Finite Group Databasebeta

← #30622102

Subgroups — #30622102

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462617C211yesmaximal, characteristic, complemented
2#21462466C211yesmaximal, characteristic
3#21462005C211yesmaximal, characteristic, complemented
4#21461935C211yesmaximal, characteristic, complemented
5#21461929C211yesmaximal, characteristic, complemented
6#21461928C211yesmaximal, characteristic, complemented
7#21461885C211yesmaximal, characteristic, complemented
8#21461884C211yesmaximal, characteristic, complemented
9#21461788C211yesmaximal, characteristic
10#21461786C211yesmaximal, characteristic
11#21461606C211yesmaximal, characteristic, complemented
12#21461598C211yesmaximal, characteristic
13#21461598C211yesmaximal, characteristic
14C4×#14519841C211yesmaximal, characteristic
15#21455604C211yesmaximal, characteristic
16C2×#14519864C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18#16840814—21no—
19#16840814—21no—
20#16840812—21no—
21#16840811—21no—
22C2×#14519848C2211yescharacteristic
23C2×#14519847C2211yescharacteristic
24#16840769C2211yescharacteristic
25#16840769C2211yescharacteristic
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840768—21no—
29#16840768—21no—
30#16840767C2211yescharacteristic
31#16840765—21no—
32C2×#14519844—21no—
33D61⋊(C4⋊C8)C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35C2×#14519841C2211yescharacteristic
36#16840727C2211yescharacteristic
37#16840727C2211yescharacteristic
38C4×#11758213C2211yescharacteristic
39C2×#14519831C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C42×#6923C2211yescharacteristic
42#16840638C2211yescharacteristic
43#16840638C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#16840318C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840070C411yescharacteristic, complemented
55#16840066C411yescharacteristic, complemented
56#16840062C411yescharacteristic, complemented
57#16840056C411yescharacteristic, complemented
58#16840050C411yescharacteristic, complemented
59#16840046C411yescharacteristic, complemented
60#16840040C411yescharacteristic, complemented
61#16839799C2211yescharacteristic
62#16839797C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#16839755C2211yescharacteristic
65#16839755C2211yescharacteristic
66C61×#478C411yescharacteristic, complemented
67#14519864—22no—
68#14519864—22no—
69#14519864—41no—
70#14519864—41no—
71C2×#11758213C2311yescharacteristic
72C2×#11758213C2311yescharacteristic
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C22×#92420—21no—
80C22×#92420—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923C2311yescharacteristic
84C2×C4×#6923C2311yescharacteristic
85#14519848—41no—
86#14519847—41no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91#14519844—21no—
92#14519844—21no—
93#14519844D411yescharacteristic
94#14519844D411yescharacteristic
95C4⋊#92420—21no—
96C4⋊#92420—21no—
97C4⋊#92420—21no—
98C4⋊#92420—21no—
99C4⋊#92420D411yescharacteristic
100C4⋊#92420D411yescharacteristic
101#14519841—22no—
102#14519841Q814yescomplemented
103#14519832—21no—
104#14519832—21no—
105#14519832—21no—
106#14519831—41no—
107#14519831—41no—
108C4×#92420—21no—
109C4×#92420—21no—
110C4×#92420—21no—
111C2×#11758224C2311yescharacteristic
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114#14519776C2×C411yescharacteristic
115#14519776C2×C411yescharacteristic
116#14519769C2×C411yescharacteristic
117#14519755—21no—
118#14519755—21no—
119C4×Dic122C2×C411yescharacteristic
120#14519742—21no—
