Finite Group Databasebeta

← #19145593

Subgroups — #19145593

Order 5504.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#14583454C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic
3#14583291C211yesmaximal, characteristic, complemented
4#14583259C211yesmaximal, characteristic, complemented
5#14583258C211yesmaximal, characteristic, complemented
6#14583123C212yesmaximal, complemented
7#14583119C212yesmaximal, complemented
8#14583053C212yesmaximal, complemented
9#14583048C212yesmaximal
10#14582954C211yesmaximal, characteristic, complemented
11C43×#497C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621885C2212yescomplemented
15C2×#10621884C2212yes—
16#13063325C2211yescharacteristic, complemented
17#13063316—21no—
18#13063314C2211yescharacteristic
19#13063313C2211yescharacteristic
20#13063312C2211yescharacteristic
21#13063311—21no—
22#13063311—21no—
23#13063305—21no—
24#13063301C2212yes—
25Q8×Dic43C2212yescomplemented
26#13063290—21no—
27#13063283—21no—
28C22⋊C4×D43—21no—
29C22⋊C4×D43—21no—
30C42×D43C2211yescharacteristic
31Dic43⋊C8C2212yescomplemented
32#13063250C2212yescomplemented
33#13063249C2212yescomplemented
34#13063247C2212yes—
35#13063246C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic, complemented
38C2×Q16×C43C2212yescomplemented
39C2×SD16×C43C2212yes—
40C4⋊Q8×C43C2211yescharacteristic, complemented
41#124×C43C2211yescharacteristic
42#97×C43C2211yescharacteristic, complemented
43C23×D43—21no—
44C2×Q8×C43C2311yescharacteristic
45C2×Q8×C43C2312yes—
46C2×D4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48Q8×D43—42no—
49D4×D43—42no—
50C2×D172C2311yescharacteristic
51C2×C4×D43—21no—
52C2×C4×D43D411yescharacteristic
53C2×C4×D43D411yescharacteristic
54C2×C4×D43C2311yescharacteristic
55C2×Dic86—21no—
56C2×Dic86—21no—
57C2×Dic86C2311yescharacteristic
58Q16×C43—42no—
59SD16×C43—42no—
60C2×C8×C43C2312yes—
61C4⋊C4×C43—21no—
62C4⋊C4×C43—21no—
63C22⋊C4×C43—21no—
64C22⋊C4×C43—21no—
65C42×C43C2311yescharacteristic
66C22⋊Dic43—21no—
67C22⋊Dic43—21no—
68#10621885—42no—
69#10621884—42no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—22no—
75C4⋊Dic43—21no—
76C4⋊Dic43—22no—
77C4⋊Dic43C2312yes—
78Dic43⋊C4—22no—
79C4×Dic43—22no—
80C4×Dic43D411yescharacteristic
81C4×Dic43D411yescharacteristic
82C4×Dic43C2311yescharacteristic
83C2×C43⋊C8C2312yes—
84C23×C43—21no—
85C22×D43—21no—
86C22×D43—42no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43C2×D411yescharacteristic
90Q8×C43—22no—
91Q8×C43—22no—
92Q8×C43—22no—
93D4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2411yescharacteristic
99C22⋊D43—42no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102C2×Dic43C2×D411yescharacteristic
103C2×Dic43C2×D411yescharacteristic
104C2×Dic43C2×D411yescharacteristic
105D172—22no—
106C4×D43—22no—
107C4×D43—22no—
108C4×D43—41no—
109C4×D43—42no—
110Dic86—22no—
111Dic86—42no—
112Dic86—42no—
113C8×C43—22no—
114C43⋊C8—22no—
115C22×C43—41no—
116C22×C43—41no—
117C22×C43—41no—
118C22×C43C22×D411yescharacteristic
119C2×D43—21no—
120C2×D43—21no—
121C2×D43—41no—
122C2×D43—41no—
123C2×D43—41no—
124C2×D43—84no—
125C2×D43#13712yes—
126C4×C43—21no—
127C4×C43—21no—
128C4×C43—41no—
129C4×C43—42no—
130C4×C43H(5,𝔽2)12yes—
131Dic43—21no—
132Dic43—21no—
133Dic43—21no—
134Dic43—41no—
135Dic43—42no—
136#3215—431nomaximal, Sylow
137C2×C43—81no—
138C2×C43#53511yescharacteristic
139C2×C43C2×#13711yescharacteristic
