Finite Group Databasebeta

← #28744236

Subgroups — #28744236

Order 15104.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434666C211yesmaximal, characteristic, complemented
2#21426372C211yesmaximal, characteristic, complemented
3#21426355C211yesmaximal, characteristic, complemented
4#21426330C211yesmaximal, characteristic, complemented
5#21426327C211yesmaximal, characteristic, complemented
6#21426194C211yesmaximal, characteristic, complemented
7#21426190C211yesmaximal, characteristic, complemented
8#21426185C211yesmaximal, characteristic, complemented
9#21426180C211yesmaximal, characteristic
10C4×#14273673C211yesmaximal, characteristic, complemented
11C4×#14273670C211yesmaximal, characteristic, complemented
12C4×#14273671C211yesmaximal, characteristic, complemented
13C4×#14273668C211yesmaximal, characteristic, complemented
14C2×C4×C59⋊C16C211yesmaximal, characteristic, complemented
15C59×#3168C211yesmaximal, characteristic, complemented
16#16837936—21no—
17C2×#14273673C2211yescharacteristic
18C2×#14273671C2211yescharacteristic
19C2×#14273670C2211yescharacteristic
20C2×#14273668C2211yescharacteristic
21C22×C59⋊C16C2211yescharacteristic
22C22×C59⋊C16C2211yescharacteristic
23#16837804C2211yescharacteristic
24#16837786C2211yescharacteristic
25#16837757—21no—
26#16837643C2211yescharacteristic
27#16837638C2211yescharacteristic
28#16837631—21no—
29C4×Dic236C2211yescharacteristic
30C4×#11745660—21no—
31C4×D472C2211yescharacteristic
32#16837229C2211yescharacteristic
33#16837229C2211yescharacteristic
34#16837227C2211yescharacteristic
35#16837227C2211yescharacteristic
36#16837206C2211yescharacteristic
37#16837206C2211yescharacteristic
38#16837205C2211yescharacteristic
39#16837205C2211yescharacteristic
40#16837203C2211yescharacteristic
41#16837203C2211yescharacteristic
42#16837202C2211yescharacteristic
43#16837202C2211yescharacteristic
44C4×C59⋊C16C2211yescharacteristic
45C4×C59⋊C16C2211yescharacteristic
46C4×C59⋊C16C2211yescharacteristic
47C4×C59⋊C16C2211yescharacteristic
48C59×#529—21no—
49C59×#499C2211yescharacteristic
50C59×#495C2211yescharacteristic
51C59×#488—21no—
52C59×#467C2211yescharacteristic
53C59×#466C2211yescharacteristic
54C59×#465—21no—
55C4×Q16×C59C2211yescharacteristic
56C4×SD16×C59—21no—
57C4×D8×C59C2211yescharacteristic
58C2×C4×C8×C59C2211yescharacteristic
59C2×Dic236C2311yescharacteristic
60C2×#11745660—21no—
61C2×D472C2311yescharacteristic
62#14273721—41no—
63#14273719—21no—
64#14273715—21no—
65#14273710—41no—
66#14273706—21no—
67#14273701—21no—
68C4×Dic118—21no—
69C4×D236—21no—
70C4×C22⋊D59—41no—
71#14273684—41no—
72#14273673—22no—
73#14273671—22no—
74#14273670—22no—
75#14273668—22no—
76C2×C59⋊C16—22no—
77C2×C59⋊C16—22no—
78C2×C59⋊C16C2311yescharacteristic
79C2×C59⋊C16C2311yescharacteristic
80C2×C59⋊C16C2311yescharacteristic
81C2×C59⋊C16C2311yescharacteristic
82#14273661C2311yescharacteristic
83#14273661C2311yescharacteristic
84#14273659—21no—
85#14273652—21no—
