Finite Group Databasebeta

← #19138872

Subgroups — #19138872

Order 5504.

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

normal subgroups only

This group has 700 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×C22⋊C4×D43C212yesmaximal
2#14582827C212yesmaximal, complemented
3#14582824C211yesmaximal, characteristic, complemented
4#14582773C212yesmaximal, complemented
5#14582770C212yesmaximal, complemented
6#14582761C212yesmaximal, complemented
7#14582761C212yesmaximal, complemented
8#14582754C211yesmaximal, characteristic
9C43×#397C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C22×C4×D43C2212yes—
12C22×C4×D43C2212yes—
13C2×C4⋊Dic43C2211yescharacteristic, complemented
14C2×Dic43⋊C4C2212yescomplemented
15C2×C22⋊Dic43C2212yes—
16C2×C22⋊Dic43C2211yescharacteristic
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C22⋊C4×D43—28no—
22C43⋊#95C2211yescharacteristic, complemented
23C43⋊#95C2212yescomplemented
24C43⋊#95C2212yescomplemented
25C43⋊#95C2212yescomplemented
26C43⋊#95C2212yescomplemented
27C2×C4⋊C4×C43C2211yescharacteristic, complemented
28C2×C22⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2211yescharacteristic
30#95×C43C2211yescharacteristic, complemented
31#95×C43C2212yescomplemented
32C24×C43C2311yescharacteristic
33C23×D43—24no—
34C23×D43—24no—
35C23×D43—41no—
36C23×D43—41no—
37C23×D43D414yes—
38C23×D43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C2×C4×D43—24no—
47C2×C4×D43—24no—
48C2×C4×D43—24no—
49C2×C4×D43—24no—
50C2×C4×D43—42no—
51C2×C4×D43—42no—
52C4⋊C4×C43—41no—
53C22⋊C4×C43—24no—
54C22⋊C4×C43—41no—
55C22⋊Dic43—24no—
56C22⋊Dic43—41no—
57(C2×D43)⋊C4—24no—
58(C2×D43)⋊C4—24no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61C4⋊Dic43—41no—
62Dic43⋊C4—42no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43—21no—
66C23×C43—21no—
67C23×C43C2×D412yes—
68C23×C43C2411yescharacteristic
69C22×D43—22no—
70C22×D43—22no—
71C22×D43—22no—
72C22×D43—22no—
73C22×D43—216no—
74C22×D43—44no—
75C22×D43—48no—
76C22×D43—44no—
77C22×D43—44no—
78C22×D43C2×D414yes—
79C22×D43#4114yes—
80C22×D43#4114yes—
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×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C4×D43—48no—
101C4×D43—48no—
102C22×C43—24no—
103C22×C43—22no—
104C22×C43—42no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43C22×D411yescharacteristic
108C22×C43C2×#4112yes—
109C22×C43C2×#4112yes—
110C22×C43H(5,𝔽2)11yescharacteristic
111C22×C43H(5,𝔽2)11yescharacteristic
112C2×D43—24no—
113C2×D43—24no—
114C2×D43—24no—
115C2×D43—24no—
116C2×D43—24no—
117C2×D43—24no—
118C2×D43—416no—
119C2×D43#12318yes—
120C4×C43—42no—
121C4×C43—42no—
122C4×C43—41no—
123C4×C43—41no—
124Dic43—42no—
125Dic43—42no—
126Dic43—42no—
127#2483—431nomaximal, Sylow
128C2×C43—42no—
129C2×C43C2×#12312yes—
130C2×C43#53411yescharacteristic
131C2×C43#55112yes—
132C2×C43#55111yescharacteristic
133C2×C43#55111yescharacteristic
134D43—28no—
135C22×C22⋊C4—432no—
136#397—431no—
137#397—432no—
138#397D4311yescharacteristic, complemented
139#385—432no—
140#385—432no—
141#381—432no—
142#381—432no—
143#379—431no—
144C43#248311yescharacteristic, complemented, Sylow
145C25—431no—
146C23×C4—432no—
147C23×C4—432no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—431no—
150C2×C4⋊C4C2×D4311yescharacteristic, complemented
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C22⋊C4—432no—
154C2×C22⋊C4—432no—
155C2×C22⋊C4—432no—
156C2×C22⋊C4—431no—
157C2×C22⋊C4—868no—
158C2×C22⋊C4C2×D4312yes—
159C2×C22⋊C4C2×D4311yescharacteristic
160#95—431no—
161#95—432no—
162#95—432no—
163#95—432no—
164#95—432no—
165#95C2×D4311yescharacteristic, complemented
166#95C2×D4312yescomplemented
167C24—432no—
168C24—434no—
169C24—864no—
170C24—864no—
171C24—1721no—
172C24—1721no—
173C24C22×D4311yescharacteristic
174C22×C4—432no—
175C22×C4—432no—
176C22×C4—432no—
177C22×C4—864no—
178C22×C4—864no—
179C22×C4—864no—
180C22×C4—864no—
181C22×C4—1722no—
182C22×C4—1722no—
183C22×C4C22×D4312yes—
184C22×C4C22×D4311yescharacteristic
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4312yes—
187C4⋊C4—41no—
188C4⋊C4—1722no—
189C4⋊C4—1721no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—864no—
193C22⋊C4—864no—
194C22⋊C4—864no—
195C22⋊C4—864no—
196C22⋊C4—864no—
197C22⋊C4—1721no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—434no—
203C23—434no—
204C23—434no—
205C23—8616no—
206C23—862no—
207C23—862no—
208C23—862no—
209C23—862no—
210C23—1724no—
211C23—1728no—
212C23—1724no—
213C23—1724no—
214C23D4×D4312yes—
215C23C23×D4311yescharacteristic
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—1728no—
236C2×C4—1728no—
237C22—24no—
238C22—22no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—438no—
243C22—864no—
244C22—864no—
245C22—864no—
246C22—864no—
247C22—864no—
248C22—864no—
249C22—17216no—
250C22C2×D4×D4311yescharacteristic
251C22#41×D4312yes—
252C22#41×D4312yes—
253C22#1306337011yescharacteristic
254C22#1306337111yescharacteristic
255C4—41no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—1722no—
260C4—1722no—
261C4—1722no—
262C2—42no—
263C2—868no—
264C2#123×D4312yes—
265C2#1458345711yescharacteristic
266C2#1458357412yes—
267C2#1458357711yescharacteristic
268C2#1458357911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2483
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #14582827C2semidirect
3. #14582824C2semidirect
4. #14582773C2semidirect
5. #14582770C2semidirect
6. #14582761C2semidirect
7. #14582761C2semidirect
9. C43×#397C2semidirect
13. C2×C4⋊Dic43C22semidirect
14. C2×Dic43⋊C4C22semidirect
22. C43⋊#95C22semidirect
23. C43⋊#95C22semidirect
24. C43⋊#95C22semidirect
25. C43⋊#95C22semidirect
26. C43⋊#95C22semidirect
27. C2×C4⋊C4×C43C22semidirect
30. #95×C43C22semidirect
31. #95×C43C22semidirect
138. #397D43semidirect
144. C43#2483semidirect
150. C2×C4⋊C4C2×D43semidirect
165. #95C2×D43semidirect
166. #95C2×D43semidirect