Finite Group Databasebeta

← #30622461

Subgroups — #30622461

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462349C211yesmaximal, characteristic, complemented
2#21462337C211yesmaximal, characteristic, complemented
3#21461966C212yesmaximal, complemented
4#21461947C211yesmaximal, characteristic, complemented
5#21461930C211yesmaximal, characteristic, complemented
6#21461896C212yesmaximal, complemented
7#21461814C212yesmaximal, complemented
8#21461612C211yesmaximal, characteristic, complemented
9#102×#6923C212yesmaximal, complemented
10C4×#14519839C211yesmaximal, characteristic, complemented
11#459×D61C211yesmaximal, characteristic
12C2×D4×#6923—21no—
13C2×D4×#6923C2212yes—
14C2×#14519856—21no—
15C2×#14519846C2212yes—
16C2×#14519839C2211yescharacteristic
17C2×#14519839C2211yescharacteristic
18C2×#14519839C2212yes—
19C2×#14519839C2212yes—
20C4×D61⋊C8C2211yescharacteristic
21C2×C8×#6923C2212yes—
22#16840714—21no—
23#16840714C2212yes—
24#16840714C2212yes—
25#16840712—22no—
26#16840710—22no—
27#16840708C2211yescharacteristic
28#16840704—21no—
29C4⋊C4×#6923C2212yes—
30C4×C4⋊#6923C2211yescharacteristic
31C4×C4⋊#6923C2211yescharacteristic
32#16840636C2212yes—
33#16840635C2211yescharacteristic
34#16840635C2211yescharacteristic
35(C2×#6923)⋊C8C2212yes—
36C2×D8×D61C2212yes—
37#127×D61C2211yescharacteristic
38C4×D4×D61C2211yescharacteristic
39#16839958C411yescharacteristic, complemented
40#16839957C411yescharacteristic, complemented
41#16839956C412yescomplemented
42#16839955C412yescomplemented
43#16839954C411yescharacteristic, complemented
44C4⋊C8×D61C2211yescharacteristic
45#102×D61C2212yes—
46C61×#459C411yescharacteristic, complemented
47C23×#6923—22no—
48C2×D61⋊C8C2311yescharacteristic
49C2×D61⋊C8C2311yescharacteristic
50D4×#6923—24no—
51D4×#6923—42no—
52D4×#6923—44no—
53#14519856—44no—
54C2×C4⋊#6923—21no—
55C2×C4⋊#6923—21no—
56C2×C4⋊#6923D411yescharacteristic
57C2×C4⋊#6923D411yescharacteristic
58C2×C4⋊#6923C2312yes—
59C2×C4⋊#6923C2311yescharacteristic
60C2×C4⋊#6923C2311yescharacteristic
61C2×C22⋊#6923—22no—
62C2×C22⋊#6923—22no—
63C2×C22⋊#6923—22no—
64C2×C22⋊#6923—22no—
65C2×C22⋊#6923—22no—
66C2×C4×#6923—22no—
67C2×C4×#6923—21no—
68C2×C4×#6923C2312yes—
69#14519846—42no—
70#14519839—22no—
71#14519839—22no—
72#14519839—24no—
73#14519839—42no—
74C4×#92420—21no—
75C4×#92420—21no—
76C8×#6923—42no—
77(C2×#6923)⋊C4—22no—
78(C2×#6923)⋊C4—21no—
79(C2×#6923)⋊C4D412yes—
80C2×D4×D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61C2311yescharacteristic
83C2×D4×D61C2312yes—
84C22×C4×D61—21no—
85C2×D488C2×C412yescomplemented
86C2×#11758199C2×C412yescomplemented
87C2×#11758199C2×C412yescomplemented
88D8×D61—42no—
89D8×D61—42no—
90C2×C8×D61C2312yes—
91#14519774C2×C411yescharacteristic
92#14519773—21no—
93#14519773—21no—
94#14519773C2×C412yes—
95C4×D244C2×C411yescharacteristic, complemented
96D4×Dic61C2×C411yescharacteristic, complemented
97#14519739C2×C411yescharacteristic, complemented
98C4×C22⋊D61—21no—
99#14519737—21no—
100C4⋊C4×D61C2311yescharacteristic
101C22⋊C4×D61—21no—
102C42×D61C2311yescharacteristic
103C4⋊#92418C2×C411yescharacteristic, complemented
104#14519706C2×C412yescomplemented
105#14519699C2×C412yescomplemented
106#14519698C2×C412yescomplemented
107#14519697C2×C412yescomplemented
108C2×D8×C61C2×C412yescomplemented
109#127×C61C2×C411yescharacteristic
110C4×D4×C61C2×C411yescharacteristic, complemented
111C4⋊C8×C61C2×C411yescharacteristic, complemented
112#102×C61C2×C412yescomplemented
113C23×D61—21no—
114C23×D61—22no—
115C22×#6923—21no—
116C22×#6923—21no—
117C22×#6923—22no—
118C22×#6923—44no—
119C22×#6923—44no—
120C22×#6923—82no—
121C22×#6923C2×D412yes—
