Finite Group Databasebeta

← #29753249

Subgroups — #29753249

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450416C211yesmaximal, characteristic
2#21447367C211yesmaximal, characteristic, complemented
3#21447134C211yesmaximal, characteristic
4#21447062C211yesmaximal, characteristic, complemented
5#21446902C211yesmaximal, characteristic
6#21446676C211yesmaximal, characteristic
7#21446457C211yesmaximal, characteristic, complemented
8#21446439C211yesmaximal, characteristic
9#21446404C211yesmaximal, characteristic, complemented
10#21446378C211yesmaximal, characteristic, complemented
11#21446174C211yesmaximal, characteristic
12#21446174C211yesmaximal, characteristic
13#21445834C211yesmaximal, characteristic, complemented
14C4×#14519701C211yesmaximal, characteristic, complemented
15C61×#2365C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839691—21no—
31#16839688—21no—
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839652—21no—
37#16839651—21no—
38#16839628C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4⋊Q8×C61C2211yescharacteristic
49C2×C4×Q8×C61C2211yescharacteristic
50C2×C4×Q8×C61C2211yescharacteristic
51C61×#391C2211yescharacteristic
52C61×#391C2211yescharacteristic
53C61×#389—21no—
54C61×#387—21no—
55C61×#387—21no—
56C4×C4⋊C4×C61—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C2×#11758201—22no—
61C2×#11758201—22no—
62C2×#11758201—22no—
63C2×#11758201—41no—
64C2×#11758201—41no—
65C2×#11758201—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81#14519710—41no—
82#14519708—22no—
83C4⋊#92418—41no—
84#14519701—22no—
85#14519701—22no—
86#14519701—22no—
87#14519701—41no—
88#14519701—41no—
89#14519701—41no—
90#14519697—22no—
91#14519697—41no—
92C4×#92418—41no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×Q8×C61C2311yescharacteristic
98C22×Q8×C61C2311yescharacteristic
99C4⋊Q8×C61—22no—
100C4⋊Q8×C61—22no—
101C4×Q8×C61—22no—
102C4×Q8×C61—22no—
103C4×Q8×C61—41no—
104C4×Q8×C61—41no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C23×D61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61#4112yes—
138C2×Q8×C61#4112yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C4⋊C4×C61—24no—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—42no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61#4112yes—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—42no—
176C42×C61—42no—
177C42×C61—42no—
178#11758201—44no—
179#11758201—44no—
180#11758198—42no—
181#11758198—42no—
182#11758198—81no—
183#11758198—81no—
184#11758198—81no—
185#11758198—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192#11758196—81no—
193C4×Dic61—81no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418#4112yes—
206C23×C61C22×D411yescharacteristic
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214Q8×C61—22no—
215Q8×C61—22no—
216Q8×C61—22no—
217Q8×C61—22no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61#13512yes—
251C2×C4×C61#13712yes—
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61H(5,𝔽2)11yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—41no—
271#92418—22no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#27069—611nomaximal, Sylow
276C22×C61#52511yescharacteristic
277C22×C61#54611yescharacteristic
278C22×C61#55011yescharacteristic
279C22×C61C2×#13511yescharacteristic
280C22×C61C2×#13711yescharacteristic
281C22×C61#57711yescharacteristic
282C22×C61#57711yescharacteristic
283C2×D61—81no—
284C2×D61—81no—
285C2×D61—81no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C4×C61—22no—
291C4×C61—22no—
292C4×C61—41no—
293C4×C61—42no—
294C4×C61—42no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—42no—
298C4×C61—41no—
299C4×C61—81no—
300C4×C61#52911yescharacteristic
301C4×C61#53811yescharacteristic
302C4×C61#55111yescharacteristic
303C4×C61#55311yescharacteristic
304Dic61—81no—
305Dic61—81no—
306Dic61—81no—
307#2513—611no—
308#2365D6111yescharacteristic, complemented
309#2097—611no—
310#2055—611no—
311#2043—611no—
312#2013—611no—
313#1968—611no—
314#1928—611no—
315#1925—611no—
316#1920—611no—
317#1916—611no—
318#1880—611no—
319#1880—611no—
320#1805—611no—
321C4×#103—611no—
322C2×C61#246711yescharacteristic
323C2×C61#310811yescharacteristic
324C2×C61#312611yescharacteristic
325C2×C61#330311yescharacteristic
326C2×C61#332011yescharacteristic
327C2×C61#339411yescharacteristic
328C2×C61#340011yescharacteristic
329D61—161no—
330C22×SD16—611no—
331C22×SD16—611no—
332C2×C4⋊Q8C2×D6111yescharacteristic
333C2×C4×Q8C2×D6111yescharacteristic
