Finite Group Databasebeta

← #28479582

Subgroups — #28479582

Order 15104.

804 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426602C211yesmaximal, characteristic
2#21423860C211yesmaximal, characteristic, complemented
3C2×#16837137C211yesmaximal, characteristic
4C2×#16837135C211yesmaximal, characteristic
5#95×Dic59C211yesmaximal, characteristic, complemented
6#21421974C211yesmaximal, characteristic, complemented
7C59×#1294C211yesmaximal, characteristic, complemented
8C2×#14273701C2211yescharacteristic
9C2×#14273689C411yescharacteristic, complemented
10C2×(C22⋊D59)⋊C4—21no—
11C22×C4×Dic59—21no—
12C22×C4×Dic59C2211yescharacteristic
13C2×C22⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273637—21no—
15#16837303C411yescharacteristic, complemented
16#16837298C411yescharacteristic, complemented
17#16837291—21no—
18#16837279—21no—
19C4⋊C4×Dic59C411yescharacteristic, complemented
20#16837249—21no—
21C2×C59⋊#95—21no—
22C2×C59⋊#95C2211yescharacteristic
23#16837156—21no—
24#16837137C414yescomplemented
25#16837135C414yescomplemented
26C2×C22⋊C8×C59C2211yescharacteristic
27C59×#380C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C22×D236C2×C411yescharacteristic
30C22×C22⋊D59—21no—
31C23×Dic59—21no—
32C23×Dic59D411yescharacteristic
33C23×Dic59D411yescharacteristic
34C22×C4×D59—21no—
35C22×C59⋊C8—21no—
36#14273701—21no—
37#14273701—21no—
38#14273701C2×C412yes—
39#14273701C2×C412yes—
40#14273689—42no—
41(C22⋊D59)⋊C4—42no—
42(C22⋊D59)⋊C4—42no—
43C2×C4⋊Dic59C2×C411yescharacteristic
44C2×Dic59⋊C4—21no—
45C2×(C2×D59)⋊C4—21no—
46C2×(C2×D59)⋊C4—21no—
47C2×(C2×D59)⋊C4—21no—
48C2×(C2×D59)⋊C4—21no—
49C2×C4×Dic59—24no—
50C2×C4×Dic59—21no—
51C2×C4×Dic59—42no—
52C2×C4×Dic59—42no—
53C2×C4×Dic59—42no—
54C2×C4×Dic59C2×C411yescharacteristic
55C2×C4×Dic59C2×C411yescharacteristic
56C2×C4×Dic59D411yescharacteristic
57C2×C4×Dic59D411yescharacteristic
58C22⋊(C59⋊C8)—21no—
59C22⋊(C59⋊C8)C2×C412yescomplemented
60#14273637—42no—
61C59⋊#95—24no—
62C59⋊#95—21no—
63C59⋊#95—21no—
64C59⋊#95—21no—
65C59⋊#95C2×C412yescomplemented
66C23×C4×C59—21no—
67C23×C4×C59C2311yescharacteristic
68C22×C8×C59—21no—
69C2×C4⋊C4×C59C2×C411yescharacteristic
70C2×C4⋊C4×C59C2×C411yescharacteristic
71C2×C22⋊C4×C59—21no—
72C22⋊C8×C59—21no—
73C22⋊C8×C59C2×C412yescomplemented
74#95×C59—21no—
75#95×C59—21no—
76#95×C59C2×C412yescomplemented
77C24×C59C2×D411yescharacteristic
78C23×D59—21no—
79C22×C4×C59—22no—
80C22×C4×C59—22no—
81C22×C4×C59—22no—
82C22×C4×C59—21no—
83C22×C4×C59—21no—
84C22×C4×C59—41no—
85C22×C4×C59—41no—
86C22×C4×C59—41no—
87C22×C4×C59—41no—
88C22×C4×C59—41no—
89C22×C4×C59—41no—
90C22×C4×C59C22×C411yescharacteristic
91C22×C4×C59C22×C411yescharacteristic
92C22×C4×C59C22×C411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59#4111yescharacteristic
95C22×C4×C59#4111yescharacteristic
96C2×C22⋊D59—22no—
97C2×C22⋊D59—22no—
98C2×C22⋊D59—41no—
99C2×C22⋊D59—41no—
100C2×C22⋊D59—41no—
101C2×C22⋊D59—41no—
102C22×Dic59—21no—
103C22×Dic59—21no—
104C22×Dic59—22no—
105C22×Dic59—22no—
106C22×Dic59—22no—
107C22×Dic59—22no—
108C22×Dic59—21no—
109C22×Dic59—22no—
110C22×Dic59—21no—
111C22×Dic59—21no—
112C22×Dic59—22no—
113C22×Dic59—41no—
114C22×Dic59—41no—
115C22×Dic59—41no—
116C22×Dic59—41no—