121#14519742—21no—
122#14519742C2×C411yescharacteristic
123D4×Dic61C2×C411yescharacteristic
124C4×C22⋊D61—21no—
125#14519737—21no—
126#14519735C2311yescharacteristic
127#14519735C2311yescharacteristic
128#14519735C2311yescharacteristic
129#14519733—21no—
130C2×C4×Dic61—21no—
131C42×D61C2311yescharacteristic
132#14519711C2×C411yescharacteristic
133#14519710C2×C411yescharacteristic
134#14519710C2×C411yescharacteristic
135#14519709C2×C411yescharacteristic
136#14519708C2×C411yescharacteristic
137#14519708C2×C411yescharacteristic
138C4⋊#92418C2×C411yescharacteristic
139#14519706C2×C411yescharacteristic
140#14519706C2×C411yescharacteristic
141#14519702C2×C411yescharacteristic
142#14519702C2×C411yescharacteristic
143#14519700C2×C411yescharacteristic
144#14519700C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519698C2×C411yescharacteristic
147#125×C61C2×C411yescharacteristic
148C4×D4×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic
150#106×C61C2×C411yescharacteristic
151C4⋊C8×C61C2×C411yescharacteristic
152#102×C61C2×C411yescharacteristic
153#102×C61C2×C411yescharacteristic
154C22×#6923—21no—
155C22×#6923—21no—
156C2×D4×C61C22×C411yescharacteristic
157C22×C4×C61—21no—
158C2×C22⋊D61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161#11758224—21no—
162#11758224—21no—
163#11758224C2×Q812yes—
164#11758224#4112yes—
165C2×C4×D61#4111yescharacteristic
166C2×C4×D61#4111yescharacteristic
167C2×C4×D61C2411yescharacteristic
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122C22×C411yescharacteristic
171#11758217—42no—
172#11758217—42no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—42no—
178C2×#92420—42no—
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C4×#6923—21no—
184C4×#6923—21no—
185C4×#6923—21no—
186C4×#6923—42no—
187C4×#6923—42no—
188C4×#6923C2×Q812yes—
189#11758213—21no—
190#11758213—21no—
191#11758213—21no—
192#11758213—21no—
193#11758213—21no—
194#11758213—21no—
195#11758213—21no—
196#11758213C2×Q812yes—
197D61⋊C8—21no—
198D61⋊C8—21no—
199D61⋊C8—21no—
200D61⋊C8—21no—
201C2×C8×C61C22×C411yescharacteristic
202C2×C8×C61C22×C411yescharacteristic
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C22×C411yescharacteristic
206C4⋊C4×C61C22×C411yescharacteristic
207C4⋊C4×C61C22×C411yescharacteristic
208C22⋊C4×C61—21no—
209C42×C61C22×C411yescharacteristic
210C22⋊Dic61—21no—
211#11758198—21no—
212#11758198—21no—
213#11758198—21no—
214C4⋊Dic61C22×C411yescharacteristic
215C4⋊Dic61C22×C411yescharacteristic
216C4⋊Dic61C22×C411yescharacteristic
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221#11758196—21no—
222#11758196—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61C22×C411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C2×#92418C22×C411yescharacteristic
232C2×#92418C22×C411yescharacteristic
233C8×D61—21no—
234C8×D61—21no—
235C8×D61—21no—
236C8×D61—21no—
237C23×C61—21no—
238C22×D61C2×#4111yescharacteristic
239C2×#6923—22no—
240C2×#6923—22no—
241C2×#6923—41no—
242C2×#6923—41no—
243C2×#6923—41no—
244C2×#6923—41no—
245D4×C61—21no—
246D4×C61C4×Q812yes—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—81no—
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C22⋊D61—22no—
255C22⋊D61—22no—
256C2×Dic61—21no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—42no—
263C2×Dic61C4×D411yescharacteristic
264C2×Dic61C4×D411yescharacteristic
265C2×Dic61C22×D411yescharacteristic
266C4×D61—22no—
267C4×D61—41no—
268C4×D61C22×Q811yescharacteristic
269C4×D61C2×#4111yescharacteristic
