Finite Group Databasebeta

← #29669399

Subgroups — #29669399

Order 15616.

736 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458162C211yesmaximal, characteristic, complemented
2#21457632C211yesmaximal, characteristic, complemented
3#21457540C211yesmaximal, characteristic, complemented
4#21445488C211yesmaximal, characteristic, complemented
5#21445308C211yesmaximal, characteristic, complemented
6#21445254C211yesmaximal, characteristic, complemented
7#21445206C211yesmaximal, characteristic, complemented
8#21445157C211yesmaximal, characteristic, complemented
9#21445054C211yesmaximal, characteristic, complemented
10#21445052C211yesmaximal, characteristic, complemented
11#21444998C211yesmaximal, characteristic, complemented
12#21444906C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3272C211yesmaximal, characteristic, complemented
16C2×#14519796—21no—
17#16840416C2211yescharacteristic
18#16840416C2211yescharacteristic, complemented
19#16840165C2211yescharacteristic, complemented
20#16840165C2211yescharacteristic, complemented
21#16840142C2211yescharacteristic, complemented
22#16840108C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840075—21no—
25#16840073—21no—
26#16840073—21no—
27#16840042C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16840039C2211yescharacteristic, complemented
30#16840004—21no—
31#16839996—21no—
32#16839996—21no—
33#16839967C2211yescharacteristic
34#16839967C2211yescharacteristic, complemented
35#16839954C2211yescharacteristic
36#16839925—21no—
37#16839925—21no—
38#16839896—21no—
39C4×#11758199C2211yescharacteristic
40C8×D244C2211yescharacteristic, complemented
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43C2×#14519710—21no—
44C2×#14519698—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839509C2211yescharacteristic, complemented
48#16839509C2211yescharacteristic, complemented
49#16839508C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C61—21no—
57C61×#547C2211yescharacteristic
58D42×C61C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#468—21no—
61C61×#461C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#450—21no—
64C61×#449—21no—
65C4×D8×C61C2211yescharacteristic
66C61×#436C2211yescharacteristic
67C2×#11758224—21no—
68C2×#11758224—21no—
69#14519796—44no—
70C2×Dic244—21no—
71C2×Dic244—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758199—21no—
75C2×#11758199D411yescharacteristic
76C22×#92418—21no—
77C22×#92418—21no—
78C2×C8×D61—21no—
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519761—41no—
82#14519761—41no—
83#14519757—21no—
84#14519757—21no—
85#14519751—21no—
86#14519751—21no—
87C4×D244C2311yescharacteristic
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—21no—
95#14519710—41no—
96#14519710D411yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519700—21no—
101#14519700—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—41no—
108#14519698D411yescharacteristic
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119AGL(1,ℤ/8)×C61—44no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61—21no—
123C2×D8×C61—21no—
124C2×D8×C61D411yescharacteristic
125C2×M16×C61—21no—
126C4⋊Q8×C61C2311yescharacteristic
127#127×C61C2311yescharacteristic
128#123×C61—41no—
129C22⋊Q8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#120×C61—41no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—21no—
138#107×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—42no—
156C2×D4×C61—42no—
157C2×D4×C61—41no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C2×D4×C61C2×D411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C22×Dic61—41no—
170C22×Dic61—41no—
171#11758224—42no—
172#11758224—42no—
173#11758224—81no—
174#11758224—81no—
175C2×D244C2×D411yescharacteristic
176C2×C4×D61—21no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179SD16×C61—42no—
180SD16×C61—42no—
181SD16×C61—81no—
182D8×C61—42no—
183D8×C61D814yescomplemented
184M16×C61—42no—
185C2×C8×C61—21no—
186C2×C8×C61C2×D411yescharacteristic
187C2×C8×C61C2×D411yescharacteristic
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C4⋊C4×C61C2×D411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C42×C61C2411yescharacteristic
200#11758200—42no—
201#11758200—42no—
202#11758199—41no—
