Finite Group Databasebeta

← #30625612

Subgroups — #30625612

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462659C214yesmaximal, complemented
2#21462656C214yesmaximal, complemented
3#21462645C214yesmaximal, complemented
4#21462644C214yesmaximal, complemented
5#21462612C212yesmaximal, complemented
6#21462548C212yesmaximal, complemented
7#21462533C214yesmaximal, complemented
8#21462506C212yesmaximal, complemented
9#21462498C211yesmaximal, characteristic, complemented
10#21462390C212yesmaximal, complemented
11C2×#16840721C211yesmaximal, characteristic, complemented
12#21459114C211yesmaximal, characteristic
13C2×#14519864C2214yes—
14C22×D61⋊C8C2212yes—
15#16840814C2218yescomplemented
16#16840813C2218yescomplemented
17#16840794C2218yes—
18#16840793C2218yes—
19#16840793C2218yescomplemented
20#16840793C2218yescomplemented
21#16840789C2218yes—
22D4×#92420C2218yes—
23#16840786C2218yescomplemented
24#16840785C2212yes—
25#16840783C2214yescomplemented
26#16840782C2212yes—
27#16840782C2214yescomplemented
28#16840780C2212yes—
29#16840779C2212yes—
30#16840769C2214yes—
31#16840767C2212yes—
32#16840736C2214yes—
33#16840733C2212yes—
34#16840727C2214yes—
35#16840726C2218yescomplemented
36C4×#11758213C2212yes—
37C4×#11758217C2214yescomplemented
38#16840721C2212yes—
39#16840721C2212yes—
40#16840721C2211yescharacteristic
41#16840721C2212yes—
42#16840721C2211yescharacteristic
43C2×#14519832C2212yes—
44C2×#14519832C2212yes—
45C2×#14519832C2214yescomplemented
46#16840319C411yescharacteristic
47#16840317C411yescharacteristic
48#16840317C2211yescharacteristic
49#16840310C411yescharacteristic
50#16840310C2211yescharacteristic
51#16840294C412yes—
52#16840294C412yes—
53#16840293C412yes—
54#16840293C2212yes—
55#16840291C412yes—
56#16840291C2212yes—
57#16840272C412yes—
58#16840272C2212yes—
59#16840269C412yes—
60#41×Dic61C2212yes—
61C4×#11758224C2212yes—
62C4×#11758224C2212yes—
63C2×C42×D61C2211yescharacteristic
64C61×#532C411yescharacteristic
65#14519864—216no—
66C2×#11758213C2314yes—
67C2×#11758217C2318yes—
68C2×D61⋊C8—28no—
69C2×D61⋊C8C2312yes—
70C2×D61⋊C8C2314yes—
71C2×D61⋊C8C2312yes—
72C22×#92420C2314yes—
73C22×#92420C2318yes—
74#14519844C2314yes—
75#14519844C2314yes—
76#14519844C2318yes—
77C4⋊#92420C2318yes—
78#14519834C2314yes—
79C22⋊#92420C2314yes—
80C22⋊#92420C2318yes—
81C22⋊#92420C2318yes—
82#14519832C2312yes—
83#14519832C2312yes—
84#14519832C2312yes—
85#14519832C2312yes—
86#14519832C2314yes—
87#14519832C2314yes—
88#14519832C2314yes—
89#14519832C2318yes—
90C4×#92420C2318yes—
91C4×#92420C2314yes—
92C2×#11758224C2×C412yes—
93C2×#11758224C2312yes—
94C22×C4×D61C2×C411yescharacteristic
95C22×C4×D61C2×C411yescharacteristic
96C22×C4×D61C2311yescharacteristic
97#14519777C2×C411yescharacteristic
98#14519777C2×C411yescharacteristic
99#14519770C2×C414yes—
100#14519770C2×C414yes—
101#14519769C2×C412yes—
102#14519768C2×C412yes—
103#14519768C2×C412yes—
104#14519764C2×C412yes—
105#14519764C2×C412yes—
106#14519759C2×C414yes—
107#14519759C2×C414yes—
108#14519758C2×C414yes—
