Finite Group Databasebeta

← #29649584

Subgroups — #29649584

Order 15616.

688 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#21454784C211yesmaximal, characteristic, complemented
2C8×#11758226C211yesmaximal, characteristic, complemented
3C4×#14519800C211yesmaximal, characteristic
4#21444697C211yesmaximal, characteristic, complemented
5#21444694C211yesmaximal, characteristic, complemented
6#21444691C211yesmaximal, characteristic, complemented
7#21444685C211yesmaximal, characteristic, complemented
8#21444682C211yesmaximal, characteristic, complemented
9#21444679C211yesmaximal, characteristic, complemented
10#21444674C211yesmaximal, characteristic, complemented
11#21444564C211yesmaximal, characteristic, complemented
12#21444200C211yesmaximal, characteristic, complemented
13#21444200C211yesmaximal, characteristic, complemented
14#322×D61C211yesmaximal, characteristic, complemented
15C61×#1587C211yesmaximal, characteristic, complemented
16C2×#14519800C411yescharacteristic
17C4×#11758226C2211yescharacteristic
18C4×#11758226C2211yescharacteristic
19#16839893C2211yescharacteristic
20Q8×#92418C2211yescharacteristic
21Q16×Dic61C411yescharacteristic
22C4×#11758201C2211yescharacteristic
23C4×#11758201C2211yescharacteristic
24#16839847C411yescharacteristic
25#16839847C411yescharacteristic
26C4×D488C2211yescharacteristic
27#16839844C411yescharacteristic
28#16839841C2211yescharacteristic
29#16839839C2211yescharacteristic
30#16839835—21no—
31#16839832—21no—
32C8×D244—21no—
33C8×D244C2211yescharacteristic
34#16839827—21no—
35#16839827C2211yescharacteristic
36#16839814—21no—
37#16839814—21no—
38#16839814C2211yescharacteristic
39#16839814C2211yescharacteristic
40#16839799C411yescharacteristic
41#16839757C411yescharacteristic
42#16839757C411yescharacteristic
43#16839714—21no—
44C4×C8×D61—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839513C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758226C2×C411yescharacteristic
68C2×#11758226C2×C411yescharacteristic
69#14519800—24no—
70C2×#11758201C2×C411yescharacteristic
71C2×#11758201C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61C2×C411yescharacteristic
80C2×C8×D61D411yescharacteristic
81C2×C8×D61D411yescharacteristic
82Q8×Dic61C2×C411yescharacteristic
83Q8×Dic61C2×C411yescharacteristic
84C4×D244—21no—
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87C4×D244C2311yescharacteristic
88#14519739—21no—
89#14519739—21no—
90#14519739C2×C411yescharacteristic
91#14519739C2×C411yescharacteristic
92#14519735—21no—
93#14519735—21no—
94#14519735C2×C411yescharacteristic
95#14519735C2×C411yescharacteristic
96C42×D61—21no—
97C42×D61—21no—
98C42×D61C2311yescharacteristic
99#14519711C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101#14519708C2×C411yescharacteristic
102C4⋊#92418—21no—
103C4⋊#92418—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106#14519701C2×C411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112#14519689—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519688—21no—
119C4×#92418—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×Q16×C61C2×C411yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147#11758226—22no—
148#11758226—22no—
149#11758226—22no—
150#11758226M1614yescomplemented
151C2×D244—21no—
152C2×D244—21no—
153C2×D244C22×C411yescharacteristic
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164Q16×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C42×C61—21no—
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179#11758201—22no—
180#11758201—22no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205D488—22no—
206#11758189—42no—
207#11758189—42no—
208C8×D61—24no—
209C8×D61—22no—
210C8×D61—22no—
211C8×D61—41no—
212C8×D61—41no—
213C8×D61—42no—
214C8×D61—42no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61C4×D411yescharacteristic
218Q8×C61—21no—
219Q8×C61—21no—
220Q8×C61—21no—
221Q8×C61C2×M1612yes—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61C4×D411yescharacteristic
232C2×Dic61C4×D411yescharacteristic
233C2×Dic61C4×D411yescharacteristic
234D244—24no—
235D244—21no—
236D244—21no—
237D244—21no—
238D244—42no—
239D244C2×M1612yes—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—24no—
243C4×D61—22no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—42no—
249C4×D61—42no—
250C4×D61—42no—
251C4×D61C2×M1612yes—
252C4×D61#13112yes—
253C8×C61—22no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—22no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—41no—
266#92418—41no—
267#17868—611nomaximal, Sylow
268C22×C61C2×C4×D411yescharacteristic
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—22no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61#43512yes—
278C4×C61—22no—
279C4×C61—21no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61C22×M1611yescharacteristic
284C4×C61C2×#13111yescharacteristic
285C4×C61#57511yescharacteristic
286C4×C61#57511yescharacteristic
287Dic61—21no—
288Dic61—41no—
289Dic61—41no—
290Dic61#43512yes—
291Dic61#44312yes—
292#2965—611no—
293C8×#41—611no—
294C4×#135—611no—
295#1588—611no—
296#1588—611no—
297#1587—611no—
298#1587D6111yescharacteristic, complemented
299#1586—611no—
300#1586—611no—
301#1585—611no—
302#1585—611no—
303#1564—611no—
304#1476—611no—
305#1476—611no—
306C2×#322—611no—
307C2×C61C2×#43511yescharacteristic
