Finite Group Databasebeta

← #29671311

Subgroups — #29671311

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458450C211yesmaximal, characteristic, complemented
2#21457632C211yesmaximal, characteristic, complemented
3#21457466C211yesmaximal, characteristic, complemented
4#21445424C211yesmaximal, characteristic, complemented
5#21445308C211yesmaximal, characteristic, complemented
6#21445295C211yesmaximal, characteristic, complemented
7#21445261C211yesmaximal, characteristic, complemented
8#21445254C211yesmaximal, characteristic, complemented
9#21445012C211yesmaximal, characteristic, complemented
10#21444998C211yesmaximal, characteristic, complemented
11#21444920C211yesmaximal, characteristic, complemented
12#21444906C211yesmaximal, characteristic, complemented
13#21444702C211yesmaximal, characteristic, complemented
14SD16×#92418C211yesmaximal, characteristic, complemented
15C61×#3274C211yesmaximal, characteristic, complemented
16C2×#14519806—21no—
17Q8×D244C2211yescharacteristic, complemented
18#16840416C2211yescharacteristic
19#16840142C2211yescharacteristic, complemented
20#16840108—21no—
21#16840108C2211yescharacteristic
22#16840108C2211yescharacteristic
23#16840108C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic, complemented
25#16840073—21no—
26#16840042—21no—
27#16840042C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16840021—21no—
30#16839996—21no—
31#16839972C2211yescharacteristic, complemented
32#16839967C2211yescharacteristic
33#16839954—21no—
34#16839954C2211yescharacteristic
35#16839954C2211yescharacteristic, complemented
36#16839925—21no—
37#16839919—21no—
38#16839896—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758199—21no—
41C4×#11758199C2211yescharacteristic
42#16839841C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic
44C2×#14519698—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839509C2211yescharacteristic, complemented
48#16839509C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839506C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C61—21no—
57C61×#550C2211yescharacteristic
58D42×C61C2211yescharacteristic
59C61×#493C2211yescharacteristic
60C61×#469—21no—
61C61×#460C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#449—21no—
64C61×#447—21no—
65C4×SD16×C61C2211yescharacteristic
66C61×#436C2211yescharacteristic
67C2×#11758224—21no—
68C2×Q8×D61—21no—
69#14519806—44no—
70C2×Dic244—21no—
71C2×Dic244—21no—
72C2×#11758202—21no—
73C2×#11758200—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199D411yescharacteristic
77C2×#11758189—21no—
78C22×#92418—21no—
79#14519777—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519761—41no—
83#14519757—21no—
84#14519757—21no—
85#14519757—41no—
86#14519751—21no—
87C4×D244—21no—
88C4×D244C2311yescharacteristic
89C2×C4⋊Dic61—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519700—21no—
98#14519700—21no—
99#14519698—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—41no—
108#14519698—41no—
109#14519698D411yescharacteristic
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119AGL(1,ℤ/8)×C61—44no—
120C2×SD16×C61—21no—
121C2×SD16×C61D411yescharacteristic
122C2×D8×C61—21no—
123C2×D8×C61—21no—
124C2×D8×C61—21no—
125C2×M16×C61—21no—
126#127×C61—21no—
127#127×C61C2311yescharacteristic
128#127×C61C2311yescharacteristic
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—41no—
133#120×C61—41no—
134C4×Q8×C61C2311yescharacteristic
135C4×D4×C61—21no—
136C4×D4×C61C2311yescharacteristic
137C4×D4×C61C2311yescharacteristic
138#106×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61—21no—
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—81no—
163C2×D4×C61—81no—
164C2×D4×C61C2×D411yescharacteristic
165C2×D4×C61C2×D411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—41no—
169C2×C22⋊D61—41no—
170C22×Dic61—41no—
171Q8×D61—42no—
172Q8×D61—81no—
173#11758224—42no—
174#11758224—81no—
175C2×D244C2×D411yescharacteristic
176C2×C4×D61—21no—
177C2×C4×D61—41no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—41no—
181SD16×C61—42no—
182SD16×C61D814yescomplemented
183D8×C61—42no—
184D8×C61—42no—
185D8×C61—81no—
186M16×C61—42no—
187C2×C8×C61—21no—
188C2×C8×C61C2×D411yescharacteristic
189C2×C8×C61C2×D411yescharacteristic
190C4⋊C4×C61—21no—
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C4⋊C4×C61C2×D411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C42×C61—21no—
