Finite Group Databasebeta

← #30613539

Subgroups — #30613539

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462752C211yesmaximal, characteristic, complemented
2#21462675C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461449C211yesmaximal, characteristic, complemented
6#21461438C211yesmaximal, characteristic, complemented
7#21461429C211yesmaximal, characteristic, complemented
8#21461418C211yesmaximal, characteristic, complemented
9#21461410C211yesmaximal, characteristic, complemented
10#21461402C211yesmaximal, characteristic, complemented
11#21461383C211yesmaximal, characteristic, complemented
12#21461152C211yesmaximal, characteristic, complemented
13#21461144C211yesmaximal, characteristic, complemented
14#21461038C211yesmaximal, characteristic, complemented
15#21454623C211yesmaximal, characteristic
16#16840811C2211yescharacteristic, complemented
17#16840811C2211yescharacteristic, complemented
18#16840797C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840796C2211yescharacteristic, complemented
21#16840796C2211yescharacteristic, complemented
22#16840795—21no—
23#16840795—21no—
24#16840793—21no—
25#16840793—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840783C2211yescharacteristic
29#16840780—21no—
30#16840779C2211yescharacteristic
31#16840779C2211yescharacteristic
32#16840767—21no—
33#16840765C2211yescharacteristic
34#16840732—21no—
35C2×C22⋊#92420—21no—
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840612C2211yescharacteristic, complemented
41#16840612C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52C2×#14519803C411yescharacteristic
53#16840230C2211yescharacteristic
54C2×D4×Dic61C2211yescharacteristic
55#16839871C411yescharacteristic
56#16839871C411yescharacteristic
57#16839859C411yescharacteristic
58#16839859C411yescharacteristic
59#16839853C2211yescharacteristic
60#16839853C2211yescharacteristic
61#16839842C2211yescharacteristic
62#16839842C2211yescharacteristic
63#16839805C411yescharacteristic
64#16839764C411yescharacteristic
65M16×Dic61C2211yescharacteristic
66C61×#418C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77#14519844—21no—
78#14519844D411yescharacteristic
79#14519844D411yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420D411yescharacteristic
93C22⋊#92420D411yescharacteristic
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758222C2×C411yescharacteristic
102C23×Dic61—21no—
103#14519803—24no—
104C2×#11758200C2×C411yescharacteristic
105C2×#11758200C2×C411yescharacteristic
106C2×#11758199C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108C2×#11758194C2×C411yescharacteristic
109#14519742C2×C411yescharacteristic
110#14519742C2311yescharacteristic
111D4×Dic61—21no—
112D4×Dic61—21no—
113D4×Dic61C2×C411yescharacteristic
114D4×Dic61C2×C411yescharacteristic
115D4×Dic61C2311yescharacteristic
116D4×Dic61C2311yescharacteristic
117#14519739C2×C411yescharacteristic
118#14519739C2311yescharacteristic
119#14519737—21no—
120#14519737—21no—
121#14519734—21no—
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×C22⋊Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125C42×D61—21no—
126#14519710C2×C411yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519708C2×C411yescharacteristic
129#14519708C2×C411yescharacteristic
130#14519702C2×C411yescharacteristic
131#14519702C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519699C2×C411yescharacteristic
134#14519687C2×C411yescharacteristic
135#14519687C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C22×D4×C61C2×C411yescharacteristic
139C2×M16×C61C2×C411yescharacteristic
140#117×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C24×C61—21no—
146C2×D4×C61—22no—
147C2×D4×C61—21no—
148C2×D4×C61—41no—
149C2×D4×C61C22×C411yescharacteristic
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—81no—
159C22×Dic61—81no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61#4111yescharacteristic
162#11758222—22no—
163#11758222—41no—
164C2×D244C22×C411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×Dic122C22×C411yescharacteristic
169#11758217—81no—
170#11758217—81no—
171#11758217—81no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—81no—
