Finite Group Databasebeta

← #28746299

Subgroups — #28746299

Order 15104.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436499C211yesmaximal, characteristic, complemented
2#21426372C211yesmaximal, characteristic, complemented
3#21426287C211yesmaximal, characteristic, complemented
4#21426284C211yesmaximal, characteristic, complemented
5#21426276C211yesmaximal, characteristic, complemented
6#21426274C211yesmaximal, characteristic, complemented
7#21426253C211yesmaximal, characteristic, complemented
8#21426250C211yesmaximal, characteristic, complemented
9#21426197C211yesmaximal, characteristic, complemented
10#21426197C211yesmaximal, characteristic, complemented
11C4×#14273668C211yesmaximal, characteristic, complemented
12#21425928C211yesmaximal, characteristic, complemented
13#21425885C211yesmaximal, characteristic, complemented
14#21425882C211yesmaximal, characteristic, complemented
15C59×#3339C211yesmaximal, characteristic, complemented
16#16838098—21no—
17C2×#14273668C2211yescharacteristic
18C2×#14273667C2211yescharacteristic
19C2×#14273667C2211yescharacteristic
20#16837804C2211yescharacteristic
21#16837727—21no—
22#16837721—21no—
23#16837703—21no—
24#16837638C2211yescharacteristic
25#16837638C2211yescharacteristic
26C4×D472C2211yescharacteristic
27#16837440C2211yescharacteristic
28C2×#14273661C2211yescharacteristic
29#16837229C2211yescharacteristic
30#16837229C2211yescharacteristic
31#16837229C2211yescharacteristic
32#16837229C2211yescharacteristic
33#16837227C2211yescharacteristic
34#16837227C2211yescharacteristic
35#16837227C2211yescharacteristic
36#16837227C2211yescharacteristic
37#16837227C2211yescharacteristic
38C4⋊(C59⋊C16)C2211yescharacteristic
39#16837203C2211yescharacteristic
40#16837203C2211yescharacteristic
41#16837203C2211yescharacteristic
42#16837202C2211yescharacteristic
43#16837202C2211yescharacteristic
44#16837202C2211yescharacteristic
45C22⋊(C59⋊C16)C2211yescharacteristic
46C22⋊(C59⋊C16)C2211yescharacteristic
47C4×C59⋊C16C2211yescharacteristic
48C59×#553—21no—
49C59×#499C2211yescharacteristic
50C59×#482—21no—
51C59×#481—21no—
52C59×#478—21no—
53C59×#466C2211yescharacteristic
54C59×#466C2211yescharacteristic
55C4×D8×C59C2211yescharacteristic
56C8×D4×C59C2211yescharacteristic
57C59×#427C2211yescharacteristic
58C2×#107×C59C2211yescharacteristic
59C2×D472C2311yescharacteristic
60#14273722—41no—
61#14273719—21no—
62#14273709—41no—
63#14273701—21no—
64#14273701—21no—
65#14273699—41no—
66C4×D236—21no—
67(C22⋊D59)⋊C4—41no—
68#14273686—21no—
69C2×C4⋊Dic59—21no—
70#14273668—22no—
71#14273667—22no—
72#14273667—22no—
73C2×C59⋊C16C2311yescharacteristic
74C2×C59⋊C16C2311yescharacteristic
75C2×C59⋊C16C2311yescharacteristic
76C2×C59⋊C16C2311yescharacteristic
77#14273661—21no—
78#14273661C2311yescharacteristic
79#14273661C2311yescharacteristic
80#14273661C2311yescharacteristic
81#14273659—21no—
82#14273659—21no—
83#14273649—21no—
84#14273649—21no—
85#14273649—21no—
86C2×D8×C59C2311yescharacteristic
87C22×C8×C59C2311yescharacteristic
88C22×C8×C59C2311yescharacteristic
89#126×C59—41no—
90#125×C59—21no—
91#123×C59—41no—
92#121×C59—21no—
93#121×C59—21no—
94#121×C59—41no—
95C4×D4×C59—21no—
96C4×D4×C59—41no—
97C4×D4×C59D411yescharacteristic
98#117×C59—21no—
99C2×C4⋊C4×C59—21no—
100#107×C59—21no—
101#107×C59C2311yescharacteristic
102#107×C59C2311yescharacteristic
103#107×C59C2311yescharacteristic
104#106×C59—21no—
105#106×C59—21no—
106C4⋊C8×C59D411yescharacteristic
107#102×C59—21no—
108#102×C59—21no—
109#102×C59—21no—
110C22⋊C8×C59D411yescharacteristic
111C22⋊C8×C59D411yescharacteristic
112C4×C8×C59C2311yescharacteristic
113C2×D4×C59—21no—
114C2×D4×C59—41no—
115C2×D4×C59—41no—
116C2×D4×C59D811yescharacteristic
117C22×C4×C59—41no—
118C22×C4×C59—41no—
119C22×C4×C59C2×D411yescharacteristic
120C22×C4×C59C2×D411yescharacteristic