308C2×C61#294311yescharacteristic
309C2×C61C2×#44311yescharacteristic
310D61—22no—
311D61—42no—
312D61—81no—
313C2×#135—611no—
314C4×#41—611no—
315C4×#41—611no—
316#446—611no—
317#446C2×D6111yescharacteristic
318C8×Q8—611no—
319C8×Q8C2×D6111yescharacteristic
320C4×Q16—611no—
321C4×Q16C2×D6111yescharacteristic
322C4×SD16—611no—
323C4×SD16—611no—
324C4×SD16—611no—
325C4×SD16—611no—
326C4×D8—611no—
327C4×D8—611no—
328#436—611no—
329#436—611no—
330#435—1221no—
331#435—1221no—
332C8×D4—611no—
333C8×D4—611no—
334C8×D4—1221no—
335C8×D4—1221no—
336#431—611no—
337#431—611no—
338#431—1221no—
339#431—1221no—
340#427—611no—
341#416—611no—
342#416—611no—
343C4×M16—1221no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346C2×C4×C8—611no—
347C2×C4×C8—1221no—
348#335—611no—
349#335—611no—
350#334—611no—
351#334C2×D6111yescharacteristic
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8C2×D6111yescharacteristic
355Q8⋊C8C2×D6111yescharacteristic
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360#322—611no—
361#322—611no—
362#322—611no—
363#322C2×D6111yescharacteristic
364C61#1786811yescharacteristic, complemented, Sylow
365C2×#41—611no—
366C2×#41—611no—
367#135—1224no—
368C2×Q16C4×D6111yescharacteristic
369C2×SD16—611no—
370C2×SD16—611no—
371C2×D8—611no—
372C2×M16—1221no—
373C2×M16—1221no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C4×Q8—611no—
382C4×Q8—611no—
383C4×Q8C22×D6111yescharacteristic
384C4×Q8C22×D6111yescharacteristic
385C4×D4—611no—
386C4×D4—611no—
387C4×D4—611no—
388C4×D4—611no—
389C4×D4—1221no—
390C4×D4—1221no—
391C4×D4—1221no—
392C4×D4—1221no—
393#117—611no—
394#117—611no—
395#117—1221no—
396#117—1221no—
397C2×C42—611no—
398C2×C42—1221no—
399C2×C42—1221no—
400#107—611no—
401#107C4×D6111yescharacteristic
402#106—611no—
403#106—611no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412#103—611no—
413#103—611no—
414#103C4×D6111yescharacteristic
415#103C4×D6111yescharacteristic
416#102—611no—
417#102—611no—
418#102—611no—
419#102—611no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—21no—
427#97—1221no—
428C4×C8—21no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—1221no—
437C4×C8—1221no—
438C4×C8—1221no—
439C4×C8—1221no—
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442C4×C8C22×D6111yescharacteristic
443#41—614no—
444#41—1222no—
445#41—1222no—
446#41—1222no—
447C2×Q8C2×C4×D6111yescharacteristic
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1221no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462Q16—22no—
463SD16—1222no—
464SD16—1222no—
465D8—1222no—
466M16—2442no—
467M16—2442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1224no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—2441no—
482C2×C8—2441no—
483C2×C8—2442no—
484C2×C8—2442no—
485C2×C8C2×C4×D6111yescharacteristic
486C2×C8C2×C4×D6111yescharacteristic
487C2×C8D4×D6111yescharacteristic
488C2×C8D4×D6111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—611no—
492C4⋊C4—611no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4C2×C4×D6111yescharacteristic
496C4⋊C4C2×C4×D6111yescharacteristic
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C42—21no—
504C42—21no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42C23×D6111yescharacteristic
513C23—611no—
514C23—1221no—
515C23—1221no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8M16×D6112yes—
520D4—612no—
521D4—1224no—
522D4—1221no—
523D4—1221no—
524D4—1221no—
525D4—2442no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—611no—
535C2×C4—1222no—
536C2×C4—1224no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4C22×C4×D6111yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4#41×D6111yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—1222no—
559C8—1221no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—2441no—
564C8—2441no—
565C22—612no—
566C22—1221no—
567C22—1221no—
568C22—1222no—
569C22—2441no—
570C22—2441no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22C4×D4×D6111yescharacteristic
575C4—21no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—612no—
581C4—612no—
582C4—1221no—
583C4—2441no—
584C4—2441no—
585C4C2×M16×D6111yescharacteristic
586C4#131×D6111yescharacteristic
587C4#1684056111yescharacteristic
588C4#1684056111yescharacteristic
589C2—1222no—
590C2—4881no—
591C2—2442no—
592C2#435×D6111yescharacteristic
593C2#2145461811yescharacteristic
594C2#443×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1587C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519800C4
cosocleC42×C61C24
hypercenter#1587D61
hypocenterC61#17868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
1. #21454784C2semidirect
2. C8×#11758226C2semidirect
4. #21444697C2semidirect
5. #21444694C2semidirect
6. #21444691C2semidirect
7. #21444685C2semidirect
8. #21444682C2semidirect
9. #21444679C2semidirect
10. #21444674C2semidirect
11. #21444564C2semidirect
12. #21444200C2semidirect
13. #21444200C2semidirect
14. #322×D61C2semidirect
15. C61×#1587C2semidirect
150. #11758226M16semidirect
298. #1587D61semidirect
364. C61#17868semidirect

Maximal subgroups

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

subgroupindex
#214547842
C8×#117582262
C4×#145198002
#214446972
#214446942
#214446912
#214446852
#214446822
#214446792
#214446742
#214445642
#214442002
#322×D612
C61×#15872
#1786861