Finite Group Databasebeta

← #19143868

Subgroups — #19143868

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×#13063370C211yesmaximal, characteristic
2C2×#13063356C211yesmaximal, characteristic, complemented
3#14583473C211yesmaximal, characteristic, complemented
4#14583058C214yesmaximal, complemented
5#14583048C214yesmaximal, complemented
6#14582904C211yesmaximal, characteristic, complemented
7#14582896C211yesmaximal, characteristic, complemented
8#14582865C211yesmaximal, characteristic, complemented
9C22×SD16×C43C211yesmaximal, characteristic, complemented
10#13063370—24no—
11#13063370—24no—
12C2×#10621898C2211yescharacteristic
13C2×#10621898C2211yescharacteristic
14C2×#10621900—21no—
15C2×#10621900C2212yes—
16C22×C22⋊D43—22no—
17C2×D4×D43—21no—
18C2×D4×D43C2212yes—
19#13063356—24no—
20C2×#10621885C2212yescomplemented
21C2×#10621884C2212yescomplemented
22C2×#10621877C2211yescharacteristic, complemented
23#13063323—21no—
24#13063314—21no—
25#13063308—22no—
26#13063301C2214yescomplemented
27#13063284C2211yescharacteristic, complemented
28#13063250C2212yescomplemented
29#13063247C2212yescomplemented
30#13063246C2214yescomplemented
31(C2×D43)⋊C8C2214yescomplemented
32C22×Q8×C43C2211yescharacteristic, complemented
33C22×D4×C43C2211yescharacteristic
34C2×SD16×C43—24no—
35C2×SD16×C43C2214yescomplemented
36C22×C8×C43C2211yescharacteristic, complemented
37C24×C43—21no—
38C23×D43—22no—
39C2×Q8×C43—21no—
40C2×Q8×C43—22no—
41C2×Q8×C43—22no—
42C2×Q8×C43C2312yes—
43C2×D4×C43—21no—
44C2×D4×C43—22no—
45C2×D4×C43D414yes—
46C2×D4×C43C2312yes—
47C22×C4×C43—21no—
48C22×C4×C43C2311yescharacteristic
49C2×C22⋊D43—216no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—21no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43D412yes—
54C22×Dic43—22no—
55#10621900—28no—
56#10621900—24no—
57#10621900—24no—
58D4×D43—28no—
59D4×D43—24no—
60D4×D43—24no—
61#10621898—22no—
62#10621898—22no—
63#10621898—22no—
64#10621898D414yes—
65C2×D172D411yescharacteristic
66C2×D172C2311yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43C2312yes—
69C2×Dic86D411yescharacteristic
70C2×Dic86C2311yescharacteristic
71SD16×C43—28no—
72C2×C8×C43—22no—
73C2×C8×C43C2312yes—
74C22⋊Dic43—21no—
75#10621885—24no—
76#10621884—24no—
77(C2×D43)⋊C4—24no—
78C4⋊Dic43C2312yes—
79Dic43⋊C4—24no—
80C4×Dic43—21no—
81#10621877—22no—
82C2×C43⋊C8C2312yes—
83C23×C43—22no—
84C23×C43—24no—
85C23×C43—82no—
86C23×C43C2×D411yescharacteristic
87C22×D43—21no—
88C22×D43—28no—
89C22×D43—84no—
90C22×D43C2×D412yes—
91Q8×C43—22no—
92Q8×C43—22no—
93Q8×C43—42no—
94D4×C43—24no—
95D4×C43—22no—
96D4×C43C2×D414yes—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2×D412yes—
101C2×C4×C43C2×D412yes—
102C2×C4×C43C2411yescharacteristic
103C22⋊D43—28no—
104C22⋊D43—28no—
105C22⋊D43—24no—
106C22⋊D43—24no—
107C2×Dic43—28no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43C2×D412yes—
111D172—22no—
112D172—21no—
113D172C2×D412yes—
114C4×D43—24no—
115C4×D43—22no—
116C4×D43—22no—
117Dic86—22no—
118Dic86—21no—
119Dic86C2×D412yes—
120C8×C43—22no—
121C43⋊C8—22no—
122C22×C43—22no—
123C22×C43—24no—
124C22×C43—44no—
125C22×C43—84no—
126C22×C43#12012yes—
127C22×C43C22×D411yescharacteristic
128C2×D43—22no—
129C2×D43—22no—
130C2×D43—24no—
131C2×D43—42no—
132C2×D43—88no—
133C4×C43—42no—
134C4×C43#12012yes—
135C4×C43C22×D411yescharacteristic
136C4×C43C22×D411yescharacteristic
137Dic43—22no—
138Dic43—22no—
139Dic43—42no—
140#3009—431nomaximal, Sylow
