Finite Group Databasebeta

← #28600771

Subgroups — #28600771

Order 15104.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837705C211yesmaximal, characteristic
2C4×#14273718C211yesmaximal, characteristic, complemented
3#21426554C211yesmaximal, characteristic
4#21425050C211yesmaximal, characteristic, complemented
5#21424867C211yesmaximal, characteristic, complemented
6#21424830C211yesmaximal, characteristic, complemented
7#21424823C211yesmaximal, characteristic, complemented
8#21424780C211yesmaximal, characteristic
9#21424777C211yesmaximal, characteristic
10#21424723C211yesmaximal, characteristic
11#21424717C211yesmaximal, characteristic
12#21424678C211yesmaximal, characteristic, complemented
13#21424105C211yesmaximal, characteristic
14#21423944C211yesmaximal, characteristic, complemented
15C59×#1921C211yesmaximal, characteristic, complemented
16C2×#14273718C2211yescharacteristic
17C2×#14273689C2211yescharacteristic
18C2×#14273685—21no—
19#16837705C418yescomplemented
20C2×#14273661C2211yescharacteristic
21C2×#14273658C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×Dic59⋊C8C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×#14273649C2211yescharacteristic
26C2×#14273649C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×C8×Dic59C2211yescharacteristic
30C2×C8×Dic59C2211yescharacteristic
31#16837304C2211yescharacteristic
32#16837303C2211yescharacteristic
33#16837301C2211yescharacteristic
34#16837301C2211yescharacteristic
35#16837298C2211yescharacteristic
36#16837294—21no—
37#16837292—21no—
38#16837289—21no—
39#16837285—21no—
40#16837267C2211yescharacteristic
41C4⋊C4×Dic59C2211yescharacteristic
42C4×Dic59⋊C4—21no—
43C4×C4⋊Dic59—21no—
44C4×C4⋊Dic59C2211yescharacteristic
45#16837249—21no—
46C42×Dic59C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837157C2211yescharacteristic
53C2×#107×C59C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C4×C4⋊C4×C59C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C22×D236C2311yescharacteristic
61C22×C4×D59—21no—
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64#14273718—22no—
65#14273718C2×C414yes—
66#14273689—22no—
67#14273689C2×C414yes—
68#14273685—44no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×(C2×D59)⋊C4—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×C4×Dic59—21no—
83C2×C4×Dic59—21no—
84C2×C4×Dic59D411yescharacteristic
85C2×C4×Dic59D411yescharacteristic
86C2×C4×Dic59D411yescharacteristic
87C2×C4×Dic59D411yescharacteristic
88C2×C4×Dic59C2311yescharacteristic
89C2×C4×Dic59C2311yescharacteristic
90#14273661—41no—
91#14273658—41no—
92#14273658C2×C414yes—
93Dic59⋊C8—22no—
94Dic59⋊C8C2×C414yes—
95#14273649—41no—
96#14273649C2×C414yes—
97#14273647—41no—
98#14273647C2×C414yes—
99C8×Dic59—41no—
100C8×Dic59—41no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C42×C59—21no—
116C2×C42×C59C2311yescharacteristic
117#107×C59C2×C414yes—
118#95×C59—21no—
119#95×C59—21no—
120C23×D59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2×D411yescharacteristic
127C22×C4×C59C2411yescharacteristic
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59C2×D411yescharacteristic
