Finite Group Databasebeta

← #29671305

Subgroups — #29671305

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#21458454C211yesmaximal, characteristic, complemented
2#21457626C211yesmaximal, characteristic, complemented
3#21457440C211yesmaximal, characteristic, complemented
4#21445426C211yesmaximal, characteristic, complemented
5#21445305C211yesmaximal, characteristic, complemented
6#21445298C211yesmaximal, characteristic, complemented
7#21445265C211yesmaximal, characteristic, complemented
8#21445258C211yesmaximal, characteristic, complemented
9#21445010C211yesmaximal, characteristic, complemented
10#21444996C211yesmaximal, characteristic, complemented
11#21444922C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444702C211yesmaximal, characteristic, complemented
14SD16×#92418C211yesmaximal, characteristic, complemented
15C61×#3276C211yesmaximal, characteristic, complemented
16C2×#14519804—21no—
17#16840434C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840139C2211yescharacteristic
20#16840110—21no—
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic, complemented
24#16840110C2211yescharacteristic, complemented
25#16840075—21no—
26#16840039—21no—
27#16840039C2211yescharacteristic
28#16840039C2211yescharacteristic
29#16840016—21no—
30#16839996—21no—
31#16839962C2211yescharacteristic
32#16839957—21no—
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839957C2211yescharacteristic, complemented
36#16839910—21no—
37#16839897—21no—
38#16839895—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758199—21no—
41C4×#11758199C2211yescharacteristic
42#16839841C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519697—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839505C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56C2×#137×C61—21no—
57D4×Q8×C61C2211yescharacteristic, complemented
58C61×#547C2211yescharacteristic
59C61×#494C2211yescharacteristic, complemented
60C61×#470—21no—
61C61×#462C2211yescharacteristic, complemented
62C61×#461C2211yescharacteristic
63C61×#452—21no—
64C61×#451—21no—
65C4×SD16×C61C2211yescharacteristic
66C61×#436C2211yescharacteristic, complemented
67C2×#11758226—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70#14519804—44no—
71C2×#11758201—21no—
72C2×D488—21no—
73C2×D488—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199D411yescharacteristic
78C2×#11758189—21no—
79C22×#92418—21no—
80#14519774—21no—
81#14519774C2311yescharacteristic
82#14519774C2311yescharacteristic
83#14519752—21no—
84#14519752—21no—
85#14519752—41no—
86#14519751—21no—
87#14519747—41no—
88C4×D244—21no—
89C4×D244C2311yescharacteristic
90#14519710—21no—
91#14519710—21no—
92#14519710D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519698D411yescharacteristic
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697—41no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×Q8×C61—21no—
118#137×C61—44no—
119C2×Q16×C61—21no—
120C2×Q16×C61—21no—
121C2×Q16×C61—21no—
122C2×SD16×C61—21no—
123C2×SD16×C61D411yescharacteristic
124C2×M16×C61—21no—
125C4⋊Q8×C61—21no—
126C4⋊Q8×C61C2311yescharacteristic
127C4⋊Q8×C61C2311yescharacteristic
128#123×C61—41no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—41no—
132#121×C61—21no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—21no—
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—21no—
138#106×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142#103×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—41no—
152C2×Q8×C61—42no—
153C2×Q8×C61—81no—
154C2×Q8×C61C2×D411yescharacteristic
155C2×D4×C61—41no—
156C2×D4×C61C2×D411yescharacteristic
157C2×D4×C61C2×D411yescharacteristic
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C2×C22⋊D61—41no—
163#11758226—42no—
164#11758226—81no—
165D4×D61—42no—
166D4×D61—81no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—42no—
174C2×D244—41no—
175C2×D244—41no—
176C2×D244—41no—
177C2×D244—81no—
178C2×D244C2×D411yescharacteristic
179C2×C4×D61—21no—
180C2×C4×D61—41no—
181Q16×C61—42no—
182Q16×C61—42no—
183Q16×C61—81no—
184SD16×C61—42no—
185SD16×C61D814yescomplemented
186M16×C61—42no—
187C2×C8×C61—21no—
188C2×C8×C61C2×D411yescharacteristic
189C2×C8×C61C2×D411yescharacteristic
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—41no—
196C4⋊C4×C61—41no—
197C4⋊C4×C61C2×D411yescharacteristic
198C4⋊C4×C61C2×D411yescharacteristic
199C4⋊C4×C61C2×D411yescharacteristic
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C42×C61—21no—
205C42×C61C2411yescharacteristic
206#11758201—42no—
207#11758199—41no—
208#11758199—42no—
209#11758199—42no—
210#11758199—81no—
211#11758198—21no—
212#11758198—41no—
213#11758198—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
222D488—42no—
223D488—81no—
224#11758189—42no—
225C23×C61—21no—
226C23×C61—21no—
227C22×D61—21no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—82no—
231C22×D61—82no—
232C22×D61—161no—
233Q8×C61—21no—
234Q8×C61—41no—
235Q8×C61—41no—
236Q8×C61—41no—
237Q8×C61—41no—
238Q8×C61—82no—
239Q8×C61C2×D812yes—
240D4×C61—21no—
241D4×C61—21no—
242D4×C61—21no—
243D4×C61—82no—
244D4×C61C2×D812yes—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—82no—
