Finite Group Databasebeta

← #28743619

Subgroups — #28743619

Order 15104.

610 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434679C211yesmaximal, characteristic, complemented
2C4×D8×D59C211yesmaximal, characteristic
3#21426295C211yesmaximal, characteristic, complemented
4#21426292C211yesmaximal, characteristic, complemented
5#21426242C211yesmaximal, characteristic, complemented
6#21426241C211yesmaximal, characteristic, complemented
7#21426140C211yesmaximal, characteristic, complemented
8#21426139C211yesmaximal, characteristic, complemented
9#21426026C211yesmaximal, characteristic
10#21426023C211yesmaximal, characteristic
11C4×#14273672C211yesmaximal, characteristic, complemented
12C4×#14273670C211yesmaximal, characteristic, complemented
13C4×#14273671C211yesmaximal, characteristic, complemented
14#21425893C211yesmaximal, characteristic, complemented
15C4×SD32×C59C211yesmaximal, characteristic, complemented
16C2×D8×D59C2211yescharacteristic
17#16837956—21no—
18C4×D4×D59—21no—
19C2×#14273672C2211yescharacteristic
20C2×#14273671C2211yescharacteristic
21C2×#14273670C2211yescharacteristic
22#16837806C2211yescharacteristic, complemented
23#16837780C2211yescharacteristic, complemented
24#16837751—21no—
25#16837644C2211yescharacteristic
26#16837642—21no—
27#16837640C2211yescharacteristic
28C4×Dic236C2211yescharacteristic, complemented
29C4×#11745672—21no—
30C4×D472C2211yescharacteristic
31D8×Dic59C2211yescharacteristic
32#16837484C2211yescharacteristic
33C4×#11745669—21no—
34#16837482—21no—
35#107×D59C2211yescharacteristic
36#102×D59—21no—
37C4×C8×D59C2211yescharacteristic
38#16837230C2211yescharacteristic, complemented
39#16837229C2211yescharacteristic, complemented
40#16837229C2211yescharacteristic, complemented
41Dic59⋊C16C2211yescharacteristic, complemented
42Dic59⋊C16C2211yescharacteristic, complemented
43#16837207C2211yescharacteristic, complemented
44#16837206C2211yescharacteristic, complemented
45#16837205C2211yescharacteristic, complemented
46#16837204C2211yescharacteristic
47#16837203C2211yescharacteristic
48#16837202C2211yescharacteristic
49(C2×D59)⋊C16C2211yescharacteristic
50(C2×D59)⋊C16C2211yescharacteristic
51C4×C59⋊C16C2211yescharacteristic, complemented
52C2×SD32×C59C2211yescharacteristic
53C4×Q16×C59C2211yescharacteristic, complemented
54C4×D8×C59C2211yescharacteristic
55C59×#367C2211yescharacteristic, complemented
56C59×#358C2211yescharacteristic, complemented
57C59×#357C2211yescharacteristic
58C4×C16×C59C2211yescharacteristic, complemented
59C2×D4×D59—21no—
60C22×C4×D59—41no—
61C2×Dic236C2311yescharacteristic
62C2×#11745672—21no—
63C2×D472C2311yescharacteristic
64C2×#11745669—21no—
65D8×D59—22no—
66D8×D59—22no—
67C2×C8×D59D411yescharacteristic
68C2×C8×D59C2311yescharacteristic
69#14273726—21no—
70#14273725—21no—
71#14273717—41no—
72#14273707—21no—
73#14273705—41no—
74#14273703—21no—
75C4×Dic118—21no—
76C4×Dic118—41no—
77C4×D236—21no—
78D4×Dic59—21no—
79#14273689—21no—
80C4×C22⋊D59—41no—
81(C22⋊D59)⋊C4—41no—
82#14273684—41no—
83C4⋊C4×D59—21no—
84C22⋊C4×D59—41no—
85C42×D59D411yescharacteristic
86#14273672—22no—
87#14273671—22no—
88#14273670—22no—
89C2×C59⋊C16C2311yescharacteristic
90C2×C59⋊C16C2311yescharacteristic
