Finite Group Databasebeta

← #30612415

Subgroups — #30612415

Order 15616.

748 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462631C211yesmaximal, characteristic, complemented
2D4×D61⋊C8C211yesmaximal, characteristic, complemented
3#21461441C211yesmaximal, characteristic, complemented
4#21461440C211yesmaximal, characteristic, complemented
5#21461435C211yesmaximal, characteristic, complemented
6#21461434C211yesmaximal, characteristic, complemented
7#21461423C211yesmaximal, characteristic, complemented
8#21461422C211yesmaximal, characteristic, complemented
9#21461421C211yesmaximal, characteristic, complemented
10#21461420C211yesmaximal, characteristic, complemented
11#21461371C211yesmaximal, characteristic, complemented
12#21461119C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14#21461027C211yesmaximal, characteristic, complemented
15#21454630C211yesmaximal, characteristic
16C22×D61⋊C8—21no—
17#16840812C2211yescharacteristic, complemented
18#16840812C2211yescharacteristic, complemented
19#16840797C2211yescharacteristic, complemented
20#16840797C2211yescharacteristic, complemented
21#16840794—21no—
22#16840794—21no—
23#16840790C2211yescharacteristic
24#16840790C2211yescharacteristic
25#16840789—21no—
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840781C2211yescharacteristic
30#16840780C2211yescharacteristic
31#16840778—21no—
32D61⋊(C4⋊C8)C2211yescharacteristic
33D61⋊(C22⋊C8)—21no—
34C4×#11758217—21no—
35C4×D61⋊C8C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, 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#92420⋊C8C2211yescharacteristic, complemented
51#92420⋊C8C2211yescharacteristic, 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×#11758217—21no—
68C2×#11758217—21no—
69C2×D61⋊C8—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—44no—
73C2×D61⋊C8D411yescharacteristic
74C2×D61⋊C8D411yescharacteristic
75C22×#92420—21no—
76C22×#92420—21no—
77#14519844—21no—
78#14519844—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420D411yescharacteristic
97C4×#92420D411yescharacteristic
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—22no—
158D4×D61—22no—
159D4×D61M1614yescomplemented
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
170#11758217—42no—
171#11758217—42no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—42no—
179C2×#92420—42no—
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C2×#92420C2×D411yescharacteristic
184D61⋊C8—22no—
185D61⋊C8—41no—
186D61⋊C8—42no—
187D61⋊C8—42no—
188D61⋊C8—42no—
189D8×C61—22no—
190C2×C8×C61C22×C411yescharacteristic
191C2×C8×C61C22×C411yescharacteristic
192C4⋊C4×C61C22×C411yescharacteristic
193C4⋊C4×C61C22×C411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C42×C61C22×C411yescharacteristic
197C22⋊Dic61—21no—
198C22⋊Dic61—21no—
199#11758200—22no—
200#11758199—22no—
201#11758198—21no—
202#11758198—21no—
203#11758198—21no—
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206#11758196—21no—
207#11758196—21no—
208#11758196—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61#4111yescharacteristic
214C4×Dic61C2411yescharacteristic
215C2×#92418C22×C411yescharacteristic
216C2×#92418C22×C411yescharacteristic
217#11758190—22no—
218#11758189—22no—
219#11758189—22no—
220C23×C61—21no—
221C23×C61—21no—
222C22×D61—21no—
223C22×D61—24no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61C4×D411yescharacteristic
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61C2×M1612yes—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C22⋊D61—24no—
239C22⋊D61—42no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—42no—
248C2×Dic61C4×D411yescharacteristic
249C2×Dic61C22×D411yescharacteristic
250C2×Dic61C2×#4111yescharacteristic
251D244—21no—
252D244C2×M1612yes—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—41no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61C2×M1612yes—
261C4×D61#13112yes—
262Dic122—21no—
263Dic122—21no—
264#92420—21no—
265#92420—21no—
266#92420—21no—
267#92420—41no—
268#92420—41no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420AGL(1,ℤ/8)12yescomplemented
274C8×C61—21no—
275C8×C61—21no—
276#92418—21no—
277#92418—21no—
278#17869—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61C2×C4×D411yescharacteristic
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—22no—
289C2×D61—48no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61#43512yes—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61C22×M1611yescharacteristic
298C4×C61C2×#13111yescharacteristic
299Dic61—21no—
300Dic61—41no—
301Dic61—41no—
302Dic61—41no—
303Dic61#43512yes—
304Dic61C2×AGL(1,ℤ/8)11yescharacteristic
305Dic61#57511yescharacteristic
306#2965—611no—
307C4×AGL(1,ℤ/8)—611no—
308C2×C8×D4—611no—
309#1586—611no—
310#1586—611no—
311#1585—611no—
312#1585—611no—
313#1582—611no—
314#1582—611no—
315#1581—611no—
316#1581—611no—
317#1565—611no—
318#1478—611no—
319#1477—611no—
320#1451—611no—
321C2×C61—42no—
322C2×C61—81no—
323C2×C61C2×#43511yescharacteristic
324C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C61#295511yescharacteristic
326D61—22no—
327D61—42no—
328C2×AGL(1,ℤ/8)—611no—
329C23×C8—1221no—
330C4×#41—611no—
331C2×C4×D4—611no—
332#446—611no—
333#446—611no—
334#442—611no—
335#442#692311yescharacteristic
336#440—611no—
