Finite Group Databasebeta

← #28746520

Subgroups — #28746520

Order 15104.

482 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436964C211yesmaximal, characteristic, complemented
2#21426341C211yesmaximal, characteristic, complemented
3#21426332C211yesmaximal, characteristic, complemented
4#21426327C211yesmaximal, characteristic, complemented
5#21426260C211yesmaximal, characteristic, complemented
6#21426253C211yesmaximal, characteristic, complemented
7#21426238C211yesmaximal, characteristic, complemented
8#21426148C211yesmaximal, characteristic
9#21426148C211yesmaximal, characteristic
10#21426138C211yesmaximal, characteristic, complemented
11#21426005C211yesmaximal, characteristic, complemented
12#21425970C211yesmaximal, characteristic
13#21425958C211yesmaximal, characteristic, complemented
14C4×#14273670C211yesmaximal, characteristic, complemented
15C59×#3393C211yesmaximal, characteristic, complemented
16#16838112—21no—
17C2×#14273670C2211yescharacteristic
18C2×#14273670C2211yescharacteristic
19C2×#14273668C2211yescharacteristic
20#16837807C2211yescharacteristic
21#16837804C2211yescharacteristic
22#16837804C2211yescharacteristic
23#16837703—21no—
24#16837703—21no—
25#16837693—21no—
26C4×D472C2211yescharacteristic
27C4×D472C2211yescharacteristic
28C4×D472C2211yescharacteristic
29#16837229C2211yescharacteristic
30#16837229C2211yescharacteristic
31#16837227C2211yescharacteristic
32C4⋊(C59⋊C16)C2211yescharacteristic
33C4⋊(C59⋊C16)C2211yescharacteristic
34C4⋊(C59⋊C16)C2211yescharacteristic
35#16837206C2211yescharacteristic
36#16837206C2211yescharacteristic
37#16837206C2211yescharacteristic
38#16837206C2211yescharacteristic
39#16837206C2211yescharacteristic
40#16837206C2211yescharacteristic
41#16837203C2211yescharacteristic
42#16837203C2211yescharacteristic
43#16837203C2211yescharacteristic
44#16837202C2211yescharacteristic
45#16837178C2211yescharacteristic
46#16837178C2211yescharacteristic
47C4×C59⋊C16C2211yescharacteristic
48C59×#556—21no—
49C59×#495C2211yescharacteristic
50C59×#495C2211yescharacteristic
51C59×#494C2211yescharacteristic
52C59×#464—21no—
53C59×#464—21no—
54C59×#461—21no—
55C8×Q8×C59C2211yescharacteristic
56C4×Q16×C59C2211yescharacteristic
57C4×Q16×C59C2211yescharacteristic
58C4×D8×C59C2211yescharacteristic
59C2×D472C2311yescharacteristic
60#14273727—21no—
61#14273719—21no—
62#14273719—21no—
63#14273705—41no—
64#14273705—41no—
65#14273703—41no—
66C4×D236—21no—
67C4×D236—21no—
68C4×D236—21no—
69C4⋊C4×D59—41no—
70#14273670—22no—
71#14273670—22no—
72#14273668—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×Q16×C59—21no—
87C2×Q16×C59C2311yescharacteristic
88C2×Q16×C59C2311yescharacteristic
89C2×SD16×C59—21no—
90C2×SD16×C59—21no—
91C2×D8×C59C2311yescharacteristic
92C4⋊Q8×C59—21no—
93#126×C59—41no—
94#126×C59—41no—
95#124×C59—21no—
96#124×C59—21no—
97C22⋊Q8×C59—41no—
98C4×Q8×C59—21no—
99C4×Q8×C59—21no—
100C4×Q8×C59D411yescharacteristic
101C4×D4×C59—21no—
102#117×C59—41no—
103#107×C59C2311yescharacteristic
104C4⋊C8×C59D411yescharacteristic
105C4⋊C8×C59D411yescharacteristic
106C4⋊C8×C59D411yescharacteristic
107#103×C59—21no—
108#103×C59—21no—
109#102×C59—21no—
110C4×C8×C59C2311yescharacteristic
111C4×C8×C59C2311yescharacteristic
112C4×C8×C59C2311yescharacteristic
113C2×Q8×C59—21no—
114C2×Q8×C59—21no—
115C2×Q8×C59D811yescharacteristic
116C2×D4×C59—21no—
117C22×C4×C59—41no—
118C2×D236—21no—
119C2×C4×D59—41no—
120C2×C4×D59—41no—
121C2×C4×D59—41no—
122C2×Dic118—41no—
123Q16×C59—21no—
124Q16×C59—21no—
125Q16×C59—21no—
126Q16×C59—21no—
127Q16×C59—81no—
128SD16×C59—81no—
129SD16×C59—81no—
130D8×C59—21no—
131D8×C59—21no—
132C2×C8×C59C2×D411yescharacteristic
