Finite Group Databasebeta

← #29654216

Subgroups — #29654216

Order 15616.

1192 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456621C211yesmaximal, characteristic, complemented
2#21456616C211yesmaximal, characteristic, complemented
3#21450750C211yesmaximal, characteristic, complemented
4#21444867C214yesmaximal, complemented
5#21444765C214yesmaximal, complemented
6#21444339C211yesmaximal, characteristic, complemented
7#21444335C211yesmaximal, characteristic, complemented
8#21444146C211yesmaximal, characteristic, complemented
9C2×C61×#538C211yesmaximal, characteristic, complemented
10C2×#14519760—21no—
11C2×#14519751C2211yescharacteristic
12C2×#14519746—21no—
13#16840095C2212yescomplemented
14#16840080—21no—
15#16840078C2212yescomplemented
16#16840075—21no—
17#16840013—22no—
18#16840010—22no—
19#16839912C2212yescomplemented
20#16839901—21no—
21#16839896—21no—
22#16839895C2212yescomplemented
23#16839726C2211yescharacteristic
24#16839726C2211yescharacteristic
25#16839698C2212yescomplemented
26#16839671C2212yescomplemented
27#16839662—22no—
28C4×C22⋊Dic61C2211yescharacteristic
29#16839499C2214yescomplemented
30#16839496C2214yescomplemented
31#16839486C2214yescomplemented
32C61×#538—22no—
33C61×#538—22no—
34C61×#538—22no—
35C61×#538C2214yes—
36C2×#126×C61—21no—
37C2×#124×C61—21no—
38C2×#123×C61—21no—
39C2×C22⋊Q8×C61C2211yescharacteristic
40C2×#121×C61—21no—
41C2×#121×C61C2211yescharacteristic
42C2×#120×C61—21no—
43C2×C4×D4×C61—21no—
44C22×C22⋊C4×C61C2211yescharacteristic
45C22×D244C2311yescharacteristic
46C22×C22⋊D61—21no—
47C22×C22⋊D61—22no—
48C2×#11758201—22no—
49C2×#11758199—22no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52#14519760—44no—
53#14519751—21no—
54#14519751—21no—
55#14519751—21no—
56#14519751—21no—
57#14519746—44no—
58C2×C4⋊Dic61C2311yescharacteristic
59C2×#11758196—22no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—22no—
62C2×#11758198—21no—
63C2×#11758198—22no—
64C2×C4×Dic61—21no—
65#14519710—22no—
66#14519708—22no—
67#14519701—22no—
68#14519698—22no—
69#14519697—22no—
70#14519697—22no—
71C22⋊#92418—21no—
72C22⋊#92418—21no—
73C22⋊#92418C2312yes—
74C22⋊#92418C2312yes—
75#14519684C2312yes—
76C25×C61D411yescharacteristic
77C22×Q8×C61D411yescharacteristic, complemented
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61D411yescharacteristic, complemented
82C23×C4×C61—21no—
83C23×C4×C61D411yescharacteristic
84C23×C4×C61C2311yescharacteristic
85#126×C61—24no—
86#126×C61—24no—
87#124×C61—24no—
88#124×C61—24no—
89#123×C61—24no—
90#123×C61—24no—
91C22⋊Q8×C61—21no—
92C22⋊Q8×C61—21no—
93C22⋊Q8×C61D412yescomplemented
94C22⋊Q8×C61C2312yes—
95#121×C61—24no—
96#121×C61—24no—
97#121×C61—21no—
98#121×C61—21no—
99#121×C61D412yescomplemented
100#121×C61C2312yes—
101#120×C61—24no—
102#120×C61—24no—
103C4×D4×C61—24no—
104C4×D4×C61—24no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61D411yescharacteristic, complemented
108C2×C4⋊C4×C61D411yescharacteristic, complemented
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61D412yes—
119C2×C22⋊C4×C61C2312yes—
120C2×C42×C61—21no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—42no—
125C24×C61—42no—
126C24×C61—81no—
127C24×C61C2×D411yescharacteristic
128C24×C61C2×D412yes—
129C23×D61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—81no—
132C2×Q8×C61C2×D412yes—
133C2×D4×C61—22no—
134C2×D4×C61—22no—
135C2×D4×C61—24no—
136C2×D4×C61—24no—
137C2×D4×C61—21no—
138C2×D4×C61—44no—
139C2×D4×C61—81no—
140C2×D4×C61—82no—
141C2×D4×C61—82no—
142C2×D4×C61C2×D412yes—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—24no—
148C22×C4×C61—21no—
149C22×C4×C61—42no—
150C22×C4×C61—81no—
151C22×C4×C61—82no—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—44no—
160C2×C22⋊D61—44no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—82no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—81no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61C2×D412yes—
177C4⋊C4×C61C2×D412yes—
178C22⋊C4×C61—24no—