132C22×Dic59C2×D411yescharacteristic
133C22×Dic59C2×D411yescharacteristic
134C22×Dic59C2×D411yescharacteristic
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236—21no—
140C2×D236C22×C412yes—
141C2×C4×D59—24no—
142C2×C4×D59—42no—
143C2×C4×D59—42no—
144C2×C8×C59—21no—
145C2×C8×C59—21no—
146C2×C8×C59—21no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59C22×C412yes—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—21no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—21no—
156C4⋊C4×C59—42no—
157C4⋊C4×C59C22×C412yes—
158C4⋊C4×C59C22×C412yes—
159C42×C59—21no—
160C42×C59—21no—
161C42×C59—42no—
162(C2×D59)⋊C4—24no—
163(C2×D59)⋊C4—42no—
164(C2×D59)⋊C4—42no—
165(C2×D59)⋊C4—42no—
166(C2×D59)⋊C4—42no—
167C4⋊Dic59—21no—
168C4⋊Dic59—24no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—42no—
174C4⋊Dic59—42no—
175C4⋊Dic59C22×C412yes—
176Dic59⋊C4—24no—
177Dic59⋊C4—42no—
178C4×Dic59—22no—
179C4×Dic59—21no—
180C4×Dic59—21no—
181C4×Dic59—22no—
182C4×Dic59—22no—
183C4×Dic59—41no—
184C4×Dic59—42no—
185C4×Dic59—42no—
186C4×Dic59C22×C412yes—
187C4×Dic59#4112yes—
188C2×C59⋊C8—21no—
189C2×C59⋊C8—21no—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8C22×C412yes—
194C23×C59C22×D411yescharacteristic
195C22×D59—22no—
196C22×D59—41no—
197C22×D59—41no—
198C22×D59—41no—
199C22×D59—41no—
200C22×D59—41no—
201C22×D59—41no—
202C2×C4×C59—21no—
203C2×C4×C59—21no—
204C2×C4×C59—22no—
205C2×C4×C59—22no—
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—21no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—41no—
213C2×C4×C59—41no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59#13512yes—
220C2×C4×C59C23×C411yescharacteristic
221C2×C4×C59C2×#4111yescharacteristic
222C2×C4×C59H(5,𝔽2)11yescharacteristic
223C2×C4×C592−1+411yescharacteristic
224C2×C4×C592−1+411yescharacteristic
225C2×C4×C592−1+411yescharacteristic
226C2×Dic59—21no—
227C2×Dic59—21no—
228C2×Dic59—21no—
229C2×Dic59—21no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—22no—
235C2×Dic59—41no—
236C2×Dic59—41no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59C4×D412yes—
244C2×Dic59C4×D412yes—
245C2×Dic59#13512yes—
246C2×Dic59AGL(1,ℤ/8)12yes—
247D236—22no—
248D236—22no—
249D236—41no—
250D236—41no—
251C4×D59—48no—
252C8×C59—22no—
253C8×C59—41no—
254C59⋊C8—22no—
255C59⋊C8—41no—
256#22114—591nomaximal, Sylow
257C22×C59C2×C4×D411yescharacteristic
258C22×C59#53611yescharacteristic
259C22×C59#53711yescharacteristic
260C22×C59C2×#13511yescharacteristic
261C22×C59C2×#13511yescharacteristic
262C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C59#57511yescharacteristic
264C2×D59—42no—
265C2×D59—42no—
266C2×D59—42no—
267C2×D59—81no—
268C2×D59—81no—
269C2×D59—81no—
270C2×D59—81no—
271C4×C59—22no—
272C4×C59—42no—
273C4×C59—42no—
274C4×C59—41no—
275C4×C59—81no—
276C4×C59—81no—
277C4×C59#51911yescharacteristic
278C4×C59#52011yescharacteristic
279C4×C59#54111yescharacteristic
280C4×C59#54211yescharacteristic
281Dic59—22no—
282Dic59—22no—
283Dic59—22no—
284Dic59—22no—
285Dic59—42no—
286Dic59—81no—
287Dic59—81no—
288C2×#478—591no—
289C4×#125—591no—
290#2293—591no—
