Finite Group Databasebeta

← #29663021

Subgroups — #29663021

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456538C211yesmaximal, characteristic, complemented
2#21455274C211yesmaximal, characteristic
3#21454839C211yesmaximal, characteristic, complemented
4#21445382C211yesmaximal, characteristic, complemented
5#21445364C211yesmaximal, characteristic, complemented
6#21445330C211yesmaximal, characteristic, complemented
7#21445286C211yesmaximal, characteristic, complemented
8#21445265C211yesmaximal, characteristic, complemented
9#21445247C211yesmaximal, characteristic, complemented
10#21445211C211yesmaximal, characteristic, complemented
11#21445169C211yesmaximal, characteristic, complemented
12#21444572C211yesmaximal, characteristic, complemented
13#21444522C211yesmaximal, characteristic, complemented
14#21444519C211yesmaximal, characteristic, complemented
15C61×#3107C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840312C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840136C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840010—21no—
23#16840010—21no—
24#16839984—21no—
25#16839977—21no—
26#16839972C2211yescharacteristic
27#16839967C2211yescharacteristic
28#16839962C2211yescharacteristic
29#16839957C2211yescharacteristic
30Q8×#92418C2211yescharacteristic
31Q8×#92418C2211yescharacteristic
32#16839860—21no—
33#16839860—21no—
34#16839840—21no—
35#16839840—21no—
36#16839840C2211yescharacteristic
37#16839840C2211yescharacteristic
38#16839819—21no—
39#16839819C2211yescharacteristic
40C2×C4⋊#92418C2211yescharacteristic
41#16839756—21no—
42C4×#11758194—21no—
43C4×#11758194C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C4×#41×C61C2211yescharacteristic
58C61×#485—21no—
59C61×#475C2211yescharacteristic
60C61×#474C2211yescharacteristic
61C61×#462C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#452—21no—
64C4×Q16×C61—21no—
65C4×SD16×C61—21no—
66C61×#431C2211yescharacteristic
67C2×#11758222—21no—
68#14519797—44no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194D411yescharacteristic
78C2×#11758194D411yescharacteristic
79C22×#92418—21no—
80#14519777C2311yescharacteristic
81#14519774C2311yescharacteristic
82#14519765—21no—
83#14519751—21no—
84#14519751—21no—
85C4×D244—21no—
86C4×D244—21no—
87#14519710—21no—
88#14519710—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519701—21no—
97#14519701—21no—
98#14519700—21no—
99#14519700—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519688—21no—
108#14519688D411yescharacteristic
109#14519688D411yescharacteristic
110C4×#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C2×#41×C61D411yescharacteristic
115C2×Q16×C61—21no—
116C2×SD16×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#125×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61D411yescharacteristic
125C4×Q8×C61C2311yescharacteristic
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61D411yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132#117×C61D411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142#102×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61—21no—
145#41×C61—22no—
146#41×C61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C2×C22⋊D61—41no—
159#11758222—42no—
160#11758222—42no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×C4×D61—41no—
165C2×Dic122—21no—
166Q16×C61—42no—
167SD16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—41no—
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61#4111yescharacteristic
191C42×C61C2411yescharacteristic
192#11758202—42no—
193#11758201—42no—
194#11758201—42no—
195#11758201—42no—
196#11758200—42no—
197#11758199—42no—
198#11758198—41no—
199#11758198—41no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202#11758194—22no—
203#11758194—41no—
204#11758194—42no—
205#11758194—42no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—42no—
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215C23×C61—21no—
216C23×C61#12111yescharacteristic
217C22×D61—41no—
218Q8×C61—21no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61AGL(1,ℤ/8)12yes—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—42no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—42no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—81no—
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—82no—
248C2×Dic61—41no—
249D244—41no—
250D244—41no—
251D244—41no—
252D244—41no—
253D244—81no—
254C4×D61—82no—
255Dic122—41no—
256Dic122—41no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418#13512yescomplemented
267#19182—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61C2×#12111yescharacteristic
275C2×D61—81no—
276C2×D61—81no—
277C2×D61—81no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—22no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61C2×#13511yescharacteristic
288C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C61#57511yescharacteristic
290C4×C61#57511yescharacteristic
291Dic61—81no—
292#3182—611no—
293#3107D6111yescharacteristic, complemented
294#3035—611no—
295#2971—611no—
296#1701—611no—
297#1699—611no—
298#1693—611no—
299#1685—611no—
300#1682—611no—
301#1680—611no—
302#1674—611no—
303#1666—611no—
304#1565—611no—
305#1553—611no—
306#1552—611no—
307C2×C61—41no—
308C2×C61—81no—
309C2×C61#303511yescharacteristic
310C2×C61#305511yescharacteristic
311C2×C61#306911yescharacteristic
312D61—161no—
