Finite Group Databasebeta

← #30613494

Subgroups — #30613494

Order 15616.

720 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462661C211yesmaximal, characteristic, complemented
2D4×#11758213C211yesmaximal, characteristic, complemented
3#21461463C211yesmaximal, characteristic, complemented
4#21461453C211yesmaximal, characteristic, complemented
5#21461439C211yesmaximal, characteristic, complemented
6#21461436C211yesmaximal, characteristic, complemented
7#21461424C211yesmaximal, characteristic, complemented
8#21461419C211yesmaximal, characteristic, complemented
9#21461416C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461385C211yesmaximal, characteristic, complemented
12#21461159C211yesmaximal, characteristic, complemented
13#21461157C211yesmaximal, characteristic, complemented
14#21461043C211yesmaximal, characteristic, complemented
15#21454624C211yesmaximal, characteristic
16C22×#11758213—21no—
17#16840813C2211yescharacteristic, complemented
18#16840813C2211yescharacteristic, complemented
19#16840796C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840792—21no—
22#16840792—21no—
23#16840791—21no—
24#16840791—21no—
25#16840790C2211yescharacteristic, complemented
26#16840790C2211yescharacteristic, complemented
27D4×#92420C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840785—21no—
30#16840784C2211yescharacteristic
31#16840766C2211yescharacteristic
32#16840733—21no—
33C4×#11758213C2211yescharacteristic
34C4×#11758213C2211yescharacteristic
35#16840721—21no—
36#16840626C2211yescharacteristic, complemented
37#16840626C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840624C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52C2×#14519804C411yescharacteristic
53C4×#11758226C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839875C411yescharacteristic
56#16839872C411yescharacteristic
57#16839860C411yescharacteristic
58SD16×Dic61C2211yescharacteristic
59#16839847C2211yescharacteristic
60#16839844C2211yescharacteristic
61#16839842C2211yescharacteristic
62#16839803C411yescharacteristic
63#16839765C411yescharacteristic
64#16839762C411yescharacteristic
65#16839714C2211yescharacteristic
66C61×#440C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×#11758213—44no—
72C2×#11758213D411yescharacteristic
73C2×#11758213D411yescharacteristic
74C2×D61⋊C8—21no—
75C2×D61⋊C8—21no—
76C22×#92420—21no—
77C22×#92420—21no—
78#14519844—21no—
79#14519844—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832D411yescharacteristic
97#14519832D411yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758226C2×C411yescharacteristic
103C2×D4×D61C2×C411yescharacteristic
104C22×C4×D61—21no—
105#14519804—24no—
106C2×#11758201C2×C411yescharacteristic
107C2×D488C2×C411yescharacteristic
108C2×#11758199C2×C411yescharacteristic
109C2×#11758189C2×C411yescharacteristic
110C2×#11758189C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112C4×D244—21no—
113C4×D244C2×C411yescharacteristic
114C4×D244C2×C411yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739—21no—
117#14519739C2311yescharacteristic
118#14519739C2311yescharacteristic
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519735—21no—
122#14519735C2×C411yescharacteristic
123C4⋊C4×D61C2×C411yescharacteristic
124C22⋊C4×D61—21no—
125C42×D61—21no—
126C42×D61C2311yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519709C2×C411yescharacteristic
129#14519708C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134#14519697C2×C411yescharacteristic
135#14519697C2×C411yescharacteristic
136#14519688C2×C411yescharacteristic
137C8×Dic61C2311yescharacteristic
138C8×Dic61C2311yescharacteristic
139C2×SD16×C61C2×C411yescharacteristic
140C4×Q8×C61C2×C411yescharacteristic
141C4×D4×C61C2×C411yescharacteristic
142#107×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145#97×C61C2×C411yescharacteristic
146C23×D61—21no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152#11758226—22no—
153#11758226—41no—
154D4×D61—22no—
155D4×D61—41no—
156C2×D244—21no—
157C2×D244C22×C411yescharacteristic
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61#4111yescharacteristic
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—42no—
