Finite Group Databasebeta

← #29653629

Subgroups — #29653629

Order 15616.

1068 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455739C211yesmaximal, characteristic, complemented
2C2×#16840073C211yesmaximal, characteristic, complemented
3#21450312C211yesmaximal, characteristic, complemented
4#21444833C214yesmaximal, complemented
5#21444805C214yesmaximal, complemented
6#21444335C211yesmaximal, characteristic, complemented
7#21444310C211yesmaximal, characteristic, complemented
8#21444179C211yesmaximal, characteristic, complemented
9C61×#3537C211yesmaximal, characteristic
10C22×C4⋊Dic61C2211yescharacteristic, complemented
11#16840095—21no—
12#16840090C2212yescomplemented
13#16840078—21no—
14#16840073—22no—
15#16840073C2214yescomplemented
16#16840073C2212yescomplemented
17#16839805—21no—
18C2×#14519710—21no—
19#16839763—21no—
20C2×#14519698—21no—
21#16839726C2211yescharacteristic, complemented
22C2×C22⋊#92418C2211yescharacteristic, complemented
23#16839687C2214yescomplemented
24#16839665—21no—
25#16839642—22no—
26#16839627—21no—
27C4×C22⋊Dic61C2211yescharacteristic, complemented
28#16839499C2212yescomplemented
29#16839496C2212yescomplemented
30#16839496C2214yescomplemented
31#16839486C2214yescomplemented
32C61×#560—22no—
33C61×#553—21no—
34C61×#553—21no—
35D42×C61—22no—
36D42×C61—21no—
37D42×C61—21no—
38C61×#540—21no—
39C61×#538—21no—
40C61×#538C2212yes—
41C61×#535—21no—
42C61×#534—21no—
43C61×#534C2212yes—
44C61×#525C2211yescharacteristic
45C2×#121×C61C2211yescharacteristic
46C2×#121×C61C2211yescharacteristic
47C23×Dic61—21no—
48C2×#11758194—21no—
49C22×#92418—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61C2312yes—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—24no—
58C2×C4×Dic61—21no—
59#14519710—24no—
60#14519710—22no—
61#14519708—22no—
62#14519701—22no—
63#14519698—24no—
64#14519698—22no—
65C22⋊#92418—21no—
66C22⋊#92418—21no—
67C22⋊#92418C2312yes—
68C22⋊#92418C2312yes—
69#14519684—24no—
70#14519684C2312yes—
71C2×#41×C61D411yescharacteristic
72C22×D4×C61—22no—
73C22×D4×C61—21no—
74C22×D4×C61—22no—
75C22×D4×C61—21no—
76C22×D4×C61D412yes—
77C22×D4×C61D411yescharacteristic
78C22×D4×C61D411yescharacteristic
79C23×C4×C61C2311yescharacteristic
80#127×C61—22no—
81#127×C61—21no—
82#126×C61—22no—
83#126×C61—22no—
84#125×C61—21no—
85#124×C61—22no—
86#123×C61—22no—
87#123×C61—21no—
88#123×C61—22no—
89#123×C61—22no—
90#123×C61—22no—
91C22⋊Q8×C61D411yescharacteristic
92C22⋊Q8×C61C2311yescharacteristic
93#121×C61—22no—
94#121×C61—21no—
95#121×C61—21no—
96#121×C61—22no—
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—21no—
101#121×C61—22no—
102#121×C61—21no—
103#121×C61—21no—
104#121×C61—21no—
105#121×C61—21no—
106#121×C61—21no—
107#121×C61D411yescharacteristic
108#121×C61D412yes—
109#121×C61C2311yescharacteristic
110#121×C61C2312yes—
111#120×C61—22no—
112#120×C61—22no—
113#120×C61—22no—
114#120×C61—22no—
115#120×C61—21no—
116#120×C61—22no—
117#120×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—21no—
120C4×D4×C61—21no—
121C4×D4×C61—22no—
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124#117×C61—21no—
125#117×C61D411yescharacteristic
126C2×C4⋊C4×C61D411yescharacteristic
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61C2312yes—
130C24×C61—22no—
131C24×C61—21no—
132C24×C61C2×D411yescharacteristic
133C24×C61C2×D412yes—
134#41×C61—42no—
135C2×Q8×C61C2×D411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—21no—
138C2×D4×C61—22no—
139C2×D4×C61—21no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—42no—
152C2×D4×C61—42no—
153C2×D4×C61—44no—
154C2×D4×C61—82no—
155C2×D4×C61—82no—
156C2×D4×C61—84no—
157C2×D4×C61—84no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D412yes—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—42no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2411yescharacteristic