133C2×C8×C59C2×D411yescharacteristic
134C2×C8×C59C2×D411yescharacteristic
135C2×C8×C59C2411yescharacteristic
136C4⋊C4×C59—21no—
137C4⋊C4×C59—41no—
138C4⋊C4×C59—41no—
139C4⋊C4×C59—41no—
140C4⋊C4×C59—41no—
141C4⋊C4×C59D811yescharacteristic
142C4⋊C4×C59D811yescharacteristic
143C4⋊C4×C59D811yescharacteristic
144C22⋊C4×C59—41no—
145C22⋊C4×C59—41no—
146C22⋊C4×C59—41no—
147C22⋊C4×C59—41no—
148C22⋊C4×C59—41no—
149C42×C59—41no—
150C42×C59—41no—
151C42×C59C2×D411yescharacteristic
152C42×C59C2×D411yescharacteristic
153C42×C59C2×D411yescharacteristic
154(C2×D59)⋊C4—41no—
155(C2×D59)⋊C4—41no—
156(C2×D59)⋊C4—41no—
157C4⋊Dic59—21no—
158C4⋊Dic59—21no—
159C4⋊Dic59—21no—
160C4⋊Dic59—41no—
161Dic59⋊C4—41no—
162Dic59⋊C4—41no—
163Dic59⋊C4—41no—
164Dic59⋊C4—41no—
165D472—21no—
166D472#4112yes—
167C59⋊C16—21no—
168C59⋊C16—21no—
169C59⋊C16—21no—
170C59⋊C16—21no—
171C23×C59—41no—
172C22×D59—41no—
173Q8×C59—41no—
174Q8×C59—41no—
175Q8×C59—41no—
176Q8×C59—41no—
177Q8×C59—41no—
178D4×C59—41no—
179D4×C59—41no—
180C2×C4×C59—41no—
181C2×C4×C59—41no—
182C2×C4×C59—41no—
183C2×C4×C59—82no—
184C2×C4×C59C2×D811yescharacteristic
185C2×C4×C59C2×D811yescharacteristic
186C2×C4×C59C2×D811yescharacteristic
187C2×C4×C59C2×D811yescharacteristic
188C2×C4×C59C2×D811yescharacteristic
189C2×C4×C59C2×D811yescharacteristic
190C2×C4×C59C22×D411yescharacteristic
191C2×Dic59—41no—
192C2×Dic59—41no—
193C2×Dic59—41no—
194D236—22no—
195D236—41no—
196C4×D59—82no—
197C4×D59—161no—
198C4×D59—161no—
199Dic118—161no—
200C8×C59—21no—
201C8×C59—21no—
202C8×C59—21no—
203C8×C59C2×#4111yescharacteristic
204C8×C592−1+411yescharacteristic
205#33943—591nomaximal, Sylow
206C22×C59—81no—
207C22×C59—81no—
208C22×C59—81no—
209C22×C59C22×D811yescharacteristic
210C2×D59—42no—
211C2×D59—81no—
212C2×D59—81no—
213C4×C59—21no—
214C4×C59—21no—
215C4×C59—21no—
216C4×C59—21no—
217C4×C59—21no—
218C4×C59—21no—
219C4×C59—81no—
220C4×C59—81no—
221C4×C59—81no—
222C4×C59#54811yescharacteristic
223C4×C59#57711yescharacteristic
224Dic59—81no—
225Dic59—81no—
226Dic59—81no—
227#3393D5911yescharacteristic, complemented
228#3380—591no—
229#2245—591no—
230#2243—591no—
231#2242—591no—
232#2229—591no—
233#2228—591no—
234#2225—591no—
235#2210—591no—
236#2210—591no—
237#2208—591no—
238#2183—591no—
239#2177—591no—
240#2175—591no—
241C4×SD32—591no—
242C2×C59—161no—
243C2×C59#335811yescharacteristic
244C2×C59#341411yescharacteristic
245C2×C59#341611yescharacteristic
246D59—82no—
247#556—21no—
248#554—1181no—
249C2×SD32—591no—
250C2×SD32—591no—
251C2×D16—591no—
252#500—591no—
253#499—591no—
254#499—591no—
255#495C2×D5911yescharacteristic
256#495C2×D5911yescharacteristic
257#494C2×D5911yescharacteristic
258#478—1181no—
259#478—1181no—
260#476—1181no—
261#464—21no—
262#464—21no—
263#461—21no—
264C8×Q8C2×D5911yescharacteristic
265C4×Q16C2×D5911yescharacteristic
266C4×Q16C2×D5911yescharacteristic
267C4×D8—591no—
268C4×D8—591no—
269C4×D8—591no—
270C4×D8C2×D5911yescharacteristic
271#367—591no—
272#367—591no—
273#366—591no—
274C4⋊C16—591no—
275C4⋊C16—591no—
276C4⋊C16—591no—
277#358—591no—
278#358—591no—
279#358—591no—
280#358—591no—
281#358—591no—
282#358—591no—
283#357—591no—
284#357—591no—
285#357—591no—
286#357—591no—
287#346—591no—
288#346—591no—
289C4×C16—591no—
290C59#3394311yescharacteristic, complemented, Sylow
291C2×Q16—21no—
292C2×Q16C22×D5911yescharacteristic
293C2×Q16C22×D5911yescharacteristic
294C2×SD16—21no—
295C2×SD16—21no—
296C2×D8—591no—
297C2×D8C22×D5911yescharacteristic
298C4⋊Q8—21no—
299C4⋊Q8—1181no—
300#126—41no—
301#126—41no—
302#125—1181no—
303#125—1181no—
304#124—21no—
305#124—21no—
306C22⋊Q8—41no—
307C22⋊Q8—2361no—
308C22⋊Q8—2361no—
