Finite Group Databasebeta

← #19143883

Subgroups — #19143883

Order 5504.

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

normal subgroups only

This group has 732 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×#13063372C211yesmaximal, characteristic, complemented
2C2×#13063353C211yesmaximal, characteristic, complemented
3C22×#10621873C211yesmaximal, characteristic, complemented
4#14583463C211yesmaximal, characteristic, complemented
5#14583046C214yesmaximal, complemented
6#14583040C214yesmaximal, complemented
7#14582909C211yesmaximal, characteristic, complemented
8#14582896C211yesmaximal, characteristic, complemented
9C43×#408C211yesmaximal, characteristic, complemented
10#13063372—24no—
11#13063372—24no—
12C2×#10621898C2211yescharacteristic
13C2×#10621898C2212yescomplemented
14C2×#10621900—21no—
15C2×#10621900—22no—
16C22×Dic86C2211yescharacteristic
17C22×Dic86C2212yescomplemented
18C2×Q8×D43—21no—
19C22×D172C2211yescharacteristic
20#13063353—24no—
21C2×#10621873—24no—
22C2×#10621873C2212yes—
23C2×#10621873C2214yes—
24C2×D344C2212yes—
25#13063321—21no—
26#13063314—21no—
27#13063299C2214yes—
28#13063293—22no—
29#13063284C2211yescharacteristic
30#13063250C2212yescomplemented
31#13063250C2214yescomplemented
32#13063247C2212yescomplemented
33C2×#41×C43C2211yescharacteristic
34C2×M16×C43C2211yescharacteristic
35C22×C8×C43C2211yescharacteristic
36C22⋊C8×C43C2214yescomplemented
37C23×D43—21no—
38#41×C43—22no—
39#41×C43—22no—
40C2×Q8×C43D411yescharacteristic
41C2×D4×C43D412yes—
42C2×D4×C43D411yescharacteristic
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—21no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—24no—
48C22×Dic43—21no—
49C22×Dic43—22no—
50Q8×D43—28no—
51#10621900—216no—
52#10621900—28no—
53#10621898—22no—
54#10621898—24no—
55#10621898—24no—
56#10621898D414yescomplemented
57C2×D172—21no—
58C2×D172—22no—
59C2×D172—22no—
60C2×D172C2312yes—
61C2×D172C2311yescharacteristic
62C2×C4×D43—21no—
63C2×C4×D43—22no—
64C2×Dic86—21no—
65C2×Dic86—22no—
66C2×Dic86—22no—
67C2×Dic86—24no—
68C2×Dic86—24no—
69C2×Dic86D414yescomplemented
70C2×Dic86C2312yes—
71C2×Dic86C2311yescharacteristic
72M16×C43—22no—
73C2×C8×C43—22no—
74C2×C8×C43C2312yes—
75C2×C8×C43C2312yes—
76C22⋊Dic43—21no—
77(C2×D43)⋊C4—24no—
78C4⋊Dic43C2312yes—
79C4×Dic43—21no—
80D344—24no—
81#10621873—28no—
82#10621873—24no—
83C23×C43C2×D412yes—
84C23×C43C2×D411yescharacteristic
85C22×D43—21no—
86C22×D43—22no—
87C22×D43—42no—
88C22×D43—82no—
89Q8×C43—22no—
90D4×C43—24no—
91D4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43C2×D412yes—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D412yes—
98C2×C4×C43C2411yescharacteristic
99C22⋊D43—28no—
100C22⋊D43—24no—
101C22⋊D43—84no—
102C2×Dic43—28no—
103C2×Dic43—24no—
104C2×Dic43—22no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107D172—21no—
108D172—22no—
109D172—22no—
110D172—42no—
111D172C2×D412yes—
112C4×D43—28no—
113C4×D43—24no—
114Dic86—28no—
115Dic86—24no—
116Dic86—22no—
117Dic86—21no—
118Dic86C2×D412yes—
119Dic86C2×D414yes—
120C8×C43—22no—
121C8×C43—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—24no—
125C22×C43#12012yes—
126C22×C43C22×D411yescharacteristic
127C2×D43—22no—
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—44no—
131C2×D43—84no—
132C4×C43—22no—
133C4×C43#12012yes—
134C4×C43C22×D411yescharacteristic
135C4×C43C22×D411yescharacteristic
136Dic43—22no—
137Dic43—24no—
138Dic43—42no—