86#14273652—21no—
87#14273649—21no—
88#14273649—21no—
89C2×Q16×C59C2311yescharacteristic
90C2×SD16×C59—21no—
91C2×D8×C59C2311yescharacteristic
92C22×C8×C59D411yescharacteristic
93C22×C8×C59C2311yescharacteristic
94#126×C59—41no—
95#125×C59—21no—
96#124×C59—21no—
97#123×C59—41no—
98C22⋊Q8×C59—21no—
99#121×C59—21no—
100C4×Q8×C59—21no—
101C4×D4×C59—21no—
102C4×D4×C59—41no—
103#117×C59—41no—
104C2×C42×C59D411yescharacteristic
105#107×C59C2311yescharacteristic
106#107×C59C2311yescharacteristic
107#106×C59—21no—
108#103×C59—21no—
109#103×C59—21no—
110#102×C59—21no—
111#102×C59—21no—
112C4×C8×C59D411yescharacteristic
113C4×C8×C59D411yescharacteristic
114C4×C8×C59C2311yescharacteristic
115C4×C8×C59C2311yescharacteristic
116C2×Q8×C59—21no—
117C2×D4×C59—21no—
118C2×D4×C59—41no—
119C22×C4×C59—41no—
120C22×C4×C59D811yescharacteristic
121C22×C4×C59D811yescharacteristic
122C22×C4×C59C2×D411yescharacteristic
123C2×C22⋊D59—41no—
124C2×D236—21no—
125C2×C4×D59—41no—
126C2×Dic118—21no—
127Q16×C59—21no—
128Q16×C59—21no—
129SD16×C59—42no—
130D8×C59—21no—
131D8×C59—21no—
132C2×C8×C59—22no—
133C2×C8×C59—21no—
134C2×C8×C59—21no—
135C2×C8×C59C2×D411yescharacteristic
136C2×C8×C59C2×D411yescharacteristic
137C2×C8×C59C2×D411yescharacteristic
138C2×C8×C59C2411yescharacteristic
139C4⋊C4×C59—21no—
140C4⋊C4×C59—21no—
141C4⋊C4×C59—41no—
142C4⋊C4×C59—41no—
143C4⋊C4×C59—41no—
144C4⋊C4×C59—41no—
145C22⋊C4×C59—41no—
146C22⋊C4×C59—41no—
147C22⋊C4×C59—41no—
148C22⋊C4×C59—41no—
149C22⋊C4×C59—41no—
150C42×C59—41no—
151C42×C59D811yescharacteristic
152C42×C59D811yescharacteristic
153C42×C59C2×D411yescharacteristic
154C42×C59C2×D411yescharacteristic
155C22⋊Dic59—41no—
156(C2×D59)⋊C4—41no—
157(C2×D59)⋊C4—41no—
158(C2×D59)⋊C4—41no—
159(C2×D59)⋊C4—41no—
160C4⋊Dic59—21no—
161C4⋊Dic59—21no—
162Dic59⋊C4—41no—
163Dic59⋊C4—41no—
164Dic59⋊C4—41no—
165Dic59⋊C4—41no—
166C4×Dic59—41no—
167Dic236—21no—
168Dic236—21no—
169D472—21no—
170D472—21no—
171#11745660—42no—
172C59⋊C16—21no—
173C59⋊C16—21no—
174C59⋊C16#4112yes—
175C59⋊C16#4112yes—
176C23×C59—41no—
177C23×C59C2×D811yescharacteristic
178C22×D59—41no—
179Q8×C59—41no—
180Q8×C59—41no—
181D4×C59—41no—
182D4×C59—41no—
183D4×C59—82no—
184C2×C4×C59—22no—
185C2×C4×C59—21no—
186C2×C4×C59—21no—
187C2×C4×C59—22no—
188C2×C4×C59—41no—
189C2×C4×C59—41no—
190C2×C4×C59—41no—
191C2×C4×C59—82no—
192C2×C4×C59C2×D811yescharacteristic
193C2×C4×C59C2×D811yescharacteristic
194C2×C4×C59C2×D811yescharacteristic
195C2×C4×C59C2×D811yescharacteristic
196C2×C4×C59C2×D811yescharacteristic
197C2×C4×C59C22×D411yescharacteristic
198C22⋊D59—82no—
199C2×Dic59—41no—
200C2×Dic59—41no—
201C2×Dic59—41no—
202D236—41no—
203D236—41no—
204C4×D59—82no—
205Dic118—41no—
206Dic118—41no—
207C8×C59—21no—
208C8×C59—21no—
209C8×C59#13512yes—
210C8×C59C2×#4111yescharacteristic
211C8×C59C2×#4111yescharacteristic
212#33735—591nomaximal, Sylow
213C22×C59—21no—
214C22×C59—21no—
215C22×C59—81no—
216C22×C59—81no—
217C22×C59—81no—
218C22×C59#50812yes—
