Finite Group Databasebeta

← #29646243

Subgroups — #29646243

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840453C211yesmaximal, characteristic
2#21454472C212yesmaximal, complemented
3#21444186C212yesmaximal, complemented
4#21444173C212yesmaximal, complemented
5#21444166C212yesmaximal
6#21444163C211yesmaximal, characteristic, complemented
7#21444152C211yesmaximal, characteristic, complemented
8#21444147C211yesmaximal, characteristic, complemented
9#21444132C211yesmaximal, characteristic, complemented
10#324×D61C211yesmaximal, characteristic, complemented
11C61×#1461C211yesmaximal, characteristic, complemented
12#16840453—22no—
13#16840453—22no—
14#16840453—22no—
15#16840453—22no—
16C2×#14519771C411yescharacteristic
17C2×#14519771C2211yescharacteristic
18C2×#14519769C411yescharacteristic
19C2×#14519767C411yescharacteristic
20C2×#14519767C2211yescharacteristic
21C2×#14519762C411yescharacteristic
22C2×#14519762C2211yescharacteristic
23C2×#14519753C411yescharacteristic
24C2×#14519753C411yescharacteristic
25C2×C4×D244C411yescharacteristic
26C2×#14519735C2211yescharacteristic
27C2×#14519734C411yescharacteristic
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839822—22no—
31#16839821—22no—
32#16839819C2212yes—
33#16839816C2212yes—
34#16839812C2212yes—
35#16839787—22no—
36#16839724C2212yes—
37C22⋊C8×D61C2212yes—
38#16839716—22no—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839488C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×C4×Q8×C61C2211yescharacteristic
47C61×#431C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#324C2212yes—
51C22×D244C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C2×#11758189—22no—
57C2×C8×D61—22no—
58#14519771—22no—
59#14519771—22no—
60#14519771—22no—
61#14519771—22no—
62#14519769—22no—
63#14519769—22no—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519767—22no—
68#14519762—22no—
69#14519762—22no—
70#14519762—22no—
71#14519762—22no—
72#14519753—22no—
73#14519753—22no—
74#14519753—22no—
75#14519753—22no—
76C4×D244—21no—
77C4×D244—21no—
78C4×D244—21no—
79C4×D244—21no—
80#14519735—22no—
81#14519735—22no—
82#14519734—21no—
83#14519734—21no—
84#14519734—21no—
85#14519734—21no—
86#14519734D412yes—
87#14519734D412yes—
88#14519734D412yes—
89#14519734D412yes—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2311yescharacteristic
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2311yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C4⋊#92418—22no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418C2312yes—
119C22⋊#92418C2312yes—
120#14519689—22no—
121#14519689—22no—
122#14519688—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C4×Q8×C61—22no—
127C4×Q8×C61—22no—
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C42×C61C2×C411yescharacteristic
132C2×C42×C61C2×C411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—22no—
135C22⋊C8×C61C2312yes—
136C22⋊C8×C61C2312yes—
137C4×C8×C61—22no—
138C23×D61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C2×Q8×C61—22no—
141C2×Q8×C61—22no—
142C2×Q8×C61—41no—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—42no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—42no—
168C2×C4×D61—41no—
169C2×C4×D61—41no—
170C2×C4×D61—42no—
171C2×C4×D61C2×D412yes—
172C2×C4×D61C2×D412yes—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61C2×D412yes—
183C42×C61C2×D412yes—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198C22⋊C411yescharacteristic
193#11758198C22⋊C411yescharacteristic
194#11758198C22⋊C411yescharacteristic
195#11758198C22⋊C411yescharacteristic
196#11758198C22⋊C412yes—
197#11758198C22⋊C412yes—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202#11758196—21no—
203#11758196—21no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—21no—
208#11758196—21no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196C22⋊C412yes—
213#11758196C22⋊C412yes—
214#11758196C22⋊C412yes—
215#11758196C22⋊C412yes—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C2×#92418—22no—
221C2×#92418—22no—
222#11758189—44no—
223C8×D61—44no—
224C23×C61C23×C411yescharacteristic
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—22no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61C2×C22⋊C411yescharacteristic
235C22×D61C2×C22⋊C411yescharacteristic
236Q8×C61—44no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C412yes—
253C2×C4×C61#13112yes—
254C2×C4×C61C22×D412yes—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C412yes—
269C2×Dic61C2×C22⋊C412yes—
270D244—42no—
271D244—42no—
272C4×D61—24no—
273C4×D61—42no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278C4×D61—42no—
279C4×D61—42no—
280C8×C61—42no—
281C8×C61—42no—
282#92418—42no—
283#92418—42no—
284#17417—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C2×#13111yescharacteristic
289C22×C61#56811yescharacteristic
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61#41012yes—
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311Dic61—21no—
312Dic61—21no—
313Dic61—22no—
314Dic61—22no—
315Dic61—41no—
316Dic61—41no—
317Dic61—41no—
318C2×#552—611no—
319#2924—612no—
320#1473—612no—
321#1470—612no—
322#1468—612no—
323#1467—611no—
324#1464—611no—