313C2×#135—1221no—
314#533C2×D6111yescharacteristic
315#532—611no—
316C4×#41C2×D6111yescharacteristic
317#500—611no—
318#492—611no—
319#487—611no—
320#486—611no—
321#485—21no—
322#475C2×D6111yescharacteristic
323#474C2×D6111yescharacteristic
324#468—1221no—
325#468—1221no—
326#464—1221no—
327#463—1221no—
328#462—611no—
329#462C2×D6111yescharacteristic
330#461—611no—
331#461C2×D6111yescharacteristic
332#460—611no—
333#459—611no—
334#452—21no—
335C8×Q8—611no—
336C8×Q8—611no—
337#440—1221no—
338#440—1221no—
339C4×Q16—21no—
340C4×SD16—21no—
341#436—611no—
342#436—611no—
343#436—1221no—
344#436—1221no—
345#432—611no—
346#432—1221no—
347#431C2×D6111yescharacteristic
348C2×C4⋊C8—611no—
349#416—1221no—
350C4×M16—611no—
351C4×M16—1221no—
352#335—611no—
353#335—611no—
354#334—611no—
355#334—611no—
356#332—611no—
357#332—611no—
358#332—611no—
359#332—611no—
360#332—611no—
361#332—611no—
362#331—611no—
363#331—611no—
364C61#1918211yescharacteristic, complemented, Sylow
365C2×#41—1221no—
366C2×#41C22⋊D6111yescharacteristic
367#135—2444no—
368C2×Q16—21no—
369C2×Q16—1221no—
370C2×SD16—21no—
371C2×SD16—1221no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×SD16—1221no—
375C2×D8—1221no—
376C2×M16—611no—
377C2×M16—611no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—1221no—
381C4⋊Q8—611no—
382C4⋊Q8C22×D6111yescharacteristic
383C4⋊Q8C22×D6111yescharacteristic
384#127—611no—
385#125—21no—
386#124—1221no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—1221no—
390#121—1221no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8C22⋊D6111yescharacteristic
394C4×Q8C22×D6111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4C22⋊D6111yescharacteristic
400C4×D4C22×D6111yescharacteristic
401#117—21no—
402#117—21no—
403#117C22⋊D6111yescharacteristic
404C2×C42—21no—
405C2×C42C22×D6111yescharacteristic
406#107—21no—
407#107—1221no—
408#107—1221no—
409#106—21no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#102—21no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431C22⋊C8—21no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—611no—
436#97—611no—
437#97—1221no—
438C4×C8—21no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—1221no—
442C4×C8—1221no—
443#41—22no—
444#41—41no—
445#41—2442no—
446#41—2442no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—1221no—
450C2×Q8C2×C22⋊D6111yescharacteristic
451C2×D4—21no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—2441no—
456C2×D4C2×C22⋊D6111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—2441no—
461C22×C4D4×D6111yescharacteristic
462C22×C4#1175822411yescharacteristic
463C22×C4C2×C22⋊D6111yescharacteristic
464Q16—42no—
465Q16—2442no—
466SD16—42no—
467SD16—2442no—
468SD16—2442no—
469SD16—2442no—
470SD16—2442no—
471D8—2442no—
472M16—1222no—
473M16—2442no—
474M16—2441no—
475M16—2442no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—2442no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4C2×C22⋊D6111yescharacteristic
498C4⋊C4C2×C22⋊D6111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—2441no—
504C22⋊C4—2441no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42D4×D6111yescharacteristic
510C42#1175822411yescharacteristic
511C42C2×C22⋊D6111yescharacteristic
512C42C23×D6111yescharacteristic
513C23—21no—
514C23—2441no—
515C23#1451974911yescharacteristic
516Q8—21no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—2441no—
522Q8—2441no—
523Q8#1451980212yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—4881no—
528D4—4882no—
529D4—2441no—
530D4—2441no—
531D4—2441no—
532D4—2441no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—4882no—
548C2×C4—2441no—
549C2×C4#1451974911yescharacteristic
550C2×C4#1451974911yescharacteristic
551C2×C4#1451974911yescharacteristic
552C2×C4C2×D4×D6111yescharacteristic
553C2×C4C22×C22⋊D6111yescharacteristic
554C2×C4C2×#1175822411yescharacteristic
555C8—41no—
556C8—41no—
557C8—612no—
558C8—1221no—
559C8—1221no—
560C8—1221no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—4881no—
572C22—4881no—
573C22—4881no—
574C22C2×#1451974911yescharacteristic
575C4—21no—
576C4—22no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—4881no—
585C4#135×D6111yescharacteristic
586C4C2×#1451980211yescharacteristic
587C4#1684055911yescharacteristic
588C4#1684056011yescharacteristic
589C2—41no—
590C2—81no—
591C2—9761no—
592C2#2145527011yescharacteristic
593C2#2145544011yescharacteristic
594C2#2145555311yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3107C2
socleC22×C61C2×#121
prime radical#21455274C2
hypercenter#3107D61
hypocenterC61#19182
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #21456538C2semidirect
3. #21454839C2semidirect
4. #21445382C2semidirect
5. #21445364C2semidirect
6. #21445330C2semidirect
7. #21445286C2semidirect
8. #21445265C2semidirect
9. #21445247C2semidirect
10. #21445211C2semidirect
11. #21445169C2semidirect
12. #21444572C2semidirect
13. #21444522C2semidirect
14. #21444519C2semidirect
15. C61×#3107C2semidirect
266. #92418#135semidirect
293. #3107D61semidirect
364. C61#19182semidirect

Maximal subgroups

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

subgroupindex
#214565382
#214552742
#214548392
#214453822
#214453642
#214453302
#214452862
#214452652
#214452472
#214452112
#214451692
#214445722
#214445222
#214445192
C61×#31072
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