Finite Group Databasebeta

← #28618316

Subgroups — #28618316

Order 15104.

820 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837510C211yesmaximal, characteristic, complemented
2#21426778C211yesmaximal, characteristic
3#21426778C211yesmaximal, characteristic
4#21425594C211yesmaximal, characteristic, complemented
5#21425529C211yesmaximal, characteristic
6#21425490C211yesmaximal, characteristic, complemented
7#21425476C211yesmaximal, characteristic, complemented
8#21425419C211yesmaximal, characteristic, complemented
9#21425300C211yesmaximal, characteristic
10#21425293C211yesmaximal, characteristic
11#21425106C211yesmaximal, characteristic
12#21423993C211yesmaximal, characteristic, complemented
13C4×#14273652C211yesmaximal, characteristic, complemented
14C4×#14273652C211yesmaximal, characteristic, complemented
15C2×C59×#433C211yesmaximal, characteristic
16C22×Dic236C2211yescharacteristic
17C2×#14273706C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20C2×C4×Dic118C2211yescharacteristic
21#16837510—24no—
22C2×#14273661C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24C2×#14273659C2211yescharacteristic
25C2×#14273652C2211yescharacteristic
26C2×#14273652C2211yescharacteristic
27C2×#14273652C2211yescharacteristic
28C2×#14273652C2211yescharacteristic
29C2×#14273652C2211yescharacteristic
30C2×#14273652C2211yescharacteristic
31#16837308C2211yescharacteristic
32#16837308C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837300C2211yescharacteristic
35#16837297—21no—
36#16837297—21no—
37#16837296—21no—
38#16837296—21no—
39#16837290—21no—
40#16837290—21no—
41#16837283—21no—
42#16837283—21no—
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic
45C4×C4⋊Dic59C2211yescharacteristic
46C4×C4⋊Dic59C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#433—24no—
55C2×C4⋊C8×C59C2211yescharacteristic
56C2×C4⋊C8×C59C2211yescharacteristic
57C2×C22⋊C8×C59C2211yescharacteristic
58C2×C22⋊C8×C59C2211yescharacteristic
59C2×#97×C59C2211yescharacteristic
60C2×C4×C8×C59C2211yescharacteristic
61C22×Dic118C2311yescharacteristic
62C22×Dic118C2311yescharacteristic
63C2×Dic236—22no—
64C2×Dic236—22no—
65C2×Dic236—22no—
66#14273706—22no—
67#14273706—22no—
68#14273706—22no—
69#14273706—22no—
70C4×Dic118—22no—
71C4×Dic118—22no—
72C4×Dic118—22no—
73C4×Dic118—22no—
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×Dic59⋊C4—21no—
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×Dic59⋊C4—21no—
85C2×Dic59⋊C4—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×C4×Dic59—21no—
91C2×C4×Dic59—21no—
92C2×C4×Dic59—21no—
93C2×C4×Dic59—21no—
94#14273661—22no—
95#14273659—22no—
96#14273659—22no—
97#14273652—22no—
98#14273652—22no—
99#14273652—22no—
100#14273652—22no—
101#14273652—22no—
102#14273652—22no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C23×C4×C59C2311yescharacteristic
114C22×C8×C59C2311yescharacteristic
115C22×C8×C59C2311yescharacteristic
116C22×C8×C59C2311yescharacteristic
117C22×C8×C59C2311yescharacteristic
118#117×C59—22no—
119#117×C59—22no—
120C2×C4⋊C4×C59D411yescharacteristic
121C2×C4⋊C4×C59D411yescharacteristic
122C2×C22⋊C4×C59D411yescharacteristic
123C2×C22⋊C4×C59D411yescharacteristic
124C2×C42×C59C2311yescharacteristic
125C2×C42×C59C2311yescharacteristic
126C4⋊C8×C59—22no—
127C4⋊C8×C59—22no—
128C22⋊C8×C59—22no—
129C22⋊C8×C59—22no—
130#97×C59D414yes—
