Group #19151512 — subgroups

Subgroups — #19151512

Order 5696.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13083553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Dic₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₈₉	C₂	1	2	yes	maximal, complemented
4	#15667919	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₉	C₂²	1	2	yes	—
7	C₂²×Dic₈₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₈₉	C₂²	1	1	yes	characteristic
9	#13083553	—	2	2	no	—
10	C₂²⋊Dic₈₉	—	2	4	no	—
11	C₂²⋊Dic₈₉	—	2	4	no	—
12	C₂⁴×C₈₉	C₂²	1	2	yes	—
13	C₂×D₄×C₈₉	—	2	4	no	—
14	C₂×D₄×C₈₉	—	2	2	no	—
15	C₂²×C₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈₉	—	2	2	no	—
17	C₂³×C₈₉	—	2	2	no	—
18	C₂³×C₈₉	—	2	2	no	—
19	C₂³×C₈₉	—	2	2	no	—
20	C₂³×C₈₉	—	2	2	no	—
21	C₂³×C₈₉	—	2	2	no	—
22	C₂³×C₈₉	D₄	1	4	yes	—
23	C₂³×C₈₉	C₂³	1	1	yes	characteristic
24	D₄×C₈₉	—	2	8	no	—
25	C₂×C₄×C₈₉	—	2	2	no	—
26	C₂×C₄×C₈₉	D₄	1	2	yes	—
27	C₂×Dic₈₉	—	2	1	no	—
28	C₂×Dic₈₉	—	2	1	no	—
29	C₂×Dic₈₉	—	2	2	no	—
30	C₂×Dic₈₉	—	2	2	no	—
31	C₂×Dic₈₉	—	2	2	no	—
32	C₂×Dic₈₉	—	2	1	no	—
33	C₂×Dic₈₉	—	2	2	no	—
34	C₂×Dic₈₉	D₄	1	2	yes	complemented
35	C₂²×C₈₉	—	2	4	no	—
36	C₂²×C₈₉	—	2	4	no	—
37	C₂²×C₈₉	—	2	4	no	—
38	C₂²×C₈₉	—	4	2	no	—
39	C₂²×C₈₉	—	4	2	no	—
40	C₂²×C₈₉	—	4	2	no	—
41	C₂²×C₈₉	—	4	2	no	—
42	C₂²×C₈₉	C₂×D₄	1	2	yes	—
43	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₈₉	#41	1	1	yes	characteristic
46	C₂²×C₈₉	#41	1	2	yes	—
47	C₄×C₈₉	—	2	2	no	—
48	Dic₈₉	—	2	2	no	—
49	Dic₈₉	—	4	1	no	—
50	Dic₈₉	—	4	2	no	—
51	C₂×C₈₉	—	4	4	no	—
52	C₂×C₈₉	#120	1	1	yes	characteristic
53	C₂×C₈₉	#121	1	1	yes	characteristic
54	C₂×C₈₉	#121	1	2	yes	—
55	C₂×C₈₉	#123	1	2	yes	—
56	C₂×C₈₉	#124	1	1	yes	characteristic
57	C₈₉	#394	1	1	yes	characteristic, complemented, Sylow
58	#394	—	89	1	no	maximal, Sylow
59	C₂²×D₄	D₈₉	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	89	1	no	—
61	C₂×C₂²⋊C₄	—	89	2	no	—
62	C₂×C₂²⋊C₄	—	89	2	no	—
63	#95	—	89	1	no	—
64	C₂⁴	C₂×D₈₉	1	2	yes	—
65	C₂×D₄	—	2	4	no	—
66	C₂×D₄	—	2	2	no	—
67	C₂²×C₄	—	89	1	no	—
68	C₂²×C₄	—	89	2	no	—
69	C₂²×C₄	—	89	1	no	—
70	C₂²×C₄	C₂×D₈₉	1	1	yes	characteristic
71	C₄⋊C₄	—	178	2	no	—
72	C₂²⋊C₄	—	178	4	no	—
73	C₂²⋊C₄	—	178	4	no	—
74	C₂³	—	2	2	no	—
75	C₂³	—	2	2	no	—
76	C₂³	—	2	2	no	—
77	C₂³	—	2	2	no	—
78	C₂³	—	2	2	no	—
79	C₂³	—	2	2	no	—
80	C₂³	C₂²⋊D₈₉	1	4	yes	—
81	C₂³	C₂²×D₈₉	1	1	yes	characteristic
82	D₄	—	2	8	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	89	2	no	—
85	C₂×C₄	—	178	2	no	—
86	C₂×C₄	—	178	2	no	—
87	C₂×C₄	—	178	2	no	—
88	C₂×C₄	—	178	1	no	—
89	C₂×C₄	—	178	2	no	—
90	C₂×C₄	—	178	1	no	—
91	C₂×C₄	—	178	1	no	—
92	C₂×C₄	C₂²⋊D₈₉	1	2	yes	—
93	C₂²	—	2	4	no	—
94	C₂²	—	2	4	no	—
95	C₂²	—	2	4	no	—
96	C₂²	—	4	2	no	—
97	C₂²	—	4	2	no	—
98	C₂²	—	4	2	no	—
99	C₂²	—	4	2	no	—
100	C₂²	D₄×D₈₉	1	1	yes	characteristic
101	C₂²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
102	C₂²	C₂×C₂²⋊D₈₉	1	2	yes	—
103	C₂²	#13083573	1	1	yes	characteristic
104	C₂²	#13083573	1	2	yes	—
105	C₄	—	2	2	no	—
106	C₄	—	356	1	no	—
107	C₄	—	356	2	no	—
108	C₄	—	178	2	no	—
109	C₂	—	4	4	no	—
110	C₂	#15667981	1	1	yes	characteristic
111	C₂	#15667983	1	1	yes	characteristic
112	C₂	#15667984	1	2	yes	—
113	C₂	#15667993	1	2	yes	—
114	C₂	#15667999	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13083553

