Finite Group Databasebeta

← #19145562

Subgroups — #19145562

Order 5504.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583433C211yesmaximal, characteristic, complemented
2C2×#13063313C211yesmaximal, characteristic, complemented
3#14583283C212yesmaximal, complemented
4#14583254C212yesmaximal, complemented
5#14583122C212yesmaximal, complemented
6#14583115C212yesmaximal, complemented
7#14583057C211yesmaximal, characteristic, complemented
8#14583052C211yesmaximal, characteristic, complemented
9#14583040C211yesmaximal, characteristic, complemented
10#14583035C211yesmaximal, characteristic
11C43×#431C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C2×Dic172C2212yescomplemented
15C2×#10621873C2212yes—
16C2×#10621873C2212yescomplemented
17C2×D344C2212yes—
18#13063319—21no—
19#13063317C2211yescharacteristic, complemented
20#13063313—21no—
21#13063313—21no—
22#13063313C2212yes—
23#13063313C2212yes—
24#13063313C2211yescharacteristic, complemented
25#13063308—21no—
26#13063304C2211yescharacteristic
27#13063299C2211yescharacteristic
28C4×Dic86C2211yescharacteristic, complemented
29C4×D172C2211yescharacteristic, complemented
30C4×C22⋊D43—21no—
31#13063282—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34#13063250C2212yescomplemented
35#13063250C2212yescomplemented
36#13063247C2212yes—
37#13063247C2212yes—
38C2×C42×C43C2211yescharacteristic
39C4⋊C8×C43C2212yescomplemented
40C22⋊C8×C43C2211yescharacteristic
41C22⋊C8×C43C2211yescharacteristic
42C4×C8×C43C2212yescomplemented
43C23×D43—21no—
44C22×C4×C43D411yescharacteristic
45C22×C4×C43D411yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48C22×Dic43—21no—
49C2×D172—21no—
50C2×D172—42no—
51C2×D172C2312yes—
52C2×D172C2311yescharacteristic
53C2×C4×D43—21no—
54C2×Dic86—21no—
55C2×Dic86—42no—
56C2×Dic86C2312yes—
57C2×Dic86C2311yescharacteristic
58C2×C8×C43C2312yes—
59C2×C8×C43C2312yes—
60C42×C43D411yescharacteristic
61C42×C43D411yescharacteristic
62C42×C43C2311yescharacteristic
63C42×C43C2311yescharacteristic
64C22⋊Dic43—21no—
65(C2×D43)⋊C4—22no—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—22no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73C4⋊Dic43C2311yescharacteristic
74C4⋊Dic43C2311yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—21no—
77Dic43⋊C4—21no—
78Dic43⋊C4—21no—
79C4×Dic43—21no—
80Dic172—42no—
81D344—42no—
82#10621873—42no—
83#10621873—42no—
84C23×C43C2×D411yescharacteristic
85C22×D43—21no—
86C22×D43—22no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—42no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—41no—
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2411yescharacteristic
99C22⋊D43—42no—
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—42no—
105D172—22no—
106D172—22no—
107D172—22no—
108D172—42no—
109C4×D43—42no—
110Dic86—22no—
111Dic86—22no—
112Dic86—22no—
113Dic86—42no—
114C8×C43—22no—
115C8×C43—22no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43#13512yes—
119C22×C43C22×D411yescharacteristic
120C2×D43—42no—
121C2×D43—41no—
122C2×D43—42no—
123C2×D43—41no—
124C2×D43—42no—
125C2×D43—41no—
126C2×D43—84no—
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—21no—
132C4×C43H(5,𝔽2)12yes—
133Dic43—42no—
134Dic43—41no—
135Dic43—41no—
136Dic43—41no—
137#3211—431nomaximal, Sylow
138C2×C43—22no—
139C2×C43#53511yescharacteristic
140C2×C43C2×#13511yescharacteristic
141C2×C43#57511yescharacteristic
142D43—81no—
143D43—82no—
144#529—431no—