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—41no—
175C22×Dic61—41no—
176C22×Dic61—82no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61C2×D412yes—
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—21no—
201C42×C61—22no—
202C42×C61—21no—
203C22⋊Dic61—42no—
204C22⋊Dic61—84no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61—41no—
208C4⋊Dic61—41no—
209C4×Dic61—42no—
210#11758194—42no—
211C2×#92418—22no—
212C2×#92418—22no—
213C2×#92418—42no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—21no—
219C23×C61—24no—
220C23×C61—41no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—81no—
225C23×C61—81no—
226C23×C61—82no—
227C23×C61—82no—
228C23×C61—82no—
229C23×C61#12011yescharacteristic
230C23×C61#12011yescharacteristic
231C23×C61C22×D411yescharacteristic
232Q8×C61—41no—
233D4×C61—42no—
234D4×C61—41no—
235D4×C61—44no—
236D4×C61—42no—
237D4×C61—44no—
238D4×C61—42no—
239D4×C61—42no—
240D4×C61—42no—
241D4×C61—81no—
242D4×C61—82no—
243D4×C61—82no—
244D4×C61—81no—
245D4×C61—82no—
246D4×C61—82no—
247D4×C61—82no—
248D4×C61—82no—
249D4×C61—82no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—81no—
264C2×C4×C61—82no—
265C2×C4×C61—82no—
266C2×C4×C61#12011yescharacteristic
267C2×C4×C61#12011yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—44no—
275C2×Dic61—82no—
276C2×Dic61—82no—
277#92418—42no—
278#92418—42no—
279#18264—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—44no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—41no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—84no—
298C22×C61—162no—
299C22×C61—164no—
300C22×C61#45512yes—
301C22×C61C2×#12011yescharacteristic
302C22×C61#57612yes—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—42no—
307C4×C61—41no—
308C4×C61—42no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61#45812yes—
312Dic61—82no—
313Dic61—82no—
314#3537D6111yescharacteristic
315#3092—611no—
316C2×#480—611no—
317#2504—611no—
318#1612—614no—
319#1607—614no—
320#1507—611no—
321#1501—611no—
322#1471—611no—
323C2×C61—22no—
324C2×C61—22no—
325C2×C61—41no—
326C2×C61—82no—
327C2×C61—82no—
328C2×C61—81no—
329C2×C61#300811yescharacteristic
330C2×C61C2×#45511yescharacteristic
331C2×C61C2×#45811yescharacteristic
332#560—22no—
333#553—21no—
334#553—21no—
335D42—22no—
336D42—21no—
337D42—21no—
338#540—21no—
339#538—21no—
340#538C2×D6112yes—
341#535—21no—
342#534—21no—
343#534C2×D6112yes—
344#525C2×D6111yescharacteristic
345C2×#121C2×D6111yescharacteristic
346C2×#121C2×D6111yescharacteristic
347C22×C4⋊C4—611no—
348#484—1221no—
349#483—612no—
350#481—1221no—
351#480—614no—
352#480—612no—
353#480—1222no—
354#428—1221no—
355C2×#107—1221no—
356#417—1221no—
357C2×#102—1221no—
358#407—611no—
359C2×C22⋊C8—611no—
360#397—614no—
361#390—1221no—
362#386—1222no—
363#382—1221no—
364C4×C22⋊C4—611no—
365#328—612no—
366#327—612no—
367#327—614no—
368#323—614no—
369C61#1826411yescharacteristic, complemented, Sylow
370C2×#41C22⋊D6111yescharacteristic
371C22×D4—22no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—22no—
375C22×D4C22⋊D6112yes—
376C22×D4C22⋊D6111yescharacteristic
377C22×D4C22⋊D6111yescharacteristic
378C23×C4—1221no—
379C23×C4C22×D6111yescharacteristic
380C2×M16—1221no—
381C22×C8—1221no—
382#127—22no—
383#127—21no—
384#126—22no—
385#126—22no—
386#125—21no—
387#124—22no—
388#123—22no—
389#123—21no—
390#123—22no—
391#123—22no—
392#123—22no—
393C22⋊Q8C22⋊D6111yescharacteristic
394C22⋊Q8C22×D6111yescharacteristic
395#121—22no—
396#121—21no—
397#121—21no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—22no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—22no—
409#121C22⋊D6112yes—
410#121C22⋊D6111yescharacteristic
411#121C22×D6112yes—
412#121C22×D6111yescharacteristic
413#120—22no—
