Finite Group Databasebeta

← #19142659

Subgroups — #19142659

Order 5504.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063323C211yesmaximal, characteristic, complemented
2C2×#13063320C211yesmaximal, characteristic
3#14582840C212yesmaximal, complemented
4#14582834C212yesmaximal
5#14582832C212yesmaximal, complemented
6#14582828C212yesmaximal
7#14582819C211yesmaximal, characteristic, complemented
8#14582812C211yesmaximal, characteristic
9#14582810C211yesmaximal, characteristic
10#14582766C211yesmaximal, characteristic, complemented
11C43×#395C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13#13063323—24no—
14#13063320—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2211yescharacteristic
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C43⋊#95C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C2×Q8×C43—22no—
39C2×Q8×C43—42no—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2312yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C2×Dic86—22no—
51C2×Dic86—42no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—42no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—42no—
58(C2×D43)⋊C4—42no—
59C4⋊Dic43—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4—24no—
62Dic43⋊C4—24no—
63Dic43⋊C4—42no—
64C4×Dic43D414yes—
65C23×C43C2411yescharacteristic
66C22×D43—21no—
67C22×D43—22no—
68C22×D43—21no—
69C22×D43—21no—
70C22×D43—22no—
71Q8×C43—44no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43C2×D412yes—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43C2×D412yes—
97C2×Dic43C2×D412yes—
98Dic86—44no—
99C22×C43C22×D411yescharacteristic
100C22×C43H(5,𝔽2)12yes—
101C22×C432−1+411yescharacteristic
102C22×C432−1+411yescharacteristic
103C22×C432−1+412yes—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—41no—
107C2×D43—42no—
108C2×D43—42no—
109C4×C43—22no—
110C4×C43—41no—
111C4×C43—42no—
112C4×C43—41no—
113C4×C43—42no—
114Dic43—22no—
115Dic43—22no—
116Dic43—42no—
117Dic43—41no—
118Dic43—42no—
119#2821—431nomaximal, Sylow
120C2×C43#53511yescharacteristic
121C2×C43#53611yescharacteristic
122C2×C43#53611yescharacteristic
123C2×C43#56312yes—
124C2×C43#56312yes—
125D43—81no—
126C2×C4⋊Q8—431no—
127C2×#126—431no—
128#400—432no—
129#399—432no—
130#398—432no—
131#397—432no—
132#395—431no—
133#395D4311yescharacteristic, complemented
134#393—431no—
135#393—431no—
136#383—431no—
137C43#282111yescharacteristic, complemented, Sylow
138C22×Q8—431no—
139C22×Q8C2×D4311yescharacteristic
140C4⋊Q8—864no—
141#126—864no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4—432no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4C2×D4311yescharacteristic
148C2×C4⋊C4C2×D4312yes—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—431no—
151C2×C22⋊C4—431no—
152C2×C22⋊C4—432no—
153C2×C22⋊C4—432no—
154C2×C42—431no—
155#95—431no—
156#95—432no—
157#95—432no—
158#95—432no—
159#95—432no—
160#95—432no—
161#95C2×D4311yescharacteristic
162#95C2×D4312yes—
163C24—431no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—862no—
167C2×Q8—1722no—
168C22×C4—431no—
169C22×C4—431no—
170C22×C4—432no—
171C22×C4—431no—
172C22×C4—432no—
173C22×C4C22×D4312yes—
174C22×C4C22×D4311yescharacteristic
175C22×C4C22×D4312yes—
176C22×C4C22×D4311yescharacteristic
177C22×C4C22×D4311yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4—864no—
183C4⋊C4—864no—
184C4⋊C4—1722no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—862no—
188C22⋊C4—1722no—
189C22⋊C4—1722no—
190C42—434no—
191C23—861no—
192C23—862no—
193C23—861no—
194C23—861no—
195C23—862no—
196C23C23×D4311yescharacteristic
197Q8—44no—
198Q8—1724no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—432no—
212C2×C4—432no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4D4×D4312yes—
225C22—1722no—
226C22—1722no—
227C22—1721no—
228C22—1721no—
229C22—1721no—
230C22C2×D4×D4311yescharacteristic
231C22#1306337012yes—
232C22#1306337211yescharacteristic
233C22#1306337311yescharacteristic
234C22#1306337312yes—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4—862no—
241C4—862no—
242C4—1722no—
243C4—1722no—
244C4—1721no—
245C2—3441no—
246C2#1458346411yescharacteristic
247C2#1458347211yescharacteristic
248C2#1458347411yescharacteristic
249C2#1458364812yes—
250C2#1458365012yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2821
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13063323C2semidirect
3. #14582840C2semidirect
5. #14582832C2semidirect
7. #14582819C2semidirect
10. #14582766C2semidirect
11. C43×#395C2semidirect
133. #395D43semidirect
137. C43#2821semidirect