C₂

C₂×#10597393

yes

—

123

C₂

C₂×#10597386

yes

characteristic

124

C₂

#11927095

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
prime radical	C₂×#10597320	C₂
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2858
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

prime radical

C₂×#10597320

C₂

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
2. C₂×#10597393	C₂	semidirect
3. #11926445	C₂	semidirect
4. C₄²×Dic₁₉	C₂	semidirect
5. C₂×C₁₉×C₄⋊Q₈	C₂	semidirect
32. C₄×Dic₁₉	D₄	semidirect
56. C₄×C₁₉	#124	semidirect
59. C₂×C₄⋊Q₈	D₁₉	semidirect
79. C₁₉	#2858	semidirect
120. C₄	#10597393	semidirect

H ≅ G/N

type

2. C₂×#10597393

C₂

semidirect

3. #11926445

C₂

semidirect

4. C₄²×Dic₁₉

C₂

semidirect

5. C₂×C₁₉×C₄⋊Q₈

C₂

semidirect

32. C₄×Dic₁₉

D₄

semidirect

56. C₄×C₁₉

#124

semidirect

59. C₂×C₄⋊Q₈

D₁₉

semidirect

79. C₁₉

#2858

semidirect

120. C₄

#10597393

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597393	2
#11926445	2
C₄²×Dic₁₉	2
C₂×C₁₉×C₄⋊Q₈	2
#2858	19

subgroup

index

C₂×#10597320

C₂×#10597393

#11926445

C₄²×Dic₁₉

C₂×C₁₉×C₄⋊Q₈

#2858

Subgroups — #14571993

Conjugacy classes of subgroups

Complements

Maximal subgroups