Finite Group Databasebeta

← #19135137

Subgroups — #19135137

Order 5504.

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

normal subgroups only

This group has 380 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#14583458C211yesmaximal, characteristic
2C2×#13063240C211yesmaximal, characteristic, complemented
3C2×#13063239C212yesmaximal, complemented
4#14582665C212yesmaximal, complemented
5C43×#518C211yesmaximal, characteristic, complemented
6C22×C22⋊D43C2211yescharacteristic
7#13063308—21no—
8#13063306C412yescomplemented
9#13063297—22no—
10#13063294—21no—
11#13063293C412yescomplemented
12C2×C22⋊Dic43C2212yes—
13C2×C22⋊Dic43C2211yescharacteristic
14#13063240—22no—
15#13063239—24no—
16C22×D4×C43C2211yescharacteristic
17C4×D4×C43—24no—
18#117×C43—21no—
19C2×C22⋊C4×C43—21no—
20C2×C22⋊C4×C43C2212yes—
21C24×C43D411yescharacteristic
22C24×C43C2311yescharacteristic
23C23×D43C2×C411yescharacteristic, complemented
24C2×D4×C43—22no—
25C2×D4×C43—22no—
26C2×D4×C43C2×C412yes—
27C2×D4×C43D412yes—
28C22×C4×C43—22no—
29C22×C4×C43—22no—
30C22×C4×C43D411yescharacteristic
31C2×C22⋊D43—22no—
32C2×C22⋊D43—22no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—22no—
36C22×Dic43—21no—
37C22×Dic43—22no—
38C22×Dic43C2×C411yescharacteristic, complemented
39C4⋊C4×C43—22no—
40C22⋊C4×C43—22no—
41C22⋊C4×C43—22no—
42C22⋊C4×C43D414yescomplemented
43C42×C43—22no—
44C22⋊Dic43—22no—
45C22⋊Dic43—21no—
46C22⋊Dic43—22no—
47C22⋊Dic43—22no—
48C22⋊Dic43C2×C412yescomplemented
49(C2×D43)⋊C4—22no—
50Dic43⋊C4—22no—
51C23×C43—21no—
52C23×C43—21no—
53C23×C43—81no—
54C23×C43—81no—
55C23×C43C22⋊C412yes—
56C23×C43C22×C411yescharacteristic
57C23×C43C2×D411yescharacteristic
58C23×C43C2×D411yescharacteristic
59C23×C43C2×D412yes—
60C23×C43#4112yes—
61C22×D43—21no—
62C22×D43—22no—
63C22×D43—81no—
64D4×C43—24no—
65D4×C43—24no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—24no—
69C2×C4×C43—82no—
70C2×C4×C43—82no—
71C2×C4×C43C22⋊C412yes—
72C22⋊D43—41no—
73C22⋊D43—42no—
74C22⋊D43—41no—
75C22⋊D43—82no—
76C2×Dic43—21no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—42no—
80C2×Dic43—81no—
81C2×Dic43—82no—
82C22×C43—22no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43—42no—
87C22×C43—42no—
88C22×C43—42no—
89C22×C43—42no—
90C22×C43—81no—
91C22×C43C2×C22⋊C411yescharacteristic
92C22×C43C4×D412yes—
93C22×C43#12011yescharacteristic
94C22×C43#12112yes—
95C22×C43#12311yescharacteristic
96C2×D43—42no—
97C2×D43—41no—
98C2×D43—82no—
99C4×C43—22no—
100C4×C43—44no—
101Dic43—42no—
102Dic43—41no—
103Dic43—82no—
104#1913—431nomaximal, Sylow
105C2×C43—21no—
106C2×C43—22no—
107C2×C43—21no—
108C2×C43—22no—
109C2×C43—21no—
110C2×C43—42no—
111C2×C43#38611yescharacteristic
112D43—81no—
113#534—431no—
114#518D4311yescharacteristic, complemented
115C2×#99—431no—
116C2×#99—432no—
117#342—432no—
118C43#191311yescharacteristic, complemented, Sylow
119C22×D4—431no—
120C22×D4C2×D4311yescharacteristic
121#123—432no—
122#123—861no—
123#121—862no—
124#120—432no—
125#120—861no—
126C4×D4—24no—
127#117—21no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—431no—
130C2×C22⋊C4—432no—
131C2×C22⋊C4C2×D4312yes—
132#99—862no—
133#99—864no—
134C24—431no—
135C24C22⋊D4311yescharacteristic
136C24C22×D4311yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—862no—
140C2×D4—861no—
141C2×D4—862no—
142C2×D4—862no—
143C2×D4—861no—
144C2×D4C4×D4312yes—
145C2×D4D17212yes—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—431no—
149C22×C4—861no—
150C22×C4—862no—
151C22×C4C22⋊D4311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—862no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—432no—
157C22⋊C4—862no—
158C22⋊C4—861no—
159C22⋊C4—862no—
160C22⋊C4—862no—
161C22⋊C4—862no—
162C22⋊C4C22⋊D4314yescomplemented
163C42—22no—
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—862no—
169C23—861no—
170C23—3441no—
171C23(C2×D43)⋊C412yes—
172C23C2×C4×D4311yescharacteristic
173C23C2×D17211yescharacteristic
174C23#1062189812yes—
175C23C2×C22⋊D4311yescharacteristic
176C23C2×C22⋊D4312yes—
177D4—24no—
178D4—24no—
179D4—3442no—
180D4—1721no—
181D4—1722no—
182D4—1721no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—24no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—862no—
189C2×C4—861no—
190C2×C4—862no—
191C2×C4—3442no—
192C2×C4—3441no—
193C2×C4—1722no—
194C2×C4(C2×D43)⋊C412yes—
195C22—22no—
196C22—42no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—3442no—
205C22—1722no—
206C22—1721no—
207C22C2×(C2×D43)⋊C411yescharacteristic
208C22C4×C22⋊D4312yes—
209C22#1306329411yescharacteristic
210C22#1306329912yes—
211C22#1306330811yescharacteristic
212C4—22no—
213C4—44no—
214C4—3442no—
215C4—1722no—
216C4—1721no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—3441no—
224C2#1458277811yescharacteristic
subgroupG/H
centerC2#14582778
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#518C2
socleC2×C43#386
hypercenter#518D43
hypocenterC43#1913
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C2×#13063240C2semidirect
3. C2×#13063239C2semidirect
4. #14582665C2semidirect
5. C43×#518C2semidirect
8. #13063306C4semidirect
11. #13063293C4semidirect
23. C23×D43C2×C4semidirect
38. C22×Dic43C2×C4semidirect
42. C22⋊C4×C43D4semidirect
48. C22⋊Dic43C2×C4semidirect
114. #518D43semidirect
118. C43#1913semidirect
162. C22⋊C4C22⋊D43semidirect