Group #19151735 — subgroups

Subgroups — #19151735

Order 5696.

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

normal subgroups only

This group has 158 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	C₂×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13083562	C₂	1	1	yes	maximal, characteristic, complemented
3	#15667983	C₂	1	1	yes	maximal, characteristic
4	#15667937	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667936	C₂	1	1	yes	maximal, characteristic, complemented
6	#15667924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₈	—	2	1	no	—
9	C₂×Dic₁₇₈	C₂²	1	1	yes	characteristic
10	Q₈×D₈₉	—	2	2	no	—
11	Q₈×D₈₉	—	2	2	no	—
12	C₂×C₂²⋊D₈₉	—	2	1	no	—
13	C₂×C₄×D₈₉	—	2	1	no	—
14	C₂×C₄×D₈₉	C₂²	1	1	yes	characteristic
15	#13083562	—	2	2	no	—
16	C₂×#10623494	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
18	C₂²⋊Dic₈₉	—	2	1	no	—
19	C₂×Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×C₈₉	C₂²	1	1	yes	characteristic
21	SD₁₆×C₈₉	—	2	2	no	—
22	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂³×C₈₉	—	2	1	no	—
24	C₂²×D₈₉	D₄	1	1	yes	characteristic
25	Q₈×C₈₉	—	2	1	no	—
26	Q₈×C₈₉	D₄	1	2	yes	complemented
27	D₄×C₈₉	—	2	1	no	—
28	D₄×C₈₉	—	2	1	no	—
29	C₂×C₄×C₈₉	—	2	1	no	—
30	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
31	C₂²⋊D₈₉	—	4	2	no	—
32	C₂×Dic₈₉	—	2	1	no	—
33	C₂×Dic₈₉	—	2	1	no	—
34	C₂×Dic₈₉	D₄	1	1	yes	characteristic
35	C₄×D₈₉	—	2	4	no	—
36	C₄×D₈₉	—	2	1	no	—
37	C₄×D₈₉	—	2	1	no	—
38	Dic₁₇₈	—	2	4	no	—
39	Dic₁₇₈	—	2	1	no	—
40	Dic₁₇₈	D₄	1	2	yes	complemented
41	C₈×C₈₉	—	2	1	no	—
42	#10623494	—	2	1	no	—
43	C₂²×C₈₉	—	4	1	no	—
44	C₂²×C₈₉	—	4	1	no	—
45	C₂²×C₈₉	—	4	1	no	—
46	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
47	C₂×D₈₉	—	2	1	no	—
48	C₂×D₈₉	—	2	1	no	—
49	C₂×D₈₉	SD₁₆	1	2	yes	complemented
50	C₄×C₈₉	—	2	2	no	—
51	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
52	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
53	Dic₈₉	—	2	1	no	—
54	Dic₈₉	—	2	2	no	—
55	Dic₈₉	—	4	1	no	—
56	C₂×C₈₉	—	8	1	no	—
57	C₂×C₈₉	#120	1	1	yes	characteristic
58	C₂×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
59	C₂×C₈₉	#137	1	1	yes	characteristic
60	D₈₉	—	2	2	no	—
61	C₈₉	#448	1	1	yes	characteristic, complemented, Sylow
62	#448	—	89	1	no	maximal, Sylow
63	C₂²×Q₈	—	89	1	no	—
64	C₂×SD₁₆	—	89	1	no	—
65	C₂×SD₁₆	D₈₉	1	1	yes	characteristic, complemented
66	#121	—	89	1	no	—
67	#103	—	89	1	no	—
68	#103	—	89	1	no	—
69	C₂²⋊C₈	—	89	1	no	—
70	C₂×Q₈	—	89	1	no	—
71	C₂×Q₈	—	178	1	no	—
72	C₂×Q₈	—	178	2	no	—
73	C₂×Q₈	—	178	2	no	—
74	C₂×Q₈	C₂×D₈₉	1	1	yes	characteristic
75	C₂×D₄	—	178	1	no	—
76	C₂×D₄	C₂×D₈₉	1	1	yes	characteristic
77	C₂²×C₄	—	89	1	no	—
78	C₂²×C₄	—	178	1	no	—
79	SD₁₆	—	2	2	no	—
80	SD₁₆	—	178	2	no	—
81	C₂×C₈	—	89	1	no	—
82	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
83	C₄⋊C₄	—	89	1	no	—
84	C₂²⋊C₄	—	178	1	no	—
85	C₂³	—	2	1	no	—
86	C₂³	—	89	1	no	—
87	Q₈	—	2	1	no	—
88	Q₈	—	89	2	no	—
89	Q₈	—	178	4	no	—
90	Q₈	—	178	1	no	—
91	Q₈	C₂²⋊D₈₉	1	2	yes	complemented
92	D₄	—	2	1	no	—
93	D₄	—	2	1	no	—
94	D₄	—	356	2	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	89	1	no	—
97	C₂×C₄	—	178	4	no	—
98	C₂×C₄	—	178	1	no	—
99	C₂×C₄	—	178	1	no	—
100	C₂×C₄	—	178	1	no	—
101	C₂×C₄	—	178	1	no	—
102	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	178	1	no	—
105	C₂²	—	4	1	no	—
106	C₂²	—	4	1	no	—
107	C₂²	—	4	1	no	—
108	C₂²	—	89	2	no	—
109	C₂²	—	178	1	no	—
110	C₂²	—	178	1	no	—
111	C₂²	D₄×D₈₉	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	356	1	no	—
114	C₄	—	178	1	no	—
115	C₄	—	178	2	no	—
116	C₄	D₄×D₈₉	1	1	yes	characteristic
117	C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
118	C₂	—	8	1	no	—
119	C₂	—	178	2	no	—
120	C₂	#15667980	1	1	yes	characteristic
121	C₂	SD₁₆×D₈₉	1	1	yes	characteristic
122	C₂	#15668041	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×D₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#13083562

