Finite Group Databasebeta

← #19140803

Subgroups — #19140803

Order 5504.

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

normal subgroups only

This group has 816 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×#13063298C212yesmaximal, complemented
2C2×#13063294C212yesmaximal, complemented
3#14582835C211yesmaximal, characteristic, complemented
4#14582827C212yesmaximal, complemented
5#14582815C212yesmaximal, complemented
6#14582808C211yesmaximal, characteristic, complemented
7#14582775C212yesmaximal, complemented
8#14582775C212yesmaximal, complemented
9C43×#379C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic, complemented
11C22×C22⋊D43C2212yes—
12C22×C22⋊D43C2212yes—
13C22×C22⋊D43C2212yes—
14C22×C4×D43C2212yescomplemented
15#13063298—28no—
16#13063294—28no—
17C2×C4⋊Dic43C2211yescharacteristic, complemented
18C2×Dic43⋊C4C2212yescomplemented
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2212yes—
22C2×(C2×D43)⋊C4C2212yescomplemented
23C2×(C2×D43)⋊C4C2212yescomplemented
24C43⋊#95C2211yescharacteristic, complemented
25C43⋊#95C2212yescomplemented
26C43⋊#95C2212yescomplemented
27C43⋊#95C2211yescharacteristic, complemented
28C25×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2211yescharacteristic
31C2×C22⋊C4×C43C2212yes—
32C2×C22⋊C4×C43C2211yescharacteristic
33C24×C43—24no—
34C24×C43—22no—
35C24×C43—41no—
36C24×C43—42no—
37C24×C43—41no—
38C24×C43C2312yes—
39C24×C43C2311yescharacteristic
40C23×D43C2312yes—
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—24no—
45C2×C22⋊D43—24no—
46C2×C22⋊D43—24no—
47C2×C22⋊D43—24no—
48C2×C22⋊D43—42no—
49C2×C22⋊D43—42no—
50C2×C22⋊D43—42no—
51C2×C22⋊D43—42no—
52C2×C22⋊D43D418yescomplemented
53C22×Dic43C2312yes—
54C22×Dic43C2312yes—
55C22×Dic43C2312yes—
56C2×D172—24no—
57C2×D172—41no—
58C2×C4×D43—24no—
59C2×C4×D43—42no—
60C2×C4×D43—42no—
61C22⋊C4×C43—24no—
62C22⋊C4×C43—41no—
63C22⋊C4×C43—42no—
64C22⋊C4×C43—41no—
65C22⋊Dic43—24no—
66C22⋊Dic43—24no—
67C22⋊Dic43—24no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—42no—
70C4⋊Dic43—41no—
71Dic43⋊C4—24no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—44no—
83C23×C43—48no—
84C23×C43—48no—
85C23×C43—44no—
86C23×C43—44no—
87C23×C43C2×D414yes—
88C23×C43#4112yes—
89C23×C43C2411yescharacteristic
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—22no—
93C22×D43—22no—
94C22×D43—22no—
95C22×D43—22no—
96C22×D43C2×D414yes—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C22⋊D43—48no—
105C22⋊D43—48no—
106C22⋊D43—48no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43C2×D414yes—
116D172—44no—
117C4×D43—48no—
118C22×C43—24no—
119C22×C43—22no—
120C22×C43—24no—
121C22×C43—24no—
122C22×C43—24no—
123C22×C43—416no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—41no—
131C22×C43C22×D412yes—
132C22×C43C2×#4111yescharacteristic
133C22×C43H(5,𝔽2)11yescharacteristic
134C22×C43H(5,𝔽2)12yes—
135C22×C43H(5,𝔽2)11yescharacteristic
136C2×D43—24no—
137C2×D43—24no—
138C2×D43—24no—
139C2×D43—42no—
140C2×D43—42no—
141C2×D43—42no—
142C2×D43—42no—
143C4×C43—42no—
144C4×C43—41no—
145C4×C43—41no—
146Dic43—24no—
147Dic43—42no—
148Dic43—42no—
149#2668—431nomaximal, Sylow
150C2×C43—44no—
151C2×C43—42no—
152C2×C43#53412yes—
153C2×C43#53811yescharacteristic
154C2×C43D4211yescharacteristic
155C2×C43#54612yes—
156C2×C43#56011yescharacteristic
