Finite Group Databasebeta

← #28661404

Subgroups — #28661404

Order 15104.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21428518C211yesmaximal, characteristic
2#21427099C211yesmaximal, characteristic
3#21425506C211yesmaximal, characteristic, complemented
4#21425476C211yesmaximal, characteristic, complemented
5#21425293C211yesmaximal, characteristic
6#21425293C211yesmaximal, characteristic
7#21424860C211yesmaximal, characteristic, complemented
8#21424824C211yesmaximal, characteristic, complemented
9#21424682C211yesmaximal, characteristic, complemented
10#21424675C211yesmaximal, characteristic, complemented
11#21424367C211yesmaximal, characteristic, complemented
12#21424291C211yesmaximal, characteristic
13#21424187C211yesmaximal, characteristic
14C4×#14273652C211yesmaximal, characteristic, complemented
15C59×#1923C211yesmaximal, characteristic
16C2×#14273720—21no—
17C2×#14273706C2211yescharacteristic
18C2×C4×Dic118C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C2×#14273659C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24C2×#14273652C2211yescharacteristic
25C2×#14273652C2211yescharacteristic
26C2×#14273652C2211yescharacteristic
27C2×#14273652C2211yescharacteristic
28#16837342—21no—
29#16837327—21no—
30#16837308C2211yescharacteristic
31#16837300C2211yescharacteristic
32#16837300C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837299—21no—
35#16837289—21no—
36#16837287—21no—
37#16837274—21no—
38#16837272C2211yescharacteristic
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42C4×C4⋊Dic59C2211yescharacteristic
43C22⋊C4×Dic59—21no—
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52C2×C4⋊C8×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic
55C2×C4×C8×C59C2211yescharacteristic
56C4×C22⋊C4×C59C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×Dic118C2311yescharacteristic
60C23×Dic59—21no—
61#14273720—44no—
62#14273706—22no—
63#14273706—22no—
64C4×Dic118—22no—
65C4×Dic118—41no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—21no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—41no—
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×Dic59⋊C4—21no—
79C2×Dic59⋊C4—21no—
80C2×Dic59⋊C4—21no—
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59—21no—
88C2×C4×Dic59—21no—
89#14273659—22no—
90#14273659—22no—
91#14273659—22no—
92#14273659—41no—
93#14273652—22no—
94#14273652—22no—
95#14273652—22no—
96#14273652—41no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C23×C4×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111C2×C22⋊C4×C59D411yescharacteristic
112C2×C22⋊C4×C59D411yescharacteristic
113C2×C42×C59C2311yescharacteristic
114C2×C42×C59C2311yescharacteristic
115C4⋊C8×C59—22no—
116C22⋊C8×C59—22no—
117C22⋊C8×C59—41no—
118C4×C8×C59—41no—
119#95×C59D411yescharacteristic
120#95×C59D411yescharacteristic
121C24×C59C2×D411yescharacteristic
122C22×C4×C59—21no—
123C22×C4×C59—21no—
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×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2×D411yescharacteristic
133C22×C4×C59C2411yescharacteristic
134C22×Dic59—21no—
135C22×Dic59—21no—
136C22×Dic59—21no—
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—21no—
142C22×Dic59—42no—
143C22×Dic59—42no—
144C22×Dic59—81no—
145C2×Dic118—21no—
146C2×Dic118—21no—
147C2×Dic118—21no—
148C2×Dic118—21no—
149C2×Dic118—21no—
150C2×Dic118#4112yes—
151C2×C8×C59—21no—
152C2×C8×C59—21no—
153C2×C8×C59—21no—
154C2×C8×C59—21no—
155C2×C8×C59—21no—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C2×C8×C59—21no—
159C2×C8×C59—21no—
160C2×C8×C59—21no—
161C2×C8×C59—21no—
162C2×C8×C59#4112yes—
163C22⋊C4×C59—41no—
164C22⋊C4×C59SD1614yes—
165C42×C59—21no—
166C42×C59—21no—
167C42×C59—21no—
168C42×C59—21no—
169C22⋊Dic59—24no—
170C22⋊Dic59—42no—
171C22⋊Dic59—42no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—21no—
180C4⋊Dic59—21no—
181C4⋊Dic59—21no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59—42no—