117C22×Dic59—41no—
118C22×Dic59C22⋊C411yescharacteristic
119C22×Dic59C22⋊C411yescharacteristic
120C22×Dic59C22⋊C411yescharacteristic
121C22×Dic59C22⋊C411yescharacteristic
122C2×D236—21no—
123C2×D236—41no—
124C2×D236—41no—
125C2×D236C4212yescomplemented
126C2×C4×D59—42no—
127C2×C4×D59—42no—
128C2×C4×D59—42no—
129C2×C8×C59—22no—
130C2×C8×C59—41no—
131C2×C8×C59—41no—
132C4⋊C4×C59—41no—
133C4⋊C4×C59—41no—
134C22⋊C4×C59—41no—
135C22⋊C4×C59—41no—
136(C2×D59)⋊C4—22no—
137(C2×D59)⋊C4—22no—
138(C2×D59)⋊C4—42no—
139(C2×D59)⋊C4—42no—
140(C2×D59)⋊C4—42no—
141C4⋊Dic59—21no—
142C4⋊Dic59C4212yescomplemented
143Dic59⋊C4—42no—
144C4×Dic59—22no—
145C4×Dic59—22no—
146C4×Dic59—41no—
147C4×Dic59—41no—
148C4×Dic59—48no—
149C4×Dic59—42no—
150C2×C59⋊C8—22no—
151C2×C59⋊C8—41no—
152C2×C59⋊C8—41no—
153C23×C59—21no—
154C23×C59—21no—
155C23×C59—21no—
156C23×C59—21no—
157C23×C59C2×C22⋊C411yescharacteristic
158C23×C59C4×D411yescharacteristic
159C23×C59C4×D411yescharacteristic
160C23×C59AGL(1,ℤ/8)11yescharacteristic
161C23×C59AGL(1,ℤ/8)11yescharacteristic
162C23×C59AGL(1,ℤ/8)11yescharacteristic
163C23×C59#13711yescharacteristic
164C22×D59—22no—
165C22×D59—41no—
166C22×D59—41no—
167C22×D59—41no—
168C22×D59—41no—
169C22×D59—41no—
170C22×D59—41no—
171C2×C4×C59—21no—
172C2×C4×C59—21no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
175C2×C4×C59—24no—
176C2×C4×C59—41no—
177C2×C4×C59—41no—
178C2×C4×C59—41no—
179C2×C4×C59—41no—
180C2×C4×C59—42no—
181C2×C4×C59—42no—
182C2×C4×C59—42no—
183C2×C4×C59—42no—
184C2×C4×C59—42no—
185C2×C4×C59—42no—
186C2×C4×C59—41no—
187C2×C4×C59—41no—
188C2×C4×C59—41no—
189C2×C4×C59—41no—
190C2×C4×C59—41no—
191C2×C4×C59—41no—
192C2×C4×C59C2×C4211yescharacteristic
193C2×C4×C59#11711yescharacteristic
194C2×C4×C59C4×D411yescharacteristic
195C2×C4×C59C4×D411yescharacteristic
196C22⋊D59—42no—
197C22⋊D59—42no—
198C22⋊D59—42no—
199C22⋊D59—42no—
200C2×Dic59—24no—
201C2×Dic59—24no—
202C2×Dic59—21no—
203C2×Dic59—21no—
204C2×Dic59—21no—
205C2×Dic59—21no—
206C2×Dic59—21no—
207C2×Dic59—21no—
208C2×Dic59—24no—
209C2×Dic59—22no—
210C2×Dic59—21no—
211C2×Dic59—21no—
212C2×Dic59—21no—
213C2×Dic59—42no—
214C2×Dic59—42no—
215C2×Dic59—42no—
216C2×Dic59—42no—
217C2×Dic59—42no—
218C2×Dic59—42no—
219C2×Dic59—42no—
220C2×Dic59—41no—
221C2×Dic59—41no—
222C2×Dic59—42no—
223C2×Dic59#9912yes—
224C2×Dic59#10412yes—
225C2×Dic59#10412yes—
226D236—42no—
227D236—42no—
228C4×D59—84no—
229C8×C59—42no—
230C59⋊C8—42no—
231#8218—591nomaximal, Sylow
232C22×C59—21no—
233C22×C59—21no—
234C22×C59—21no—
235C22×C59—21no—
236C22×C59—21no—
237C22×C59—21no—
238C22×C59—21no—
239C22×C59—21no—
240C22×C59—21no—
241C22×C59—21no—
242C22×C59—21no—
243C22×C59—21no—
244C22×C59C4×C22⋊C411yescharacteristic
245C22×C59C2×#9911yescharacteristic
246C22×C59#41011yescharacteristic
247C22×C59#41711yescharacteristic
248C22×C59#41811yescharacteristic
249C22×C59C2×#10411yescharacteristic
250C22×C59C2×#10411yescharacteristic
251C22×C59#44011yescharacteristic
252C22×C59#44011yescharacteristic
253C22×C59#44211yescharacteristic
254C22×C59#44211yescharacteristic
255C2×D59—42no—
256C2×D59—42no—
257C2×D59—42no—
258C2×D59—81no—
259C2×D59—81no—
260C2×D59—81no—
261C2×D59—81no—
262C4×C59—21no—
263C4×C59—21no—
