Finite Group Databasebeta

← #29649715

Subgroups — #29649715

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454934C211yesmaximal, characteristic, complemented
2#21454926C211yesmaximal, characteristic, complemented
3C4×#14519796C211yesmaximal, characteristic
4#21444700C211yesmaximal, characteristic, complemented
5#21444695C211yesmaximal, characteristic, complemented
6#21444676C211yesmaximal, characteristic, complemented
7#21444673C211yesmaximal, characteristic, complemented
8#21444671C211yesmaximal, characteristic, complemented
9#21444668C211yesmaximal, characteristic, complemented
10#21444649C211yesmaximal, characteristic, complemented
11#335×D61C211yesmaximal, characteristic, complemented
12#21444203C211yesmaximal, characteristic, complemented
13#21444203C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1581C211yesmaximal, characteristic, complemented
16C2×#14519796C411yescharacteristic
17C4×#11758224C2211yescharacteristic
18C4×#11758224C2211yescharacteristic
19#16839892C2211yescharacteristic
20#16839889C2211yescharacteristic
21C8×Dic122C2211yescharacteristic
22#16839886C2211yescharacteristic
23C4×Dic244C2211yescharacteristic
24#16839856C411yescharacteristic
25#16839853C411yescharacteristic
26#16839853C411yescharacteristic
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29D8×Dic61C411yescharacteristic
30#16839840C2211yescharacteristic
31#16839836—21no—
32#16839831—21no—
33D4×#92418C2211yescharacteristic
34C8×C22⋊D61—21no—
35#16839825—21no—
36#16839816—21no—
37#16839813C2211yescharacteristic
38#16839813C2211yescharacteristic
39#16839812—21no—
40#16839799C411yescharacteristic
41#16839785—21no—
42C2×#14519706—21no—
43C4⋊C8×D61C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45#16839755C411yescharacteristic
46#16839755C411yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839492C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758224C2×C411yescharacteristic
68C2×#11758224C2×C411yescharacteristic
69#14519796—24no—
70C2×Dic244C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758200C2×C411yescharacteristic
73C2×#11758194—21no—
74C22×#92418—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61C2×C411yescharacteristic
78C2×C8×D61C2×C411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×Dic122C2311yescharacteristic
81#14519742C2×C411yescharacteristic
82#14519742C2×C411yescharacteristic
83D4×Dic61C2×C411yescharacteristic
84D4×Dic61C2×C411yescharacteristic
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87#14519737—21no—
88#14519737—21no—
89#14519735C2×C411yescharacteristic
90#14519735C2×C411yescharacteristic
91#14519733—21no—
92#14519733—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C42×D61C2311yescharacteristic
96#14519711C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706D411yescharacteristic
109#14519706D411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519702C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519700C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519698C2×C411yescharacteristic
116C22⋊#92418—21no—
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689D411yescharacteristic
120#14519689D411yescharacteristic
121#14519687—21no—
122#14519687—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C2×D8×C61C2×C411yescharacteristic
131C2×M16×C61—21no—
132C22×C8×C61—21no—
133C4×D4×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#107×C61C2×C411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#102×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155#11758224—22no—
156#11758224—22no—
157#11758224—22no—
158#11758224M1614yescomplemented
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122C22×C411yescharacteristic
163C2×Dic122C22×C411yescharacteristic
164D8×C61—22no—
165M16×C61—81no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—81no—
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180C22⋊Dic61—21no—
181#11758200—22no—
182#11758200—22no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61C22×C411yescharacteristic
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61#4111yescharacteristic
200#11758194—81no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—81no—
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209Dic244—22no—
210C8×D61—22no—
211C8×D61—22no—
212C8×D61—81no—
213C8×D61—81no—
214C23×C61—21no—
215C23×C61—21no—
216C22×D61C4×D411yescharacteristic
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61C2×M1612yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—24no—
231C22⋊D61—42no—
232C2×Dic61—21no—
233C2×Dic61—24no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—42no—
238C2×Dic61—81no—
239C2×Dic61—81no—
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C4×D411yescharacteristic
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—41no—
246C4×D61C2×M1612yes—
247C4×D61#13112yes—
248Dic122—21no—
249Dic122—21no—
250Dic122—21no—
251Dic122C2×M1612yes—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#17881—611nomaximal, Sylow
267C22×C61—22no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61C2×C4×D411yescharacteristic
274C2×D61—21no—
275C2×D61—21no—
276C2×D61#43512yes—
277C4×C61—21no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61C22×M1611yescharacteristic
281C4×C61C2×#13111yescharacteristic
282C4×C61#57611yescharacteristic
283C4×C61#57811yescharacteristic
284Dic61—22no—
285Dic61—21no—
286Dic61—21no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61#43512yes—
291#2989—611no—
292#2988—611no—
293C4×#135—611no—
294#1588—611no—
295#1588—611no—
296#1585—611no—
297#1585—611no—