270C4×D61H(5,𝔽2)11yescharacteristic
271C4×D612−1+411yescharacteristic
272Dic122—21no—
273Dic122—42no—
274Dic122—81no—
275Dic122C4×Q812yes—
276#92420—21no—
277#92420—21no—
278#92420—21no—
279#92420—21no—
280#92420—22no—
281#92420—41no—
282#92420—41no—
283#92420—41no—
284C8×C61—21no—
285C8×C61—21no—
286#92418—21no—
287#92418—21no—
288#22983—611nomaximal, Sylow
289C22×C61—22no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61C2×C4×D411yescharacteristic
293C2×D61—21no—
294C2×D61—21no—
295C2×D61#55211yescharacteristic
296C2×D61#55411yescharacteristic
297#6923—42no—
298#6923—42no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61C2×C4×Q811yescharacteristic
305C4×C61#52011yescharacteristic
306Dic61—22no—
307Dic61—21no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61#44412yes—
312Dic61#54611yescharacteristic
313Dic61D4×Q811yescharacteristic
314#3076—611no—
315#2962—611no—
316#2906—611no—
317#1994—611no—
318#1950—611no—
319#1946—611no—
320#1946—611no—
321#1922—611no—
322#1922—611no—
323#1866—611no—
324#1866—611no—
325#1767—611no—
326#1765—611no—
327#1765—611no—
328C4×#104—611no—
329C2×C61—42no—
330C2×C61#236011yescharacteristic
331C2×C61C2×#44411yescharacteristic
332C2×C61#295611yescharacteristic
333D61—21no—
334D61—21no—
335C2×#131—611no—
336C2×#131—611no—
337#533—611no—
338C4×#41—611no—
339#479—611no—
340#479—611no—
341#478—611no—
342#478#692311yescharacteristic, complemented
343#477—611no—
344#476—611no—
345#475—611no—
346#474—611no—
347#446—1221no—
348#446—1221no—
349#446—1221no—
350C8×Q8—1221no—
351C2×#108—611no—
352C2×#108—611no—
353#427—611no—
354#427—611no—
355#424—611no—
356#424—611no—
357#424—611no—
358#424—611no—
359#424—1221no—
360#424—1221no—
361#423—611no—
362#423—1221no—
363C2×C4⋊C8—611no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—1221no—
366C2×#104—611no—
367C2×#104—611no—
368#416—611no—
369#416—611no—
370#405—611no—
371#405—611no—
372C4×M16—611no—
373C2×#97—611no—
374C2×#97—611no—
375C43—611no—
376#341—611no—
377#341—611no—
378#339—611no—
379#339—611no—
380#339—611no—
381#339—611no—
382#339—611no—
383#339—611no—
384#336—611no—
385#336—611no—
386C61#2298311yescharacteristic, complemented, Sylow
387C2×#41—611no—
388#131—1222no—
389#131—1222no—
390#131—2441no—
391#131—2441no—
392C2×M16—611no—
393C2×M16—611no—
394C2×M16—611no—
395C2×M16—611no—
396C2×M16—1221no—
397C2×M16—1221no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—1221no—
403C22×C8—1221no—
404C4⋊Q8—611no—
405C4⋊Q8—611no—
406#125—611no—
407#125C2×#692311yescharacteristic
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410C4×Q8—611no—
411C4×Q8—611no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×D4—611no—
415C4×D4—1221no—
416C4×D4—1221no—
417C4×D4C2×#692311yescharacteristic
418#117—611no—
419#117—611no—
420#117—611no—
421#117—1221no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1221no—
426C2×C42—1221no—
427C2×C42—1221no—
428#108—2441no—
429#108—2441no—
430#107—611no—
431#107—611no—
432#107—611no—
433#107C2×#692311yescharacteristic
434#106—611no—
435#106—611no—
436#106—611no—
437#106C2×#692311yescharacteristic
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—611no—
443C4⋊C8—611no—
444C4⋊C8—611no—
445C4⋊C8—1221no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8—1221no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8—1221no—
452C4⋊C8—1221no—
453C4⋊C8—1221no—
454C4⋊C8—1221no—
455C4⋊C8C2×#692311yescharacteristic
456#104—614no—
457#104—1222no—
458#103—611no—
459#103—611no—
