Finite Group Databasebeta

← #28746041

Subgroups — #28746041

Order 15104.

548 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436441C211yesmaximal, characteristic, complemented
2#21436440C211yesmaximal, characteristic, complemented
3#21426370C211yesmaximal, characteristic, complemented
4#21426278C211yesmaximal, characteristic, complemented
5#21426277C211yesmaximal, characteristic, complemented
6#21426275C211yesmaximal, characteristic, complemented
7#21426232C211yesmaximal, characteristic, complemented
8#21426231C211yesmaximal, characteristic, complemented
9#21426181C211yesmaximal, characteristic, complemented
10#21426180C211yesmaximal, characteristic, complemented
11#21425940C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C16C211yesmaximal, characteristic, complemented
13C2×#16837227C211yesmaximal, characteristic, complemented
14#366×D59C211yesmaximal, characteristic, complemented
15C59×#2232C211yesmaximal, characteristic, complemented
16#16838053—21no—
17#16838052—21no—
18C2×#14273668C2211yescharacteristic
19C22×C59⋊C16C2211yescharacteristic
20C2×C16×D59C2211yescharacteristic
21#16837806C2211yescharacteristic
22#16837806C2211yescharacteristic
23#16837717—21no—
24#16837715—21no—
25#16837714—21no—
26#16837713—21no—
27#16837681—21no—
28#16837680—21no—
29#16837639C2211yescharacteristic
30#16837638C2211yescharacteristic
31#16837635C2211yescharacteristic
32D8×Dic59C2211yescharacteristic
33#16837484C2211yescharacteristic
34C8×C22⋊D59C2211yescharacteristic
35C2×#14273661C2211yescharacteristic
36#107×D59C2211yescharacteristic
37#107×D59C2211yescharacteristic
38#16837228C2211yescharacteristic
39#16837228C2211yescharacteristic
40#16837227C2211yescharacteristic
41#16837227C2211yescharacteristic
42#16837227C2211yescharacteristic
43#16837227C2211yescharacteristic
44#16837227C2211yescharacteristic
45Dic59⋊C16C2211yescharacteristic
46#16837204C2211yescharacteristic
47#16837204C2211yescharacteristic
48#16837203C2211yescharacteristic
49#16837202C2211yescharacteristic
50(C2×D59)⋊C16C2211yescharacteristic
51C16×Dic59C2211yescharacteristic
52C59×#466C2211yescharacteristic
53C2×#107×C59C2211yescharacteristic
54C59×#366C2211yescharacteristic
55C59×#366C2211yescharacteristic
56C59×#357C2211yescharacteristic
57C59×#357C2211yescharacteristic
58C59×C22⋊C16C2211yescharacteristic
59C2×#11745685—41no—
60C2×#11745687—41no—
61C2×D472C2311yescharacteristic
62C2×C8×D59C2311yescharacteristic
63#14273726—21no—
64#14273726—21no—
65#14273712—41no—
66#14273710—41no—
67#14273709—41no—
68#14273708—41no—
69#14273705—41no—
70#14273704—41no—
71#14273702—21no—
72#14273701—21no—
73#14273698—21no—
74D4×Dic59—21no—
75#14273689—21no—
76C4×C22⋊D59D411yescharacteristic
77C2×C4⋊Dic59—21no—
78C4⋊C4×D59—21no—
79C4⋊C4×D59—21no—
80#14273668—22no—
81C2×C59⋊C16—22no—
82C2×C59⋊C16C2311yescharacteristic
83C2×C59⋊C16C2311yescharacteristic
84C16×D59—22no—
85#14273661—21no—
86#14273661C2311yescharacteristic
