Group #18085378 — subgroups

Subgroups — #18085378

Order 4864.

586 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 169 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	C₂×#11926942	C₂	1	3	yes	maximal
2	#14564437	C₂	1	3	yes	maximal
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597315	C₂²	1	3	yes	—
5	#11926942	—	2	12	no	—
6	C₂×#10597274	—	2	6	no	—
7	C₂×#10597273	—	2	6	no	—
8	#11926414	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
10	C₂²×Dic₃₈	—	2	3	no	—
11	C₂²×C₈×C₁₉	D₄	1	6	yes	—
12	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	—	2	6	no	—
14	C₂×C₄⋊Dic₁₉	—	2	3	no	—
15	#10597315	—	2	6	no	—
16	#10597315	—	2	3	no	—
17	#10597315	D₄	1	6	yes	—
18	C₄×C₈×C₁₉	—	2	6	no	—
19	#10597274	—	2	24	no	—
20	#10597273	—	4	12	no	—
21	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
22	C₂²×Dic₁₉	—	4	3	no	—
23	C₂²×Dic₁₉	—	4	1	no	—
24	C₂×Dic₃₈	—	2	6	no	—
25	C₂×Dic₃₈	—	4	6	no	—
26	C₂×Dic₃₈	—	4	6	no	—
27	C₂×Dic₃₈	—	4	3	no	—
28	C₂×C₈×C₁₉	—	2	6	no	—
29	C₂×C₈×C₁₉	—	2	6	no	—
30	C₂×C₈×C₁₉	SD₁₆	1	12	yes	—
31	C₄²×C₁₉	C₂×D₄	1	3	yes	—
32	C₄²×C₁₉	#41	1	1	yes	characteristic
33	C₄⋊Dic₁₉	—	2	12	no	—
34	C₄⋊Dic₁₉	—	4	6	no	—
35	C₄⋊Dic₁₉	—	4	6	no	—
36	#10316	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	#127	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#120	1	3	yes	—
39	C₂×C₄×C₁₉	#121	1	3	yes	—
40	C₂×C₄×C₁₉	C₂×SD₁₆	1	6	yes	—
41	C₂×C₄×C₁₉	#137	1	6	yes	—
42	C₂×Dic₁₉	—	4	6	no	—
43	C₂×Dic₁₉	—	8	3	no	—
44	C₂×Dic₁₉	—	8	3	no	—
45	C₂×Dic₁₉	—	8	3	no	—
46	Dic₃₈	—	4	12	no	—
47	Dic₃₈	—	8	6	no	—
48	C₈×C₁₉	—	2	12	no	—
49	C₂×#498	—	19	3	no	—
50	#1956	—	19	3	no	—
51	#1273	D₁₉	1	1	yes	characteristic
52	C₂²×C₁₉	#392	1	1	yes	characteristic
53	C₂²×C₁₉	#492	1	3	yes	—
54	C₂²×C₁₉	#497	1	3	yes	—
55	C₄×C₁₉	#448	1	6	yes	—
56	C₄×C₁₉	#461	1	6	yes	—
57	Dic₁₉	—	8	6	no	—
58	Dic₁₉	—	16	1	no	—
59	C₂×C₄⋊Q₈	—	19	3	no	—
60	#498	—	38	12	no	—
61	C₂×#106	—	38	6	no	—
62	C₂×#103	—	38	6	no	—
63	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
64	#384	—	19	1	no	—
65	C₂×C₁₉	#1705	1	1	yes	characteristic
66	C₂×C₁₉	#1716	1	3	yes	—
67	C₂×C₁₉	#2013	1	3	yes	—
68	C₂²×Q₈	—	38	3	no	—
69	C₂²×C₈	D₇₆	1	6	yes	—
70	C₄⋊Q₈	—	19	6	no	—
71	C₄⋊Q₈	—	38	6	no	—
72	C₄⋊Q₈	—	38	3	no	—
73	C₂×C₄⋊C₄	—	38	6	no	—
74	C₂×C₄⋊C₄	—	38	3	no	—
75	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
76	#106	—	38	24	no	—
77	#103	—	76	12	no	—
78	C₄×C₈	—	2	6	no	—
79	C₁₉	#10316	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₈	—	38	6	no	—
81	C₂×Q₈	—	76	3	no	—
82	C₂×Q₈	—	76	6	no	—
83	C₂×Q₈	—	76	6	no	—
84	C₂²×C₄	—	76	3	no	—
85	C₂²×C₄	—	76	1	no	—
86	C₂²×C₄	C₂×D₇₆	1	3	yes	—
87	C₂×C₈	—	2	6	no	—
88	C₂×C₈	—	2	6	no	—
89	C₂×C₈	#64516	1	12	yes	—
90	C₄⋊C₄	—	38	12	no	—
91	C₄⋊C₄	—	76	6	no	—
92	C₄⋊C₄	—	76	6	no	—
93	C₄²	D₄×D₁₉	1	3	yes	—
94	C₄²	#64545	1	1	yes	characteristic
95	C₂³	#10597320	1	1	yes	characteristic
96	Q₈	—	76	12	no	—
97	Q₈	—	152	6	no	—
98	C₂×C₄	—	76	6	no	—
99	C₂×C₄	—	152	3	no	—
100	C₂×C₄	—	152	3	no	—
101	C₂×C₄	—	152	3	no	—
102	C₂×C₄	#10597328	1	3	yes	—
103	C₂×C₄	#10597341	1	3	yes	—
104	C₂×C₄	C₂×#64516	1	6	yes	—
105	C₂×C₄	#10597355	1	6	yes	—
106	C₈	—	2	12	no	—
107	C₂²	#11926454	1	1	yes	characteristic
108	C₂²	#11926917	1	3	yes	—
109	C₂²	#11926938	1	3	yes	—
110	C₄	—	304	1	no	—
111	C₄	—	152	6	no	—
112	C₄	#11926685	1	6	yes	—
113	C₄	#11926750	1	6	yes	—
114	C₂	#14563222	1	1	yes	characteristic
115	C₂	#14563268	1	3	yes	—
116	C₂	#14564720	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926942