91#14273661C2311yescharacteristic
92#14273661C2311yescharacteristic
93#14273660—21no—
94#14273660—21no—
95#14273652—21no—
96#14273651—21no—
97#14273650—21no—
98#14273649—21no—
99#14273648—21no—
100#14273647—21no—
101C4×C59⋊C8D411yescharacteristic
102C8×Dic59D411yescharacteristic
103C8×Dic59C2311yescharacteristic
104C2×Q16×C59C2311yescharacteristic
105C2×D8×C59C2311yescharacteristic
106C4×Q8×C59—21no—
107C4×D4×C59—21no—
108SD32×C59—22no—
109C2×C16×C59C2311yescharacteristic
110C2×C16×C59C2311yescharacteristic
111#107×C59C2311yescharacteristic
112#107×C59C2311yescharacteristic
113#103×C59—21no—
114#102×C59—21no—
115C4×C8×C59C2311yescharacteristic
116C23×D59—41no—
117C2×Q8×C59—21no—
118C2×D4×C59—21no—
119C22×C4×C59—41no—
120C2×C22⋊D59—41no—
121C22×Dic59—41no—
122D4×D59—24no—
123D4×D59—42no—
124C2×D236—21no—
125C2×C4×D59—41no—
126C2×C4×D59—41no—
127C2×C4×D59—41no—
128C2×C4×D59—84no—
129C2×C4×D59D811yescharacteristic
130C2×C4×D59D811yescharacteristic
131C2×C4×D59C2×D411yescharacteristic
132C2×Dic118—21no—
133C2×Dic118—41no—
134Q16×C59—21no—
135Q16×C59—21no—
136D8×C59—21no—
137D8×C59#4112yes—
138C2×C8×C59C2×D411yescharacteristic
139C2×C8×C59C2411yescharacteristic
140C4⋊C4×C59—21no—
141C4⋊C4×C59—21no—
142C4⋊C4×C59—41no—
143C22⋊C4×C59—41no—
144C42×C59—41no—
145C42×C59C2×D411yescharacteristic
146C22⋊Dic59—41no—
147#11745672—42no—
148#11745669—24no—
149(C2×D59)⋊C4—41no—
150(C2×D59)⋊C4—41no—
151(C2×D59)⋊C4—41no—
152(C2×D59)⋊C4—41no—
153C4⋊Dic59—21no—
154C4⋊Dic59—21no—
155C4⋊Dic59—41no—
156Dic59⋊C4—41no—
157Dic59⋊C4—41no—
158Dic59⋊C4—41no—
159Dic59⋊C4—41no—
160Dic59⋊C4—41no—
161Dic59⋊C4—41no—
162C4×Dic59—41no—
163C4×Dic59D811yescharacteristic
164C4×Dic59D811yescharacteristic
165C4×Dic59C2×D411yescharacteristic
166C2×C59⋊C8C2×D411yescharacteristic
167C2×C59⋊C8C2×D411yescharacteristic
168Dic236—21no—
169Dic236—21no—
170D472—21no—
171D472#4112yes—
172C8×D59—21no—
173C8×D59—21no—
174C8×D59—41no—
175C16×C59—21no—
176C16×C59—21no—
177C59⋊C16—21no—
178C59⋊C16—21no—
179C23×C59—41no—
180C22×D59—44no—
181C22×D59—41no—
182C22×D59—82no—
183C22×D59—82no—
184C22×D59C2×D811yescharacteristic
185Q8×C59—41no—
186Q8×C59—41no—
187D4×C59—22no—
188D4×C59—41no—
189C2×C4×C59—41no—
190C2×C4×C59—41no—
191C2×C4×C59—41no—
192C2×C4×C59—82no—
193C2×C4×C59C2×D811yescharacteristic
194C2×C4×C59C2×D811yescharacteristic
195C2×C4×C59C22×D411yescharacteristic
196C22⋊D59—44no—
197C2×Dic59—41no—
198C2×Dic59—41no—
199C2×Dic59—41no—
200C2×Dic59—82no—
201C2×Dic59C2×D811yescharacteristic
202C2×Dic59C2×D811yescharacteristic
203C2×Dic59C2×D811yescharacteristic
204D236—22no—
205D236—41no—
206C4×D59—21no—
207C4×D59—21no—
208C4×D59—41no—
209C4×D59—82no—
210C4×D59—82no—
211C4×D59—82no—
212C4×D59SD3214yescomplemented
213Dic118—41no—
214Dic118—41no—
215Dic118—82no—
216C8×C59—21no—
217C8×C59C2×#4111yescharacteristic
218C8×C59C2×#4111yescharacteristic
219C59⋊C8—21no—
220C59⋊C8—21no—
221#33661—591nomaximal, Sylow
222C22×C59—42no—
223C22×C59—81no—
224C22×C59—81no—
225C22×C59C22×D811yescharacteristic
226C2×D59—21no—
227C2×D59—21no—
228C2×D59—42no—
229C2×D59—88no—
230C2×D59—81no—
231C2×D59—81no—
232C2×D59C2×SD3212yes—
233C4×C59—21no—
234C4×C59—81no—
235C4×C59—81no—
236C4×C59—81no—
