Finite Group Databasebeta

← #21433733

Subgroups — #21433733

Order 7552.

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×D59C211yesmaximal, characteristic, complemented
2C2×#14273735C211yesmaximal, characteristic, complemented
3#16837975C211yesmaximal, characteristic, complemented
4#16837968C211yesmaximal, characteristic
5#16837649C211yesmaximal, characteristic, complemented
6#16837648C211yesmaximal, characteristic, complemented
7#16837645C211yesmaximal, characteristic, complemented
8#16837634C211yesmaximal, characteristic, complemented
9#16837633C211yesmaximal, characteristic, complemented
10#16837630C211yesmaximal, characteristic, complemented
11#16837629C211yesmaximal, characteristic, complemented
12#16837439C211yesmaximal, characteristic, complemented
13#16837409C211yesmaximal, characteristic, complemented
14#16837405C211yesmaximal, characteristic, complemented
15C59×#468C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19C2×#11745660C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745671C2211yescharacteristic
22SD16×D59—24no—
23#14273735—24no—
24C2×#11745659C2211yescharacteristic
25C2×#11745659C2211yescharacteristic, complemented
26C22×C59⋊C8C2211yescharacteristic, complemented
27C2×C8×D59C2211yescharacteristic
28C2×C8×D59C2211yescharacteristic, complemented
29#14273726—21no—
30#14273723—21no—
31#14273713—21no—
32#14273713—21no—
33#14273712—21no—
34#14273709—21no—
35#14273707C2211yescharacteristic, complemented
36#14273706C2211yescharacteristic, complemented
37#14273703C2211yescharacteristic, complemented
38#14273702C2211yescharacteristic
39#14273701C2211yescharacteristic
40#14273698C2211yescharacteristic
41#14273697—21no—
42#14273695—21no—
43#14273685C2211yescharacteristic
44#14273685C2211yescharacteristic
45#14273661C2211yescharacteristic, complemented
46#14273658C2211yescharacteristic, complemented
47#14273658C2211yescharacteristic, complemented
48#14273652C2211yescharacteristic, complemented
49#14273651C2211yescharacteristic, complemented
50#14273650C2211yescharacteristic, complemented
51#14273649C2211yescharacteristic
52#14273648C2211yescharacteristic
53#14273647C2211yescharacteristic
54C2×SD16×C59C2211yescharacteristic
55C2×M16×C59C2211yescharacteristic, complemented
56C22⋊Q8×C59C2211yescharacteristic, complemented
57#121×C59C2211yescharacteristic
58#107×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59—21no—
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59D411yescharacteristic
70C2×C22⋊D59D411yescharacteristic
71Q8×D59—22no—
72Q8×D59—22no—
73D4×D59—22no—
74D4×D59—22no—
75#11745685—22no—
76#11745685—22no—
77C2×D236—21no—
78C2×D236D411yescharacteristic
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59C2311yescharacteristic
82C2×C4×D59C2311yescharacteristic
83C2×Dic118—21no—
84C2×Dic118D411yescharacteristic
85C2×Dic118C2311yescharacteristic
86SD16×C59—22no—
87M16×C59—22no—
88C2×C8×C59C2311yescharacteristic
89C2×C8×C59C2311yescharacteristic
90C4⋊C4×C59—21no—
91C4⋊C4×C59C2311yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97#11745671—22no—
98#11745670—22no—
99(C2×D59)⋊C4—21no—
100(C2×D59)⋊C4—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105C4⋊Dic59—21no—
