Finite Group Databasebeta

← #29646256

Subgroups — #29646256

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840476C211yesmaximal, characteristic
2#21454479C211yesmaximal, characteristic, complemented
3#21454473C211yesmaximal, characteristic, complemented
4#21444179C211yesmaximal, characteristic, complemented
5#21444169C212yesmaximal, complemented
6#21444169C212yesmaximal, complemented
7#21444155C211yesmaximal, characteristic, complemented
8#21444150C212yesmaximal, complemented
9#21444135C211yesmaximal, characteristic, complemented
10#21444130C212yesmaximal, complemented
11C61×#1471C211yesmaximal, characteristic, complemented
12#16840476—21no—
13#16840476—21no—
14#16840476—21no—
15#16840476—21no—
16#16840476—22no—
17#16840476—22no—
18C2×#14519776C411yescharacteristic
19C2×#14519764C412yes—
20C2×#14519763C2212yes—
21C2×#14519749C412yes—
22C2×#14519748C411yescharacteristic
23C2×D4×Dic61C411yescharacteristic
24C2×C4×C22⋊D61C2211yescharacteristic
25C2×#14519736C2211yescharacteristic
26C2×#14519735C411yescharacteristic
27C2×#14519733C2212yes—
28#16839820—22no—
29#16839820—22no—
30#16839816C2212yes—
31#16839816C2212yes—
32#16839812C2212yes—
33#16839812C2212yes—
34#16839790—21no—
35#16839788—21no—
36#16839726C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38#16839720—21no—
39#16839717—21no—
40#16839487C2211yescharacteristic
41#16839487C2212yes—
42#16839487C2211yescharacteristic
43#16839486C2212yes—
44#16839486C2212yes—
45#16839485C2211yescharacteristic
46#16839485C2211yescharacteristic
47#16839485C2212yes—
48C2×#121×C61C2211yescharacteristic
49C61×#407C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C61×#323C2212yes—
52C61×#323C2212yes—
53C22×Dic122C2×C412yes—
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C412yes—
56C23×Dic61C2×C412yes—
57C22×C4×D61C2×C411yescharacteristic
58C2×#11758194—21no—
59C22×#92418—21no—
60#14519776—22no—
61#14519776—21no—
62#14519776—21no—
63#14519764—22no—
64#14519764—22no—
65#14519764—22no—
66#14519764—22no—
67#14519763—22no—
68#14519763—22no—
69#14519763—22no—
70#14519763—22no—
71#14519749—22no—
72#14519749—22no—
73#14519749—22no—
74#14519749—22no—
75#14519748—22no—
76#14519748—21no—
77#14519748—21no—
78D4×Dic61—22no—
79D4×Dic61—21no—
80D4×Dic61—21no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85#14519736D411yescharacteristic
86#14519736D411yescharacteristic
87#14519736D411yescharacteristic
88#14519736D411yescharacteristic
89#14519736D412yes—
90#14519736D412yes—
91#14519735—22no—
92#14519735—21no—
93#14519735—21no—
94#14519733—22no—
95#14519733—22no—
96#14519733—22no—
97#14519733—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196C2×C412yes—
101C2×#11758196C2311yescharacteristic
102C2×C22⋊Dic61C2×C412yes—
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C412yes—
105C2×C22⋊Dic61C2×C412yes—
106C2×#11758198C2×C412yes—
107C2×#11758198C2311yescharacteristic
108C2×C4×Dic61C2×C412yes—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2312yes—
111#14519706—22no—
112#14519706—22no—
113#14519706—22no—
114#14519706—22no—
115C22⋊#92418—21no—
116C22⋊#92418—21no—
117C22⋊#92418C2311yescharacteristic
118C22⋊#92418C2311yescharacteristic
119C22⋊#92418C2312yes—
120#14519687—22no—
121#14519687—22no—
122C8×Dic61—22no—
123C8×Dic61—22no—
124C22×D4×C61C2×C411yescharacteristic
125C22×D4×C61C2×C412yes—
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2312yes—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137C22⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61C2312yes—
140C24×C61C22×C412yes—
141C24×C61C22×C411yescharacteristic
142C23×D61C22×C411yescharacteristic
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61—82no—
149C22×C4×C61—42no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—21no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—82no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—24no—
167C22×Dic61—42no—
168C22×Dic61C22×C412yes—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C412yes—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—42no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—82no—
179M16×C61—42no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—22no—
183C2×C8×C61—42no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊Dic61—21no—
189C22⋊Dic61—21no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61C22⋊C412yes—
195C22⋊Dic61C22⋊C412yes—
196C22⋊Dic61C22⋊C412yes—
197C22⋊Dic61C22⋊C412yes—
198#11758198—21no—
199#11758198—21no—
200#11758198—22no—
201#11758198—22no—
202C4⋊Dic61C22⋊C412yes—
203C4⋊Dic61C22⋊C411yescharacteristic
204C4⋊Dic61C22⋊C411yescharacteristic
205C4⋊Dic61C22⋊C412yes—
206C4⋊Dic61C22⋊C411yescharacteristic
207C4⋊Dic61C22⋊C411yescharacteristic
208#11758196—21no—
209#11758196—21no—
210#11758196—22no—
211#11758196—22no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220#11758194—42no—
221C2×#92418—21no—
222C2×#92418—22no—
223C2×#92418—21no—
224C2×#92418—42no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61C2×C22⋊C411yescharacteristic
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—41no—
241C22×D61—41no—
242D4×C61—42no—
243D4×C61—42no—
244D4×C61—82no—
245D4×C61—82no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—42no—
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C22⋊D61—42no—
259C22⋊D61—42no—
260C22⋊D61—82no—
261C22⋊D61—82no—
262C2×Dic61—21no—
263C2×Dic61—22no—
264C2×Dic61—21no—
265C2×Dic61—22no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—42no—
269C2×Dic61—44no—
270C2×Dic61—44no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61C2×C22⋊C412yes—
274C2×Dic61C2×C22⋊C412yes—
275C2×Dic61C2×C22⋊C412yes—
276C2×Dic61C2×C22⋊C412yes—
277C2×Dic61#13112yes—
278C4×D61—42no—
279C4×D61—42no—
280Dic122—82no—
281Dic122—82no—
282C8×C61—41no—
283C8×C61—41no—
284C8×C61—42no—
285#92418—41no—
286#92418—41no—
287#92418—42no—
288#17418—611nomaximal, Sylow
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—82no—
303C22×C61—82no—
304C22×C61C22×C22⋊C411yescharacteristic
305C22×C61C2×#13111yescharacteristic
306C22×C61#56811yescharacteristic
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—81no—
311C2×D61—81no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—42no—
316C4×C61#41012yes—
317Dic61—22no—
318Dic61—22no—
319Dic61—22no—
320Dic61—22no—
321Dic61—22no—
322Dic61—41no—
323Dic61—41no—
324C2×#555—611no—
325#2924—611no—
326#2924—611no—
327#1471—611no—
328#1471D6111yescharacteristic, complemented
329#1469—612no—
330#1469—612no—
331#1465—611no—
332#1464—612no—
333#1459—611no—
334#1458—612no—
335C2×C61—21no—
336C2×C61—21no—
337C2×C61—41no—
338C2×C61—41no—
339C2×C61—82no—
340C2×C61#288011yescharacteristic
341C2×C61C2×#41011yescharacteristic
342C2×C61#288811yescharacteristic
343D61—81no—
344#555—1221no—
345#555—1221no—
346#555—1221no—
347#555—1221no—
348#555—1222no—
349#555—1222no—
350C2×C4⋊Q8—611no—
351C2×#124—612no—
352C2×#124—612no—
353C2×#121—611no—
354C2×#121—612no—
355C2×#121C2×D6111yescharacteristic
356C2×C4×D4—611no—
357C2×C4×D4—611no—
358C2×#117—611no—
359C2×#117—611no—
360C2×#117—612no—
361#433—1222no—
362#433—1222no—
363#432—612no—
364#432—612no—
365#431—612no—
366#431—612no—
367#424—1221no—
368#424—1221no—
369#407—611no—
370#407C2×D6111yescharacteristic
371C2×C22⋊C8—611no—
372C2×C22⋊C8C2×D6111yescharacteristic
373#405—1221no—
374#405—1221no—
375#324—611no—
376#324—612no—
377#324—611no—
378#323—612no—
379#323—612no—
380#323—611no—
381#323—611no—
382#323—612no—
383#323C2×D6112yes—
384#323C2×D6112yes—
385C61#1741811yescharacteristic, complemented, Sylow
386C22×Q8—612no—
387C22×D4—611no—
388C22×D4—612no—
389C22×D4C4×D6111yescharacteristic
390C22×D4C4×D6112yes—
391C23×C4—612no—
392C23×C4—611no—
393C23×C4C22×D6111yescharacteristic
394C2×M16—21no—
395C2×M16—1221no—
396C22×C8—21no—
397C22×C8—1221no—
398C4⋊Q8—1222no—
399C4⋊Q8—1221no—
400C4⋊Q8—1221no—
401#124—1222no—
402#124—1222no—
403#124—1222no—
404#124—1222no—
405#124—1222no—
406#124—1222no—
407#124—1222no—
408#124—1222no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—1222no—
414#121—1222no—
415#121—1222no—
416#121—1222no—
417#121—1222no—
418#121—1221no—
419#121—1221no—
420C4×D4—1222no—
421C4×D4—1221no—
422C4×D4—1221no—
423C4×D4—1221no—
424C4×D4—1221no—
425C4×D4—1221no—
426C4×D4—1221no—
427#117—611no—
428#117—611no—
429#117—611no—
430#117—611no—
431#117—612no—
432#117—612no—
433#117—1222no—
434#117—1222no—
435#117—1222no—
436#117—1222no—
437#117—1222no—
438#117—1221no—
