Finite Group Databasebeta

← #19145383

Subgroups — #19145383

Order 5504.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583410C211yesmaximal, characteristic, complemented
2#14583240C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583138C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583130C211yesmaximal, characteristic, complemented
9#14583126C211yesmaximal, characteristic, complemented
10#14583061C211yesmaximal, characteristic, complemented
11#14583059C211yesmaximal, characteristic, complemented
12#14583044C211yesmaximal, characteristic, complemented
13#14583042C211yesmaximal, characteristic, complemented
14C2×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#525C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic, complemented
18C2×#10621883C2211yescharacteristic, complemented
19C2×#10621884C2211yescharacteristic, complemented
20C2×#10621882C2211yescharacteristic, complemented
21C22×C43⋊C8C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063308—21no—
24#13063304C2211yescharacteristic
25#13063304C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063299C2211yescharacteristic
28#13063294—21no—
29C4×C22⋊D43—21no—
30C4×C22⋊D43—21no—
31#13063284C2211yescharacteristic
32#13063258C2211yescharacteristic, complemented
33#13063258C2211yescharacteristic, complemented
34#13063256C2211yescharacteristic, complemented
35#13063256C2211yescharacteristic, complemented
36#13063249C2211yescharacteristic, complemented
37#13063249C2211yescharacteristic, complemented
38#13063248C2211yescharacteristic, complemented
39#13063248C2211yescharacteristic, complemented
40#13063246C2211yescharacteristic, complemented
41#13063246C2211yescharacteristic, complemented
42#13063245C2211yescharacteristic, complemented
43#13063245C2211yescharacteristic, complemented
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C23×C4×C43C2211yescharacteristic
50#123×C43—21no—
51C22⋊Q8×C43C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic
55#120×C43—21no—
56C4×D4×C43—21no—
57C4×D4×C43—21no—
58#117×C43C2211yescharacteristic
59C24×C43D411yescharacteristic
60#41×C43—41no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43D411yescharacteristic
71C22×C4×C43D411yescharacteristic
72C22×C4×C43D411yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79#10621898—41no—
80#10621898—41no—
81C2×D172C2311yescharacteristic
82C2×C4×D43—21no—
83C2×Dic86C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C42×C43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97#10621885—41no—
98#10621884—41no—
99#10621883—41no—
100#10621882—41no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114C23×C43—22no—
115C23×C43—21no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43C2×D411yescharacteristic
119C23×C43C2×D411yescharacteristic
120C23×C43C2×D411yescharacteristic
121C22×D43—21no—
122Q8×C43—21no—
123Q8×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—42no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43C2×D411yescharacteristic
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2411yescharacteristic
146C22⋊D43—42no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152D172—21no—
153D172—21no—
154C4×D43—42no—
155Dic86—21no—
156Dic86—21no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—44no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43#13512yes—
174C22×C43C22×D411yescharacteristic
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43H(5,𝔽2)11yescharacteristic
185C4×C43H(5,𝔽2)11yescharacteristic
186Dic43—41no—
187Dic43—41no—
188Dic43—41no—
189#3191—431nomaximal, Sylow
190C2×C43—22no—
191C2×C43—41no—
192C2×C43—41no—
193C2×C43—81no—
194C2×C43#53411yescharacteristic
195C2×C43C2×#13511yescharacteristic
196C2×C43#57511yescharacteristic
197D43—81no—
198#525—431no—
199#525D4311yescharacteristic, complemented
200#485—431no—
201#485—431no—
202#482—431no—
203#482—431no—
204#467—431no—
205#466—431no—
206#465—431no—