237C4×C59C2×SD3212yes—
238C4×C59#52511yescharacteristic
239C4×C59#57511yescharacteristic
240Dic59—21no—
241Dic59—21no—
242Dic59—81no—
243Dic59—81no—
244Dic59—81no—
245Dic59C2×SD3212yes—
246#3170—591no—
247C2×C4×D8—591no—
248#2235—591no—
249#2235—591no—
250#2226—591no—
251#2226—591no—
252#2208—591no—
253#2208—591no—
254#2187—591no—
255#2187—591no—
256C4×SD32—591no—
257C4×SD32—591no—
258C4×SD32—591no—
259C4×SD32D5911yescharacteristic, complemented
260#2162—591no—
261C2×C59—82no—
262C2×C59#310011yescharacteristic
263C2×C59C22×SD3211yescharacteristic
264C2×C59#341411yescharacteristic
265D59—22no—
266D59—82no—
267C22×D8—591no—
268#533—1181no—
269C2×C4×D4—1181no—
270C2×SD32—591no—
271C2×SD32—591no—
272C2×SD32—591no—
273C2×SD32C2×D5911yescharacteristic
274#500—591no—
275#494—591no—
276#487—1181no—
277#467—591no—
278#467—591no—
279#467—1181no—
280C4×Q16—591no—
281C4×Q16—1181no—
282C4×Q16C2×D5911yescharacteristic, complemented
283C4×D8—591no—
284C4×D8—591no—
285C4×D8—591no—
286C4×D8—1181no—
287C4×D8—1181no—
288C4×D8C2×D5911yescharacteristic
289C2×#107—591no—
290C2×#102—1181no—
291C2×C4×C8—591no—
292#367—591no—
293#367—591no—
294#367—591no—
295#367C2×D5911yescharacteristic, complemented
296C4⋊C16—591no—
297C4⋊C16—591no—
298#358—591no—
299#358—591no—
300#358—591no—
301#358C2×D5911yescharacteristic, complemented
302#357—591no—
303#357—591no—
304#357—591no—
305#357C2×D5911yescharacteristic
306C22⋊C16—591no—
307C22⋊C16—591no—
308C4×C16—591no—
309C4×C16C2×D5911yescharacteristic, complemented
310C59#3366111yescharacteristic, complemented, Sylow
311C22×D4—1181no—
312C23×C4—2361no—
313C2×Q16—591no—
314C2×Q16—1181no—
315C2×Q16C22×D5911yescharacteristic
316C2×D8—591no—
317C2×D8—1181no—
318C2×D8—1182no—
319C2×D8—1182no—
320C2×D8C22×D5911yescharacteristic
321C22×C8—591no—
322C22×C8—591no—
323C4⋊Q8—1181no—
324C4⋊Q8—1181no—
325#125—2361no—
326C22⋊Q8—1181no—
327C22⋊Q8—1181no—
328C22⋊Q8—2361no—
329C4×Q8—21no—
330C4×Q8—1181no—
331C4×Q8—2361no—
332C4×D4—21no—
333C4×D4—1181no—
334C4×D4—1181no—
335C4×D4—1181no—
336C4×D4—2361no—
337C4×D4—2361no—
338#117—2361no—
339C2×C4⋊C4—1181no—
340C2×C22⋊C4—2361no—
341C2×C42—591no—
342SD32—22no—
343SD32—1182no—
344SD32—1182no—
345SD32—1182no—
346C2×C16—591no—
347C2×C16—591no—
348C2×C16C22×D5911yescharacteristic
349C2×C16C22×D5911yescharacteristic
350#107—591no—
351#107—591no—
352#107—1181no—
353#107—1181no—
354#107C22×D5911yescharacteristic
355#107C22×D5911yescharacteristic
356#103—21no—
357#103—1181no—
358#103—1181no—
359#103—1181no—
360#102—21no—
361#102—1181no—
362#102—1181no—
363#102—1181no—
364C4×C8—591no—
365C4×C8—591no—
366C4×C8—591no—
367C4×C8C22×D5911yescharacteristic
368C24—2361no—
369C2×Q8—21no—
370C2×Q8—1181no—
371C2×Q8—2361no—
372C2×D4—21no—
373C2×D4—1184no—
374C2×D4—1181no—
375C2×D4—2361no—
376C2×D4—2362no—
377C22×C4—41no—
378C22×C4—591no—
379C22×C4—591no—
380C22×C4—591no—
381C22×C4—4724no—
382C22×C4—2361no—
383C22×C4—2361no—
384C22×C4—2361no—
385C22×C4—2361no—
386Q16—21no—
387Q16—21no—
388Q16—1181no—
389Q16—1181no—
390Q16—2362no—
391D8—21no—
392D8—592no—
393D8—1184no—
394D8—1181no—
395D8#1174568512yes—
396C2×C8—591no—
397C2×C8—591no—
398C2×C8—1181no—
399C2×C8—1181no—
400C2×C8—2361no—
401C2×C8D4×D5911yescharacteristic