109#14519757C2×C412yes—
110#14519757C2×C412yes—
111#14519756C2×C412yes—
112#14519756C2×C412yes—
113#14519753C2×C412yes—
114#14519753C2×C412yes—
115#14519748C2×C412yes—
116#14519748C2×C412yes—
117#14519748C2×C412yes—
118#14519748C2×C412yes—
119#14519745C2×C414yes—
120Q8×Dic61C2×C412yes—
121Q8×Dic61C2312yes—
122C4×Dic122C2×C412yes—
123C4×Dic122C2×C412yes—
124#14519742C2×C412yes—
125#14519742C2312yes—
126D4×Dic61C2×C412yes—
127D4×Dic61C2×C414yes—
128D4×Dic61C2×C412yes—
129D4×Dic61C2312yes—
130D4×Dic61C2314yes—
131D4×Dic61C2312yes—
132C4×C22⋊D61C2×C414yes—
133C4×C22⋊D61C2×C414yes—
134#14519737C2×C414yes—
135#14519737C2314yes—
136#14519736C2×C412yes—
137#14519736C2×C414yes—
138#14519735C2×C412yes—
139#14519735C2312yes—
140#14519733C2×C414yes—
141#14519733C2314yes—
142C2×C4×Dic61C2×C411yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145C2×C4×Dic61C2314yes—
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61C2×C411yescharacteristic
150C42×D61C2311yescharacteristic
151C42×D61C2311yescharacteristic
152C42×D61C2311yescharacteristic
153C42×D61C2311yescharacteristic
154C2×#41×C61C2×C412yes—
155C4⋊Q8×C61C2×C411yescharacteristic
156#127×C61C2×C411yescharacteristic
157#124×C61C2×C412yes—
158#121×C61C2×C412yes—
159#121×C61C2×C412yes—
160C4×D4×C61C2×C412yes—
161C4×D4×C61C2×C412yes—
162C2×C42×C61C2×C411yescharacteristic
163C23×D61C22×C411yescharacteristic
164#41×C61—44no—
165C2×Q8×C61C22×C412yes—
166C2×D4×C61C22×C412yes—
167C2×D4×C61C22×C414yes—
168C2×D4×C61C22×C412yes—
169C2×D4×C61C22×C412yes—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C414yes—
174C2×C22⋊D61C22×C414yes—
175C2×C22⋊D61C22×C414yes—
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C414yes—
179C22×Dic61C2411yescharacteristic
180C22×Dic61C2414yes—
181#11758224—28no—
182#11758224—44no—
183C2×C4×D61—24no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61C22×C411yescharacteristic
187C2×C4×D61C22×C411yescharacteristic
188C2×C4×D61C22×C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C22×C411yescharacteristic
191C2×C4×D61C22×C411yescharacteristic
192C2×C4×D61C22×C411yescharacteristic
193C2×C4×D61C22×C411yescharacteristic
194C2×C4×D61C22×C411yescharacteristic
195C2×C4×D61C22×C411yescharacteristic
196C2×C4×D61C2411yescharacteristic
197C2×C4×D61C2411yescharacteristic
198C2×Dic122C22×C412yes—
199C2×Dic122C22×C412yes—
200#11758217—216no—
201C2×#92420—28no—
202C2×#92420—216no—
203C2×#92420C2418yes—
204C2×#92420C2414yes—
205C2×#92420C2414yes—
206#11758213—28no—
207D61⋊C8—24no—
208D61⋊C8—28no—
209D61⋊C8#4118yescomplemented
210C4⋊C4×C61C22×C412yes—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61C22×C414yes—
213C22⋊C4×C61C22×C414yes—
214C42×C61C22×C411yescharacteristic
215C42×C61C22×C411yescharacteristic
216C42×C61C22×C411yescharacteristic
217C42×C61C22×C411yescharacteristic
218C22⋊Dic61C22×C414yes—
219C22⋊Dic61C22×C414yes—
220C22⋊Dic61C22×C414yes—
221C22⋊Dic61C22×C414yes—
222C22⋊Dic61C22×C414yes—
223#11758198C22×C414yes—
224#11758198C22×C414yes—
225C4⋊Dic61C22×C412yes—
