Finite Group Databasebeta

← #19137884

Subgroups — #19137884

Order 5504.

568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063290C211yesmaximal, characteristic, complemented
2C2×#13063287C211yesmaximal, characteristic
3#14582837C211yesmaximal, characteristic, complemented
4#14582828C212yesmaximal, complemented
5#14582817C211yesmaximal, characteristic
6#14582816C211yesmaximal, characteristic
7#14582812C212yesmaximal, complemented
8#14582746C212yesmaximal, complemented
9#14582746C212yesmaximal, complemented
10#14582744C211yesmaximal, characteristic, complemented
11C43×#400C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×C4×D43C2212yes—
15#13063290—24no—
16#13063287—24no—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2312yes—
38C22×C4×C43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—24no—
50C2×C4×D43—24no—
51C2×C4×D43—24no—
52C2×C4×D43—24no—
53C2×Dic86—22no—
54C2×Dic86—22no—
55C2×Dic86—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—22no—
58(C2×D43)⋊C4—24no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—24no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65C4×Dic43—22no—
66C4×Dic43—22no—
67C4×Dic43—24no—
68C4×Dic43D414yes—
69C23×C43C2411yescharacteristic
70C22×D43—22no—
71C22×D43—22no—
72C22×D43—22no—
73C22×D43—22no—
74C22×D43—22no—
75C22×D43—22no—
76C22×D43#4114yes—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43C2×D412yes—
89C2×C4×C43#4112yes—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43C2×D412yes—
100C2×Dic43C2×D412yes—
101C2×Dic43#4112yes—
102C2×Dic43#4114yes—
103D172—28no—
104C4×D43—48no—
105Dic86—28no—
106C22×C43C22×D411yescharacteristic
107C22×C43C2×#4111yescharacteristic
108C22×C43C2×#4112yes—
109C22×C43C2×#4112yes—
110C22×C43C2×#4111yescharacteristic
111C2×D43—24no—
112C2×D43—24no—
113C2×D43—24no—
114C2×D43—42no—
115C2×D43—42no—
116C2×D43—42no—
117C2×D43—42no—
118C4×C43—22no—
119C4×C43—22no—
120C4×C43—41no—
121C4×C43—42no—
122C4×C43—42no—
123Dic43—22no—
124Dic43—22no—
125Dic43—41no—
126Dic43—42no—
127Dic43#12414yes—
128#2398—431nomaximal, Sylow
129C2×C43#52511yescharacteristic
130C2×C43#52511yescharacteristic
131C2×C43C2×#12411yescharacteristic
132C2×C43#52912yes—
133C2×C43#52912yes—
134D43—44no—
135C2×C4×Q8—431no—
136C2×C4×D4—431no—
137#400—431no—
138#400D4311yescharacteristic, complemented
139#397—432no—
140#394—431no—
141#394—431no—
142#393—432no—
143C4×C22⋊C4—432no—
144C4×C22⋊C4—432no—
145#376—431no—
146C43#239811yescharacteristic, complemented, Sylow
147C22×Q8—431no—
148C22×D4—431no—
149C23×C4—432no—
150C4×Q8—864no—
151C4×D4—864no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—431no—
154C2×C4⋊C4C2×D4311yescharacteristic
155C2×C4⋊C4C2×D4311yescharacteristic
156C2×C22⋊C4—432no—
157C2×C22⋊C4—432no—
158C2×C22⋊C4—432no—
159C2×C22⋊C4—432no—
160C2×C22⋊C4—432no—
161C2×C42—431no—
162C2×C42—431no—
163C2×C42—431no—
164C2×C42—432no—
165#95—432no—
166#95—431no—
167#95—432no—
168#95—432no—
169#95C2×D4311yescharacteristic
170#95C2×D4312yes—
171#95C2×D4312yes—
172C24—432no—
173C2×Q8—862no—
174C2×Q8—862no—
175C2×Q8—862no—
176C2×D4—864no—
177C2×D4—862no—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—432no—
182C22×C4—431no—
183C22×C4—864no—
184C22×C4—864no—
185C22×C4—864no—
186C22×C4C22×D4312yes—
187C22×C4C22×D4312yes—
188C22×C4C22×D4311yescharacteristic
189C22×C4C22×D4311yescharacteristic
190C22×C4C22×D4311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—862no—
194C4⋊C4—862no—
195C22⋊C4—864no—
196C22⋊C4—864no—
197C22⋊C4—864no—
198C22⋊C4—864no—
199C22⋊C4—864no—
200C42—434no—
201C42—862no—
202C42—862no—
203C42—864no—
204C23—434no—
205C23—862no—
206C23—862no—
207C23—862no—
208C23—862no—
209C23—862no—
210C23—862no—
211C23C23×D4311yescharacteristic
212Q8—868no—
213D4—868no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—432no—
226C2×C4—434no—
227C2×C4—432no—
228C2×C4—432no—
229C2×C4—861no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—861no—
233C2×C4—861no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—1728no—
239C2×C4D4×D4312yes—
240C2×C4#1062190212yes—
241C22—864no—
242C22—864no—
243C22—864no—
244C22—1722no—
245C22—1722no—
246C22—1722no—
247C22—1722no—
248C22C2×D4×D4311yescharacteristic
249C22#41×D4312yes—
250C22#41×D4311yescharacteristic
251C22#41×D4312yes—
252C22C2×#1062190211yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—42no—
258C4—434no—
259C4—862no—
260C4—862no—
261C4—1721no—
262C4—1722no—
263C2—1724no—
264C2#1458340711yescharacteristic
265C2#1458341211yescharacteristic
266C2#124×D4311yescharacteristic
267C2#1458343212yes—
268C2#1458343412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2398
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13063290C2semidirect
3. #14582837C2semidirect
4. #14582828C2semidirect
7. #14582812C2semidirect
8. #14582746C2semidirect
9. #14582746C2semidirect
10. #14582744C2semidirect
11. C43×#400C2semidirect
138. #400D43semidirect
146. C43#2398semidirect