139#3010—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—42no—
142C2×C43C2×#12011yescharacteristic
143C2×C43#57712yes—
144D43—42no—
145D43—82no—
146C2×2−1+4—431no—
147C2×AGL(1,ℤ/8)—431no—
148C22×SD16—431no—
149#535—431no—
150#449—434no—
151#448—434no—
152#419—431no—
153#416—431no—
154#408D4311yescharacteristic, complemented
155C43#301011yescharacteristic, complemented, Sylow
1562−1+4—864no—
1572−1+4—864no—
158C2×#41—431no—
159C2×#41—432no—
160C2×#41—862no—
161C2×#41—861no—
162C2×#41C2×D4311yescharacteristic
163C22×Q8—431no—
164C22×Q8—432no—
165C22×Q8—861no—
166C22×D4—431no—
167AGL(1,ℤ/8)—864no—
168C2×SD16—434no—
169C2×SD16—432no—
170C2×SD16—864no—
171C2×D8—432no—
172C2×M16C2×D4311yescharacteristic
173C22×C8C2×D4311yescharacteristic
174#127—861no—
175#124—861no—
176#121—434no—
177#120—862no—
178#117—431no—
179#103—432no—
180#103—434no—
181#102—432no—
182C22⋊C8C2×D4314yescomplemented
183C24—861no—
184#41—22no—
185#41—22no—
186#41—434no—
187#41—864no—
188#41—864no—
189#41—8616no—
190#41—868no—
191#41—862no—
192C2×Q8—434no—
193C2×Q8—432no—
194C2×Q8—431no—
195C2×Q8—864no—
196C2×Q8—864no—
197C2×Q8—868no—
198C2×Q8—862no—
199C2×Q8—861no—
200C2×Q8—862no—
201C2×Q8D17211yescharacteristic
202C2×D4—431no—
203C2×D4—432no—
204C2×D4—862no—
205C2×D4—861no—
206C2×D4—864no—
207C2×D4—861no—
208C2×D4—862no—
209C2×D4—862no—
210C2×D4D17212yes—
211C2×D4D17211yescharacteristic
212C22×C4—862no—
213C22×C4—861no—
214C22×C4—862no—
215C22×C4—861no—
216C22×C4C22×D4312yes—
217C22×C4C22×D4311yescharacteristic
218SD16—868no—
219SD16—864no—
220D8—864no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D4312yes—
224C2×C8C22×D4312yes—
225C4⋊C4—432no—
226C22⋊C4—861no—
227C22⋊C4—864no—
228C42—861no—
229C23—861no—
230C23—862no—
231C23—3442no—
232C23—1722no—
233C23C2×D17212yes—
234C23C2×D17211yescharacteristic
235Q8—22no—
236Q8—434no—
237Q8—432no—
238Q8—868no—
239Q8—864no—
240Q8—862no—
241Q8—861no—
242D4—24no—
243D4—22no—
244D4—432no—
245D4—868no—
246D4—864no—
247D4—861no—
248D4—862no—
249D4—862no—
250D4—3444no—
251D4—1722no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—868no—
255C2×C4—868no—
256C2×C4—864no—
257C2×C4—862no—
258C2×C4—861no—
259C2×C4—864no—
260C2×C4—862no—
261C2×C4C2×D17212yes—
262C2×C4C2×D17211yescharacteristic
263C2×C4D4×D4312yes—
264C2×C4D4×D4312yes—
265C2×C4C23×D4311yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—862no—
272C22—3444no—
273C22—1722no—
274C22—1724no—
275C22—1722no—
276C22#1306329512yes—
277C22C22×D17211yescharacteristic
278C4—22no—
279C4—864no—
280C4—862no—
281C4—1722no—
282C4#1306329512yes—
283C4C2×D4×D4311yescharacteristic
284C4C2×D4×D4311yescharacteristic
285C2—22no—
286C2—42no—
287C2—3442no—
288C2—1722no—
289C2C2×#1306329511yescharacteristic
290C2#1458371112yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#408C2
socleC22×C43C22×D4
hypercenter#408D43
hypocenterC43#3010
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#13063372C2semidirect
2. C2×#13063353C2semidirect
3. C22×#10621873C2semidirect
4. #14583463C2semidirect
5. #14583046C2semidirect
6. #14583040C2semidirect
7. #14582909C2semidirect
8. #14582896C2semidirect
9. C43×#408C2semidirect
13. C2×#10621898C22semidirect
17. C22×Dic86C22semidirect
30. #13063250C22semidirect
31. #13063250C22semidirect
32. #13063247C22semidirect
36. C22⋊C8×C43C22semidirect
56. #10621898D4semidirect
69. C2×Dic86D4semidirect
154. #408D43semidirect
155. C43#3010semidirect
182. C22⋊C8C2×D43semidirect