Finite Group Databasebeta

← #19135041

Subgroups — #19135041

Order 5504.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583410C211yesmaximal, characteristic
2C2×#13063284C211yesmaximal, characteristic, complemented
3C2×#13063251C212yesmaximal, complemented
4#14582660C212yesmaximal, complemented
5C43×#407C211yesmaximal, characteristic, complemented
6C2×#10621898C2211yescharacteristic
7#13063308—21no—
8#13063304C412yescomplemented
9#13063299C412yescomplemented
10#13063294—21no—
11C4×C22⋊D43—22no—
12#13063284—24no—
13#13063284C2211yescharacteristic
14C2×C4⋊Dic43—21no—
15C2×C22⋊Dic43—21no—
16C2×C4×Dic43C2212yes—
17#13063251—24no—
18C23×C4×C43C2211yescharacteristic
19C2×M16×C43C2212yes—
20C22⋊C8×C43—22no—
21C24×C43D411yescharacteristic
22C22×C4×C43—22no—
23C22×C4×C43—22no—
24C22×C4×C43C2×C412yes—
25C22×C4×C43D412yes—
26C22×C4×C43D411yescharacteristic
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—22no—
29C2×C22⋊D43—21no—
30C22×Dic43—22no—
31#10621898—22no—
32#10621898—22no—
33C2×D172C2×C411yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86C2×C411yescharacteristic
36M16×C43—22no—
37M16×C43—22no—
38C2×C8×C43—22no—
39C22⋊Dic43—24no—
40C22⋊Dic43—22no—
41C22⋊Dic43—21no—
42(C2×D43)⋊C4—22no—
43C4⋊Dic43—24no—
44C4⋊Dic43C2×C412yes—
45Dic43⋊C4—22no—
46C4×Dic43—22no—
47C4×Dic43—21no—
48C4×Dic43D414yescomplemented
49C23×C43—21no—
50C23×C43—21no—
51C23×C43—42no—
52C23×C43C22⋊C412yes—
53C23×C43C2×D411yescharacteristic
54C22×D43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—24no—
58C2×C4×C43—24no—
59C2×C4×C43C22⋊C412yes—
60C2×C4×C43C22×C411yescharacteristic
61C2×C4×C43C2×D412yes—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43#4112yes—
64C22⋊D43—44no—
65C22⋊D43—41no—
66C22⋊D43—41no—
67C2×Dic43—22no—
68C2×Dic43—21no—
69C2×Dic43—24no—
70C2×Dic43—44no—
71D172—22no—
72C4×D43—42no—
73Dic86—22no—
74C8×C43—42no—
75C22×C43—22no—
76C22×C43—22no—
77C22×C43—22no—
78C22×C43—22no—
79C22×C43—42no—
80C22×C43—42no—
81C22×C43C2×C22⋊C411yescharacteristic
82C22×C43#12011yescharacteristic
83C22×C43#12311yescharacteristic
84C2×D43—41no—
85C2×D43—42no—
86C4×C43—22no—
87C4×C43C4×D412yes—
88C4×C43#12112yes—
89Dic43—44no—
90Dic43—41no—
91Dic43—42no—
92#1897—431nomaximal, Sylow
93C2×C43—21no—
94C2×C43—21no—
95C2×C43—42no—
96C2×C43#38611yescharacteristic
97C2×C43#42112yes—
98D43—81no—
99#525—431no—
100C2×#117—431no—
101C2×#104—432no—
102#407D4311yescharacteristic, complemented
103#339—432no—
104C43#189711yescharacteristic, complemented, Sylow
105C2×#41—431no—
106C23×C4C2×D4311yescharacteristic
107C2×M16C2×D4312yes—
108#123—861no—
109C22⋊Q8—432no—
110#121—432no—
111#120—861no—
112C4×D4—862no—
113#117—431no—
114#117—864no—
115C2×C4⋊C4—861no—
116C2×C22⋊C4—861no—
117C2×C42—432no—
118#104—864no—
119C22⋊C8—22no—
120C24D17211yescharacteristic
121#41—862no—
122#41—862no—
123C2×Q8—431no—
124C2×D4—431no—
125C2×D4—862no—
126C2×D4—861no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—862no—
130C22×C4—861no—
131C22×C4C4×D4312yes—
132C22×C4D17211yescharacteristic
133C22×C4C22⋊D4312yes—
134C22×C4C22×D4311yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—432no—
139C4⋊C4—864no—
140C4⋊C4—862no—
141C22⋊C4—864no—
142C22⋊C4—862no—
143C22⋊C4—861no—
144C22⋊C4—862no—
145C42—434no—
146C42—862no—
147C42—861no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—861no—
152C23(C2×D43)⋊C412yes—
153C23C2×D17211yescharacteristic
154Q8—862no—
155D4—862no—
156D4—1724no—
157D4—1721no—
158D4—1721no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—862no—
164C2×C4—861no—
165C2×C4—864no—
166C2×C4—1724no—
167C2×C4—1722no—
168C2×C4(C2×D43)⋊C412yes—
169C2×C4C2×C4×D4311yescharacteristic
170C2×C4D4×D4312yes—
171C2×C4#1062190012yes—
172C2×C4C2×C22⋊D4311yescharacteristic
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—1722no—
181C22—1721no—
182C22C2×(C2×D43)⋊C411yescharacteristic
183C22#1306329511yescharacteristic
184C22#1306330911yescharacteristic
185C4—22no—
186C4—1724no—
187C4—1722no—
188C4—1721no—
189C4(C22⋊D43)⋊C412yes—
190C4#1306329712yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—3441no—
195C2#1458277611yescharacteristic
196C2#1458291512yes—
subgroupG/H
centerC2×C4C2×C22⋊D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#407C2
socleC22×C43C2×C22⋊C4
hypercenter#407D43
hypocenterC43#1897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#13063284C2semidirect
3. C2×#13063251C2semidirect
4. #14582660C2semidirect
5. C43×#407C2semidirect
8. #13063304C4semidirect
9. #13063299C4semidirect
48. C4×Dic43D4semidirect
102. #407D43semidirect
104. C43#1897semidirect