Finite Group Databasebeta

← #30613490

Subgroups — #30613490

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#21462657C211yesmaximal, characteristic, complemented
2D4×#11758213C211yesmaximal, characteristic, complemented
3#21461461C211yesmaximal, characteristic, complemented
4#21461454C211yesmaximal, characteristic, complemented
5#21461438C211yesmaximal, characteristic, complemented
6#21461434C211yesmaximal, characteristic, complemented
7#21461422C211yesmaximal, characteristic, complemented
8#21461418C211yesmaximal, characteristic, complemented
9#21461415C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461384C211yesmaximal, characteristic, complemented
12#21461159C211yesmaximal, characteristic, complemented
13#21461155C211yesmaximal, characteristic, complemented
14#21461043C211yesmaximal, characteristic, complemented
15#21454630C211yesmaximal, characteristic
16C22×#11758213—21no—
17#16840812C2211yescharacteristic, complemented
18#16840812C2211yescharacteristic, complemented
19#16840796C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840791—21no—
22#16840791—21no—
23#16840791—21no—
24#16840791—21no—
25D4×#92420C2211yescharacteristic
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic, complemented
28D4×#92420C2211yescharacteristic, complemented
29#16840784C2211yescharacteristic
30#16840783—21no—
31#16840766C2211yescharacteristic
32#16840733—21no—
33C4×#11758213C2211yescharacteristic
34C4×#11758213C2211yescharacteristic
35C2×#14519832—21no—
36#16840625C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840623C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840612C2211yescharacteristic, complemented
41#16840612C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52C2×#14519801C411yescharacteristic
53C4×#11758224C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839872C411yescharacteristic
56#16839864C411yescharacteristic
57#16839862C411yescharacteristic
58#16839853C2211yescharacteristic
59#16839849C2211yescharacteristic
60D8×Dic61C2211yescharacteristic
61#16839842C2211yescharacteristic
62#16839801C411yescharacteristic
63#16839765C411yescharacteristic
64#16839760C411yescharacteristic
65#16839714C2211yescharacteristic
66C61×#442C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×#11758213—44no—
72C2×#11758213D411yescharacteristic
73C2×#11758213D411yescharacteristic
74C22×#92420—21no—
75C22×#92420—21no—
76C22×#92420—21no—
77C22×#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88C22⋊#92420—21no—
89C22⋊#92420—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×#11758224C2×C411yescharacteristic
103C2×D4×D61C2×C411yescharacteristic
104C22×C4×D61—21no—
105#14519801—24no—
106C2×#11758190C2×C411yescharacteristic
107C2×#11758200C2×C411yescharacteristic
108C2×#11758199C2×C411yescharacteristic
109C2×#11758189C2×C411yescharacteristic
110C2×#11758189C2×C411yescharacteristic
111C4×Dic122C2×C411yescharacteristic
112#14519742C2311yescharacteristic
113C4×D244C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739C2311yescharacteristic
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119#14519737—21no—
120#14519737—21no—
121#14519735C2×C411yescharacteristic
122#14519733—21no—
123C4⋊C4×D61C2×C411yescharacteristic
124C22⋊C4×D61—21no—
125C2×C4×Dic61—21no—
126C42×D61C2311yescharacteristic
127#14519711C2×C411yescharacteristic
128#14519710C2×C411yescharacteristic
129#14519708C2×C411yescharacteristic
130#14519702C2×C411yescharacteristic
131#14519700C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134#14519698C2×C411yescharacteristic
135#14519697C2×C411yescharacteristic
136#14519688C2×C411yescharacteristic
137C8×Dic61C2311yescharacteristic
138C8×Dic61C2311yescharacteristic
139C2×D8×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C4×D4×C61C2×C411yescharacteristic
142#106×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145#97×C61C2×C411yescharacteristic
146C23×D61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156#11758224—22no—
157#11758224—41no—
158D4×D61—22no—
159D4×D61—41no—
160C2×D244C22×C411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61#4111yescharacteristic
169C2×Dic122C22×C411yescharacteristic
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×#92420—42no—
179C2×#92420—42no—
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C2×#92420C2×D411yescharacteristic
184#11758213—22no—
185#11758213—41no—
186#11758213—42no—
187#11758213—42no—
188#11758213—42no—
189#11758213—42no—
190D8×C61M1614yescomplemented
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C4⋊C4×C61C22×C411yescharacteristic
194C4⋊C4×C61C22×C411yescharacteristic
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C42×C61C22×C411yescharacteristic
198C22⋊Dic61—21no—
199C22⋊Dic61—21no—
200#11758200—22no—
201#11758199—22no—
202#11758198—21no—
203#11758198—21no—
204#11758198—21no—
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207#11758196—21no—
208#11758196—21no—
209#11758196—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61#4111yescharacteristic
215C4×Dic61C2411yescharacteristic
216C2×#92418C22×C411yescharacteristic
217C2×#92418C22×C411yescharacteristic
218#11758190—22no—
219#11758189—22no—
220#11758189—41no—
221C23×C61—21no—
222C23×C61—21no—
223C22×D61—21no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—81no—
227C22×D61C4×D411yescharacteristic
228D4×C61—21no—
229D4×C61—21no—
