Finite Group Databasebeta

← #19146309

Subgroups — #19146309

Order 5504.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063347C211yesmaximal, characteristic, complemented
2C2×SD16×D43C211yesmaximal, characteristic, complemented
3#14583559C211yesmaximal, characteristic, complemented
4#14583546C211yesmaximal, characteristic, complemented
5#14583280C211yesmaximal, characteristic, complemented
6#14583129C211yesmaximal, characteristic, complemented
7#14583120C211yesmaximal, characteristic, complemented
8#14583117C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583042C211yesmaximal, characteristic, complemented
12#14583034C211yesmaximal, characteristic, complemented
13#14582986C211yesmaximal, characteristic, complemented
14C8×C22⋊D43C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic, complemented
18C2×Q8×D43C2211yescharacteristic
19C2×D4×D43C2211yescharacteristic
20#13063347—24no—
21C2×Dic172C2211yescharacteristic, complemented
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic
24C2×#10621873C2211yescharacteristic, complemented
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27SD16×D43—24no—
28C2×D344C2211yescharacteristic
29C2×#10621882C2211yescharacteristic
30C2×C8×D43C2211yescharacteristic
31#13063314C2211yescharacteristic, complemented
32#13063312C2211yescharacteristic
33#13063311—21no—
34#13063307—21no—
35#13063305C2211yescharacteristic
36#13063303—21no—
37#13063300C2211yescharacteristic
38#13063298—21no—
39#13063296—21no—
40#13063293—21no—
41#13063290C2211yescharacteristic, complemented
42#13063287—21no—
43#13063287C2211yescharacteristic
44C4×C22⋊D43C2211yescharacteristic
45C22⋊C4×D43—21no—
46Dic43⋊C8C2211yescharacteristic, complemented
47#13063248C2211yescharacteristic, complemented
48#13063248C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic
50#13063245C2211yescharacteristic, complemented
51C22⋊(C43⋊C8)C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic
53C8×Dic43C2211yescharacteristic, complemented
54C2×SD16×C43C2211yescharacteristic
55C22×C8×C43C2211yescharacteristic, complemented
56C22⋊Q8×C43C2211yescharacteristic, complemented
57#121×C43C2211yescharacteristic
58#106×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60#102×C43C2211yescharacteristic
61C23×D43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43D411yescharacteristic
70Q8×D43—22no—
71Q8×D43—41no—
72D4×D43—22no—
73D4×D43—41no—
74#10621898—22no—
75#10621898—22no—
76#10621898—41no—
77#10621898—41no—
78C2×D172—21no—
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43C2311yescharacteristic
86C2×Dic86—21no—
87C2×Dic86C2311yescharacteristic
88C2×Dic86C2311yescharacteristic
89SD16×C43—22no—
90C2×C8×C43—22no—
91C2×C8×C43C2311yescharacteristic
92C2×C8×C43C2311yescharacteristic
93C4⋊C4×C43—21no—
94C4⋊C4×C43C2311yescharacteristic
95C4⋊C4×C43C2311yescharacteristic
96C22⋊C4×C43—21no—
97C22⋊C4×C43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43D411yescharacteristic
101#10621885—41no—
102#10621884—22no—
103#10621883—22no—
104#10621882—41no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111C4⋊Dic43—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4D411yescharacteristic
114C4×Dic43—21no—
115C4×Dic43C2311yescharacteristic
116C2×C43⋊C8C2311yescharacteristic
117C2×C43⋊C8C2311yescharacteristic
118Dic172—22no—
119D344—22no—
120#10621873—22no—
121#10621873D414yescomplemented
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131Q8×C43—21no—
132Q8×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—81no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43C2×D411yescharacteristic
142C2×C4×C43C2411yescharacteristic
143C22⋊D43—22no—
144C22⋊D43—42no—
145C22⋊D43—42no—
146C22⋊D43—42no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43C2×D411yescharacteristic
150C2×Dic43C2×D411yescharacteristic
151C2×Dic43C2×D411yescharacteristic
152D172—21no—
153D172—21no—
154D172—21no—
155D172—42no—
156D172C2×D412yes—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—81no—
163Dic86—21no—
164Dic86—21no—
165Dic86—21no—
166Dic86—42no—
167Dic86C2×D412yes—
168C8×C43—21no—
169C8×C43C2×D412yes—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43C22×D411yescharacteristic
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—22no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—84no—
188C2×D43#13512yescomplemented
189C4×C43—21no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43C22×D411yescharacteristic
194C4×C43H(5,𝔽2)11yescharacteristic
195Dic43—22no—
196Dic43—21no—
197Dic43—21no—
198Dic43—21no—
199Dic43—41no—
200#3282—431nomaximal, Sylow
201C2×C43—41no—
202C2×C43—81no—
203C2×C43D4211yescharacteristic