226C4⋊Dic61C22×C412yes—
227C4⋊Dic61C22×C412yes—
228C4⋊Dic61C22×C414yes—
229C4⋊Dic61C22×C412yes—
230C4⋊Dic61C22×C414yes—
231#11758196C22×C414yes—
232#11758196C22×C414yes—
233#11758196C22×C414yes—
234#11758196C22×C414yes—
235C4×Dic61C22×C411yescharacteristic
236C4×Dic61C22×C411yescharacteristic
237C4×Dic61C22×C411yescharacteristic
238C4×Dic61C22×C411yescharacteristic
239C4×Dic61C22×C411yescharacteristic
240C4×Dic61C22×C411yescharacteristic
241C4×Dic61C22×C411yescharacteristic
242C4×Dic61C22×C411yescharacteristic
243C4×Dic61C22×C414yes—
244C4×Dic61C22×C414yes—
245C4×Dic61C2411yescharacteristic
246C4×Dic61C2414yes—
247C4×Dic61C2411yescharacteristic
248C4×Dic61C2411yescharacteristic
249C4×Dic61C2411yescharacteristic
250C23×C61C23×C414yes—
251C23×C61C23×C411yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61C23×C411yescharacteristic
256C22×D61C23×C411yescharacteristic
257Q8×C61—42no—
258D4×C61—28no—
259D4×C61—24no—
260D4×C61—42no—
261D4×C61—42no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—41no—
265C2×C4×C61—44no—
266C2×C4×C61C23×C411yescharacteristic
267C2×C4×C61C23×C411yescharacteristic
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C23×C414yes—
270C2×C4×C61C23×C411yescharacteristic
271C2×C4×C61C23×C411yescharacteristic
272C2×C4×C61C23×C411yescharacteristic
273C22⋊D61—28no—
274C22⋊D61—28no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—28no—
278C2×Dic61—41no—
279C2×Dic61—44no—
280C2×Dic61C23×C411yescharacteristic
281C2×Dic61C23×C411yescharacteristic
282C2×Dic61C23×C411yescharacteristic
283C2×Dic61C23×C411yescharacteristic
284C2×Dic61C23×C411yescharacteristic
285C2×Dic61C23×C414yes—
286C2×Dic61C23×C414yes—
287C2×Dic61C2511yescharacteristic
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61—41no—
298C4×D61—41no—
299C4×D61C2×#4114yes—
300Dic122—24no—
301Dic122—42no—
302#92420—24no—
303#92420—28no—
304#92420C2×#4118yes—
305#60207—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61—24no—
309C22×C61—24no—
310C22×C61—24no—
311C22×C61#56812yes—
312C22×C61C24×C411yescharacteristic
313C2×D61—28no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61C4×#4112yes—
319C2×D61#56812yes—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—21no—
324C4×C61—21no—
325C4×C61—24no—
326C4×C61C4×#4112yes—
327Dic61—24no—
328Dic61—21no—
329Dic61—24no—
330Dic61—21no—
331Dic61—21no—
332Dic61—21no—
333Dic61—21no—
334Dic61C22×#4112yes—
335#3444—611no—
336#2970—614no—
337#2970—614no—
338#2968—614no—
339#2968—614no—
340#2961—612no—
341#2932—612no—
342#2929—614no—
343#2923—612no—
344#2920—611no—
345#2875—612no—
346C22×#97—611no—
347C2×C61—22no—
348C2×C61—44no—
349C2×C61C2×C4×#4111yescharacteristic
350C2×C61C2×#56811yescharacteristic
351C2×C61C2×#56811yescharacteristic
352D61—22no—
353D61—22no—
354C2×#131—614no—
355C23×C8—612no—
356#533—611no—
357#533—611no—
358#533—611no—
359#532—611no—
360#532—611no—
361#532#692311yescharacteristic
362#529—612no—
363#529—612no—
364#529—612no—
365#529—612no—
366#529—612no—
367#529—612no—
368#525—612no—
369#525—612no—
