Finite Group Databasebeta

← #30606278

Subgroups — #30606278

Order 15616.

768 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840742C211yesmaximal, characteristic
2#21462403C211yesmaximal, characteristic
3#21460906C214yesmaximal, complemented
4C2×#16839734C211yesmaximal, characteristic
5C22×#11758217C411yescharacteristic, complemented
6C22×#11758217C411yescharacteristic, complemented
7C2×#14519856—21no—
8#16840742—21no—
9#16840742—21no—
10#16840742C412yescomplemented
11#16840742C2212yes—
12C2×#14519835—21no—
13C2×#14519835C412yescomplemented
14#16840735—21no—
15#16840735—21no—
16#16840735C412yescomplemented
17#16840735C2212yes—
18#16840734—21no—
19#16840732—21no—
20C22×#11758224C2211yescharacteristic
21C2×#14519733—21no—
22#16839734—21no—
23#16839734—21no—
24#16839734C412yescomplemented
25#16839734C2212yes—
26C2×#14519692C411yescharacteristic, complemented
27C2×#14519691—21no—
28C2×#99×C61C411yescharacteristic, complemented
29C2×#11758217—21no—
30C2×#11758217—21no—
31C2×#11758217—21no—
32C2×#11758217—41no—
33C2×#11758217—41no—
34C2×#11758217—41no—
35C2×#11758217—41no—
36C2×#11758217C2×C412yescomplemented
37C22×#92420—21no—
38C22×#92420C2×C412yescomplemented
39#14519856—22no—
40#14519856—22no—
41#14519856—41no—
42#14519856—41no—
43C2×C4⋊#6923—41no—
44C2×C22⋊#6923—22no—
45C2×C4×#6923—41no—
46#14519835—22no—
47#14519835—22no—
48#14519835—22no—
49#14519835C2×C414yescomplemented
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53C22⋊#92420—22no—
54C2×#11758224—41no—
55C2×#11758224—41no—
56C2×#11758224—41no—
57C2×#11758224—41no—
58C2×#11758224C2×C411yescharacteristic
59C2×#11758224C2×C411yescharacteristic
60C2×#11758224C2×C411yescharacteristic
61C2×#11758224D411yescharacteristic
62C2×#11758224D411yescharacteristic
63C2×#11758224D411yescharacteristic
64C2×#11758224Q811yescharacteristic
65C2×#11758224C2311yescharacteristic
66C22×Dic122Q811yescharacteristic
67C22×C22⋊D61C2×C411yescharacteristic
68C22×C22⋊D61D411yescharacteristic
69C23×Dic61C2×C411yescharacteristic
70C23×Dic61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72#14519733—22no—
73#14519733—22no—
74#14519733—41no—
75#14519733—41no—
76C2×#11758196—41no—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—41no—
79#14519692—21no—
80#14519692C2×C412yescomplemented
81#14519691—22no—
82#14519691—22no—
83C22×D4×C61C2×C411yescharacteristic
84C2×C22⋊C4×C61—21no—
85#99×C61—21no—
86#99×C61C2×C412yescomplemented
87C24×C61C4211yescharacteristic
88C24×C61C22⋊C411yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C22×#6923—42no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61C4211yescharacteristic
94C2×D4×C61C22⋊C411yescharacteristic
95C2×D4×C61C4⋊C411yescharacteristic
96C2×D4×C61C22×C411yescharacteristic
97C22×C4×C61—41no—
98C22×C4×C61C4⋊C411yescharacteristic
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61C4211yescharacteristic
104C2×C22⋊D61C22⋊C411yescharacteristic
105C2×C22⋊D61C22⋊C411yescharacteristic
106C2×C22⋊D61C22⋊C411yescharacteristic
107C2×C22⋊D61C4⋊C411yescharacteristic
108C2×C22⋊D61C4⋊C411yescharacteristic
109C2×C22⋊D61C22×C411yescharacteristic
110C2×C22⋊D61C2×D411yescharacteristic
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—21no—
119C22×Dic61—41no—
120C22×Dic61C4211yescharacteristic
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C4⋊C411yescharacteristic
126C22×Dic61C4⋊C411yescharacteristic
127C22×Dic61C4⋊C411yescharacteristic
128C22×Dic61C4⋊C411yescharacteristic
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C2×D411yescharacteristic
131#11758224—41no—
132#11758224—41no—
133#11758224—41no—
134#11758224—41no—
135#11758224—41no—
136#11758224—41no—
137#11758224—41no—
138#11758224—41no—
139#11758224—41no—
140#11758224—41no—
141#11758224—41no—
142#11758224—41no—
143#11758224—41no—
144#11758224—41no—
145#11758224—41no—
146#11758224—41no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C4⋊C411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×Dic122—41no—
156C2×Dic122—41no—
157C2×Dic122C4⋊C411yescharacteristic
