Finite Group Databasebeta

← #29669594

Subgroups — #29669594

Order 15616.

736 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457741C211yesmaximal, characteristic, complemented
2#21457634C211yesmaximal, characteristic, complemented
3D4×#11758199C211yesmaximal, characteristic, complemented
4#21445459C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic, complemented
6#21445272C211yesmaximal, characteristic, complemented
7#21445225C211yesmaximal, characteristic, complemented
8#21445172C211yesmaximal, characteristic, complemented
9#21444998C211yesmaximal, characteristic, complemented
10#21444934C211yesmaximal, characteristic, complemented
11#21444907C211yesmaximal, characteristic, complemented
12#21444902C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3325C211yesmaximal, characteristic, complemented
16C22×#11758199—21no—
17#16840417C2211yescharacteristic, complemented
18D4×D244C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840136C2211yescharacteristic, complemented
21#16840114C2211yescharacteristic, complemented
22#16840109C2211yescharacteristic, complemented
23#16840108C2211yescharacteristic, complemented
24#16840103—21no—
25#16840077—21no—
26#16840049C2211yescharacteristic, complemented
27#16840042C2211yescharacteristic
28#16839997—21no—
29#16839996—21no—
30#16839989—21no—
31#16839967C2211yescharacteristic, complemented
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic, complemented
34#16839954C2211yescharacteristic
35#16839905—21no—
36#16839896—21no—
37#16839895—21no—
38#16839894—21no—
39C4×#11758199C2211yescharacteristic
40C8×D244C2211yescharacteristic, complemented
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43#16839756—21no—
44#102×D61—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic, complemented
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#476C2211yescharacteristic
61C61×#469—21no—
62C61×#459C2211yescharacteristic, complemented
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic, complemented
66C61×#418—21no—
67C2×#11758222—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×#11758200—21no—
71C2×#11758201—41no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—44no—
78C2×#11758199D411yescharacteristic
79C22×#92418—21no—
80C22×#92418—21no—
81C2×C8×D61—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519759—41no—
85#14519756—21no—
86#14519752—21no—
87#14519751—21no—
88#14519748—21no—
89#14519747—41no—
90C4×D244C2311yescharacteristic
91C4⋊C4×D61—21no—
92#14519710—21no—
93#14519710D411yescharacteristic
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—41no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×D8×C61—21no—
119C2×D8×C61D411yescharacteristic
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#124×C61—41no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61—41no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D411yescharacteristic
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166D4×D61—42no—
167D4×D61—81no—
168#11758222—42no—
169#11758222—81no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—42no—
174C2×D244—41no—
175C2×D244—81no—
176C2×D244C2×D411yescharacteristic
177C2×C4×D61—21no—
178C2×C4×D61—41no—
179C2×Dic122—21no—
180D8×C61—22no—
181D8×C61—81no—
182M16×C61—81no—
183C2×C8×C61—21no—
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61C2×D411yescharacteristic
189C4⋊C4×C61C2×D411yescharacteristic
190C4⋊C4×C61C2×D411yescharacteristic
191C22⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—41no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C42×C61—41no—
198C42×C61C2411yescharacteristic
199C22⋊Dic61—41no—
200#11758201—82no—
201#11758200—81no—
202#11758199—22no—
203#11758199—42no—
204#11758199—42no—
205#11758199—42no—
206#11758199—81no—
207#11758199—81no—
208#11758198—21no—
209#11758198—41no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61C2×D411yescharacteristic
213#11758196—41no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—42no—
219C2×#92418—81no—
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222C8×D61—81no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—41no—
227C23×C61—82no—
228C23×C61—82no—
229C23×C61—161no—
230C22×D61—21no—
231C22×D61—41no—
232C22×D61—82no—
233C22×D61—82no—
234C22×D61—161no—