179C2×#92420—81no—
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183C2×#92420C2×D411yescharacteristic
184#11758213—81no—
185#11758213—81no—
186M16×C61—41no—
187C2×C8×C61C22×C411yescharacteristic
188C2×C8×C61C22×C411yescharacteristic
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C22⋊C4×C61—21no—
192C42×C61—21no—
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197#11758200—22no—
198#11758200M1614yescomplemented
199#11758199—22no—
200#11758199—22no—
201#11758198—21no—
202#11758198—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206#11758196—21no—
207#11758196—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61#4111yescharacteristic
213C4×Dic61C2411yescharacteristic
214#11758194—22no—
215C2×#92418C22×C411yescharacteristic
216C2×#92418C22×C411yescharacteristic
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—81no—
222C23×C61C4×D411yescharacteristic
223C22×D61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—42no—
228D4×C61C2×M1612yes—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C23×C411yescharacteristic
235C22⋊D61—42no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—81no—
247C2×Dic61—81no—
248C2×Dic61—81no—
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61C4×D411yescharacteristic
251C2×Dic61C22×D411yescharacteristic
252C2×Dic61C2×#4111yescharacteristic
253D244—21no—
254D244—21no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—41no—
258C4×D61—41no—
259Dic122—21no—
260Dic122C2×M1612yes—
261#92420—21no—
262#92420—21no—
263#92420—21no—
264#92420—21no—
265#92420—41no—
266#92420—41no—
267#92420—41no—
268#92420—41no—
269#92420—41no—
270#92420—41no—
271C8×C61—21no—
272C8×C61—21no—
273#92418—21no—
274#92418C2×M1612yes—
275#18052—611nomaximal, Sylow
276C22×C61—21no—
277C22×C61—22no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—84no—
286C22×C61C2×C4×D411yescharacteristic
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61C22×M1611yescharacteristic
294C4×C61#56811yescharacteristic
295Dic61—22no—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—41no—
300Dic61—41no—
301Dic61#57611yescharacteristic
302Dic61#57711yescharacteristic
303#2991—611no—
304#2974—611no—
305C4×AGL(1,ℤ/8)—611no—
306#1594—611no—
307#1589—611no—
308#1588—611no—
309#1586—611no—
310#1583—611no—
311#1581—611no—
312SD16⋊C8—611no—
313C8×SD16—611no—
314#1569—611no—
315#1488—611no—
316#1486—611no—
317#1453—611no—
318C2×C61—41no—
319C2×C61—42no—
320C2×C61—81no—
321C2×C61D4×M1611yescharacteristic
322C2×C61#294611yescharacteristic
323C2×C61#295511yescharacteristic
324D61—81no—
325C2×AGL(1,ℤ/8)—611no—
326C4×#41—611no—
327C2×C4×D4—611no—
328C8×Q8—611no—
329C8×Q8—611no—
330#442—611no—
331#442—611no—
332#440—611no—
333#440—611no—
334C4×SD16—611no—
335C4×SD16—611no—
336C4×D8—611no—
337C4×D8—611no—
338#436—611no—
339#436—611no—
340#436—611no—
341#436—611no—
342#436—1221no—
343#436—1221no—
344#435—1221no—
345#435—1221no—
346C8×D4—611no—
347C8×D4—611no—
348#432—611no—
349#431—611no—
350#431—611no—
351#431—1221no—
352#428—611no—
353#423—611no—
354#423—1221no—
355#418#692311yescharacteristic
356#417—611no—
357#407—1221no—
358C2×C22⋊C8—1221no—
359C4×M16—611no—
360#335—611no—
361#335—611no—
362#334—611no—
363#334—611no—
364Q8⋊C8—611no—
365Q8⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372#322—611no—
373#322—611no—
374#322—611no—
375C82—611no—
376C61#1805211yescharacteristic, complemented, Sylow
377C2×#41—611no—
378C22×D4C2×#692311yescharacteristic
379C23×C4—1221no—
380AGL(1,ℤ/8)—1224no—
381C2×SD16—611no—
382C2×SD16—611no—
383C2×D8—611no—
384C2×D8—611no—
385C2×M16—611no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16—1221no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16C2×#692311yescharacteristic
392C22×C8—1221no—
393C22×C8—1221no—
394C4×Q8—611no—
395C4×Q8—611no—
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—611no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4—1221no—
405C4×D4—1221no—
406#117—1221no—
407#117C2×#692311yescharacteristic
408C2×C4⋊C4—611no—
409C2×C22⋊C4—1221no—
410C2×C42—611no—
411C2×C42—1221no—
412#107—611no—
413#107—611no—