460#103—611no—
461#103—611no—
462#102—611no—
463#102—611no—
464#102C2×#692311yescharacteristic
465#102C2×#692311yescharacteristic
466#97—1221no—
467#97—1221no—
468#97—1221no—
469#97—2441no—
470#97—2441no—
471C4×C8—1221no—
472C4×C8—1221no—
473C4×C8—1221no—
474#41—612no—
475#41—612no—
476#41—1221no—
477#41—1221no—
478C2×Q8—611no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×D4—1221no—
482C2×D4C22×#692311yescharacteristic
483C22×C4—21no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491M16—612no—
492M16—1221no—
493M16—1221no—
494M16—1221no—
495M16—1221no—
496M16—1221no—
497M16—1221no—
498M16—1221no—
499M16—2442no—
500M16—2442no—
501C2×C8—611no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—611no—
505C2×C8—611no—
506C2×C8—611no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—2442no—
520C2×C8—2442no—
521C2×C8C22×#692311yescharacteristic
522C2×C8C22×#692311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—611no—
526C4⋊C4—611no—
527C4⋊C4—611no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4C22×#692311yescharacteristic
535C4⋊C4C22×#692311yescharacteristic
536C4⋊C4C22×#692311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C22⋊C4—1221no—
541C22⋊C4—1221no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—612no—
546C42—1221no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C42—1221no—
554C42—2442no—
555C42—2442no—
556C42C22×#692311yescharacteristic
557C23—21no—
558C23—611no—
559Q8—612no—
560Q8—1221no—
561Q8—4881no—
562Q8—2442no—
563D4—21no—
564D4—1222no—
565D4—1222no—
566D4Q8×#692312yes—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—81no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—2441no—
588C2×C4—2442no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4D4×#692311yescharacteristic
594C2×C4D4×#692311yescharacteristic
595C2×C4C23×#692311yescharacteristic
596C8—21no—
597C8—21no—
598C8—1221no—
599C8—1221no—
600C8—1221no—
601C8—1221no—
602C8—1222no—
603C8—1221no—
604C8—1221no—
605C8—2441no—
606C8—2441no—
607C8—2441no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22—611no—
612C22—611no—
613C22—1221no—
614C22—1221no—
615C22C2×D4×#692311yescharacteristic
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—612no—
622C4—611no—
623C4—611no—
624C4—1221no—
625C4—1222no—
626C4—2442no—
627C4—2442no—
628C4—2441no—
629C4—2441no—
630C4—2441no—
631C4C2×Q8×#692311yescharacteristic
632C4#1684083111yescharacteristic
633C2—42no—
634C2—1221no—
635C2—1221no—
636C2#2146234311yescharacteristic
637C2D61⋊#44411yescharacteristic
638C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#478C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C23
cosocleC2×C4×D61C24
hypercenter#478#6923
hypocenterC61#22983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #21462617C2semidirect
3. #21462005C2semidirect
4. #21461935C2semidirect
5. #21461929C2semidirect
6. #21461928C2semidirect
7. #21461885C2semidirect
8. #21461884C2semidirect
11. #21461606C2semidirect
54. #16840070C4semidirect
55. #16840066C4semidirect
56. #16840062C4semidirect
57. #16840056C4semidirect
58. #16840050C4semidirect
59. #16840046C4semidirect
60. #16840040C4semidirect
66. C61×#478C4semidirect
102. #14519841Q8semidirect
342. #478#6923semidirect
386. C61#22983semidirect

Maximal subgroups

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

subgroupindex
#214626172
#214624662
#214620052
#214619352
#214619292
#214619282
#214618852
#214618842
#214617882
#214617862
#214616062
#214615982
C4×#145198412
#214556042
#2298361