235Q8×C61—81no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—21no—
240D4×C61—21no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—41no—
245D4×C61—81no—
246D4×C61—82no—
247D4×C61—82no—
248D4×C61—161no—
249D4×C61#13512yes—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61H(5,𝔽2)11yescharacteristic
263C22⋊D61—82no—
264C22⋊D61—82no—
265C2×Dic61—21no—
266C2×Dic61—41no—
267D244—21no—
268D244—41no—
269D244—41no—
270D244—41no—
271D244—41no—
272D244—81no—
273D244—82no—
274D244AGL(1,ℤ/8)12yes—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—82no—
278Dic122—41no—
279Dic122—41no—
280C8×C61—21no—
281C8×C61—21no—
282C8×C61—41no—
283#92418—21no—
284#92418—21no—
285#92418—41no—
286#92418—41no—
287#92418—41no—
288#92418—41no—
289#19771—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—164no—
303C22×C61D4211yescharacteristic
304C2×D61—22no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—81no—
308C2×D61—81no—
309C2×D61—81no—
310C2×D61—164no—
311C4×C61—21no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—81no—
316C4×C61C2×#13511yescharacteristic
317C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
318C4×C61#57611yescharacteristic
319C4×C61#57611yescharacteristic
320Dic61—41no—
321Dic61—81no—
322#3325D6111yescharacteristic, complemented
323#3303—611no—
324#3294—611no—
325D4×D8—611no—
326#1717—611no—
327#1701—611no—
328#1683—611no—
329#1677—611no—
330#1667—611no—
331#1639—611no—
332#1629—611no—
333#1625—611no—
334#1624—611no—
335#1581—611no—
336#1580—611no—
337C2×C61—42no—
338C2×C61—81no—
339C2×C61—81no—
340C2×C61—161no—
341C2×C61#326411yescharacteristic
342C2×C61#328011yescharacteristic
343C2×C61#328811yescharacteristic
344D61—42no—
345D61—161no—
346C22×D8—1221no—
347#555C2×D6111yescharacteristic, complemented
348#547—611no—
349D42—611no—
350D42C2×D6111yescharacteristic
351#493—611no—
352#492—611no—
353#487—611no—
354#486—611no—
355#486—611no—
356#486C2×D6111yescharacteristic, complemented
357#485—1221no—
358#482—21no—
359#480—1221no—
360#476—611no—
361#476C2×D6111yescharacteristic
362#474—611no—
363#469—21no—
364#466—1221no—
365#466—1221no—
366#465—1221no—
367#461—611no—
368#459—611no—
369#459—611no—
370#459—611no—
371#459C2×D6111yescharacteristic, complemented
372#449—1221no—
373#447—21no—
374#447—1221no—
375#447—1221no—
376#447—1221no—
377C4×D8—611no—
378C4×D8C2×D6111yescharacteristic
379#436C2×D6111yescharacteristic, complemented
380C8×D4—611no—
381C8×D4—611no—
382C8×D4—611no—
383#418—21no—
384#416—1221no—
385C2×#102—1221no—
386#335—611no—
387#334—611no—
388#333—611no—
389#332—611no—
390#331—611no—
391#331—611no—
392D4⋊C8—611no—
393D4⋊C8—611no—
394D4⋊C8—611no—
395D4⋊C8—611no—
396#322—611no—
397C61#1977111yescharacteristic, complemented, Sylow
398C2×#41—1221no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—1221no—
402C22×D4—1221no—
403C2×SD16—1221no—
404C2×SD16—2441no—
405C2×D8—21no—
406C2×D8—611no—
407C2×D8—1221no—
408C2×D8—1221no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×D8—1221no—
412C2×D8—2444no—
413C2×D8C22⋊D6111yescharacteristic
414C2×M16—21no—
415C22×C8—1221no—
416C22×C8—1221no—
417C22×C8—1221no—
418C4⋊Q8—611no—
419C4⋊Q8C22×D6111yescharacteristic
420#127—611no—
421#127C22×D6111yescharacteristic
422#124—41no—
423#123—2441no—
424C22⋊Q8—1221no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—1221no—
430#121—1221no—
431#121—1221no—
432#120—41no—
433#120—2441no—
434C4×D4—611no—
435C4×D4C22×D6111yescharacteristic
436C4×D4C22×D6111yescharacteristic
437C4×D4C22×D6111yescharacteristic
438#117—21no—
439#117—21no—
440C2×C4⋊C4—1221no—
441#107—611no—
442#107—1221no—
443#107C22⋊D6111yescharacteristic
444#106—21no—
445#106—1221no—
446C4⋊C8—611no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8C22×D6111yescharacteristic
450#103—1221no—
451#103—1221no—
452#103—1221no—
453#102—21no—
454#102—21no—
455#102—21no—
456#102—21no—
457#102—611no—
458#102—611no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102—1221no—
464#102—1221no—
465#102—1221no—
466#102—2441no—
467#102C22⋊D6111yescharacteristic
468#102C22⋊D6111yescharacteristic
469C22⋊C8—21no—
470C22⋊C8—1221no—
471C22⋊C8—1221no—
472C22⋊C8—1221no—
473C4×C8—611no—
474C4×C8—611no—
475C4×C8C22×D6111yescharacteristic
476C24—41no—
477C24—2441no—
