Finite Group Databasebeta

← #28593585

Subgroups — #28593585

Order 15104.

850 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837458C211yesmaximal, characteristic
2#21426489C211yesmaximal, characteristic
3C4×#14273685C211yesmaximal, characteristic
4#21424866C211yesmaximal, characteristic, complemented
5#21424864C211yesmaximal, characteristic, complemented
6#21424862C211yesmaximal, characteristic, complemented
7#21424298C211yesmaximal, characteristic
8#21424296C211yesmaximal, characteristic
9#21424294C211yesmaximal, characteristic
10#21424292C211yesmaximal, characteristic
11#21423996C211yesmaximal, characteristic, complemented
12#21423995C211yesmaximal, characteristic, complemented
13#21423992C211yesmaximal, characteristic, complemented
14#21423992C211yesmaximal, characteristic, complemented
15C59×#1949C211yesmaximal, characteristic, complemented
16C2×#14273685C2211yescharacteristic
17C2×#14273685C2211yescharacteristic
18C2×C42×D59C2211yescharacteristic
19#16837458C418yescomplemented
20C2×#14273661C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×#14273637C2211yescharacteristic
30C2×#14273637C2211yescharacteristic
31#16837269—21no—
32#16837268C2211yescharacteristic
33#16837264—21no—
34#16837259C2211yescharacteristic
35#16837259C2211yescharacteristic
36C4⋊C4×Dic59C2211yescharacteristic
37C4⋊C4×Dic59C2211yescharacteristic
38C4⋊C4×Dic59C2211yescharacteristic
39C4⋊C4×Dic59C2211yescharacteristic
40C4×C4⋊Dic59C2211yescharacteristic
41C4×(C2×D59)⋊C4—21no—
42#16837249—21no—
43#16837249—21no—
44#16837247—21no—
45#16837247—21no—
46C42×Dic59—21no—
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53C2×#107×C59C2211yescharacteristic
54C2×#106×C59C2211yescharacteristic
55C2×C4⋊C8×C59C2211yescharacteristic
56C59×#382C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C22×C4×D59D411yescharacteristic
61C22×C4×D59D411yescharacteristic
62C22×C4×D59C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65#14273685—22no—
66#14273685—22no—
67#14273685—22no—
68#14273685—22no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×(C2×D59)⋊C4—21no—
74C2×(C2×D59)⋊C4—21no—
75C2×(C2×D59)⋊C4—21no—
76C2×(C2×D59)⋊C4—21no—
77C2×C4×Dic59—21no—
78C2×C4×Dic59—21no—
79C2×C4×Dic59—21no—
80C2×C4×Dic59—21no—
81C2×C4×Dic59—21no—
82C2×C4×Dic59—21no—
83C2×C4×Dic59—21no—
84C2×C4×Dic59D411yescharacteristic
85C2×C4×Dic59D411yescharacteristic
86C2×C4×Dic59C2311yescharacteristic
87C42×D59C2×C414yes—
88C42×D59Q814yes—
89#14273661—22no—
90#14273660—22no—
91#14273660—22no—
92#14273659—22no—
93#14273658—22no—
94#14273658—22no—
95C4⋊(C59⋊C8)C2×C414yes—
96(C2×D59)⋊C8C2×C414yes—
97(C2×D59)⋊C8C2×C414yes—
98#14273637C2×C414yes—
99#14273637C2×C414yes—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
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×C59—22no—
118#106×C59—22no—
119C4⋊C8×C59C2×C414yes—
120#95×C59—21no—
121#95×C59—21no—
122#95×C59—21no—
123C23×D59C2×D411yescharacteristic
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2411yescharacteristic
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C22×Dic59—21no—
135C22×Dic59C2×D411yescharacteristic
