Finite Group Databasebeta

← #29836684

Subgroups — #29836684

Order 15616.

738 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
1C22×#14519722C211yesmaximal, characteristic, complemented
2C2×SD32×D61C211yesmaximal, characteristic, complemented
3#21457568C211yesmaximal, characteristic, complemented
4#21457493C211yesmaximal, characteristic
5#21448073C211yesmaximal, characteristic, complemented
6#21447916C211yesmaximal, characteristic, complemented
7#21447863C211yesmaximal, characteristic, complemented
8#21447858C211yesmaximal, characteristic, complemented
9#21447749C211yesmaximal, characteristic, complemented
10#21447747C211yesmaximal, characteristic, complemented
11#21447737C211yesmaximal, characteristic, complemented
12#21447735C211yesmaximal, characteristic, complemented
13#21447670C211yesmaximal, characteristic, complemented
14C16×C22⋊D61C211yesmaximal, characteristic, complemented
15C61×#2217C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic, complemented
17C2×Q16×D61C2211yescharacteristic, complemented
18C22×D488C2211yescharacteristic
19C2×D8×D61C2211yescharacteristic
20#16840425—21no—
21#16840396—21no—
22C2×#14519722—24no—
23C2×#14519722C2211yescharacteristic
24C2×#14519722C2211yescharacteristic
25C2×#14519722C2211yescharacteristic, complemented
26C2×#14519722C2211yescharacteristic, complemented
27C2×#14519721C2211yescharacteristic, complemented
28C2×#14519721C2211yescharacteristic, complemented
29C2×#14519720C2211yescharacteristic
30C2×#14519720C2211yescharacteristic, complemented
31SD32×D61—24no—
32C2×C16×D61C2211yescharacteristic, complemented
33#16840140C2211yescharacteristic, complemented
34#16840137C2211yescharacteristic
35#16840004C2211yescharacteristic, complemented
36#16839999C2211yescharacteristic
37#16839971—21no—
38#16839956—21no—
39#16839919—21no—
40#16839917—21no—
41#16839897—21no—
42#16839895—21no—
43#16839856C2211yescharacteristic, complemented
44#16839844C2211yescharacteristic
45C8×C22⋊D61C2211yescharacteristic
46#16839580C2211yescharacteristic, complemented
47#16839565C2211yescharacteristic, complemented
48#16839565C2211yescharacteristic, complemented
49#16839562C2211yescharacteristic
50#16839562C2211yescharacteristic, complemented
51C22⋊#11758185C2211yescharacteristic, complemented
52#16839541C2211yescharacteristic, complemented
53C16×Dic61C2211yescharacteristic, complemented
54C2×SD32×C61C2211yescharacteristic, complemented
55C22×C16×C61C2211yescharacteristic, complemented
56C61×#467C2211yescharacteristic, complemented
57C61×#466C2211yescharacteristic
58C61×#367C2211yescharacteristic, complemented
59C61×#358C2211yescharacteristic, complemented
60C61×#357C2211yescharacteristic, complemented
61C22×Dic122—21no—
62C2×Q8×D61—21no—
63C22×D244—21no—
64C2×D4×D61—21no—
65C2×D4×D61—41no—
66C2×Dic244—22no—
67C2×Dic244—21no—
68C2×Dic244—41no—
69C2×Dic244C2311yescharacteristic
70C2×Dic244C2311yescharacteristic
71C2×#11758202—21no—
72C2×#11758202—21no—
73Q16×D61—22no—
74Q16×D61—41no—
75C2×D488—22no—
76C2×D488—21no—
77C2×D488—41no—
78C2×D488C2311yescharacteristic
79C2×D488C2311yescharacteristic
80C2×#11758199—21no—
81C2×#11758199—21no—
82D8×D61—22no—
83D8×D61—41no—
84C2×C8×D61C2311yescharacteristic
85#14519776—41no—
86#14519775—21no—
87#14519773—21no—
88#14519757—21no—
89#14519755—41no—
90#14519754—41no—
91#14519752—21no—
92#14519750—41no—
93#14519747—41no—
94#14519745—41no—
95#14519742—21no—
96#14519739—21no—
97C4×C22⋊D61D411yescharacteristic
98#14519737—41no—
99#14519722—22no—
100#14519722—22no—
101#14519722—22no—
102#14519722D414yescomplemented
103#14519721—22no—
104#14519721—41no—
105#14519720—22no—
106#14519720—41no—
107C2×#11758185C2311yescharacteristic
108C2×#11758185C2311yescharacteristic
