Finite Group Databasebeta

← #19138261

Subgroups — #19138261

Order 5504.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063302C212yesmaximal, complemented
2C22×C22⋊Dic43C212yesmaximal
3#14582835C211yesmaximal, characteristic, complemented
4#14582822C212yesmaximal, complemented
5#14582811C211yesmaximal, characteristic, complemented
6#14582774C212yesmaximal, complemented
7#14582771C212yesmaximal, complemented
8#14582757C212yesmaximal, complemented
9C43×#379C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic, complemented
11C23×Dic43C2212yes—
12C23×Dic43C2212yes—
13#13063302—28no—
14C2×C4⋊Dic43C2212yescomplemented
15C2×C4⋊Dic43C2211yescharacteristic, complemented
16C2×Dic43⋊C4C2212yescomplemented
17C2×Dic43⋊C4C2212yescomplemented
18C2×Dic43⋊C4C2212yescomplemented
19C2×C22⋊Dic43—28no—
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2212yes—
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2212yes—
24C43⋊#95C2211yescharacteristic, complemented
25C43⋊#95C2212yescomplemented
26C43⋊#95C2212yescomplemented
27C43⋊#95C2211yescharacteristic, complemented
28C25×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2212yes—
31C2×C22⋊C4×C43C2211yescharacteristic
32C2×C22⋊C4×C43C2211yescharacteristic
33C24×C43—24no—
34C24×C43—24no—
35C24×C43—41no—
36C24×C43—41no—
37C24×C43Q814yescomplemented
38C24×C43C2311yescharacteristic
39C24×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×Dic43—24no—
44C22×Dic43—24no—
45C22×Dic43—24no—
46C22×Dic43—24no—
47C22×Dic43—42no—
48C22×Dic43—42no—
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C22×Dic43C2312yes—
52C22×Dic43C2312yes—
53C2×Dic86—24no—
54C2×Dic86—41no—
55C22⋊C4×C43—24no—
56C22⋊C4×C43—24no—
57C22⋊C4×C43—41no—
58C22⋊C4×C43—41no—
59C22⋊Dic43—24no—
60C22⋊Dic43—24no—
61C22⋊Dic43—24no—
62C22⋊Dic43D418yes—
63C4⋊Dic43—24no—
64C4⋊Dic43—41no—
65Dic43⋊C4—24no—
66Dic43⋊C4—24no—
67Dic43⋊C4—42no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43—216no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—44no—
78C23×C43—44no—
79C23×C43—48no—
80C23×C43—44no—
81C23×C43C2×D414yes—
82C23×C43C2×Q812yes—
83C23×C43C2×Q814yes—
84C23×C43#4114yes—
85C23×C43C2411yescharacteristic
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—48no—
104C2×Dic43—48no—
105C2×Dic43C2×D414yes—
106C2×Dic43C2×D414yes—
107Dic86—44no—
108C22×C43—24no—
109C22×C43—24no—
110C22×C43—24no—
111C22×C43—24no—
112C22×C43—24no—
113C22×C43—24no—
114C22×C43—24no—
115C22×C43—22no—
116C22×C43—416no—
117C22×C43—41no—
118C22×C43—42no—
119C22×C43—41no—
120C22×C43C22⋊Q818yescomplemented
121C22×C43C22×D412yes—
122C22×C43C22×Q811yescharacteristic
123C22×C43C2×#4112yes—
124C22×C43H(5,𝔽2)11yescharacteristic
125C22×C43H(5,𝔽2)11yescharacteristic
126C4×C43—41no—
127C4×C43—42no—
128C4×C43—41no—
129Dic43—24no—
130Dic43—24no—
131Dic43—42no—
132Dic43—42no—
133#2437—431nomaximal, Sylow
134C2×C43—28no—
135C2×C43—42no—
136C2×C43C2×C22⋊Q812yes—
137C2×C43#54311yescharacteristic
138C2×C43D4211yescharacteristic
139C2×C43#54612yes—
140C2×C43#55111yescharacteristic