230D4×C61C2×M1612yes—
231D4×C61C2×M1612yescomplemented
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—42no—
235C2×C4×C61—81no—
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C23×C411yescharacteristic
239C22⋊D61—42no—
240C22⋊D61—42no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—42no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61C22×D411yescharacteristic
251C2×Dic61C2×#4111yescharacteristic
252D244—21no—
253D244—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—41no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—41no—
262C4×D61—41no—
263Dic122—21no—
264Dic122—21no—
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×C61C2×M1612yescomplemented
277#92418—21no—
278#92418—21no—
279#18046—611nomaximal, Sylow
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61C2×C4×D411yescharacteristic
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
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×C61C22×M1611yescharacteristic
299C4×C61#56811yescharacteristic
300Dic61—21no—
301Dic61—21no—
302Dic61—41no—
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×C61—42no—
324C2×C61D4×M1611yescharacteristic
325C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
326C2×C61#295611yescharacteristic
327D61—41no—
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#692311yescharacteristic
337#440—611no—
338#440—611no—
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×SD16—611no—
387C2×D8—611no—
388C2×D8C2×#692311yescharacteristic
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×Q8—611no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4C2×#692311yescharacteristic
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#107—611no—
422#106—611no—
423#106C2×#692311yescharacteristic
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#103—611no—
433#102—611no—
434#102—611no—
435#102—611no—
436#102—611no—
437#102C2×#692311yescharacteristic
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×Q8—611no—
464C2×D4—611no—
465C2×D4—1221no—
466C2×D4—1222no—
467C2×D4—1221no—
468C2×D4—2441no—
469C2×D4C22×#692311yescharacteristic
470C2×D4C22×#692311yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
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—1222no—
485SD16—1222no—
486D8—1222no—
487D8#1175821314yescomplemented
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—611no—
515C4⋊C4—611no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4C22×#692311yescharacteristic
520C4⋊C4C22×#692311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42C22×#692311yescharacteristic
535C23—21no—
536C23—21no—
537C23—611no—
538C23—1221no—
539C23—4881no—
540C23—2442no—
541C23—2442no—
542Q8—1221no—
543Q8—1221no—
544D4—21no—
545D4—21no—
546D4—1221no—
547D4—1221no—
548D4—2442no—
549D4—2442no—
550D4C2×#1175821312yes—
551D4C2×#1175821312yescomplemented
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—42no—
555C2×C4—81no—
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—1221no—
566C2×C4—2441no—
567C2×C4—2442no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2442no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2442no—
576C2×C4D4×#692311yescharacteristic
577C2×C4D4×#692311yescharacteristic
578C2×C4C23×#692311yescharacteristic
579C8—21no—
580C8—612no—
581C8—1221no—
582C8—1221no—
583C8—1221no—
584C8—1222no—
585C8—1221no—
586C8—1221no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C8C2×#1175821312yescomplemented
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—1221no—
600C22—1221no—
601C22—1221no—
602C22—4884no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22C2×D4×#692311yescharacteristic
607C4—21no—
608C4—21no—
609C4—41no—
610C4—41no—
611C4—611no—
612C4—611no—
613C4—1221no—
614C4—1221no—
615C4—2441no—
616C4—2441no—
617C4—2441no—
618C4C22×#1175821311yescharacteristic
619C4#1684084111yescharacteristic
620C2—42no—
621C2—42no—
622C2—4881no—
623C2—2441no—
624C2D4×#1175821311yescharacteristic
625C2AGL(1,ℤ/8)×#692311yescharacteristic
626C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#442C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519801C4
cosocleC4×Dic61C24
hypercenter#442#6923
hypocenterC61#18046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462657C2semidirect
2. D4×#11758213C2semidirect
3. #21461461C2semidirect
4. #21461454C2semidirect
5. #21461438C2semidirect
6. #21461434C2semidirect
7. #21461422C2semidirect
8. #21461418C2semidirect
9. #21461415C2semidirect
10. D8×#92420C2semidirect
11. #21461384C2semidirect
12. #21461159C2semidirect
13. #21461155C2semidirect
14. #21461043C2semidirect
17. #16840812C22semidirect
18. #16840812C22semidirect
27. D4×#92420C22semidirect
28. D4×#92420C22semidirect
36. #16840625C22semidirect
37. #16840625C22semidirect
38. #16840623C22semidirect
39. #16840623C22semidirect
40. #16840612C22semidirect
41. #16840612C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
190. D8×C61M16semidirect
231. D4×C61C2×M16semidirect
274. #92420AGL(1,ℤ/8)semidirect
276. C8×C61C2×M16semidirect
380. C61#18046semidirect
487. D8#11758213semidirect
551. D4C2×#11758213semidirect
592. C8C2×#11758213semidirect

Maximal subgroups

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

subgroupindex
#214626572
D4×#117582132
#214614612
#214614542
#214614382
#214614342
#214614222
#214614182
#214614152
D8×#924202
#214613842
#214611592
#214611552
#214610432
#214546302
#1804661