Finite Group Databasebeta

← #19143837

Subgroups — #19143837

Order 5504.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063356C211yesmaximal, characteristic, complemented
2C2×#13063351C211yesmaximal, characteristic, complemented
3#14583410C211yesmaximal, characteristic, complemented
4#14583061C214yesmaximal, complemented
5#14583044C214yesmaximal, complemented
6#14582908C211yesmaximal, characteristic, complemented
7#14582904C211yesmaximal, characteristic, complemented
8#14582863C211yesmaximal, characteristic, complemented
9C22×#41×C43C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11#13063356—24no—
12#13063351—24no—
13C2×#10621885C2212yescomplemented
14C2×#10621883C2212yescomplemented
15C2×#10621884C2212yescomplemented
16C2×#10621882C2212yescomplemented
17C2×#10621877C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19#13063308—21no—
20#13063304C2212yescomplemented
21#13063299C2212yescomplemented
22#13063294—21no—
23C4×C22⋊D43—22no—
24#13063284C2211yescharacteristic
25#13063249C2214yescomplemented
26#13063246C2214yescomplemented
27C22⋊(C43⋊C8)C2214yescomplemented
28C2×#41×C43—24no—
29C2×#41×C43—24no—
30C2×#41×C43—22no—
31C2×#41×C43C2214yes—
32C22×Q8×C43C2211yescharacteristic
33C22×D4×C43—21no—
34C22×D4×C43C2211yescharacteristic
35C23×C4×C43—21no—
36C23×C4×C43C2211yescharacteristic
37C24×C43—21no—
38C24×C43D411yescharacteristic
39#41×C43—216no—
40#41×C43—28no—
41#41×C43—28no—
42C2×Q8×C43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43D414yescomplemented
45C2×Q8×C43C2312yes—
46C2×D4×C43—28no—
47C2×D4×C43—22no—
48C2×D4×C43—21no—
49C2×D4×C43—24no—
50C2×D4×C43D414yescomplemented
51C2×D4×C43C2312yes—
52C22×C4×C43—28no—
53C22×C4×C43—24no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—21no—
57C22×C4×C43D411yescharacteristic
58C22×C4×C43D412yes—
59C22×C4×C43C2312yes—
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—22no—
62C2×C22⋊D43—21no—
63#10621898—22no—
64#10621898—22no—
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×Dic86C2311yescharacteristic
68C22⋊Dic43—21no—
69C22⋊Dic43—22no—
70#10621885—24no—
71#10621884—24no—
72#10621883—24no—
73#10621882—24no—
74(C2×D43)⋊C4—22no—
75C4⋊Dic43C2312yes—
76Dic43⋊C4—22no—
77C4×Dic43—21no—
78#10621877—22no—
79#10621877—22no—
80C2×C43⋊C8C2312yes—
81C2×C43⋊C8C2312yes—
82C23×C43—22no—
83C23×C43—24no—
84C23×C43—22no—
85C23×C43—42no—
86C23×C43—44no—
87C23×C43C2×D412yes—
88C23×C43C2×D411yescharacteristic
89C22×D43—21no—
90Q8×C43—24no—
91Q8×C43—22no—
92Q8×C43C2×D414yes—
93D4×C43—216no—
94D4×C43—24no—
95D4×C43—22no—
96D4×C43C2×D414yes—
97C2×C4×C43—216no—
98C2×C4×C43—22no—
99C2×C4×C43—24no—
100C2×C4×C43—22no—
101C2×C4×C43—24no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D412yes—
108C2×C4×C43C2411yescharacteristic
109C22⋊D43—44no—
110C22⋊D43—42no—
111C2×Dic43—22no—
112C2×Dic43—21no—
113D172—21no—
114D172—21no—
115C4×D43—42no—
116Dic86—21no—
117Dic86—21no—
118C43⋊C8—22no—
119C43⋊C8—22no—
120C22×C43—22no—
121C22×C43—24no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—22no—
125C22×C43—44no—
126C22×C43—48no—
127C22×C43—44no—
128C22×C43#12012yes—
129C22×C43C22×D411yescharacteristic
130C2×D43—41no—
131C2×D43—42no—
132C4×C43—22no—
133C4×C43—24no—
134C4×C43#12012yes—
135C4×C43C22×D411yescharacteristic
136C4×C43C22×D411yescharacteristic
137Dic43—41no—
138Dic43—42no—
139#3005—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—42no—