158C2×Dic122C4⋊C411yescharacteristic
159C2×Dic122C4⋊C411yescharacteristic
160C2×Dic122C2×Q811yescharacteristic
161C22⋊#6923—24no—
162C22⋊#6923—42no—
163#11758217—42no—
164#11758217—41no—
165#11758217—41no—
166#11758217—41no—
167#11758217—41no—
168#11758217—42no—
169C2×#92420—22no—
170C2×#92420—22no—
171C2×#92420—42no—
172C2×#92420—42no—
173C4⋊#6923—42no—
174C4⋊#6923—42no—
175C4×#6923—42no—
176C4×#6923—42no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—41no—
179C22⋊Dic61—22no—
180C22⋊Dic61—41no—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—42no—
184C4×Dic61—42no—
185C23×C61—21no—
186C23×C61—21no—
187C23×C61—21no—
188C23×C61—21no—
189C23×C61—81no—
190C23×C61—81no—
191C23×C61#9511yescharacteristic
192C23×C61#9511yescharacteristic
193C23×C61#9511yescharacteristic
194C23×C61C2×C4211yescharacteristic
195C23×C61C2×C22⋊C411yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—81no—
199C22×D61#9511yescharacteristic
200C22×D61C2×C22⋊C411yescharacteristic
201C2×#6923—44no—
202C2×#6923—84no—
203D4×C61—41no—
204D4×C61—41no—
205D4×C61—41no—
206D4×C61—41no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—42no—
210C2×C4×C61—82no—
211C2×C4×C61#9511yescharacteristic
212C2×C4×C61C2×C4⋊C411yescharacteristic
213C22⋊D61—41no—
214C22⋊D61—41no—
215C22⋊D61—41no—
216C22⋊D61—41no—
217C22⋊D61—41no—
218C22⋊D61—41no—
219C22⋊D61—41no—
220C22⋊D61—41no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—42no—
242C2×Dic61—82no—
243C2×Dic61#9511yescharacteristic
244C2×Dic61#9511yescharacteristic
245C2×Dic61#9511yescharacteristic
246C2×Dic61#9911yescharacteristic
247C2×Dic61#9911yescharacteristic
248C2×Dic61#9911yescharacteristic
249C2×Dic61#9911yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C4⋊C411yescharacteristic
252C2×Dic61C2×C4⋊C411yescharacteristic
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—21no—
259C4×D61—21no—
260C4×D61—21no—
261Dic122—41no—
262Dic122—41no—
263Dic122—41no—
264Dic122—41no—
265#92420—42no—
266#92420—42no—
267#12577—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—42no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61#34211yescharacteristic
282C22×C61#34211yescharacteristic
283C22×C61C2×#9511yescharacteristic
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—42no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—81no—
290#6923—84no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—82no—
294Dic61—21no—
295Dic61—21no—
296Dic61—21no—
297Dic61—21no—
298Dic61—82no—
299Dic61#34211yescharacteristic
300Dic61#34211yescharacteristic
301Dic61C2×#9911yescharacteristic
302Dic61C2×#9911yescharacteristic
303C2×#410—611no—
304C2×#410—611no—
305#2879—611no—
306#1391—614no—
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—41no—
311C2×C61—41no—
312C2×C61—41no—
313C2×C61—41no—
314C2×C61C2×#34211yescharacteristic
315D61—41no—
316D61—41no—
317C22×#41—611no—
318C22×M16—611no—
319C22×M16—611no—
320C2×#117—1221no—
321C2×#117—1221no—
322#410—612no—
323#410—612no—
324#410—612no—
325#410—612no—
326#410—1221no—
327#410—1221no—
328#410—1221no—
329#410—1221no—
330C2×#99—612no—
331C2×#99—611no—
332C2×#99—1221no—
333C2×#99—1221no—
334C2×#99#692311yescharacteristic, complemented
335#408—612no—
336#408—612no—
337#408—1221no—
338#408—1221no—
339#407—1221no—
340#407—1221no—
341C61#1257711yescharacteristic, complemented, Sylow
342C2×#41—611no—
343C2×#41—611no—
344C2×#41—611no—
345C2×#41—611no—
346C2×#41—611no—
347C2×#41—611no—
348C2×#41—611no—
349C2×#41—611no—
350C2×#41—2441no—
351C2×#41—2441no—
352C2×#41—2441no—
353C2×#41—2441no—
354C22×Q8—611no—
355C22×D4—611no—
356C22×D4—611no—
357C22×D4C2×#692311yescharacteristic
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C2×M16—612no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—2441no—
366C2×M16—2441no—
367C2×M16—2441no—
368C2×M16—2441no—
369C22×C8—612no—
370C22×C8—1221no—
371#117—1222no—
372#117—1222no—
373#117—1222no—
374#117—1222no—
375#117—2441no—
376#117—2441no—
377#117—2441no—
378#117—2441no—
379C2×C4⋊C4—2441no—