439#117—1221no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—612no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4C4×D6111yescharacteristic
445C2×C22⋊C4—612no—
446C2×C22⋊C4—612no—
447C2×C22⋊C4—612no—
448C2×C22⋊C4—611no—
449C2×C22⋊C4—612no—
450C2×C22⋊C4—611no—
451C2×C22⋊C4C22×D6112yes—
452C2×C42—612no—
453C2×C42—612no—
454C2×C42—611no—
455C4⋊C8—1222no—
456C4⋊C8—1222no—
457C4⋊C8—1222no—
458C4⋊C8—1222no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8—611no—
462C22⋊C8—611no—
463C22⋊C8—612no—
464C22⋊C8—1221no—
465C22⋊C8—1221no—
466C22⋊C8C22×D6111yescharacteristic
467C22⋊C8C22×D6111yescharacteristic
468C22⋊C8C22×D6112yes—
469#97—1222no—
470#97—1222no—
471C4×C8—1222no—
472C4×C8—1222no—
473C24—611no—
474C24C2×C4×D6112yes—
475C24C2×C4×D6111yescharacteristic
476C2×Q8—1222no—
477C2×Q8—1222no—
478C2×Q8—4882no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—82no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1221no—
489C2×D4—1221no—
490C2×D4—4882no—
491C2×D4—2441no—
492C22×C4—42no—
493C22×C4—612no—
494C22×C4—611no—
495C22×C4—612no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1224no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—2442no—
504C22×C4—2442no—
505C22×C4C2×C4×D6111yescharacteristic
506C22×C4C2×C4×D6112yes—
507C22×C4D4×D6111yescharacteristic
508C22×C4D4×D6111yescharacteristic
509C22×C4D4×D6111yescharacteristic
510C22×C4D4×D6111yescharacteristic
511C22×C4C23×D6111yescharacteristic
512M16—42no—
513M16—2442no—
514C2×C8—21no—
515C2×C8—22no—
516C2×C8—21no—
517C2×C8—42no—
518C2×C8—1221no—
519C2×C8—1222no—
520C2×C8—1221no—
521C2×C8—2442no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—612no—
525C4⋊C4—611no—
526C4⋊C4—611no—
527C4⋊C4—612no—
528C4⋊C4—611no—
529C4⋊C4—611no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—612no—
537C22⋊C4—612no—
538C22⋊C4—612no—
539C22⋊C4—612no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1221no—
547C22⋊C4—1221no—
548C22⋊C4—1221no—
549C22⋊C4—1221no—
550C42—612no—
551C42—612no—
552C42—612no—
553C42—612no—
554C42—1222no—
555C42—1222no—
556C42—1221no—
557C42—1221no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—42no—
566C23—42no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—2441no—
571C23—2441no—
572C23C22⋊C4×D6111yescharacteristic
573C23C22⋊C4×D6111yescharacteristic
574C23C22×C4×D6111yescharacteristic
575Q8—4882no—
576Q8—4882no—
577D4—42no—
578D4—42no—
579D4—82no—
580D4—82no—
581D4—4882no—
582D4—4882no—
583D4—2442no—
584D4—2442no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—612no—
594C2×C4—612no—
595C2×C4—612no—
596C2×C4—612no—
597C2×C4—612no—
598C2×C4—1221no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2444no—
607C2×C4—2444no—
608C2×C4—2442no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4C22⋊C4×D6111yescharacteristic
612C2×C4C22⋊C4×D6111yescharacteristic
613C2×C4C2×D4×D6111yescharacteristic
614C2×C4C2×D4×D6111yescharacteristic
615C8—41no—
616C8—41no—
617C8—42no—
618C8—2441no—
619C8—2441no—
620C8—2442no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—82no—
635C22—82no—
636C22—4881no—
637C22—4881no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22C2×C22⋊C4×D6111yescharacteristic
642C22#131×D6111yescharacteristic
643C22#1684052711yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—42no—
648C4—1222no—
649C4—1222no—
650C4—1222no—
651C4—1222no—
652C4—1222no—
653C4—2441no—
654C4—2441no—
655C4#1683973412yes—
656C2—21no—
657C2—21no—
658C2—41no—
659C2—41no—
660C2—82no—
661C2—4881no—
662C2#2145426711yescharacteristic
663C2C2×#1683973411yescharacteristic
664C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1471C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840476C2
cosocleC22×C4×C61C24
hypercenter#1471D61
hypocenterC61#17418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #21454479C2semidirect
3. #21454473C2semidirect
4. #21444179C2semidirect
5. #21444169C2semidirect
6. #21444169C2semidirect
7. #21444155C2semidirect
8. #21444150C2semidirect
9. #21444135C2semidirect
10. #21444130C2semidirect
11. C61×#1471C2semidirect
328. #1471D61semidirect
385. C61#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#168404762
#214544792
#214544732
#214441792
#214441692
#214441552
#214441502
#214441352
#214441302
C61×#14712
#1741861