136C22×Dic59C2×D411yescharacteristic
137C22×Dic59C2×D411yescharacteristic
138C2×C4×D59—21no—
139C2×C4×D59—21no—
140C2×C4×D59—21no—
141C2×C4×D59—21no—
142C2×C4×D59—41no—
143C2×C4×D59—41no—
144C2×C4×D59—41no—
145C2×C4×D59—41no—
146C2×C4×D59C4⋊C414yes—
147C2×C4×D59C4⋊C414yes—
148C2×C4×D59C22×C412yes—
149C2×C4×D59C2×Q812yes—
150C2×C8×C59—21no—
151C2×C8×C59—21no—
152C2×C8×C59—21no—
153C2×C8×C59—21no—
154C2×C8×C59C22×C412yes—
155C2×C8×C59C22×C412yes—
156C4⋊C4×C59—21no—
157C4⋊C4×C59—21no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59#4112yes—
163C4⋊C4×C59#4112yes—
164C42×C59—42no—
165C42×C59C22×C412yes—
166C42×C59C2×Q812yes—
167(C2×D59)⋊C4—24no—
168(C2×D59)⋊C4—24no—
169(C2×D59)⋊C4—42no—
170(C2×D59)⋊C4—42no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59—21no—
177C4⋊Dic59#4112yes—
178C4⋊Dic59#4112yes—
179C4×Dic59—24no—
180C4×Dic59—24no—
181C4×Dic59—42no—
182C4×Dic59—42no—
183C4×Dic59—42no—
184C4×Dic59—42no—
185C4×Dic59—42no—
186C4×Dic59C4⋊C414yes—
187C4×Dic59C4⋊C414yes—
188C4×Dic59C22×C412yes—
189C4×Dic59C2×Q812yes—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8C22×C412yes—
195C2×C59⋊C8C22×C412yes—
196C23×C59C22×D411yescharacteristic
197C22×D59—21no—
198C22×D59—21no—
199C22×D59—21no—
200C22×D59—21no—
201C22×D59—21no—
202C22×D59—21no—
203C22×D59C2×C4⋊C412yes—
204C2×C4×C59—21no—
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
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—41no—
220C2×C4×C59C2×C4⋊C412yes—
221C2×C4×C59C2×C4⋊C412yes—
222C2×C4×C59C23×C411yescharacteristic
223C2×C4×C59C22×Q811yescharacteristic
224C2×C4×C59C2×#4111yescharacteristic
225C2×C4×C59C2×#4111yescharacteristic
226C2×C4×C59C2×#4111yescharacteristic
227C2×C4×C59C2×#4111yescharacteristic
228C2×Dic59—21no—
229C2×Dic59—21no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—22no—
235C2×Dic59—22no—
236C2×Dic59—41no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59C2×C4⋊C412yes—
247C2×Dic59C2×C4⋊C412yes—
248C2×Dic59C2×C4⋊C412yes—
249C4×D59—22no—
250C4×D59—22no—
251C4×D59—22no—
252C4×D59—22no—
253C4×D59—44no—
254C4×D59—44no—
255C8×C59—22no—
256C8×C59—22no—
257C59⋊C8—22no—
258C59⋊C8—22no—
259#21366—591nomaximal, Sylow
260C22×C59C22×C4⋊C411yescharacteristic
261C22×C59#52511yescharacteristic
262C22×C59#52511yescharacteristic
263C22×C59#57511yescharacteristic
264C22×C59#57511yescharacteristic
265C22×C59#57511yescharacteristic
266C22×C59#57511yescharacteristic
267C2×D59—22no—
268C2×D59—22no—
269C2×D59—22no—
270C2×D59—41no—
271C2×D59—41no—
272C2×D59—41no—
273C2×D59—41no—
274C4×C59—22no—
275C4×C59—22no—
276C4×C59—42no—
277C4×C59—42no—
278C4×C59—81no—
279C4×C59—81no—
280C4×C59C4×#4111yescharacteristic
281C4×C59C4×#4111yescharacteristic
282C4×C59#53311yescharacteristic
283C4×C59#53311yescharacteristic
284Dic59—22no—
285Dic59—22no—
286Dic59—22no—
287Dic59—42no—
288Dic59—42no—
289Dic59—81no—
290Dic59—81no—
291C2×#432—591no—
292#2283—591no—
293C4×#117—591no—
294#1949—591no—
295#1949—591no—
296#1949—591no—
297#1949D5911yescharacteristic, complemented
298#1854—591no—
299#1854—591no—
300#1854—591no—
301#1854—591no—
302#1776—591no—
