Finite Group Databasebeta

← #19135847

Subgroups — #19135847

Order 5504.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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#14583461C211yesmaximal, characteristic
2C2×#13063239C212yesmaximal, complemented
3#14582776C212yesmaximal, complemented
4#14582771C211yesmaximal, characteristic, complemented
5C43×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D43C2212yes—
7C23×Dic43C2211yescharacteristic
8#13063309—22no—
9#13063299—21no—
10#13063299—21no—
11#13063295—22no—
12C2×Dic43⋊C4—21no—
13C2×C22⋊Dic43C2211yescharacteristic
14C2×(C2×D43)⋊C4—22no—
15#13063239—24no—
16C43⋊#95—21no—
17C43⋊#95—22no—
18C2×C22⋊C4×C43C2212yes—
19C2×C22⋊C4×C43C2211yescharacteristic
20C24×C43C2311yescharacteristic
21C23×D43D412yes—
22C22×C4×C43—22no—
23C22×C4×C43D411yescharacteristic
24C22×C4×C43D411yescharacteristic
25C2×C22⋊D43—22no—
26C2×C22⋊D43—22no—
27C2×C22⋊D43—22no—
28C2×C22⋊D43—22no—
29C2×C22⋊D43—22no—
30C2×C22⋊D43—22no—
31C22×Dic43—22no—
32C22×Dic43—21no—
33C22×Dic43—21no—
34C22×Dic43—42no—
35C22×Dic43D412yes—
36C2×D172—21no—
37C2×D172—21no—
38C22⋊C4×C43—22no—
39C22⋊C4×C43—22no—
40C22⋊C4×C43—22no—
41C22⋊Dic43—21no—
42C22⋊Dic43D412yescomplemented
43(C2×D43)⋊C4—22no—
44(C2×D43)⋊C4—22no—
45(C2×D43)⋊C4—44no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48Dic43⋊C4—42no—
49C23×C43—41no—
50C23×C43—41no—
51C23×C43C2×D411yescharacteristic
52C23×C43C2×D412yes—
53C23×C43C2×D411yescharacteristic
54C23×C43#4112yes—
55C23×C43#4111yescharacteristic
56C22×D43—22no—
57C22×D43—22no—
58C22×D43—22no—
59C22×D43—42no—
60C22×D43—42no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—42no—
66C2×C4×C43—42no—
67C2×C4×C43—42no—
68C22⋊D43—42no—
69C22⋊D43—42no—
70C22⋊D43—42no—
71C22⋊D43—42no—
72C2×Dic43—22no—
73C2×Dic43—24no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—42no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83D172—81no—
84D172—81no—
85C22×C43—22no—
86C22×C43—21no—
87C22×C43—22no—
88C22×C43—21no—
89C22×C43—41no—
90C22×C43—42no—
91C22×C43—41no—
92C22×C43#12011yescharacteristic
93C22×C43#12112yes—
94C22×C43#12111yescharacteristic
95C22×C43#12312yes—
96C22×C43#12411yescharacteristic
97C2×D43—44no—
98C2×D43—42no—
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—82no—
102C4×C43—41no—
103C4×C43—41no—
104C4×C43—82no—
105Dic43—42no—
106Dic43—42no—
107Dic43—42no—
108#2044—431nomaximal, Sylow
109C2×C43—21no—
110C2×C43—22no—
111C2×C43—22no—
112C2×C43—21no—
113C2×C43#39411yescharacteristic
114C2×C43B(4,𝔽2)11yescharacteristic
115C2×C43#45811yescharacteristic
116D43—82no—
117#534—431no—
118C2×#99—432no—
119#386—432no—
120#385—431no—
121#342D4311yescharacteristic, complemented
122C43#204411yescharacteristic, complemented, Sylow
123C22×D4—432no—
124C23×C4—431no—
125#123—862no—
126#121—861no—
127#121—861no—
128#120—862no—
129C2×C4⋊C4—861no—
130C2×C22⋊C4—431no—
131C2×C22⋊C4—862no—
132C2×C22⋊C4C2×D4312yes—
133C2×C22⋊C4C2×D4311yescharacteristic
134#99—864no—
135#95—862no—
136#95—861no—
137C24—432no—
138C24C22×D4311yescharacteristic
139C2×D4—861no—
140C2×D4—861no—
141C2×D4—862no—
142C2×D4—862no—
143C2×D4—862no—
144C2×D4—862no—
145C2×D4—862no—
146C2×D4—862no—
147C22×C4—22no—
148C22×C4—432no—
149C22×C4—861no—
150C22×C4—861no—
151C22×C4—862no—
152C22×C4—1722no—
153C22×C4D17211yescharacteristic
154C22×C4D17211yescharacteristic
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—1722no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—432no—
162C22⋊C4—862no—
163C22⋊C4—862no—
164C22⋊C4—861no—
165C22⋊C4—1724no—
166C23—41no—
167C23—41no—
168C23—862no—
169C23—862no—
170C23—862no—
171C23—1722no—
172C23—1722no—
173C23C2×D17211yescharacteristic
174C23#1062189812yes—
175C23D4×D4312yes—
176C23D4×D4311yescharacteristic
177C23#1062190211yescharacteristic
178D4—3441no—
179D4—3441no—
180D4—1722no—
181D4—1722no—
182D4—1722no—
183D4—1722no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—864no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4—1722no—
200C2×C4—1721no—
201C2×C4—1721no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—42no—
207C22—41no—
208C22—41no—
209C22—3442no—
210C22—1724no—
211C22—1722no—
212C22—1722no—
213C22—1722no—
214C22#1306329511yescharacteristic
215C22#1306329812yes—
216C22#1306330011yescharacteristic
217C22#1306331012yes—
218C22#1306331311yescharacteristic
219C4—41no—
220C4—41no—
221C4—82no—
222C4—1722no—
223C4—1722no—
224C4—1722no—
225C2—22no—
226C2—21no—
227C2—22no—
228C2—21no—
229C2—3442no—
230C2#1458281711yescharacteristic
231C2#1458308711yescharacteristic
232C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43#120
hypercenter#342D43
hypocenterC43#2044
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#13063239C2semidirect
3. #14582776C2semidirect
4. #14582771C2semidirect
5. C43×#342C2semidirect
42. C22⋊Dic43D4semidirect
121. #342D43semidirect
122. C43#2044semidirect