Finite Group Databasebeta

← #29748222

Subgroups — #29748222

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450160C211yesmaximal, characteristic
2#21448844C211yesmaximal, characteristic
3#21447142C211yesmaximal, characteristic, complemented
4#21447023C211yesmaximal, characteristic
5#21446971C211yesmaximal, characteristic, complemented
6#21446829C211yesmaximal, characteristic
7#21446774C211yesmaximal, characteristic, complemented
8#21446495C211yesmaximal, characteristic, complemented
9#21446461C211yesmaximal, characteristic, complemented
10#21446391C211yesmaximal, characteristic, complemented
11#21446159C211yesmaximal, characteristic, complemented
12#21446129C211yesmaximal, characteristic
13#21445915C211yesmaximal, characteristic
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic
16C22×Dic244C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29#16839703—21no—
30#16839690—21no—
31#16839668C2211yescharacteristic
32#16839668C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839656—21no—
36#16839650—21no—
37#16839650—21no—
38#16839644—21no—
39#16839626—21no—
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839613—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×Dic122C2311yescharacteristic
61C2×Dic244—22no—
62C2×Dic244—41no—
63C2×Dic244—41no—
64#14519769—22no—
65#14519769—41no—
66#14519756—22no—
67#14519756—22no—
68#14519756—22no—
69#14519756—41no—
70C4×Dic122—22no—
71C4×Dic122—41no—
72#14519736—22no—
73#14519736—41no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94#14519711—22no—
95#14519702—22no—
96#14519702—22no—
97#14519702—22no—
98#14519702—22no—
99#14519702—41no—
100#14519702—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—41no—
121C22⋊C8×C61—41no—
122C22⋊C8×C61—41no—
123C4×C8×C61—41no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61C2×D411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122#4112yes—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—41no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C22⋊Dic61—24no—
178C22⋊Dic61—42no—
179C22⋊Dic61—42no—
180C22⋊Dic61—42no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61#4112yes—
191C4⋊Dic61#4112yes—
192C4⋊Dic61#4112yes—
193#11758196—24no—
194#11758196—42no—
195#11758196—42no—
196#11758196—42no—
197#11758196—42no—
198#11758196—42no—
199C4×Dic61—42no—
200C4×Dic61—42no—
201C4×Dic61—42no—
202C4×Dic61—42no—
203Dic244—44no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61C22×D411yescharacteristic
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61#13512yes—
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261Dic122—22no—
262Dic122—22no—
263Dic122—41no—
264Dic122—41no—
265Dic122—41no—
266Dic122—41no—
267Dic122—41no—
268Dic122—41no—
269C8×C61—41no—
270C8×C61—41no—
271C8×C61—41no—
272C8×C61—41no—
273#26732—611nomaximal, Sylow
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61#52511yescharacteristic
282C22×C61#54611yescharacteristic
283C22×C61#54611yescharacteristic
284C22×C61C2×#13511yescharacteristic
285C22×C61#57511yescharacteristic
286C22×C61#57811yescharacteristic
287C22×C61#57811yescharacteristic
288C4×C61—22no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61#52911yescharacteristic
294C4×C61#53811yescharacteristic
295C4×C61#55511yescharacteristic
296C4×C61#55911yescharacteristic
297Dic61—42no—
298Dic61—42no—
299Dic61—42no—
300Dic61—42no—
301Dic61—81no—
302Dic61—81no—
303Dic61—81no—
304Dic61—81no—
305#2489—611no—
306#2362—611no—
307#2056—611no—
308#2036—611no—
309#2026—611no—
310#2001—611no—
311#1989—611no—
312#1933—611no—
313#1928—611no—
314#1923D6111yescharacteristic
315#1918—611no—
316#1878—611no—
317#1873—611no—
318#1825—611no—
319C4×#103—611no—
320C2×C61—81no—
321C2×C61#245911yescharacteristic
322C2×C61#310211yescharacteristic
323C2×C61#312711yescharacteristic
324C2×C61#330011yescharacteristic
325C2×C61#330211yescharacteristic
326C2×C61#331511yescharacteristic
327C2×C61#332711yescharacteristic
328C22×Q16—611no—
329C2×#125—611no—
330C2×C22⋊Q8—611no—
331C2×C22⋊Q8—611no—
332C2×C4×Q8—611no—
333C2×#117—611no—
334C2×#107—611no—
335C2×C4⋊C8C2×D6111yescharacteristic
336C2×#103—611no—
337C2×#103—611no—
338C2×#103—611no—
339C2×#103—611no—
340C2×#103—611no—
341C2×#103—611no—
342C2×C22⋊C8C2×D6111yescharacteristic