145C2×#124—431no—
146#495—432no—
147#488—432no—
148#464—432no—
149#463—432no—
150#451—431no—
151#450—431no—
152#448—431no—
153#447—431no—
154#431D4311yescharacteristic, complemented
155C43#321111yescharacteristic, complemented, Sylow
156C22×Q8—431no—
157C22×D4—431no—
158C2×Q16—432no—
159C2×SD16—432no—
160C2×SD16—432no—
161C2×D8—432no—
162#126—861no—
163#125—431no—
164#124—432no—
165#124—432no—
166#124—431no—
167#124—861no—
168#124—861no—
169#123—861no—
170C22⋊Q8—431no—
171#121—431no—
172C4×Q8—431no—
173C4×D4—431no—
174C4×D4—861no—
175#117—861no—
176C2×C22⋊C4—861no—
177C2×C22⋊C4—861no—
178C2×C42C2×D4311yescharacteristic
179C4⋊C8C2×D4312yescomplemented
180#103—432no—
181#103—432no—
182#102—432no—
183#102—432no—
184C22⋊C8C2×D4311yescharacteristic
185C22⋊C8C2×D4311yescharacteristic
186C4×C8C2×D4312yescomplemented
187C24—861no—
188C2×Q8—432no—
189C2×Q8—431no—
190C2×Q8—861no—
191C2×Q8—1722no—
192C2×D4—432no—
193C2×D4—431no—
194C2×D4—861no—
195C2×D4—861no—
196C2×D4—1722no—
197C22×C4—861no—
198C22×C4—861no—
199C22×C4D17211yescharacteristic
200C22×C4D17211yescharacteristic
201C22×C4C22×D4311yescharacteristic
202Q16—1722no—
203SD16—1722no—
204SD16—1722no—
205D8—1722no—
206C2×C8C22×D4312yes—
207C2×C8C22×D4312yes—
208C4⋊C4—431no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—861no—
212C4⋊C4—861no—
213C4⋊C4—861no—
214C22⋊C4—861no—
215C22⋊C4—862no—
216C22⋊C4—862no—
217C22⋊C4—862no—
218C22⋊C4—862no—
219C22⋊C4—861no—
220C22⋊C4—861no—
221C22⋊C4—861no—
222C22⋊C4—861no—
223C42—861no—
224C42D17211yescharacteristic
225C42D17211yescharacteristic
226C42C22×D4311yescharacteristic
227C42C22×D4311yescharacteristic
228C23—861no—
229C23—862no—
230C23—1722no—
231C23—1722no—
232C23—1722no—
233C23C2×D17211yescharacteristic
234Q8—862no—
235Q8—862no—
236Q8—862no—
237Q8—1722no—
238D4—862no—
239D4—862no—
240D4—862no—
241D4—1722no—
242D4—1722no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—862no—
249C2×C4—861no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4C2×D17211yescharacteristic
253C2×C4C2×D17211yescharacteristic
254C2×C4C2×D17211yescharacteristic
255C2×C4C2×D17211yescharacteristic
256C2×C4C2×D17211yescharacteristic
257C2×C4C23×D4311yescharacteristic
258C8—22no—
259C8—22no—
260C22—21no—
261C22—21no—
262C22—3444no—
263C22—1721no—
264C22—1722no—
265C22—1721no—
266C22—1722no—
267C22—1722no—
268C22—1721no—
269C22#1306334712yes—
270C22C22×D17211yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—1721no—
277C4—1721no—
278C4—1722no—
279C4—1721no—
280C4#1306337112yes—
281C2—22no—
282C2—3442no—
283C2—3441no—
284C2#1458346811yescharacteristic
285C2C2×#1306334711yescharacteristic
286C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#431C2
socleC22×C43C22×D4
hypercenter#431D43
hypocenterC43#3211
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #14583433C2semidirect
2. C2×#13063313C2semidirect
3. #14583283C2semidirect
4. #14583254C2semidirect
5. #14583122C2semidirect
6. #14583115C2semidirect
7. #14583057C2semidirect
8. #14583052C2semidirect
9. #14583040C2semidirect
11. C43×#431C2semidirect
14. C2×Dic172C22semidirect
16. C2×#10621873C22semidirect
19. #13063317C22semidirect
24. #13063313C22semidirect
28. C4×Dic86C22semidirect
29. C4×D172C22semidirect
34. #13063250C22semidirect
35. #13063250C22semidirect
39. C4⋊C8×C43C22semidirect
42. C4×C8×C43C22semidirect
154. #431D43semidirect
155. C43#3211semidirect
179. C4⋊C8C2×D43semidirect
186. C4×C8C2×D43semidirect