109C16×D61—22no—
110#14519706D411yescharacteristic
111#14519700—21no—
112#14519700—21no—
113#14519697—21no—
114#14519697—21no—
115C22⋊#92418D411yescharacteristic
116#14519689D411yescharacteristic
117C8×Dic61C2311yescharacteristic
118C2×Q16×C61C2311yescharacteristic
119C2×D8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22⋊Q8×C61—21no—
122#121×C61—21no—
123SD32×C61—22no—
124C2×C16×C61—22no—
125C2×C16×C61C2311yescharacteristic
126C2×C16×C61C2311yescharacteristic
127#107×C61C2311yescharacteristic
128#107×C61C2311yescharacteristic
129#103×C61—21no—
130#102×C61—21no—
131C23×D61—41no—
132C23×D61—41no—
133C2×Q8×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—41no—
136C22×C4×C61C2×D411yescharacteristic
137C2×C22⋊D61—41no—
138C2×C22⋊D61—41no—
139C2×C22⋊D61—41no—
140C2×C22⋊D61D811yescharacteristic
141C22×Dic61—41no—
142Q8×D61—42no—
143Q8×D61—81no—
144D4×D61—42no—
145D4×D61—81no—
146D4×D61—84no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—42no—
150C2×D244—41no—
151C2×D244—41no—
152C2×D244—81no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61C2×D411yescharacteristic
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—42no—
159C2×Dic122—41no—
160C2×Dic122—41no—
161C2×Dic122—81no—
162Q16×C61—21no—
163Q16×C61—21no—
164D8×C61—21no—
165D8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—41no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C22⋊Dic61D811yescharacteristic
176#11758202—42no—
177#11758202—81no—
178#11758199—42no—
179#11758199—81no—
180#11758198—41no—
181#11758198—41no—
182#11758198—41no—
183#11758198D811yescharacteristic
184C4⋊Dic61—41no—
185#11758196—41no—
186#11758196—41no—
187#11758196—41no—
188#11758196D811yescharacteristic
189C4×Dic61—41no—
190C4×Dic61C2×D411yescharacteristic
191C2×#92418C2×D411yescharacteristic
192C2×#92418C2×D411yescharacteristic
193Dic244—21no—
194Dic244—21no—
195Dic244—21no—
196Dic244—42no—
197Dic244C2×D412yescomplemented
198D488—21no—
199D488—21no—
200D488—21no—
201D488—42no—
202D488C2×D412yes—
203C8×D61—21no—
204C8×D61—21no—
205C16×C61—21no—
206C16×C61C2×D412yescomplemented
207#11758185—21no—
208#11758185—21no—
209C23×C61—41no—
210C23×C61C2×D811yescharacteristic
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—82no—
214C22×D61—82no—
215C22×D61—82no—
216C22×D61—82no—
217C22×D61—161no—
218C22×D61—161no—
219C22×D61C2×D811yescharacteristic
220Q8×C61—41no—
221Q8×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—82no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61C2×D811yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C22⋊D61—82no—
233C22⋊D61—82no—
234C22⋊D61—161no—
235C22⋊D61SD3214yescomplemented
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—82no—
239C2×Dic61C2×D811yescharacteristic
240C2×Dic61C2×D811yescharacteristic
241C2×Dic61C2×D811yescharacteristic
242D244—22no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—82no—
247D244—82no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—82no—
251C4×D61—82no—
252Dic122—22no—
253Dic122—41no—
254Dic122—41no—
255Dic122—41no—
256Dic122—82no—
257Dic122—82no—
258C8×C61—21no—
259C8×C61C22×D411yescharacteristic
260C8×C61H(5,𝔽2)11yescharacteristic
261#92418—21no—
262#92418—21no—
263D4×SD32—611nomaximal, Sylow
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61C2×SD3212yescomplemented
270C22×C61C22×D811yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—42no—
274C2×D61—81no—
275C2×D61—81no—
276C2×D61—81no—
277C2×D61—81no—
278C2×D61—81no—
279C2×D61—164no—
280C2×D61—164no—
281C2×D61C2×SD3212yescomplemented
282C4×C61—21no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61D4211yescharacteristic
287C4×C61#57611yescharacteristic
288Dic61—21no—
289Dic61—21no—
290Dic61—42no—
291Dic61—81no—
