Finite Group Databasebeta

← #19145378

Subgroups — #19145378

Order 5504.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583410C211yesmaximal, characteristic
2C2×#13063304C211yesmaximal, characteristic, complemented
3#14583241C212yesmaximal, complemented
4#14583230C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583140C212yesmaximal, complemented
7#14583128C212yesmaximal, complemented
8#14583063C212yesmaximal, complemented
9#14583057C211yesmaximal, characteristic, complemented
10#14583040C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C43C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14C2×Dic172C2212yescomplemented
15C2×#10621873C2212yescomplemented
16#13063308—21no—
17#13063304—21no—
18#13063304—21no—
19#13063304C2211yescharacteristic
20#13063304C2212yes—
21#13063304C2212yes—
22#13063304C2211yescharacteristic
23#13063299C2211yescharacteristic
24#13063299C2211yescharacteristic
25#13063294—21no—
26C4×C22⋊D43—21no—
27C4×C22⋊D43—21no—
28#13063284C2211yescharacteristic
29C2×C4⋊Dic43C2211yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32#13063259C2212yescomplemented
33#13063257C2212yescomplemented
34#13063250C2212yescomplemented
35#13063250C2212yescomplemented
36#13063250C2212yescomplemented
37#13063247C2212yescomplemented
38C23×C4×C43C2211yescharacteristic
39C22×C8×C43C2212yes—
40C22⋊C8×C43C2211yescharacteristic
41C22⋊C8×C43C2211yescharacteristic
42C22⋊C8×C43C2212yes—
43C24×C43D411yescharacteristic
44C22×C4×C43—42no—
45C22×C4×C43D411yescharacteristic
46C22×C4×C43D411yescharacteristic
47C22×C4×C43D411yescharacteristic
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—21no—
52C2×C22⋊D43—21no—
53C2×C22⋊D43—21no—
54C22×Dic43—21no—
55C22×Dic43—21no—
56#10621898—42no—
57C2×D172C2311yescharacteristic
58C2×C4×D43—21no—
59C2×Dic86—21no—
60C2×Dic86—42no—
61C2×Dic86C2312yes—
62C2×Dic86C2311yescharacteristic
63C2×C8×C43—42no—
64C2×C8×C43C2312yes—
65C2×C8×C43C2312yes—
66C22⋊Dic43—22no—
67C22⋊Dic43—22no—
68C22⋊Dic43—21no—
69C22⋊Dic43—21no—
70C22⋊Dic43—21no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73C4⋊Dic43—21no—
74C4⋊Dic43C2312yes—
75C4⋊Dic43C2311yescharacteristic
76C4⋊Dic43C2311yescharacteristic
77Dic43⋊C4—22no—
78Dic43⋊C4—22no—
79Dic43⋊C4—21no—
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82Dic172—42no—
83#10621873—42no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—41no—
87C23×C43C2×D411yescharacteristic
88C23×C43C2×D411yescharacteristic
89C23×C43C2×D411yescharacteristic
90C22×D43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2411yescharacteristic
101C22⋊D43—42no—
102C22⋊D43—42no—
103C22⋊D43—42no—
104C2×Dic43—21no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111D172—22no—
112C4×D43—42no—
113Dic86—22no—
114Dic86—22no—
115Dic86—22no—
116Dic86—42no—
117C8×C43—22no—
118C8×C43—22no—
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—44no—
127C22×C43#13512yes—
128C22×C43#13712yes—
129C22×C43C22×D411yescharacteristic
130C2×D43—41no—
131C2×D43—41no—
132C2×D43—41no—
133C4×C43—21no—
134C4×C43—21no—
135C4×C43—21no—
136C4×C43H(5,𝔽2)12yes—
137Dic43—42no—
138Dic43—41no—
139Dic43—42no—
140Dic43—41no—
141Dic43—41no—
142#3190—431nomaximal, Sylow
143C2×C43—22no—
144C2×C43—22no—
145C2×C43—41no—
146C2×C43#53411yescharacteristic
147C2×C43C2×#13511yescharacteristic
148C2×C43C2×#13711yescharacteristic
149D43—81no—
150#525—431no—
151C2×C22⋊Q8—431no—
152#485—432no—