256C2×C4×C61—82no—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C22⋊D61—82no—
261C2×Dic61—21no—
262D244—21no—
263D244—21no—
264D244—41no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—41no—
271D244—41no—
272D244—82no—
273D244—81no—
274D244—81no—
275D244—82no—
276D244—161no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—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×C61D4211yescharacteristic
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—164no—
307C4×C61—22no—
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—81no—
313C4×C61—81no—
314C4×C61C22×D811yescharacteristic
315C4×C61#57511yescharacteristic
316C4×C61#57611yescharacteristic
317C4×C61#57711yescharacteristic
318Dic61—41no—
319#3358—611no—
320#3294—611no—
321#3276D6111yescharacteristic, complemented
322#3274—611no—
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#327511yescharacteristic
337C2×C61D4×D811yescharacteristic
338C2×C61#329011yescharacteristic
339D61—81no—
340D61—161no—
341D61—161no—
342C2×#137—21no—
343C2×AGL(1,ℤ/8)—1221no—
344#550—611no—
345D4×Q8C2×D6111yescharacteristic, complemented
346#547C2×D6111yescharacteristic
347D42—611no—
348#494C2×D6111yescharacteristic, complemented
349#493—611no—
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—21no—
360#469—1221no—
361#466—1221no—
362#462C2×D6111yescharacteristic, complemented
363#461C2×D6111yescharacteristic
364#460—611no—
365#459—611no—
366#459—611no—
367#459—611no—
368#459—1221no—
369#452—21no—
370#451—21no—
371#449—1221no—
372#447—1221no—
373#447—1221no—
374C8×Q8—611no—
375C4×SD16C2×D6111yescharacteristic
376C4×D8—611no—
377C4×D8—1221no—
378#436—611no—
379#436C2×D6111yescharacteristic, complemented
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—21no—
397C22×D4—1221no—
398C22×D4—1221no—
399#137—44no—
400AGL(1,ℤ/8)—2444no—
401C2×Q16—21no—
402C2×Q16—21no—
403C2×Q16—21no—
404C2×SD16—21no—
405C2×SD16—1221no—
406C2×SD16C22⋊D6111yescharacteristic
407C2×D8—611no—
408C2×D8—1221no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×D8—1221no—
412C2×D8—1221no—
413C2×M16—21no—
414C2×M16—1221no—
415C22×C8—1221no—
416C4⋊Q8—21no—
417C4⋊Q8C22×D6111yescharacteristic
418C4⋊Q8C22×D6111yescharacteristic
419#127—611no—
420#127—611no—
421#127—1221no—
422#123—41no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—41no—
426#121—21no—
427#121—1221no—
428#121—1221no—
429#121—1221no—
430#121—2441no—
431#120—2441no—
432C4×Q8C22×D6111yescharacteristic
433C4×D4—21no—
434C4×D4—611no—
435C4×D4—1221no—
436C4×D4C22×D6111yescharacteristic
437C4×D4C22×D6111yescharacteristic
438C2×C4⋊C4—21no—
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—21no—
449#103—21no—
450#103C22⋊D6111yescharacteristic
451#102—611no—
452#102—611no—
453#102—1221no—
454#102—1221no—
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—2441no—
474#41—42no—
475#41—81no—
476#41—4881no—
477#41—2442no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—41no—
481C2×Q8—42no—
482C2×Q8—81no—
483C2×Q8C2×C22⋊D6111yescharacteristic
484C2×D4—41no—
485C2×D4—611no—
486C2×D4—1221no—
487C2×D4—1221no—
488C2×D4—1221no—
489C2×D4—1221no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—4881no—
493C2×D4—4881no—
494C2×D4—2441no—
495C2×D4—2441no—
496C2×D4—2441no—
497C2×D4—2442no—
498C2×D4—2441no—
499C2×D4—2442no—
500C2×D4D4×D6111yescharacteristic
501C2×D4C2×C22⋊D6111yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—1221no—
507C22×C4—2441no—
508Q16—42no—
509Q16—42no—
510Q16—81no—
511SD16—42no—
512SD16—2442no—
513SD16#1175819914yescomplemented
514D8—4881no—
515D8—4881no—
516D8—2441no—
517D8—2442no—
518D8—2442no—
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—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—611no—
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—1221no—
555C23—9761no—
556C23—4882no—
557C23—4882no—
558C23—2441no—
559C23—2441no—
560Q8—21no—
561Q8—41no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—82no—
566Q8C2×#1175819912yes—
567D4—21no—
568D4—21no—
569D4—21no—
570D4—82no—
571D4—1221no—
572D4—1221no—
573D4—9761no—
574D4—4881no—
575D4—4881no—
576D4—4882no—
577D4—4882no—
578D4—4882no—
579D4—2441no—
580D4—2441no—
581D4—2441no—
582D4—2441no—
583D4—2441no—
584D4—2441no—
585D4—2441no—
586D4—2441no—
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—41no—
597C2×C4—41no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—1221no—
601C2×C4—4882no—
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—9764no—
623C22—4881no—
624C22—4881no—
625C22—4881no—
626C22—4881no—
627C22—4881no—
628C22—4881no—
629C22—2441no—
630C22—2441no—
631C22—2441no—
632C22D4×C22⋊D6111yescharacteristic
633C4—22no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—81no—
639C4—81no—
640C4—2441no—
641C4C22×#1175819911yescharacteristic
642C4#1684056111yescharacteristic
643C4#1684056511yescharacteristic
644C4#1684057111yescharacteristic
645C2—42no—
646C2—81no—
647C2—9761no—
648C2—9761no—
649C2—4881no—
650C2#2145744411yescharacteristic
651C2D4×#1175819911yescharacteristic
652C2#2145760511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3276C2
socleC22×C61D42
hypercenter#3276D61
hypocenterC61#19886
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3276