122C22×#6923C2×D412yes—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61C22×C412yes—
126C2×D4×C61C22×C411yescharacteristic
127C22×C4×C61—21no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—21no—
131C2×C22⋊D61—22no—
132C22×Dic61—21no—
133D4×D61—21no—
134D4×D61—22no—
135D4×D61—21no—
136D4×D61—22no—
137D4×D61—22no—
138D4×D61—22no—
139D4×D61—21no—
140D4×D61—21no—
141D4×D61—42no—
142D4×D61—42no—
143D4×D61—81no—
144D4×D61—81no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244C22×C412yes—
148C2×D244C22×C411yescharacteristic
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2411yescharacteristic
157C22⋊#6923—44no—
158C22⋊#6923—44no—
159C22⋊#6923—44no—
160C22⋊#6923—82no—
161C22⋊#6923—82no—
162C2×#92420—21no—
163C2×#92420—21no—
164C4⋊#6923—22no—
165C4⋊#6923—22no—
166C4⋊#6923—21no—
167C4⋊#6923—21no—
168C4⋊#6923—22no—
169C4⋊#6923—21no—
170C4⋊#6923—42no—
171C4⋊#6923—81no—
172C4⋊#6923D814yescomplemented
173C4⋊#6923#4112yes—
174C4×#6923—22no—
175C4×#6923—22no—
176C4×#6923—44no—
177C4×#6923—42no—
178D61⋊C8—21no—
179D61⋊C8—21no—
180D61⋊C8—21no—
181D61⋊C8#4112yes—
182D8×C61—42no—
183C2×C8×C61C22×C412yes—
184C4⋊C4×C61C22×C411yescharacteristic
185C22⋊C4×C61—21no—
186C42×C61C22×C411yescharacteristic
187C22⋊Dic61—21no—
188#11758199—42no—
189#11758199—42no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C22×C411yescharacteristic
193#11758196—21no—
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61#4111yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418C22×C412yes—
198D488—42no—
199C8×D61—22no—
200C8×D61—22no—
201C23×C61—21no—
202C23×C61—22no—
203C22×D61—21no—
204C22×D61—22no—
205C22×D61—42no—
206C22×D61—41no—
207C22×D61—42no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—42no—
211C22×D61—41no—
212C22×D61—42no—
213C22×D61—41no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—41no—
217C22×D61C22×D411yescharacteristic
218C2×#6923—22no—
219C2×#6923—22no—
220C2×#6923—22no—
221C2×#6923—22no—
222C2×#6923—22no—
223C2×#6923—22no—
224C2×#6923—41no—
225C2×#6923—41no—
226C2×#6923—42no—
227C2×#6923—41no—
228C2×#6923—42no—
229C2×#6923—41no—
230C2×#6923—42no—
231C2×#6923—41no—
232C2×#6923—88no—
233C2×#6923C2×D814yes—
234D4×C61—21no—
235D4×C61—22no—
236D4×C61—21no—
237D4×C61—22no—
238D4×C61—42no—
239D4×C61—81no—
240C2×C4×C61—21no—
241C2×C4×C61—42no—
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C23×C411yescharacteristic
245C22⋊D61—42no—
246C22⋊D61—41no—
247C22⋊D61—41no—
248C22⋊D61—42no—
249C22⋊D61—44no—
250C22⋊D61—82no—
251C2×Dic61—21no—
252C2×Dic61—42no—
253C2×Dic61C4×D411yescharacteristic
254C2×Dic61C4×D411yescharacteristic
255C2×Dic61C2×#4111yescharacteristic
256D244—22no—
257D244—21no—
258D244—21no—
259D244—22no—
260D244—42no—
261D244—81no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—42no—
267C4×D61—42no—
268C4×D61C2×D812yes—
269C4×D61#13512yes—
270C4×D61C2×#4111yescharacteristic
271C4×D61C2×#4111yescharacteristic
272C4×D61H(5,𝔽2)11yescharacteristic
273C4×D61H(5,𝔽2)11yescharacteristic
274#92420—22no—
275#92420—41no—
276C8×C61—22no—
277#92418—22no—
278#23093—611nomaximal, Sylow
279C22×C61—41no—
280C22×C61—42no—
281C22×C61—41no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—41no—
285C22×C61C2×C4×D411yescharacteristic
286C2×D61—41no—
287C2×D61—42no—
288C2×D61—41no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—41no—
292C2×D61—81no—
293C2×D61—82no—
294C2×D61—81no—
295C2×D61—82no—
296C2×D61—82no—
297C2×D61—81no—
298C2×D61—82no—
299C2×D61—81no—
300C2×D61#54611yescharacteristic
301C2×D61#55011yescharacteristic
302C2×D61C22×D811yescharacteristic
303C2×D61C2×#13511yescharacteristic
304C2×D61#57611yescharacteristic