414#106—611no—
415#106—611no—
416C4⋊C8—611no—
417C4⋊C8—611no—
418C4⋊C8—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—1221no—
423C4⋊C8—1221no—
424C4⋊C8—1221no—
425C4⋊C8—1221no—
426#103—611no—
427#103—611no—
428#102—611no—
429#102—611no—
430#102C2×#692311yescharacteristic
431#102C2×#692311yescharacteristic
432#102C2×#692311yescharacteristic
433#102C2×#692311yescharacteristic
434C22⋊C8—611no—
435C22⋊C8—611no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444#97—611no—
445#97—611no—
446#97—1221no—
447C4×C8—611no—
448C4×C8—611no—
449C4×C8—611no—
450C4×C8—611no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—1221no—
454C4×C8—1221no—
455C24—21no—
456#41—1222no—
457#41—2441no—
458C2×Q8—611no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—611no—
463C2×D4—1221no—
464C2×D4C22×#692311yescharacteristic
465C2×D4C22×#692311yescharacteristic
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4881no—
477C22×C4—4881no—
478C22×C4C22×#692311yescharacteristic
479SD16—614no—
480SD16—1222no—
481D8—1222no—
482D8—1222no—
483M16—41no—
484M16—1222no—
485M16—4881no—
486M16—4881no—
487M16—4881no—
488M16—4881no—
489M16—4881no—
490C2×C8—611no—
491C2×C8—611no—
492C2×C8—611no—
493C2×C8—611no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—4881no—
503C2×C8—4881no—
504C2×C8C22×#692311yescharacteristic
505C2×C8C22×#692311yescharacteristic
506C4⋊C4—611no—
507C4⋊C4—611no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4C22×#692311yescharacteristic
512C4⋊C4C22×#692311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—1221no—
515C22⋊C4—1221no—
516C22⋊C4—1221no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C42—21no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—1221no—
526C42—1221no—
527C23—21no—
528C23—21no—
529C23—42no—
530C23—42no—
531C23—81no—
532C23—1221no—
533C23D4×#692311yescharacteristic
534Q8—612no—
535Q8—1221no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—1221no—
541D4—1221no—
542D4—2442no—
543D4D61⋊M1612yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—4881no—
558C2×C4—4881no—
559C2×C4—4881no—
560C2×C4—2442no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2442no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4D4×#692311yescharacteristic
570C2×C4C23×#692311yescharacteristic
571C8—21no—
572C8—21no—
573C8—612no—
574C8—1221no—
575C8—1221no—
576C8—1221no—
577C8—1221no—
578C8—1221no—
579C8—2441no—
580C8—2441no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C8—2441no—
585C22—21no—
586C22—22no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—84no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22C2×D4×#692311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—611no—
603C4—611no—
604C4—1222no—
605C4—1221no—
606C4—1221no—
607C4—1221no—
608C4—2441no—
609C4—2441no—
610C4C2×D61⋊M1611yescharacteristic
611C4#1684084011yescharacteristic
612C2—41no—
613C2—42no—
614C2—81no—
615C2—4881no—
616C2#2146255711yescharacteristic
617C2#2146257611yescharacteristic
618C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#418C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519803C4
cosocleC4×Dic61C24
hypercenter#418#6923
hypocenterC61#18052
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #21462752C2semidirect
2. #21462675C2semidirect
3. #21461467C2semidirect
4. #21461450C2semidirect
5. #21461449C2semidirect
6. #21461438C2semidirect
7. #21461429C2semidirect
8. #21461418C2semidirect
9. #21461410C2semidirect
10. #21461402C2semidirect
11. #21461383C2semidirect
12. #21461152C2semidirect
13. #21461144C2semidirect
14. #21461038C2semidirect
16. #16840811C22semidirect
17. #16840811C22semidirect
20. #16840796C22semidirect
21. #16840796C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. #16840612C22semidirect
41. #16840612C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
198. #11758200M16semidirect
376. C61#18052semidirect

Maximal subgroups

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

subgroupindex
#214627522
#214626752
#214614672
#214614502
#214614492
#214614382
#214614292
#214614182
#214614102
#214614022
#214613832
#214611522
#214611442
#214610382
#214546232
#1805261