Finite Group Databasebeta

← #29669601

Subgroups — #29669601

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#21458055C211yesmaximal, characteristic, complemented
2#21457626C211yesmaximal, characteristic, complemented
3D8×D244C211yesmaximal, characteristic, complemented
4#21445461C211yesmaximal, characteristic, complemented
5#21445382C211yesmaximal, characteristic, complemented
6#21445267C211yesmaximal, characteristic, complemented
7#21445230C211yesmaximal, characteristic, complemented
8#21445174C211yesmaximal, characteristic, complemented
9#21444996C211yesmaximal, characteristic, complemented
10#21444934C211yesmaximal, characteristic, complemented
11#21444908C211yesmaximal, characteristic, complemented
12#21444902C211yesmaximal, characteristic, complemented
13#21444649C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic, complemented
15C61×#3303C211yesmaximal, characteristic, complemented
16C2×D8×D61—21no—
17D4×D244C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840139C2211yescharacteristic
20#16840136C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic, complemented
23#16840110C2211yescharacteristic, complemented
24#16840086—21no—
25#16840075—21no—
26#16840049C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840013—21no—
29#16839999—21no—
30#16839996—21no—
31#16839957C2211yescharacteristic
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic, complemented
34#16839957C2211yescharacteristic, complemented
35#16839897—21no—
36#16839897—21no—
37#16839895—21no—
38#16839895—21no—
39C4×#11758199C2211yescharacteristic
40#16839840C2211yescharacteristic, complemented
41C8×D244C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43#16839766—21no—
44C2×#14519697—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839505C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic, complemented
57C61×#547C2211yescharacteristic, complemented
58C61×#487C2211yescharacteristic, complemented
59C61×#485—21no—
60C61×#476C2211yescharacteristic, complemented
61C61×#465—21no—
62C61×#461C2211yescharacteristic, complemented
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic, complemented
66C61×#416—21no—
67C22×D244—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×#11758201—41no—
72C2×D488—21no—
73C2×D488—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—21no—
78C2×#11758199D411yescharacteristic
79D8×D61—44no—
80C2×#11758194—21no—
81C22×#92418—21no—
82C2×C8×D61—21no—
83#14519774C2311yescharacteristic
84#14519774C2311yescharacteristic
85#14519752—21no—
86#14519752—21no—
87#14519751—21no—
88#14519751—21no—
89#14519747—41no—
90#14519747—41no—
91C4×D244C2311yescharacteristic
92#14519710—21no—
93#14519710D411yescharacteristic
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519698D411yescharacteristic
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—21no—
109#14519697—41no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×SD16×C61—21no—
118C2×D8×C61D411yescharacteristic
119C22×C8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#124×C61—41no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#117×C61—21no—
133C2×C4⋊C4×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146C23×D61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162D4×D61—42no—
163D4×D61—42no—
164D4×D61—81no—
165D4×D61—81no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—42no—
173C2×D244—42no—
174C2×D244—41no—
175C2×D244—41no—
176C2×D244—81no—
177C2×D244—81no—
178C2×D244C2×D411yescharacteristic
179C2×C4×D61—21no—
180SD16×C61—81no—
181D8×C61—22no—
182C2×C8×C61—21no—
183C2×C8×C61—81no—
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C4⋊C4×C61C2×D411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C22⋊C4×C61—41no—
200C42×C61—41no—
201C42×C61C2411yescharacteristic
202#11758201—82no—
203#11758199—22no—
204#11758199—42no—