140C2×C43#57511yescharacteristic
141D43—22no—
142D43—81no—
143#533—431no—
144C2×#124—431no—
145#497—431no—
146#497D4311yescharacteristic, complemented
147#489—431no—
148#489—431no—
149#464—432no—
150#464—432no—
151#451—432no—
152#450—432no—
153#432—431no—
154C43#321511yescharacteristic, complemented, Sylow
155C22×Q8—431no—
156C22×D4—431no—
157C2×Q16—432no—
158C2×Q16C2×D4312yescomplemented
159C2×SD16—432no—
160C2×SD16C2×D4312yes—
161C4⋊Q8—431no—
162C4⋊Q8C2×D4311yescharacteristic, complemented
163#125—861no—
164#124—431no—
165#124—431no—
166#124—431no—
167#124—861no—
168#124—861no—
169#124C2×D4311yescharacteristic
170C22⋊Q8—432no—
171C22⋊Q8—861no—
172C4×Q8—432no—
173C4×Q8—861no—
174#117—861no—
175C2×C22⋊C4—861no—
176C2×C22⋊C4—861no—
177C2×C42—431no—
178C4⋊C8—432no—
179#103—432no—
180#103—432no—
181#102—432no—
182#102—432no—
183C22⋊C8—432no—
184#97—431no—
185#97C2×D4311yescharacteristic, complemented
186C24—861no—
187C2×Q8—431no—
188C2×Q8—861no—
189C2×Q8—861no—
190C2×Q8—1722no—
191C2×Q8C22×D4311yescharacteristic
192C2×Q8C22×D4312yes—
193C2×D4—431no—
194C2×D4—861no—
195C2×D4—1722no—
196C2×D4C22×D4311yescharacteristic
197C22×C4—431no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—861no—
201Q16—42no—
202Q16—1722no—
203SD16—42no—
204SD16—1722no—
205C2×C8—432no—
206C2×C8C22×D4312yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—432no—
210C4⋊C4—862no—
211C4⋊C4—862no—
212C4⋊C4—861no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—861no—
216C22⋊C4—861no—
217C22⋊C4—862no—
218C22⋊C4—861no—
219C22⋊C4—861no—
220C22⋊C4—861no—
221C22⋊C4—861no—
222C42—431no—
223C42—431no—
224C42—431no—
225C42—862no—
226C42C22×D4311yescharacteristic
227C23—21no—
228C23—431no—
229C23—861no—
230C23—1722no—
231C23—1722no—
232C23—1722no—
233Q8—22no—
234Q8—22no—
235Q8—22no—
236Q8—862no—
237Q8—1722no—
238Q8—1722no—
239D4—22no—
240D4—862no—
241D4—1722no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—431no—
245C2×C4—431no—
246C2×C4—431no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—861no—
251C2×C4—1721no—
252C2×C4—1722no—
253C2×C4D4×D4311yescharacteristic
254C2×C4D4×D4311yescharacteristic
255C2×C4C23×D4311yescharacteristic
256C8—22no—
257C8—862no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—432no—
262C22—861no—
263C22—861no—
264C22—3444no—
265C22—1721no—
266C22—1721no—
267C22—1721no—
268C22C2×D4×D4311yescharacteristic
269C4—21no—
270C4—21no—
271C4—41no—
272C4—42no—
273C4—861no—
274C4—861no—
275C4—861no—
276C4—1722no—
277C4—1721no—
278C4#1306337012yes—
279C2—81no—
280C2—862no—
281C2—3441no—
282C2#1458346211yescharacteristic
283C2#137×D4311yescharacteristic
284C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#497C2
socleC22×C43C22×D4
hypercenter#497D43
hypocenterC43#3215
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583291C2semidirect
4. #14583259C2semidirect
5. #14583258C2semidirect
6. #14583123C2semidirect
7. #14583119C2semidirect
8. #14583053C2semidirect
10. #14582954C2semidirect
11. C43×#497C2semidirect
14. C2×#10621885C22semidirect
16. #13063325C22semidirect
25. Q8×Dic43C22semidirect
31. Dic43⋊C8C22semidirect
32. #13063250C22semidirect
33. #13063249C22semidirect
37. #13063236C22semidirect
38. C2×Q16×C43C22semidirect
40. C4⋊Q8×C43C22semidirect
42. #97×C43C22semidirect
146. #497D43semidirect
154. C43#3215semidirect
158. C2×Q16C2×D43semidirect
162. C4⋊Q8C2×D43semidirect
185. #97C2×D43semidirect