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊Dic₈₉

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₈₉

C₂

yes

maximal, complemented

#15667919

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₈₉

C₂

yes

maximal, characteristic

C₂²×Dic₈₉

C₂²

yes

—

C₂²×Dic₈₉

C₂²

yes

characteristic

C₂²×Dic₈₉

C₂²

yes

characteristic

#13083553

—

C₂²⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₂⁴×C₈₉

C₂²

yes

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²

yes

characteristic

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

D₄

yes

—

C₂³×C₈₉

C₂³

yes

characteristic

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

D₄

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

D₄

yes

complemented

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₄

yes

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₈₉

C₂×D₄

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₄×C₈₉

—

Dic₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#123

yes

—

C₂×C₈₉

#124

yes

characteristic

C₈₉

#394

yes

characteristic, complemented, Sylow

#394

—

maximal, Sylow

C₂²×D₄

D₈₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₂⁴

C₂×D₈₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₈₉

yes

characteristic

C₄⋊C₄

—

178

—

C₂²⋊C₄

—

178

—

C₂²⋊C₄

—

178

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊D₈₉

yes

—

C₂³

C₂²×D₈₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂²⋊D₈₉

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

D₄×D₈₉

yes

characteristic

101

C₂²

C₂×C₂²⋊D₈₉

yes

characteristic

102

C₂²

C₂×C₂²⋊D₈₉

yes

—

103

C₂²

#13083573

yes

characteristic

104

C₂²

#13083573

yes

—

105

C₄

—

106

C₄

—

356

—

107

C₄

—

356

—

108

C₄

—

178

—

109

C₂

—

110

C₂

#15667981

yes

characteristic

111

C₂

#15667983

yes

characteristic

112

C₂

#15667984

yes

—

113

C₂

#15667993

yes

—

114

C₂

#15667999

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂³
Fitting	C₂²×D₄×C₈₉	C₂
hypercenter	C₂²×D₄	D₈₉
hypocenter	C₈₉	#394
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₈₉

commutator, socle

C₂³×C₈₉

C₂³

Fitting

C₂²×D₄×C₈₉

C₂

hypercenter

C₂²×D₄

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂³ ◁ C₂²×D₄

N	H ≅ G/N	type
1. C₂×#13083553	C₂	semidirect
2. C₂×C₂²⋊Dic₈₉	C₂	semidirect
3. C₂×C₂²⋊Dic₈₉	C₂	semidirect
4. #15667919	C₂	semidirect
34. C₂×Dic₈₉	D₄	semidirect
57. C₈₉	#394	semidirect

H ≅ G/N

type

1. C₂×#13083553

C₂

semidirect

2. C₂×C₂²⋊Dic₈₉

C₂

semidirect

3. C₂×C₂²⋊Dic₈₉

C₂

semidirect

4. #15667919

C₂

semidirect

34. C₂×Dic₈₉

D₄

semidirect

57. C₈₉

#394

semidirect

Subgroups — #19151512

Conjugacy classes of subgroups

Complements