305C2×D61#57711yescharacteristic
306#6923—24no—
307#6923—42no—
308#6923—42no—
309#6923—82no—
310#6923—81no—
311C4×C61—21no—
312C4×C61—41no—
313C4×C61C4×D812yes—
314C4×C61C4×#4111yescharacteristic
315C4×C61#51811yescharacteristic
316Dic61—21no—
317Dic61—41no—
318Dic61C4×D812yes—
319Dic61#55311yescharacteristic
320Dic61#55511yescharacteristic
321C2×#459—611no—
322#2366—611no—
323#2354—611no—
324#1970—612no—
325#1957—611no—
326#1947—611no—
327#1925—612no—
328#1879—612no—
329C8×C4⋊C4—611no—
330C4×#102—611no—
331C4×#102—612no—
332C2×C61—82no—
333C2×C61—81no—
334C2×C61#236311yescharacteristic
335C2×C61C2×C4×D811yescharacteristic
336C2×C61#294611yescharacteristic
337D61—81no—
338D61—82no—
339D61#329411yescharacteristic
340D61#330511yescharacteristic
341D61#339111yescharacteristic
342D61#339411yescharacteristic
343C22×D8—612no—
344C2×#127—611no—
345C2×C4×D4—611no—
346C2×C4×D4—612no—
347C2×C4×D4—1221no—
348C2×#117—1221no—
349#459—612no—
350#459—611no—
351#459—611no—
352#459—611no—
353#459—612no—
354#459#692311yescharacteristic, complemented
355C2×#107—612no—
356C2×C4⋊C8—611no—
357C2×#102—612no—
358C2×#102—611no—
359C2×#102—612no—
360C2×#102—611no—
361C2×#102—612no—
362C2×C4×C8—611no—
363C2×C4×C8—612no—
364#390—612no—
365#390—612no—
366#390—1221no—
367#388—1222no—
368#386—1222no—
369#384—611no—
370#380—1221no—
371C4×C4⋊C4—611no—
372C4×C4⋊C4—612no—
373C4×C4⋊C4—611no—
374#340—612no—
375#340—611no—
376#340—611no—
377#336—612no—
378C61#2309311yescharacteristic, complemented, Sylow
379C22×D4—612no—
380C22×D4—611no—
381C22×D4—1221no—
382C22×D4—1221no—
383C23×C4—1221no—
384C23×C4—1222no—
385C2×D8—612no—
386C2×D8—612no—
387C2×D8—612no—
388C2×D8—2442no—
389C2×D8—2442no—
390C2×D8C2×#692312yescomplemented
391C22×C8—611no—
392C22×C8—612no—
393C22×C8—611no—
394#127—612no—
395#127—611no—
396#127—1221no—
397#127—1221no—
398#127C2×#692311yescharacteristic
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—611no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4—1224no—
405C4×D4—2442no—
406C4×D4—2444no—
407C4×D4C2×#692311yescharacteristic, complemented
408#117—2444no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—612no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1222no—
419C2×C22⋊C4—1222no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1222no—
422C2×C22⋊C4—1222no—
423C2×C42—611no—
424C2×C42—612no—
425C2×C42—1222no—
426C2×C42—1221no—
427#107—2442no—
428C4⋊C8—612no—
429C4⋊C8—611no—
430C4⋊C8C2×#692311yescharacteristic, complemented
431#102—612no—
432#102—612no—
433#102—612no—
434#102—1222no—
435#102—1224no—
436#102—1222no—
437#102—2442no—
438#102C2×#692312yescomplemented
439C4×C8—1221no—
440C4×C8—1221no—
441C4×C8—2442no—
442#95—612no—
443#95—1222no—
444#95—1221no—
445C24—1221no—
446C24—1222no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—612no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1222no—
453C2×D4—1221no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1222no—
460C2×D4—1221no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—4881no—
466C2×D4—4881no—
467C2×D4—2442no—
468C2×D4—2442no—
469C2×D4C22×#692312yes—
470C2×D4C22×#692311yescharacteristic
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—612no—
475C22×C4—611no—
476C22×C4—612no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—4882no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4—2444no—
488C22×C4—2444no—
489D8—42no—
490D8—2442no—
491D8—2442no—
492D8—2442no—
493C2×C8—612no—
494C2×C8—612no—
495C2×C8—1222no—
496C2×C8—1222no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8C22×#692312yes—
503C4⋊C4—614no—
504C4⋊C4—612no—
