Finite Group Databasebeta

← #29669616

Subgroups — #29669616

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458118C211yesmaximal, characteristic, complemented
2#21457634C211yesmaximal, characteristic, complemented
3#21457626C211yesmaximal, characteristic, complemented
4#21445482C211yesmaximal, characteristic, complemented
5#21445382C211yesmaximal, characteristic, complemented
6#21445256C211yesmaximal, characteristic, complemented
7#21445244C211yesmaximal, characteristic, complemented
8#21445181C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic, complemented
10#21445101C211yesmaximal, characteristic, complemented
11#21444996C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444649C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic, complemented
15C61×#3283C211yesmaximal, characteristic, complemented
16#16840417C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840158C2211yescharacteristic, complemented
19#16840114C2211yescharacteristic, complemented
20#16840110C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840097—21no—
24#16840077—21no—
25#16840075—21no—
26#16840042C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840039C2211yescharacteristic
29#16840006—21no—
30#16839997—21no—
31#16839996—21no—
32#16839967C2211yescharacteristic, complemented
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839905—21no—
36#16839895—21no—
37#16839894—21no—
38C4×#11758199C2211yescharacteristic
39#16839840C2211yescharacteristic, complemented
40C8×D244C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42#16839761—21no—
43C2×#14519697—21no—
44#102×D61—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C2×#135×C61—21no—
57C61×#547C2211yescharacteristic
58C61×#547C2211yescharacteristic, complemented
59C61×#494C2211yescharacteristic, complemented
60C61×#467—21no—
61C61×#461C2211yescharacteristic
62C61×#461C2211yescharacteristic, complemented
63C61×#452—21no—
64C61×#452—21no—
65C4×D8×C61C2211yescharacteristic
66C8×D4×C61C2211yescharacteristic, complemented
67C2×#11758222—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×#11758200—21no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758199D411yescharacteristic
74C2×#11758194—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519759—41no—
80#14519756—21no—
81#14519752—21no—
82#14519751—21no—
83#14519748—21no—
84#14519747—41no—
85C4×D244C2311yescharacteristic
86C4⋊C4×D61—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—41no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519700—21no—
96#14519700—21no—
97#14519700—21no—
98#14519699—21no—
99#14519699—21no—
100#14519698—21no—
101#14519698D411yescharacteristic
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117#135×C61—44no—
118C2×Q16×C61—21no—
119C2×Q16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×D8×C61D411yescharacteristic
123C22×C8×C61—21no—
124C4⋊Q8×C61C2311yescharacteristic
125C4⋊Q8×C61C2311yescharacteristic
126#123×C61—41no—
127#123×C61—41no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137#107×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146#41×C61—42no—
147#41×C61—42no—
148#41×C61—81no—
149#41×C61—81no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C2×D4×C61C2×D411yescharacteristic
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—41no—
164D4×D61—42no—
165D4×D61—81no—
166#11758222—42no—
167#11758222—81no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—42no—
172C2×D244—41no—
173C2×D244—81no—
174C2×D244C2×D411yescharacteristic
175C2×C4×D61—21no—
176C2×C4×D61—41no—
177C2×Dic122—21no—
178Q16×C61—42no—
179Q16×C61—81no—
180SD16×C61—42no—
181SD16×C61—42no—
182D8×C61—22no—
183C2×C8×C61—21no—
184C2×C8×C61—42no—
185C2×C8×C61C2×D411yescharacteristic
186C2×C8×C61C2×D411yescharacteristic
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C22⋊C4×C61—21no—
197C22⋊C4×C61—21no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C42×C61C2411yescharacteristic
202C22⋊Dic61—41no—
203#11758200—81no—
204#11758199—22no—
205#11758199—81no—
206#11758199—81no—
207#11758198—21no—
208#11758198—41no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61C2×D411yescharacteristic