325#1463—611no—
326#1461D6111yescharacteristic, complemented
327#1458—611no—
328C2×#324—611no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61#288011yescharacteristic
332C2×C61C2×#41011yescharacteristic
333C2×C61#288911yescharacteristic
334D61—22no—
335D61—41no—
336D61—81no—
337#552—1222no—
338#552—1222no—
339#552—1222no—
340#552—1222no—
341C2×#126—611no—
342C2×#126—611no—
343C2×#125—611no—
344C2×#125—611no—
345C2×#125—611no—
346C2×#123—611no—
347C2×#123—611no—
348C2×C22⋊Q8—611no—
349C2×C22⋊Q8—611no—
350C2×C4×Q8C2×D6111yescharacteristic
351C2×C4×D4—611no—
352C2×#117—611no—
353C2×#117—611no—
354C2×#117—611no—
355C22×C4⋊C4—611no—
356#433—1222no—
357#433—1222no—
358#432—612no—
359#432—612no—
360#431—612no—
361#431C2×D6112yes—
362#424—1222no—
363#407—612no—
364C2×C22⋊C8—612no—
365#405—1222no—
366#324—611no—
367#324—611no—
368#324—612no—
369#324—612no—
370#324—612no—
371#324C2×D6111yescharacteristic
372#324C2×D6111yescharacteristic
373#324C2×D6112yes—
374#323—612no—
375#323—612no—
376C61#1741711yescharacteristic, complemented, Sylow
377C22×Q8C4×D6111yescharacteristic
378C22×D4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C2×M16—1222no—
384C22×C8—1222no—
385#126—1222no—
386#126—1222no—
387#126—1222no—
388#126—1222no—
389#125—1222no—
390#125—1222no—
391#125—1222no—
392#125—1222no—
393#125—1222no—
394#125—1222no—
395#123—1222no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8—1222no—
402C22⋊Q8—1222no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×D4—1221no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409#117—612no—
410#117—612no—
411#117—612no—
412#117—612no—
413#117—1221no—
414#117—1221no—
415#117—1221no—
416#117—1221no—
417#117—1222no—
418#117—1222no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4C4×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C4⋊C4C22×D6111yescharacteristic
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—611no—
440C2×C22⋊C4—611no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42C4×D6111yescharacteristic
448C2×C42C4×D6111yescharacteristic
449C2×C42C22×D6111yescharacteristic
450C4⋊C8—22no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C22⋊C8—612no—
455C22⋊C8—612no—
456C22⋊C8—1222no—
457C22⋊C8—1222no—
458C22⋊C8C22×D6112yes—
459C22⋊C8C22×D6112yes—
460#97—1222no—
461#97—1222no—
462C4×C8—22no—
463C4×C8—1222no—
464C24—611no—
465C24—611no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—41no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—2442no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—2441no—
489C22×C4—2441no—
490C22×C4—2442no—
491C22×C4—2442no—
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4C2×C4×D6111yescharacteristic
498C22×C4C23×D6111yescharacteristic
499M16—2444no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—2444no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—612no—
509C4⋊C4—612no—
510C4⋊C4—612no—
511C4⋊C4—612no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1222no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1222no—
526C22⋊C4—611no—
527C22⋊C4—611no—
528C22⋊C4—611no—
529C22⋊C4—611no—
530C22⋊C4—612no—
531C22⋊C4—612no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1222no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1222no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—612no—
545C42—612no—
546C42—1221no—
547C42—1221no—
548C42D4×D6112yes—
549C42D4×D6112yes—
550C23—611no—
551C23—611no—
552C23—1222no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—2441no—
559C23—2441no—
560C23—2441no—
561C23C22×C4×D6111yescharacteristic
562Q8—44no—
563D4—2442no—
564D4—2442no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—1224no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4C22⋊C4×D6111yescharacteristic
602C2×C4C22⋊C4×D6111yescharacteristic
603C2×C4C22⋊C4×D6112yes—
604C2×C4#1451978312yes—
605C2×C4C2×D4×D6112yes—
606C8—42no—
607C8—42no—
608C8—2442no—
609C8—2442no—
610C22—21no—
611C22—21no—
612C22—612no—
613C22—1221no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1221no—
618C22—4881no—
619C22—4881no—
620C22—2442no—
621C22—2442no—
622C22—2441no—
623C22—2441no—
624C22—2441no—
625C22C2×C22⋊C4×D6111yescharacteristic
626C22C2×#1451978311yescharacteristic
627C22#1684052811yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—1221no—
637C4—1221no—
638C4—1222no—
639C4—1222no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C2—21no—
644C2—21no—
645C2—1222no—
646C2—4881no—
647C2—2441no—
648C2#2145426511yescharacteristic
649C2#410×D6111yescharacteristic
650C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1461C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1461D61
hypocenterC61#17417
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #21454472C2semidirect
3. #21444186C2semidirect
4. #21444173C2semidirect
6. #21444163C2semidirect
7. #21444152C2semidirect
8. #21444147C2semidirect
9. #21444132C2semidirect
10. #324×D61C2semidirect
11. C61×#1461C2semidirect
326. #1461D61semidirect
376. C61#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#168404532
#214544722
#214441862
#214441732
#214441662
#214441632
#214441522
#214441472
#214441322
#324×D612
C61×#14612
#1741761