298#1584—611no—
299#1584—611no—
300#1581—611no—
301#1581D6111yescharacteristic, complemented
302C2×#335—611no—
303#1477—611no—
304#1477—611no—
305#1452—611no—
306C2×C61—42no—
307C2×C61—81no—
308C2×C61C2×#43511yescharacteristic
309C2×C61#295111yescharacteristic
310C2×C61#295711yescharacteristic
311D61—22no—
312C2×#135—611no—
313C4×#41—611no—
314C4×#41—611no—
315#446—611no—
316#446—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×SD16—611no—
324C4×SD16—611no—
325C4×D8—611no—
326C4×D8C2×D6111yescharacteristic
327#436—611no—
328#436C2×D6111yescharacteristic
329#435—1221no—
330#435—1221no—
331C8×D4—611no—
332C8×D4—1221no—
333C8×D4—1221no—
334C8×D4C2×D6111yescharacteristic
335#432—1221no—
336#431—611no—
337#431—611no—
338#431—1221no—
339#427—611no—
340#423—1221no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—611no—
343C2×C4⋊C8—1221no—
344#416—611no—
345#416—611no—
346C2×C4×C8—611no—
347#335—611no—
348#335—611no—
349#335—611no—
350#335C2×D6111yescharacteristic
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8—611no—
355D4⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8C2×D6111yescharacteristic
358D4⋊C8C2×D6111yescharacteristic
359#322—611no—
360#322—611no—
361#322—611no—
362#322C2×D6111yescharacteristic
363C61#1788111yescharacteristic, complemented, Sylow
364C2×#41—611no—
365C2×#41—611no—
366#135—1224no—
367C2×Q16—611no—
368C2×SD16—611no—
369C2×SD16—611no—
370C2×D8C4×D6111yescharacteristic
371C2×M16—21no—
372C2×M16—1221no—
373C22×C8—21no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—1221no—
377C22×C8—1221no—
378C22×C8—1221no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8—611no—
382C4×Q8—611no—
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—1221no—
386C4×D4—1221no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4C22×D6111yescharacteristic
390C4×D4C22×D6111yescharacteristic
391#117—611no—
392#117—611no—
393#117—1221no—
394#117—1221no—
395C2×C42—611no—
396C2×C42—1221no—
397C2×C42—1221no—
398#107—611no—
399#107C4×D6111yescharacteristic
400#106—611no—
401#106—611no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8C22×D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415#103—611no—
416#103—611no—
417#103—611no—
418#103—611no—
419#102—611no—
420#102—611no—
421#102C4×D6111yescharacteristic
422#102C4×D6111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—611no—
426C22⋊C8—611no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430#97—1221no—
431#97—1221no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—1221no—
438C4×C8—1221no—
439C4×C8C22×D6111yescharacteristic
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442#41—614no—
443#41—1222no—
444#41—1222no—
445#41—1222no—
446C2×Q8—611no—
447C2×Q8—611no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4C2×C4×D6111yescharacteristic
451C2×D4C2×C4×D6111yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461Q16—1222no—
462SD16—1222no—
463SD16—1222no—
464D8—22no—
465M16—81no—
466M16—4881no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—4881no—
481C2×C8—4881no—
482C2×C8—4881no—
483C2×C8C2×C4×D6111yescharacteristic
484C2×C8C2×C4×D6111yescharacteristic
485C2×C8D4×D6111yescharacteristic
486C2×C8D4×D6111yescharacteristic
487C4⋊C4—611no—
488C4⋊C4—611no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4C2×C4×D6111yescharacteristic
494C4⋊C4C2×C4×D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—1221no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42C23×D6111yescharacteristic
511C23—21no—
512C23—21no—
513C23—611no—
514Q8—612no—
515Q8—1221no—
516Q8—1221no—
517Q8—1221no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—1224no—
522D4—2442no—
523D4M16×D6112yes—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—611no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—611no—
534C2×C4—611no—
535C2×C4—1224no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—4881no—
543C2×C4—4881no—
544C2×C4—2441no—
545C2×C4—2442no—
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4#41×D6111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—1221no—
557C8—1221no—
558C8—1221no—
559C8—1221no—
560C8—2441no—
561C8—2441no—
562C8—2441no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—612no—
570C22—1221no—
571C22—1221no—
572C22C4×D4×D6111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—612no—
577C4—1221no—
578C4—1221no—
579C4—1222no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4C2×M16×D6111yescharacteristic
584C4#131×D6111yescharacteristic
585C4#1684056311yescharacteristic
586C4#1684057611yescharacteristic
587C2—42no—
588C2—81no—
589C2—1222no—
590C2#435×D6111yescharacteristic
591C2#2145468911yescharacteristic
592C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1581C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519796C4
cosocleC42×C61C24
hypercenter#1581D61
hypocenterC61#17881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #21454934C2semidirect
2. #21454926C2semidirect
4. #21444700C2semidirect
5. #21444695C2semidirect
6. #21444676C2semidirect
7. #21444673C2semidirect
8. #21444671C2semidirect
9. #21444668C2semidirect
10. #21444649C2semidirect
11. #335×D61C2semidirect
12. #21444203C2semidirect
13. #21444203C2semidirect
14. #21444110C2semidirect
15. C61×#1581C2semidirect
158. #11758224M16semidirect
301. #1581D61semidirect
363. C61#17881semidirect

Maximal subgroups

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

subgroupindex
#214549342
#214549262
C4×#145197962
#214447002
#214446952
#214446762
#214446732
#214446712
#214446682
#214446492
#335×D612
#214442032
#214441102
C61×#15812
#1788161