292Dic61C2×SD3212yescomplemented
293C22×SD32—611no—
294C22×SD32—611no—
295D4×Q16—611no—
296D4×D8—611no—
297#2248—611no—
298#2217—611no—
299#2217D6111yescharacteristic, complemented
300#2208—611no—
301#2207—611no—
302#2187—611no—
303#2187—611no—
304#2185—611no—
305#2185—611no—
306C4×SD32—611no—
307D4×C16—611no—
308C2×C61—22no—
309C2×C61—161no—
310C2×C61D4×D811yescharacteristic
311C2×C61C22×SD3211yescharacteristic
312C2×C61#341611yescharacteristic
313D61—22no—
314D61—82no—
315D61—161no—
316C22×Q16—611no—
317C22×Q16—611no—
318C22×D8—611no—
319C22×D8—611no—
320D4×Q8—1221no—
321D42—1221no—
322C2×SD32—611no—
323C2×SD32—611no—
324C2×SD32—611no—
325C2×SD32—611no—
326C2×SD32—611no—
327C2×SD32—611no—
328C2×SD32—611no—
329C2×SD32—611no—
330C2×SD32—1224no—
331C2×SD32—1224no—
332C2×SD32C2×D6111yescharacteristic, complemented
333C22×C16—611no—
334C22×C16C2×D6111yescharacteristic, complemented
335#494—611no—
336#493—611no—
337#467—611no—
338#467C2×D6111yescharacteristic, complemented
339#466—611no—
340#466C2×D6111yescharacteristic
341#462—1221no—
342#459—1221no—
343#451—1221no—
344#451—1221no—
345#447—1221no—
346#447—1221no—
347C4×Q16—611no—
348C4×D8—611no—
349C8×D4—611no—
350#367C2×D6111yescharacteristic, complemented
351C4⋊C16—611no—
352#358—611no—
353#358—611no—
354#358C2×D6111yescharacteristic, complemented
355#357—611no—
356#357—611no—
357#357C2×D6111yescharacteristic, complemented
358C22⋊C16—611no—
359C22⋊C16—611no—
360C4×C16—611no—
361C61D4×SD3211yescharacteristic, complemented, Sylow
362C22×Q8—1221no—
363C22×Q8—1221no—
364C22×D4—1221no—
365C22×D4—1221no—
366C22×D4—2441no—
367C2×Q16—611no—
368C2×Q16—611no—
369C2×Q16—1222no—
370C2×Q16—1221no—
371C2×Q16—1221no—
372C2×Q16—1222no—
373C2×Q16—1221no—
374C2×Q16—2441no—
375C2×Q16—2441no—
376C2×Q16C22×D6111yescharacteristic
377C2×D8—611no—
378C2×D8—611no—
379C2×D8—1222no—
380C2×D8—1221no—
381C2×D8—1221no—
382C2×D8—1222no—
383C2×D8—1221no—
384C2×D8—2441no—
385C2×D8—2441no—
386C2×D8C22×D6111yescharacteristic
387C22×C8—611no—
388C22×C8C22×D6111yescharacteristic
389C4⋊Q8—1221no—
390C4⋊Q8—2441no—
391#127—1221no—
392C22⋊Q8—21no—
393C22⋊Q8—1221no—
394C22⋊Q8—2441no—
395C22⋊Q8—2441no—
396#121—21no—
397#121—1221no—
398#121—2441no—
399#120—2441no—
400#120—2441no—
401C4×Q8—1221no—
402C4×D4—611no—
403C4×D4—1221no—
404C4×D4—2441no—
405SD32—22no—
406SD32—614no—
407SD32—1222no—
408SD32—1222no—
409SD32—1222no—
410SD32—1222no—
411SD32—1222no—
412SD32—2441no—
413SD32—2441no—
414C2×C16—22no—
415C2×C16—611no—
416C2×C16—611no—
417C2×C16—1222no—
418C2×C16C22×D6111yescharacteristic
419C2×C16C22×D6111yescharacteristic
420#107C22×D6111yescharacteristic
421#107C22×D6111yescharacteristic
422C4⋊C8—611no—
423#103—21no—
424#103—1221no—
425#103—1221no—
426#102—21no—
427#102—1221no—
428#102—1221no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C4×C8—611no—
432C24—2441no—
433C24—2441no—
434C2×Q8—21no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—4881no—
438C2×Q8—4881no—
439C2×Q8—2442no—
440C2×Q8—2441no—
441C2×Q8—2442no—
442C2×Q8—2441no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—611no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—4881no—
449C2×D4—4881no—
450C2×D4—4884no—
451C2×D4—2442no—
452C2×D4—2441no—
453C2×D4—2441no—
454C2×D4—2441no—
455C2×D4—2441no—
456C2×D4—2442no—
457C2×D4—2441no—
458C22×C4—611no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4D4×D6111yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—612no—
466Q16—1221no—
467Q16—1221no—
468Q16—1221no—
469Q16—4881no—
470Q16—2442no—
471Q16—2442no—
472D8—21no—
473D8—21no—
474D8—612no—
475D8—1221no—
476D8—1221no—
477D8—1221no—
478D8—4881no—
479D8—2442no—
480D8—2442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8D4×D6111yescharacteristic
