Group #19151746 — subgroups

Subgroups — #19151746

Order 5696.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667987	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667932	C₂	1	1	yes	maximal, characteristic, complemented
6	#15667924	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#13083575	—	2	2	no	—
9	#13083575	—	2	2	no	—
10	C₂×D₃₅₆	—	2	1	no	—
11	C₂×D₃₅₆	—	2	1	no	—
12	C₂×D₃₅₆	C₂²	1	1	yes	characteristic
13	C₂×D₃₅₆	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₈₉	—	2	1	no	—
15	C₂×C₄×D₈₉	C₂²	1	1	yes	characteristic
16	#13083561	—	2	2	no	—
17	D₇₁₂	—	2	2	no	—
18	C₂×#10623494	C₂²	1	1	yes	characteristic
19	#13083551	—	2	1	no	—
20	C₂×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×D₈₉	—	2	1	no	—
24	C₂²×D₈₉	—	2	1	no	—
25	C₂²×D₈₉	D₄	1	1	yes	characteristic
26	Q₈×C₈₉	—	2	1	no	—
27	Q₈×C₈₉	D₄	1	2	yes	complemented
28	C₂×C₄×C₈₉	—	2	1	no	—
29	C₂×C₄×C₈₉	—	2	1	no	—
30	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
31	C₂×Dic₈₉	D₄	1	1	yes	characteristic
32	D₃₅₆	—	2	4	no	—
33	D₃₅₆	—	2	1	no	—
34	D₃₅₆	—	2	1	no	—
35	D₃₅₆	—	2	1	no	—
36	D₃₅₆	—	4	2	no	—
37	D₃₅₆	D₄	1	2	yes	complemented
38	C₄×D₈₉	—	2	4	no	—
39	C₄×D₈₉	—	2	1	no	—
40	C₄×D₈₉	—	2	1	no	—
41	C₈×C₈₉	—	2	1	no	—
42	#10623494	—	2	1	no	—
43	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
44	C₂×D₈₉	—	2	1	no	—
45	C₂×D₈₉	—	2	2	no	—
46	C₂×D₈₉	—	2	1	no	—
47	C₂×D₈₉	—	2	1	no	—
48	C₂×D₈₉	—	4	1	no	—
49	C₂×D₈₉	—	4	1	no	—
50	C₂×D₈₉	—	4	1	no	—
51	C₂×D₈₉	—	4	1	no	—
52	C₂×D₈₉	—	4	1	no	—
53	C₄×C₈₉	—	2	2	no	—
54	C₄×C₈₉	—	4	1	no	—
55	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
56	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
57	Dic₈₉	—	2	1	no	—
58	C₂×C₈₉	#120	1	1	yes	characteristic
59	C₂×C₈₉	#135	1	1	yes	characteristic
60	C₂×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	D₈₉	—	4	1	no	—
62	D₈₉	—	4	2	no	—
63	D₈₉	—	8	1	no	—
64	C₈₉	#449	1	1	yes	characteristic, complemented, Sylow
65	#449	—	89	1	no	maximal, Sylow
66	C₂×#41	—	89	1	no	—
67	C₂×SD₁₆	—	89	1	no	—
68	C₂×D₈	—	89	1	no	—
69	#121	—	89	1	no	—
70	#103	D₈₉	1	1	yes	characteristic, complemented
71	#102	—	89	1	no	—
72	C₂²⋊C₈	—	89	1	no	—
73	#41	—	178	2	no	—
74	#41	—	178	2	no	—
75	C₂×Q₈	C₂×D₈₉	1	1	yes	characteristic
76	C₂×D₄	—	89	1	no	—
77	C₂×D₄	—	89	1	no	—
78	C₂×D₄	—	178	1	no	—
79	C₂×D₄	—	178	1	no	—
80	C₂²×C₄	—	89	1	no	—
81	C₂²×C₄	—	178	1	no	—
82	SD₁₆	—	178	2	no	—
83	D₈	—	178	2	no	—
84	C₂×C₈	—	89	1	no	—
85	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
86	C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
87	C₂²⋊C₄	—	178	1	no	—
88	C₂³	—	89	1	no	—
89	C₂³	—	178	1	no	—
90	C₂³	—	178	1	no	—
91	Q₈	—	2	1	no	—
92	Q₈	D₃₅₆	1	2	yes	complemented
93	D₄	—	89	2	no	—
94	D₄	—	356	2	no	—
95	D₄	—	178	4	no	—
96	D₄	—	178	1	no	—
97	D₄	—	178	1	no	—
98	D₄	—	178	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	89	1	no	—
102	C₂×C₄	—	178	4	no	—
103	C₂×C₄	—	178	1	no	—
104	C₂×C₄	—	178	1	no	—
105	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	178	1	no	—
108	C₂²	—	356	1	no	—
109	C₂²	—	356	1	no	—
110	C₂²	—	356	1	no	—
111	C₂²	—	356	1	no	—
112	C₂²	—	356	1	no	—
113	C₂²	—	178	2	no	—
114	C₂²	—	178	1	no	—
115	C₂²	—	178	1	no	—
116	C₂²	—	178	1	no	—
117	C₂²	D₄×D₈₉	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	4	1	no	—
120	C₄	—	178	1	no	—
121	C₄	D₄×D₈₉	1	1	yes	characteristic
122	C₄	C₂×D₃₅₆	1	1	yes	characteristic
123	C₂	—	356	2	no	—
124	C₂	—	356	1	no	—
125	C₂	—	712	1	no	—
126	C₂	#15667982	1	1	yes	characteristic
127	C₂	#15668035	1	1	yes	characteristic
128	C₂	#15668039	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13083575

