Finite Group Databasebeta

← #19143865

Subgroups — #19143865

Order 5504.

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

normal subgroups only

This group has 784 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, complemented
2C2×#13063353C211yesmaximal, characteristic, complemented
3C22×D344C211yesmaximal, characteristic, complemented
4#14583463C211yesmaximal, characteristic, complemented
5#14583046C214yesmaximal, complemented
6#14583035C214yesmaximal, complemented
7#14582905C211yesmaximal, characteristic, complemented
8#14582896C211yesmaximal, characteristic, complemented
9C43×#408C211yesmaximal, characteristic, complemented
10#13063371—24no—
11#13063371—24no—
12C2×#10621902—21no—
13C2×#10621898C2211yescharacteristic
14C2×#10621898C2212yescomplemented
15C22×D172C2211yescharacteristic
16C22×D172C2211yescharacteristic, complemented
17C22×D172C2212yescomplemented
18C2×D4×D43—21no—
19C2×D4×D43—22no—
20#13063353—24no—
21C2×#10621873C2212yescomplemented
22C2×D344—24no—
23C2×D344C2214yescomplemented
24C2×D344C2212yescomplemented
25#13063321—21no—
26#13063314—21no—
27#13063299C2214yescomplemented
28#13063293—22no—
29#13063284C2211yescharacteristic, complemented
30#13063250C2212yescomplemented
31#13063247C2214yescomplemented
32#13063247C2212yescomplemented
33C2×#41×C43C2211yescharacteristic
34C2×M16×C43C2211yescharacteristic, complemented
35C22×C8×C43C2211yescharacteristic, complemented
36C22⋊C8×C43C2214yescomplemented
37C23×D43—21no—
38C23×D43—22no—
39C23×D43—21no—
40#41×C43—22no—
41#41×C43—22no—
42C2×Q8×C43D411yescharacteristic
43C2×D4×C43D412yes—
44C2×D4×C43D411yescharacteristic
45C22×C4×C43C2312yes—
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—24no—
50#10621902—28no—
51D4×D43—28no—
52D4×D43—216no—
53#10621898—22no—
54#10621898—24no—
55#10621898—24no—
56#10621898D414yescomplemented
57C2×D172—21no—
58C2×D172—22no—
59C2×D172—22no—
60C2×D172—24no—
61C2×D172—24no—
62C2×D172—21no—
63C2×D172—22no—
64C2×D172—22no—
65C2×D172D414yescomplemented
66C2×D172C2312yes—
67C2×D172C2312yes—
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—22no—
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—28no—
81D344—24no—
82#10621873—24no—
83C23×C43C2×D412yes—
84C23×C43C2×D411yescharacteristic
85C22×D43—21no—
86C22×D43—22no—
87C22×D43—28no—
88C22×D43—24no—
89C22×D43—22no—
90C22×D43—42no—
91C22×D43—82no—
92C22×D43—84no—
93C22×D43—82no—
94Q8×C43—22no—
95D4×C43—24no—
96D4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43C2×D412yes—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2×D412yes—
102C2×C4×C43C2×D412yes—
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—28no—
105C22⋊D43—24no—
106C22⋊D43—84no—
107C2×Dic43—21no—
108C2×Dic43—22no—
109D172—28no—
110D172—24no—
111D172—21no—
112D172—22no—
113D172—22no—
114D172—22no—
115D172—42no—
116D172C2×D412yes—
117D172C2×D414yes—
118C4×D43—28no—
119C4×D43—24no—
120Dic86—21no—
121Dic86C2×D412yes—
122C8×C43—22no—
123C8×C43—22no—
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—24no—
127C22×C43#12012yes—
128C22×C43C22×D411yescharacteristic
129C2×D43—22no—
130C2×D43—24no—
131C2×D43—44no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—44no—
135C2×D43—84no—
136C2×D43—88no—
137C2×D43—84no—
138C4×C43—22no—
139C4×C43#12012yes—
140C4×C43C22×D411yescharacteristic
141C4×C43C22×D411yescharacteristic
142Dic43—22no—
143Dic43—42no—
144#3008—431nomaximal, Sylow
145C2×C43—22no—
146C2×C43—42no—
147C2×C43C2×#12011yescharacteristic
148C2×C43#57612yes—
149D43—44no—
150D43—42no—
151D43—82no—
152C2×H(5,𝔽2)—431no—
153C2×AGL(1,ℤ/8)—431no—
154C22×D8—431no—
155#535—431no—