212#11758196—41no—
213#11758194—81no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—81no—
219C2×#92418C2×D411yescharacteristic
220C2×#92418C2×D411yescharacteristic
221C8×D61—81no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C22×D61—21no—
226C22×D61—41no—
227C22×D61—82no—
228C22×D61—82no—
229C22×D61—161no—
230Q8×C61—41no—
231Q8×C61—41no—
232Q8×C61—41no—
233Q8×C61—41no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—82no—
240D4×C61—82no—
241D4×C61AGL(1,ℤ/8)12yes—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—82no—
254C2×C4×C61—82no—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C22⋊D61—82no—
259C22⋊D61—82no—
260C2×Dic61—21no—
261C2×Dic61—41no—
262D244—21no—
263D244—41no—
264D244—41no—
265D244—41no—
266D244—41no—
267D244—81no—
268D244—82no—
269D244#13512yescomplemented
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—82no—
273Dic122—41no—
274Dic122—41no—
275C8×C61—21no—
276C8×C61—21no—
277C8×C61—41no—
278#92418—21no—
279#92418—21no—
280#92418—41no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#19772—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61D4211yescharacteristic
295C2×D61—22no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—164no—
302C4×C61—21no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61C2×#13511yescharacteristic
309C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C61#57611yescharacteristic
311C4×C61#57611yescharacteristic
312Dic61—41no—
313Dic61—81no—
314#3330—611no—
315#3294—611no—
316#3294—611no—
317#3283D6111yescharacteristic, complemented
318#1720—611no—
319#1701—611no—
320#1681—611no—
321#1679—611no—
322#1669—611no—
323#1654—611no—
324#1654—611no—
325#1639—611no—
326#1625—611no—
327#1581—611no—
328#1580—611no—
329C2×C61—42no—
330C2×C61—81no—
331C2×C61—81no—
332C2×C61#326411yescharacteristic
333C2×C61#328011yescharacteristic
334C2×C61#328911yescharacteristic
335D61—42no—
336D61—161no—
337C2×#135—21no—
338#547—611no—
339#547C2×D6111yescharacteristic
340#547C2×D6111yescharacteristic, complemented
341D42—611no—
342#498—611no—
343#494C2×D6111yescharacteristic, complemented
344#487—611no—
345#486—611no—
346#486—611no—
347#486—611no—
348#484—1221no—
349#480—1221no—
350#480—1221no—
351#474—611no—
352#474—611no—
353#474—611no—
354#468—1221no—
355#467—21no—
356#466—1221no—
357#466—1221no—
358#461—611no—
359#461C2×D6111yescharacteristic
360#461C2×D6111yescharacteristic, complemented
361#459—611no—
362#459—611no—
363#452—21no—
364#452—21no—
365#449—1221no—
366#447—1221no—
367#447—1221no—
368C4×D8—611no—
369C4×D8C2×D6111yescharacteristic
370#436—611no—
371C8×D4—611no—
372C8×D4—611no—
373C8×D4C2×D6111yescharacteristic, complemented
374#417—1221no—
375C2×#102—1221no—
376C2×#102—1221no—
377#335—611no—
378#334—611no—
379#332—611no—
380#332—611no—
381#332—611no—
382#331—611no—
383D4⋊C8—611no—
384D4⋊C8—611no—
385D4⋊C8—611no—
386D4⋊C8—611no—
387#322—611no—
388C61#1977211yescharacteristic, complemented, Sylow
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—1221no—
392C22×D4—1221no—
393C22×D4—1221no—
394#135—44no—
395C2×Q16—21no—
396C2×Q16—21no—
397C2×SD16—21no—
398C2×SD16—21no—
399C2×SD16—1221no—
400C2×D8—611no—
401C2×D8—1221no—
402C2×D8—1221no—
403C2×D8C22⋊D6111yescharacteristic
404C2×M16—1221no—
405C22×C8—21no—
406C22×C8—1221no—
407C22×C8—1221no—
408C4⋊Q8—611no—
409C4⋊Q8C22×D6111yescharacteristic
410C4⋊Q8C22×D6111yescharacteristic
411#127—611no—
412#123—41no—
413#123—41no—
414#123—2441no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—1221no—
418#121—21no—
419#121—21no—
420#121—1221no—
421#121—1221no—
422#121—1221no—
423#120—2441no—
424C4×D4—611no—
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427C4×D4C22×D6111yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—1221no—
431#107—611no—
432#107—1221no—
433#107—1221no—
434#107—1221no—
435#107C22⋊D6111yescharacteristic
436#106—2441no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8C22×D6111yescharacteristic
441#103—21no—
442#103—21no—
443#103—1221no—
444#103—1221no—
445#103—1221no—
446#102—611no—
447#102—611no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102—2441no—