205#11758199—42no—
206#11758199—81no—
207#11758199—81no—
208#11758198—21no—
209#11758198—41no—
210#11758198—41no—
211C4⋊Dic61C2×D411yescharacteristic
212#11758194—81no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—81no—
218C2×#92418C2×D411yescharacteristic
219C2×#92418C2×D411yescharacteristic
220D488—42no—
221D488—81no—
222C8×D61—42no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C22×D61—21no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—82no—
230C22×D61—82no—
231C22×D61—82no—
232C22×D61—82no—
233C22×D61—161no—
234C22×D61—161no—
235Q8×C61—41no—
236Q8×C61—41no—
237Q8×C61—81no—
238D4×C61—21no—
239D4×C61—21no—
240D4×C61—21no—
241D4×C61—21no—
242D4×C61—21no—
243D4×C61—82no—
244D4×C61—161no—
245D4×C61AGL(1,ℤ/8)12yes—
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—41no—
256C2×C4×C61—41no—
257C2×C4×C61—82no—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61H(5,𝔽2)11yescharacteristic
261C22⋊D61—82no—
262C22⋊D61—82no—
263C2×Dic61—21no—
264D244—21no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—41no—
271D244—41no—
272D244—41no—
273D244—81no—
274D244—81no—
275D244—82no—
276D244—82no—
277D244#13512yes—
278C4×D61—41no—
279C4×D61—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×C61D4211yescharacteristic
300C2×D61—22no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61—81no—
308C2×D61—81no—
309C2×D61—164no—
310C2×D61—164no—
311C4×C61—21no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—81no—
316C4×C61—81no—
317C4×C61C2×#13511yescharacteristic
318C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
319C4×C61#57611yescharacteristic
320C4×C61#57611yescharacteristic
321Dic61—41no—
322#3325—611no—
323#3303D6111yescharacteristic, complemented
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#326411yescharacteristic
341C2×C61#328011yescharacteristic
342C2×C61#328811yescharacteristic
343D61—42no—
344D61—161no—
345D61—161no—
346C22×D8—1221no—
347#555C2×D6111yescharacteristic, complemented
348#547C2×D6111yescharacteristic, complemented
349D42—611no—
350D42—611no—
351#493—611no—
352#492—611no—
353#487C2×D6111yescharacteristic, complemented
354#486—611no—
355#486—611no—
356#486—611no—
357#485—21no—
358#482—1221no—
359#480—1221no—
360#476—611no—
361#476C2×D6111yescharacteristic, complemented
362#474—611no—
363#469—1221no—
364#466—1221no—
365#466—1221no—
366#465—21no—
367#461C2×D6111yescharacteristic, complemented
368#459—611no—
369#459—611no—
370#459—611no—
371#459—611no—
372#449—21no—
373#447—1221no—
374#447—1221no—
375#447—1221no—
376#447—1221no—
377C4×D8—611no—
378C4×D8C2×D6111yescharacteristic
379#436—611no—
380C8×D4—611no—
381C8×D4—611no—
382C8×D4C2×D6111yescharacteristic, complemented
383#418—1221no—
384#416—21no—
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—21no—
399C22×D4—1221no—
400C22×D4—1221no—
401C22×D4—1221no—
402C22×D4—1221no—
403C2×SD16—21no—
404C2×SD16—2441no—
405C2×D8—611no—
406C2×D8—1221no—
407C2×D8—1221no—
408C2×D8—1221no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×D8—1221no—
412C2×D8—2444no—
413C2×D8C22⋊D6111yescharacteristic
414C2×M16—1221no—
415C22×C8—21no—
416C22×C8—1221no—
417C22×C8—1221no—
418C4⋊Q8C22×D6111yescharacteristic
419C4⋊Q8C22×D6111yescharacteristic
420#127—611no—
421#127—611no—
422#124—41no—
423#123—41no—
424C22⋊Q8—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—1221no—
429#121—1221no—
430#121—1221no—
431#121—1221no—
432#120—2441no—
433#120—2441no—
434C4×D4—611no—
435C4×D4C22×D6111yescharacteristic
436C4×D4C22×D6111yescharacteristic
437C4×D4C22×D6111yescharacteristic
438#117—21no—
439#117—21no—
440C2×C4⋊C4—21no—
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—21no—
451#103—21no—
452#103—21no—
453#102—21no—
454#102—611no—
455#102—611no—
456#102—1221no—
457#102—1221no—
458#102—1221no—
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—2441no—