207#465—431no—
208#452—431no—
209#452—431no—
210#449—431no—
211#449—431no—
212C2×C22⋊C8—431no—
213C43#319111yescharacteristic, complemented, Sylow
214C2×#41—431no—
215C2×#41C2×D4311yescharacteristic
216C23×C4C2×D4311yescharacteristic
217C2×Q16—431no—
218C2×SD16—431no—
219C2×SD16—431no—
220C2×D8—431no—
221C22×C8—431no—
222C22×C8—431no—
223#123—21no—
224#123—861no—
225C22⋊Q8—431no—
226C22⋊Q8—431no—
227C22⋊Q8C2×D4311yescharacteristic
228C22⋊Q8C2×D4311yescharacteristic
229#121—431no—
230#121—431no—
231#121C2×D4311yescharacteristic
232#121C2×D4311yescharacteristic
233#120—21no—
234#120—861no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—861no—
238C4×D4—861no—
239#117—431no—
240#117C2×D4311yescharacteristic
241#107—431no—
242#107—431no—
243#106—431no—
244#106—431no—
245#103—431no—
246#103—431no—
247#103—431no—
248#103—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252#102—431no—
253C22⋊C8—431no—
254C22⋊C8—431no—
255C22⋊C8—431no—
256C22⋊C8—431no—
257C24C22⋊D4311yescharacteristic
258#41—41no—
259#41—41no—
260#41—1721no—
261#41—1721no—
262C2×Q8—431no—
263C2×Q8C22×D4311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—431no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4C22×D4311yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—861no—
276C22×C4C22⋊D4311yescharacteristic
277C22×C4C22⋊D4311yescharacteristic
278C22×C4C22⋊D4311yescharacteristic
279C22×C4C22×D4311yescharacteristic
280C22×C4C22×D4311yescharacteristic
281C22×C4C22×D4311yescharacteristic
282Q16—1721no—
283SD16—1721no—
284SD16—1721no—
285D8—1721no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—1721no—
291C2×C8—1721no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—431no—
295C4⋊C4—431no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4C22×D4311yescharacteristic
299C4⋊C4C22×D4311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C42—21no—
311C42—861no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—861no—
317C23C2×C22⋊D4311yescharacteristic
318C23C2×C22⋊D4311yescharacteristic
319C23C2×C22⋊D4311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—861no—
323Q8—861no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—861no—
330D4—861no—
331D4—1722no—
332D4—1722no—
333D4—1722no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—1722no—
351C2×C4C2×C22⋊D4311yescharacteristic
352C2×C4C2×C22⋊D4311yescharacteristic
353C2×C4C2×C22⋊D4311yescharacteristic
354C2×C4C23×D4311yescharacteristic
355C8—861no—
356C8—861no—
357C8—861no—
358C8—861no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22#1306334512yes—
375C22C22×C22⋊D4311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—1721no—
383C4—1721no—
384C4—1721no—
385C4#1306337011yescharacteristic
386C4#1306337011yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—3441no—
392C2#1458345811yescharacteristic
393C2C2×#1306334511yescharacteristic
394C2#1458369711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#525C2
socleC22×C43C22×D4
hypercenter#525D43
hypocenterC43#3191
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14583410C2semidirect
2. #14583240C2semidirect
3. #14583237C2semidirect
4. #14583223C2semidirect
5. #14583220C2semidirect
6. #14583138C2semidirect
7. #14583133C2semidirect
8. #14583130C2semidirect
9. #14583126C2semidirect
10. #14583061C2semidirect
11. #14583059C2semidirect
12. #14583044C2semidirect
13. #14583042C2semidirect
14. C2×C22⋊(C43⋊C8)C2semidirect
15. C43×#525C2semidirect
17. C2×#10621885C22semidirect
18. C2×#10621883C22semidirect
19. C2×#10621884C22semidirect
20. C2×#10621882C22semidirect
32. #13063258C22semidirect
33. #13063258C22semidirect
34. #13063256C22semidirect
35. #13063256C22semidirect
36. #13063249C22semidirect
37. #13063249C22semidirect
38. #13063248C22semidirect
39. #13063248C22semidirect
40. #13063246C22semidirect
41. #13063246C22semidirect
42. #13063245C22semidirect
43. #13063245C22semidirect
199. #525D43semidirect
213. C43#3191semidirect