Finite Group Databasebeta

← #19143870

Subgroups — #19143870

Order 5504.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063371C211yesmaximal, characteristic
2C2×#13063356C211yesmaximal, characteristic, complemented
3C22×#10621884C211yesmaximal, characteristic, complemented
4#14583059C214yesmaximal, complemented
5#14583049C214yesmaximal, complemented
6#14582903C211yesmaximal, characteristic, complemented
7#14582893C211yesmaximal, characteristic, complemented
8#14582866C211yesmaximal, characteristic, complemented
9C43×#536C211yesmaximal, characteristic, complemented
10#13063371—24no—
11#13063371—24no—
12C2×#10621902—21no—
13C2×#10621898C2212yes—
14C2×#10621898C2211yescharacteristic
15C22×D172C2212yes—
16C22×D172C2211yescharacteristic
17C2×D4×D43—22no—
18C2×D4×D43—21no—
19#13063356—24no—
20C2×#10621885C2212yescomplemented
21C2×#10621884—24no—
22C2×#10621884C2212yescomplemented
23C2×#10621884C2214yescomplemented
24C2×#10621877C2211yescharacteristic, complemented
25C22×C43⋊C8C2211yescharacteristic, complemented
26#13063248C2212yescomplemented
27#13063245C2212yescomplemented
28#13063245C2214yescomplemented
29C22⋊(C43⋊C8)C2214yescomplemented
30C2×#41×C43C2211yescharacteristic
31C22×Q8×C43C2211yescharacteristic, complemented
32C4⋊Q8×C43—21no—
33#124×C43—21no—
34#123×C43—22no—
35C22⋊Q8×C43C2214yescomplemented
36#117×C43C2211yescharacteristic, complemented
37C23×D43—22no—
38C23×D43—21no—
39#41×C43—22no—
40#41×C43—22no—
41C2×Q8×C43—21no—
42C2×Q8×C43—22no—
43C2×Q8×C43—22no—
44C2×Q8×C43D411yescharacteristic
45C2×Q8×C43C2312yes—
46C2×D4×C43D412yes—
47C2×D4×C43D411yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43C2312yes—
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—22no—
52C2×C22⋊D43—21no—
53#10621902—28no—
54D4×D43—28no—
55D4×D43—216no—
56#10621898—22no—
57#10621898—24no—
58#10621898—24no—
59#10621898D414yes—
60C2×D172—22no—
61C2×D172—21no—
62C2×D172—22no—
63C2×D172—24no—
64C2×D172—24no—
65C2×D172D414yes—
66C2×D172C2311yescharacteristic
67C2×D172C2312yes—
68C2×C4×D43—22no—
69C2×C4×D43—21no—
70C2×Dic86C2311yescharacteristic
71C4⋊C4×C43—24no—
72C4⋊C4×C43C2312yes—
73C22⋊C4×C43—21no—
74C22⋊C4×C43—24no—
75C42×C43—21no—
76#10621885—24no—
77#10621884—28no—
78#10621884—24no—
79#10621877—22no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8C2312yes—
82C2×C43⋊C8C2312yes—
83C23×C43C2×D412yes—
84C23×C43C2×D411yescharacteristic
85C22×D43—21no—
86C22×D43—22no—
87C22×D43—28no—
88C22×D43—24no—
89C22×D43—82no—
90C22×D43—84no—
91Q8×C43—22no—
92Q8×C43—22no—
93Q8×C43—22no—
94Q8×C43—42no—
95D4×C43—24no—
96D4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—42no—
102C2×C4×C43C2×D412yes—
103C2×C4×C43C2×D412yes—
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2411yescharacteristic
107C22⋊D43—28no—
108C22⋊D43—24no—
109C2×Dic43—21no—
110D172—28no—
111D172—24no—
112D172—21no—
113D172—22no—
114D172C2×D412yes—
115D172C2×D414yes—
116C4×D43—28no—
117C4×D43—24no—
118Dic86—21no—
119Dic86C2×D412yes—
120C43⋊C8—22no—
121C43⋊C8—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—24no—
125C22×C43#12012yes—
126C22×C43C22×D411yescharacteristic
127C2×D43—22no—
128C2×D43—24no—
129C2×D43—44no—
130C2×D43—42no—
131C2×D43—84no—
132C2×D43—88no—
133C4×C43—22no—
134C4×C43—42no—
135C4×C43—42no—
136C4×C43#12012yes—
137C4×C43C22×D411yescharacteristic
138C4×C43C22×D411yescharacteristic
139Dic43—22no—
140#3009—431nomaximal, Sylow
141C2×C43—22no—
142C2×C43—42no—
143C2×C43C2×#12011yescharacteristic
144C2×C43#57712yes—
