Finite Group Databasebeta

← #29646883

Subgroups — #29646883

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459377C211yesmaximal, characteristic
2#21454775C211yesmaximal, characteristic, complemented
3#21454487C211yesmaximal, characteristic, complemented
4#21444276C212yesmaximal, complemented
5#21444273C211yesmaximal, characteristic, complemented
6#21444250C212yesmaximal, complemented
7#21444224C212yesmaximal, complemented
8#21444223C211yesmaximal, characteristic, complemented
9#21444198C212yesmaximal, complemented
10C2×D4⋊#92418C211yesmaximal, characteristic, complemented
11C61×#1486C211yesmaximal, characteristic, complemented
12#16840482C411yescharacteristic
13#16840477C411yescharacteristic
14#16840469C411yescharacteristic
15#16840458—21no—
16#16840452—21no—
17#16840447C412yes—
18#16840438—22no—
19#16840416C411yescharacteristic
20#16840406C412yes—
21#16840319C2211yescharacteristic
22#16840294C2212yes—
23#16840292—22no—
24#16840273—21no—
25C4×#11758222C2211yescharacteristic
26C4×#11758224C2212yes—
27C2×#14519736—21no—
28#16839886—21no—
29#16839827—21no—
30#16839825—22no—
31#16839822—22no—
32#16839818C2212yescomplemented
33#16839814C2212yescomplemented
34#16839813C2212yescomplemented
35C2×C4⋊#92418C2211yescharacteristic
36#16839730—21no—
37#16839720—21no—
38C2×C4×#92418C2211yescharacteristic
39C4×C8×D61C2212yescomplemented
40#16839494C2212yescomplemented
41#16839494C2212yescomplemented
42#16839492C2212yescomplemented
43#16839492C2212yescomplemented
44D4⋊#92418C2211yescharacteristic
45D4⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C61×#431C2211yescharacteristic
50C61×#423C2211yescharacteristic
51C61×D4⋊C8C2212yes—
52C61×D4⋊C8C2212yes—
53C2×#11758222D411yescharacteristic
54C2×#11758224C2×C412yes—
55C22×#92418—21no—
56C22×#92418—21no—
57C2×C8×D61—22no—
58#14519777C2×C411yescharacteristic
59#14519777C2×C411yescharacteristic
60#14519772—22no—
61#14519770—22no—
62#14519770—22no—
63#14519769—21no—
64#14519768C2×C412yes—
65#14519767—22no—
66#14519764C2×C412yes—
67#14519763—22no—
68#14519761—22no—
69#14519760—22no—
70#14519759—22no—
71#14519758—22no—
72#14519757C2×C412yes—
73#14519756—21no—
74#14519756—21no—
75#14519756—21no—
76#14519756C2×C412yes—
77#14519754—22no—
78#14519751—21no—
79#14519751—21no—
80#14519749—22no—
81#14519748C2×C412yes—
82#14519746—22no—
83C4×Dic122—21no—
84C4×Dic122C2×C411yescharacteristic
85C4×Dic122D411yescharacteristic
86C4×Dic122C2312yes—
87#14519742C2×C412yes—
88C4×D244C2×C411yescharacteristic
89C4×D244D411yescharacteristic
90D4×Dic61C2×C412yes—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93C4×C22⋊D61C2×C412yes—
94C4×C22⋊D61D412yes—
95#14519737—22no—
96#14519736—21no—
97#14519736—22no—
98#14519736—21no—
99#14519736—21no—
100#14519736—22no—
101#14519736D411yescharacteristic
102#14519735C2×C412yes—
103#14519734D412yes—
104#14519733—22no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61—21no—
107C2×C22⋊Dic61—22no—
108C2×C4×Dic61—22no—
109C42×D61C2312yes—
110C4⋊#92418—21no—
111C4⋊#92418C2311yescharacteristic
112C4⋊#92418C2311yescharacteristic
113#14519706—22no—
114#14519689—22no—
115#14519689—22no—
116#14519689—22no—
117#14519687—22no—
118C4×#92418—21no—
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C8×Dic61—22no—
122C8×Dic61—22no—
123C22×D4×C61C2×C411yescharacteristic
124C23×C4×C61—21no—
125C2×M16×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61C2×C411yescharacteristic