C₂

yes

maximal

#14564437

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597315

—

#10597315

—

#10597315

D₄

yes

—

C₄×C₈×C₁₉

—

#10597274

—

#10597273

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₂×#498

—

#1956

—

#1273

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

#448

yes

—

C₄×C₁₉

#461

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

#498

—

C₂×#106

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

#384

—

C₂×C₁₉

#1705

yes

characteristic

C₂×C₁₉

#1716

yes

—

C₂×C₁₉

#2013

yes

—

C₂²×Q₈

—

C₂²×C₈

D₇₆

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#106

—

#103

—

C₄×C₈

—

C₁₉

#10316

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64516

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×D₁₉

yes

—

C₄²

yes

C₂³

yes

Q₈

—

Q₈

—

152

—

C₂×C₄

—

C₂×C₄

—

152

—

100

C₂×C₄

—

152

—

101

C₂×C₄

—

152

—

102

C₂×C₄

#10597328

yes

—

103

C₂×C₄

#10597341

yes

—

104

C₂×C₄

C₂×#64516

yes

—

105

C₂×C₄

#10597355

yes

—

106

C₈

—

107

C₂²

#11926454

yes

characteristic

108

C₂²

#11926917

yes

—

109

C₂²

#11926938

yes

—

110

C₄

—

304

—

111

C₄

—

152

—

112

C₄

#11926685

yes

—

113

C₄

#11926750

yes

—

114

C₂

#14563222

yes

characteristic

115

C₂

#14563268

yes

—

116

C₂

#14564720

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1273	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#10316
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1273

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
79. C₁₉	#10316	semidirect

H ≅ G/N

type

79. C₁₉

#10316

semidirect

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

subgroup	index
C₂×#11926942	2
#14564437	2
C₁₉×#1273	2
#10316	19

subgroup

index

C₂×#11926942

#14564437

C₁₉×#1273

#10316

Subgroups — #18085378

Conjugacy classes of subgroups

Complements

Maximal subgroups