145D43—44no—
146D43—42no—
147C2×H(5,𝔽2)—431no—
148C2×#137—431no—
149C22×SD16—431no—
150#536D4311yescharacteristic, complemented
151#452—434no—
152#450—434no—
153#418—431no—
154#416—431no—
155#408—431no—
156C43#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—864no—
158H(5,𝔽2)—864no—
159C2×#41—431no—
160C2×#41—432no—
161C2×#41—861no—
162C2×#41C2×D4311yescharacteristic
163C22×Q8C2×D4311yescharacteristic, complemented
164C22×D4—431no—
165C22×D4—432no—
166C22×D4—862no—
167C22×D4—861no—
168#137—864no—
169C2×Q16—432no—
170C2×SD16—434no—
171C2×SD16—432no—
172C2×SD16—864no—
173C2×M16—431no—
174C22×C8—431no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D4314yescomplemented
179#117C2×D4311yescharacteristic, complemented
180#103—432no—
181#102—432no—
182#102—434no—
183C22⋊C8—434no—
184C24—862no—
185C24—861no—
186#41—22no—
187#41—22no—
188#41—434no—
189#41—864no—
190#41—864no—
191#41—868no—
192#41—862no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—431no—
197C2×Q8C22⋊D4311yescharacteristic
198C2×Q8C22×D4312yes—
199C2×D4—434no—
200C2×D4—432no—
201C2×D4—431no—
202C2×D4—864no—
203C2×D4—864no—
204C2×D4—8616no—
205C2×D4—868no—
206C2×D4—862no—
207C2×D4—861no—
208C2×D4—862no—
209C2×D4—862no—
210C2×D4—861no—
211C2×D4C22⋊D4312yes—
212C2×D4C22⋊D4311yescharacteristic
213C22×C4—21no—
214C22×C4—862no—
215C22×C4—861no—
216C22×C4C22×D4312yes—
217C22×C4C22×D4311yescharacteristic
218Q16—864no—
219SD16—868no—
220SD16—864no—
221M16—862no—
222C2×C8—432no—
223C2×C8—432no—
224C2×C8—862no—
225C4⋊C4—24no—
226C4⋊C4C22×D4312yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—868no—
231C23—864no—
232C23—862no—
233C23—861no—
234C23—3442no—
235C23—3444no—
236C23C2×C22⋊D4312yes—
237C23C2×C22⋊D4311yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—432no—
243Q8—861no—
244D4—24no—
245D4—22no—
246D4—434no—
247D4—432no—
248D4—868no—
249D4—868no—
250D4—864no—
251D4—864no—
252D4—861no—
253D4—862no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—868no—
260C2×C4—861no—
261C2×C4—864no—
262C2×C4D4×D4312yes—
263C2×C4D4×D4312yes—
264C2×C4C2×C22⋊D4312yes—
265C2×C4C2×C22⋊D4311yescharacteristic
266C2×C4C23×D4311yescharacteristic
267C8—862no—
268C8—862no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—864no—
273C22—862no—
274C22—3444no—
275C22—3448no—
276C22—1724no—
277C22—1722no—
278C22#1306329312yes—
279C22C22×C22⋊D4311yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—862no—
284C4#1306329312yes—
285C4C2×D4×D4311yescharacteristic
286C4C2×D4×D4311yescharacteristic
287C2—22no—
288C2—42no—
289C2—1724no—
290C2—1722no—
291C2C2×#1306329311yescharacteristic
292C2#1458370712yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#536C2
socleC22×C43C22×D4
hypercenter#536D43
hypocenterC43#3009
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#13063356C2semidirect
3. C22×#10621884C2semidirect
4. #14583059C2semidirect
5. #14583049C2semidirect
6. #14582903C2semidirect
7. #14582893C2semidirect
8. #14582866C2semidirect
9. C43×#536C2semidirect
20. C2×#10621885C22semidirect
22. C2×#10621884C22semidirect
23. C2×#10621884C22semidirect
24. C2×#10621877C22semidirect
25. C22×C43⋊C8C22semidirect
26. #13063248C22semidirect
27. #13063245C22semidirect
28. #13063245C22semidirect
29. C22⋊(C43⋊C8)C22semidirect
31. C22×Q8×C43C22semidirect
35. C22⋊Q8×C43C22semidirect
36. #117×C43C22semidirect
150. #536D43semidirect
156. C43#3009semidirect
163. C22×Q8C2×D43semidirect
178. C22⋊Q8C2×D43semidirect
179. #117C2×D43semidirect