219C22×C59C22×D811yescharacteristic
220C2×D59—81no—
221C2×D59—81no—
222C2×D59—81no—
223C4×C59—21no—
224C4×C59—21no—
225C4×C59—21no—
226C4×C59—21no—
227C4×C59—81no—
228C4×C59—81no—
229C4×C59—81no—
230C4×C59#50812yes—
231C4×C59#53211yescharacteristic
232C4×C59C2×#13511yescharacteristic
233Dic59—81no—
234Dic59—81no—
235Dic59—81no—
236#3168—591no—
237#3168D5911yescharacteristic, complemented
238#2253—591no—
239#2249—591no—
240#2242—591no—
241#2242—591no—
242#2217—591no—
243#2217—591no—
244#2216—591no—
245#2215—591no—
246C4×Q32—591no—
247C4×SD32—591no—
248C4×SD32—591no—
249C4×D16—591no—
250C2×C4×C16—591no—
251C2×C59—22no—
252C2×C59—161no—
253C2×C59#316911yescharacteristic
254C2×C59C2×#50811yescharacteristic
255C2×C59C2×#50811yescharacteristic
256D59—161no—
257#529—21no—
258#529—1181no—
259C2×Q32—591no—
260C2×SD32—591no—
261C2×SD32—591no—
262C2×D16—591no—
263C22×C16—591no—
264C22×C16—591no—
265#499—591no—
266#499C2×D5911yescharacteristic
267#495—591no—
268#495C2×D5911yescharacteristic
269#488—21no—
270#488—1181no—
271#467—591no—
272#467C2×D5911yescharacteristic
273#466—591no—
274#466C2×D5911yescharacteristic
275#465—21no—
276#465—1181no—
277C4×Q16—591no—
278C4×Q16C2×D5911yescharacteristic
279C4×SD16—21no—
280C4×SD16—1181no—
281C4×D8—591no—
282C4×D8C2×D5911yescharacteristic
283C2×C4×C8C2×D5911yescharacteristic
284#367—591no—
285#367—591no—
286#366—591no—
287#366—591no—
288#358—591no—
289#358—591no—
290#358—591no—
291#358—591no—
292#357—591no—
293#357—591no—
294#357—591no—
295#357—591no—
296C4×C16—591no—
297C4×C16—591no—
298C4×C16—591no—
299C4×C16—591no—
300C59#3373511yescharacteristic, complemented, Sylow
301C2×Q16—591no—
302C2×Q16C22×D5911yescharacteristic
303C2×SD16—21no—
304C2×SD16—1181no—
305C2×D8—591no—
306C2×D8C22×D5911yescharacteristic
307C22×C8C22⋊D5911yescharacteristic
308C22×C8C22×D5911yescharacteristic
309#126—41no—
310#126—2361no—
311#125—21no—
312#125—1181no—
313#124—21no—
314#124—1181no—
315#123—41no—
316#123—2361no—
317C22⋊Q8—21no—
318C22⋊Q8—1181no—
319#121—21no—
320#121—1181no—
321C4×Q8—21no—
322C4×Q8—1181no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—1181no—
326C4×D4—2361no—
327#117—41no—
328#117—2361no—
329C2×C42C22⋊D5911yescharacteristic
330Q32—1182no—
331SD32—1182no—
332SD32—1182no—
333D16—1182no—
334C2×C16—591no—
335C2×C16—591no—
336C2×C16—591no—
337C2×C16—591no—
338C2×C16—1182no—
339C2×C16—1182no—
340#107—591no—
341#107—591no—
342#107C22×D5911yescharacteristic
343#107C22×D5911yescharacteristic
344#106—21no—
345#106—1181no—
346#103—21no—
347#103—21no—
348#103—1181no—
349#103—1181no—
350#102—21no—
351#102—21no—
352#102—1181no—
353#102—1181no—
354C4×C8C22⋊D5911yescharacteristic
355C4×C8C22⋊D5911yescharacteristic
356C4×C8C22×D5911yescharacteristic
357C4×C8C22×D5911yescharacteristic
358C2×Q8—21no—
359C2×Q8—1181no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—1181no—
363C2×D4—2361no—
364C22×C4—41no—
365C22×C4—2361no—
366C22×C4#1174566911yescharacteristic