477C24—2441no—
478#41—42no—
479#41—81no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—611no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—1221no—
488C2×D4—1221no—
489C2×D4—1221no—
490C2×D4—1221no—
491C2×D4—4881no—
492C2×D4—4881no—
493C2×D4—4881no—
494C2×D4—4881no—
495C2×D4—2441no—
496C2×D4—2441no—
497C2×D4—2442no—
498C2×D4—2442no—
499C2×D4—2441no—
500C2×D4—2441no—
501C2×D4—2442no—
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—41no—
510C22×C4—1221no—
511SD16—81no—
512SD16—4882no—
513D8—22no—
514D8—1222no—
515D8—4881no—
516D8—4881no—
517D8—4881no—
518D8—2442no—
519D8—2442no—
520D8—2442no—
521M16—4881no—
522C2×C8—21no—
523C2×C8—81no—
524C2×C8—611no—
525C2×C8—611no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—4881no—
531C2×C8—2442no—
532C2×C8C2×C22⋊D6111yescharacteristic
533C2×C8C2×C22⋊D6111yescharacteristic
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
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—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—1221no—
558C23—9761no—
559C23—9761no—
560C23—4882no—
561C23—4882no—
562C23—4882no—
563C23—4882no—
564C23—2441no—
565C23—2441no—
566Q8—41no—
567Q8—41no—
568Q8—81no—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—21no—
573D4—21no—
574D4—82no—
575D4—161no—
576D4—612no—
577D4—1221no—
578D4—4881no—
579D4—4881no—
580D4—4882no—
581D4—4882no—
582D4—4882no—
583D4—4882no—
584D4—2441no—
585D4—2441no—
586D4—2441no—
587D4—2441no—
588D4—2441no—
589D4—2441no—
590D4—2441no—
591D4—2441no—
592D4#1451980212yes—
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—41no—
604C2×C4—82no—
605C2×C4—1221no—
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—1222no—
630C22—9764no—
631C22—9764no—
632C22—4881no—
633C22—4881no—
634C22—4881no—
635C22—4881no—
636C22—4881no—
637C22—4881no—
638C22—2441no—
639C22—2441no—
640C22D4×C22⋊D6111yescharacteristic
641C4—21no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—81no—
647C4—2441no—
648C4#135×D6111yescharacteristic
649C4C2×#1451980211yescharacteristic
650C4#1684056411yescharacteristic
651C4#1684056511yescharacteristic
652C2—42no—
653C2—81no—
654C2—81no—
655C2—9761no—
656C2—9761no—
657C2—2442no—
658C2#2145730011yescharacteristic
659C2#2145749811yescharacteristic
660C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3303C2
socleC22×C61D42
hypercenter#3303D61
hypocenterC61#19771
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #21458055C2semidirect
2. #21457626C2semidirect
3. D8×D244C2semidirect
4. #21445461C2semidirect
5. #21445382C2semidirect
6. #21445267C2semidirect
7. #21445230C2semidirect
8. #21445174C2semidirect
9. #21444996C2semidirect
10. #21444934C2semidirect
11. #21444908C2semidirect
12. #21444902C2semidirect
13. #21444649C2semidirect
14. #21444641C2semidirect
15. C61×#3303C2semidirect
20. #16840136C22semidirect
21. #16840110C22semidirect
22. #16840110C22semidirect
23. #16840110C22semidirect
33. #16839957C22semidirect
34. #16839957C22semidirect
40. #16839840C22semidirect
42. D4×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839508C22semidirect
49. #16839505C22semidirect
50. #16839505C22semidirect
51. D4⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839484C22semidirect
56. C61×#555C22semidirect
57. C61×#547C22semidirect
58. C61×#487C22semidirect
60. C61×#476C22semidirect
62. C61×#461C22semidirect
65. C8×D4×C61C22semidirect
323. #3303D61semidirect
347. #555C2×D61semidirect
348. #547C2×D61semidirect
353. #487C2×D61semidirect
361. #476C2×D61semidirect
367. #461C2×D61semidirect
382. C8×D4C2×D61semidirect
397. C61#19771semidirect

Maximal subgroups

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

subgroupindex
#214580552
#214576262
D8×D2442
#214454612
#214453822
#214452672
#214452302
#214451742
#214449962
#214449342
#214449082
#214449022
#214446492
#214446412
C61×#33032
#1977161