156#449—434no—
157#447—434no—
158#418—431no—
159#416—431no—
160#408D4311yescharacteristic, complemented
161C43#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—864no—
163H(5,𝔽2)—864no—
164C2×#41—431no—
165C2×#41—432no—
166C2×#41—861no—
167C2×#41C2×D4311yescharacteristic
168C22×D4—431no—
169C22×D4—431no—
170C22×D4—432no—
171C22×D4—862no—
172C22×D4—861no—
173AGL(1,ℤ/8)—864no—
174C2×SD16—432no—
175C2×D8—434no—
176C2×D8—432no—
177C2×D8—864no—
178C2×M16C2×D4311yescharacteristic, complemented
179C22×C8C2×D4311yescharacteristic, complemented
180#127—861no—
181#124—861no—
182#121—434no—
183#120—862no—
184#117—431no—
185#103—432no—
186#102—432no—
187#102—434no—
188C22⋊C8C2×D4314yescomplemented
189C24—862no—
190C24—861no—
191C24—861no—
192#41—22no—
193#41—22no—
194#41—434no—
195#41—864no—
196#41—864no—
197#41—868no—
198#41—862no—
199C2×Q8—431no—
200C2×Q8D17211yescharacteristic
201C2×D4—434no—
202C2×D4—432no—
203C2×D4—431no—
204C2×D4—432no—
205C2×D4—864no—
206C2×D4—864no—
207C2×D4—8616no—
208C2×D4—868no—
209C2×D4—862no—
210C2×D4—861no—
211C2×D4—864no—
212C2×D4—862no—
213C2×D4—861no—
214C2×D4—861no—
215C2×D4—862no—
216C2×D4—862no—
217C2×D4—862no—
218C2×D4D17212yes—
219C2×D4D17211yescharacteristic
220C22×C4—862no—
221C22×C4—861no—
222C22×C4C22×D4312yes—
223C22×C4C22×D4311yescharacteristic
224SD16—864no—
225D8—868no—
226D8—864no—
227M16—22no—
228C2×C8—22no—
229C2×C8C22×D4312yes—
230C2×C8C22×D4312yes—
231C4⋊C4—432no—
232C22⋊C4—861no—
233C22⋊C4—864no—
234C42—861no—
235C23—868no—
236C23—864no—
237C23—862no—
238C23—861no—
239C23—862no—
240C23—3442no—
241C23—3442no—
242C23—3444no—
243C23—1722no—
244C23C2×D17212yes—
245C23C2×D17211yescharacteristic
246Q8—22no—
247Q8—432no—
248Q8—861no—
249D4—24no—
250D4—22no—
251D4—434no—
252D4—432no—
253D4—868no—
254D4—868no—
255D4—864no—
256D4—864no—
257D4—861no—
258D4—862no—
259D4—862no—
260D4—862no—
261D4—3444no—
262D4—1722no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—868no—
266C2×C4—861no—
267C2×C4—864no—
268C2×C4—862no—
269C2×C4C2×D17212yes—
270C2×C4C2×D17211yescharacteristic
271C2×C4D4×D4312yes—
272C2×C4D4×D4312yes—
273C2×C4C23×D4311yescharacteristic
274C8—22no—
275C8—22no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—864no—
280C22—862no—
281C22—3444no—
282C22—3444no—
283C22—3448no—
284C22—1722no—
285C22—1724no—
286C22—1724no—
287C22—1722no—
288C22#1306329512yes—
289C22C22×D17211yescharacteristic
290C4—22no—
291C4—862no—
292C4—1722no—
293C4#1306329512yes—
294C4C2×D4×D4311yescharacteristic
295C4C2×D4×D4311yescharacteristic
296C2—22no—
297C2—42no—
298C2—3442no—
299C2—1724no—
300C2—1722no—
301C2C2×#1306329511yescharacteristic
302C2#1458370412yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#408C2
socleC22×C43C22×D4
hypercenter#408D43
hypocenterC43#3008
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×#13063371C2semidirect
2. C2×#13063353C2semidirect
3. C22×D344C2semidirect
4. #14583463C2semidirect
5. #14583046C2semidirect
6. #14583035C2semidirect
7. #14582905C2semidirect
8. #14582896C2semidirect
9. C43×#408C2semidirect
14. C2×#10621898C22semidirect
16. C22×D172C22semidirect
17. C22×D172C22semidirect
21. C2×#10621873C22semidirect
23. C2×D344C22semidirect
24. C2×D344C22semidirect
27. #13063299C22semidirect
29. #13063284C22semidirect
30. #13063250C22semidirect
31. #13063247C22semidirect
32. #13063247C22semidirect
34. C2×M16×C43C22semidirect
35. C22×C8×C43C22semidirect
36. C22⋊C8×C43C22semidirect
56. #10621898D4semidirect
65. C2×D172D4semidirect
160. #408D43semidirect
161. C43#3008semidirect
178. C2×M16C2×D43semidirect
179. C22×C8C2×D43semidirect
188. C22⋊C8C2×D43semidirect