Finite Group Databasebeta

← #29650649

Subgroups — #29650649

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456415C211yesmaximal, characteristic
2#21454968C211yesmaximal, characteristic, complemented
3#21454897C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444724C211yesmaximal, characteristic, complemented
6#21444706C211yesmaximal, characteristic, complemented
7#21444701C211yesmaximal, characteristic, complemented
8#21444640C211yesmaximal, characteristic, complemented
9#21444634C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444611C211yesmaximal, characteristic, complemented
12#21444587C211yesmaximal, characteristic, complemented
13#21444271C211yesmaximal, characteristic, complemented
14C8×#11758194C211yesmaximal, characteristic, complemented
15C61×#1494C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840172C411yescharacteristic
18#16840152C411yescharacteristic
19#16840128C411yescharacteristic
20#16840121C411yescharacteristic
21#16840013C411yescharacteristic
22#16840013C411yescharacteristic
23#16840010C411yescharacteristic
24#16840010C411yescharacteristic
25#16839893C2211yescharacteristic
26Q8×#92418C2211yescharacteristic
27C4×#11758201C2211yescharacteristic
28C4×#11758201C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839840—21no—
32#16839840C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839839C2211yescharacteristic
35#16839835—21no—
36#16839835—21no—
37#16839834—21no—
38D4×#92418C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839827C2211yescharacteristic
41#16839823—21no—
42#16839815C2211yescharacteristic
43#16839789—21no—
44#16839786C2211yescharacteristic
45#16839727—21no—
46#16839727—21no—
47C4×#11758194C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#529C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758194C2×C411yescharacteristic
75C2×#11758194C2×C411yescharacteristic
76C2×#11758189—21no—
77C2×#11758189—21no—
78C22×#92418—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81#14519777C2×C411yescharacteristic
82#14519774C2×C411yescharacteristic
83#14519765—21no—
84#14519751—21no—
85#14519751C2×C411yescharacteristic
86#14519751C2×C411yescharacteristic
87C4×D244—21no—
88C4×D244C2311yescharacteristic
89C4×D244C2311yescharacteristic
90#14519710C2×C411yescharacteristic
91#14519710C2×C411yescharacteristic
92#14519708C2×C411yescharacteristic
93#14519708C2×C411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96C4⋊#92418—21no—
97C4⋊#92418D411yescharacteristic
98C4⋊#92418D411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418D411yescharacteristic
112C22⋊#92418D411yescharacteristic
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519688—21no—
118#14519688C2×C411yescharacteristic
119#14519688C2×C411yescharacteristic
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C22×C8×C61—21no—
126#126×C61—21no—
127#125×C61C2×C411yescharacteristic
128#124×C61C2×C411yescharacteristic
129#123×C61—21no—
130C22⋊Q8×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153#11758222—81no—
154#11758222—81no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244C22×C411yescharacteristic
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×Dic122—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—42no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C42×C61—21no—
179C42×C61C22×C411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183#11758201—22no—
184#11758201—22no—
185#11758199—22no—
186#11758199—22no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758194—22no—
195#11758194—22no—
196#11758194—81no—
197#11758194—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—81no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758189—81no—
210#11758189—81no—
211C8×D61—81no—
212C8×D61—81no—
213C23×C61—21no—
214C23×C61C4×D411yescharacteristic
215C22×D61—21no—
216C22×D61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—81no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C23×C411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C22⋊D61—81no—
239C22⋊D61—81no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242D244—21no—
243D244—21no—
244D244—21no—
245D244—21no—
246D244—81no—
247D244—81no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252Dic122—81no—
253C8×C61—22no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257#92418—21no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418#13112yes—
266#92418#13112yes—
267#17968—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61C2×C4×D411yescharacteristic
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61C2×#13111yescharacteristic
289C4×C61C2×#13111yescharacteristic
290C4×C61#57611yescharacteristic
291C4×C61#57711yescharacteristic
292Dic61—41no—
293Dic61—41no—
294#3171—611no—
295#2993—611no—
296#2981—611no—
297#1594—611no—
298#1592—611no—
299#1590—611no—
300#1589—611no—
301#1580—611no—
302SD16⋊C8—611no—
303C8×SD16—611no—
304C8×D8—611no—
305#1569—611no—
306#1494D6111yescharacteristic, complemented
307#1492—611no—
308C8×M16—611no—
309C2×C61—41no—
310C2×C61—81no—