129C4×D4×C61C2×C411yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C22⋊C8×C61—21no—
139C4×C8×C61C2312yes—
140C24×C61—21no—
141C2×D4×C61—22no—
142C2×D4×C61—21no—
143C2×D4×C61—41no—
144C2×D4×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61C22⋊C412yes—
159C22×Dic61—22no—
160C22×Dic61—22no—
161#11758224—24no—
162#11758224—42no—
163#11758222—22no—
164#11758222—22no—
165C2×D244C22⋊C411yescharacteristic
166C2×C4×D61C22×C412yes—
167C2×C4×D61C2×D412yes—
168C2×C4×D61C2×D412yes—
169C2×Dic122—21no—
170C2×Dic122C22⋊C411yescharacteristic
171C2×Dic122C22×C412yes—
172M16×C61—42no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C22×C411yescharacteristic
177C4⋊C4×C61C22×C411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C42×C61C22×C411yescharacteristic
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61C2411yescharacteristic
186C22⋊Dic61—22no—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61C22⋊C412yes—
192#11758198—22no—
193#11758198—22no—
194#11758198C22⋊C412yes—
195#11758198C22⋊C412yes—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61C22⋊C411yescharacteristic
202C4⋊Dic61C22⋊C411yescharacteristic
203C4⋊Dic61C22×C412yes—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196C22⋊C412yes—
209#11758196C22⋊C412yes—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61C22×C412yes—
214C4×Dic61C2×D412yes—
215C4×Dic61C2×D412yes—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—42no—
221C2×#92418—42no—
222C8×D61—44no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—81no—
228C23×C61C2×C22⋊C411yescharacteristic
229C22×D61C2×C22⋊C412yes—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—42no—
234D4×C61#13112yes—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61#13512yes—
251C2×C4×C61#13512yes—
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—24no—
256C22⋊D61—44no—
257C22⋊D61—82no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—44no—
261C2×Dic61—82no—
262C2×Dic61C2×C22⋊C412yes—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C2×C22⋊C412yes—
265D244—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—42no—
271Dic122—22no—
272Dic122—22no—
273Dic122—22no—
274Dic122—81no—
275C8×C61—42no—
276C8×C61—42no—
277#92418—22no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#17508—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—22no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—84no—
291C22×C61#41612yes—
292C22×C61C22×C22⋊C411yescharacteristic
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61#41612yes—
302C4×C61C2×#13111yescharacteristic
303C4×C61#56811yescharacteristic
304C4×C61C2×#13511yescharacteristic
305C4×C61C2×#13511yescharacteristic
306Dic61—22no—
307Dic61—22no—
308Dic61—22no—
309Dic61—42no—
310Dic61—42no—
311#3475—611no—
312C8×#41—611no—
313#2925—611no—
314#1494—612no—
315#1493—611no—
316#1488—612no—
317#1486D6111yescharacteristic, complemented
318#1482—612no—
319#1481—611no—
320#1476—612no—
321C2×D4⋊C8—611no—
322C2×C61—22no—
323C2×C61—42no—
324C2×C61—81no—
325C2×C61#288011yescharacteristic
326C2×C61C2×#41611yescharacteristic
327C2×C61#290111yescharacteristic
328D61—42no—
329#556—611no—
330#555—611no—
331#554—611no—
332#553—1221no—
333#552—612no—
334#552—1221no—
335#551—1222no—
336#547—611no—
337#546—612no—
338#533—611no—
339#529—612no—
340#529—1222no—
341#525—1221no—
342C4×#41—611no—
343C4×#41—612no—
344C2×C4×D4C2×D6111yescharacteristic
345C2×#117—1221no—
346C8×Q8—1221no—