488C2×C8C23×D6111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—611no—
493C4⋊C4—2441no—
494C4⋊C4—2441no—
495C4⋊C4—2441no—
496C4⋊C4—2441no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—611no—
500C22⋊C4—611no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—611no—
505C42—2441no—
506C16—21no—
507C16—1221no—
508C16—1221no—
509C16D4×D6112yescomplemented
510C23—41no—
511C23—611no—
512C23—9761no—
513C23—9761no—
514C23—4882no—
515C23—4882no—
516C23—4882no—
517C23—4882no—
518C23—2441no—
519C23—2441no—
520C23D8×D6111yescharacteristic
521Q8—41no—
522Q8—41no—
523Q8—1222no—
524Q8—4882no—
525Q8—4882no—
526Q8—2441no—
527Q8—2441no—
528Q8—2441no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—614no—
533D4—1222no—
534D4—9761no—
535D4—4882no—
536D4—4882no—
537D4—4882no—
538D4—4882no—
539D4—2441no—
540D4—2441no—
541D4—2441no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—4882no—
553C2×C4—4882no—
554C2×C4—4882no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4D8×D6111yescharacteristic
558C2×C4C2×D4×D6111yescharacteristic
559C8—21no—
560C8—1221no—
561C8—1221no—
562C8C2×D4×D6111yescharacteristic
563C8#1451982311yescharacteristic
564C22—21no—
565C22—21no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—612no—
570C22—1221no—
571C22—1221no—
572C22—9764no—
573C22—9764no—
574C22—4881no—
575C22—4881no—
576C22—4881no—
577C22—4881no—
578C22—4881no—
579C22—2442no—
580C22SD32×D6112yescomplemented
581C22C2×D8×D6111yescharacteristic
582C4—21no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—612no—
587C4—1221no—
588C4—1221no—
589C4—4881no—
590C4—2442no—
591C4#1684039611yescharacteristic
592C4#1684056411yescharacteristic
593C2—22no—
594C2—161no—
595C2—1222no—
596C2—9761no—
597C2—4882no—
598C2#2145749311yescharacteristic
599C2C2×SD32×D6111yescharacteristic
600C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2217C2
socleC22×C61C22×D8
prime radical#21457493C2
hypercenter#2217D61
hypocenterC61D4×SD32
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C22×#14519722C2semidirect
2. C2×SD32×D61C2semidirect
3. #21457568C2semidirect
5. #21448073C2semidirect
6. #21447916C2semidirect
7. #21447863C2semidirect
8. #21447858C2semidirect
9. #21447749C2semidirect
10. #21447747C2semidirect
11. #21447737C2semidirect
12. #21447735C2semidirect
13. #21447670C2semidirect
14. C16×C22⋊D61C2semidirect
15. C61×#2217C2semidirect
16. C22×Dic244C22semidirect
17. C2×Q16×D61C22semidirect
25. C2×#14519722C22semidirect
26. C2×#14519722C22semidirect
27. C2×#14519721C22semidirect
28. C2×#14519721C22semidirect
30. C2×#14519720C22semidirect
32. C2×C16×D61C22semidirect
33. #16840140C22semidirect
35. #16840004C22semidirect
43. #16839856C22semidirect
46. #16839580C22semidirect
47. #16839565C22semidirect
48. #16839565C22semidirect
50. #16839562C22semidirect
51. C22⋊#11758185C22semidirect
52. #16839541C22semidirect
53. C16×Dic61C22semidirect
54. C2×SD32×C61C22semidirect
55. C22×C16×C61C22semidirect
56. C61×#467C22semidirect
58. C61×#367C22semidirect
59. C61×#358C22semidirect
60. C61×#357C22semidirect
102. #14519722D4semidirect
197. Dic244C2×D4semidirect
206. C16×C61C2×D4semidirect
235. C22⋊D61SD32semidirect
269. C22×C61C2×SD32semidirect
281. C2×D61C2×SD32semidirect
292. Dic61C2×SD32semidirect
299. #2217D61semidirect
332. C2×SD32C2×D61semidirect
334. C22×C16C2×D61semidirect
338. #467C2×D61semidirect
350. #367C2×D61semidirect
354. #358C2×D61semidirect
357. #357C2×D61semidirect
361. C61D4×SD32semidirect
509. C16D4×D61semidirect
580. C22SD32×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×SD32×D612
#214575682
#214574932
#214480732
#214479162
#214478632
#214478582
#214477492
#214477472
#214477372
#214477352
#214476702
C16×C22⋊D612
C61×#22172
D4×SD3261