106C4⋊Dic59C2311yescharacteristic
107C4⋊Dic59C2311yescharacteristic
108Dic59⋊C4—21no—
109Dic59⋊C4—21no—
110C4×Dic59—21no—
111C4×Dic59—21no—
112C2×C59⋊C8—22no—
113C2×C59⋊C8C2311yescharacteristic
114C2×C59⋊C8C2311yescharacteristic
115#11745660—22no—
116#11745659—22no—
117#11745659—22no—
118C8×D59—22no—
119C8×D59D414yescomplemented
120C23×C59—21no—
121C23×C59C2×D411yescharacteristic
122C22×D59—21no—
123C22×D59—42no—
124C22×D59—81no—
125C22×D59—81no—
126C22×D59C2×D411yescharacteristic
127C22×D59C2×D411yescharacteristic
128Q8×C59—21no—
129Q8×C59—21no—
130D4×C59—21no—
131D4×C59—21no—
132D4×C59—81no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—22no—
141C22⋊D59—22no—
142C22⋊D59—42no—
143C22⋊D59—81no—
144C22⋊D59—81no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59C2×D411yescharacteristic
149C2×Dic59C2×D411yescharacteristic
150D236—22no—
151D236—21no—
152D236—21no—
153D236—81no—
154C4×D59—21no—
155C4×D59—21no—
156C4×D59—42no—
157C4×D59C2×D412yes—
158C4×D59#4112yes—
159Dic118—22no—
160Dic118—21no—
161Dic118—21no—
162Dic118—42no—
163C8×C59—21no—
164C8×C59C2×D412yes—
165C59⋊C8—21no—
166C59⋊C8C2×D412yes—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59C22×D411yescharacteristic
174C2×D59—21no—
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—84no—
183C2×D59#12112yes—
184C4×C59—21no—
185C4×C59—41no—
186C4×C59—41no—
187C4×C59—41no—
188C4×C59C22×D411yescharacteristic
189C4×C59C2×#4111yescharacteristic
190Dic59—21no—
191Dic59—41no—
192Dic59—41no—
193Dic59—41no—
194Dic59#12112yes—
195#3057—591nomaximal, Sylow
196C2×C59—41no—
197C2×C59—81no—
198C2×C59C2×#12111yescharacteristic
199C2×C59#57711yescharacteristic
200C2×C59#57711yescharacteristic
201D59—22no—
202D59—41no—
203D59—81no—
204C22×SD16—591no—
205C2×#131—591no—
206#536—591no—
207#535—591no—
208#468—591no—
209#468—591no—
210#468—591no—
211#468D5911yescharacteristic, complemented
212#465—591no—
213#465—591no—
214#465—591no—
215#465—591no—
216#427—591no—
217#419—591no—
218#418—591no—
219C59#305711yescharacteristic, complemented, Sylow
220C2×#41—591no—
221C22×Q8—591no—
222C22×D4—591no—
223C2×SD16—591no—
224C2×SD16—591no—
225C2×SD16—591no—
226C2×SD16—1184no—
227C2×SD16C2×D5911yescharacteristic
228#131—1184no—
229C2×M16—591no—
230C2×M16—591no—
231C2×M16C2×D5911yescharacteristic, complemented
232C22×C8—591no—
233C22×C8—591no—
234C22×C8—591no—
235C4⋊Q8—1181no—
236#127—1181no—
237#124—1181no—
238#124—1181no—
239#123—1181no—
240#123—1181no—
241C22⋊Q8—591no—
242C22⋊Q8—591no—
243C22⋊Q8—591no—
244C22⋊Q8C2×D5911yescharacteristic, complemented
245#121—591no—
246#121—591no—
247#121—591no—
248#121C2×D5911yescharacteristic
249#120—1181no—
250#120—1181no—
251#117—591no—
252#117—591no—
253#107—591no—
254#107C2×D5911yescharacteristic, complemented
255#106—591no—
256#106—591no—
257#103—591no—
258#103—591no—
259#103—591no—
260#103C2×D5911yescharacteristic, complemented
261#102—591no—
262#102—591no—
263#102—591no—
264#102C2×D5911yescharacteristic
265C24—1181no—
266#41—1182no—
267#41—1182no—
268C2×Q8—591no—
269C2×Q8—591no—
270C2×Q8—1181no—
271C2×Q8—1182no—
272C2×Q8—1182no—
273C2×Q8C22×D5911yescharacteristic
274C2×D4—21no—
275C2×D4—591no—
276C2×D4—591no—
277C2×D4—591no—