309C22⋊Q8—2361no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8C22⋊D5911yescharacteristic
313C4×D4—21no—
314C4×D4—1181no—
315C4×D4—1181no—
316C4×D4—1181no—
317#117—41no—
318C2×C4⋊C4—2361no—
319SD32—1182no—
320SD32—1182no—
321D16—1182no—
322C2×C16—591no—
323C2×C16—591no—
324C2×C16—591no—
325C2×C16—591no—
326#107—591no—
327#107—591no—
328#107—591no—
329#107—1181no—
330#107C22×D5911yescharacteristic
331#106—1181no—
332#106—1181no—
333C4⋊C8C22⋊D5911yescharacteristic
334C4⋊C8C22⋊D5911yescharacteristic
335C4⋊C8C22⋊D5911yescharacteristic
336#103—21no—
337#103—21no—
338#102—21no—
339#102—1181no—
340#102—1181no—
341#102—1181no—
342C4×C8C22×D5911yescharacteristic
343C4×C8C22×D5911yescharacteristic
344C4×C8C22×D5911yescharacteristic
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—2361no—
348C2×Q8#1174566911yescharacteristic
349C2×D4—21no—
350C2×D4—1181no—
351C22×C4—41no—
352C22×C4—2361no—
353C22×C4—2361no—
354C22×C4—2361no—
355Q16—21no—
356Q16—21no—
357Q16—21no—
358Q16—21no—
359Q16—81no—
360SD16—81no—
361SD16—81no—
362D8—21no—
363D8—21no—
364D8—592no—
365D8—1181no—
366C2×C8C2×C22⋊D5911yescharacteristic
367C2×C8C2×C22⋊D5911yescharacteristic
368C2×C8C2×C22⋊D5911yescharacteristic
369C2×C8C23×D5911yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—1181no—
376C4⋊C4—1181no—
377C4⋊C4—1181no—
378C4⋊C4—2361no—
379C4⋊C4—2361no—
380C4⋊C4—2361no—
381C4⋊C4—2361no—
382C4⋊C4—2361no—
383C4⋊C4#1174566911yescharacteristic
384C4⋊C4#1174566911yescharacteristic
385C4⋊C4#1174566911yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—2361no—
392C22⋊C4—2361no—
393C22⋊C4—2361no—
394C42—41no—
395C42—41no—
396C42C2×C22⋊D5911yescharacteristic
397C42C2×C22⋊D5911yescharacteristic
398C42C2×C22⋊D5911yescharacteristic
399C16—1181no—
400C16—1181no—
401C16—1181no—
402C16—1181no—
403C23—41no—
404C23—2361no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—9441no—
411D4—41no—
412D4—41no—
413D4—1182no—
414D4—2361no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4—9441no—
420C2×C4—9441no—
421C2×C4—4722no—
422C2×C4—2361no—
423C2×C4—2361no—
424C2×C4—2361no—
425C2×C4C2×#1174566911yescharacteristic
426C2×C4C2×#1174566911yescharacteristic
427C2×C4C2×#1174566911yescharacteristic
428C2×C4C2×#1174566911yescharacteristic
429C2×C4C2×#1174566911yescharacteristic
430C2×C4C2×#1174566911yescharacteristic
431C2×C4C22×C22⋊D5911yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8#41×D5911yescharacteristic
436C8#1427377411yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—4721no—
441C22—4721no—
442C22—2362no—
443C22C22×#1174566911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—4721no—
454C4—4721no—
455C4—4721no—
456C4#1683805911yescharacteristic
457C4#1683821311yescharacteristic
458C2—161no—
459C2—4722no—
460C2#2143672711yescharacteristic
461C2#2143723011yescharacteristic
462C2#2143724011yescharacteristic
subgroupG/H
centerC22C22×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#3393C2
socleC22×C59C22×D8
prime radicalC2×#14273668C22
hypercenter#3393D59
hypocenterC59#33943
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #21436964C2semidirect
2. #21426341C2semidirect
3. #21426332C2semidirect
4. #21426327C2semidirect
5. #21426260C2semidirect
6. #21426253C2semidirect
7. #21426238C2semidirect
10. #21426138C2semidirect
11. #21426005C2semidirect
13. #21425958C2semidirect
14. C4×#14273670C2semidirect
15. C59×#3393C2semidirect
227. #3393D59semidirect
290. C59#33943semidirect

Maximal subgroups

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

subgroupindex
#214369642
#214263412
#214263322
#214263272
#214262602
#214262532
#214262382
#214261482
#214261382
#214260052
#214259702
#214259582
C4×#142736702
C59×#33932
#3394359