141C2×C22⋊Q8—432no—
142C22×C22⋊C4—432no—
143#399—431no—
144#396—432no—
145#393—431no—
146#385—432no—
147#385—432no—
148#380—432no—
149#379D4311yescharacteristic
150C43#243711yescharacteristic, complemented, Sylow
151C25C2×D4311yescharacteristic
152C22×Q8—431no—
153C23×C4—432no—
154C23×C4—432no—
155C22⋊Q8—868no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4—432no—
160C2×C4⋊C4—431no—
161C2×C22⋊C4—432no—
162C2×C22⋊C4—432no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4—868no—
166C2×C22⋊C4C2×D4312yes—
167C2×C22⋊C4C2×D4312yes—
168C2×C22⋊C4C2×D4311yescharacteristic
169C2×C22⋊C4C2×D4311yescharacteristic
170#95—431no—
171#95—432no—
172#95—432no—
173#95—431no—
174C24—24no—
175C24—24no—
176C24—41no—
177C24—41no—
178C24Dic8614yescomplemented
179C24C22×D4311yescharacteristic
180C24C22×D4312yes—
181C2×Q8—864no—
182C2×Q8—1721no—
183C22×C4—432no—
184C22×C4—432no—
185C22×C4—432no—
186C22×C4—432no—
187C22×C4—864no—
188C22×C4—864no—
189C22×C4—864no—
190C22×C4—864no—
191C22×C4—1722no—
192C22×C4—1722no—
193C22×C4C22×D4311yescharacteristic
194C22×C4C22×D4312yes—
195C22×C4C22×D4311yescharacteristic
196C4⋊C4—864no—
197C4⋊C4—864no—
198C4⋊C4—864no—
199C4⋊C4—1722no—
200C4⋊C4—1721no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—438no—
206C22⋊C4—864no—
207C22⋊C4—864no—
208C22⋊C4—864no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—216no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—44no—
219C23—44no—
220C23—44no—
221C23—48no—
222C23C2×Dic8612yes—
223C23C2×Dic8614yes—
224C23D4×D4314yes—
225C23#1062190014yes—
226C23C23×D4311yescharacteristic
227Q8—1724no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—434no—
236C2×C4—434no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—862no—
247C2×C4—1728no—
248C2×C4—1728no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—416no—
258C22—41no—
259C22—41no—
260C22—42no—
261C22#1306330218yescomplemented
262C22C2×D4×D4312yes—
263C22C22×Dic8611yescharacteristic
264C22C2×#1062190012yes—
265C22#1306337011yescharacteristic
266C22#1306337011yescharacteristic
267C4—41no—
268C4—41no—
269C4—42no—
270C4—864no—
271C4—864no—
272C4—1722no—
273C4—1722no—
274C2—28no—
275C2—42no—
276C2C2×#1306330212yes—
277C2#1458352511yescharacteristic
278C2#1458353111yescharacteristic
279C2#1458353612yes—
280C2#1458358011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#379C2
hypercenter#379D43
hypocenterC43#2437
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#13063302C2semidirect
3. #14582835C2semidirect
4. #14582822C2semidirect
5. #14582811C2semidirect
6. #14582774C2semidirect
7. #14582771C2semidirect
8. #14582757C2semidirect
10. C22×Dic86C22semidirect
14. C2×C4⋊Dic43C22semidirect
15. C2×C4⋊Dic43C22semidirect
16. C2×Dic43⋊C4C22semidirect
17. C2×Dic43⋊C4C22semidirect
18. C2×Dic43⋊C4C22semidirect
24. C43⋊#95C22semidirect
25. C43⋊#95C22semidirect
26. C43⋊#95C22semidirect
27. C43⋊#95C22semidirect
37. C24×C43Q8semidirect
120. C22×C43C22⋊Q8semidirect
150. C43#2437semidirect
178. C24Dic86semidirect
261. C22#13063302semidirect