121C2×C22⋊D59—41no—
122C2×C22⋊D59—41no—
123C22×Dic59—41no—
124C2×D236—21no—
125C2×C4×D59—41no—
126D8×C59—21no—
127D8×C59—21no—
128C2×C8×C59—21no—
129C2×C8×C59—21no—
130C2×C8×C59—21no—
131C2×C8×C59—21no—
132C2×C8×C59C2×D411yescharacteristic
133C2×C8×C59C2×D411yescharacteristic
134C2×C8×C59C2×D411yescharacteristic
135C2×C8×C59C2411yescharacteristic
136C4⋊C4×C59—21no—
137C4⋊C4×C59—21no—
138C4⋊C4×C59—21no—
139C4⋊C4×C59—41no—
140C4⋊C4×C59—41no—
141C4⋊C4×C59—41no—
142C4⋊C4×C59D811yescharacteristic
143C22⋊C4×C59—41no—
144C22⋊C4×C59—41no—
145C22⋊C4×C59—41no—
146C22⋊C4×C59—41no—
147C22⋊C4×C59D811yescharacteristic
148C22⋊C4×C59D811yescharacteristic
149C42×C59—41no—
150C42×C59C2×D411yescharacteristic
151C22⋊Dic59—41no—
152(C2×D59)⋊C4—41no—
153(C2×D59)⋊C4—41no—
154(C2×D59)⋊C4—41no—
155C4⋊Dic59—21no—
156C4⋊Dic59—21no—
157C4⋊Dic59—21no—
158C4⋊Dic59—41no—
159Dic59⋊C4—41no—
160Dic59⋊C4—41no—
161C4×Dic59—41no—
162D472—21no—
163D472—21no—
164C59⋊C16—21no—
165C59⋊C16—21no—
166C59⋊C16—21no—
167C59⋊C16#4112yes—
168C23×C59—41no—
169C23×C59C2×D811yescharacteristic
170C23×C59C2×D811yescharacteristic
171C22×D59—41no—
172D4×C59—41no—
173D4×C59—41no—
174D4×C59—41no—
175D4×C59—82no—
176D4×C59—161no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—21no—
181C2×C4×C59—41no—
182C2×C4×C59—41no—
183C2×C4×C59—41no—
184C2×C4×C59—161no—
185C2×C4×C59—161no—
186C2×C4×C59C2×D811yescharacteristic
187C2×C4×C59C2×D811yescharacteristic
188C2×C4×C59C2×D811yescharacteristic
189C2×C4×C59C2×D811yescharacteristic
190C2×C4×C59C22×D411yescharacteristic
191C22⋊D59—82no—
192C22⋊D59—161no—
193C2×Dic59—41no—
194C2×Dic59—41no—
195C2×Dic59—41no—
196C2×Dic59—161no—
197D236—41no—
198D236—41no—
199C4×D59—161no—
200C8×C59—21no—
201C8×C59—21no—
202C8×C59—21no—
203C8×C59C2×#4111yescharacteristic
204C8×C592−1+411yescharacteristic
205#33922—591nomaximal, Sylow
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—21no—
209C22×C59—21no—
210C22×C59—21no—
211C22×C59—21no—
212C22×C59—81no—
213C22×C59—81no—
214C22×C59—81no—
215C22×C59C22×D811yescharacteristic
216C2×D59—81no—
217C2×D59—81no—
218C2×D59—81no—
219C4×C59—21no—
220C4×C59—21no—
221C4×C59—21no—
222C4×C59—21no—
223C4×C59—81no—
224C4×C59—81no—
225C4×C59—81no—
226C4×C59#54711yescharacteristic
227C4×C59#57811yescharacteristic
228Dic59—81no—
229Dic59—81no—
230Dic59—81no—
231#3339—591no—
232#3339D5911yescharacteristic, complemented
233#2253—591no—
234#2234—591no—
235#2234—591no—
236#2232—591no—
237#2232—591no—
238#2228—591no—
239#2228—591no—
240#2218—591no—
241#2218—591no—
242C4×D16—591no—
243#2169—591no—
244#2159—591no—
245#2159—591no—
246C2×C59—41no—
247C2×C59—41no—
248C2×C59—161no—
249C2×C59#333411yescharacteristic
250C2×C59#341411yescharacteristic
251C2×C59#341511yescharacteristic
252D59—161no—
253#553—21no—
254#553—1181no—
255C2×D16—591no—
256C2×M32—591no—
257C2×M32—591no—
258#499—591no—
259#499C2×D5911yescharacteristic
260#482—21no—
261#482—1181no—
262#481—21no—
263#481—1181no—
264#478—21no—
265#478—1181no—
266#466—591no—
267#466—591no—
268#466C2×D5911yescharacteristic
269#466C2×D5911yescharacteristic
270C4×D8—591no—
271C4×D8C2×D5911yescharacteristic
272C8×D4C2×D5911yescharacteristic
273#427—591no—
274#427C2×D5911yescharacteristic
275C2×#107—591no—
276C2×#107C2×D5911yescharacteristic
277#367—591no—
278#367—591no—
279#367—591no—
280#367—591no—
281#366—591no—
282#366—591no—
283#366—591no—
284#366—591no—
285#366—591no—
286C4⋊C16—591no—
287#357—591no—
288#357—591no—
289#357—591no—
290#357—591no—
291#357—591no—
292#357—591no—
293C22⋊C16—591no—
294C22⋊C16—591no—
295C4×C16—591no—
296C59#3392211yescharacteristic, complemented, Sylow
297C2×D8—591no—
298C2×D8C22×D5911yescharacteristic
299C22×C8C22×D5911yescharacteristic
300C22×C8C22×D5911yescharacteristic
301#126—41no—
302#126—2361no—
303#125—21no—
304#125—1181no—
305#123—41no—