264C4×C59—21no—
265C4×C59—21no—
266C4×C59—44no—
267C4×C59—81no—
268C4×C59—81no—
269Dic59—22no—
270Dic59—22no—
271Dic59—22no—
272Dic59—44no—
273Dic59—42no—
274Dic59—41no—
275C4×#121—591no—
276#1749—591no—
277C2×#327—591no—
278C2×#327—591no—
279C4×#95—591no—
280#1294—591no—
281#1294D5911yescharacteristic, complemented
282C2×C59—21no—
283C2×C59—21no—
284C2×C59—21no—
285C2×C59—21no—
286C2×C59#150411yescharacteristic
287C2×C59#150511yescharacteristic
288C2×C59#150711yescharacteristic
289C2×C59#150911yescharacteristic
290C2×C59C4×#9911yescharacteristic
291C2×C59C4×#10411yescharacteristic
292C2×C59#176211yescharacteristic
293D59—82no—
294C2×#121—591no—
295C2×C4×D4—591no—
296C2×C4×D4—1181no—
297C22×C42—591no—
298C22×C42—1181no—
299C2×C22⋊C8—591no—
300C2×C22⋊C8C2×D5911yescharacteristic
301C2×#97—1181no—
302#390—591no—
303#389—591no—
304#388—1181no—
305#386—1181no—
306#380C2×D5911yescharacteristic
307C4×C4⋊C4—591no—
308C4×C22⋊C4—1181no—
309C2×#95—591no—
310C2×#95—1181no—
311C2×#95C2×D5911yescharacteristic
312#336—1181no—
313#327—594no—
314#327—594no—
315C59#821811yescharacteristic, complemented, Sylow
316C22×D4—591no—
317C22×D4—1181no—
318C23×C4—21no—
319C23×C4—591no—
320C23×C4—591no—
321C23×C4—1181no—
322C23×C4—1181no—
323C23×C4C22×D5911yescharacteristic
324C22×C8—21no—
325C22×C8—1181no—
326#121—592no—
327#121—592no—
328#121—1181no—
329#121—1181no—
330C4×D4—2362no—
331C4×D4—2362no—
332C4×D4—2362no—
333C2×C4⋊C4—591no—
334C2×C4⋊C4—1181no—
335C2×C4⋊C4C4×D5911yescharacteristic
336C2×C4⋊C4C4×D5911yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—1181no—
339C2×C22⋊C4—1181no—
340C2×C22⋊C4—1181no—
341C2×C22⋊C4—1181no—
342C2×C42—591no—
343C2×C42—591no—
344C2×C42—591no—
345C2×C42—591no—
346C2×C42—1181no—
347C2×C42—1184no—
348C2×C42—2362no—
349C2×C42—2362no—
350C2×C42—2362no—
351C22⋊C8—21no—
352C22⋊C8—592no—
353C22⋊C8—1181no—
354C22⋊C8C4×D5912yescomplemented
355#97—2362no—
356#95—21no—
357#95—21no—
358#95—592no—
359#95—1181no—
360#95—1181no—
361#95—1184no—
362#95—1181no—
363#95C4×D5912yescomplemented
364C24—1181no—
365C24D4×D5911yescharacteristic
366C2×D4—592no—
367C2×D4—1182no—
368C2×D4—1182no—
369C2×D4—1181no—
370C2×D4—2361no—
371C2×D4—2361no—
372C2×D4—2361no—
373C2×D4—2361no—
374C2×D4—2361no—
375C2×D4—2361no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—591no—
388C22×C4—591no—
389C22×C4—591no—
390C22×C4—591no—
391C22×C4—1182no—
392C22×C4—1182no—
393C22×C4—1182no—
394C22×C4—1181no—
395C22×C4—1181no—
396C22×C4—1182no—
397C22×C4—1182no—
398C22×C4—1181no—
399C22×C4—1182no—
400C22×C4—1181no—
401C22×C4—1181no—
402C22×C4—2362no—
403C22×C4—2362no—
404C22×C4—2362no—
405C22×C4—2361no—
406C22×C4—2361no—
407C22×C4—2361no—
408C22×C4—2361no—
409C22×C4—2361no—
410C22×C4C2×C4×D5911yescharacteristic
411C22×C4C2×C4×D5911yescharacteristic
412C22×C4C2×C4×D5911yescharacteristic
413C22×C4D4×D5911yescharacteristic
414C22×C4#1174568711yescharacteristic
415C22×C4#1174568911yescharacteristic
416C2×C8—22no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—1182no—
420C2×C8—2361no—
421C2×C8—2361no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—592no—
425C4⋊C4—1181no—
426C4⋊C4—2362no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—1182no—
430C22⋊C4—1182no—