402C2×C8C23×D5911yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—1181no—
407C4⋊C4—1181no—
408C4⋊C4—2361no—
409C4⋊C4—2361no—
410C4⋊C4—2361no—
411C4⋊C4—2361no—
412C4⋊C4—2361no—
413C4⋊C4—2361no—
414C4⋊C4—2361no—
415C22⋊C4—41no—
416C22⋊C4—2361no—
417C22⋊C4—2361no—
418C22⋊C4—2361no—
419C22⋊C4—2361no—
420C22⋊C4—2361no—
421C42—41no—
422C42—591no—
423C42—591no—
424C42—591no—
425C42—2361no—
426C42D4×D5911yescharacteristic
427C16—21no—
428C16—21no—
429C16—1181no—
430C16—1181no—
431C23—41no—
432C23—591no—
433C23—4722no—
434C23—4722no—
435C23—2364no—
436C23—2361no—
437Q8—41no—
438Q8—41no—
439Q8—4722no—
440Q8—2361no—
441Q8—2361no—
442D4—22no—
443D4—41no—
444D4—1182no—
445D4—2364no—
446D4—2361no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—82no—
451C2×C4—591no—
452C2×C4—594no—
453C2×C4—591no—
454C2×C4—591no—
455C2×C4—1181no—
456C2×C4—1181no—
457C2×C4—4722no—
458C2×C4—4722no—
459C2×C4—4722no—
460C2×C4—4722no—
461C2×C4—2361no—
462C2×C4—2361no—
463C2×C4—2361no—
464C2×C4—2361no—
465C2×C4D8×D5911yescharacteristic
466C2×C4D8×D5911yescharacteristic
467C2×C4C2×D4×D5911yescharacteristic
468C8—21no—
469C8—1181no—
470C8—1181no—
471C8#41×D5911yescharacteristic
472C8C2×#1174568511yescharacteristic
473C22—42no—
474C22—81no—
475C22—81no—
476C22—592no—
477C22—1181no—
478C22—1181no—
479C22—4728no—
480C22—4721no—
481C22—4721no—
482C22—2362no—
483C22C2×D8×D5911yescharacteristic
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—592no—
489C4—1181no—
490C4—1181no—
491C4—4721no—
492C4—4721no—
493C4—4721no—
494C4SD32×D5912yes—
495C4#1683791111yescharacteristic
496C4#1683819911yescharacteristic
497C2—82no—
498C2—1182no—
499C2—4722no—
500C2#2143409411yescharacteristic
501C2C2×SD32×D5911yescharacteristic
502C2#2143722911yescharacteristic
subgroupG/H
centerC2×C4D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC4×SD32×C59C2
socleC22×C59C22×D8
prime radicalC2×D8×D59C22
hypercenterC4×SD32D59
hypocenterC59#33661
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #21434679C2semidirect
3. #21426295C2semidirect
4. #21426292C2semidirect
5. #21426242C2semidirect
6. #21426241C2semidirect
7. #21426140C2semidirect
8. #21426139C2semidirect
11. C4×#14273672C2semidirect
12. C4×#14273670C2semidirect
13. C4×#14273671C2semidirect
14. #21425893C2semidirect
15. C4×SD32×C59C2semidirect
22. #16837806C22semidirect
23. #16837780C22semidirect
28. C4×Dic236C22semidirect
38. #16837230C22semidirect
39. #16837229C22semidirect
40. #16837229C22semidirect
41. Dic59⋊C16C22semidirect
42. Dic59⋊C16C22semidirect
43. #16837207C22semidirect
44. #16837206C22semidirect
45. #16837205C22semidirect
51. C4×C59⋊C16C22semidirect
53. C4×Q16×C59C22semidirect
55. C59×#367C22semidirect
56. C59×#358C22semidirect
58. C4×C16×C59C22semidirect
212. C4×D59SD32semidirect
259. C4×SD32D59semidirect
282. C4×Q16C2×D59semidirect
295. #367C2×D59semidirect
301. #358C2×D59semidirect
309. C4×C16C2×D59semidirect
310. C59#33661semidirect

Maximal subgroups

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

subgroupindex
#214346792
C4×D8×D592
#214262952
#214262922
#214262422
#214262412
#214261402
#214261392
#214260262
#214260232
C4×#142736722
C4×#142736702
C4×#142736712
#214258932
C4×SD32×C592
#3366159