Group #18070183 — subgroups

Subgroups — #18070183

Order 4864.

146 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14565885	C₂	1	1	yes	maximal, characteristic
2	#14561833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₀₄	—	2	1	no	—
5	C₂×D₃₀₄	C₄	1	2	yes	—
6	#11926921	—	2	1	no	—
7	#11926378	—	2	1	no	—
8	C₁₉×#364	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×D₁₅₂	—	2	2	no	—
11	C₂×D₁₅₂	—	4	1	no	—
12	#10597320	—	4	1	no	—
13	C₁₉×M₃₂	—	4	1	no	—
14	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	D₃₀₄	—	4	2	no	—
18	D₃₀₄	—	4	1	no	—
19	D₃₀₄	—	4	1	no	—
20	C₁₉⋊C₃₂	—	4	1	no	—
21	C₂×D₇₆	—	4	2	no	—
22	C₂×D₇₆	—	8	2	no	—
23	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
25	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
26	D₁₅₂	—	4	2	no	—
27	D₁₅₂	—	4	2	no	—
28	D₁₅₂	—	8	1	no	—
29	D₁₅₂	—	8	1	no	—
30	C₁₆×C₁₉	—	2	1	no	—
31	C₁₆×C₁₉	—	8	1	no	—
32	C₁₆×C₁₉	D₈	1	1	yes	characteristic
33	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
34	#7448	—	19	1	no	maximal, Sylow
35	C₂²×D₁₉	—	8	2	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
38	D₇₆	—	8	2	no	—
39	D₇₆	—	8	2	no	—
40	D₇₆	—	16	4	no	—
41	C₈×C₁₉	#100	1	1	yes	characteristic
42	C₈×C₁₉	#102	1	1	yes	characteristic
43	C₈×C₁₉	D₁₆	1	1	yes	characteristic
44	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
45	#2246	—	19	1	no	—
46	#1422	—	19	1	no	—
47	#1373	D₁₉	1	1	yes	characteristic, complemented
48	C₂²×C₁₉	#361	1	1	yes	characteristic
49	C₂×D₁₉	—	16	4	no	—
50	C₂×D₁₉	—	16	2	no	—
51	C₄×C₁₉	—	2	2	no	—
52	C₄×C₁₉	#331	1	1	yes	characteristic
53	C₄×C₁₉	#357	1	1	yes	characteristic
54	C₂×D₁₆	—	19	2	no	—
55	C₂×D₁₆	—	38	1	no	—
56	#493	—	38	1	no	—
57	M₆₄	—	38	1	no	—
58	#364	—	2	1	no	—
59	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
60	C₂×C₁₉	—	2	1	no	—
61	C₂×C₁₉	#1361	1	1	yes	characteristic
62	D₁₉	—	32	2	no	—
63	C₂×D₈	—	38	2	no	—
64	C₂×D₈	—	76	1	no	—
65	#127	—	76	1	no	—
66	D₁₆	—	76	2	no	—
67	D₁₆	—	76	1	no	—
68	D₁₆	—	76	1	no	—
69	M₃₂	—	4	1	no	—
70	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
71	C₂×C₁₆	D₇₆	1	1	yes	characteristic
72	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
73	C₃₂	—	76	1	no	—
74	C₁₉	#7448	1	1	yes	characteristic, complemented, Sylow
75	C₂×D₄	—	76	2	no	—
76	C₂×D₄	—	152	2	no	—
77	D₈	—	76	2	no	—
78	D₈	—	76	2	no	—
79	D₈	—	152	1	no	—
80	D₈	—	152	1	no	—
81	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
82	C₂×C₈	#64525	1	1	yes	characteristic
83	C₄²	#64527	1	1	yes	characteristic
84	C₁₆	—	2	1	no	—
85	C₁₆	—	8	1	no	—
86	C₁₆	#64516	1	1	yes	characteristic
87	C₁₆	D₁₅₂	1	1	yes	characteristic
88	C₂³	—	152	2	no	—
89	D₄	—	304	4	no	—
90	D₄	—	152	2	no	—
91	D₄	—	152	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	#10597266	1	1	yes	characteristic
94	C₈	#10597278	1	1	yes	characteristic
95	C₈	#10597280	1	1	yes	characteristic
96	C₈	#10597283	1	1	yes	characteristic
97	C₈	#10597285	1	1	yes	characteristic
98	C₂²	—	304	4	no	—
99	C₂²	—	304	2	no	—
100	C₂²	#11926356	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	#11926287	1	1	yes	characteristic
103	C₄	#11926344	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	608	2	no	—
106	C₂	#14561680	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565885

C₂

yes

maximal, characteristic

#14561833

C₂

yes

maximal, characteristic, complemented

C₁₉×#1373

C₂

yes

maximal, characteristic, complemented

C₂×D₃₀₄

—

C₂×D₃₀₄

C₄

yes

—

#11926921

—

#11926378

—

C₁₉×#364

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597320

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

D₃₀₄

—

D₃₀₄

—

D₃₀₄

—

C₁₉⋊C₃₂

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

#7448

—

maximal, Sylow

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#361

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₆

—

C₂×D₁₆

—

#493

—

M₆₄

—

#364

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1361

yes

characteristic

D₁₉

—

C₂×D₈

—

C₂×D₈

—

#127

—

D₁₆

—

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7448

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

152

—

D₈

—

D₈

—

D₈

—

152

—

D₈

—

152

—

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

C₂×C₈

yes

C₄²

yes

C₁₆

—

C₁₆

—

C₁₆

#64516

yes

characteristic

C₁₆

D₁₅₂

yes

characteristic

C₂³

—

152

—

D₄

—

304

—

D₄

—

152

—

D₄

—

152

—

C₂×C₄

—

C₂×C₄

yes

C₈

yes

C₈

yes

C₈

yes

C₈

yes

C₂²

—

304

—

C₂²

—

304

—

100

C₂²

#11926356

yes

characteristic

101

C₄

—

102

C₄

#11926287

yes

characteristic

103

C₄

#11926344

yes

characteristic

104

C₂

—

105

C₂

—

608

—

106

C₂

#14561680

yes

characteristic

	subgroup	G/H
center	C₂	#14561680
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1373	C₂
socle	C₂×C₁₉	#1361
prime radical	#14565885	C₂
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1373	D₁₉
hypocenter	C₁₉	#7448
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

subgroup

G/H

center

C₂

#14561680

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1373

C₂

C₂×C₁₉

C₂

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

N	H ≅ G/N	type
2. #14561833	C₂	semidirect
3. C₁₉×#1373	C₂	semidirect
47. #1373	D₁₉	semidirect
74. C₁₉	#7448	semidirect

H ≅ G/N

type

2. #14561833

C₂

semidirect

3. C₁₉×#1373

C₂

semidirect

47. #1373

D₁₉

semidirect

74. C₁₉

#7448

semidirect

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

subgroup	index
#14565885	2
#14561833	2
C₁₉×#1373	2
#7448	19

subgroup

index

#14565885

#14561833

C₁₉×#1373

#7448

Subgroups — #18070183

Conjugacy classes of subgroups

Complements

Maximal subgroups