203#11758199—81no—
204#11758198—21no—
205#11758198—41no—
206#11758198—41no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—41no—
212C4⋊Dic61—41no—
213C4⋊Dic61C2×D411yescharacteristic
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—42no—
219C2×#92418—81no—
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222Dic244—42no—
223Dic244—81no—
224C8×D61—42no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—41no—
229C23×C61—82no—
230C23×C61—82no—
231C23×C61—161no—
232C22×D61—21no—
233Q8×C61—41no—
234Q8×C61—41no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—81no—
244D4×C61—82no—
245D4×C61—82no—
246D4×C61—82no—
247D4×C61C2×D812yes—
248D4×C61C2×D812yes—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—82no—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61H(5,𝔽2)11yescharacteristic
263C22⋊D61—82no—
264C22⋊D61—82no—
265C2×Dic61—21no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—82no—
269C2×Dic61—82no—
270D244—21no—
271D244—21no—
272C4×D61—41no—
273C4×D61—41no—
274Dic122—41no—
275Dic122—41no—
276Dic122—41no—
277Dic122—41no—
278C8×C61—21no—
279C8×C61—41no—
280C8×C61C2×D812yes—
281#92418—21no—
282#92418—21no—
283#92418—41no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287#19758—611nomaximal, Sylow
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61—81no—
300C22×C61—164no—
301C22×C61D4211yescharacteristic
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C4×C61—21no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—81no—
310C4×C61C22×D811yescharacteristic
311C4×C61#57511yescharacteristic
312C4×C61#57611yescharacteristic
313C4×C61#57711yescharacteristic
314Dic61—41no—
315Dic61—81no—
316Dic61—81no—
317#3334—611no—
318#3294—611no—
319#3283—611no—
320#3272D6111yescharacteristic, complemented
321#1722—611no—
322#1689—611no—
323#1681—611no—
324#1673—611no—
325#1665—611no—
326#1647—611no—
327#1647—611no—
328#1639—611no—
329#1625—611no—
330#1581—611no—
331#1580—611no—
332C2×C61—42no—
333C2×C61—42no—
334C2×C61—81no—
335C2×C61—161no—
336C2×C61#326711yescharacteristic
337C2×C61D4×D811yescharacteristic
338C2×C61#328911yescharacteristic
339D61—81no—
340C2×AGL(1,ℤ/8)—21no—
341C2×#135—1221no—
342#547—611no—
343#547—611no—
344#547C2×D6111yescharacteristic
345D42C2×D6111yescharacteristic
346#500—611no—
347#500—611no—
348#494—611no—
349#492C2×D6111yescharacteristic
350#486—611no—
351#486—611no—
352#480—1221no—
353#480—1221no—
354#480—1221no—
355#474—611no—
356#474—611no—
357#474—611no—
358#468—21no—
359#467—1221no—
360#466—1221no—
361#466—1221no—
362#461—611no—
363#461—611no—
364#461C2×D6111yescharacteristic
365#459—611no—
366#459C2×D6111yescharacteristic
367#452—1221no—
368#452—1221no—
369#450—21no—
370#449—21no—
371#447—1221no—
372C4×D8—611no—
373C4×D8C2×D6111yescharacteristic
374#436C2×D6111yescharacteristic
375C8×D4—611no—
376C8×D4—611no—
377C8×D4—611no—
378C2×#107—1221no—
379C2×#102—1221no—
380#335—611no—
381#334—611no—
382#332—611no—
383#332—611no—
384#332—611no—
385#331—611no—
386D4⋊C8—611no—
387D4⋊C8—611no—
388D4⋊C8—611no—
389D4⋊C8—611no—
390#322—611no—
391C61#1975811yescharacteristic, complemented, Sylow
392C2×#41—21no—
393C2×#41—1221no—
394C2×#41—1221no—
395C22×D4—21no—
396C22×D4—21no—
397AGL(1,ℤ/8)—44no—
398#135—2444no—
399C2×Q16—1221no—
400C2×Q16—1221no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—1221no—
405C2×SD16—1221no—
406C2×D8—21no—
407C2×D8—611no—
408C2×D8—1221no—
409C2×D8C22⋊D6111yescharacteristic
410C2×M16—21no—
411C22×C8—1221no—
412C22×C8—1221no—
413C22×C8—1221no—
414C4⋊Q8—611no—
415C4⋊Q8—611no—
416C4⋊Q8C22×D6111yescharacteristic
417#127C22×D6111yescharacteristic
418#123—41no—
419#123—2441no—
420#123—2441no—
421C22⋊Q8—21no—
422C22⋊Q8—1221no—
423C22⋊Q8—1221no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—1221no—
428#121—1221no—
429#120—41no—
430C4×D4—611no—
431C4×D4C22×D6111yescharacteristic
432C4×D4C22×D6111yescharacteristic
433C4×D4C22×D6111yescharacteristic
434C2×C4⋊C4—21no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437#107—611no—
438#107—1221no—
439#107—1221no—
440#107—1221no—
441#107—1221no—
442#107—1221no—
443#107—2441no—
444#107C22⋊D6111yescharacteristic
445C4⋊C8—611no—
446C4⋊C8—611no—
447C4⋊C8—611no—
448C4⋊C8C22×D6111yescharacteristic
