Finite Group Databasebeta

← #19135843

Subgroups — #19135843

Order 5504.

382 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 71 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×#13063240C212yesmaximal, complemented
2#14582779C212yesmaximal, complemented
3#14582771C211yesmaximal, characteristic, complemented
4#14582666C211yesmaximal, characteristic, complemented
5C43×#534C211yesmaximal, characteristic
6C23×Dic43C2211yescharacteristic
7C2×Dic43⋊C4—21no—
8C2×C22⋊Dic43—22no—
9C2×C22⋊Dic43C2212yes—
10C2×C22⋊Dic43C2211yescharacteristic
11#13063240—24no—
12C43⋊#95—21no—
13C43⋊#95—22no—
14C22×D4×C43C2212yes—
15#123×C43—22no—
16#121×C43—21no—
17#121×C43—21no—
18#120×C43—22no—
19C2×C22⋊C4×C43C2211yescharacteristic
20C24×C43D412yes—
21C24×C43C2311yescharacteristic
22C2×D4×C43—21no—
23C2×D4×C43—21no—
24C2×D4×C43—22no—
25C2×D4×C43—22no—
26C2×D4×C43—22no—
27C2×D4×C43—22no—
28C2×D4×C43—22no—
29C2×D4×C43—22no—
30C22×C4×C43D412yes—
31C22×C4×C43D411yescharacteristic
32C22×C4×C43D411yescharacteristic
33C22×Dic43—22no—
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43—22no—
37C22×Dic43—42no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43—21no—
40C22⋊C4×C43—22no—
41C22⋊C4×C43—22no—
42C22⋊C4×C43—22no—
43C22⋊Dic43—22no—
44C22⋊Dic43—21no—
45C22⋊Dic43—22no—
46C22⋊Dic43—44no—
47C22⋊Dic43D412yescomplemented
48Dic43⋊C4—42no—
49C23×C43—22no—
50C23×C43—22no—
51C23×C43—22no—
52C23×C43—41no—
53C23×C43—41no—
54C23×C43—42no—
55C23×C43—42no—
56C23×C43C2×D411yescharacteristic
57C23×C43C2×D412yes—
58C23×C43C2×D411yescharacteristic
59C23×C43#4111yescharacteristic
60C23×C43#4112yes—
61D4×C43—42no—
62D4×C43—42no—
63D4×C43—42no—
64D4×C43—42no—
65D4×C43—81no—
66D4×C43—81no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×Dic43—22no—
75C2×Dic43—24no—
76C2×Dic43—22no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—42no—
80C2×Dic43—41no—
81C2×Dic43—41no—
82C2×Dic43—42no—
83C2×Dic43—42no—
84C2×Dic43—42no—
85C22×C43—22no—
86C22×C43—21no—
87C22×C43—22no—
88C22×C43—21no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43—42no—
92C22×C43—44no—
93C22×C43—42no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43—82no—
97C22×C43#12011yescharacteristic
98C22×C43#12111yescharacteristic
99C22×C43#12112yes—
100C22×C43#12312yes—
101C22×C43#12411yescharacteristic
102C4×C43—42no—
103C4×C43—41no—
104C4×C43—41no—
105Dic43—42no—
106Dic43—42no—
107Dic43—82no—
108#2044—431nomaximal, Sylow
109C2×C43—21no—
110C2×C43—22no—
111C2×C43—22no—
112C2×C43—21no—
113C2×C43—82no—
114C2×C43#39411yescharacteristic
115C2×C43B(4,𝔽2)11yescharacteristic
116C2×C43#45811yescharacteristic
117#534D4311yescharacteristic
118C2×#99—432no—
119#386—432no—
120#385—431no—
121#342—431no—
122C43#204411yescharacteristic, complemented, Sylow
123C22×D4C2×D4312yes—
124C23×C4—431no—
125#123—22no—
126#121—21no—
127#121—21no—
128#120—22no—
129C2×C4⋊C4—861no—
130C2×C22⋊C4—431no—
131C2×C22⋊C4—432no—
132C2×C22⋊C4—862no—
133C2×C22⋊C4C2×D4311yescharacteristic
134#99—864no—
135#95—861no—
136#95—862no—
137C24C22⋊D4312yes—
138C24C22×D4311yescharacteristic
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—21no—
146C2×D4—21no—
147C22×C4—861no—
148C22×C4—862no—
149C22×C4—861no—
150C22×C4—862no—
151C22×C4—1722no—
152C22×C4C22⋊D4312yes—
153C22×C4C22⋊D4311yescharacteristic
154C22×C4C22⋊D4311yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—1722no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—432no—
162C22⋊C4—861no—
163C22⋊C4—862no—
164C22⋊C4—862no—
165C22⋊C4—1724no—
166C23—22no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—42no—
172C23—42no—
173C23D4×D4311yescharacteristic
174C23#1062190011yescharacteristic
175C23#1062190012yes—
176C23C2×C22⋊D4311yescharacteristic
177C23C2×C22⋊D4312yes—
178D4—42no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—81no—
183D4—81no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—864no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—1722no—
195C2×C4—1722no—
196C2×C4—1722no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4—1722no—
200C2×C4—1721no—
201C2×C4—1721no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—42no—
208C22—41no—
209C22—44no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—82no—
214C22#1306329411yescharacteristic
215C22#1306329611yescharacteristic
216C22#1306329712yes—
217C22#1306330612yes—
218C22#1306331211yescharacteristic
219C4—42no—
220C4—41no—
221C4—41no—
222C4—3442no—
223C4—1722no—
224C4—1722no—
225C2—22no—
226C2—21no—
227C2—22no—
228C2—21no—
229C2—82no—
230C2#1458281311yescharacteristic
231C2#1458308611yescharacteristic
232C2#1458308911yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC43×#534C2
socleC22×C43#120
hypercenter#534D43
hypocenterC43#2044
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#13063240C2semidirect
2. #14582779C2semidirect
3. #14582771C2semidirect
4. #14582666C2semidirect
47. C22⋊Dic43D4semidirect
122. C43#2044semidirect