Finite Group Databasebeta

← #30613541

Subgroups — #30613541

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#21462751C211yesmaximal, characteristic, complemented
2#21462680C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461446C211yesmaximal, characteristic, complemented
6#21461441C211yesmaximal, characteristic, complemented
7#21461426C211yesmaximal, characteristic, complemented
8#21461421C211yesmaximal, characteristic, complemented
9#21461409C211yesmaximal, characteristic, complemented
10#21461403C211yesmaximal, characteristic, complemented
11#21461383C211yesmaximal, characteristic, complemented
12#21461150C211yesmaximal, characteristic, complemented
13#21461146C211yesmaximal, characteristic, complemented
14#21461038C211yesmaximal, characteristic, complemented
15#21454632C211yesmaximal, characteristic
16Q8×#92420C2211yescharacteristic, complemented
17Q8×#92420C2211yescharacteristic, complemented
18#16840797—21no—
19#16840797—21no—
20#16840797C2211yescharacteristic, complemented
21#16840797C2211yescharacteristic, complemented
22#16840796C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840792—21no—
25#16840792—21no—
26#16840790C2211yescharacteristic
27#16840790C2211yescharacteristic
28#16840783C2211yescharacteristic
29#16840779—21no—
30#16840779C2211yescharacteristic
31#16840779C2211yescharacteristic
32#16840765—21no—
33#16840765C2211yescharacteristic
34#16840733—21no—
35D61⋊(C22⋊C8)—21no—
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52C2×#14519802C411yescharacteristic
53#41×Dic61C2211yescharacteristic
54C2×#14519739C2211yescharacteristic
55#16839871C411yescharacteristic
56#16839871C411yescharacteristic
57#16839865C411yescharacteristic
58#16839865C411yescharacteristic
59#16839847C2211yescharacteristic
60#16839847C2211yescharacteristic
61#16839842C2211yescharacteristic
62#16839842C2211yescharacteristic
63#16839802C411yescharacteristic
64#16839768C411yescharacteristic
65M16×Dic61C2211yescharacteristic
66C61×#417C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834—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
101C22×D244C2×C411yescharacteristic
102C22×C4×D61—21no—
103#14519802—24no—
104C2×#11758201C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106C2×#11758199C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108C2×#11758194C2×C411yescharacteristic
109Q8×Dic61C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111D4×Dic61—21no—
112D4×Dic61—21no—
113D4×Dic61C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115#14519739—21no—
116#14519739—21no—
117#14519739C2×C411yescharacteristic
118#14519739C2×C411yescharacteristic
119#14519739C2311yescharacteristic
120#14519739C2311yescharacteristic
121#14519736—21no—
122#14519736C2×C411yescharacteristic
123C2×#11758198—21no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519708C2×C411yescharacteristic
129#14519708C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519699C2×C411yescharacteristic
134#14519687C2×C411yescharacteristic
135#14519687C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×#41×C61C2×C411yescharacteristic
139C2×M16×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C23×D61—21no—
146#41×C61—22no—
147#41×C61—41no—
148C2×Q8×C61C22×C411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61C22×C411yescharacteristic
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61#4111yescharacteristic
158C2×D244—22no—
159C2×D244—21no—
160C2×D244—41no—
161C2×D244C22×C411yescharacteristic
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—81no—
168C2×C4×D61—81no—
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×#92420C2×D411yescharacteristic
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182#11758213—81no—
183#11758213—81no—
184D61⋊C8—81no—
185D61⋊C8—81no—
186M16×C61—41no—
187C2×C8×C61C22×C411yescharacteristic
188C2×C8×C61C22×C411yescharacteristic
189C4⋊C4×C61—21no—
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C22⋊Dic61—21no—
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195#11758201—22no—
196#11758201M1614yescomplemented
197#11758199—22no—
198#11758199—22no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207C4×Dic61—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×C61C4×D411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—81no—
224Q8×C61—21no—