179C22⋊C4×C61—24no—
180C22⋊C4×C61—24no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C42×C61—24no—
190C22⋊Dic61—24no—
191C22⋊Dic61—44no—
192#11758201—82no—
193#11758199—82no—
194#11758198—44no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199#11758196—44no—
200C4×Dic61—81no—
201#11758194—81no—
202#11758194—81no—
203C2×#92418—22no—
204C2×#92418—22no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—41no—
212C23×C61—42no—
213C23×C61—42no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—81no—
222C23×C61—81no—
223C23×C61—88no—
224C23×C61#12011yescharacteristic
225C23×C61#12011yescharacteristic
226C23×C61C22×D411yescharacteristic
227C22×D61—41no—
228C22×D61—42no—
229C22×D61—41no—
230C22×D61—41no—
231C22×D61—42no—
232Q8×C61—42no—
233Q8×C61—81no—
234D4×C61—42no—
235D4×C61—44no—
236D4×C61—44no—
237D4×C61—81no—
238D4×C61—84no—
239D4×C61—84no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
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—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—81no—
256C2×C4×C61—84no—
257C2×C4×C61#12011yescharacteristic
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C22⋊D61—88no—
262C22⋊D61—82no—
263C22⋊D61—82no—
264C2×Dic61—24no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270D244—42no—
271D244—42no—
272#92418—42no—
273#92418—42no—
274#18328—611nomaximal, Sylow
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—44no—
283C22×C61—44no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—82no—
291C22×C61—84no—
292C22×C61—84no—
293C22×C61—84no—
294C22×C61#45312yes—
295C22×C61C2×#12011yescharacteristic
296C22×C61#57512yes—
297C2×D61—82no—
298C2×D61—82no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—81no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—42no—
307C4×C61—42no—
308C4×C61—42no—
309C4×C61—42no—
310Dic61—44no—
311Dic61—81no—
312C2×#538D6111yescharacteristic, complemented
313#3193—611no—
314#3192—611no—
315#2539—611no—
316#1618—614no—
317#1600—614no—
318#1508—611no—
319#1507—611no—
320#1462—611no—
321C2×C61—22no—
322C2×C61—22no—
323C2×C61—41no—
324C2×C61—82no—
325C2×C61—82no—
326C2×C61#300511yescharacteristic
327C2×C61C2×#45311yescharacteristic
328C2×C61#302611yescharacteristic
329D61—161no—
330#538—22no—
331#538—22no—
332#538—22no—
333#538C2×D6114yes—
334C2×#126—21no—
335C2×#124—21no—
336C2×#123—21no—
337C2×#123—1221no—
338C2×C22⋊Q8C2×D6111yescharacteristic
339C2×#121—21no—
340C2×#121—611no—
341C2×#121C2×D6111yescharacteristic
342C2×#120—21no—
343C2×#120—1221no—
344C2×C4×D4—21no—
345C22×C22⋊C4C2×D6111yescharacteristic
346#484—612no—
347#481—612no—
348#481—1221no—
349#480—1221no—
350#469—1222no—
351#468—1222no—
352#450—612no—
353#448—1221no—
354#447—612no—
355#447—1221no—
356#407—611no—
357#407—611no—
358#399—612no—
359#392—612no—
360#390—1222no—
361C4×C22⋊C4—611no—
362#328—614no—
363#327—614no—
364#323—614no—
365C61#1832811yescharacteristic, complemented, Sylow
366C25C22⋊D6111yescharacteristic
367C22×Q8C22⋊D6111yescharacteristic, complemented
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—611no—
372C22×D4—1222no—
373C22×D4—1221no—
374C22×D4C22⋊D6111yescharacteristic, complemented
375C23×C4—21no—
376C23×C4C22⋊D6111yescharacteristic
377C23×C4C22×D6111yescharacteristic
378C2×SD16—1222no—
379C2×D8—1222no—
380C2×M16—1221no—
381C2×M16—1221no—
382#126—24no—
383#126—24no—
384#124—24no—
385#124—24no—
386#123—24no—
387#123—24no—
388#123—2444no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8C22⋊D6112yescomplemented
392C22⋊Q8C22×D6112yes—
393#121—24no—
394#121—24no—
395#121—21no—
396#121—21no—
397#121—1221no—
398#121—1221no—
399#121—1221no—
400#121—1221no—
401#121C22⋊D6112yescomplemented
402#121C22×D6112yes—
403#120—24no—
404#120—24no—
405#120—2444no—
406C4×D4—24no—
407C4×D4—24no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—1222no—
412C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
413C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1222no—
427C2×C22⋊C4C22⋊D6112yes—