343C2×C22⋊C8C2×D6111yescharacteristic
344C2×C4×C8C2×D6111yescharacteristic
345#400—1221no—
346#397—1221no—
347#391—611no—
348#391—611no—
349#391—611no—
350#389—611no—
351#388—1221no—
352#388—1221no—
353#388—1221no—
354#387—1221no—
355#382—1221no—
356#380—611no—
357C4×C4⋊C4—611no—
358C4×C4⋊C4—611no—
359C4×C4⋊C4—1221no—
360C4×C22⋊C4C2×D6111yescharacteristic
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#336C2×D6111yescharacteristic
370#336C2×D6111yescharacteristic
371C61#2673211yescharacteristic, complemented, Sylow
372C22×Q8—611no—
373C22×Q8—611no—
374C23×C4C22×D6111yescharacteristic
375C2×Q16—1222no—
376C2×Q16—2441no—
377C2×Q16—2441no—
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380C22×C8C22×D6111yescharacteristic
381C22×C8C22×D6111yescharacteristic
382#125—1222no—
383#125—2441no—
384C22⋊Q8—1222no—
385C22⋊Q8—1222no—
386C22⋊Q8—1222no—
387C22⋊Q8—2441no—
388C4×Q8—1222no—
389C4×Q8—2441no—
390#117—1222no—
391#117—2441no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4D24411yescharacteristic
409C2×C22⋊C4D24411yescharacteristic
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42—1221no—
413C2×C42—1221no—
414C2×C42C22×D6111yescharacteristic
415C2×C42C22×D6111yescharacteristic
416#107—1222no—
417C4⋊C8—41no—
418#103—1222no—
419#103—1222no—
420#103—1222no—
421#103—1222no—
422#103—2441no—
423#103—2441no—
424C22⋊C8—41no—
425C22⋊C8—41no—
426C4×C8—41no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437#95D24411yescharacteristic
438#95D24411yescharacteristic
439C24C2×D24411yescharacteristic
440C2×Q8—612no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4C2×D24411yescharacteristic
467C22×C4C2×D24411yescharacteristic
468C22×C4C2×D24411yescharacteristic
469C22×C4C2×D24411yescharacteristic
470C22×C4C2×D24411yescharacteristic
471C22×C4C23×D6111yescharacteristic
472Q16—2444no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C4⋊C4—612no—
486C4⋊C4—612no—
487C4⋊C4—612no—
488C4⋊C4—1224no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—2442no—
499C4⋊C4—2442no—
500C4⋊C4—2442no—
501C4⋊C4—2442no—
502C4⋊C4—2442no—
503C22⋊C4—22no—
504C22⋊C4—41no—
505C22⋊C4—1224no—
506C22⋊C4—2442no—
507C22⋊C4—2442no—
508C22⋊C4—2442no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—2442no—
514C42—2442no—
515C42—2442no—
516C42—2442no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C22×D24411yescharacteristic
525Q8—1222no—
526Q8—1222no—
527Q8—2441no—
528Q8—2441no—
529Q8—2441no—
530Q8—2441no—
531Q8—2441no—
532Q8—2441no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4#1451979912yes—
576C2×C4#41×D6111yescharacteristic
577C2×C4#41×D6111yescharacteristic
578C2×C4#41×D6111yescharacteristic
579C2×C4#41×D6111yescharacteristic
580C2×C4#1451982211yescharacteristic
581C2×C4#1451982211yescharacteristic
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1684027411yescharacteristic
594C22#1684040711yescharacteristic
595C22#1684040711yescharacteristic
596C22C2×#1451979911yescharacteristic
597C22#1684056211yescharacteristic
598C22#1684057911yescharacteristic
599C22#1684057911yescharacteristic
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—4881no—
606C4—4881no—
607C4—4881no—
608C4—4881no—
609C4—2442no—
610C4—2442no—
611C4—2442no—
612C4—2442no—
613C4#1684029511yescharacteristic
614C4#1684034411yescharacteristic
615C4#1684047411yescharacteristic
616C4#1684049611yescharacteristic
617C2—81no—
618C2#2144975411yescharacteristic
619C2#2145583911yescharacteristic
620C2#2145612011yescharacteristic
621C2#2145770811yescharacteristic
622C2#2145773711yescharacteristic
623C2#2145791711yescharacteristic
624C2#2145808911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#1923D61
hypocenterC61#26732
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #21447142C2semidirect
5. #21446971C2semidirect
7. #21446774C2semidirect
8. #21446495C2semidirect
9. #21446461C2semidirect
10. #21446391C2semidirect
11. #21446159C2semidirect
14. C4×#14519702C2semidirect
371. C61#26732semidirect

Maximal subgroups

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

subgroupindex
#214501602
#214488442
#214471422
#214470232
#214469712
#214468292
#214467742
#214464952
#214464612
#214463912
#214461592
#214461292
#214459152
C4×#145197022
C61×#19232
#2673261