Group #18070400 — subgroups

Subgroups — #18070400

Order 4864.

146 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14563242	C₂	1	1	yes	maximal, characteristic
2	#14561804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1411	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926921	C₄	1	1	yes	characteristic
5	#11926892	—	2	1	no	—
6	#11926892	—	2	1	no	—
7	#11926343	—	2	1	no	—
8	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
9	C₁₉×#494	C₂²	1	1	yes	characteristic
10	C₁₉×#356	—	2	1	no	—
11	C₂×Q₁₆×C₁₉	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
13	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
14	C₂×D₁₅₂	—	4	1	no	—
15	#10597320	—	2	1	no	—
16	C₁₉×#101	—	4	1	no	—
17	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	#10597293	—	4	1	no	—
19	#10597266	—	4	2	no	—
20	#10597266	—	4	2	no	—
21	C₄×C₁₉⋊C₈	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×D₇₆	—	4	1	no	—
25	C₂×D₇₆	—	4	1	no	—
26	C₂×D₇₆	—	4	1	no	—
27	Q₁₆×C₁₉	—	8	2	no	—
28	M₁₆×C₁₉	—	8	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	#64520	—	8	1	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	D₁₅₂	—	8	2	no	—
36	#7531	—	19	1	no	maximal, Sylow
37	C₂²×D₁₉	—	8	1	no	—
38	Q₈×C₁₉	—	8	1	no	—
39	Q₈×C₁₉	—	8	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
44	D₇₆	—	8	2	no	—
45	D₇₆	—	8	2	no	—
46	D₇₆	—	8	2	no	—
47	C₈×C₁₉	—	2	2	no	—
48	C₈×C₁₉	—	16	1	no	—
49	C₁₉⋊C₈	—	4	2	no	—
50	C₁₉⋊C₈	—	16	1	no	—
51	#1709	—	19	1	no	—
52	#1411	—	19	1	no	—
53	#1411	D₁₉	1	1	yes	characteristic, complemented
54	C₂²×C₁₉	#353	1	1	yes	characteristic
55	C₂×D₁₉	—	16	1	no	—
56	C₂×D₁₉	—	16	1	no	—
57	C₂×D₁₉	—	16	1	no	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	—	8	1	no	—
61	C₄×C₁₉	—	8	1	no	—
62	#494	C₂×D₁₉	1	1	yes	characteristic
63	#493	—	19	1	no	—
64	#486	—	38	1	no	—
65	#486	—	38	1	no	—
66	#356	—	2	1	no	—
67	#356	—	38	1	no	—
68	C₈²	—	19	1	no	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	#1408	1	1	yes	characteristic
71	D₁₉	—	32	1	no	—
72	C₂×Q₁₆	—	4	1	no	—
73	C₂×D₈	—	76	1	no	—
74	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
75	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
76	#127	—	38	1	no	—
77	#102	—	76	2	no	—
78	#102	—	76	2	no	—
79	#101	—	4	1	no	—
80	#101	—	76	1	no	—
81	C₄×C₈	—	38	1	no	—
82	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
83	C₁₉	#7531	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₈	—	2	1	no	—
85	C₂×Q₈	—	2	1	no	—
86	C₂×D₄	—	76	1	no	—
87	C₂×D₄	—	76	1	no	—
88	C₂×D₄	—	76	1	no	—
89	Q₁₆	—	8	2	no	—
90	D₈	—	152	2	no	—
91	M₁₆	—	8	1	no	—
92	M₁₆	—	152	1	no	—
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	38	2	no	—
95	C₄⋊C₄	—	4	1	no	—
96	C₄⋊C₄	—	4	1	no	—
97	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
98	C₂³	—	152	1	no	—
99	Q₈	—	8	1	no	—
100	Q₈	—	8	1	no	—
101	D₄	—	152	2	no	—
102	D₄	—	152	2	no	—
103	D₄	—	152	2	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	#10597263	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	16	1	no	—
110	C₈	—	304	1	no	—
111	C₈	—	76	2	no	—
112	C₂²	—	304	1	no	—
113	C₂²	—	304	1	no	—
114	C₂²	—	304	1	no	—
115	C₂²	#11926336	1	1	yes	characteristic
116	C₄	—	2	2	no	—
117	C₄	—	2	1	no	—
118	C₄	—	8	1	no	—
119	C₄	—	8	1	no	—
120	C₂	—	2	1	no	—
121	C₂	—	608	1	no	—
122	C₂	#14561797	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563242

C₂

yes

maximal, characteristic

#14561804

C₂

yes

maximal, characteristic, complemented

C₁₉×#1411

C₂

yes

maximal, characteristic, complemented

#11926921

C₄

yes

—

—

—

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₁₉×#494

C₂²

yes

characteristic

C₁₉×#356

—

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₂×D₁₅₂

—

#10597320

—

C₁₉×#101

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

—

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

#7531

—

maximal, Sylow

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1709

—

#1411

—

#1411

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#353

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

#494

C₂×D₁₉

yes

—

—

—

—

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

#1408

yes

characteristic

D₁₉

—

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

D₇₆

yes

characteristic

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₁₉

#7531

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

D₈

—

152

—

M₁₆

—

M₁₆

—

152

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂³

—

152

—

Q₈

—

100

Q₈

—

101

D₄

—

152

—

102

D₄

—

152

—

103

D₄

—

152

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

#10597263

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

304

—

111

C₈

—

112

C₂²

—

304

—

113

C₂²

—

304

—

114

C₂²

—

304

—

115

C₂²

#11926336

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

—

121

C₂

—

608

—

122

C₂

#14561797

yes

characteristic

	subgroup	G/H
center	C₂	#14561797
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#494	C₂×D₁₉
Fitting	C₁₉×#1411	C₂
socle	C₂×C₁₉	#1408
prime radical	#11926921	C₄
cosocle	C₁₉×#494	C₂²
hypercenter	#1411	D₁₉
hypocenter	C₁₉	#7531
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1411

subgroup

G/H

center

C₂

#14561797

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

#494

C₂×D₁₉

Fitting

C₁₉×#1411

C₂

C₂×C₁₉

C₄

C₁₉×#494

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1411

N	H ≅ G/N	type
2. #14561804	C₂	semidirect
3. C₁₉×#1411	C₂	semidirect
53. #1411	D₁₉	semidirect
83. C₁₉	#7531	semidirect

H ≅ G/N

type

2. #14561804

C₂

semidirect

3. C₁₉×#1411

C₂

semidirect

53. #1411

D₁₉

semidirect

83. C₁₉

#7531

semidirect

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

subgroup	index
#14563242	2
#14561804	2
C₁₉×#1411	2
#7531	19

subgroup

index

#14563242

#14561804

C₁₉×#1411

#7531

Subgroups — #18070400

Conjugacy classes of subgroups

Complements

Maximal subgroups