428C2×C22⋊C4C22×D6112yes—
429C2×C42—21no—
430C2×C42—1221no—
431#107—1222no—
432#106—1222no—
433#103—1222no—
434#102—1222no—
435#102—1222no—
436#102—1222no—
437C22⋊C8—612no—
438C22⋊C8—612no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441#95—612no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—42no—
446C24—42no—
447C24—81no—
448C24—1221no—
449C24C2×C22⋊D6111yescharacteristic
450C24C2×C22⋊D6112yes—
451C2×Q8—21no—
452C2×Q8—81no—
453C2×Q8C2×C22⋊D6112yes—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—21no—
459C2×D4—44no—
460C2×D4—81no—
461C2×D4—82no—
462C2×D4—82no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—4881no—
466C2×D4—4882no—
467C2×D4—2444no—
468C2×D4—2442no—
469C2×D4—2442no—
470C2×D4—2444no—
471C2×D4—2441no—
472C2×D4—2441no—
473C2×D4C2×C22⋊D6112yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—82no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4C2×C22⋊D6112yes—
486C22×C4C2×C22⋊D6111yescharacteristic
487C22×C4C2×C22⋊D6111yescharacteristic
488C22×C4C2×C22⋊D6111yescharacteristic
489C22×C4C2×C22⋊D6111yescharacteristic
490C22×C4C2×C22⋊D6111yescharacteristic
491C22×C4C23×D6111yescharacteristic
492SD16—4882no—
493D8—4882no—
494M16—4881no—
495M16—4881no—
496C2×C8—1222no—
497C2×C8—1222no—
498C4⋊C4—24no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—2444no—
506C4⋊C4C2×C22⋊D6112yes—
507C4⋊C4C2×C22⋊D6112yes—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—1224no—
520C22⋊C4—2444no—
521C22⋊C4—2444no—
522C22⋊C4—2441no—
523C22⋊C4—2441no—
524C42—24no—
525C42—4881no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—81no—
543C23—81no—
544C23—88no—
545C23—2441no—
546C23—2442no—
547C23—2441no—
548C23—2441no—
549C23—2442no—
550C23#1451974611yescharacteristic
551C23#1451974611yescharacteristic
552C23C22×C22⋊D6111yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—42no—
556D4—44no—
557D4—44no—
558D4—81no—
559D4—84no—
560D4—84no—
561D4—4882no—
562D4—4882no—
563D4—4888no—
564D4—2442no—
565D4—2442no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—81no—
582C2×C4—84no—
583C2×C4—1224no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4#1451974611yescharacteristic
590C2×C4#1451974611yescharacteristic
591C2×C4C22×C22⋊D6111yescharacteristic
592C2×C4C22×C22⋊D6111yescharacteristic
593C8—2442no—
594C8—2442no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—82no—
611C22—84no—
612C22—84no—
613C22—84no—
614C22—4882no—
615C22—4882no—
616C22—4881no—
617C22—4881no—
618C22—4881no—
619C22#1683993012yes—
620C22C2×#1451974611yescharacteristic
621C22#1684056012yes—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—4881no—
631C4—2444no—
632C2—22no—
633C2—22no—
634C2—41no—
635C2—82no—
636C2—82no—
637C2—9761no—
638C2#2145506111yescharacteristic
639C2C2×#1683993011yescharacteristic
640C2#2145521611yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#538C2
socleC22×C61C2×#120
hypercenterC2×#538D61
hypocenterC61#18328
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #21456621C2semidirect
2. #21456616C2semidirect
3. #21450750C2semidirect
4. #21444867C2semidirect
5. #21444765C2semidirect
6. #21444339C2semidirect
7. #21444335C2semidirect
8. #21444146C2semidirect
9. C2×C61×#538C2semidirect
13. #16840095C22semidirect
15. #16840078C22semidirect
19. #16839912C22semidirect
22. #16839895C22semidirect
25. #16839698C22semidirect
26. #16839671C22semidirect
29. #16839499C22semidirect
30. #16839496C22semidirect
31. #16839486C22semidirect
77. C22×Q8×C61D4semidirect
81. C22×D4×C61D4semidirect
93. C22⋊Q8×C61D4semidirect
99. #121×C61D4semidirect
107. C2×C4⋊C4×C61D4semidirect
108. C2×C4⋊C4×C61D4semidirect
312. C2×#538D61semidirect
365. C61#18328semidirect
367. C22×Q8C22⋊D61semidirect
374. C22×D4C22⋊D61semidirect
391. C22⋊Q8C22⋊D61semidirect
401. #121C22⋊D61semidirect
412. C2×C4⋊C4C22⋊D61semidirect
413. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214566212
#214566162
#214507502
#214448672
#214447652
#214443392
#214443352
#214441462
C2×C61×#5382
#1832861