278C2×D4—591no—
279C2×D4—1181no—
280C2×D4—1182no—
281C2×D4—1182no—
282C2×D4—1181no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4C22×D5911yescharacteristic
286C22×C4—591no—
287C22×C4—591no—
288C22×C4—1181no—
289C22×C4C22×D5911yescharacteristic
290SD16—22no—
291SD16—1182no—
292SD16—1182no—
293SD16—1182no—
294M16—22no—
295M16—1182no—
296M16—1182no—
297C2×C8—591no—
298C2×C8—594no—
299C2×C8—591no—
300C2×C8—1182no—
301C2×C8—1182no—
302C2×C8C22×D5911yescharacteristic
303C2×C8C22×D5911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—591no—
306C4⋊C4—591no—
307C4⋊C4—1181no—
308C4⋊C4—1181no—
309C4⋊C4—1181no—
310C4⋊C4C22×D5911yescharacteristic
311C4⋊C4C22×D5911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C22⋊C4—1181no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C42—1181no—
323C42—1181no—
324C23—21no—
325C23—591no—
326C23—591no—
327C23—1181no—
328C23—4721no—
329C23—4721no—
330C23—2362no—
331C23D4×D5911yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—1182no—
335Q8—1181no—
336Q8—1181no—
337Q8—2362no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—1182no—
342D4—1182no—
343D4—1182no—
344D4—1181no—
345D4—1181no—
346D4—4721no—
347D4—4721no—
348D4—4721no—
349D4—2362no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—591no—
356C2×C4—592no—
357C2×C4—592no—
358C2×C4—591no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—2362no—
365C2×C4D4×D5911yescharacteristic
366C2×C4C23×D5911yescharacteristic
367C8—21no—
368C8—592no—
369C8—1181no—
370C8D4×D5912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—592no—
378C22—1181no—
379C22—1181no—
380C22—1181no—
381C22—1181no—
382C22—1181no—
383C22—4724no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22C2×D4×D5911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—592no—
393C4—1181no—
394C4—2361no—
395C4—2361no—
396C4—2361no—
397C4C2×D4×D5911yescharacteristic
398C4#41×D5911yescharacteristic
399C2—41no—
400C2—81no—
401C2—1182no—
402C2—4721no—
403C2—2361no—
404C2#121×D5911yescharacteristic
405C2#1683821111yescharacteristic
406C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#468C2
socleC22×C59C22×D4
hypercenter#468D59
hypocenterC59#3057
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D59C2semidirect
2. C2×#14273735C2semidirect
3. #16837975C2semidirect
5. #16837649C2semidirect
6. #16837648C2semidirect
7. #16837645C2semidirect
8. #16837634C2semidirect
9. #16837633C2semidirect
10. #16837630C2semidirect
11. #16837629C2semidirect
12. #16837439C2semidirect
13. #16837409C2semidirect
14. #16837405C2semidirect
15. C59×#468C2semidirect
25. C2×#11745659C22semidirect
26. C22×C59⋊C8C22semidirect
28. C2×C8×D59C22semidirect
35. #14273707C22semidirect
36. #14273706C22semidirect
37. #14273703C22semidirect
45. #14273661C22semidirect
46. #14273658C22semidirect
47. #14273658C22semidirect
48. #14273652C22semidirect
49. #14273651C22semidirect
50. #14273650C22semidirect
55. C2×M16×C59C22semidirect
56. C22⋊Q8×C59C22semidirect
58. #107×C59C22semidirect
59. #103×C59C22semidirect
119. C8×D59D4semidirect
211. #468D59semidirect
219. C59#3057semidirect
231. C2×M16C2×D59semidirect
244. C22⋊Q8C2×D59semidirect
254. #107C2×D59semidirect
260. #103C2×D59semidirect