131C4×C8×C59—22no—
132C24×C59C2×D411yescharacteristic
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59C2×D411yescharacteristic
140C22×C4×C59C2×D411yescharacteristic
141C22×C4×C59C2×D411yescharacteristic
142C22×C4×C59C2×D411yescharacteristic
143C22×C4×C59C2×D411yescharacteristic
144C22×C4×C59C2411yescharacteristic
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—21no—
152C22×Dic59—21no—
153C2×Dic118—21no—
154C2×Dic118—21no—
155C2×Dic118—21no—
156C2×Dic118—21no—
157C2×Dic118—21no—
158C2×Dic118—21no—
159C2×Dic118—21no—
160C2×Dic118—21no—
161C2×Dic118—21no—
162C2×Dic118—21no—
163C2×Dic118#4112yes—
164C2×Dic118#4112yes—
165C2×C8×C59—21no—
166C2×C8×C59—21no—
167C2×C8×C59—21no—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59—21no—
175C2×C8×C59C2×D412yes—
176C2×C8×C59C2×D412yes—
177C4⋊C4×C59—22no—
178C4⋊C4×C59—22no—
179C22⋊C4×C59—22no—
180C22⋊C4×C59—22no—
181C42×C59—21no—
182C42×C59—21no—
183C42×C59C2×D412yes—
184C42×C59#4112yes—
185C22⋊Dic59—24no—
186C22⋊Dic59—24no—
187C22⋊Dic59—81no—
188C22⋊Dic59—81no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191C4⋊Dic59—21no—
192C4⋊Dic59—21no—
193C4⋊Dic59—21no—
194C4⋊Dic59—21no—
195C4⋊Dic59—21no—
196C4⋊Dic59—21no—
197C4⋊Dic59—21no—
198C4⋊Dic59—21no—
199C4⋊Dic59#4112yes—
200C4⋊Dic59#4112yes—
201Dic59⋊C4—24no—
202Dic59⋊C4—24no—
203Dic59⋊C4—42no—
204Dic59⋊C4—42no—
205Dic59⋊C4—81no—
206Dic59⋊C4—81no—
207C4×Dic59—42no—
208C4×Dic59—42no—
209C4×Dic59—81no—
210C4×Dic59—81no—
211Dic236—28no—
212C23×C59—21no—
213C23×C59—21no—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—21no—
219C23×C59C22×D411yescharacteristic
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—21no—
226C2×C4×C59—21no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—21no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—21no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59#12112yes—
238C2×C4×C59#12112yes—
239C2×C4×C59C22×D411yescharacteristic
240C2×C4×C59C2×#4111yescharacteristic
241C2×C4×C59C2×#4111yescharacteristic
242C2×C4×C59C2×#4111yescharacteristic
243C2×C4×C59C2×#4111yescharacteristic
244C2×C4×C59C2×#4111yescharacteristic
245C2×Dic59—22no—
246C2×Dic59—22no—
247C2×Dic59—22no—
248C2×Dic59—22no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—41no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—41no—
265C2×Dic59—41no—
266C2×Dic59—41no—
267C2×Dic59—41no—
268C2×Dic59—41no—
269Dic118—22no—
270Dic118—22no—
271Dic118—22no—
272Dic118—22no—
273Dic118—41no—
274Dic118—41no—
275Dic118—41no—
276Dic118—41no—
277C8×C59—22no—
278C8×C59—22no—
279C8×C59—41no—
280C8×C59—41no—
281#23713—591nomaximal, Sylow
282C22×C59—41no—
283C22×C59—41no—
284C22×C59—41no—
285C22×C59—41no—
286C22×C59—41no—
287C22×C59—41no—
288C22×C59—41no—
289C22×C59C2×#12111yescharacteristic
290C22×C59#52511yescharacteristic
291C22×C59#52511yescharacteristic
292C22×C59#57711yescharacteristic
293C22×C59#57711yescharacteristic
294C22×C59#57811yescharacteristic
295C22×C59#57811yescharacteristic
296C4×C59—22no—
297C4×C59—22no—
298C4×C59—41no—
299C4×C59—41no—
300C4×C59—41no—
301C4×C59#52511yescharacteristic
302C4×C59#52911yescharacteristic
303C4×C59#52911yescharacteristic
304C4×C59#53211yescharacteristic
305Dic59—42no—
306Dic59—42no—
307Dic59—42no—
308Dic59—42no—
309Dic59—81no—
310Dic59—81no—
311Dic59—81no—
312Dic59—81no—
313C2×#441—591no—
314C2×#433D5911yescharacteristic