337#440—611no—
338C4×SD16—611no—
339C4×SD16—611no—
340C4×D8—611no—
341C4×D8—611no—
342#436—611no—
343#436—611no—
344#435—1221no—
345#435—1221no—
346C8×D4—611no—
347C8×D4—611no—
348C8×D4—611no—
349C8×D4—611no—
350C8×D4—1221no—
351C8×D4—1221no—
352#431—611no—
353#431—611no—
354#431—1221no—
355#428—611no—
356C2×C4⋊C8—611no—
357#418—611no—
358#417—611no—
359C2×C22⋊C8—1221no—
360C4×M16—611no—
361C4×M16—1221no—
362C2×C4×C8—611no—
363#335—611no—
364#335—611no—
365#334—611no—
366#334—611no—
367Q8⋊C8—611no—
368Q8⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375#322—611no—
376#322—611no—
377#322—611no—
378#322—611no—
379C61#1786911yescharacteristic, complemented, Sylow
380C2×#41—611no—
381C22×D4—611no—
382C23×C4—1221no—
383AGL(1,ℤ/8)—1224no—
384C2×SD16—611no—
385C2×SD16—611no—
386C2×D8—611no—
387C2×D8C2×#692311yescharacteristic
388C2×M16—611no—
389C2×M16—611no—
390C2×M16—1221no—
391C2×M16—1221no—
392C22×C8—611no—
393C22×C8—611no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C22×C8—2444no—
400C4×Q8—611no—
401C4×Q8—611no—
402C4×D4—611no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4C2×#692311yescharacteristic
411C4×D4C2×#692311yescharacteristic
412#117—611no—
413#117—1221no—
414C2×C4⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417C2×C42—1221no—
418#107—611no—
419#107—611no—
420#106—611no—
421#106C2×#692311yescharacteristic
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8—1221no—
429C4⋊C8—1221no—
430#103—611no—
431#103—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102—611no—
436#102C2×#692311yescharacteristic
437#102C2×#692311yescharacteristic
438C22⋊C8—1221no—
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—1221no—
448#97—1221no—
449#97C2×#692311yescharacteristic
450C4×C8—611no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—1221no—
459C24—1221no—
460#41—1222no—
461#41—1222no—
462C2×Q8—611no—
463C2×D4—614no—
464C2×D4—611no—
465C2×D4—1222no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4C22×#692311yescharacteristic
469C2×D4C22×#692311yescharacteristic
470C22×C4—21no—
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—2442no—
482C22×C4—2442no—
483SD16—1222no—
484SD16—1222no—
485D8—22no—
486D8—1222no—
487M16—1222no—
488M16—1222no—
489M16—2442no—
490M16—2442no—
491C2×C8—611no—
492C2×C8—611no—
493C2×C8—611no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—1222no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—2442no—
505C2×C8—2442no—
506C2×C8—2441no—
507C2×C8—2442no—
508C2×C8—2442no—
509C2×C8—2442no—
510C2×C8C22×#692311yescharacteristic
511C2×C8C22×#692311yescharacteristic
512C4⋊C4—611no—
513C4⋊C4—611no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4C22×#692311yescharacteristic
518C4⋊C4C22×#692311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42C22×#692311yescharacteristic
533C23—21no—
534C23—21no—
535C23—611no—
536C23—1224no—
537C23—1221no—
538C23—2442no—
539C23—2442no—
540Q8—1221no—
541Q8—1221no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—612no—
546D4—1224no—
547D4—1221no—
548D4—2442no—
549D4D61⋊M1612yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—612no—
557C2×C4—612no—
558C2×C4—611no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—2441no—
565C2×C4—2442no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2442no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2442no—
574C2×C4D4×#692311yescharacteristic
575C2×C4D4×#692311yescharacteristic
576C2×C4C23×#692311yescharacteristic
577C8—21no—
578C8—21no—
579C8—612no—
580C8—1221no—
581C8—1221no—
582C8—1221no—
583C8—1221no—
584C8—1221no—
585C8—2441no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—612no—
598C22—1221no—
599C22—1221no—
600C22—1222no—
601C22—2448no—
602C22—2441no—
603C22—2441no—
604C22C2×D4×#692311yescharacteristic
605C4—21no—
606C4—21no—
607C4—41no—
608C4—41no—
609C4—611no—
610C4—611no—
611C4—612no—
612C4—1221no—
613C4—2441no—
614C4—2441no—
615C4—2441no—
616C4C2×D61⋊M1611yescharacteristic
617C4D61⋊#13111yescharacteristic
618C2—42no—
619C2—81no—
620C2—1222no—
621C2—2442no—
622C2D61⋊#43511yescharacteristic
623C2AGL(1,ℤ/8)×#692311yescharacteristic
624C2#2146259111yescharacteristic
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#17869
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. #21462631C2semidirect
2. D4×D61⋊C8C2semidirect
3. #21461441C2semidirect
4. #21461440C2semidirect
5. #21461435C2semidirect
6. #21461434C2semidirect
7. #21461423C2semidirect
8. #21461422C2semidirect
9. #21461421C2semidirect
10. #21461420C2semidirect
11. #21461371C2semidirect
12. #21461119C2semidirect
13. #21461115C2semidirect
14. #21461027C2semidirect
17. #16840812C22semidirect
18. #16840812C22semidirect
19. #16840797C22semidirect
20. #16840797C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. #16840612C22semidirect
41. #16840612C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #92420⋊C8C22semidirect
51. #92420⋊C8C22semidirect
159. D4×D61M16semidirect
273. #92420AGL(1,ℤ/8)semidirect
379. C61#17869semidirect

Maximal subgroups

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

subgroupindex
#214626312
D4×D61⋊C82
#214614412
#214614402
#214614352
#214614342
#214614232
#214614222
#214614212
#214614202
#214613712
#214611192
#214611152
#214610272
#214546302
#1786961