157D43—44no—
158C2×#121—432no—
159C2×#120—432no—
160#399—431no—
161#397—432no—
162#394—432no—
163#392—431no—
164#386—432no—
165#386—432no—
166#379D4311yescharacteristic, complemented
167C43#266811yescharacteristic, complemented, Sylow
168C25C2×D4311yescharacteristic
169C22×D4—432no—
170C22×D4—432no—
171C22×D4—432no—
172C22×D4—431no—
173C23×C4—432no—
174#121—868no—
175#120—868no—
176C2×C4⋊C4—432no—
177C2×C4⋊C4—431no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—432no—
181C2×C22⋊C4—432no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4C2×D4312yes—
184C2×C22⋊C4C2×D4311yescharacteristic
185C2×C22⋊C4C2×D4312yes—
186C2×C22⋊C4C2×D4311yescharacteristic
187#95—432no—
188#95—431no—
189#95—432no—
190#95—431no—
191C24—22no—
192C24—24no—
193C24—41no—
194C24—42no—
195C24—41no—
196C24—432no—
197C24C22×D4311yescharacteristic
198C24C22×D4312yes—
199C2×D4—438no—
200C2×D4—864no—
201C2×D4—864no—
202C2×D4—864no—
203C2×D4—864no—
204C2×D4—864no—
205C2×D4—1721no—
206C2×D4—1722no—
207C2×D4—1722no—
208C2×D4—1722no—
209C2×D4—1722no—
210C22×C4—432no—
211C22×C4—432no—
212C22×C4—432no—
213C22×C4—864no—
214C22×C4—1722no—
215C22×C4—1722no—
216C22×C4C22×D4312yes—
217C22×C4C22×D4311yescharacteristic
218C22×C4C22×D4311yescharacteristic
219C4⋊C4—864no—
220C4⋊C4—1721no—
221C22⋊C4—24no—
222C22⋊C4—42no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—864no—
226C22⋊C4—864no—
227C22⋊C4—864no—
228C22⋊C4—864no—
229C22⋊C4—1722no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—44no—
241C23—48no—
242C23—48no—
243C23—44no—
244C23—44no—
245C23—434no—
246C23—862no—
247C23—862no—
248C23—862no—
249C23—862no—
250C23—862no—
251C23—862no—
252C23#1062189812yes—
253C23D4×D4314yes—
254C23C23×D4311yescharacteristic
255D4—1724no—
256D4—1728no—
257D4—1728no—
258D4—1728no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—434no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—862no—
275C2×C4—1728no—
276C22—24no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—416no—
282C22—42no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—42no—
289C22—864no—
290C22—864no—
291C22—864no—
292C22—1722no—
293C22—1722no—
294C22—1722no—
295C22—1722no—
296C22C2×D4×D4312yes—
297C22C2×#1062189811yescharacteristic
298C22#1306337012yes—
299C22#1306337011yescharacteristic
300C22#1306337011yescharacteristic
301C4—41no—
302C4—42no—
303C4—41no—
304C4—864no—
305C4—1722no—
306C4—1722no—
307C2—44no—
308C2—42no—
309C2—1724no—
310C2#1458345912yes—
311C2#1458348711yescharacteristic
312C2#1458353111yescharacteristic
313C2#1458353912yes—
314C2#1458363811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#379C2
hypercenter#379D43
hypocenterC43#2668
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#13063298C2semidirect
2. C2×#13063294C2semidirect
3. #14582835C2semidirect
4. #14582827C2semidirect
5. #14582815C2semidirect
6. #14582808C2semidirect
7. #14582775C2semidirect
8. #14582775C2semidirect
9. C43×#379C2semidirect
10. C22×D172C22semidirect
14. C22×C4×D43C22semidirect
17. C2×C4⋊Dic43C22semidirect
18. C2×Dic43⋊C4C22semidirect
22. C2×(C2×D43)⋊C4C22semidirect
23. C2×(C2×D43)⋊C4C22semidirect
24. C43⋊#95C22semidirect
25. C43⋊#95C22semidirect
26. C43⋊#95C22semidirect
27. C43⋊#95C22semidirect
52. C2×C22⋊D43D4semidirect
166. #379D43semidirect
167. C43#2668semidirect