Finite Group Databasebeta

← #19145390

Subgroups — #19145390

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#14583412C211yesmaximal, characteristic, complemented
2#14583411C211yesmaximal, characteristic, complemented
3#14583242C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583223C211yesmaximal, characteristic, complemented
6#14583139C211yesmaximal, characteristic, complemented
7#14583136C211yesmaximal, characteristic, complemented
8#14583131C211yesmaximal, characteristic, complemented
9#14583129C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583059C211yesmaximal, characteristic, complemented
12#14583047C211yesmaximal, characteristic, complemented
13#14583046C211yesmaximal, characteristic, complemented
14C22⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#485C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C2×#10621885C2211yescharacteristic, complemented
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621884C2211yescharacteristic, complemented
22C2×D344C2211yescharacteristic, complemented
23C2×C8×D43C2211yescharacteristic
24C2×C8×D43C2211yescharacteristic
25#13063310—21no—
26#13063309—21no—
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic
29#13063301C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic
33#13063299C2211yescharacteristic
34#13063295—21no—
35#13063295—21no—
36C4×D172—21no—
37C4×D172—21no—
38#13063287—21no—
39(C22⋊D43)⋊C4—21no—
40#13063283C2211yescharacteristic
41#13063258C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic
59C23×D43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43D411yescharacteristic
65#10621902—41no—
66#10621902—41no—
67#10621898—41no—
68#10621898—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172C2311yescharacteristic
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—41no—
78C2×C4×D43—41no—
79C2×C4×D43D411yescharacteristic
80C2×C4×D43D411yescharacteristic
81C2×C4×D43C2311yescharacteristic
82C2×C4×D43C2311yescharacteristic
83C2×Dic86C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43—21no—
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C42×C43—21no—
93#10621885—41no—
94#10621884—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110D344—41no—
111#10621873—41no—
112C8×D43—41no—
113C8×D43—41no—
114C23×C43C2×D411yescharacteristic
115C22×D43—22no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43C2×D411yescharacteristic
121C22×D43C2×D411yescharacteristic
122Q8×C43—21no—
123Q8×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—42no—
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—41no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—42no—
144D172—42no—
145D172—42no—
146D172—42no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—41no—
152C4×D43—41no—
153C4×D43—42no—
154C4×D43—42no—
155Dic86—21no—
156Dic86—21no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—44no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43#13512yes—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43H(5,𝔽2)11yescharacteristic
184C4×C43H(5,𝔽2)11yescharacteristic
185Dic43—21no—
186Dic43—21no—
187Dic43—41no—
188Dic43—41no—
189#3191—431nomaximal, Sylow
190C2×C43—41no—
191C2×C43#53411yescharacteristic
192C2×C43C2×#13511yescharacteristic
193C2×C43#57511yescharacteristic
194D43—22no—
195D43—41no—
196D43—81no—
197D43—81no—
198#525—431no—
199#525—431no—
200#485—431no—
201#485D4311yescharacteristic, complemented
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×#41—431no—
216C23×C4—431no—
217C2×Q16—431no—
218C2×SD16—431no—
219C2×SD16—431no—
220C2×D8—431no—
221C22×C8—431no—
222C22×C8—431no—
223#123—861no—
224#123—861no—
225C22⋊Q8—431no—
226C22⋊Q8—431no—
227C22⋊Q8—431no—
228C22⋊Q8C2×D4311yescharacteristic
229#121—431no—
230#121—431no—
231#121—431no—
232#121—431no—
233#120—861no—
234#120—861no—
235C4×D4—861no—
236C4×D4—861no—
237C4×D4—861no—
238C4×D4—861no—
239#117—431no—
240#117C2×D4311yescharacteristic
241#107—431no—
242#107C2×D4311yescharacteristic, complemented
243#106—431no—
244#106C2×D4311yescharacteristic, complemented
245#103—431no—
246#103—431no—
247#103C2×D4311yescharacteristic, complemented
248#103C2×D4311yescharacteristic, complemented
249#102—431no—
250#102—431no—
251#102—431no—
252#102—431no—
253C22⋊C8—431no—
254C22⋊C8—431no—
255C22⋊C8—431no—
256C22⋊C8C2×D4311yescharacteristic
257C24—431no—
258#41—1721no—
259#41—1721no—
260#41—1721no—
261#41—1721no—
262C2×Q8—431no—
263C2×Q8C22×D4311yescharacteristic
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—1721no—
280C22×C4—1721no—
281C22×C4C22×D4311yescharacteristic
282Q16—1721no—
283SD16—1721no—
284SD16—1721no—
285D8—1721no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8C22×D4311yescharacteristic
291C2×C8C22×D4311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—431no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4C22×D4311yescharacteristic
298C4⋊C4C22×D4311yescharacteristic
299C4⋊C4C22×D4311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C42—21no—
311C42—861no—
312C23—431no—
313C23—431no—
314C23—862no—
315C23—861no—
316C23—861no—
317C23—1721no—
318C23—1721no—
319C23D4×D4311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—861no—
323Q8—861no—
324D4—861no—
325D4—861no—
326D4—861no—
327D4—861no—
328D4—1722no—
329D4—1722no—
330D4—1722no—
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—431no—
341C2×C4—431no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4D4×D4311yescharacteristic
354C2×C4C23×D4311yescharacteristic
355C8—21no—
356C8—21no—
357C8—861no—
358C8—861no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—432no—
363C22—861no—
364C22—861no—
365C22—861no—
366C22—861no—
367C22—861no—
368C22—1724no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22—1721no—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—861no—
382C4—861no—
383C4—1721no—
384C4—1721no—
385C4#1306337111yescharacteristic
386C4#1306337111yescharacteristic
387C2—41no—
388C2—862no—
389C2—3441no—
390C2—3441no—
391C2—1721no—
392C2#1458346011yescharacteristic
393C2#135×D4311yescharacteristic
394C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#485C2
socleC22×C43C22×D4
hypercenter#485D43
hypocenterC43#3191
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14583412C2semidirect
2. #14583411C2semidirect
3. #14583242C2semidirect
4. #14583225C2semidirect
5. #14583223C2semidirect
6. #14583139C2semidirect
7. #14583136C2semidirect
8. #14583131C2semidirect
9. #14583129C2semidirect
10. #14583064C2semidirect
11. #14583059C2semidirect
12. #14583047C2semidirect
13. #14583046C2semidirect
14. C22⋊C8×D43C2semidirect
15. C43×#485C2semidirect
19. C2×#10621885C22semidirect
20. C2×#10621873C22semidirect
21. C2×#10621884C22semidirect
22. C2×D344C22semidirect
41. #13063258C22semidirect
42. #13063256C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
45. #13063247C22semidirect
46. #13063245C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #103×C43C22semidirect
57. #103×C43C22semidirect
201. #485D43semidirect
213. C43#3191semidirect
242. #107C2×D43semidirect
244. #106C2×D43semidirect
247. #103C2×D43semidirect
248. #103C2×D43semidirect