414#120—22no—
415#120—22no—
416#120—21no—
417#120—22no—
418#120—22no—
419#120—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—22no—
426#117—21no—
427#117C22⋊D6111yescharacteristic
428C2×C4⋊C4—612no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4C22⋊D6111yescharacteristic
435C2×C4⋊C4C22⋊D6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1224no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4C22×D6112yes—
440C2×C42—1221no—
441#107—1224no—
442#107—1222no—
443#106—1222no—
444#103—1222no—
445#102—1224no—
446#102—1222no—
447C22⋊C8—612no—
448C22⋊C8—612no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451#95—612no—
452#95—1224no—
453C24—22no—
454C24—21no—
455C24C2×C22⋊D6111yescharacteristic
456C24C2×C22⋊D6112yes—
457#41—42no—
458C2×Q8C2×C22⋊D6111yescharacteristic
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4—84no—
480C2×D4—84no—
481C2×D4C2×C22⋊D6111yescharacteristic
482C2×D4C2×C22⋊D6112yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—4882no—
491C22×C4—2441no—
492C22×C4—2441no—
493C22×C4C2×C22⋊D6111yescharacteristic
494C22×C4C2×C22⋊D6111yescharacteristic
495C22×C4C2×C22⋊D6111yescharacteristic
496C22×C4C2×C22⋊D6112yes—
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500M16—2442no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2442no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—2441no—
514C4⋊C4—2441no—
515C4⋊C4C2×C22⋊D6111yescharacteristic
516C4⋊C4C2×C22⋊D6112yes—
517C4⋊C4C2×C22⋊D6111yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—4884no—
533C22⋊C4—2442no—
534C42—22no—
535C42—21no—
536C42—2442no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—24no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23#1451974611yescharacteristic
553C23#1451974611yescharacteristic
554C23C22×C22⋊D6111yescharacteristic
555Q8—41no—
556D4—42no—
557D4—41no—
558D4—44no—
559D4—42no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—81no—
565D4—82no—
566D4—82no—
567D4—81no—
568D4—82no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4—82no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—81no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—4882no—
590C2×C4—4882no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2444no—
596C2×C4#1451974611yescharacteristic
597C2×C4#1451974611yescharacteristic
598C2×C4C22×C22⋊D6111yescharacteristic
599C2×C4C22×C22⋊D6111yescharacteristic
600C8—2442no—
601C8—2442no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—84no—
620C22—162no—
621C22—164no—
622C22#1683994012yes—
623C22C2×#1451974611yescharacteristic
624C22#1684056512yes—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4—4882no—
634C4—4882no—
635C4#1683995212yes—
636C2—22no—
637C2—22no—
638C2—41no—
639C2—82no—
640C2—82no—
641C2—81no—
642C2#2145508711yescharacteristic
643C2C2×#1683994011yescharacteristic
644C2C2×#1683995211yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3537C2
socleC22×C61C2×#120
hypercenter#3537D61
hypocenterC61#18264
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #21455739C2semidirect
2. C2×#16840073C2semidirect
3. #21450312C2semidirect
4. #21444833C2semidirect
5. #21444805C2semidirect
6. #21444335C2semidirect
7. #21444310C2semidirect
8. #21444179C2semidirect
10. C22×C4⋊Dic61C22semidirect
12. #16840090C22semidirect
15. #16840073C22semidirect
16. #16840073C22semidirect
21. #16839726C22semidirect
22. C2×C22⋊#92418C22semidirect
23. #16839687C22semidirect
27. C4×C22⋊Dic61C22semidirect
28. #16839499C22semidirect
29. #16839496C22semidirect
30. #16839496C22semidirect
31. #16839486C22semidirect
369. C61#18264semidirect

Maximal subgroups

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

subgroupindex
#214557392
C2×#168400732
#214503122
#214448332
#214448052
#214443352
#214443102
#214441792
C61×#35372
#1826461