478#41—4881no—
479#41—2442no—
480C2×Q8—21no—
481C2×Q8—1221no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—41no—
490C2×D4—81no—
491C2×D4—81no—
492C2×D4—611no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—1221no—
496C2×D4—4881no—
497C2×D4—4881no—
498C2×D4—2441no—
499C2×D4—2442no—
500C2×D4—2441no—
501C2×D4—2441no—
502C2×D4—2442no—
503C2×D4D4×D6111yescharacteristic
504C2×D4C2×C22⋊D6111yescharacteristic
505C2×D4C2×C22⋊D6111yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—1221no—
510C22×C4—2441no—
511SD16—4881no—
512SD16—4882no—
513D8—22no—
514D8—81no—
515D8—1222no—
516D8—4881no—
517D8—4881no—
518D8—2442no—
519D8—2442no—
520D8—2442no—
521M16—81no—
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×C8—4881no—
531C2×C8—2442no—
532C2×C8C2×C22⋊D6111yescharacteristic
533C2×C8C2×C22⋊D6111yescharacteristic
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—611no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—2441no—
540C4⋊C4D4×D6111yescharacteristic
541C4⋊C4C2×C22⋊D6111yescharacteristic
542C4⋊C4C2×C22⋊D6111yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—1221no—
550C22⋊C4—2441no—
551C22⋊C4—2441no—
552C42—41no—
553C42C23×D6111yescharacteristic
554C23—21no—
555C23—21no—
556C23—21no—
557C23—41no—
558C23—82no—
559C23—82no—
560C23—161no—
561C23—1221no—
562C23—9761no—
563C23—4882no—
564C23—4882no—
565C23—2441no—
566Q8—81no—
567Q8—2441no—
568Q8—2441no—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—21no—
573D4—21no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—81no—
579D4—82no—
580D4—82no—
581D4—161no—
582D4—612no—
583D4—1221no—
584D4—4881no—
585D4—4882no—
586D4—4882no—
587D4—4882no—
588D4—2441no—
589D4—2441no—
590D4—2441no—
591D4—2441no—
592D4#1451979712yes—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—1221no—
604C2×C4—4882no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4C2×D4×D6111yescharacteristic
609C2×C4C22×C22⋊D6111yescharacteristic
610C2×C4#1451982211yescharacteristic
611C8—21no—
612C8—21no—
613C8—41no—
614C8—1221no—
615C8—1221no—
616C8—2441no—
617C8—2441no—
618C8—2441no—
619C8—2441no—
620C22—22no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—164no—
633C22—1222no—
634C22—9764no—
635C22—4881no—
636C22—4881no—
637C22—4881no—
638C22—2441no—
639C22—2441no—
640C22D4×C22⋊D6111yescharacteristic
641C4—21no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—4881no—
647C4—2441no—
648C4C2×#1451979711yescharacteristic
649C4AGL(1,ℤ/8)×D6111yescharacteristic
650C4#1684056511yescharacteristic
651C4#1684056611yescharacteristic
652C2—42no—
653C2—81no—
654C2—81no—
655C2—161no—
656C2—9761no—
657C2—2442no—
658C2#2145729311yescharacteristic
659C2#2145750011yescharacteristic
660C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3325C2
socleC22×C61D42
hypercenter#3325D61
hypocenterC61#19771
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #21457741C2semidirect
2. #21457634C2semidirect
3. D4×#11758199C2semidirect
4. #21445459C2semidirect
5. #21445380C2semidirect
6. #21445272C2semidirect
7. #21445225C2semidirect
8. #21445172C2semidirect
9. #21444998C2semidirect
10. #21444934C2semidirect
11. #21444907C2semidirect
12. #21444902C2semidirect
13. #21444646C2semidirect
14. #21444643C2semidirect
15. C61×#3325C2semidirect
17. #16840417C22semidirect
20. #16840136C22semidirect
21. #16840114C22semidirect
22. #16840109C22semidirect
23. #16840108C22semidirect
26. #16840049C22semidirect
31. #16839967C22semidirect
33. #16839957C22semidirect
40. C8×D244C22semidirect
42. D4×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839511C22semidirect
48. #16839507C22semidirect
49. #16839506C22semidirect
50. #16839505C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839483C22semidirect
56. C61×#555C22semidirect
58. C61×#486C22semidirect
62. C61×#459C22semidirect
65. C61×#436C22semidirect
322. #3325D61semidirect
347. #555C2×D61semidirect
356. #486C2×D61semidirect
371. #459C2×D61semidirect
379. #436C2×D61semidirect
397. C61#19771semidirect

Maximal subgroups

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

subgroupindex
#214577412
#214576342
D4×#117581992
#214454592
#214453802
#214452722
#214452252
#214451722
#214449982
#214449342
#214449072
#214449022
#214446462
#214446432
C61×#33252
#1977161