Finite Group Databasebeta

← #19142694

Subgroups — #19142694

Order 5504.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#14582840C212yesmaximal, complemented
2#14582835C211yesmaximal, characteristic, complemented
3#14582827C212yesmaximal, complemented
4#14582822C212yesmaximal, complemented
5#14582813C212yesmaximal, complemented
6#14582813C212yesmaximal, complemented
7#14582779C212yesmaximal, complemented
8#14582771C211yesmaximal, characteristic, complemented
9C43×#392C211yesmaximal, characteristic
10C23×Dic43C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12C2×Dic43⋊C4C2212yes—
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×C22⋊Dic43C2211yescharacteristic
16C2×C22⋊Dic43C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C22×D4×C43C2212yes—
27C22×D4×C43C2211yescharacteristic
28C2×C22⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2211yescharacteristic
30#95×C43C2211yescharacteristic
31C24×C43C2312yes—
32C24×C43C2311yescharacteristic
33C2×D4×C43—24no—
34C2×D4×C43—42no—
35C2×D4×C43—42no—
36C2×D4×C43—41no—
37C2×D4×C43—42no—
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×Dic43—41no—
42C22×Dic43—42no—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2312yes—
47C22⋊C4×C43—41no—
48C22⋊C4×C43—42no—
49C22⋊Dic43—22no—
50C22⋊Dic43—42no—
51C22⋊Dic43—42no—
52C22⋊Dic43—42no—
53C22⋊Dic43—42no—
54C22⋊Dic43—42no—
55C4⋊Dic43—41no—
56Dic43⋊C4—42no—
57Dic43⋊C4—42no—
58Dic43⋊C4—42no—
59C23×C43—22no—
60C23×C43—21no—
61C23×C43—22no—
62C23×C43—21no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43—22no—
66C23×C43—22no—
67C23×C43—22no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43#4112yes—
71C23×C43C2411yescharacteristic
72D4×C43—48no—
73D4×C43—44no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—44no—
94C22×C43—24no—
95C22×C43—22no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—42no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43C2×#4111yescharacteristic
107C22×C43H(5,𝔽2)12yes—
108C22×C43H(5,𝔽2)12yes—
109C22×C43H(5,𝔽2)11yescharacteristic
110C22×C432−1+411yescharacteristic
111C4×C43—42no—
112C4×C43—41no—
113C4×C43—41no—
114Dic43—42no—
115Dic43—42no—
116Dic43—42no—
117Dic43—42no—
118#2826—431nomaximal, Sylow
119C2×C43—42no—
120C2×C43—82no—
121C2×C43#53812yes—
122C2×C43#53911yescharacteristic
123C2×C43#56011yescharacteristic
124C2×C43#56011yescharacteristic
125C2×C43#56212yes—
126#400—432no—
127#399—431no—
128#397—432no—
129#396—432no—
130#394—432no—
131#394—432no—
132#392D4311yescharacteristic
133#386—432no—
134#385—431no—
135C43#282611yescharacteristic, complemented, Sylow
136C22×D4C2×D4312yes—
137C22×D4C2×D4311yescharacteristic
138C23×C4—431no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—431no—
143C2×C22⋊C4—431no—
144C2×C22⋊C4—432no—
145C2×C22⋊C4—432no—
146C2×C22⋊C4—432no—
147C2×C22⋊C4—432no—
148C2×C22⋊C4—432no—
149C2×C22⋊C4C2×D4311yescharacteristic
150C2×C22⋊C4C2×D4312yes—
151#95—432no—
152#95—432no—
153#95—432no—
154#95—432no—
155#95—431no—
156#95C2×D4311yescharacteristic
157C24C22×D4312yes—
158C24C22×D4311yescharacteristic
159C2×D4—24no—
160C2×D4—42no—
161C2×D4—41no—
162C2×D4—42no—
163C2×D4—42no—
164C22×C4—432no—
165C22×C4—432no—
166C22×C4—432no—
167C22×C4—432no—
168C22×C4—1721no—
169C22×C4—1722no—
170C22×C4C22×D4312yes—
171C22×C4C22×D4311yescharacteristic
172C22×C4C22×D4311yescharacteristic
173C4⋊C4—1722no—
174C4⋊C4—1722no—
175C4⋊C4—1722no—
176C4⋊C4—1721no—
177C22⋊C4—41no—
178C22⋊C4—42no—
179C22⋊C4—862no—
180C22⋊C4—1722no—
181C22⋊C4—1722no—
182C22⋊C4—1722no—
183C22⋊C4—1722no—
184C22⋊C4—1722no—
185C23—21no—
186C23—22no—
187C23—22no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23#1062190012yes—
197C23C23×D4311yescharacteristic
198D4—48no—
199D4—44no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—1724no—
220C22—24no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22C2×#1062190011yescharacteristic
233C22#1306337011yescharacteristic
234C22#1306337012yes—
235C22#1306337012yes—
236C22#1306337211yescharacteristic
237C4—41no—
238C4—41no—
239C4—42no—
240C4—1722no—
241C4—1722no—
242C4—1722no—
243C4—1722no—
244C2—42no—
245C2—82no—
246C2#1458348412yes—
247C2#1458349411yescharacteristic
248C2#1458363611yescharacteristic
249C2#1458363811yescharacteristic
250C2#1458364412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2826
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #14582840C2semidirect
2. #14582835C2semidirect
3. #14582827C2semidirect
4. #14582822C2semidirect
5. #14582813C2semidirect
6. #14582813C2semidirect
7. #14582779C2semidirect
8. #14582771C2semidirect
135. C43#2826semidirect