Group #11927271 — subgroups

Subgroups — #11927271

Order 1216.

200 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	#10597336	C₂	1	1	yes	maximal, characteristic
3	#10597335	C₂	1	2	yes	maximal
4	#10597335	C₂	1	2	yes	maximal
5	#10597334	C₂	1	1	yes	maximal, characteristic
6	#10597334	C₂	1	2	yes	maximal
7	#10597333	C₂	1	1	yes	maximal, characteristic
8	#10597333	C₂	1	2	yes	maximal
9	#10597333	C₂	1	1	yes	maximal, characteristic
10	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
12	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
13	C₂×Dic₃₈	C₂²	1	2	yes	—
14	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	C₄⋊Dic₁₉	C₂²	1	2	yes	—
23	Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
24	Dic₁₉⋊C₄	C₂²	1	2	yes	—
25	Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
26	Dic₁₉⋊C₄	C₂²	1	2	yes	—
27	Dic₁₉⋊C₄	C₂²	1	2	yes	—
28	Dic₁₉⋊C₄	C₂²	1	2	yes	—
29	Dic₁₉⋊C₄	C₂²	1	2	yes	—
30	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
31	C₄×Dic₁₉	C₂²	1	2	yes	—
32	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
33	C₄×Dic₁₉	C₂²	1	2	yes	—
34	C₄×Dic₁₉	C₂²	1	2	yes	—
35	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×Dic₁₉	C₂³	1	1	yes	characteristic
41	C₂×Dic₁₉	C₂³	1	1	yes	characteristic
42	C₂×Dic₁₉	C₂³	1	2	yes	—
43	C₂×Dic₁₉	C₂³	1	1	yes	characteristic
44	C₂×Dic₁₉	C₂³	1	2	yes	—
45	C₂×Dic₁₉	C₂³	1	1	yes	characteristic
46	Dic₃₈	—	2	2	no	—
47	Dic₃₈	—	2	4	no	—
48	Dic₃₈	Q₈	1	4	yes	complemented
49	C₂²×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₄×C₁₉	—	2	2	no	—
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	—	2	2	no	—
54	C₄×C₁₉	C₂×Q₈	1	2	yes	—
55	Dic₁₉	—	2	1	no	—
56	Dic₁₉	—	2	2	no	—
57	Dic₁₉	—	2	1	no	—
58	Dic₁₉	—	2	1	no	—
59	Dic₁₉	C₂×Q₈	1	4	yes	—
60	Dic₁₉	#41	1	2	yes	—
61	#557	—	19	1	no	maximal, Sylow
62	C₂×C₁₉	C₂²×Q₈	1	1	yes	characteristic
63	C₂×C₁₉	C₂×#41	1	1	yes	characteristic
64	C₂×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
65	C₄⋊Q₈	—	19	2	no	—
66	C₄⋊Q₈	—	19	1	no	—
67	#125	—	19	2	no	—
68	#125	—	19	2	no	—
69	#125	—	19	1	no	—
70	#125	D₁₉	1	1	yes	characteristic
71	C₄×Q₈	—	19	1	no	—
72	C₄×Q₈	—	19	2	no	—
73	C₄×Q₈	—	19	1	no	—
74	C₄×Q₈	—	19	1	no	—
75	C₄×Q₈	—	19	1	no	—
76	C₁₉	#557	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	19	1	no	—
78	C₂×Q₈	—	19	2	no	—
79	C₂×Q₈	—	19	1	no	—
80	C₄⋊C₄	—	19	1	no	—
81	C₄⋊C₄	—	19	2	no	—
82	C₄⋊C₄	—	19	2	no	—
83	C₄⋊C₄	—	19	1	no	—
84	C₄⋊C₄	—	19	2	no	—
85	C₄⋊C₄	—	19	2	no	—
86	C₄⋊C₄	—	19	2	no	—
87	C₄⋊C₄	—	19	1	no	—
88	C₄⋊C₄	—	19	1	no	—
89	C₄⋊C₄	—	19	2	no	—
90	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
91	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
92	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
93	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
94	C₄²	—	19	2	no	—
95	C₄²	—	19	2	no	—
96	C₄²	—	19	1	no	—
97	C₄²	—	19	2	no	—
98	C₄²	—	19	1	no	—
99	C₄²	C₂×D₁₉	1	1	yes	characteristic
100	Q₈	—	19	4	no	—
101	Q₈	—	38	4	no	—
102	Q₈	—	38	2	no	—
103	C₂×C₄	—	19	2	no	—
104	C₂×C₄	—	19	1	no	—
105	C₂×C₄	—	19	1	no	—
106	C₂×C₄	—	19	1	no	—
107	C₂×C₄	—	19	1	no	—
108	C₂×C₄	—	19	2	no	—
109	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
110	C₂×C₄	C₂²×D₁₉	1	2	yes	—
111	C₂×C₄	C₂²×D₁₉	1	2	yes	—
112	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
113	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
114	C₂²	C₂³×D₁₉	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	2	1	no	—
117	C₄	—	2	1	no	—
118	C₄	—	2	2	no	—
119	C₄	—	19	4	no	—
120	C₄	—	19	2	no	—
121	C₄	—	38	1	no	—
122	C₄	—	38	2	no	—
123	C₄	—	38	1	no	—
124	C₄	—	38	1	no	—
125	C₄	Q₈×D₁₉	1	2	yes	—
126	C₂	C₂×Q₈×D₁₉	1	1	yes	characteristic
127	C₂	#41×D₁₉	1	1	yes	characteristic
128	C₂	#10597436	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#125

