Finite Group Databasebeta

← #19140754

Subgroups — #19140754

Order 5504.

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

normal subgroups only

This group has 434 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×#13063319C211yesmaximal, characteristic
2C2×#13063317C211yesmaximal, characteristic, complemented
3#14582839C211yesmaximal, characteristic, complemented
4#14582836C211yesmaximal, characteristic
5#14582831C211yesmaximal, characteristic, complemented
6#14582829C212yesmaximal, complemented
7#14582826C211yesmaximal, characteristic
8#14582821C212yesmaximal
9#14582797C212yesmaximal, complemented
10#14582790C212yesmaximal
11C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
12#13063319—24no—
13#13063317—24no—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2212yes—
33C2×C42×C43C2212yes—
34C2×C42×C43C2211yescharacteristic
35#95×C43C2211yescharacteristic
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C4⋊C4×C43—24no—
49C42×C43—42no—
50C42×C43D414yes—
51(C2×D43)⋊C4—22no—
52(C2×D43)⋊C4—22no—
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—24no—
55(C2×D43)⋊C4—42no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43—24no—
59C4⋊Dic43—42no—
60Dic43⋊C4—24no—
61Dic43⋊C4—24no—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65C23×C43C2411yescharacteristic
66C22×D43—21no—
67C22×D43—22no—
68C22×D43—21no—
69C22×D43—22no—
70C22×D43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D412yes—
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2×D412yes—
83C2×C4×C43#4114yes—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97C22×C43C22×D411yescharacteristic
98C22×C43C2×#4112yes—
99C22×C43H(5,𝔽2)11yescharacteristic
100C22×C432−1+412yes—
101C22×C432−1+411yescharacteristic
102C2×D43—41no—
103C2×D43—41no—
104C2×D43—41no—
105C2×D43—42no—
106C2×D43—42no—
107C4×C43—22no—
108C4×C43—22no—
109C4×C43—22no—
110C4×C43—24no—
111C4×C43—42no—
112Dic43—42no—
113Dic43—41no—
114Dic43—41no—
115Dic43—42no—
116Dic43—41no—
117#2664—431nomaximal, Sylow
118C2×C43#53211yescharacteristic
119C2×C43#53611yescharacteristic
120C2×C43#53711yescharacteristic
121C2×C43#53912yes—
122C2×C43#54112yes—
123D43—81no—
124C2×#126—431no—
125C2×#125—431no—
126#400—431no—
127#399—431no—
128#398—432no—
129#398—431no—
130#397—431no—
131#396—432no—
132#389—432no—
133#388—432no—
134C4×C4⋊C4D4311yescharacteristic, complemented
135C43#266411yescharacteristic, complemented, Sylow
136#126—864no—
137#125—864no—
138C2×C4⋊C4—432no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—431no—
145C2×C4⋊C4—432no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4C2×D4312yes—
148C2×C22⋊C4—431no—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—431no—
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C42C2×D4312yes—
154C2×C42C2×D4311yescharacteristic
155#95—432no—
156#95—432no—
157#95—432no—
158#95—432no—
159#95C2×D4311yescharacteristic
160#95C2×D4311yescharacteristic
161C24—431no—
162C22×C4—431no—
163C22×C4—431no—
164C22×C4—431no—
165C22×C4—432no—
166C22×C4—432no—
167C22×C4C22×D4312yes—
168C22×C4C22×D4311yescharacteristic
169C22×C4C22×D4311yescharacteristic
170C22×C4C22×D4311yescharacteristic
171C22×C4C22×D4312yes—
172C4⋊C4—24no—
173C4⋊C4—864no—
174C4⋊C4—864no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—864no—
181C4⋊C4—1722no—
182C22⋊C4—862no—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—864no—
186C22⋊C4—1722no—
187C42—42no—
188C42D17214yes—
189C23—861no—
190C23—862no—
191C23—861no—
192C23—862no—
193C23—861no—
194C23C23×D4311yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—861no—
214C2×C4—862no—
215C2×C4—861no—
216C2×C4—862no—
217C2×C4C2×D17212yes—
218C2×C4C2×D17212yes—
219C2×C4C2×D17212yes—
220C2×C4#1062189814yes—
221C22—1721no—
222C22—1721no—
223C22—1721no—
224C22—1722no—
225C22—1722no—
226C22C22×D17211yescharacteristic
227C22C2×#1062189812yes—
228C22#1306337011yescharacteristic
229C22#1306337212yes—
230C22#1306337311yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—24no—
235C4—42no—
236C4—1721no—
237C4—1722no—
238C4—1721no—
239C4—1721no—
240C4—1722no—
241C2—3441no—
242C2#1458344911yescharacteristic
243C2#1458347511yescharacteristic
244C2#1458348011yescharacteristic
245C2#1458349112yes—
246C2#1458350712yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC4×C4⋊C4×C43C2
hypercenterC4×C4⋊C4D43
hypocenterC43#2664
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#13063317C2semidirect
3. #14582839C2semidirect
5. #14582831C2semidirect
6. #14582829C2semidirect
9. #14582797C2semidirect
11. C4×C4⋊C4×C43C2semidirect
134. C4×C4⋊C4D43semidirect
135. C43#2664semidirect