225Q8×C61C2×M1612yes—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—42no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—42no—
235C2×C4×C61—81no—
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—41no—
243C2×Dic61—42no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61C4×D411yescharacteristic
247C2×Dic61C4×D411yescharacteristic
248C2×Dic61C22×D411yescharacteristic
249C2×Dic61C2×#4111yescharacteristic
250D244—21no—
251D244—21no—
252D244—21no—
253D244—42no—
254D244C2×M1612yes—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—81no—
260C4×D61—81no—
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—21no—
278C22×C61—21no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C2×C4×D411yescharacteristic
283C2×D61—22no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—84no—
290C4×C61—21no—
291C4×C61—22no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61C22×M1611yescharacteristic
295C4×C61#56811yescharacteristic
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—81no—
320C2×C61D4×M1611yescharacteristic
321C2×C61#294611yescharacteristic
322C2×C61#295511yescharacteristic
323D61—42no—
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—611no—
356#417#692311yescharacteristic
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×#41C2×#692311yescharacteristic
378C22×D4—611no—
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—611no—
407#117—1221no—
408C2×C4⋊C4C2×#692311yescharacteristic
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#103C2×#692311yescharacteristic
427#103C2×#692311yescharacteristic
428#102—611no—
429#102—611no—
430#102—611no—
431#102—611no—
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—1221no—
456#41—22no—
457#41—41no—
458C2×Q8C22×#692311yescharacteristic
459C2×D4—21no—
460C2×D4—611no—
461C2×D4—611no—
462C2×D4—1222no—
463C2×D4—1221no—
464C2×D4—2441no—
465C2×D4C22×#692311yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—611no—
469C22×C4—611no—
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—21no—
507C4⋊C4—611no—
508C4⋊C4—611no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4C22×#692311yescharacteristic
512C4⋊C4C22×#692311yescharacteristic
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C22⋊C4—1221no—
516C22⋊C4—1221no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—1221no—
525C42—1221no—
526C42—1221no—
527C23—21no—
528C23—1221no—
529C23—1221no—
530C23—4881no—
531C23—2442no—
532C23—2442no—
533C23D4×#692311yescharacteristic
534Q8—21no—
535Q8D61⋊M1612yes—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—612no—
540D4—1221no—
541D4—1221no—
542D4—1221no—
543D4—2442no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—42no—
550C2×C4—81no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—4881no—
560C2×C4—4881no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2442no—
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—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—1222no—
592C22—4884no—
593C22—2441no—
594C22—2441no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22C2×D4×#692311yescharacteristic
599C4—21no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—611no—
604C4—611no—
605C4—1221no—
606C4—1221no—
607C4—1221no—
608C4—2441no—
609C4—2441no—
610C4C2×D61⋊M1611yescharacteristic
611C4#1684084011yescharacteristic
612C2—41no—
613C2—81no—
614C2—4881no—
615C2—2442no—
616C2#2146255711yescharacteristic
617C2#2146257611yescharacteristic
618C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519802C4
cosocleC4×Dic61C24
hypercenter#417#6923
hypocenterC61#18052
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #21462751C2semidirect
2. #21462680C2semidirect
3. #21461467C2semidirect
4. #21461450C2semidirect
5. #21461446C2semidirect
6. #21461441C2semidirect
7. #21461426C2semidirect
8. #21461421C2semidirect
9. #21461409C2semidirect
10. #21461403C2semidirect
11. #21461383C2semidirect
12. #21461150C2semidirect
13. #21461146C2semidirect
14. #21461038C2semidirect
16. Q8×#92420C22semidirect
17. Q8×#92420C22semidirect
20. #16840797C22semidirect
21. #16840797C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
196. #11758201M16semidirect
376. C61#18052semidirect

Maximal subgroups

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

subgroupindex
#214627512
#214626802
#214614672
#214614502
#214614462
#214614412
#214614262
#214614212
#214614092
#214614032
#214613832
#214611502
#214611462
#214610382
#214546322
#1805261