Finite Group Databasebeta

← #19140295

Subgroups — #19140295

Order 5504.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063282C211yesmaximal, characteristic
2#14582837C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic
4#14582830C211yesmaximal, characteristic, complemented
5#14582825C211yesmaximal, characteristic
6#14582794C212yesmaximal, complemented
7#14582789C212yesmaximal
8#14582780C212yesmaximal, complemented
9#14582770C212yesmaximal
10#14582745C211yesmaximal, characteristic, complemented
11C2×#125×C43C211yesmaximal, characteristic, complemented
12C22×C4×D43C2211yescharacteristic
13#13063282—24no—
14C2×Dic43⋊C4C2211yescharacteristic
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×(C2×D43)⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×C4×Dic43C2212yes—
23C2×C4×Dic43C2211yescharacteristic
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31#125×C43—24no—
32C2×C4⋊C4×C43C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2212yes—
36C2×C42×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×C4×D43—22no—
51C4⋊C4×C43—24no—
52C4⋊C4×C43—24no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C42×C43D414yes—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—24no—
59(C2×D43)⋊C4—24no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62Dic43⋊C4—24no—
63Dic43⋊C4—24no—
64C4×Dic43—22no—
65C4×Dic43—24no—
66C23×C43C2411yescharacteristic
67C22×D43—21no—
68C22×D43—22no—
69C22×D43—21no—
70C22×D43—22no—
71C22×D43#4112yes—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2×D412yes—
84C2×C4×C43C2×D412yes—
85C2×Dic43—21no—
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43#4114yes—
97C2×Dic43#4112yes—
98C4×D43—28no—
99C22×C43C22×D411yescharacteristic
100C22×C43C2×#4111yescharacteristic
101C22×C43C2×#4111yescharacteristic
102C22×C43C2×#4112yes—
103C22×C432−1+412yes—
104C2×D43—22no—
105C2×D43—24no—
106C2×D43—41no—
107C2×D43—41no—
108C2×D43—42no—
109C4×C43—22no—
110C4×C43—22no—
111C4×C43—22no—
112C4×C43—42no—
113C4×C43—42no—
114Dic43—22no—
115Dic43—24no—
116Dic43—41no—
117Dic43—41no—
118Dic43—42no—
119#2611—431nomaximal, Sylow
120C2×C43#52511yescharacteristic
121C2×C43#53211yescharacteristic
122C2×C43#53611yescharacteristic
123C2×C43#55212yes—
124C2×C43#55212yes—
125D43—42no—
126C2×#125D4311yescharacteristic, complemented
127C2×#117—431no—
128#400—431no—
129#399—431no—
130#398—431no—
131#397—431no—
132#389—432no—
133#388—432no—
134#387—432no—
135#385—432no—
136#376—431no—
137C43#261111yescharacteristic, complemented, Sylow
138C23×C4—431no—
139#125—24no—
140#117—864no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—432no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4C2×D4312yes—
146C2×C4⋊C4C2×D4312yes—
147C2×C4⋊C4C2×D4311yescharacteristic
148C2×C4⋊C4C2×D4311yescharacteristic
149C2×C22⋊C4—431no—
150C2×C22⋊C4—431no—
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C42—431no—
154C2×C42—432no—
155C2×C42C2×D4311yescharacteristic
156#95—432no—
157#95—431no—
158#95—431no—
159#95—432no—
160#95—432no—
161#95—432no—
162#95—432no—
163C24—431no—
164C22×C4—432no—
165C22×C4—431no—
166C22×C4—432no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4—862no—
170C22×C4—862no—
171C22×C4—862no—
172C22×C4C22×D4312yes—
173C22×C4C22×D4312yes—
174C22×C4C22×D4311yescharacteristic
175C22×C4C22×D4311yescharacteristic
176C22×C4C22×D4311yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—864no—
182C4⋊C4—864no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C22⋊C4—864no—
186C22⋊C4—864no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C42—864no—
190C42—862no—
191C42C22⋊D4314yes—
192C23—432no—
193C23—861no—
194C23—862no—
195C23—861no—
196C23—862no—
197C23C23×D4311yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—434no—
209C2×C4—432no—
210C2×C4—868no—
211C2×C4—861no—
212C2×C4—862no—
213C2×C4—861no—
214C2×C4—862no—
215C2×C4—861no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4C2×C22⋊D4312yes—
223C2×C4C2×C22⋊D4312yes—
224C2×C4C2×C22⋊D4312yes—
225C22—864no—
226C22—862no—
227C22—1722no—
228C22—1721no—
229C22—1721no—
230C22C22×C22⋊D4311yescharacteristic
231C22#41×D4311yescharacteristic
232C22#41×D4311yescharacteristic
233C22#41×D4312yes—
234C22#1306337312yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—864no—
241C4—862no—
242C4—1722no—
243C4—1721no—
244C4—1721no—
245C2—1722no—
246C2#1458340611yescharacteristic
247C2#1458344511yescharacteristic
248C2#1458347311yescharacteristic
249C2#1458358112yes—
250C2#1458358112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#125×C43C2
hypercenterC2×#125D43
hypocenterC43#2611
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
4. #14582830C2semidirect
6. #14582794C2semidirect
8. #14582780C2semidirect
10. #14582745C2semidirect
11. C2×#125×C43C2semidirect
126. C2×#125D43semidirect
137. C43#2611semidirect