Complements

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

NH ≅ G/Ntype
1. #21458454C2semidirect
2. #21457626C2semidirect
3. #21457440C2semidirect
4. #21445426C2semidirect
5. #21445305C2semidirect
6. #21445298C2semidirect
7. #21445265C2semidirect
8. #21445258C2semidirect
9. #21445010C2semidirect
10. #21444996C2semidirect
11. #21444922C2semidirect
12. #21444908C2semidirect
13. #21444702C2semidirect
14. SD16×#92418C2semidirect
15. C61×#3276C2semidirect
23. #16840110C22semidirect
24. #16840110C22semidirect
35. #16839957C22semidirect
39. Q8×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839508C22semidirect
48. #16839508C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
57. D4×Q8×C61C22semidirect
59. C61×#494C22semidirect
61. C61×#462C22semidirect
66. C61×#436C22semidirect
185. SD16×C61D8semidirect
321. #3276D61semidirect
345. D4×Q8C2×D61semidirect
348. #494C2×D61semidirect
362. #462C2×D61semidirect
379. #436C2×D61semidirect
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
#214584542
#214576262
#214574402
#214454262
#214453052
#214452982
#214452652
#214452582
#214450102
#214449962
#214449222
#214449082
#214447022
SD16×#924182
C61×#32762
#1988661