Finite Group Databasebeta

← #19145663

Subgroups — #19145663

Order 5504.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583509C211yesmaximal, characteristic, complemented
2#14583466C211yesmaximal, characteristic
3#14583290C211yesmaximal, characteristic, complemented
4#14583270C211yesmaximal, characteristic, complemented
5#14583262C211yesmaximal, characteristic, complemented
6#14583252C211yesmaximal, characteristic, complemented
7#14583120C211yesmaximal, characteristic, complemented
8#14583119C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583097C211yesmaximal, characteristic, complemented
11#14583063C211yesmaximal, characteristic, complemented
12#14583059C211yesmaximal, characteristic, complemented
13#14583050C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Dic172C2211yescharacteristic, complemented
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic, complemented
20C2×#10621883C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621884C2211yescharacteristic, complemented
23#13063323C2211yescharacteristic, complemented
24#13063321C2211yescharacteristic
25#13063321C2211yescharacteristic
26#13063318—21no—
27#13063318—21no—
28#13063316—21no—
29#13063316C2211yescharacteristic, complemented
30#13063315—21no—
31#13063312C2211yescharacteristic
32#13063312C2211yescharacteristic
33#13063304C2211yescharacteristic
34#13063296—21no—
35#13063296—21no—
36#13063294—21no—
37#13063294—21no—
38Q8×Dic43C2211yescharacteristic, complemented
39#13063290C2211yescharacteristic, complemented
40#13063284C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72#10621898—41no—
73#10621898—41no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×Dic86C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78SD16×C43—41no—
79SD16×C43—41no—
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43D411yescharacteristic
91C22⋊Dic43D411yescharacteristic
92#10621885—41no—
93#10621884—41no—
94#10621883—41no—
95#10621883—41no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43D411yescharacteristic
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112Dic172—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—42no—
117C23×C43—81no—
118C23×C43—81no—
119C23×C43C2×D411yescharacteristic
120C22×D43—21no—
121Q8×C43—21no—
122Q8×C43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—42no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—81no—
136C22⋊D43—81no—
137C22⋊D43—81no—
138C22⋊D43—81no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145C2×Dic43C2×D411yescharacteristic
146D172—21no—
147D172—21no—
148C4×D43—42no—
149Dic86—21no—
150Dic86—21no—
151Dic86—21no—
152Dic86—21no—
153C8×C43—21no—
154C8×C43—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—84no—
167C22×C43C22×D411yescharacteristic
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43H(5,𝔽2)11yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—21no—
177Dic43—21no—
178Dic43—21no—
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3222—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—81no—
186C2×C43—81no—
187C2×C43#53511yescharacteristic
188C2×C43#57711yescharacteristic
189C2×C43#57711yescharacteristic
190D43—81no—
191#541—431no—
192#535—431no—
193#497—431no—
194#492—431no—
195#490—431no—
196#488—431no—
197#464—431no—
198#464—431no—
199#460—431no—
200#460—431no—
201#452—431no—
202#452—431no—
203#450—431no—
204#450D4311yescharacteristic, complemented
205#433—431no—
206C43#322211yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C22×D4C2×D4311yescharacteristic
209C2×Q16—431no—
210C2×Q16—431no—
211C2×SD16—431no—
212C2×SD16—431no—
213C2×SD16—431no—
214C2×SD16—431no—
215C2×SD16C2×D4311yescharacteristic
216C2×SD16C2×D4311yescharacteristic
217C4⋊Q8—431no—
218#127—431no—
219#127—431no—
220#126—861no—
221#126—861no—
222#125—431no—
223#125—861no—
224#125—861no—
225#124—431no—
226#124—431no—
227C22⋊Q8—431no—
228C22⋊Q8C2×D4311yescharacteristic
229#121—861no—
230#121—861no—
231#120—861no—
232#120—861no—
233C4×Q8—431no—
234C4×Q8—431no—
235#117—431no—
236C4⋊C8—431no—
237C4⋊C8—431no—
238#103—431no—
239#103—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102C2×D4311yescharacteristic
245#102C2×D4311yescharacteristic
246C22⋊C8—431no—
247C22⋊C8C2×D4311yescharacteristic
248#97—431no—
249C4×C8—431no—
250C24—21no—
251#41—1721no—
252#41—1721no—
253C2×Q8—431no—
254C2×Q8—431no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—431no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4C22×D4311yescharacteristic
266C2×D4C22×D4311yescharacteristic
267C22×C4—861no—
268C22×C4C22×D4311yescharacteristic
269Q16—1721no—
270Q16—1721no—
271SD16—41no—
272SD16—41no—
273SD16—1721no—
274SD16—1721no—
275SD16—1721no—
276SD16—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4C22×D4311yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—431no—
295C22⋊C4—431no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C42—431no—
302C42—431no—
303C42—861no—
304C42—861no—
305C23—21no—
306C23—21no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—861no—
311C23D4×D4311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—861no—
315Q8—861no—
316Q8—861no—
317Q8—861no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—861no—
324D4—861no—
325D4—3441no—
326D4—3441no—
327D4—3441no—
328D4—3441no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—431no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—1722no—
342C2×C4D4×D4311yescharacteristic
343C2×C4C23×D4311yescharacteristic
344C8—21no—
345C8—21no—
346C8—861no—
347C8—861no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—84no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—861no—
366C4—861no—
367C4—861no—
368C4—861no—
369C4—1721no—
370C4—1721no—
371C4—1721no—
372C4#1306337011yescharacteristic
373C4#1306337011yescharacteristic
374C2—41no—
375C2—81no—
376C2—81no—
377C2—3441no—
378C2#1458346411yescharacteristic
379C2#1458370511yescharacteristic
380C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3222
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583509C2semidirect
3. #14583290C2semidirect
4. #14583270C2semidirect
5. #14583262C2semidirect
6. #14583252C2semidirect
7. #14583120C2semidirect
8. #14583119C2semidirect
9. #14583098C2semidirect
10. #14583097C2semidirect
11. #14583063C2semidirect
12. #14583059C2semidirect
13. #14583050C2semidirect
14. #14582957C2semidirect
15. C43×#450C2semidirect
17. C2×Dic172C22semidirect
18. C2×#10621885C22semidirect
19. C2×#10621873C22semidirect
22. C2×#10621884C22semidirect
23. #13063323C22semidirect
29. #13063316C22semidirect
38. Q8×Dic43C22semidirect
39. #13063290C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
45. #13063247C22semidirect
48. #13063245C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
204. #450D43semidirect
206. C43#3222semidirect