Group #18076343 — subgroups

Subgroups — #18076343

Order 4864.

354 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 203 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	#14563807	C₂	1	2	yes	maximal
2	#14562394	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	4	no	—
5	#11926568	C₂²	1	4	yes	—
6	#11926297	—	2	8	no	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
9	C₈²×C₁₉	C₄	1	1	yes	characteristic
10	C₈²×C₁₉	C₄	1	2	yes	—
11	C₈²×C₁₉	C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	2	yes	—
13	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
14	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
15	C₂×#64520	—	2	4	no	—
16	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₉	D₄	1	4	yes	—
21	C₄×C₈×C₁₉	Q₈	1	2	yes	—
22	#10597276	—	4	8	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
24	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
26	C₂×C₈×C₁₉	—	2	8	no	—
27	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
28	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₁₉	D₈	1	4	yes	—
32	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
33	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₂×D₄	1	2	yes	—
35	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
36	#64520	—	4	8	no	—
37	C₂×C₁₉⋊C₈	—	4	4	no	—
38	#8823	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
45	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
47	C₈×C₁₉	—	2	4	no	—
48	C₈×C₁₉	#107	1	4	yes	—
49	C₈×C₁₉	#107	1	4	yes	—
50	C₈×C₁₉	#108	1	8	yes	complemented
51	C₁₉⋊C₈	—	8	4	no	—
52	#1848	—	19	2	no	—
53	#1567	—	19	4	no	—
54	C₂×C₈²	D₁₉	1	1	yes	characteristic
55	C₂²×C₁₉	—	2	2	no	—
56	C₂²×C₁₉	#384	1	1	yes	characteristic
57	C₂²×C₁₉	#500	1	2	yes	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	C₂×#107	1	2	yes	—
60	C₄×C₁₉	C₂×#108	1	4	yes	—
61	C₄×C₁₉	#493	1	1	yes	characteristic
62	C₄×C₁₉	#494	1	1	yes	characteristic
63	C₂×#108	—	38	4	no	—
64	#423	—	19	4	no	—
65	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
66	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
67	#335	—	38	8	no	—
68	C₈²	Dic₁₉	1	1	yes	characteristic
69	C₈²	Dic₁₉	1	2	yes	—
70	C₈²	Dic₁₉	1	1	yes	characteristic
71	C₂×C₁₉	—	2	2	no	—
72	C₂×C₁₉	#1845	1	1	yes	characteristic
73	C₂×C₁₉	#1848	1	2	yes	—
74	C₂×M₁₆	—	38	4	no	—
75	C₂²×C₈	Dic₃₈	1	4	yes	—
76	C₂²×C₈	D₇₆	1	2	yes	—
77	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
78	#108	—	76	8	no	—
79	C₄⋊C₈	—	38	8	no	—
80	C₄×C₈	Dic₃₈	1	2	yes	—
81	C₄×C₈	D₇₆	1	4	yes	—
82	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
83	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
84	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
85	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
86	C₁₉	#8823	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄	C₂×Dic₃₈	1	2	yes	—
88	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
89	M₁₆	—	76	8	no	—
90	C₂×C₈	—	2	8	no	—
91	C₂×C₈	—	76	4	no	—
92	C₂×C₈	D₁₅₂	1	4	yes	—
93	C₂×C₈	Dic₇₆	1	4	yes	—
94	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
95	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
96	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
97	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
98	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
99	C₄²	C₂×D₇₆	1	2	yes	—
100	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
101	C₂³	#10597315	1	1	yes	characteristic
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	#10597315	1	2	yes	—
104	C₂×C₄	#10597320	1	1	yes	characteristic
105	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
106	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
107	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
108	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
109	C₈	—	2	4	no	—
110	C₈	—	152	4	no	—
111	C₈	#10597275	1	4	yes	—
112	C₈	#10597275	1	4	yes	—
113	C₈	#10597276	1	8	yes	complemented
114	C₂²	—	2	2	no	—
115	C₂²	#11926414	1	1	yes	characteristic
116	C₂²	#11926949	1	2	yes	—
117	C₄	—	2	2	no	—
118	C₄	C₂×#10597275	1	2	yes	—
119	C₄	C₂×#10597276	1	4	yes	—
120	C₄	#11926921	1	1	yes	characteristic
121	C₄	#11926924	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#14563795	1	1	yes	characteristic
124	C₂	#14563807	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563807

C₂

yes

maximal

#14562394

C₂

yes

maximal

C₂×C₈²×C₁₉

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926568

C₂²

yes

—

#11926297

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₈²×C₁₉

C₄

yes

characteristic

C₈²×C₁₉

C₄

yes

—

C₈²×C₁₉

C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

#8823

—

maximal, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

#107

yes

—

C₈×C₁₉

#107

yes

—

C₈×C₁₉

#108

yes

complemented

C₁₉⋊C₈

—

#1848

—

#1567

—

C₂×C₈²

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#500

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

C₂×#108

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

—

#335

—

C₈²

Dic₁₉

yes

characteristic

C₈²

Dic₁₉

yes

—

C₈²

Dic₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1845

yes

characteristic

C₂×C₁₉

#1848

yes

—

C₂×M₁₆

—

C₂²×C₈

Dic₃₈

yes

—

C₂²×C₈

D₇₆

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

D₇₆

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂×Dic₁₉

yes

—

C₁₉

#8823

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₃₈

yes

—

C₂²×C₄

C₂×D₇₆

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₅₂

yes

—

C₂×C₈

Dic₇₆

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄²

C₂×Dic₃₈

yes

characteristic

C₄²

C₂×D₇₆

yes

—

100

C₄²

C₂²×Dic₁₉

yes

characteristic

101

C₂³

#10597315

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

#10597315

yes

—

104

C₂×C₄

#10597320

yes

characteristic

105

C₂×C₄

C₂×D₁₅₂

yes

—

106

C₂×C₄

C₂×Dic₇₆

yes

—

107

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

108

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

—

109

C₈

—

110

C₈

—

152

—

111

C₈

#10597275

yes

—

112

C₈

#10597275

yes

—

113

C₈

#10597276

yes

complemented

114

C₂²

—

115

C₂²

#11926414

yes

characteristic

116

C₂²

#11926949

yes

—

117

C₄

—

118

C₄

C₂×#10597275

yes

—

119

C₄

C₂×#10597276

yes

—

120

C₄

#11926921

yes

characteristic

121

C₄

#11926924

yes

characteristic

122

C₂

—

123

C₂

#14563795

yes

characteristic

124

C₂

#14563807

yes

—

	subgroup	G/H
center	C₂×C₄	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈²×C₁₉	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#8823
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center

C₂×C₄

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₈²×C₁₉

C₂

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₂×C₈²

D₁₉

hypocenter

C₁₉

#8823

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
50. C₈×C₁₉	#108	semidirect
86. C₁₉	#8823	semidirect
113. C₈	#10597276	semidirect

H ≅ G/N

type

50. C₈×C₁₉

#108

semidirect

86. C₁₉

#8823

semidirect

113. C₈

#10597276

semidirect

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

subgroup	index
#14563807	2
#14562394	2
C₂×C₈²×C₁₉	2
#8823	19

subgroup

index

#14563807

#14562394

C₂×C₈²×C₁₉

#8823

Subgroups — #18076343

Conjugacy classes of subgroups

Complements

Maximal subgroups