306#123—2361no—
307#121—21no—
308#121—21no—
309#121—41no—
310#121—1181no—
311#121—1181no—
312#121—2361no—
313C4×D4—21no—
314C4×D4—41no—
315C4×D4—1181no—
316C4×D4—2361no—
317C4×D4C22⋊D5911yescharacteristic
318#117—21no—
319#117—1181no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—1181no—
322D16—1182no—
323M32—1182no—
324M32—1182no—
325C2×C16—591no—
326C2×C16—591no—
327C2×C16—591no—
328C2×C16—591no—
329#107—21no—
330#107—591no—
331#107—591no—
332#107—591no—
333#107—1181no—
334#107C22×D5911yescharacteristic
335#107C22×D5911yescharacteristic
336#107C22×D5911yescharacteristic
337#106—21no—
338#106—21no—
339#106—1181no—
340#106—1181no—
341C4⋊C8C22⋊D5911yescharacteristic
342#102—21no—
343#102—21no—
344#102—21no—
345#102—1181no—
346#102—1181no—
347#102—1181no—
348C22⋊C8C22⋊D5911yescharacteristic
349C22⋊C8C22⋊D5911yescharacteristic
350C4×C8C22×D5911yescharacteristic
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—1181no—
355C2×D4—2361no—
356C2×D4—2361no—
357C2×D4#1174566911yescharacteristic
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—2361no—
361C22×C4—2361no—
362C22×C4C2×C22⋊D5911yescharacteristic
363C22×C4C2×C22⋊D5911yescharacteristic
364D8—21no—
365D8—21no—
366D8—1181no—
367D8—1181no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×C22⋊D5911yescharacteristic
373C2×C8C2×C22⋊D5911yescharacteristic
374C2×C8C2×C22⋊D5911yescharacteristic
375C2×C8C23×D5911yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—1181no—
383C4⋊C4—1181no—
384C4⋊C4—1181no—
385C4⋊C4—2361no—
386C4⋊C4—2361no—
387C4⋊C4—2361no—
388C4⋊C4#1174566911yescharacteristic
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—2361no—
394C22⋊C4—2361no—
395C22⋊C4—2361no—
396C22⋊C4—2361no—
397C22⋊C4#1174566911yescharacteristic
398C22⋊C4#1174566911yescharacteristic
399C42—41no—
400C42—2361no—
401C42C2×C22⋊D5911yescharacteristic
402C16—592no—
403C16—1181no—
404C16—1181no—
405C16—1181no—
406C23—41no—
407C23—2361no—
408C23C2×#1174566911yescharacteristic
409C23C2×#1174566911yescharacteristic
410D4—41no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—161no—
415D4—9441no—
416D4—4722no—
417D4—2361no—
418D4—2361no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—9441no—
429C2×C4—9441no—
430C2×C4—2361no—
431C2×C4—2361no—
432C2×C4—2361no—
433C2×C4C2×#1174566911yescharacteristic
434C2×C4C2×#1174566911yescharacteristic
435C2×C4C2×#1174566911yescharacteristic
436C2×C4C2×#1174566911yescharacteristic
437C2×C4C22×C22⋊D5911yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8#41×D5911yescharacteristic
442C8#1427377411yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—4721no—
453C22—4721no—
454C22—4721no—
455C22C22×#1174566911yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—4721no—
464C4—4721no—
465C4—4721no—
466C4#1683805111yescharacteristic
467C4#1683821711yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—9441no—
472C2#2143643911yescharacteristic
473C2#2143723011yescharacteristic
474C2#2143723511yescharacteristic
subgroupG/H
centerC22C22×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#3339C2
socleC22×C59C22×D8
hypercenter#3339D59
hypocenterC59#33922
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #21436499C2semidirect
2. #21426372C2semidirect
3. #21426287C2semidirect
4. #21426284C2semidirect
5. #21426276C2semidirect
6. #21426274C2semidirect
7. #21426253C2semidirect
8. #21426250C2semidirect
9. #21426197C2semidirect
10. #21426197C2semidirect
11. C4×#14273668C2semidirect
12. #21425928C2semidirect
13. #21425885C2semidirect
14. #21425882C2semidirect
15. C59×#3339C2semidirect
232. #3339D59semidirect
296. C59#33922semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214364992
#214263722
#214262872
#214262842
#214262762
#214262742
#214262532
#214262502
#214261972
C4×#142736682
#214259282
#214258852
#214258822
C59×#33392
#3392259