311C2×C61#293111yescharacteristic
312C2×C61#294611yescharacteristic
313C2×C61#295611yescharacteristic
314D61—81no—
315D61—81no—
316#532—611no—
317#529C2×D6111yescharacteristic
318#501—611no—
319#496—611no—
320#490—611no—
321#489—611no—
322#469—611no—
323#469—611no—
324#468—611no—
325#468—611no—
326#446—611no—
327C8×Q8—611no—
328C4×SD16—611no—
329C4×SD16—611no—
330C4×D8—611no—
331C4×D8—611no—
332#436—611no—
333#436—611no—
334#436—611no—
335#436—1221no—
336#435—1221no—
337#435—1221no—
338#435—1221no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342#433—1221no—
343#432C2×D6111yescharacteristic
344#431—611no—
345#424—1221no—
346#423—611no—
347#408—1221no—
348#408—1221no—
349C4×M16—611no—
350C2×C4×C8C2×D6111yescharacteristic
351#335—611no—
352#335—611no—
353#334—611no—
354#334—611no—
355Q8⋊C8C2×D6111yescharacteristic
356Q8⋊C8C2×D6111yescharacteristic
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8C2×D6111yescharacteristic
362D4⋊C8C2×D6111yescharacteristic
363#322—611no—
364#322—611no—
365C82—611no—
366C82—611no—
367C61#1796811yescharacteristic, complemented, Sylow
368C2×#41—1221no—
369C2×SD16—611no—
370C2×SD16—611no—
371C2×D8—611no—
372C2×D8—611no—
373C2×M16—611no—
374C2×M16—611no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C22×C8—21no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C4⋊Q8—611no—
384#127—611no—
385#126—21no—
386#125C4×D6111yescharacteristic
387#124—1221no—
388#124C4×D6111yescharacteristic
389#123—21no—
390C22⋊Q8C4×D6111yescharacteristic
391#121—611no—
392#121—611no—
393#121—1221no—
394#121C4×D6111yescharacteristic
395C4×Q8C22×D6111yescharacteristic
396C4×D4—21no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4C22×D6111yescharacteristic
401#117—21no—
402C2×C42C22×D6111yescharacteristic
403#107—611no—
404#107—611no—
405#106—611no—
406#106—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416#103—611no—
417#103—611no—
418#102—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424C22⋊C8—21no—
425C22⋊C8—611no—
426C22⋊C8—611no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—21no—
434#97—611no—
435#97—611no—
436#97—1221no—
437C4×C8—21no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8C22×D6111yescharacteristic
444C4×C8C22×D6111yescharacteristic
445#41—4881no—
446#41—4881no—
447C2×Q8—1221no—
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—21no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4C2×C4×D6111yescharacteristic
457C22×C4—21no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4#1175822411yescharacteristic
463SD16—1222no—
464SD16—1222no—
465D8—1222no—
466D8—1222no—
467M16—1222no—
468M16—1222no—
469M16—4881no—
470M16—4881no—
471M16—4881no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—4881no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4C2×C4×D6111yescharacteristic
499C4⋊C4C2×C4×D6111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—21no—
510C42C2×C4×D6111yescharacteristic
511C42D4×D6111yescharacteristic
512C42#1175822411yescharacteristic
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—1221no—
516C23—1221no—
517C23#1451973711yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—4881no—
521D4—21no—
522D4—21no—
523D4—81no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—1221no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4—4881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4#1451973711yescharacteristic
549C2×C4#1451973711yescharacteristic
550C2×C4#1451973711yescharacteristic
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C2×D4×D6111yescharacteristic
553C2×C4C2×#1175822411yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—612no—
559C8—612no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—2441no—
567C8—2441no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22C2×#1451973711yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—2441no—
589C4—2441no—
590C4#131×D6111yescharacteristic
591C4#131×D6111yescharacteristic
592C4#1684056411yescharacteristic
593C4#1684056911yescharacteristic
594C2—41no—
595C2—81no—
596C2—4881no—
597C2—4881no—
598C2#2145452711yescharacteristic
599C2#2145465411yescharacteristic
600C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C2×C4×D4
prime radical#21456415C2
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#17968
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #21454968C2semidirect
3. #21454897C2semidirect
4. #21444730C2semidirect
5. #21444724C2semidirect
6. #21444706C2semidirect
7. #21444701C2semidirect
8. #21444640C2semidirect
9. #21444634C2semidirect
10. #21444616C2semidirect
11. #21444611C2semidirect
12. #21444587C2semidirect
13. #21444271C2semidirect
14. C8×#11758194C2semidirect
15. C61×#1494C2semidirect
306. #1494D61semidirect
367. C61#17968semidirect

Maximal subgroups

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

subgroupindex
#214564152
#214549682
#214548972
#214447302
#214447242
#214447062
#214447012
#214446402
#214446342
#214446162
#214446112
#214445872
#214442712
C8×#117581942
C61×#14942
#1796861