291#1989—591no—
292#1949—591no—
293#1942—591no—
294#1941—591no—
295#1934—591no—
296#1934—591no—
297#1926—591no—
298#1925—591no—
299#1921D5911yescharacteristic, complemented
300#1920—591no—
301#1804—591no—
302C4×C4⋊C8—591no—
303C2×C59#232311yescharacteristic
304C2×C59C4×#13511yescharacteristic
305C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
306C2×C59#322811yescharacteristic
307C2×C59#323211yescharacteristic
308C2×C59#324711yescharacteristic
309C2×C59#325011yescharacteristic
310D59—82no—
311C2×#125—591no—
312C2×C4×D4—591no—
313C2×#117—1181no—
314#478—598no—
315C2×#107—591no—
316C2×#107C2×D5911yescharacteristic
317C2×#106—591no—
318C2×#106—591no—
319C2×C4⋊C8—591no—
320C2×C4⋊C8—591no—
321C2×#102—591no—
322C2×#102—591no—
323C2×#102—591no—
324C2×#102—591no—
325C2×C4×C8—591no—
326C2×C4×C8—591no—
327#390—591no—
328#390—591no—
329#389—591no—
330#389—591no—
331#389—591no—
332#389C2×D5911yescharacteristic
333#388—1181no—
334#388—1181no—
335#387—1181no—
336#387—1181no—
337#382—591no—
338C4×C4⋊C4—591no—
339C4×C4⋊C4—591no—
340C4×C4⋊C4—1181no—
341C4×C4⋊C4—1181no—
342C4×C4⋊C4C2×D5911yescharacteristic
343C4×C22⋊C4—1181no—
344C43—591no—
345#340—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#340C2×D5911yescharacteristic
351#340C2×D5911yescharacteristic
352#340C2×D5911yescharacteristic
353#336—591no—
354#336C2×D5911yescharacteristic
355C59#2211411yescharacteristic, complemented, Sylow
356C22×D4—591no—
357C23×C4—1181no—
358C22×C8—591no—
359C22×C8—591no—
360C22×C8C22×D5911yescharacteristic
361C22×C8C22×D5911yescharacteristic
362#125—594no—
363#125—1182no—
364C4×D4—594no—
365C4×D4—1182no—
366#117—2364no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—591no—
369C2×C4⋊C4—591no—
370C2×C4⋊C4—591no—
371C2×C4⋊C4—1181no—
372C2×C4⋊C4—1181no—
373C2×C4⋊C4—1181no—
374C2×C4⋊C4—1181no—
375C2×C4⋊C4—1181no—
376C2×C4⋊C4C22×D5911yescharacteristic
377C2×C4⋊C4C22×D5911yescharacteristic
378C2×C4⋊C4C22×D5911yescharacteristic
379C2×C4⋊C4C22×D5911yescharacteristic
380C2×C22⋊C4—1181no—
381C2×C22⋊C4—1181no—
382C2×C22⋊C4—1181no—
383C2×C22⋊C4—1181no—
384C2×C22⋊C4—1181no—
385C2×C42—21no—
386C2×C42—591no—
387C2×C42—591no—
388C2×C42—591no—
389C2×C42—591no—
390C2×C42—591no—
391C2×C42—591no—
392C2×C42—1181no—
393C2×C42—1181no—
394C2×C42C22×D5911yescharacteristic
395#107—2361no—
396#107C4×D5914yes—
397#106—594no—
398#106—2361no—
399C4⋊C8—594no—
400C4⋊C8—1182no—
401#102—594no—
402#102—594no—
403#102—2361no—
404#102—2361no—
405C4×C8—2361no—
406C4×C8—2361no—
407#95—21no—
408#95—21no—
409#95—1181no—
410#95—1181no—
411#95—1181no—
412#95—1181no—
413#95—1181no—
414#95—1181no—
415#95—1181no—
416C24—1181no—
417C2×D4—592no—
418C2×D4—1181no—
419C2×D4—1181no—
420C2×D4—1181no—
421C2×D4—1181no—
422C2×D4—1181no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—591no—
428C22×C4—591no—
429C22×C4—591no—
430C22×C4—591no—
431C22×C4—1184no—
432C22×C4—1181no—
433C22×C4—1181no—
434C22×C4—1181no—
435C22×C4—2362no—
436C22×C4—2362no—
437C22×C4D4×D5911yescharacteristic
438C22×C4D4×D5911yescharacteristic
439C22×C4C23×D5911yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—592no—
446C2×C8—1181no—