367C22×C4#1174566911yescharacteristic
368C22×C4C2×C22⋊D5911yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—1181no—
372Q16—1181no—
373SD16—42no—
374SD16—2362no—
375D8—21no—
376D8—21no—
377D8—1181no—
378D8—1181no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8C2×C22⋊D5911yescharacteristic
383C2×C8C2×C22⋊D5911yescharacteristic
384C2×C8C2×C22⋊D5911yescharacteristic
385C2×C8C23×D5911yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—1181no—
393C4⋊C4—1181no—
394C4⋊C4—2361no—
395C4⋊C4—2361no—
396C4⋊C4—2361no—
397C4⋊C4—2361no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—2361no—
404C22⋊C4—2361no—
405C22⋊C4—2361no—
406C22⋊C4—2361no—
407C22⋊C4—2361no—
408C42—41no—
409C42—2361no—
410C42#1174566911yescharacteristic
411C42#1174566911yescharacteristic
412C42C2×C22⋊D5911yescharacteristic
413C42C2×C22⋊D5911yescharacteristic
414C16—592no—
415C16—592no—
416C16—1181no—
417C16—1181no—
418C23—41no—
419C23—2361no—
420C23C2×#1174566911yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—2361no—
424Q8—2361no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—4722no—
429D4—2361no—
430D4—2361no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—4722no—
440C2×C4—2361no—
441C2×C4—2361no—
442C2×C4—2361no—
443C2×C4C2×#1174566911yescharacteristic
444C2×C4C2×#1174566911yescharacteristic
445C2×C4C2×#1174566911yescharacteristic
446C2×C4C2×#1174566911yescharacteristic
447C2×C4C2×#1174566911yescharacteristic
448C2×C4C22×C22⋊D5911yescharacteristic
449C8—21no—
450C8—21no—
451C8#1427374712yes—
452C8#41×D5911yescharacteristic
453C8#41×D5911yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—4721no—
460C22—4721no—
461C22—4721no—
462C22#1683783212yes—
463C22C22×#1174566911yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—4721no—
472C4—4721no—
473C4—4721no—
474C4#1683783212yes—
475C4#1683794811yescharacteristic
476C4C2×#1427374711yescharacteristic
477C2—22no—
478C2—161no—
479C2—9441no—
480C2#2143467111yescharacteristic
481C2C2×#1683783211yescharacteristic
482C2C2×#1683783211yescharacteristic
subgroupG/H
centerC2×C4C2×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#3168C2
socleC22×C59C22×D8
prime radical#21426180C2
hypercenter#3168D59
hypocenterC59#33735
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #21434666C2semidirect
2. #21426372C2semidirect
3. #21426355C2semidirect
4. #21426330C2semidirect
5. #21426327C2semidirect
6. #21426194C2semidirect
7. #21426190C2semidirect
8. #21426185C2semidirect
10. C4×#14273673C2semidirect
11. C4×#14273670C2semidirect
12. C4×#14273671C2semidirect
13. C4×#14273668C2semidirect
14. C2×C4×C59⋊C16C2semidirect
15. C59×#3168C2semidirect
237. #3168D59semidirect
300. C59#33735semidirect

Maximal subgroups

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

subgroupindex
#214346662
#214263722
#214263552
#214263302
#214263272
#214261942
#214261902
#214261852
#214261802
C4×#142736732
C4×#142736702
C4×#142736712
C4×#142736682
C2×C4×C59⋊C162
C59×#31682
#3373559