87#14273661C2311yescharacteristic
88#14273661C2311yescharacteristic
89#14273660—21no—
90#14273660—21no—
91#14273660—21no—
92#14273660—21no—
93Dic59⋊C8D411yescharacteristic
94#14273649—21no—
95#14273648—21no—
96#14273648—21no—
97#14273647—21no—
98#14273647—21no—
99C22⋊(C59⋊C8)D411yescharacteristic
100(C2×D59)⋊C8D411yescharacteristic
101C8×Dic59C2311yescharacteristic
102C2×D8×C59C2311yescharacteristic
103C22×C8×C59C2311yescharacteristic
104#121×C59—21no—
105C2×C4⋊C4×C59—21no—
106C2×C16×C59C2311yescharacteristic
107C2×C16×C59C2311yescharacteristic
108#107×C59—21no—
109#107×C59C2311yescharacteristic
110#107×C59C2311yescharacteristic
111#107×C59C2311yescharacteristic
112#102×C59—21no—
113C2×D4×C59—21no—
114C2×D4×C59—41no—
115C22×C4×C59—41no—
116C22×C4×C59C2×D411yescharacteristic
117C2×C22⋊D59—41no—
118C2×C22⋊D59—41no—
119C2×C22⋊D59D811yescharacteristic
120C22×Dic59—41no—
121C22×Dic59—41no—
122#11745687—84no—
123#11745685—84no—
124C2×D236—21no—
125C2×D236—41no—
126C2×C4×D59—41no—
127C2×C4×D59—41no—
128C2×C4×D59—41no—
129C2×C4×D59C2×D411yescharacteristic
130C2×Dic118—41no—
131C2×Dic118—41no—
132D8×C59—21no—
133D8×C59—21no—
134C2×C8×C59—21no—
135C2×C8×C59—21no—
136C2×C8×C59C2×D411yescharacteristic
137C2×C8×C59C2411yescharacteristic
138C4⋊C4×C59—21no—
139C4⋊C4×C59—21no—
140C4⋊C4×C59—21no—
141C4⋊C4×C59—41no—
142C22⋊C4×C59—41no—
143C22⋊Dic59—41no—
144C22⋊Dic59—41no—
145C22⋊Dic59D811yescharacteristic
146(C2×D59)⋊C4—41no—
147(C2×D59)⋊C4—41no—
148(C2×D59)⋊C4—41no—
149(C2×D59)⋊C4D811yescharacteristic
150C4⋊Dic59—21no—
151C4⋊Dic59—21no—
152C4⋊Dic59—21no—
153C4⋊Dic59—41no—
154Dic59⋊C4—41no—
155Dic59⋊C4—41no—
156Dic59⋊C4—41no—
157Dic59⋊C4—41no—
158Dic59⋊C4D811yescharacteristic
159C4×Dic59C2×D411yescharacteristic
160C2×C59⋊C8C2×D411yescharacteristic
161C2×C59⋊C8C2×D411yescharacteristic
162D472—21no—
163D472—21no—
164C8×D59—21no—
165C8×D59—21no—
166C16×C59—21no—
167C16×C59—21no—
168C59⋊C16—21no—
169C59⋊C16#4112yescomplemented
170C23×C59—41no—
171C23×C59C2×D811yescharacteristic
172C22×D59—41no—
173C22×D59C2×D811yescharacteristic
174D4×C59—41no—
175D4×C59—41no—
176D4×C59—82no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—41no—
180C2×C4×C59—41no—
181C2×C4×C59—41no—
182C2×C4×C59—82no—
183C2×C4×C59C2×D811yescharacteristic
184C2×C4×C59C22×D411yescharacteristic
185C22⋊D59—82no—
186C22⋊D59—82no—
187C22⋊D59D1614yescomplemented
188C2×Dic59—41no—
189C2×Dic59—41no—
190C2×Dic59—41no—
191C2×Dic59—82no—
192C2×Dic59—82no—
193C2×Dic59C2×D811yescharacteristic
194C2×Dic59C2×D811yescharacteristic
195C2×Dic59C2×D811yescharacteristic
196D236—41no—
197D236—41no—
198D236—82no—
199C4×D59—21no—
200C4×D59—21no—
201C4×D59—82no—
202C4×D59—82no—
203C4×D59—82no—
204Dic118—82no—
205Dic118—82no—
206C8×C59—21no—
207C8×C59C2×#4111yescharacteristic
208C8×C592−1+411yescharacteristic
209C59⋊C8—21no—
210C59⋊C8—21no—
211#33901—591nomaximal, Sylow
212C22×C59—21no—
213C22×C59—21no—
214C22×C59—81no—
215C22×C59—81no—
216C22×C59—81no—