380C2×C4⋊C4—2441no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—1222no—
383C2×C22⋊C4—1221no—
384C2×C42—2441no—
385C2×C42—2441no—
386#99—21no—
387#99—614no—
388#99—612no—
389#99—1222no—
390#99—1222no—
391#99—1222no—
392#99—1222no—
393#99—1222no—
394#99—1221no—
395#99C2×#692312yescomplemented
396C22⋊C8—1222no—
397C22⋊C8—1222no—
398C22⋊C8—1222no—
399C22⋊C8—1222no—
400C24—611no—
401C24C4×#692311yescharacteristic
402C24C22⋊#692311yescharacteristic
403#41—2441no—
404#41—2441no—
405#41—2441no—
406#41—2441no—
407#41—2441no—
408#41—2441no—
409#41—2441no—
410#41—2441no—
411#41—2441no—
412#41—2441no—
413#41—2441no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419C2×Q8—611no—
420C2×Q8—611no—
421C2×Q8—611no—
422C2×Q8—611no—
423C2×Q8—2441no—
424C2×Q8—2441no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—611no—
428C2×D4—611no—
429C2×D4—611no—
430C2×D4—611no—
431C2×D4—611no—
432C2×D4—611no—
433C2×D4—611no—
434C2×D4—611no—
435C2×D4—2441no—
436C2×D4—2441no—
437C2×D4—2441no—
438C2×D4—2441no—
439C2×D4C4×#692311yescharacteristic
440C2×D4C4⋊#692311yescharacteristic
441C2×D4C22⋊#692311yescharacteristic
442C2×D4C22×#692311yescharacteristic
443C22×C4—41no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—2441no—
472C22×C4—2442no—
473C22×C4C4⋊#692311yescharacteristic
474M16—2441no—
475M16—2441no—
476M16—2441no—
477M16—2441no—
478M16—2442no—
479M16—2442no—
480C2×C8—1222no—
481C2×C8—1222no—
482C2×C8—2442no—
483C2×C8—2442no—
484C4⋊C4—2442no—
485C4⋊C4—2442no—
486C4⋊C4—2442no—
487C4⋊C4—2442no—
488C22⋊C4—22no—
489C22⋊C4—41no—
490C22⋊C4—1224no—
491C22⋊C4—1222no—
492C22⋊C4—2441no—
493C22⋊C4—2442no—
494C42—2442no—
495C42—2442no—
496C42—2442no—
497C42—2442no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—81no—
503C23—81no—
504C23—611no—
505C23—611no—
506C23—1221no—
507C23—1221no—
508C23—4881no—
509C23(C2×#6923)⋊C411yescharacteristic
510C23(C2×#6923)⋊C411yescharacteristic
511C23(C2×#6923)⋊C411yescharacteristic
512C23C2×C4×#692311yescharacteristic
513C23C2×C22⋊#692311yescharacteristic
514Q8—2441no—
515Q8—2441no—
516Q8—2441no—
517Q8—2441no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—2441no—
523D4—2441no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528D4—2441no—
529D4—2441no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—42no—
533C2×C4—82no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—4882no—
573C2×C4—4884no—
574C2×C4—2442no—
575C2×C4—2444no—
576C2×C4(C2×#6923)⋊C411yescharacteristic
577C2×C4C2×C4⋊#692311yescharacteristic
578C8—2442no—
579C8—2442no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—42no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—1221no—
594C22—1221no—
595C22—4881no—
596C22—2441no—
597C22—2441no—
598C22—2442no—
599C22#1684063911yescharacteristic
600C22#1684063911yescharacteristic
601C22C2×(C2×#6923)⋊C411yescharacteristic
602C4—21no—
603C4—21no—
604C4—82no—
605C4—611no—
606C4—611no—
607C4—611no—
608C4—611no—
609C4—1221no—
610C4—1221no—
611C4—1221no—
612C4—1221no—
613C4—4882no—
614C4—4884no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—41no—
619C2—41no—
620C2—41no—
621C2—41no—
622C2—2441no—
623C2—2441no—
624C2C2×#1684063911yescharacteristic
subgroupG/H
centerC2C2×#16840639
commutatorC23×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC2×#99×C61C4
socleC2×C61C2×#342
prime radicalC22×#11758224C22
cosocleC2×#11758224C23
hypercenterC2×#99#6923
hypocenterC61#12577
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #21460906C2semidirect
5. C22×#11758217C4semidirect
6. C22×#11758217C4semidirect
10. #16840742C4semidirect
13. C2×#14519835C4semidirect
16. #16840735C4semidirect
24. #16839734C4semidirect
26. C2×#14519692C4semidirect
28. C2×#99×C61C4semidirect
36. C2×#11758217C2×C4semidirect
38. C22×#92420C2×C4semidirect
49. #14519835C2×C4semidirect
80. #14519692C2×C4semidirect
86. #99×C61C2×C4semidirect
334. C2×#99#6923semidirect
341. C61#12577semidirect
395. #99C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407422
#214624032
#214609062
C2×#168397342
#1257761