315#2323—591no—
316#2323—591no—
317#2088—591no—
318#2077—591no—
319#2068—591no—
320#2066—591no—
321#2056—591no—
322#2036—591no—
323#2035—591no—
324#2001—591no—
325#1776—591no—
326C4×#103—591no—
327C4×#103—591no—
328C2×C59—81no—
329C2×C59#239211yescharacteristic
330C2×C59#306311yescharacteristic
331C2×C59#306311yescharacteristic
332C2×C59#312011yescharacteristic
333C2×C59#312111yescharacteristic
334C2×C59#312511yescharacteristic
335C2×C59#312711yescharacteristic
336C22×Q16—591no—
337C2×C22⋊Q8—591no—
338C2×C22⋊Q8—591no—
339C2×C4×Q8—591no—
340C2×C4×Q8—591no—
341C2×#117C2×D5911yescharacteristic
342#441—1184no—
343#433—24no—
344C2×#107—591no—
345C2×#106—591no—
346C2×#106—591no—
347C2×C4⋊C8C2×D5911yescharacteristic
348C2×C4⋊C8C2×D5911yescharacteristic
349C2×#103—591no—
350C2×#103—591no—
351C2×#103—591no—
352C2×#103—591no—
353C2×#103—591no—
354C2×#103—591no—
355C2×C22⋊C8C2×D5911yescharacteristic
356C2×C22⋊C8C2×D5911yescharacteristic
357C2×#97C2×D5911yescharacteristic
358C2×C4×C8C2×D5911yescharacteristic
359#391—591no—
360#391—591no—
361#389—591no—
362#389—591no—
363#389—1181no—
364#389—1181no—
365#388—1181no—
366#388—1181no—
367#388—1181no—
368#388—1181no—
369#387—1181no—
370#387—1181no—
371#380—591no—
372#380—591no—
373C4×C4⋊C4—591no—
374C4×C4⋊C4—591no—
375#340—591no—
376#340—591no—
377#340—591no—
378#340—591no—
379#340—591no—
380#340—591no—
381C59#2371311yescharacteristic, complemented, Sylow
382C22×Q8—591no—
383C22×Q8—591no—
384C23×C4C22×D5911yescharacteristic
385C2×Q16—1182no—
386C2×Q16—1182no—
387C2×Q16—1182no—
388C22×C8C22×D5911yescharacteristic
389C22×C8C22×D5911yescharacteristic
390C22×C8C22×D5911yescharacteristic
391C22×C8C22×D5911yescharacteristic
392C22⋊Q8—1182no—
393C22⋊Q8—1182no—
394C22⋊Q8—1182no—
395C22⋊Q8—1182no—
396C4×Q8—1182no—
397C4×Q8—1182no—
398C4×Q8—1182no—
399C4×Q8—1182no—
400#117—22no—
401#117—22no—
402C2×C4⋊C4—591no—
403C2×C4⋊C4—591no—
404C2×C4⋊C4—591no—
405C2×C4⋊C4—591no—
406C2×C4⋊C4—591no—
407C2×C4⋊C4—591no—
408C2×C4⋊C4—1181no—
409C2×C4⋊C4—1181no—
410C2×C4⋊C4—1181no—
411C2×C4⋊C4—1181no—
412C2×C4⋊C4—1181no—
413C2×C4⋊C4—1181no—
414C2×C4⋊C4D23611yescharacteristic
415C2×C4⋊C4D23611yescharacteristic
416C2×C22⋊C4—1181no—
417C2×C22⋊C4—1181no—
418C2×C22⋊C4—1181no—
419C2×C22⋊C4—1181no—
420C2×C22⋊C4D23611yescharacteristic
421C2×C22⋊C4D23611yescharacteristic
422C2×C42—1181no—
423C2×C42—1181no—
424C2×C42—1181no—
425C2×C42—1181no—
426C2×C42C22×D5911yescharacteristic
427C2×C42C22×D5911yescharacteristic
428#107—1182no—
429#106—1182no—
430#106—1182no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433#103—1182no—
434#103—1182no—
435#103—1182no—
436#103—1182no—
437#103—1182no—
438#103—1182no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441#97C22⋊D5914yes—
442C4×C8—22no—
443#95—1181no—
444#95—1181no—
445#95—1181no—
446#95—1181no—
447#95—1181no—
448#95—1181no—
449#95—1181no—
450#95—1181no—
451#95—1181no—
452#95—1181no—
453C24C2×D23611yescharacteristic
454C2×Q8—592no—
455C2×Q8—592no—
456C2×Q8—1181no—
457C2×Q8—1181no—
458C2×Q8—1181no—
459C2×Q8—1181no—
460C2×Q8—1181no—
461C2×Q8—1181no—
462C2×Q8—1181no—
463C2×Q8—1181no—
464C2×Q8—1181no—
465C2×Q8—1181no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—1181no—
473C22×C4—1181no—
474C22×C4—1181no—
475C22×C4—1181no—
476C22×C4—1181no—
477C22×C4—1181no—
478C22×C4—1181no—
479C22×C4—1181no—
480C22×C4C2×D23611yescharacteristic