177C2×#92420—42no—
178C2×#92420C2×D411yescharacteristic
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182#11758213—22no—
183#11758213—41no—
184#11758213—42no—
185#11758213—42no—
186#11758213—42no—
187#11758213—42no—
188D61⋊C8—42no—
189D61⋊C8—42no—
190SD16×C61—22no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C4⋊C4×C61—21no—
194C4⋊C4×C61C22×C411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C22⋊C4×C61—21no—
197C42×C61—21no—
198C42×C61C22×C411yescharacteristic
199C22⋊Dic61—21no—
200#11758201—22no—
201#11758199M1614yescomplemented
202#11758198—21no—
203#11758198—21no—
204#11758198—21no—
205#11758198—21no—
206#11758198—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61C22×C411yescharacteristic
209C4⋊Dic61C22×C411yescharacteristic
210#11758196—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61#4111yescharacteristic
215C4×Dic61C2411yescharacteristic
216C2×#92418C22×C411yescharacteristic
217C2×#92418C22×C411yescharacteristic
218D488—22no—
219#11758189—22no—
220#11758189—41no—
221C23×C61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—81no—
227C22×D61C4×D411yescharacteristic
228Q8×C61—21no—
229Q8×C61—21no—
230D4×C61—21no—
231D4×C61C2×M1612yes—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—42no—
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C23×C411yescharacteristic
239C22⋊D61—42no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C22×D411yescharacteristic
246C2×Dic61C2×#4111yescharacteristic
247D244—21no—
248D244—21no—
249D244—21no—
250D244—42no—
251D244C2×M1612yescomplemented
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—41no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—81no—
265#92420—22no—
266#92420—21no—
267#92420—21no—
268#92420—21no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274#92420AGL(1,ℤ/8)12yescomplemented
275C8×C61—21no—
276C8×C61—21no—
277#92418—21no—
278#92418C2×M1612yescomplemented
279#18046—611nomaximal, Sylow
280C22×C61—22no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61C2×C4×D411yescharacteristic
284C2×D61—21no—
285C2×D61—22no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—84no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61C22×M1611yescharacteristic
300C4×C61#56811yescharacteristic
301Dic61—21no—
302Dic61—21no—
303Dic61—41no—
304Dic61—41no—
305Dic61C2×AGL(1,ℤ/8)11yescharacteristic
306Dic61#57511yescharacteristic
307#2970—611no—
308C4×AGL(1,ℤ/8)—611no—
309D4×M16—611no—
310#1592—611no—
311#1590—611no—
312#1586—611no—
313#1585—611no—
314#1582—611no—
315#1581—611no—
316#1580—611no—
317C8×D8—611no—
318#1569—611no—
319#1490—611no—
320#1489—611no—
321#1455—611no—
322C2×C61—42no—
323C2×C61D4×M1611yescharacteristic
324C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C61#295611yescharacteristic
326D61—41no—
327D61—42no—
328D61—81no—
329C2×AGL(1,ℤ/8)—611no—
330C22×M16—1221no—
331C4×#41—611no—
332C2×C4×D4—611no—
333#446—611no—
334#446—611no—
335#442—611no—
336#442—611no—
337#440—611no—
338#440#692311yescharacteristic
339C4×SD16—611no—
340C4×SD16—611no—
341C4×D8—611no—
342C4×D8—611no—
343#436—611no—
344#436—611no—
345#435—1221no—
346#435—1221no—
347#435—1221no—
348#435—1221no—
349C8×D4—611no—
350C8×D4—611no—
351C8×D4—611no—
352C8×D4—611no—
353#432—611no—
354#432—1221no—
355#428—611no—
356#423—611no—
357#418—611no—
358#417—611no—
359#407—1221no—
360C4×M16—611no—
361C4×M16—611no—
362C4×M16—611no—
363C2×#97—1221no—
364#335—611no—
365#335—611no—
366#334—611no—
367#334—611no—
368Q8⋊C8—611no—
369Q8⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376#322—611no—
377#322—611no—
378#322—611no—
379C82—611no—
380C61#1804611yescharacteristic, complemented, Sylow
381C2×#41—611no—
382C22×D4—611no—
383C23×C4—1221no—
384AGL(1,ℤ/8)—1224no—
385C2×SD16—611no—
386C2×SD16C2×#692311yescharacteristic
387C2×D8—611no—
388C2×D8—611no—
389C2×M16—611no—
390C2×M16—611no—
391C2×M16—611no—
392C2×M16—611no—
393C2×M16—1221no—
394C2×M16—1221no—
395C2×M16—1221no—
396C2×M16—1221no—
397C2×M16—2444no—
398C22×C8—1221no—
399C22×C8—1221no—
400C22×C8—1221no—
401C22×C8—1221no—
402C4×Q8—611no—
403C4×Q8C2×#692311yescharacteristic