217C22×C59C2×D1612yes—
218C22×C59C22×D811yescharacteristic
219C2×D59—21no—
220C2×D59—21no—
221C2×D59—81no—
222C2×D59—81no—
223C2×D59—81no—
224C2×D59C2×D1612yes—
225C4×C59—21no—
226C4×C59—81no—
227C4×C59—81no—
228C4×C59—81no—
229C4×C59#54711yescharacteristic
230C4×C59#57811yescharacteristic
231Dic59—21no—
232Dic59—21no—
233Dic59—81no—
234Dic59—81no—
235Dic59—81no—
236Dic59C2×D1612yes—
237#3334—591no—
238#3334—591no—
239#2252—591no—
240#2232—591no—
241#2232—591no—
242#2232—591no—
243#2232D5911yescharacteristic, complemented
244#2224—591no—
245#2224—591no—
246#2215—591no—
247#2215—591no—
248C4×D16—591no—
249D4×C16—591no—
250C2×#366—591no—
251C2×#366—591no—
252C2×C59—22no—
253C2×C59—161no—
254C2×C59#333411yescharacteristic
255C2×C59C22×D1611yescharacteristic
256C2×C59#341711yescharacteristic
257D59—22no—
258D59—161no—
259#547—1181no—
260#547—1181no—
261C2×D16—591no—
262C22×C16—591no—
263C22×C16—591no—
264#500—591no—
265#500—591no—
266#480—1181no—
267#480—1181no—
268#480—1181no—
269#480—1181no—
270#474—1181no—
271#474—1181no—
272#466—591no—
273#466—591no—
274#466—591no—
275#466C2×D5911yescharacteristic
276C4×D8—591no—
277C4×D8—591no—
278C8×D4—591no—
279C2×#107—591no—
280C2×#107—591no—
281C2×#107—591no—
282C2×#107C2×D5911yescharacteristic
283#366—591no—
284#366—591no—
285#366—591no—
286#366—591no—
287#366—591no—
288#366—591no—
289#366—591no—
290#366C2×D5911yescharacteristic
291#366C2×D5911yescharacteristic
292C4⋊C16—591no—
293#357—591no—
294#357—591no—
295#357—591no—
296#357—591no—
297#357C2×D5911yescharacteristic
298#357C2×D5911yescharacteristic
299C22⋊C16—591no—
300C22⋊C16C2×D5911yescharacteristic
301C4×C16—591no—
302C59#3390111yescharacteristic, complemented, Sylow
303C2×#41—2361no—
304C2×#41—2361no—
305C2×D8—591no—
306C2×D8C22×D5911yescharacteristic
307C22×C8—591no—
308C22×C8C22×D5911yescharacteristic
309C4⋊Q8—1181no—
310C4⋊Q8—1181no—
311#123—2361no—
312#123—2361no—
313#123—2361no—
314#123—2361no—
315C22⋊Q8—2361no—
316C22⋊Q8—2361no—
317#121—21no—
318#121—1181no—
319#121—1181no—
320#121—1181no—
321C4×D4—591no—
322C4×D4—1181no—
323C4×D4—1181no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—1181no—
326C2×C4⋊C4—1181no—
327C2×C4⋊C4—1181no—
328D16—1182no—
329C2×C16—591no—
330C2×C16—591no—
331C2×C16—1182no—
332C2×C16—1182no—
333C2×C16C22×D5911yescharacteristic
334C2×C16C22×D5911yescharacteristic
335#107—21no—
336#107—591no—
337#107—591no—
338#107—591no—
339#107—1181no—
340#107—1181no—
341#107—1181no—
342#107—1181no—
343#107—1181no—
344#107C22×D5911yescharacteristic
345#107C22×D5911yescharacteristic
346#107C22×D5911yescharacteristic
347C4⋊C8—591no—
348#102—21no—
349#102—1181no—
350#102—1181no—
351#102—1181no—
352#102—1181no—
353#102—1181no—
354C22⋊C8—591no—
355C22⋊C8—591no—
356C4×C8—591no—
357#41—4724no—
358#41—4724no—
359C2×Q8—2361no—
360C2×Q8—2361no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—591no—
364C2×D4—1181no—
365C2×D4—2361no—
366C2×D4—2361no—
367C2×D4—2361no—