185C4⋊Dic59—42no—
186C4⋊Dic59—42no—
187C4⋊Dic59#4112yes—
188C4⋊Dic59#4112yes—
189Dic59⋊C4—24no—
190Dic59⋊C4—42no—
191Dic59⋊C4—42no—
192Dic59⋊C4—42no—
193Dic59⋊C4—81no—
194C4×Dic59—42no—
195C4×Dic59—42no—
196C4×Dic59—81no—
197C23×C59—21no—
198C23×C59—21no—
199C23×C59—21no—
200C23×C59—21no—
201C23×C59—21no—
202C23×C59—21no—
203C23×C59C2×SD1612yes—
204C23×C59C22×D411yescharacteristic
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—21no—
209C2×C4×C59—21no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59C2×SD1612yes—
223C2×C4×C59C2×SD1612yes—
224C2×C4×C59C2×#4111yescharacteristic
225C2×C4×C59C2×#4111yescharacteristic
226C2×C4×C59C2×#4111yescharacteristic
227C2×C4×C59C2×#4111yescharacteristic
228C2×C4×C59H(5,𝔽2)11yescharacteristic
229C2×C4×C592−1+411yescharacteristic
230C2×Dic59—22no—
231C2×Dic59—22no—
232C2×Dic59—22no—
233C2×Dic59—41no—
234C2×Dic59—41no—
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×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—84no—
255Dic118—22no—
256Dic118—22no—
257Dic118—41no—
258Dic118—41no—
259C8×C59—22no—
260C8×C59—41no—
261C8×C59—41no—
262C8×C59—41no—
263#27034—591nomaximal, Sylow
264C22×C59—22no—
265C22×C59—22no—
266C22×C59—22no—
267C22×C59—41no—
268C22×C59—41no—
269C22×C59—41no—
270C22×C59—41no—
271C22×C59#52511yescharacteristic
272C22×C59#54611yescharacteristic
273C22×C59#54711yescharacteristic
274C22×C59C22×SD1611yescharacteristic
275C22×C59#57511yescharacteristic
276C22×C59#57711yescharacteristic
277C22×C59#57811yescharacteristic
278C4×C59—22no—
279C4×C59—22no—
280C4×C59—41no—
281C4×C59—41no—
282C4×C59—41no—
283C4×C59#52911yescharacteristic
284C4×C59#53911yescharacteristic
285C4×C59#55311yescharacteristic
286C4×C59#55611yescharacteristic
287Dic59—42no—
288Dic59—42no—
289Dic59—42no—
290Dic59—81no—
291Dic59—81no—
292Dic59—81no—
293Dic59—81no—
294Dic59—81no—
295#2496—591no—
296#2360—591no—
297#2072—591no—
298#2066—591no—
299#2035—591no—
300#2035—591no—
301#1948—591no—
302#1941—591no—
303#1923D5911yescharacteristic
304#1920—591no—
305#1919—591no—
306#1865—591no—
307#1853—591no—
308#1824—591no—
309C4×#103—591no—
310C2×C59—42no—
311C2×C59#246611yescharacteristic
312C2×C59#310311yescharacteristic
313C2×C59#312011yescharacteristic
314C2×C59#329811yescharacteristic
315C2×C59#331111yescharacteristic
316C2×C59#333511yescharacteristic
317C2×C59#335211yescharacteristic
318C2×#126—1181no—
319C2×C22⋊Q8—591no—
320C2×C4×Q8—591no—
321C22×C4⋊C4—591no—
322C2×#106—591no—
323C2×#106—591no—
324C2×#106—591no—
325C2×#106—591no—
326C2×C4⋊C8C2×D5911yescharacteristic
327C2×#103—591no—
328C2×#103—591no—
329C2×#103—591no—
330C2×#103—591no—
331C2×C22⋊C8C2×D5911yescharacteristic
332C2×C22⋊C8C2×D5911yescharacteristic
333C2×C4×C8C2×D5911yescharacteristic
334#400—1181no—
335#397—1181no—
336#391—591no—
337#389—591no—
338#389—591no—
339#389—591no—
340#389—1181no—
341#387—1181no—
342#387—1181no—
343#385—1181no—
344#384—591no—
345#380—591no—
346#380—591no—
347C4×C4⋊C4—591no—
348C4×C4⋊C4—591no—
349C4×C22⋊C4—1181no—
350C4×C22⋊C4C2×D5911yescharacteristic
351#340—591no—
352#340—591no—
353#340—591no—
354#340—591no—
355#340—591no—
356#340—591no—
357#340—591no—
358#340—591no—
359#336C2×D5911yescharacteristic
360#336C2×D5911yescharacteristic
361C59#2703411yescharacteristic, complemented, Sylow
362C22×Q8—591no—
363C23×C4—1181no—
364C23×C4C22×D5911yescharacteristic
365C22×C8C22×D5911yescharacteristic
366C22×C8C22×D5911yescharacteristic
367C22×C8C22×D5911yescharacteristic
368C22×C8C22×D5911yescharacteristic
369#126—2364no—
370C22⋊Q8—1182no—
371C22⋊Q8—1182no—
372C4×Q8—1182no—
373C4×Q8—2361no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—591no—
377C2×C4⋊C4—591no—
378C2×C4⋊C4—591no—
379C2×C4⋊C4—591no—
380C2×C4⋊C4—591no—
381C2×C4⋊C4—1182no—
382C2×C4⋊C4—1181no—
383C2×C4⋊C4—1181no—
384C2×C4⋊C4—1181no—
385C2×C4⋊C4—1181no—
386C2×C4⋊C4—1181no—
387C2×C4⋊C4—1181no—
388C2×C4⋊C4—1181no—
389C2×C4⋊C4—1181no—
390C2×C4⋊C4—2361no—
391C2×C22⋊C4—1181no—