199C42×C61C2411yescharacteristic
200#11758202—42no—
201#11758200—42no—
202#11758199—41no—
203#11758199—42no—
204#11758199—81no—
205#11758198—21no—
206#11758198—41no—
207#11758198—41no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—41no—
213C4⋊Dic61—41no—
214C4⋊Dic61C2×D411yescharacteristic
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—81no—
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222Dic244—42no—
223Dic244—81no—
224#11758189—42no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—82no—
230C23×C61—82no—
231C23×C61—161no—
232C22×D61—21no—
233Q8×C61—21no—
234Q8×C61C2×D812yes—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—41no—
245D4×C61—41no—
246D4×C61—82no—
247D4×C61—81no—
248D4×C61—81no—
249D4×C61—82no—
250D4×C61—82no—
251D4×C61—161no—
252D4×C61C2×D812yes—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—82no—
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61H(5,𝔽2)11yescharacteristic
265C22⋊D61—82no—
266C2×Dic61—21no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—82no—
270D244—21no—
271D244—21no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—82no—
275Dic122—41no—
276Dic122—41no—
277Dic122—41no—
278Dic122—41no—
279Dic122—82no—
280C8×C61—21no—
281C8×C61—41no—
282C8×C61C2×D812yes—
283#92418—21no—
284#92418—21no—
285#92418—41no—
286#92418—41no—
287#92418—41no—
288#92418—41no—
289#19886—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—164no—
303C22×C61D4211yescharacteristic
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C4×C61—22no—
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61C22×D811yescharacteristic
313C4×C61#57511yescharacteristic
314C4×C61#57611yescharacteristic
315C4×C61#57711yescharacteristic
316Dic61—41no—
317Dic61—81no—
318Dic61—81no—
319#3358—611no—
320#3294—611no—
321#3276—611no—
322#3274D6111yescharacteristic, complemented
323#1709—611no—
324#1689—611no—
325#1687—611no—
326#1682—611no—
327#1681—611no—
328#1641—611no—
329#1639—611no—
330#1627—611no—
331#1625—611no—
332#1589—611no—
333C8×SD16—611no—
334C2×C61—42no—
335C2×C61—81no—
336C2×C61—161no—
337C2×C61—161no—
338C2×C61#327511yescharacteristic
339C2×C61D4×D811yescharacteristic
340C2×C61#329011yescharacteristic
341D61—81no—
342C2×#137—1221no—
343C2×AGL(1,ℤ/8)—21no—
344#550C2×D6111yescharacteristic
345D4×Q8—611no—
346#547—611no—
347D42C2×D6111yescharacteristic
348#494—611no—
349#493C2×D6111yescharacteristic
350#486—611no—
351#486—611no—
352#486—611no—
353#486—611no—
354#486—1221no—
355#480—1221no—
356#474—611no—
357#474—611no—
358#474—1221no—
359#470—1221no—
360#469—21no—
361#466—1221no—
362#462—611no—
363#461—611no—
364#460C2×D6111yescharacteristic
365#459—611no—
366#459—611no—
367#459—1221no—
368#459C2×D6111yescharacteristic
369#452—1221no—
370#451—1221no—
371#449—21no—
372#447—21no—
373#447—1221no—
374C8×Q8—611no—
375C4×SD16C2×D6111yescharacteristic
376C4×D8—611no—
377C4×D8—1221no—
378#436—611no—
379#436C2×D6111yescharacteristic
380C8×D4—611no—
381C2×#102—1221no—
382#335—611no—
383#334—611no—
384#332—611no—
385#332—611no—
386#331—611no—
387#331—611no—
388Q8⋊C8—611no—
389D4⋊C8—611no—
390D4⋊C8—611no—
391D4⋊C8—611no—
392C82—611no—
393C61#1988611yescharacteristic, complemented, Sylow
394C2×#41—21no—
395C2×#41—1221no—
396C22×Q8—1221no—
397C22×D4—21no—
398C22×D4—21no—
399#137—2444no—
400AGL(1,ℤ/8)—44no—
401C2×Q16—1221no—
402C2×Q16—1221no—
403C2×Q16—1221no—
404C2×SD16—21no—
405C2×SD16—1221no—
406C2×SD16C22⋊D6111yescharacteristic
407C2×D8—21no—
408C2×D8—21no—
409C2×D8—21no—
410C2×D8—611no—
411C2×D8—1221no—
412C2×D8—1221no—
413C2×M16—21no—
414C2×M16—1221no—
415C22×C8—1221no—
416C4⋊Q8—611no—
417C4⋊Q8—611no—
418C4⋊Q8—1221no—
419#127—21no—
420#127C22×D6111yescharacteristic
421#127C22×D6111yescharacteristic
422#123—2441no—
423C22⋊Q8—1221no—
424C22⋊Q8—1221no—
425C22⋊Q8—2441no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—41no—
430#121—1221no—
431#120—41no—
432C4×Q8C22×D6111yescharacteristic
433C4×D4—21no—
434C4×D4—611no—
435C4×D4—1221no—
436C4×D4C22×D6111yescharacteristic
437C4×D4C22×D6111yescharacteristic
438C2×C4⋊C4—1221no—
439#107—611no—
440#107—1221no—
441#107—1221no—
442#106C22⋊D6111yescharacteristic
443C4⋊C8—611no—
444C4⋊C8—611no—
445C4⋊C8—611no—
446C4⋊C8—1221no—
447C4⋊C8C22×D6111yescharacteristic
448#103—1221no—