370#525—612no—
371C4×#41—612no—
372C4×#41—612no—
373C4×#41—612no—
374C22×C42—611no—
375#446—618no—
376#446—618no—
377#435—618no—
378#435—618no—
379#435—618no—
380#435—618no—
381C8×D4—618no—
382C8×D4—618no—
383#433—618no—
384#432—612no—
385#432—614no—
386#432—614no—
387#432—612no—
388#431—612no—
389#431—612no—
390#424—614no—
391#423—612no—
392#408—614no—
393#407—612no—
394#405—618no—
395#405—614no—
396C4×M16—614no—
397C4×M16—612no—
398C2×#97—612no—
399C2×#97—612no—
400C2×#97—614no—
401C2×#97—611no—
402C2×#97—611no—
403C2×#97—612no—
404C2×#97—612no—
405C2×#97—612no—
406C61#6020711yescharacteristic, complemented, Sylow
407C2×#41—612no—
408C2×#41—612no—
409C2×#41C2×#692312yes—
410C23×C4—611no—
411C23×C4—611no—
412C23×C4—611no—
413#131—12216no—
414C2×M16—618no—
415C2×M16—614no—
416C22×C8—612no—
417C22×C8—614no—
418C22×C8—618no—
419C22×C8—612no—
420C22×C8—614no—
421C22×C8—1228no—
422C4⋊Q8—611no—
423C4⋊Q8—611no—
424C4⋊Q8C2×#692311yescharacteristic
425#127C2×#692311yescharacteristic
426#126—614no—
427#126—614no—
428#125—612no—
429#125—612no—
430#125—612no—
431#124—612no—
432#124—612no—
433#124C2×#692312yes—
434#123—614no—
435#123—614no—
436#123—614no—
437C22⋊Q8—612no—
438C22⋊Q8—612no—
439C22⋊Q8—612no—
440C22⋊Q8—612no—
441C22⋊Q8—612no—
442C22⋊Q8—612no—
443#121—612no—
444#121—612no—
445#121—612no—
446#121—612no—
447#121C2×#692312yes—
448#121C2×#692312yes—
449#120—614no—
450C4×Q8—612no—
451C4×Q8—612no—
452C4×Q8—612no—
453C4×Q8—612no—
454C4×Q8—612no—
455C4×Q8—612no—
456C4×D4—614no—
457C4×D4—614no—
458C4×D4—612no—
459C4×D4—612no—
460C4×D4—612no—
461C4×D4—612no—
462C4×D4—614no—
463C4×D4—614no—
464C4×D4—614no—
465C4×D4—614no—
466C4×D4C2×#692312yes—
467C4×D4C2×#692312yes—
468#117—612no—
469#117—614no—
470#117—612no—
471#117—612no—
472#117—614no—
473#117—614no—
474C2×C42—614no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42C2×#692311yescharacteristic
487C4⋊C8—618no—
488C4⋊C8—614no—
489C4⋊C8—614no—
490C4⋊C8—618no—
491C22⋊C8—614no—
492C22⋊C8—618no—
493C22⋊C8—618no—
494C22⋊C8—614no—
495#97—612no—
496#97—612no—
497#97—612no—
498#97—612no—
499#97—614no—
500#97—614no—
501#97—614no—
502#97—618no—
503C4×C8—614no—
504C4×C8—618no—
505C24—611no—
506#41—44no—
507#41—1228no—
508#41—2444no—
509C2×Q8—612no—
510C2×Q8—612no—
511C2×Q8C22×#692312yes—
512C2×D4—614no—
513C2×D4—614no—
514C2×D4C22×#692314yes—
515C2×D4C22×#692312yes—
516C2×D4C22×#692312yes—
517C2×D4C22×#692312yes—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—614no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—614no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—1224no—
536C22×C4—2442no—
537C22×C4—2442no—
538C22×C4C22×#692311yescharacteristic
539C22×C4C22×#692311yescharacteristic
540C22×C4C22×#692311yescharacteristic
541C22×C4C22×#692314yes—
542M16—12216no—
543M16—1228no—
544C2×C8—614no—
545C2×C8—618no—
546C2×C8—618no—
547C2×C8—614no—
548C2×C8—1228no—
549C2×C8—1228no—
550C2×C8—12216no—
551C2×C8—1224no—
552C4⋊C4—614no—
553C4⋊C4—614no—
554C4⋊C4—614no—
555C4⋊C4—614no—
556C4⋊C4—612no—
557C4⋊C4—612no—