392C2×C22⋊C4—1181no—
393C2×C22⋊C4—1181no—
394C2×C22⋊C4D23611yescharacteristic
395C2×C22⋊C4D23611yescharacteristic
396C2×C42—1181no—
397C2×C42—1181no—
398C2×C42—1181no—
399C2×C42C22×D5911yescharacteristic
400C2×C42C22×D5911yescharacteristic
401#106—1182no—
402#106—1182no—
403#106—1182no—
404#106—2361no—
405C4⋊C8—22no—
406#103—1182no—
407#103—1182no—
408#103—1182no—
409#103—2361no—
410C22⋊C8—22no—
411C22⋊C8—41no—
412C4×C8—41no—
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—
422#95D23611yescharacteristic
423#95D23611yescharacteristic
424C24C2×D23611yescharacteristic
425C2×Q8—592no—
426C2×Q8—1181no—
427C2×Q8—1181no—
428C2×Q8—1181no—
429C2×Q8—1181no—
430C2×Q8—1181no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1181no—
438C22×C4—1181no—
439C22×C4—1181no—
440C22×C4—1181no—
441C22×C4—1181no—
442C22×C4—1181no—
443C22×C4—1181no—
444C22×C4—1181no—
445C22×C4—4721no—
446C22×C4—2362no—
447C22×C4—2362no—
448C22×C4C2×D23611yescharacteristic
449C22×C4C2×D23611yescharacteristic
450C22×C4C2×D23611yescharacteristic
451C22×C4C2×D23611yescharacteristic
452C22×C4C2×D23611yescharacteristic
453C22×C4C23×D5911yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8#1174568712yes—
466C4⋊C4—592no—
467C4⋊C4—592no—
468C4⋊C4—1184no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4—1181no—
477C4⋊C4—1181no—
478C4⋊C4—1181no—
479C4⋊C4—1181no—
480C4⋊C4—1181no—
481C4⋊C4—4721no—
482C4⋊C4—2362no—
483C4⋊C4—2362no—
484C4⋊C4—2362no—
485C4⋊C4—2362no—
486C4⋊C4—2362no—
487C4⋊C4—2362no—
488C22⋊C4—41no—
489C22⋊C4—1184no—
490C22⋊C4—2362no—
491C22⋊C4—2362no—
492C22⋊C4#1174566014yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—4721no—
498C42—2362no—
499C42—2362no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C2×#1174566012yes—
507C23C22×D23611yescharacteristic
508Q8—1182no—
509Q8—1182no—
510Q8—2361no—
511Q8—2361no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—1182no—
530C2×C4—1182no—
531C2×C4—1182no—
532C2×C4—4724no—
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—2361no—
542C2×C4—2361no—
543C2×C4—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4—2361no—
552C2×C4—2361no—
553C2×C4—2361no—
554C2×C4C2×#1174566012yes—
555C2×C4C2×#1174566012yes—
556C2×C4#41×D5911yescharacteristic
557C2×C4#41×D5911yescharacteristic
558C2×C4#41×D5911yescharacteristic
559C2×C4C2×#1174568711yescharacteristic
560C2×C4#1427377211yescharacteristic
561C2×C4#1427377411yescharacteristic
562C8—22no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1683791411yescharacteristic
574C22#1683804711yescharacteristic
575C22#1683805611yescharacteristic
576C22C22×#1174566011yescharacteristic
577C22#1683820211yescharacteristic
578C22#1683821411yescharacteristic
579C22#1683821911yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—4721no—
586C4—4721no—
587C4—4721no—
588C4—4721no—
589C4—4721no—
590C4—2362no—
591C4—2362no—
592C4—2362no—
593C4#1683793111yescharacteristic
594C4#1683799511yescharacteristic
595C4#1683809511yescharacteristic
596C4#1683811911yescharacteristic
597C2—42no—
598C2#2142813011yescharacteristic
599C2#2143412811yescharacteristic
600C2#2143431211yescharacteristic
601C2#2143596211yescharacteristic
602C2#2143613411yescharacteristic
603C2#2143645411yescharacteristic
604C2#2143667011yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#1923C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenter#1923D59
hypocenterC59#27034
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #21425506C2semidirect
4. #21425476C2semidirect
7. #21424860C2semidirect
8. #21424824C2semidirect
9. #21424682C2semidirect
10. #21424675C2semidirect
11. #21424367C2semidirect
14. C4×#14273652C2semidirect
361. C59#27034semidirect

Maximal subgroups

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

subgroupindex
#214285182
#214270992
#214255062
#214254762
#214252932
#214248602
#214248242
#214246822
#214246752
#214243672
#214242912
#214241872
C4×#142736522
C59×#19232
#2703459