447C2×C8—1181no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8—1181no—
451C2×C8C2×C4×D5912yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—592no—
460C4⋊C4—1184no—
461C4⋊C4—1184no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—2362no—
468C4⋊C4—2362no—
469C4⋊C4—2362no—
470C4⋊C4C2×C4×D5912yes—
471C4⋊C4C2×C4×D5912yes—
472C22⋊C4—1184no—
473C22⋊C4—2362no—
474C22⋊C4—2362no—
475C22⋊C4—2362no—
476C22⋊C4—2362no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—592no—
481C42—592no—
482C42—1182no—
483C42—1182no—
484C42—1182no—
485C42—1181no—
486C42—1181no—
487C42—2361no—
488C42—2362no—
489C42—2362no—
490C23—1182no—
491C23—2361no—
492C23—2361no—
493C23—2361no—
494C23—2361no—
495C23—2361no—
496C23—2361no—
497C23C2×D4×D5911yescharacteristic
498D4—1182no—
499D4—1182no—
500D4—2361no—
501D4—2361no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—592no—
520C2×C4—592no—
521C2×C4—592no—
522C2×C4—592no—
523C2×C4—1181no—
524C2×C4—1181no—
525C2×C4—1181no—
526C2×C4—1181no—
527C2×C4—1181no—
528C2×C4—1181no—
529C2×C4—1181no—
530C2×C4—1181no—
531C2×C4—1182no—
532C2×C4—2368no—
533C2×C4—2361no—
534C2×C4—2361no—
535C2×C4—2361no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4—2361no—
539C2×C4—2361no—
540C2×C4—2361no—
541C2×C4#1427375012yes—
542C2×C4C22×C4×D5911yescharacteristic
543C2×C4#41×D5911yescharacteristic
544C2×C4#1427377311yescharacteristic
545C2×C4#1427377411yescharacteristic
546C2×C4#1427377411yescharacteristic
547C2×C4#1427377511yescharacteristic
548C8—22no—
549C8—41no—
550C8—1182no—
551C8—2361no—
552C22—4721no—
553C22—4721no—
554C22—4721no—
555C22—4721no—
556C22—2362no—
557C22—2362no—
558C22—2362no—
559C22C4×D4×D5911yescharacteristic
560C22#1683797411yescharacteristic
561C22#1683798211yescharacteristic
562C22#135×D5911yescharacteristic
563C22C2×#1427375011yescharacteristic
564C22AGL(1,ℤ/8)×D5911yescharacteristic
565C22#1683819811yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—1182no—
573C4—1182no—
574C4—1182no—
575C4—1182no—
576C4—4721no—
577C4—4721no—
578C4—2362no—
579C4#1683787811yescharacteristic
580C4#1683788211yescharacteristic
581C4#1683801111yescharacteristic
582C4#1683801811yescharacteristic
583C2—4722no—
584C2#2142677711yescharacteristic
585C2C4×#1427375011yescharacteristic
586C2#2143290711yescharacteristic
587C2#2143523011yescharacteristic
588C2#2143526911yescharacteristic
589C2#2143542511yescharacteristic
590C2#2143544711yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1921C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenter#1921D59
hypocenterC59#22114
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
2. C4×#14273718C2semidirect
4. #21425050C2semidirect
5. #21424867C2semidirect
6. #21424830C2semidirect
7. #21424823C2semidirect
12. #21424678C2semidirect
14. #21423944C2semidirect
15. C59×#1921C2semidirect
19. #16837705C4semidirect
299. #1921D59semidirect
355. C59#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#168377052
C4×#142737182
#214265542
#214250502
#214248672
#214248302
#214248232
#214247802
#214247772
#214247232
#214247172
#214246782
#214241052
#214239442
C59×#19212
#2211459