Finite Group Databasebeta

← #19135051

Subgroups — #19135051

Order 5504.

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

normal subgroups only

This group has 378 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
1C2×#13063308C211yesmaximal, characteristic
2C2×#13063284C211yesmaximal, characteristic, complemented
3C2×#13063239C212yesmaximal
4#14582665C212yesmaximal, complemented
5C43×#381C211yesmaximal, characteristic, complemented
6C22×C22⋊D43C2211yescharacteristic
7#13063308—21no—
8#13063308—21no—
9#13063308—22no—
10#13063284—24no—
11C2×C4⋊Dic43—21no—
12C2×Dic43⋊C4C412yescomplemented
13C2×C22⋊Dic43C2211yescharacteristic
14C2×C22⋊Dic43C2212yes—
15C2×(C2×D43)⋊C4C412yescomplemented
16C2×C4×Dic43—21no—
17#13063239—24no—
18C23×C4×C43C2211yescharacteristic
19C2×C22⋊C4×C43C2212yes—
20#95×C43—22no—
21C24×C43C2311yescharacteristic
22C23×D43C2×C411yescharacteristic
23C22×C4×C43—22no—
24C22×C4×C43—22no—
25C22×C4×C43—22no—
26C22×C4×C43C2×C412yes—
27C22×C4×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D412yes—
30C2×C22⋊D43—22no—
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—22no—
34C22×Dic43—22no—
35C22×Dic43C2×C411yescharacteristic
36C22×Dic43C2×C412yes—
37C22⋊C4×C43—22no—
38C22⋊C4×C43—22no—
39C22⋊Dic43—22no—
40C22⋊Dic43—21no—
41C22⋊Dic43—21no—
42C22⋊Dic43D414yes—
43(C2×D43)⋊C4—22no—
44(C2×D43)⋊C4—22no—
45C4⋊Dic43—24no—
46Dic43⋊C4—22no—
47Dic43⋊C4—22no—
48C4×Dic43—24no—
49C23×C43—42no—
50C23×C43C22×C411yescharacteristic
51C23×C43C2×D411yescharacteristic
52C23×C43C2×D412yes—
53C23×C43C2×D411yescharacteristic
54C23×C43#4112yes—
55C22×D43—21no—
56C22×D43—22no—
57C22×D43—42no—
58C2×C4×C43—24no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—24no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43—44no—
65C2×C4×C43—42no—
66C2×C4×C43C22⋊C412yes—
67C2×C4×C43C22⋊C412yes—
68C22⋊D43—41no—
69C22⋊D43—42no—
70C22⋊D43—41no—
71C2×Dic43—21no—
72C2×Dic43—22no—
73C2×Dic43—22no—
74C2×Dic43—24no—
75C2×Dic43—44no—
76C2×Dic43—42no—
77C22×C43—22no—
78C22×C43—22no—
79C22×C43—22no—
80C22×C43—42no—
81C22×C43—42no—
82C22×C43C2×C22⋊C411yescharacteristic
83C22×C43C4×D412yes—
84C22×C43#12011yescharacteristic
85C22×C43#12112yes—
86C22×C43#12311yescharacteristic
87C2×D43—41no—
88C2×D43—42no—
89C2×D43—82no—
90C4×C43—22no—
91C4×C43—22no—
92C4×C43—82no—
93Dic43—44no—
94Dic43—41no—
95Dic43—42no—
96#1899—431nomaximal, Sylow
97C2×C43—21no—
98C2×C43—22no—
99C2×C43—22no—
100C2×C43—21no—
101C2×C43#38611yescharacteristic
102C2×C43#41012yes—
103D43—81no—
104C2×#123—431no—
105C2×#117—431no—
106C2×#99—432no—
107#381D4311yescharacteristic, complemented
108#342—432no—
109C43#189911yescharacteristic, complemented, Sylow
110C22×D4—431no—
111C23×C4C2×D4311yescharacteristic
112#123—861no—
113#123—861no—
114#123—862no—
115#117—864no—
116C2×C4⋊C4—432no—
117C2×C4⋊C4—861no—
118C2×C22⋊C4—432no—
119C2×C22⋊C4—431no—
120C2×C22⋊C4—432no—
121C2×C22⋊C4C2×D4312yes—
122C2×C42—861no—
123#99—864no—
124#95—22no—
125C24—431no—
126C24C22×D4311yescharacteristic
127C2×D4—861no—
128C2×D4—862no—
129C2×D4—862no—
130C2×D4—861no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—431no—
135C22×C4—432no—
136C22×C4—862no—
137C22×C4C4×D4312yes—
138C22×C4D17211yescharacteristic
139C22×C4D17211yescharacteristic
140C22×C4C22⋊D4312yes—
141C4⋊C4—864no—
142C4⋊C4—862no—
143C4⋊C4—862no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—434no—
147C22⋊C4—861no—
148C22⋊C4—862no—
149C22⋊C4—861no—
150C22⋊C4—862no—
151C22⋊C4—862no—
152C42—864no—
153C23—42no—
154C23—862no—
155C23—861no—
156C23—1722no—
157C23C2×C4×D4311yescharacteristic
158C23C2×D17211yescharacteristic
159C23D4×D4312yes—
160C23#1062190012yes—
161C23C2×C22⋊D4311yescharacteristic
162D4—1721no—
163D4—1722no—
164D4—1721no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—862no—
174C2×C4—861no—
175C2×C4—862no—
176C2×C4—864no—
177C2×C4—1724no—
178C2×C4—1722no—
179C2×C4(C2×D43)⋊C412yes—
180C2×C4(C2×D43)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—3442no—
187C22—1722no—
188C22—1721no—
189C22C2×(C2×D43)⋊C411yescharacteristic
190C22(C22⋊D43)⋊C412yes—
191C22#1306329511yescharacteristic
192C22#1306329712yes—
193C22#1306330911yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—1724no—
198C4—1722no—
199C4—1721no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—3441no—
205C2#1458277611yescharacteristic
206C2#1458287212yes—
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#381C2
socleC22×C43C2×C22⋊C4
hypercenter#381D43
hypocenterC43#1899
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#13063284C2semidirect
4. #14582665C2semidirect
5. C43×#381C2semidirect
12. C2×Dic43⋊C4C4semidirect
15. C2×(C2×D43)⋊C4C4semidirect
107. #381D43semidirect
109. C43#1899semidirect