Finite Group Databasebeta

← #19144232

Subgroups — #19144232

Order 5504.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D43C211yesmaximal, characteristic, complemented
2C2×#13063333C211yesmaximal, characteristic, complemented
3#14583472C211yesmaximal, characteristic, complemented
4#14583465C211yesmaximal, characteristic
5#14583146C211yesmaximal, characteristic, complemented
6#14583145C211yesmaximal, characteristic, complemented
7#14583142C211yesmaximal, characteristic, complemented
8#14583131C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583127C211yesmaximal, characteristic, complemented
11#14583126C211yesmaximal, characteristic, complemented
12#14582936C211yesmaximal, characteristic, complemented
13#14582906C211yesmaximal, characteristic, complemented
14#14582902C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22SD16×D43—24no—
23#13063333—24no—
24C2×#10621872C2211yescharacteristic
25C2×#10621872C2211yescharacteristic, complemented
26C22×C43⋊C8C2211yescharacteristic, complemented
27C2×C8×D43C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic, complemented
29#13063324—21no—
30#13063321—21no—
31#13063311—21no—
32#13063311—21no—
33#13063310—21no—
34#13063307—21no—
35#13063305C2211yescharacteristic, complemented
36#13063304C2211yescharacteristic, complemented
37#13063301C2211yescharacteristic, complemented
38#13063300C2211yescharacteristic
39#13063299C2211yescharacteristic
40#13063296C2211yescharacteristic
41#13063295—21no—
42#13063293—21no—
43#13063283C2211yescharacteristic
44#13063283C2211yescharacteristic
45#13063259C2211yescharacteristic, complemented
46#13063256C2211yescharacteristic, complemented
47#13063256C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063249C2211yescharacteristic, complemented
50#13063248C2211yescharacteristic, complemented
51#13063247C2211yescharacteristic
52#13063246C2211yescharacteristic
53#13063245C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C2×M16×C43C2211yescharacteristic, complemented
56C22⋊Q8×C43C2211yescharacteristic, complemented
57#121×C43C2211yescharacteristic
58#107×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
70C2×C22⋊D43D411yescharacteristic
71Q8×D43—22no—
72Q8×D43—22no—
73D4×D43—22no—
74D4×D43—22no—
75#10621898—22no—
76#10621898—22no—
77C2×D172—21no—
78C2×D172D411yescharacteristic
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×C4×D43C2311yescharacteristic
83C2×Dic86—21no—
84C2×Dic86D411yescharacteristic
85C2×Dic86C2311yescharacteristic
86SD16×C43—22no—
87M16×C43—22no—
88C2×C8×C43C2311yescharacteristic
89C2×C8×C43C2311yescharacteristic
90C4⋊C4×C43—21no—
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97#10621884—22no—
98#10621883—22no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43C2311yescharacteristic
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8C2311yescharacteristic
114C2×C43⋊C8C2311yescharacteristic
115#10621873—22no—
116#10621872—22no—
117#10621872—22no—
118C8×D43—22no—
119C8×D43D414yescomplemented
120C23×C43—21no—
121C23×C43C2×D411yescharacteristic
122C22×D43—21no—
123C22×D43—42no—
124C22×D43—81no—
125C22×D43—81no—
126C22×D43C2×D411yescharacteristic
127C22×D43C2×D411yescharacteristic
128Q8×C43—21no—
129Q8×C43—21no—
130D4×C43—21no—
131D4×C43—21no—
132D4×C43—81no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2411yescharacteristic
140C22⋊D43—22no—
141C22⋊D43—22no—
142C22⋊D43—42no—
143C22⋊D43—81no—
144C22⋊D43—81no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43C2×D411yescharacteristic
149C2×Dic43C2×D411yescharacteristic
150D172—22no—
151D172—21no—
152D172—21no—
153D172—81no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—42no—
157C4×D43C2×D412yes—
158C4×D43#4112yes—
159Dic86—22no—
160Dic86—21no—
161Dic86—21no—
162Dic86—42no—
163C8×C43—21no—
164C8×C43C2×D412yes—
165C43⋊C8—21no—
166C43⋊C8C2×D412yes—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43C22×D411yescharacteristic
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—84no—
183C2×D43#12112yes—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43C22×D411yescharacteristic
189C4×C43C2×#4111yescharacteristic
190Dic43—21no—
191Dic43—41no—
192Dic43—41no—
193Dic43—41no—
194Dic43#12112yes—
195#3057—431nomaximal, Sylow
196C2×C43—41no—
197C2×C43—81no—
198C2×C43C2×#12111yescharacteristic
199C2×C43#57711yescharacteristic
200C2×C43#57711yescharacteristic
201D43—22no—
202D43—41no—
203D43—81no—
204C22×SD16—431no—
205C2×#131—431no—
