Group #18070174 — subgroups

Subgroups — #18070174

Order 4864.

132 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14565888	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1371	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₅₂	—	2	1	no	—
5	C₂×Dic₁₅₂	C₄	1	2	yes	—
6	#11926924	—	2	1	no	—
7	C₂×C₁₉⋊C₃₂	—	2	1	no	—
8	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#335	—	2	1	no	—
10	C₂×Dic₇₆	—	2	2	no	—
11	C₂×Dic₇₆	—	4	1	no	—
12	#10597315	—	4	1	no	—
13	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
15	C₁₉×C₄⋊C₈	—	4	1	no	—
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	Dic₁₅₂	—	4	2	no	—
18	Dic₁₅₂	—	4	1	no	—
19	Dic₁₅₂	—	4	1	no	—
20	C₁₉⋊C₃₂	—	4	1	no	—
21	C₂×Dic₃₈	—	4	2	no	—
22	C₂×C₈×C₁₉	—	8	1	no	—
23	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
25	C₄²×C₁₉	D₈	1	1	yes	characteristic
26	C₄⋊Dic₁₉	—	8	1	no	—
27	C₄⋊Dic₁₉	—	8	1	no	—
28	Dic₇₆	—	4	2	no	—
29	Dic₇₆	—	4	2	no	—
30	Dic₇₆	—	8	2	no	—
31	C₁₆×C₁₉	—	2	1	no	—
32	C₁₆×C₁₉	D₈	1	1	yes	characteristic
33	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
34	#7445	—	19	1	no	maximal, Sylow
35	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
36	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
37	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
38	C₂×Dic₁₉	—	8	2	no	—
39	Dic₃₈	—	8	2	no	—
40	Dic₃₈	—	8	2	no	—
41	C₈×C₁₉	—	2	1	no	—
42	C₈×C₁₉	—	16	1	no	—
43	C₈×C₁₉	#100	1	1	yes	characteristic
44	C₈×C₁₉	#102	1	1	yes	characteristic
45	#2247	—	19	1	no	—
46	C₄⋊C₃₂	—	19	1	no	—
47	#1371	D₁₉	1	1	yes	characteristic
48	C₂²×C₁₉	#357	1	1	yes	characteristic
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	#331	1	1	yes	characteristic
51	C₄×C₁₉	#361	1	1	yes	characteristic
52	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
53	C₄×C₁₉	Q₆₄	1	1	yes	characteristic
54	Dic₁₉	—	16	2	no	—
55	C₂×Q₃₂	—	19	2	no	—
56	C₂×Q₃₂	—	38	1	no	—
57	#494	—	38	1	no	—
58	C₂×C₃₂	—	38	1	no	—
59	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
60	#335	—	2	1	no	—
61	C₂×C₁₉	#1361	1	1	yes	characteristic
62	C₂×C₁₉	#1416	1	1	yes	characteristic
63	C₂×C₁₉	#1420	1	1	yes	characteristic
64	C₂×Q₁₆	—	38	2	no	—
65	C₂×Q₁₆	—	76	1	no	—
66	C₄⋊Q₈	—	76	1	no	—
67	Q₃₂	—	76	2	no	—
68	Q₃₂	—	76	1	no	—
69	Q₃₂	—	76	1	no	—
70	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
71	C₂×C₁₆	D₇₆	1	1	yes	characteristic
72	C₄⋊C₈	—	4	1	no	—
73	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
74	C₃₂	—	76	1	no	—
75	C₁₉	#7445	1	1	yes	characteristic, complemented, Sylow
76	C₂×Q₈	—	76	2	no	—
77	Q₁₆	—	76	2	no	—
78	Q₁₆	—	76	2	no	—
79	Q₁₆	—	152	2	no	—
80	C₂×C₈	—	8	1	no	—
81	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
82	C₂×C₈	#64527	1	1	yes	characteristic
83	C₄⋊C₄	—	152	1	no	—
84	C₄⋊C₄	—	152	1	no	—
85	C₄²	#64525	1	1	yes	characteristic
86	C₁₆	—	2	1	no	—
87	C₁₆	#64516	1	1	yes	characteristic
88	C₁₆	D₁₅₂	1	1	yes	characteristic
89	Q₈	—	152	2	no	—
90	Q₈	—	152	2	no	—
91	C₂×C₄	—	152	2	no	—
92	C₂×C₄	#10597266	1	1	yes	characteristic
93	C₂×C₄	#10597283	1	1	yes	characteristic
94	C₂×C₄	#10597285	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	16	1	no	—
97	C₈	#10597278	1	1	yes	characteristic
98	C₈	#10597280	1	1	yes	characteristic
99	C₂²	#11926344	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	304	2	no	—
102	C₄	#11926287	1	1	yes	characteristic
103	C₄	#11926356	1	1	yes	characteristic
104	C₄	#11926382	1	1	yes	characteristic
105	C₄	#11926384	1	1	yes	characteristic
106	C₂	#14561680	1	1	yes	characteristic
107	C₂	#14561815	1	1	yes	characteristic
108	C₂	#14561827	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565888

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₃₂)

C₂

yes

maximal, characteristic

C₁₉×#1371

C₂

yes

maximal, characteristic

C₂×Dic₁₅₂

—

C₂×Dic₁₅₂

C₄

yes

—

#11926924

—

C₂×C₁₉⋊C₃₂

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597315

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

characteristic

Dic₁₅₂

—

Dic₁₅₂

—

Dic₁₅₂

—

C₁₉⋊C₃₂

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

—

C₄⋊C₃₂

—

#1371

D₁₉

yes

characteristic

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

SD₆₄

yes

characteristic

C₄×C₁₉

Q₆₄

yes

characteristic

Dic₁₉

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

C₂×C₃₂

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

#335

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

characteristic

C₄⋊C₈

—

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7445

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

152

—

C₂×C₈

—

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₈

#64527

yes

characteristic

C₄⋊C₄

—

152

—

C₄⋊C₄

—

152

—

C₄²

#64525

yes

characteristic

C₁₆

—

C₁₆

#64516

yes

characteristic

C₁₆

D₁₅₂

yes

characteristic

Q₈

—

152

—

Q₈

—

152

—

C₂×C₄

—

152

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

yes

100

C₄

—

101

C₄

—

304

—

102

C₄

#11926287

yes

characteristic

103

C₄

#11926356

yes

characteristic

104

C₄

#11926382

yes

characteristic

105

C₄

#11926384

yes

characteristic

106

C₂

#14561680

yes

characteristic

107

C₂

#14561815

yes

characteristic

108

C₂

#14561827

yes

characteristic

	subgroup	G/H
center	C₂²	#11926344
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1371	C₂
socle, prime radical	C₂²×C₁₉	#357
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1371	D₁₉
hypocenter	C₁₉	#7445
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

subgroup

G/H

center

C₂²

#11926344

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1371

C₂

socle, prime radical

C₂²×C₁₉

#357

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

N	H ≅ G/N	type
75. C₁₉	#7445	semidirect

H ≅ G/N

type

75. C₁₉

#7445

semidirect

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

subgroup	index
#14565888	2
C₄⋊(C₁₉⋊C₃₂)	2
C₁₉×#1371	2
#7445	19

subgroup

index

#14565888

C₄⋊(C₁₉⋊C₃₂)

C₁₉×#1371

#7445

Subgroups — #18070174

Conjugacy classes of subgroups

Complements

Maximal subgroups