431C22⋊C4—2362no—
432C22⋊C4—2362no—
433C22⋊C4—2362no—
434C42—1182no—
435C42—1182no—
436C42—2361no—
437C42—2361no—
438C42—2368no—
439C42—2362no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—1182no—
445C23—2361no—
446C23—2361no—
447C23—2361no—
448C23—2361no—
449C23—2361no—
450C23—2361no—
451C23C22⋊C4×D5911yescharacteristic
452C23(C22⋊D59)⋊C411yescharacteristic
453C23#1427368911yescharacteristic
454C23#1427375111yescharacteristic
455C23#1427375411yescharacteristic
456C23#1427375411yescharacteristic
457C23#1427375911yescharacteristic
458D4—2362no—
459D4—2362no—
460D4—2362no—
461D4—2362no—
462D4—2362no—
463D4—2362no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—592no—
486C2×C4—592no—
487C2×C4—592no—
488C2×C4—1184no—
489C2×C4—1184no—
490C2×C4—1181no—
491C2×C4—1181no—
492C2×C4—1181no—
493C2×C4—1181no—
494C2×C4—1181no—
495C2×C4—1181no—
496C2×C4—1184no—
497C2×C4—1181no—
498C2×C4—1181no—
499C2×C4—1182no—
500C2×C4—1181no—
501C2×C4—4724no—
502C2×C4—2362no—
503C2×C4—2362no—
504C2×C4—2362no—
505C2×C4—2362no—
506C2×C4—2362no—
507C2×C4—2362no—
508C2×C4—2362no—
509C2×C4—2361no—
510C2×C4—2361no—
511C2×C4—2362no—
512C2×C4C42×D5911yescharacteristic
513C2×C4#1427368511yescharacteristic
514C2×C4(C22⋊D59)⋊C411yescharacteristic
515C2×C4#1427368911yescharacteristic
516C8—42no—
517C8—2362no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—4721no—
531C22—4721no—
532C22—4721no—
533C22—4721no—
534C22—2362no—
535C22—2362no—
536C22—2362no—
537C22#1683724911yescharacteristic
538C22#99×D5911yescharacteristic
539C22#1683737411yescharacteristic
540C22#1683740211yescharacteristic
541C22#1683740511yescharacteristic
542C22#104×D5911yescharacteristic
543C22#104×D5911yescharacteristic
544C22#1683750111yescharacteristic
545C22#1683750511yescharacteristic
546C22#1683751111yescharacteristic
547C22#1683751311yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—81no—
554C4—81no—
555C4—1182no—
556C4—1182no—
557C4—1182no—
558C4—2364no—
559C4—2361no—
560C4—2362no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—4722no—
566C2#2142259911yescharacteristic
567C2#2142260211yescharacteristic
568C2#2142261011yescharacteristic
569C2#2142262011yescharacteristic
570C2#2142388311yescharacteristic
571C2#2142390011yescharacteristic
572C2#2142392011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC59×#1294C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#14273701C22
cosocleC23×C4×C59C23
hypercenter#1294D59
hypocenterC59#8218
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #21423860C2semidirect
5. #95×Dic59C2semidirect
6. #21421974C2semidirect
7. C59×#1294C2semidirect
9. C2×#14273689C4semidirect
15. #16837303C4semidirect
16. #16837298C4semidirect
19. C4⋊C4×Dic59C4semidirect
24. #16837137C4semidirect
25. #16837135C4semidirect
59. C22⋊(C59⋊C8)C2×C4semidirect
65. C59⋊#95C2×C4semidirect
73. C22⋊C8×C59C2×C4semidirect
76. #95×C59C2×C4semidirect
125. C2×D236C42semidirect
142. C4⋊Dic59C42semidirect
281. #1294D59semidirect
315. C59#8218semidirect
354. C22⋊C8C4×D59semidirect
363. #95C4×D59semidirect

Maximal subgroups

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

subgroupindex
#214266022
#214238602
C2×#168371372
C2×#168371352
#95×Dic592
#214219742
C59×#12942
#821859