505C4⋊C4—611no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1221no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—4881no—
514C4⋊C4—2442no—
515C4⋊C4C22×#692311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—4882no—
521C22⋊C4—4882no—
522C22⋊C4—2444no—
523C22⋊C4—2444no—
524C22⋊C4—2444no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—1222no—
529C42—1222no—
530C42—2444no—
531C42—2442no—
532C42C22×#692311yescharacteristic
533C23—21no—
534C23—22no—
535C23—611no—
536C23—1221no—
537C23—1222no—
538C23—2441no—
539C23—2442no—
540C23—2441no—
541C23—2442no—
542C23—2442no—
543C23—2442no—
544C23—2441no—
545C23—2441no—
546C23—2442no—
547C23—2441no—
548C23—2442no—
549C23—2441no—
550D4—21no—
551D4—22no—
552D4—21no—
553D4—22no—
554D4—42no—
555D4—81no—
556D4—1222no—
557D4—1221no—
558D4—1221no—
559D4—1222no—
560D4—4881no—
561D4—4882no—
562D4—2442no—
563D4—2441no—
564D4—2441no—
565D4—2442no—
566D4—2444no—
567D4—2442no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—614no—
579C2×C4—611no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1221no—
589C2×C4—4888no—
590C2×C4—2442no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2442no—
594C2×C4—2441no—
595C2×C4—2442no—
596C2×C4—2441no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2442no—
603C2×C4D4×#692311yescharacteristic
604C2×C4D4×#692311yescharacteristic
605C2×C4C23×#692311yescharacteristic
606C8—22no—
607C8—1222no—
608C8—1222no—
609C8—2441no—
610C22—41no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—41no—
615C22—42no—
616C22—611no—
617C22—611no—
618C22—611no—
619C22—611no—
620C22—611no—
621C22—611no—
622C22—4882no—
623C22—4881no—
624C22—4881no—
625C22—4882no—
626C22—4881no—
627C22—4882no—
628C22—4882no—
629C22—4881no—
630C22—2441no—
631C22—2442no—
632C22—2442no—
633C22—2441no—
634C22—2441no—
635C22—2442no—
636C22C2×D4×#692311yescharacteristic
637C4—21no—
638C4—41no—
639C4—612no—
640C4—611no—
641C4—611no—
642C4—1224no—
643C4—1221no—
644C4—4881no—
645C4—4882no—
646C4—2442no—
647C4—2442no—
648C4—2441no—
649C4D8×#692312yes—
650C4#41×#692311yescharacteristic
651C4#1684082911yescharacteristic
652C2—81no—
653C2—82no—
654C2—611no—
655C2—611no—
656C2—611no—
657C2—611no—
658C2—4882no—
659C2—4881no—
660C2#2146234611yescharacteristic
661C2C2×D8×#692311yescharacteristic
662C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#459×D61C2
cosocleC2×C4×D61C24
hypercenter#459#6923
hypocenterC61#23093
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #21462349C2semidirect
2. #21462337C2semidirect
3. #21461966C2semidirect
4. #21461947C2semidirect
5. #21461930C2semidirect
6. #21461896C2semidirect
7. #21461814C2semidirect
8. #21461612C2semidirect
9. #102×#6923C2semidirect
10. C4×#14519839C2semidirect
39. #16839958C4semidirect
40. #16839957C4semidirect
41. #16839956C4semidirect
42. #16839955C4semidirect
43. #16839954C4semidirect
46. C61×#459C4semidirect
85. C2×D488C2×C4semidirect
86. C2×#11758199C2×C4semidirect
87. C2×#11758199C2×C4semidirect
95. C4×D244C2×C4semidirect
96. D4×Dic61C2×C4semidirect
97. #14519739C2×C4semidirect
103. C4⋊#92418C2×C4semidirect
104. #14519706C2×C4semidirect
105. #14519699C2×C4semidirect
106. #14519698C2×C4semidirect
107. #14519697C2×C4semidirect
108. C2×D8×C61C2×C4semidirect
110. C4×D4×C61C2×C4semidirect
111. C4⋊C8×C61C2×C4semidirect
112. #102×C61C2×C4semidirect
172. C4⋊#6923D8semidirect
354. #459#6923semidirect
378. C61#23093semidirect
390. C2×D8C2×#6923semidirect
407. C4×D4C2×#6923semidirect
430. C4⋊C8C2×#6923semidirect
438. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623492
#214623372
#214619662
#214619472
#214619302
#214618962
#214618142
#214616122
#102×#69232
C4×#145198392
#459×D612
#2309361