141C2×C43—22no—
142C2×C43—44no—
143C2×C43C2×#12011yescharacteristic
144C2×C43#57712yes—
145D43—42no—
146D43—42no—
147C2×H(5,𝔽2)—431no—
148C2×#137—431no—
149C22×SD16D4311yescharacteristic, complemented
150#536—431no—
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—431no—
162C2×#41—861no—
163C22×Q8C2×D4311yescharacteristic, complemented
164C22×D4—432no—
165C22×D4—861no—
166C22×D4—862no—
167C22×D4C2×D4311yescharacteristic
168#137—864no—
169C2×Q16—432no—
170C2×SD16—24no—
171C2×SD16—432no—
172C2×SD16C2×D4314yescomplemented
173C2×M16—431no—
174C22×C8C2×D4311yescharacteristic, complemented
175C4⋊Q8—861no—
176#124—861no—
177#123—862no—
178C22⋊Q8—434no—
179#117—431no—
180#103—432no—
181#102—434no—
182#102—432no—
183C22⋊C8—434no—
184C24—21no—
185C24—862no—
186#41—434no—
187#41—864no—
188#41—868no—
189#41—864no—
190#41—862no—
191#41—862no—
192#41—862no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—431no—
197C2×Q8—431no—
198C2×Q8C22×D4312yes—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—432no—
202C2×D4—431no—
203C2×D4—431no—
204C2×D4—862no—
205C2×D4—864no—
206C2×D4—868no—
207C2×D4—862no—
208C2×D4—8616no—
209C2×D4—861no—
210C2×D4—864no—
211C2×D4C22⋊D4314yes—
212C2×D4C22×D4312yes—
213C22×C4—21no—
214C22×C4—432no—
215C22×C4—862no—
216C22×C4—861no—
217C22×C4C22×D4311yescharacteristic
218Q16—864no—
219SD16—28no—
220SD16—864no—
221M16—862no—
222C2×C8—22no—
223C2×C8—432no—
224C2×C8C22×D4312yes—
225C4⋊C4—432no—
226C4⋊C4—864no—
227C22⋊C4—864no—
228C22⋊C4—861no—
229C42—861no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—432no—
234C23—868no—
235C23—861no—
236C23—3444no—
237C23D4×D4311yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—42no—
241Q8—432no—
242Q8—862no—
243Q8—861no—
244D4—24no—
245D4—22no—
246D4—432no—
247D4—868no—
248D4—868no—
249D4—864no—
250D4—864no—
251D4—862no—
252D4—861no—
253D4C2×C22⋊D4314yes—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—432no—
257C2×C4—868no—
258C2×C4—861no—
259C2×C4—864no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4D4×D4311yescharacteristic
264C2×C4D4×D4312yes—
265C2×C4C2×C22⋊D4312yes—
266C2×C4C23×D4311yescharacteristic
267C8—22no—
268C8—862no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—862no—
274C22—862no—
275C22—864no—
276C22—3448no—
277C22—1722no—
278C22#1306329312yes—
279C22C2×D4×D4311yescharacteristic
280C4—42no—
281C4—862no—
282C4—862no—
283C4—1722no—
284C4#1306329312yes—
285C4C2×D4×D4311yescharacteristic
286C4C22×C22⋊D4311yescharacteristic
287C2—22no—
288C2—44no—
289C2—1722no—
290C2—1722no—
291C2C2×#1306329311yescharacteristic
292C2#1458370512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC22×SD16×C43C2
socleC22×C43C22×D4
hypercenterC22×SD16D43
hypocenterC43#3009
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#13063356C2semidirect
3. #14583473C2semidirect
4. #14583058C2semidirect
5. #14583048C2semidirect
6. #14582904C2semidirect
7. #14582896C2semidirect
8. #14582865C2semidirect
9. C22×SD16×C43C2semidirect
20. C2×#10621885C22semidirect
21. C2×#10621884C22semidirect
22. C2×#10621877C22semidirect
26. #13063301C22semidirect
27. #13063284C22semidirect
28. #13063250C22semidirect
29. #13063247C22semidirect
30. #13063246C22semidirect
31. (C2×D43)⋊C8C22semidirect
32. C22×Q8×C43C22semidirect
35. C2×SD16×C43C22semidirect
36. C22×C8×C43C22semidirect
149. C22×SD16D43semidirect
156. C43#3009semidirect
163. C22×Q8C2×D43semidirect
172. C2×SD16C2×D43semidirect
174. C22×C8C2×D43semidirect