C₂

yes

maximal, characteristic, complemented

C₂×#13083561

C₂

yes

maximal, characteristic, complemented

C₂×D₇₁₂

C₂

yes

maximal, characteristic, complemented

#15667987

C₂

yes

maximal, characteristic, complemented

#15667932

C₂

yes

maximal, characteristic, complemented

#15667924

C₂

yes

maximal, characteristic, complemented

#103×C₈₉

C₂

yes

maximal, characteristic, complemented

#13083575

—

#13083575

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

C₂²

yes

characteristic

C₂×D₃₅₆

C₂²

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

C₂²

yes

characteristic

#13083561

—

D₇₁₂

—

C₂×#10623494

C₂²

yes

characteristic

#13083551

—

C₂×Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₈×C₈₉

C₂²

yes

characteristic

C₄⋊C₄×C₈₉

C₂²

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

D₄

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

D₄

yes

complemented

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂³

yes

characteristic

C₂×Dic₈₉

D₄

yes

characteristic

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

D₄

yes

complemented

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

C₂×D₄

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

C₂×D₄

yes

characteristic

C₄×C₈₉

C₂×D₄

yes

characteristic

Dic₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

D₈₉

—

D₈₉

—

D₈₉

—

C₈₉

#449

yes

characteristic, complemented, Sylow

#449

—

maximal, Sylow

C₂×#41

—

C₂×SD₁₆

—

C₂×D₈

—

#121

—

#103

D₈₉

yes

characteristic, complemented

#102

—

C₂²⋊C₈

—

#41

—

178

—

#41

—

178

—

C₂×Q₈

C₂×D₈₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

178

—

C₂×D₄

—

178

—

C₂²×C₄

—

C₂²×C₄

—

178

—

SD₁₆

—

178

—

D₈

—

178

—

C₂×C₈

—

C₂×C₈

C₂×D₈₉

yes

characteristic

C₄⋊C₄

C₂×D₈₉

yes

characteristic

C₂²⋊C₄

—

178

—

C₂³

—

C₂³

—

178

—

C₂³

—

178

—

Q₈

—

Q₈

D₃₅₆

yes

complemented

D₄

—

D₄

—

356

—

D₄

—

178

—

D₄

—

178

—

D₄

—

178

—

D₄

—

178

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

178

—

103

C₂×C₄

—

178

—

104

C₂×C₄

—

178

—

105

C₂×C₄

C₂²×D₈₉

yes

characteristic

106

C₈

—

107

C₈

—

178

—

108

C₂²

—

356

—

109

C₂²

—

356

—

110

C₂²

—

356

—

111

C₂²

—

356

—

112

C₂²

—

356

—

113

C₂²

—

178

—

114

C₂²

—

178

—

115

C₂²

—

178

—

116

C₂²

—

178

—

117

C₂²

D₄×D₈₉

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

178

—

121

C₄

D₄×D₈₉

yes

characteristic

122

C₄

C₂×D₃₅₆

yes

characteristic

123

C₂

—

356

—

124

C₂

—

356

—

125

C₂

—

712

—

126

C₂

#15667982

yes

characteristic

127

C₂

#15668035

yes

characteristic

128

C₂

#15668039

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₈₉
Fitting	#103×C₈₉	C₂
socle	C₂²×C₈₉	C₂×D₄
hypercenter	#103	D₈₉
hypocenter	C₈₉	#449
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×D₈₉

commutator

C₂×C₄×C₈₉

C₂³

Frattini

C₂×C₄

C₂²×D₈₉

Fitting

#103×C₈₉

C₂

socle

C₂²×C₈₉

C₂×D₄

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
1. C₂×#13083575	C₂	semidirect
2. C₂×#13083561	C₂	semidirect
3. C₂×D₇₁₂	C₂	semidirect
4. #15667987	C₂	semidirect
5. #15667932	C₂	semidirect
6. #15667924	C₂	semidirect
7. #103×C₈₉	C₂	semidirect
27. Q₈×C₈₉	D₄	semidirect
37. D₃₅₆	D₄	semidirect
64. C₈₉	#449	semidirect
70. #103	D₈₉	semidirect
92. Q₈	D₃₅₆	semidirect

H ≅ G/N

type

1. C₂×#13083575

C₂

semidirect

2. C₂×#13083561

C₂

semidirect

3. C₂×D₇₁₂

C₂

semidirect

4. #15667987

C₂

semidirect

5. #15667932

C₂

semidirect

6. #15667924

C₂

semidirect

7. #103×C₈₉

C₂

semidirect

27. Q₈×C₈₉

D₄

semidirect

37. D₃₅₆

D₄

semidirect

64. C₈₉

#449

semidirect

70. #103

D₈₉

semidirect

92. Q₈

D₃₅₆

semidirect

Subgroups — #19151746

Conjugacy classes of subgroups

Complements