334C2×C4×Q8C2×D6111yescharacteristic
335C2×#107—611no—
336C2×#106—611no—
337C2×C4⋊C8—611no—
338C2×#103—611no—
339C2×#103—611no—
340C2×#103—611no—
341C2×#103—611no—
342C2×#103—611no—
343C2×#103—611no—
344C2×#102—611no—
345C2×#102—611no—
346C2×C4×C8—611no—
347#397—1221no—
348#397—1221no—
349#391C2×D6111yescharacteristic
350#391C2×D6111yescharacteristic
351#390—611no—
352#390—611no—
353#390—611no—
354#389—21no—
355#389—611no—
356#388—1221no—
357#388—1221no—
358#387—21no—
359#387—21no—
360#382—611no—
361C4×C4⋊C4—21no—
362C4×C4⋊C4—611no—
363C4×C4⋊C4C2×D6111yescharacteristic
364C4×C4⋊C4C2×D6111yescharacteristic
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#336—611no—
370#336—611no—
371#336—611no—
372#336—611no—
373C61#2706911yescharacteristic, complemented, Sylow
374C22×Q8C22×D6111yescharacteristic
375C22×Q8C22×D6111yescharacteristic
376C22×D4—611no—
377C2×SD16—1222no—
378C2×SD16—1222no—
379C2×SD16—1222no—
380C2×SD16—2441no—
381C2×SD16—2441no—
382C2×SD16—2441no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—611no—
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—41no—
392C4×Q8—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C22⋊D6111yescharacteristic
402C2×C4⋊C4C22⋊D6111yescharacteristic
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—1221no—
415C2×C42C22×D6111yescharacteristic
416C2×C42C22×D6111yescharacteristic
417C2×C42C22×D6111yescharacteristic
418#107—2441no—
419#106—1222no—
420C4⋊C8—2441no—
421#103—1222no—
422#103—1222no—
423#103—1222no—
424#103—2441no—
425#103—2441no—
426#103—2441no—
427#102—1222no—
428#102—2441no—
429C4×C8—2441no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95C22⋊D6111yescharacteristic
440#95C22⋊D6111yescharacteristic
441C24—1221no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8#1175822212yes—
453C2×Q8#1175822212yes—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C2×C22⋊D6111yescharacteristic
473C22×C4C23×D6111yescharacteristic
474SD16—2444no—
475SD16—2444no—
476C2×C8—612no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—4881no—
504C4⋊C4#1175822412yes—
505C22⋊C4—4881no—
506C22⋊C4—4881no—
507C22⋊C4—4881no—
508C22⋊C4—4881no—
509C22⋊C4—2442no—
510C22⋊C4—2442no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—42no—
519C42—42no—
520C42—4881no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23—2441no—
528C23C22×C22⋊D6111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—2441no—
538D4—2441no—
539D4—2441no—
540D4—2441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
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—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4#1451979712yes—
579C2×C4#1451980812yes—
580C2×C4#41×D6111yescharacteristic
581C2×C4C2×#1175822411yescharacteristic
582C2×C4C2×#1175822211yescharacteristic
583C2×C4C2×#1175822211yescharacteristic
584C2×C4#1451982211yescharacteristic
585C2×C4#1451982311yescharacteristic
586C8—1222no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C22—4881no—
591C22—4881no—
592C22—4881no—
593C22—4881no—
594C22—4881no—
595C22—4881no—
596C22—4881no—
597C22#1684027311yescharacteristic
598C22#1684040611yescharacteristic
599C22#1684043111yescharacteristic
600C22C2×#1451979711yescharacteristic
601C22C2×#1451980811yescharacteristic
602C22#1684057011yescharacteristic
603C22#1684057011yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—41no—
613C4—81no—
614C4—4881no—
615C4—4881no—
616C4—4881no—
617C4#1684029211yescharacteristic
618C4#1684034511yescharacteristic
619C4#1684044111yescharacteristic
620C4#1684045811yescharacteristic
621C2—9761no—
622C2#2144986411yescharacteristic
623C2#2145589911yescharacteristic
624C2#2145611011yescharacteristic
625C2#2145774711yescharacteristic
626C2#2145799011yescharacteristic
627C2#2145881511yescharacteristic
628C2#2145886811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2365C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2365D61
hypocenterC61#27069
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #21447367C2semidirect
4. #21447062C2semidirect
7. #21446457C2semidirect
9. #21446404C2semidirect
10. #21446378C2semidirect
13. #21445834C2semidirect
14. C4×#14519701C2semidirect
15. C61×#2365C2semidirect
308. #2365D61semidirect
373. C61#27069semidirect

Maximal subgroups

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

subgroupindex
#214504162
#214473672
#214471342
#214470622
#214469022
#214466762
#214464572
#214464392
#214464042
#214463782
#214461742
#214458342
C4×#145197012
C61×#23652
#2706961