303#1776—591no—
304#1776—591no—
305#1776—591no—
306C2×C59#229611yescharacteristic
307C2×C59#291111yescharacteristic
308C2×C59#291111yescharacteristic
309C2×C59#311111yescharacteristic
310C2×C59#311111yescharacteristic
311C2×C59#311111yescharacteristic
312C2×C59#311111yescharacteristic
313D59—42no—
314C2×#117—591no—
315C2×#117—591no—
316C22×C42—591no—
317#432—598no—
318C2×#107—591no—
319C2×#107—591no—
320C2×#107—591no—
321C2×#107C2×D5911yescharacteristic
322C2×#106—591no—
323C2×#106—591no—
324C2×#106—591no—
325C2×#106C2×D5911yescharacteristic
326C2×C4⋊C8—591no—
327C2×C4⋊C8C2×D5911yescharacteristic
328C2×C22⋊C8—591no—
329C2×C22⋊C8—591no—
330C2×#97—591no—
331C2×#97—591no—
332#383—1181no—
333#382—591no—
334#382C2×D5911yescharacteristic
335#381—1181no—
336#380—591no—
337#380—591no—
338C4×C4⋊C4—591no—
339C4×C4⋊C4—591no—
340C4×C4⋊C4—591no—
341C4×C4⋊C4—591no—
342C4×C4⋊C4—591no—
343C4×C4⋊C4C2×D5911yescharacteristic
344C4×C22⋊C4—1181no—
345C4×C22⋊C4—1181no—
346C4×C22⋊C4—1181no—
347#376—1181no—
348#376—1181no—
349C43—1181no—
350#340—591no—
351#340—591no—
352#340—591no—
353#340—591no—
354#340—591no—
355#340—591no—
356#340C2×D5911yescharacteristic
357#340C2×D5911yescharacteristic
358C59#2136611yescharacteristic, complemented, Sylow
359C23×C4—591no—
360C23×C4—591no—
361C23×C4—591no—
362C22×C8—591no—
363C22×C8—591no—
364C22×C8C22×D5911yescharacteristic
365C22×C8C22×D5911yescharacteristic
366#117—1182no—
367#117—1182no—
368#117—1182no—
369#117—1182no—
370C2×C4⋊C4—591no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4C22×D5911yescharacteristic
375C2×C4⋊C4C22×D5911yescharacteristic
376C2×C4⋊C4C22×D5911yescharacteristic
377C2×C4⋊C4C22×D5911yescharacteristic
378C2×C22⋊C4—1181no—
379C2×C22⋊C4—1181no—
380C2×C22⋊C4—1181no—
381C2×C22⋊C4—1181no—
382C2×C42—21no—
383C2×C42—591no—
384C2×C42—591no—
385C2×C42—591no—
386C2×C42—594no—
387C2×C42—594no—
388C2×C42—1181no—
389C2×C42—1181no—
390C2×C42—1181no—
391C2×C42—1181no—
392C2×C42—1181no—
393C2×C42—1181no—
394C2×C42—1181no—
395C2×C42C22×D5911yescharacteristic
396#107—22no—
397#107—1182no—
398#107—1182no—
399#107—1182no—
400#106—22no—
401#106—1182no—
402#106—1182no—
403#106—1182no—
404C4⋊C8—594no—
405C4⋊C8C4×D5914yes—
406C22⋊C8—594no—
407C22⋊C8—594no—
408#97—594no—
409#97—594no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1181no—
414#95—1181no—
415#95—1181no—
416#95—1181no—
417#95—1181no—
418#95—1181no—
419#95—1181no—
420#95—1181no—
421#95—1181no—
422C24—591no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—591no—
428C22×C4—591no—
429C22×C4—591no—
430C22×C4—592no—
431C22×C4—592no—
432C22×C4—594no—
433C22×C4—594no—
434C22×C4—1181no—
435C22×C4—1181no—
436C22×C4—1181no—
437C22×C4—1181no—
438C22×C4—1181no—
439C22×C4—1181no—
440C22×C4—1181no—
441C22×C4—1181no—
442C22×C4—2361no—
443C22×C4—2361no—
444C22×C4—2361no—
445C22×C4—2361no—
446C22×C4D4×D5911yescharacteristic
447C22×C4D4×D5911yescharacteristic
448C22×C4C23×D5911yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—592no—
454C2×C8—592no—
455C2×C8—1181no—
456C2×C8—1181no—
457C2×C8—1181no—
458C2×C8—1181no—
459C2×C8C2×C4×D5912yes—