153#483—431no—
154#480—431no—
155#467—432no—
156#465—432no—
157#452—432no—
158#451—431no—
159#448—431no—
160C2×C22⋊C8D4311yescharacteristic, complemented
161C43#319011yescharacteristic, complemented, Sylow
162C2×#41—431no—
163C22×Q8—431no—
164C23×C4C2×D4311yescharacteristic
165C2×Q16—432no—
166C2×SD16—432no—
167C22×C8C2×D4312yes—
168#123—861no—
169C22⋊Q8—432no—
170C22⋊Q8—432no—
171C22⋊Q8—431no—
172C22⋊Q8—431no—
173C22⋊Q8—861no—
174C22⋊Q8—861no—
175#121—431no—
176#121—431no—
177#120—861no—
178C4×D4—861no—
179C4×D4—861no—
180#117—431no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4—861no—
183C2×C22⋊C4—861no—
184#107—432no—
185#106—432no—
186#103—432no—
187#103—432no—
188#103—432no—
189#102—432no—
190C22⋊C8C2×D4311yescharacteristic
191C22⋊C8C2×D4311yescharacteristic
192C22⋊C8C2×D4312yes—
193C24D17211yescharacteristic
194#41—1722no—
195C2×Q8—432no—
196C2×Q8—431no—
197C2×Q8—861no—
198C2×Q8—1722no—
199C2×D4—431no—
200C2×D4—861no—
201C2×D4—861no—
202C2×D4—861no—
203C22×C4—42no—
204C22×C4—861no—
205C22×C4—861no—
206C22×C4—861no—
207C22×C4D17211yescharacteristic
208C22×C4D17211yescharacteristic
209C22×C4D17211yescharacteristic
210C22×C4C22×D4311yescharacteristic
211C22×C4C22×D4311yescharacteristic
212C22×C4C22×D4311yescharacteristic
213Q16—1722no—
214SD16—1722no—
215C2×C8—42no—
216C2×C8C22×D4312yes—
217C2×C8C22×D4312yes—
218C4⋊C4—432no—
219C4⋊C4—431no—
220C4⋊C4—431no—
221C4⋊C4—861no—
222C4⋊C4—862no—
223C4⋊C4—862no—
224C4⋊C4—861no—
225C4⋊C4—861no—
226C22⋊C4—862no—
227C22⋊C4—862no—
228C22⋊C4—861no—
229C22⋊C4—861no—
230C22⋊C4—861no—
231C22⋊C4—861no—
232C22⋊C4—861no—
233C42—861no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23—861no—
238C23C2×D17211yescharacteristic
239C23C2×D17211yescharacteristic
240C23C2×D17211yescharacteristic
241Q8—862no—
242Q8—862no—
243Q8—862no—
244Q8—1722no—
245D4—862no—
246D4—1722no—
247D4—1722no—
248D4—1722no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—861no—
256C2×C4—861no—
257C2×C4—862no—
258C2×C4—861no—
259C2×C4—862no—
260C2×C4—1722no—
261C2×C4—1722no—
262C2×C4—1722no—
263C2×C4C2×D17211yescharacteristic
264C2×C4C2×D17211yescharacteristic
265C2×C4C2×D17211yescharacteristic
266C2×C4C23×D4311yescharacteristic
267C8—22no—
268C8—22no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—1721no—
278C22—1721no—
279C22—1721no—
280C22#1306334712yes—
281C22#1306335812yes—
282C22C22×D17211yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—1722no—
287C4—1721no—
288C4—1721no—
289C4—1721no—
290C4—1722no—
291C4#1306337012yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—3441no—
296C2#1458346111yescharacteristic
297C2C2×#1306334711yescharacteristic
298C2C2×#1306335811yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×C22⋊C8×C43C2
socleC22×C43C22×D4
hypercenterC2×C22⋊C8D43
hypocenterC43#3190
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13063304C2semidirect
3. #14583241C2semidirect
4. #14583230C2semidirect
5. #14583213C2semidirect
6. #14583140C2semidirect
7. #14583128C2semidirect
8. #14583063C2semidirect
9. #14583057C2semidirect
10. #14583040C2semidirect
11. C2×C22⋊C8×C43C2semidirect
14. C2×Dic172C22semidirect
15. C2×#10621873C22semidirect
32. #13063259C22semidirect
33. #13063257C22semidirect
34. #13063250C22semidirect
35. #13063250C22semidirect
36. #13063250C22semidirect
37. #13063247C22semidirect
160. C2×C22⋊C8D43semidirect
161. C43#3190semidirect