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4C2×#692311yescharacteristic
414#117—611no—
415#117—1221no—
416C2×C4⋊C4—611no—
417C2×C22⋊C4—1221no—
418C2×C42—611no—
419C2×C42—1221no—
420#107—611no—
421#107C2×#692311yescharacteristic
422#106—611no—
423#106—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8—1221no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431#103—611no—
432#103C2×#692311yescharacteristic
433#102—611no—
434#102—611no—
435#102—611no—
436#102—611no—
437#102—611no—
438#102C2×#692311yescharacteristic
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446#97—611no—
447#97—611no—
448#97—611no—
449#97—1221no—
450#97—1221no—
451#97—1221no—
452#97—1221no—
453#97C2×#692311yescharacteristic
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—611no—
460C24—1221no—
461#41—1222no—
462#41—2441no—
463C2×Q8C22×#692311yescharacteristic
464C2×D4—611no—
465C2×D4—611no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1222no—
469C2×D4—2441no—
470C2×D4C22×#692311yescharacteristic
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—2442no—
483C22×C4—2442no—
484SD16—22no—
485SD16—1222no—
486D8—614no—
487D8—1222no—
488M16—1222no—
489M16—1222no—
490M16—2441no—
491M16—2442no—
492M16—2441no—
493M16—2442no—
494M16—2442no—
495M16—2442no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—2442no—
509C2×C8—2442no—
510C2×C8—2442no—
511C2×C8—2442no—
512C2×C8C22×#692311yescharacteristic
513C2×C8C22×#692311yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4C22×#692311yescharacteristic
520C4⋊C4C22×#692311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C42—21no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—1221no—
533C42—1221no—
534C42C22×#692311yescharacteristic
535C23—21no—
536C23—611no—
537C23—1221no—
538C23—1221no—
539C23—4881no—
540C23—2442no—
541C23—2442no—
542Q8—21no—
543Q8—21no—
544D4—21no—
545D4—612no—
546D4—1221no—
547D4—1221no—
548D4—1221no—
549D4—2442no—
550D4—2442no—
551D4D61⋊M1612yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—4881no—
566C2×C4—2441no—
567C2×C4—2442no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4D4×#692311yescharacteristic
577C2×C4D4×#692311yescharacteristic
578C2×C4C23×#692311yescharacteristic
579C8—21no—
580C8—21no—
581C8—612no—
582C8—612no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—1222no—
587C8—1221no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C8—2441no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—1221no—
597C22—1222no—
598C22—1221no—
599C22—1221no—
600C22—4884no—
601C22—2441no—
602C22—2441no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22C2×D4×#692311yescharacteristic
607C4—21no—
608C4—21no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—611no—
613C4—611no—
614C4—1221no—
615C4—1221no—
616C4—2441no—
617C4—2441no—
618C4C2×D61⋊M1611yescharacteristic
619C4#1684084111yescharacteristic
620C2—42no—
621C2—4881no—
622C2—2441no—
623C2—2442no—
624C2#2146255811yescharacteristic
625C2AGL(1,ℤ/8)×#692311yescharacteristic
626C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519804C4
cosocleC4×Dic61C24
hypercenter#440#6923
hypocenterC61#18046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #21462661C2semidirect
2. D4×#11758213C2semidirect
3. #21461463C2semidirect
4. #21461453C2semidirect
5. #21461439C2semidirect
6. #21461436C2semidirect
7. #21461424C2semidirect
8. #21461419C2semidirect
9. #21461416C2semidirect
10. #21461399C2semidirect
11. #21461385C2semidirect
12. #21461159C2semidirect
13. #21461157C2semidirect
14. #21461043C2semidirect
17. #16840813C22semidirect
18. #16840813C22semidirect
25. #16840790C22semidirect
26. #16840790C22semidirect
36. #16840626C22semidirect
37. #16840626C22semidirect
38. #16840624C22semidirect
39. #16840624C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
201. #11758199M16semidirect
251. D244C2×M16semidirect
274. #92420AGL(1,ℤ/8)semidirect
278. #92418C2×M16semidirect
380. C61#18046semidirect

Maximal subgroups

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

subgroupindex
#214626612
D4×#117582132
#214614632
#214614532
#214614392
#214614362
#214614242
#214614192
#214614162
#214613992
#214613852
#214611592
#214611572
#214610432
#214546242
#1804661