Group #18070186 — subgroups

Subgroups — #18070186

Order 4864.

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

normal subgroups only

This group has 126 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	#14565888	C₂	1	1	yes	maximal, characteristic
2	#14561833	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1373	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	#11926378	—	2	1	no	—
8	C₁₉×#364	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₆	—	2	2	no	—
11	C₂×Dic₇₆	—	4	1	no	—
12	#10597315	—	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	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	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
24	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
25	C₄⋊Dic₁₉	—	8	2	no	—
26	Dic₇₆	—	4	2	no	—
27	Dic₇₆	—	4	2	no	—
28	Dic₇₆	—	8	1	no	—
29	Dic₇₆	—	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	#7449	—	19	1	no	maximal, Sylow
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
37	C₂×Dic₁₉	—	8	2	no	—
38	Dic₃₈	—	8	2	no	—
39	Dic₃₈	—	8	2	no	—
40	C₈×C₁₉	#100	1	1	yes	characteristic
41	C₈×C₁₉	#102	1	1	yes	characteristic
42	C₈×C₁₉	D₁₆	1	1	yes	characteristic
43	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
44	#2247	—	19	1	no	—
45	#1422	—	19	1	no	—
46	#1373	D₁₉	1	1	yes	characteristic
47	C₂²×C₁₉	#361	1	1	yes	characteristic
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	#331	1	1	yes	characteristic
50	C₄×C₁₉	#357	1	1	yes	characteristic
51	Dic₁₉	—	16	2	no	—
52	C₂×Q₃₂	—	19	2	no	—
53	C₂×Q₃₂	—	38	1	no	—
54	#494	—	38	1	no	—
55	M₆₄	—	38	1	no	—
56	#364	—	2	1	no	—
57	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	#1361	1	1	yes	characteristic
60	C₂×Q₁₆	—	38	2	no	—
61	C₂×Q₁₆	—	76	1	no	—
62	C₄⋊Q₈	—	76	1	no	—
63	Q₃₂	—	76	2	no	—
64	Q₃₂	—	76	1	no	—
65	Q₃₂	—	76	1	no	—
66	M₃₂	—	4	1	no	—
67	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
68	C₂×C₁₆	D₇₆	1	1	yes	characteristic
69	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₃₂	—	76	1	no	—
71	C₁₉	#7449	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	76	2	no	—
73	Q₁₆	—	76	2	no	—
74	Q₁₆	—	76	2	no	—
75	Q₁₆	—	152	1	no	—
76	Q₁₆	—	152	1	no	—
77	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
78	C₂×C₈	#64525	1	1	yes	characteristic
79	C₄⋊C₄	—	152	2	no	—
80	C₄²	#64527	1	1	yes	characteristic
81	C₁₆	—	2	1	no	—
82	C₁₆	—	8	1	no	—
83	C₁₆	#64516	1	1	yes	characteristic
84	C₁₆	D₁₅₂	1	1	yes	characteristic
85	Q₈	—	152	2	no	—
86	Q₈	—	152	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	152	2	no	—
89	C₂×C₄	#10597266	1	1	yes	characteristic
90	C₈	#10597278	1	1	yes	characteristic
91	C₈	#10597280	1	1	yes	characteristic
92	C₈	#10597283	1	1	yes	characteristic
93	C₈	#10597285	1	1	yes	characteristic
94	C₂²	#11926356	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	304	2	no	—
97	C₄	#11926287	1	1	yes	characteristic
98	C₄	#11926344	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	#14561680	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565888

C₂

yes

maximal, characteristic

#14561833

C₂

yes

maximal, characteristic

C₁₉×#1373

C₂

yes

maximal, characteristic

C₂×Dic₁₅₂

—

C₂×Dic₁₅₂

C₄

yes

—

#11926924

—

#11926378

—

C₁₉×#364

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597315

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

Dic₁₅₂

—

Dic₁₅₂

—

Dic₁₅₂

—

C₁₉⋊C₃₂

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄⋊Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

#7449

—

maximal, Sylow

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

#361

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

M₆₄

—

#364

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1361

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7449

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

152

—

Q₁₆

—

152

—

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₈

#64525

yes

characteristic

C₄⋊C₄

—

152

—

C₄²

#64527

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

#64516

yes

characteristic

C₁₆

D₁₅₂

yes

characteristic

Q₈

—

152

—

Q₈

—

152

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

yes

C₈

yes

C₈

yes

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

304

—

C₄

yes

C₄

yes

C₂

—

100

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	C₂²×C₁₉	#361
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1373	D₁₉
hypocenter	C₁₉	#7449
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

C₂²×C₁₉

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
71. C₁₉	#7449	semidirect

H ≅ G/N

type

71. C₁₉

#7449

semidirect

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

subgroup	index
#14565888	2
#14561833	2
C₁₉×#1373	2
#7449	19

subgroup

index

#14565888

#14561833

C₁₉×#1373

#7449

Subgroups — #18070186

Conjugacy classes of subgroups

Complements

Maximal subgroups