460C2×C8C2×C4×D5912yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—592no—
468C4⋊C4—592no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4#1174568712yes—
476C4⋊C4#1174568912yes—
477C22⋊C4—1184no—
478C22⋊C4—1184no—
479C22⋊C4—2362no—
480C22⋊C4—2362no—
481C42—42no—
482C42—594no—
483C42—594no—
484C42—592no—
485C42—592no—
486C42—1184no—
487C42—1184no—
488C42—2362no—
489C42—2362no—
490C42—2362no—
491C42—2362no—
492C42—2362no—
493C42C2×C4×D5912yes—
494C42Q8×D5912yes—
495C23—592no—
496C23—1181no—
497C23—1181no—
498C23—1181no—
499C23—1181no—
500C23—1181no—
501C23—1181no—
502C23C2×D4×D5911yescharacteristic
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—1181no—
523C2×C4—1181no—
524C2×C4—1181no—
525C2×C4—1181no—
526C2×C4—1181no—
527C2×C4—1181no—
528C2×C4—1182no—
529C2×C4—1182no—
530C2×C4—1182no—
531C2×C4—1182no—
532C2×C4—1182no—
533C2×C4—1182no—
534C2×C4—2364no—
535C2×C4—2364no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4—2361no—
539C2×C4—2361no—
540C2×C4—2361no—
541C2×C4—2361no—
542C2×C4—2361no—
543C2×C4—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4C4⋊C4×D5912yes—
547C2×C4C4⋊C4×D5912yes—
548C2×C4C22×C4×D5911yescharacteristic
549C2×C4C2×Q8×D5911yescharacteristic
550C2×C4#41×D5911yescharacteristic
551C2×C4#41×D5911yescharacteristic
552C2×C4C2×#1174568711yescharacteristic
553C2×C4C2×#1174568911yescharacteristic
554C8—22no—
555C8—22no—
556C8—1182no—
557C8—1182no—
558C22—1182no—
559C22—1182no—
560C22—1182no—
561C22—2361no—
562C22—2361no—
563C22—2361no—
564C22—2361no—
565C22C2×C4⋊C4×D5911yescharacteristic
566C22#1683791211yescharacteristic
567C22#1683791511yescharacteristic
568C22#1683819811yescharacteristic
569C22#1683819911yescharacteristic
570C22#1683819911yescharacteristic
571C22#1683820111yescharacteristic
572C4—22no—
573C4—22no—
574C4—42no—
575C4—42no—
576C4—81no—
577C4—81no—
578C4—1182no—
579C4—1182no—
580C4—1182no—
581C4—4721no—
582C4—4721no—
583C4—2362no—
584C4—2362no—
585C4C4×#1174568711yescharacteristic
586C4C4×#1174568911yescharacteristic
587C4#1683795711yescharacteristic
588C4#1683795811yescharacteristic
589C2—2362no—
590C2#2142657711yescharacteristic
591C2#2143268311yescharacteristic
592C2#2143268411yescharacteristic
593C2#2143420211yescharacteristic
594C2#2143420411yescharacteristic
595C2#2143421011yescharacteristic
596C2#2143421211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1949C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
cosocleC22×C4×C59C24
hypercenter#1949D59
hypocenterC59#21366
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #21424866C2semidirect
5. #21424864C2semidirect
6. #21424862C2semidirect
11. #21423996C2semidirect
12. #21423995C2semidirect
13. #21423992C2semidirect
14. #21423992C2semidirect
15. C59×#1949C2semidirect
19. #16837458C4semidirect
297. #1949D59semidirect
358. C59#21366semidirect

Maximal subgroups

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

subgroupindex
C2×#168374582
#214264892
C4×#142736852
#214248662
#214248642
#214248622
#214242982
#214242962
#214242942
#214242922
#214239962
#214239952
#214239922
C59×#19492
#2136659