204C2×C43C2×#13511yescharacteristic
205C2×C43#57711yescharacteristic
206D43—22no—
207D43—42no—
208D43—81no—
209C2×#135—431no—
210C22×SD16—431no—
211#548—431no—
212#546—431no—
213#495—431no—
214#465—431no—
215#465D4311yescharacteristic, complemented
216#464—431no—
217#463—431no—
218#452—431no—
219#451—431no—
220#449—431no—
221#447—431no—
222C4×SD16—431no—
223C8×D4—431no—
224C43#328211yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41—431no—
227C22×Q8—431no—
228C22×D4—431no—
229#135—864no—
230C2×Q16—431no—
231C2×Q16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—864no—
237C2×SD16C2×D4311yescharacteristic
238C2×D8—431no—
239C2×D8—431no—
240C22×C8—431no—
241C22×C8C2×D4311yescharacteristic, complemented
242#124—431no—
243#124—431no—
244#124—861no—
245#123—861no—
246C22⋊Q8—431no—
247C22⋊Q8—861no—
248C22⋊Q8C2×D4311yescharacteristic, complemented
249#121—431no—
250#121—861no—
251#121—861no—
252#121C2×D4311yescharacteristic
253#120—861no—
254C4×Q8—431no—
255C4×D4—431no—
256C4×D4—431no—
257C4×D4—861no—
258C2×C22⋊C4—861no—
259#106C2×D4311yescharacteristic, complemented
260C4⋊C8—431no—
261#103—431no—
262#103—431no—
263#103C2×D4311yescharacteristic, complemented
264#102—431no—
265#102—431no—
266#102C2×D4311yescharacteristic
267C22⋊C8—431no—
268C22⋊C8—431no—
269C4×C8—431no—
270C24—861no—
271#41—862no—
272#41—862no—
273#41—1721no—
274#41—1721no—
275C2×Q8—431no—
276C2×Q8—431no—
277C2×Q8—861no—
278C2×Q8—862no—
279C2×Q8—1721no—
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—431no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—862no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—1721no—
291C2×D4C22×D4311yescharacteristic
292C22×C4—431no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298Q16—862no—
299Q16—1721no—
300SD16—22no—
301SD16—434no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305D8—862no—
306D8—1721no—
307C2×C8—22no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—862no—
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—431no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4C22×D4311yescharacteristic
318C4⋊C4C22×D4311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—431no—
322C22⋊C4—431no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C42—431no—
331C42—861no—
332C23—21no—
333C23—431no—
334C23—861no—
335C23—861no—
336C23—3441no—
337C23—1722no—
338C23—1722no—
339C23D4×D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—432no—
343Q8—861no—
344Q8—861no—
345Q8—861no—
346Q8—1722no—
347D4—21no—
348D4—21no—
349D4—81no—
350D4—432no—
351D4—862no—
352D4—861no—
353D4—861no—
354D4—861no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
358D4—1722no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—431no—
365C2×C4—431no—
366C2×C4—431no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—3441no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4D4×D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—21no—
378C8—861no—
379C8—861no—
380C8D4×D4312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—432no—
388C22—861no—
389C22—861no—
390C22—862no—
391C22—3444no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22—1721no—
397C22C2×D4×D4311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—861no—
403C4—861no—
404C4—861no—
405C4—862no—
406C4—1721no—
407C4C2×D4×D4311yescharacteristic
408C4#1306337111yescharacteristic
409C2—41no—
410C2—81no—
411C2—862no—
412C2—3441no—
413C2—1722no—
414C2#1458353311yescharacteristic
415C2#135×D4311yescharacteristic
416C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3282
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#13063347C2semidirect
2. C2×SD16×D43C2semidirect
3. #14583559C2semidirect
4. #14583546C2semidirect
5. #14583280C2semidirect
6. #14583129C2semidirect
7. #14583120C2semidirect
8. #14583117C2semidirect
9. #14583059C2semidirect
10. #14583056C2semidirect
11. #14583042C2semidirect
12. #14583034C2semidirect
13. #14582986C2semidirect
14. C8×C22⋊D43C2semidirect
15. C43×#465C2semidirect
17. C2×#10621898C22semidirect
21. C2×Dic172C22semidirect
22. C2×#10621885C22semidirect
24. C2×#10621873C22semidirect
31. #13063314C22semidirect
41. #13063290C22semidirect
46. Dic43⋊C8C22semidirect
47. #13063248C22semidirect
48. #13063248C22semidirect
50. #13063245C22semidirect
51. C22⋊(C43⋊C8)C22semidirect
53. C8×Dic43C22semidirect
55. C22×C8×C43C22semidirect
56. C22⋊Q8×C43C22semidirect
58. #106×C43C22semidirect
59. #103×C43C22semidirect
121. #10621873D4semidirect
188. C2×D43#135semidirect
215. #465D43semidirect
224. C43#3282semidirect
241. C22×C8C2×D43semidirect
248. C22⋊Q8C2×D43semidirect
259. #106C2×D43semidirect
263. #103C2×D43semidirect