142C2×C43—44no—
143C2×C43C2×#12011yescharacteristic
144C2×C43#57512yes—
145D43—81no—
146C22×#41D4311yescharacteristic, complemented
147C2×#137—431no—
148C2×AGL(1,ℤ/8)—431no—
149#525—431no—
150#452—434no—
151#449—434no—
152#419—431no—
153#418—431no—
154#407—431no—
155C43#300511yescharacteristic, complemented, Sylow
156C2×#41—24no—
157C2×#41—24no—
158C2×#41—22no—
159C2×#41—431no—
160C2×#41C2×D4314yes—
161C22×Q8C2×D4311yescharacteristic
162C22×D4—21no—
163C22×D4C2×D4311yescharacteristic
164C23×C4—21no—
165C23×C4C2×D4311yescharacteristic
166#137—864no—
167AGL(1,ℤ/8)—864no—
168C2×Q16—432no—
169C2×SD16—432no—
170C2×SD16—432no—
171C2×D8—432no—
172C2×M16—431no—
173C2×M16—431no—
174#123—861no—
175C22⋊Q8—432no—
176#121—432no—
177#120—861no—
178C4×D4—862no—
179#117—431no—
180#103—434no—
181#102—434no—
182C22⋊C8—434no—
183C24—21no—
184C24C22⋊D4311yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—862no—
189#41—862no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—431no—
193C2×Q8C22⋊D4314yescomplemented
194C2×Q8C22×D4312yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—431no—
200C2×D4—862no—
201C2×D4—861no—
202C2×D4C22⋊D4314yescomplemented
203C2×D4C22×D4312yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—861no—
210C22×C4C22⋊D4312yes—
211C22×C4C22⋊D4311yescharacteristic
212C22×C4C22×D4312yes—
213C22×C4C22×D4311yescharacteristic
214Q16—864no—
215SD16—864no—
216SD16—864no—
217D8—864no—
218M16—862no—
219M16—862no—
220C2×C8—432no—
221C2×C8—432no—
222C4⋊C4—432no—
223C4⋊C4—862no—
224C22⋊C4—861no—
225C22⋊C4—862no—
226C22⋊C4—862no—
227C42—861no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—861no—
234C23C2×C22⋊D4312yes—
235C23C2×C22⋊D4311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—861no—
239Q8—861no—
240Q8C2×C22⋊D4314yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—861no—
245D4—861no—
246D4—1724no—
247D4—1722no—
248D4C2×C22⋊D4314yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—862no—
257C2×C4—861no—
258C2×C4—1722no—
259C2×C4C2×C22⋊D4312yes—
260C2×C4C2×C22⋊D4311yescharacteristic
261C2×C4C2×C22⋊D4312yes—
262C2×C4C2×C22⋊D4312yes—
263C2×C4C23×D4311yescharacteristic
264C8—862no—
265C8—862no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—1721no—
275C22—1722no—
276C22#1306329412yes—
277C22C22×C22⋊D4311yescharacteristic
278C4—22no—
279C4—24no—
280C4—1721no—
281C4—1722no—
282C4#1306329412yes—
283C4C22×C22⋊D4311yescharacteristic
284C4C22×C22⋊D4311yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—3441no—
289C2C2×#1306329411yescharacteristic
290C2#1458369712yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC22×#41×C43C2
socleC22×C43C22×D4
hypercenterC22×#41D43
hypocenterC43#3005
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C2×#13063351C2semidirect
3. #14583410C2semidirect
4. #14583061C2semidirect
5. #14583044C2semidirect
6. #14582908C2semidirect
7. #14582904C2semidirect
8. #14582863C2semidirect
9. C22×#41×C43C2semidirect
13. C2×#10621885C22semidirect
14. C2×#10621883C22semidirect
15. C2×#10621884C22semidirect
16. C2×#10621882C22semidirect
20. #13063304C22semidirect
21. #13063299C22semidirect
25. #13063249C22semidirect
26. #13063246C22semidirect
27. C22⋊(C43⋊C8)C22semidirect
44. C2×Q8×C43D4semidirect
50. C2×D4×C43D4semidirect
146. C22×#41D43semidirect
155. C43#3005semidirect
193. C2×Q8C22⋊D43semidirect
202. C2×D4C22⋊D43semidirect