449#103—21no—
450#103—1221no—
451#103—1221no—
452#102—21no—
453#102—611no—
454#102—611no—
455#102—1221no—
456#102—1221no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—2441no—
462#102C22⋊D6111yescharacteristic
463#102C22⋊D6111yescharacteristic
464C22⋊C8—21no—
465C22⋊C8—1221no—
466C22⋊C8—1221no—
467C22⋊C8—1221no—
468C4×C8—611no—
469C4×C8—611no—
470C4×C8C22×D6111yescharacteristic
471C24—41no—
472#41—42no—
473#41—81no—
474#41—4881no—
475#41—4881no—
476#41—2442no—
477#41—2442no—
478C2×Q8—21no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—41no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4—611no—
492C2×D4—2441no—
493C2×D4—2441no—
494C2×D4D4×D6111yescharacteristic
495C2×D4C2×C22⋊D6111yescharacteristic
496C2×D4C2×C22⋊D6111yescharacteristic
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—41no—
501C22×C4—1221no—
502C22×C4—2441no—
503C22×C4—2441no—
504Q16—4881no—
505Q16—2442no—
506SD16—42no—
507SD16—42no—
508SD16—81no—
509SD16—2442no—
510SD16—2442no—
511D8—42no—
512D8—4881no—
513D8—2441no—
514D8#1175819914yescomplemented
515M16—42no—
516C2×C8—21no—
517C2×C8—611no—
518C2×C8—611no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—4881no—
524C2×C8—2442no—
525C2×C8—2442no—
526C2×C8C2×C22⋊D6111yescharacteristic
527C2×C8C2×C22⋊D6111yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—41no—
531C4⋊C4—611no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—2441no—
537C4⋊C4—2441no—
538C4⋊C4D4×D6111yescharacteristic
539C4⋊C4C2×C22⋊D6111yescharacteristic
540C4⋊C4C2×C22⋊D6111yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—1221no—
547C22⋊C4—2441no—
548C22⋊C4—2441no—
549C42C23×D6111yescharacteristic
550C23—21no—
551C23—21no—
552C23—21no—
553C23—41no—
554C23—82no—
555C23—82no—
556C23—161no—
557C23—1221no—
558Q8—41no—
559Q8—41no—
560Q8—2441no—
561Q8—2441no—
562Q8—2441no—
563Q8—2441no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—21no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—1221no—
577D4—1221no—
578D4—4882no—
579D4—4882no—
580D4C2×#1175819912yes—
581D4C2×#1175819912yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—82no—
593C2×C4—1221no—
594C2×C4—4882no—
595C2×C4—4882no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C22×C22⋊D6111yescharacteristic
602C2×C4#1451982211yescharacteristic
603C8—21no—
604C8—41no—
605C8—1221no—
606C8—1221no—
607C8—2441no—
608C8—2441no—
609C8—2441no—
610C8—2441no—
611C8C2×#1175819912yes—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—164no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22D4×C22⋊D6111yescharacteristic
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—4881no—
635C4—4881no—
636C4—2441no—
637C4C22×#1175819911yescharacteristic
638C4#1684055811yescharacteristic
639C4#1684056511yescharacteristic
640C4#1684057211yescharacteristic
641C2—42no—
642C2—42no—
643C2—81no—
644C2—161no—
645C2—4881no—
646C2#2145733811yescharacteristic
647C2D4×#1175819911yescharacteristic
648C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3272C2
socleC22×C61D42
hypercenter#3272D61
hypocenterC61#19758
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. #21458162C2semidirect
2. #21457632C2semidirect
3. #21457540C2semidirect
4. #21445488C2semidirect
5. #21445308C2semidirect
6. #21445254C2semidirect
7. #21445206C2semidirect
8. #21445157C2semidirect
9. #21445054C2semidirect
10. #21445052C2semidirect
11. #21444998C2semidirect
12. #21444906C2semidirect
13. #21444646C2semidirect
14. #21444643C2semidirect
15. C61×#3272C2semidirect
18. #16840416C22semidirect
19. #16840165C22semidirect
20. #16840165C22semidirect
21. #16840142C22semidirect
29. #16840039C22semidirect
34. #16839967C22semidirect
40. C8×D244C22semidirect
42. D4×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839509C22semidirect
48. #16839509C22semidirect
49. #16839508C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839483C22semidirect
183. D8×C61D8semidirect
320. #3272D61semidirect
391. C61#19758semidirect
514. D8#11758199semidirect

Maximal subgroups

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

subgroupindex
#214581622
#214576322
#214575402
#214454882
#214453082
#214452542
#214452062
#214451572
#214450542
#214450522
#214449982
#214449062
#214446462
#214446432
C61×#32722
#1975861