206#536—431no—
207#535—431no—
208#468—431no—
209#468—431no—
210#468—431no—
211#468D4311yescharacteristic, complemented
212#465—431no—
213#465—431no—
214#465—431no—
215#465—431no—
216#427—431no—
217#419—431no—
218#418—431no—
219C43#305711yescharacteristic, complemented, Sylow
220C2×#41—431no—
221C22×Q8—431no—
222C22×D4—431no—
223C2×SD16—431no—
224C2×SD16—431no—
225C2×SD16—431no—
226C2×SD16—864no—
227C2×SD16C2×D4311yescharacteristic
228#131—864no—
229C2×M16—431no—
230C2×M16—431no—
231C2×M16C2×D4311yescharacteristic, complemented
232C22×C8—431no—
233C22×C8—431no—
234C22×C8—431no—
235C4⋊Q8—861no—
236#127—861no—
237#124—861no—
238#124—861no—
239#123—861no—
240#123—861no—
241C22⋊Q8—431no—
242C22⋊Q8—431no—
243C22⋊Q8—431no—
244C22⋊Q8C2×D4311yescharacteristic, complemented
245#121—431no—
246#121—431no—
247#121—431no—
248#121C2×D4311yescharacteristic
249#120—861no—
250#120—861no—
251#117—431no—
252#117—431no—
253#107—431no—
254#107C2×D4311yescharacteristic, complemented
255#106—431no—
256#106—431no—
257#103—431no—
258#103—431no—
259#103—431no—
260#103C2×D4311yescharacteristic, complemented
261#102—431no—
262#102—431no—
263#102—431no—
264#102C2×D4311yescharacteristic
265C24—861no—
266#41—862no—
267#41—862no—
268C2×Q8—431no—
269C2×Q8—431no—
270C2×Q8—861no—
271C2×Q8—862no—
272C2×Q8—862no—
273C2×Q8C22×D4311yescharacteristic
274C2×D4—21no—
275C2×D4—431no—
276C2×D4—431no—
277C2×D4—431no—
278C2×D4—431no—
279C2×D4—861no—
280C2×D4—862no—
281C2×D4—862no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4C22×D4311yescharacteristic
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—861no—
289C22×C4C22×D4311yescharacteristic
290SD16—22no—
291SD16—862no—
292SD16—862no—
293SD16—862no—
294M16—22no—
295M16—862no—
296M16—862no—
297C2×C8—431no—
298C2×C8—434no—
299C2×C8—431no—
300C2×C8—862no—
301C2×C8—862no—
302C2×C8C22×D4311yescharacteristic
303C2×C8C22×D4311yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—431no—
306C4⋊C4—431no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4C22×D4311yescharacteristic
311C4⋊C4C22×D4311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C42—861no—
323C42—861no—
324C23—21no—
325C23—431no—
326C23—431no—
327C23—861no—
328C23—3441no—
329C23—3441no—
330C23—1722no—
331C23D4×D4311yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—862no—
335Q8—861no—
336Q8—861no—
337Q8—1722no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—862no—
342D4—862no—
343D4—862no—
344D4—861no—
345D4—861no—
346D4—3441no—
347D4—3441no—
348D4—3441no—
349D4—1722no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—431no—
356C2×C4—432no—
357C2×C4—432no—
358C2×C4—431no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—1722no—
365C2×C4D4×D4311yescharacteristic
366C2×C4C23×D4311yescharacteristic
367C8—21no—
368C8—432no—
369C8—861no—
370C8D4×D4312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—432no—
378C22—861no—
379C22—861no—
380C22—861no—
381C22—861no—
382C22—861no—
383C22—3444no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C2×D4×D4311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—432no—
393C4—861no—
394C4—1721no—
395C4—1721no—
396C4—1721no—
397C4C2×D4×D4311yescharacteristic
398C4#41×D4311yescharacteristic
399C2—41no—
400C2—81no—
401C2—862no—
402C2—3441no—
403C2—1721no—
404C2#121×D4311yescharacteristic
405C2#1458370811yescharacteristic
406C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3057
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D43C2semidirect
2. C2×#13063333C2semidirect
3. #14583472C2semidirect
5. #14583146C2semidirect
6. #14583145C2semidirect
7. #14583142C2semidirect
8. #14583131C2semidirect
9. #14583130C2semidirect
10. #14583127C2semidirect
11. #14583126C2semidirect
12. #14582936C2semidirect
13. #14582906C2semidirect
14. #14582902C2semidirect
15. C43×#468C2semidirect
25. C2×#10621872C22semidirect
26. C22×C43⋊C8C22semidirect
28. C2×C8×D43C22semidirect
35. #13063305C22semidirect
36. #13063304C22semidirect
37. #13063301C22semidirect
45. #13063259C22semidirect
46. #13063256C22semidirect
47. #13063256C22semidirect
48. #13063250C22semidirect
49. #13063249C22semidirect
50. #13063248C22semidirect
55. C2×M16×C43C22semidirect
56. C22⋊Q8×C43C22semidirect
58. #107×C43C22semidirect
59. #103×C43C22semidirect
119. C8×D43D4semidirect
211. #468D43semidirect
219. C43#3057semidirect
231. C2×M16C2×D43semidirect
244. C22⋊Q8C2×D43semidirect
254. #107C2×D43semidirect
260. #103C2×D43semidirect