C₂

yes

maximal, characteristic, complemented

#15667983

C₂

yes

maximal, characteristic

#15667937

C₂

yes

maximal, characteristic, complemented

#15667936

C₂

yes

maximal, characteristic, complemented

#15667924

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂²

yes

characteristic

Q₈×D₈₉

—

Q₈×D₈₉

—

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

C₂²

yes

characteristic

#13083562

—

C₂×#10623494

C₂²

yes

characteristic

C₄⋊Dic₈₉

C₂²

yes

characteristic

C₂²⋊Dic₈₉

—

C₂×Q₈×C₈₉

C₂²

yes

characteristic

C₂×D₄×C₈₉

C₂²

yes

characteristic

SD₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂²

yes

characteristic

C₂³×C₈₉

—

C₂²×D₈₉

D₄

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

D₄

yes

complemented

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂³

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

D₄

yes

characteristic

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

D₄

yes

complemented

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

SD₁₆

yes

complemented

C₄×C₈₉

—

C₄×C₈₉

C₂×D₄

yes

characteristic

C₄×C₈₉

C₂×D₄

yes

characteristic

Dic₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#120

yes

characteristic

C₂×C₈₉

C₂×SD₁₆

yes

characteristic

C₂×C₈₉

#137

yes

characteristic

D₈₉

—

C₈₉

#448

yes

characteristic, complemented, Sylow

#448

—

maximal, Sylow

C₂²×Q₈

—

C₂×SD₁₆

—

C₂×SD₁₆

D₈₉

yes

characteristic, complemented

#121

—

#103

—

#103

—

C₂²⋊C₈

—

C₂×Q₈

—

C₂×Q₈

—

178

—

C₂×Q₈

—

178

—

C₂×Q₈

—

178

—

C₂×Q₈

C₂×D₈₉

yes

characteristic

C₂×D₄

—

178

—

C₂×D₄

C₂×D₈₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

178

—

SD₁₆

—

SD₁₆

—

178

—

C₂×C₈

—

C₂×C₈

C₂×D₈₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

178

—

C₂³

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

178

—

Q₈

—

178

—

Q₈

C₂²⋊D₈₉

yes

complemented

D₄

—

D₄

—

D₄

—

356

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

100

C₂×C₄

—

178

—

101

C₂×C₄

—

178

—

102

C₂×C₄

C₂²×D₈₉

yes

characteristic

103

C₈

—

104

C₈

—

178

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

178

—

110

C₂²

—

178

—

111

C₂²

D₄×D₈₉

yes

characteristic

112

C₄

—

113

C₄

—

356

—

114

C₄

—

178

—

115

C₄

—

178

—

116

C₄

D₄×D₈₉

yes

characteristic

117

C₄

C₂×C₂²⋊D₈₉

yes

characteristic

118

C₂

—

119

C₂

—

178

—

120

C₂

#15667980

yes

characteristic

121

C₂

SD₁₆×D₈₉

yes

characteristic

122

C₂

#15668041

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	C₂×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	C₂×SD₁₆	D₈₉
hypocenter	C₈₉	#448
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

subgroup

G/H

center

C₂²

D₄×D₈₉

commutator

C₂×C₄×C₈₉

C₂³

Frattini

C₂×C₄

C₂²×D₈₉

Fitting

C₂×SD₁₆×C₈₉

C₂

socle

C₂²×C₈₉

C₂×D₄

hypercenter

C₂×SD₁₆

D₈₉

hypocenter

C₈₉

#448

LCS

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

N	H ≅ G/N	type
1. C₂×Q₈×D₈₉	C₂	semidirect
2. C₂×#13083562	C₂	semidirect
4. #15667937	C₂	semidirect
5. #15667936	C₂	semidirect
6. #15667924	C₂	semidirect
7. C₂×SD₁₆×C₈₉	C₂	semidirect
26. Q₈×C₈₉	D₄	semidirect
40. Dic₁₇₈	D₄	semidirect
49. C₂×D₈₉	SD₁₆	semidirect
61. C₈₉	#448	semidirect
65. C₂×SD₁₆	D₈₉	semidirect
91. Q₈	C₂²⋊D₈₉	semidirect

H ≅ G/N

type

1. C₂×Q₈×D₈₉

C₂

semidirect

2. C₂×#13083562

C₂

semidirect

4. #15667937

C₂

semidirect

5. #15667936

C₂

semidirect

6. #15667924

C₂

semidirect

7. C₂×SD₁₆×C₈₉

C₂

semidirect

26. Q₈×C₈₉

D₄

semidirect

40. Dic₁₇₈

D₄

semidirect

49. C₂×D₈₉

SD₁₆

semidirect

61. C₈₉

#448

semidirect

65. C₂×SD₁₆

D₈₉

semidirect

91. Q₈

C₂²⋊D₈₉

semidirect

Subgroups — #19151735

Conjugacy classes of subgroups

Complements