458#102C22⋊D6111yescharacteristic
459#102C22⋊D6111yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—1221no—
462C22⋊C8—1221no—
463C22⋊C8—1221no—
464C4×C8—611no—
465C4×C8—611no—
466C4×C8C22×D6111yescharacteristic
467C24—2441no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—4881no—
473#41—2442no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—1221no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—611no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—4881no—
484C2×D4—4881no—
485C2×D4—2441no—
486C2×D4—2442no—
487C2×D4—2441no—
488C2×D4—2441no—
489C2×D4—2442no—
490C2×D4D4×D6111yescharacteristic
491C2×D4C2×C22⋊D6111yescharacteristic
492C2×D4C2×C22⋊D6111yescharacteristic
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—1221no—
499C22×C4—2441no—
500Q16—42no—
501Q16—81no—
502SD16—42no—
503SD16—42no—
504SD16—4881no—
505D8—22no—
506D8—1222no—
507D8—4881no—
508D8—4881no—
509M16—4881no—
510C2×C8—21no—
511C2×C8—42no—
512C2×C8—611no—
513C2×C8—611no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—4881no—
519C2×C8—4881no—
520C2×C8C2×C22⋊D6111yescharacteristic
521C2×C8C2×C22⋊D6111yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—611no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—2441no—
532C4⋊C4D4×D6111yescharacteristic
533C4⋊C4C2×C22⋊D6111yescharacteristic
534C4⋊C4C2×C22⋊D6111yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—1221no—
541C22⋊C4—2441no—
542C22⋊C4—2441no—
543C42C23×D6111yescharacteristic
544C23—21no—
545C23—21no—
546C23—21no—
547C23—1221no—
548C23—9761no—
549C23—4882no—
550C23—4882no—
551C23—2441no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—2441no—
557Q8—2441no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—21no—
563D4—82no—
564D4—82no—
565D4—612no—
566D4—1221no—
567D4—4881no—
568D4—4882no—
569D4—4882no—
570D4—4882no—
571D4—2441no—
572D4—2441no—
573D4—2441no—
574D4—2441no—
575D4#1451980312yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—1221no—
590C2×C4—4882no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4C2×D4×D6111yescharacteristic
595C2×C4C22×C22⋊D6111yescharacteristic
596C2×C4#1451982211yescharacteristic
597C8—21no—
598C8—21no—
599C8—41no—
600C8—1221no—
601C8—1221no—
602C8—2441no—
603C8—2441no—
604C8—2441no—
605C8—2441no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—1222no—
616C22—9764no—
617C22—4881no—
618C22—4881no—
619C22—4881no—
620C22—2441no—
621C22—2441no—
622C22D4×C22⋊D6111yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—4881no—
630C4—2441no—
631C4#135×D6111yescharacteristic
632C4C2×#1451980311yescharacteristic
633C4#1684056411yescharacteristic
634C4#1684056511yescharacteristic
635C2—42no—
636C2—81no—
637C2—81no—
638C2—9761no—
639C2—2442no—
640C2#2145729511yescharacteristic
641C2#2145749811yescharacteristic
642C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3283C2
socleC22×C61D42
hypercenter#3283D61
hypocenterC61#19772
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #21458118C2semidirect
2. #21457634C2semidirect
3. #21457626C2semidirect
4. #21445482C2semidirect
5. #21445382C2semidirect
6. #21445256C2semidirect
7. #21445244C2semidirect
8. #21445181C2semidirect
9. #21445103C2semidirect
10. #21445101C2semidirect
11. #21444996C2semidirect
12. #21444908C2semidirect
13. #21444649C2semidirect
14. #21444641C2semidirect
15. C61×#3283C2semidirect
18. #16840158C22semidirect
19. #16840114C22semidirect
32. #16839967C22semidirect
39. #16839840C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839508C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839484C22semidirect
58. C61×#547C22semidirect
59. C61×#494C22semidirect
62. C61×#461C22semidirect
66. C8×D4×C61C22semidirect
269. D244#135semidirect
317. #3283D61semidirect
340. #547C2×D61semidirect
343. #494C2×D61semidirect
360. #461C2×D61semidirect
373. C8×D4C2×D61semidirect
388. C61#19772semidirect

Maximal subgroups

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

subgroupindex
#214581182
#214576342
#214576262
#214454822
#214453822
#214452562
#214452442
#214451812
#214451032
#214451012
#214449962
#214449082
#214446492
#214446412
C61×#32832
#1977261