558C4⋊C4—612no—
559C4⋊C4—612no—
560C4⋊C4—614no—
561C4⋊C4—614no—
562C4⋊C4C22×#692312yes—
563C4⋊C4C22×#692312yes—
564C22⋊C4—614no—
565C22⋊C4—614no—
566C22⋊C4—614no—
567C22⋊C4—614no—
568C22⋊C4—614no—
569C22⋊C4—614no—
570C22⋊C4—614no—
571C22⋊C4C22×#692314yes—
572C22⋊C4C22×#692314yes—
573C42—611no—
574C42—614no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—614no—
587C42—614no—
588C42C22×#692311yescharacteristic
589C42C22×#692311yescharacteristic
590C42C22×#692311yescharacteristic
591C42C22×#692311yescharacteristic
592C23—611no—
593C23—611no—
594C23—1222no—
595C23—1222no—
596C23—1222no—
597C23C23×#692314yes—
598C23C23×#692311yescharacteristic
599Q8—42no—
600Q8—1224no—
601Q8—2442no—
602D4—28no—
603D4—24no—
604D4—42no—
605D4—42no—
606D4—1228no—
607D4—1228no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—44no—
612C2×C4—611no—
613C2×C4—614no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—611no—
617C2×C4—611no—
618C2×C4—611no—
619C2×C4—614no—
620C2×C4—614no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1228no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2444no—
637C2×C4C23×#692311yescharacteristic
638C2×C4C23×#692311yescharacteristic
639C2×C4C23×#692311yescharacteristic
640C2×C4C23×#692311yescharacteristic
641C2×C4C23×#692311yescharacteristic
642C2×C4C23×#692314yes—
643C2×C4C23×#692311yescharacteristic
644C8—618no—
645C8—1224no—
646C8—1228no—
647C22—21no—
648C22—21no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—612no—
653C22—612no—
654C22—1228no—
655C22—1221no—
656C22—1221no—
657C22—1221no—
658C22—1221no—
659C22#1684084012yes—
660C22C24×#692311yescharacteristic
661C4—21no—
662C4—21no—
663C4—21no—
664C4—24no—
665C4—21no—
666C4—21no—
667C4—612no—
668C4—1221no—
669C4—1224no—
670C4—1221no—
671C4—1221no—
672C4—1221no—
673C4—1221no—
674C4—1224no—
675C4#41×#692312yes—
676C2—22no—
677C2—44no—
678C2—1222no—
679C2—1222no—
680C2C2×#41×#692311yescharacteristic
681C2C2×#1684084011yescharacteristic
682C2D61⋊#56811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingC61×#532C4
prime radical#21459114C2
cosocleC2×Dic61C25
hypercenter#532#6923
hypocenterC61#60207
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462659C2semidirect
2. #21462656C2semidirect
3. #21462645C2semidirect
4. #21462644C2semidirect
5. #21462612C2semidirect
6. #21462548C2semidirect
7. #21462533C2semidirect
8. #21462506C2semidirect
9. #21462498C2semidirect
10. #21462390C2semidirect
11. C2×#16840721C2semidirect
15. #16840814C22semidirect
16. #16840813C22semidirect
19. #16840793C22semidirect
20. #16840793C22semidirect
23. #16840786C22semidirect
25. #16840783C22semidirect
27. #16840782C22semidirect
35. #16840726C22semidirect
37. C4×#11758217C22semidirect
45. C2×#14519832C22semidirect
209. D61⋊C8#41semidirect
406. C61#60207semidirect

Maximal subgroups

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

subgroupindex
#214626592
#214626562
#214626452
#214626442
#214626122
#214625482
#214625332
#214625062
#214624982
#214623902
C2×#168407212
#214591142
#6020761