449#103—1221no—
450#103C22⋊D6111yescharacteristic
451#102—21no—
452#102—21no—
453#102—611no—
454#102—611no—
455#102—1221no—
456#102—1221no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102—2441no—
464#102—2441no—
465#102C22⋊D6111yescharacteristic
466C22⋊C8—21no—
467C22⋊C8—1221no—
468C22⋊C8—1221no—
469C4×C8—611no—
470C4×C8—611no—
471C4×C8—1221no—
472C4×C8C22×D6111yescharacteristic
473C24—41no—
474#41—42no—
475#41—81no—
476#41—4881no—
477#41—2442no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8—4881no—
481C2×Q8—2441no—
482C2×Q8—2442no—
483C2×Q8C2×C22⋊D6111yescharacteristic
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—611no—
499C2×D4—2441no—
500C2×D4D4×D6111yescharacteristic
501C2×D4C2×C22⋊D6111yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—1221no—
506C22×C4—2441no—
507C22×C4—2441no—
508Q16—4881no—
509Q16—2442no—
510Q16—2442no—
511SD16—42no—
512SD16—2442no—
513SD16#1175819914yescomplemented
514D8—42no—
515D8—42no—
516D8—81no—
517D8—4881no—
518D8—2441no—
519D8—2442no—
520M16—42no—
521M16—2442no—
522C2×C8—21no—
523C2×C8—611no—
524C2×C8—611no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—4881no—
530C2×C8C2×C22⋊D6111yescharacteristic
531C2×C8C2×C22⋊D6111yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—611no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—2441no—
539C4⋊C4—2441no—
540C4⋊C4D4×D6111yescharacteristic
541C4⋊C4C2×C22⋊D6111yescharacteristic
542C4⋊C4C2×C22⋊D6111yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—1221no—
548C22⋊C4—2441no—
549C22⋊C4—2441no—
550C42—21no—
551C42C23×D6111yescharacteristic
552C23—21no—
553C23—21no—
554C23—41no—
555C23—41no—
556C23—82no—
557C23—82no—
558C23—161no—
559C23—1221no—
560Q8—21no—
561Q8—4882no—
562Q8—2441no—
563Q8—2441no—
564Q8—2441no—
565Q8—2441no—
566Q8C2×#1175819912yes—
567D4—21no—
568D4—21no—
569D4—21no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—82no—
579D4—81no—
580D4—81no—
581D4—82no—
582D4—82no—
583D4—161no—
584D4—1221no—
585D4—1221no—
586D4—4882no—
587D4C2×#1175819912yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—82no—
597C2×C4—1221no—
598C2×C4—4882no—
599C2×C4—4882no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4C2×D4×D6111yescharacteristic
605C2×C4C22×C22⋊D6111yescharacteristic
606C2×C4#1451982211yescharacteristic
607C8—21no—
608C8—41no—
609C8—1221no—
610C8—1221no—
611C8—2441no—
612C8—2441no—
613C8—2441no—
614C8—2441no—
615C8C2×#1175819912yes—
616C22—22no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—164no—
629C22—2441no—
630C22—2441no—
631C22—2441no—
632C22D4×C22⋊D6111yescharacteristic
633C4—22no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—4881no—
639C4—4881no—
640C4—2441no—
641C4C22×#1175819911yescharacteristic
642C4#1684055811yescharacteristic
643C4#1684056511yescharacteristic
644C4#1684057211yescharacteristic
645C2—42no—
646C2—81no—
647C2—161no—
648C2—161no—
649C2—4881no—
650C2#2145745011yescharacteristic
651C2D4×#1175819911yescharacteristic
652C2#2145760111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3274C2
socleC22×C61D42
hypercenter#3274D61
hypocenterC61#19886
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #21458450C2semidirect
2. #21457632C2semidirect
3. #21457466C2semidirect
4. #21445424C2semidirect
5. #21445308C2semidirect
6. #21445295C2semidirect
7. #21445261C2semidirect
8. #21445254C2semidirect
9. #21445012C2semidirect
10. #21444998C2semidirect
11. #21444920C2semidirect
12. #21444906C2semidirect
13. #21444702C2semidirect
14. SD16×#92418C2semidirect
15. C61×#3274C2semidirect
17. Q8×D244C22semidirect
19. #16840142C22semidirect
23. #16840108C22semidirect
24. #16840108C22semidirect
31. #16839972C22semidirect
35. #16839954C22semidirect
39. Q8×#92418C22semidirect
42. #16839841C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839509C22semidirect
48. #16839509C22semidirect
50. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
54. #16839489C22semidirect
55. C8×#92418C22semidirect
182. SD16×C61D8semidirect
322. #3274D61semidirect
393. C61#19886semidirect
513. SD16#11758199semidirect

Maximal subgroups

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

subgroupindex
#214584502
#214576322
#214574662
#214454242
#214453082
#214452952
#214452612
#214452542
#214450122
#214449982
#214449202
#214449062
#214447022
SD16×#924182
C61×#32742
#1988661