C₂

yes

maximal, characteristic

#10597336

C₂

yes

maximal, characteristic

#10597335

C₂

yes

maximal

#10597335

C₂

yes

maximal

#10597334

C₂

yes

maximal, characteristic

#10597334

C₂

yes

maximal

#10597333

C₂

yes

maximal, characteristic

#10597333

C₂

yes

maximal

#10597333

C₂

yes

maximal, characteristic

C₄×Dic₃₈

C₂

yes

maximal, characteristic

C₄×Dic₃₈

C₂

yes

maximal, characteristic

C₂×Dic₃₈

C₂²

yes

characteristic

C₂×Dic₃₈

C₂²

yes

—

C₂×Dic₃₈

C₂²

yes

characteristic

C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₉

C₂²

yes

—

C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₉

C₂²

yes

—

C₄²×C₁₉

C₂²

yes

characteristic

C₄⋊Dic₁₉

C₂²

yes

characteristic

C₄⋊Dic₁₉

C₂²

yes

characteristic

C₄⋊Dic₁₉

C₂²

yes

—

Dic₁₉⋊C₄

C₂²

yes

characteristic

Dic₁₉⋊C₄

C₂²

yes

—

Dic₁₉⋊C₄

C₂²

yes

characteristic

Dic₁₉⋊C₄

C₂²

yes

—

Dic₁₉⋊C₄

C₂²

yes

—

Dic₁₉⋊C₄

C₂²

yes

—

Dic₁₉⋊C₄

C₂²

yes

—

C₄×Dic₁₉

C₂²

yes

characteristic

C₄×Dic₁₉

C₂²

yes

—

C₄×Dic₁₉

C₂²

yes

characteristic

C₄×Dic₁₉

C₂²

yes

—

C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄×C₁₉

C₂³

yes

—

C₂×C₄×C₁₉

C₂³

yes

—

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₁₉

C₂³

yes

characteristic

C₂×Dic₁₉

C₂³

yes

characteristic

C₂×Dic₁₉

C₂³

yes

—

C₂×Dic₁₉

C₂³

yes

characteristic

C₂×Dic₁₉

C₂³

yes

—

C₂×Dic₁₉

C₂³

yes

characteristic

Dic₃₈

—

Dic₃₈

—

Dic₃₈

Q₈

yes

complemented

C₂²×C₁₉

C₂⁴

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

C₂×Q₈

yes

—

Dic₁₉

#41

yes

—

#557

—

maximal, Sylow

C₂×C₁₉

C₂²×Q₈

yes

characteristic

C₂×C₁₉

C₂×#41

yes

characteristic

C₂×C₁₉

2₋¹⁺⁴

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

D₁₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₁₉

#557

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₁₉

yes

—

C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₄⋊C₄

C₂×D₁₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×D₁₉

yes

characteristic

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂²×D₁₉

yes

characteristic

110

C₂×C₄

C₂²×D₁₉

yes

—

111

C₂×C₄

C₂²×D₁₉

yes

—

112

C₂×C₄

C₂²×D₁₉

yes

characteristic

113

C₂×C₄

C₂²×D₁₉

yes

characteristic

114

C₂²

C₂³×D₁₉

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

Q₈×D₁₉

yes

—

126

C₂

C₂×Q₈×D₁₉

yes

characteristic

127

C₂

#41×D₁₉

yes

characteristic

128

C₂

#10597436

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂²×C₁₉	C₂⁴
Fitting	C₁₉×#125	C₂
hypercenter	#125	D₁₉
hypocenter	C₁₉	#557
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂²×C₁₉

C₂⁴

Fitting

C₁₉×#125

C₂

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
48. Dic₃₈	Q₈	semidirect
76. C₁₉	#557	semidirect

H ≅ G/N

type

48. Dic₃₈

Q₈

semidirect

76. C₁₉

#557

semidirect

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

subgroup	index
C₁₉×#125	2
#10597336	2
#10597335	2
#10597334	2
#10597333	2
C₄×Dic₃₈	2
#557	19

subgroup

index

C₁₉×#125

C₄×Dic₃₈

Subgroups — #11927271

Conjugacy classes of subgroups

Complements

Maximal subgroups