481C22×C4C2×D23611yescharacteristic
482C22×C4C2×D23611yescharacteristic
483C22×C4C2×D23611yescharacteristic
484C22×C4C2×D23611yescharacteristic
485C22×C4C23×D5911yescharacteristic
486Q16—1188no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C2×C22⋊D5912yes—
498C2×C8C2×C22⋊D5912yes—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—592no—
502C4⋊C4—592no—
503C4⋊C4—1184no—
504C4⋊C4—1184no—
505C4⋊C4—1181no—
506C4⋊C4—1181no—
507C4⋊C4—1181no—
508C4⋊C4—1181no—
509C4⋊C4—1181no—
510C4⋊C4—1181no—
511C4⋊C4—1181no—
512C4⋊C4—1181no—
513C4⋊C4—1181no—
514C4⋊C4—1181no—
515C4⋊C4—4721no—
516C4⋊C4—4721no—
517C4⋊C4—2362no—
518C4⋊C4—2362no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—1184no—
522C22⋊C4—1184no—
523C22⋊C4—4721no—
524C22⋊C4—4721no—
525C42—21no—
526C42—21no—
527C42—4721no—
528C42—4721no—
529C42—2362no—
530C42—2362no—
531C42#1174568512yes—
532C42C2×C22⋊D5912yes—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23C22×D23611yescharacteristic
541Q8—1182no—
542Q8—1182no—
543Q8—1182no—
544Q8—1182no—
545Q8—2361no—
546Q8—2361no—
547Q8—2361no—
548Q8—2361no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—1182no—
567C2×C4—1182no—
568C2×C4—1182no—
569C2×C4—1182no—
570C2×C4—2361no—
571C2×C4—2361no—
572C2×C4—2361no—
573C2×C4—2361no—
574C2×C4—2361no—
575C2×C4—2361no—
576C2×C4—2361no—
577C2×C4—2361no—
578C2×C4—2361no—
579C2×C4—2361no—
580C2×C4—2361no—
581C2×C4—2361no—
582C2×C4—2361no—
583C2×C4—2361no—
584C2×C4—2361no—
585C2×C4—2361no—
586C2×C4—2361no—
587C2×C4—2361no—
588C2×C4—2361no—
589C2×C4—2361no—
590C2×C4#1427370112yes—
591C2×C4#1427370112yes—
592C2×C4C22×C22⋊D5911yescharacteristic
593C2×C4#41×D5911yescharacteristic
594C2×C4#41×D5911yescharacteristic
595C2×C4#41×D5911yescharacteristic
596C2×C4#41×D5911yescharacteristic
597C2×C4C2×#1174568511yescharacteristic
598C8—22no—
599C8—22no—
600C8—41no—
601C8—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22C2×#1427370111yescharacteristic
610C22#1683791411yescharacteristic
611C22#1683791411yescharacteristic
612C22#1683821411yescharacteristic
613C22#1683821411yescharacteristic
614C22#1683821911yescharacteristic
615C22#1683821911yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—4721no—
622C4—4721no—
623C4—4721no—
624C4—4721no—
625C4—2362no—
626C4—2362no—
627C4—2362no—
628C4—2362no—
629C4#1683790911yescharacteristic
630C4#1683793011yescharacteristic
631C4#1683793011yescharacteristic
632C4#1683794811yescharacteristic
633C2—81no—
634C2#2142733211yescharacteristic
635C2#2143378711yescharacteristic
636C2#2143378711yescharacteristic
637C2#2143431211yescharacteristic
638C2#2143432711yescharacteristic
639C2#2143437511yescharacteristic
640C2#2143439711yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#433C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC2×#433D59
hypocenterC59#23713
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16837510C2semidirect
4. #21425594C2semidirect
6. #21425490C2semidirect
7. #21425476C2semidirect
8. #21425419C2semidirect
12. #21423993C2semidirect
13. C4×#14273652C2semidirect
14. C4×#14273652C2semidirect
381. C59#23713semidirect

Maximal subgroups

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

subgroupindex
C2×#168375102
#214267782
#214255942
#214255292
#214254902
#214254762
#214254192
#214253002
#214252932
#214251062
#214239932
C4×#142736522
C2×C59×#4332
#2371359