368C22×C4—41no—
369C22×C4—591no—
370C22×C4—2361no—
371C22×C4—2361no—
372C22×C4—2361no—
373C22×C4—2361no—
374C22×C4—2361no—
375C22×C4D4×D5911yescharacteristic
376D8—21no—
377D8—21no—
378D8—1181no—
379D8—1181no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—591no—
383C2×C8—591no—
384C2×C8—1181no—
385C2×C8—1181no—
386C2×C8D4×D5911yescharacteristic
387C2×C8C23×D5911yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—591no—
393C4⋊C4—1181no—
394C4⋊C4—1181no—
395C4⋊C4—1181no—
396C4⋊C4—2361no—
397C4⋊C4—2361no—
398C4⋊C4—2361no—
399C4⋊C4—2361no—
400C4⋊C4—2361no—
401C22⋊C4—41no—
402C22⋊C4—591no—
403C22⋊C4—591no—
404C22⋊C4—2361no—
405C22⋊C4—2361no—
406C22⋊C4—2361no—
407C22⋊C4—2361no—
408C22⋊C4—2361no—
409C42—591no—
410C16—21no—
411C16—21no—
412C16—592no—
413C16—1181no—
414C23—41no—
415C23—591no—
416C23—2361no—
417C23D8×D5911yescharacteristic
418Q8—4722no—
419Q8—4722no—
420D4—41no—
421D4—41no—
422D4—82no—
423D4—594no—
424D4—4722no—
425D4—4722no—
426D4—4722no—
427D4—2361no—
428D4—2361no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—591no—
436C2×C4—591no—
437C2×C4—591no—
438C2×C4—1181no—
439C2×C4—1181no—
440C2×C4—4722no—
441C2×C4—4722no—
442C2×C4—4722no—
443C2×C4—4722no—
444C2×C4—4722no—
445C2×C4—2361no—
446C2×C4—2361no—
447C2×C4—2361no—
448C2×C4D8×D5911yescharacteristic
449C2×C4C2×D4×D5911yescharacteristic
450C8—21no—
451C8—1181no—
452C8—1181no—
453C8#41×D5911yescharacteristic
454C8#1427377411yescharacteristic
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—592no—
461C22—1181no—
462C22—1181no—
463C22—4721no—
464C22—4721no—
465C22—4721no—
466C22D16×D5912yes—
467C22C2×D8×D5911yescharacteristic
468C4—21no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—592no—
473C4—1181no—
474C4—1181no—
475C4—4721no—
476C4—4721no—
477C4—4721no—
478C4#1683805011yescharacteristic
479C4#1683821811yescharacteristic
480C2—22no—
481C2—161no—
482C2—1182no—
483C2—9441no—
484C2#2143643811yescharacteristic
485C2C2×D16×D5911yescharacteristic
486C2#2143724811yescharacteristic
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2232C2
socleC22×C59C22×D8
hypercenter#2232D59
hypocenterC59#33901
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #21436441C2semidirect
2. #21436440C2semidirect
3. #21426370C2semidirect
4. #21426278C2semidirect
5. #21426277C2semidirect
6. #21426275C2semidirect
7. #21426232C2semidirect
8. #21426231C2semidirect
9. #21426181C2semidirect
10. #21426180C2semidirect
11. #21425940C2semidirect
12. (C22⋊D59)⋊C16C2semidirect
13. C2×#16837227C2semidirect
14. #366×D59C2semidirect
15. C59×#2232C2semidirect
169. C59⋊C16#41semidirect
187. C22⋊D59D16semidirect
243. #2232D59semidirect
302. C59#33901semidirect

Maximal subgroups

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

subgroupindex
#214364412
#214364402
#214263702
#214262782
#214262772
#214262752
#214262322
#214262312
#214261812
#214261802
#214259402
(C22⋊D59)⋊C162
C2×#168372272
#366×D592
C59×#22322
#3390159