347C8×D4—1222no—
348C8×D4—1221no—
349#433—1222no—
350#432—612no—
351#431—612no—
352#431—612no—
353#431C2×D6111yescharacteristic
354#423C2×D6111yescharacteristic
355C2×C4⋊C8—611no—
356#408—1221no—
357#405—1221no—
358C2×C4×C8—611no—
359C2×C4×C8—612no—
360Q8⋊C8—612no—
361Q8⋊C8—612no—
362Q8⋊C8—612no—
363Q8⋊C8—612no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8C2×D6112yes—
369D4⋊C8C2×D6112yes—
370C61#1750811yescharacteristic, complemented, Sylow
371C2×#41—611no—
372C2×#41—612no—
373C22×D4C4×D6111yescharacteristic
374C23×C4—21no—
375C2×M16—21no—
376C22×C8—1222no—
377C22×C8—1221no—
378C22×C8—1221no—
379C4⋊Q8—611no—
380C4⋊Q8—611no—
381#126—1222no—
382#126—1222no—
383#126—1222no—
384#125—612no—
385#125—1222no—
386#125—1221no—
387#124—612no—
388#124—1222no—
389#123—1222no—
390#123—1222no—
391#123—1222no—
392#123—1222no—
393C22⋊Q8—612no—
394C22⋊Q8—612no—
395C22⋊Q8—1222no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398C22⋊Q8—1221no—
399#121—612no—
400#121—1222no—
401#121—1221no—
402#121—1221no—
403#120—1222no—
404C4×Q8—611no—
405C4×Q8—611no—
406C4×Q8—612no—
407C4×Q8—612no—
408C4×Q8—1221no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—612no—
412C4×D4—612no—
413C4×D4—612no—
414C4×D4—611no—
415C4×D4—611no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1222no—
419C4×D4C4×D6111yescharacteristic
420C4×D4C4×D6111yescharacteristic
421C4×D4C22×D6111yescharacteristic
422C4×D4C22×D6111yescharacteristic
423#117—611no—
424#117—612no—
425#117—612no—
426#117—1222no—
427#117—1222no—
428#117—1222no—
429#117—1221no—
430#117—1221no—
431#117—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4C4×D6111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—1222no—
437C2×C42—612no—
438C2×C42—1222no—
439C2×C42C22×D6111yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—611no—
443C4⋊C8—611no—
444C4⋊C8—1222no—
445C4⋊C8—1221no—
446C4⋊C8C22×D6112yes—
447C22⋊C8—21no—
448C22⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451#97—1222no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—1222no—
455C4×C8—1222no—
456C4×C8—1221no—
457C4×C8C22×D6112yes—
458C24—21no—
459#41—1222no—
460#41—1222no—
461#41—1224no—
462#41—2442no—
463C2×Q8—611no—
464C2×Q8—612no—
465C2×Q8—1221no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—612no—
470C2×D4—611no—
471C2×D4—1222no—
472C2×D4—1222no—
473C2×D4C2×C4×D6111yescharacteristic
474C2×D4C2×C4×D6111yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4D4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490M16—42no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—2444no—
498C2×C8—2442no—
499C2×C8—2442no—
500C4⋊C4—21no—
501C4⋊C4—611no—
502C4⋊C4—611no—
503C4⋊C4—612no—
504C4⋊C4—612no—
505C4⋊C4—612no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1222no—
514C4⋊C4—1221no—
515C4⋊C4C2×C4×D6111yescharacteristic
516C4⋊C4C2×C4×D6111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—612no—
522C22⋊C4—612no—
523C22⋊C4—612no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C42—612no—
532C42—612no—
533C42—612no—
534C42—1222no—
535C42—1222no—
536C42—1222no—
537C42C2×C4×D6111yescharacteristic
538C42D4×D6111yescharacteristic
539C42D4×D6111yescharacteristic
540C42C23×D6111yescharacteristic
541C23—21no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—81no—
546C23—612no—
547C23C22⋊C4×D6111yescharacteristic
548Q8—1222no—
549Q8—1222no—
550Q8—1222no—
551Q8—4881no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—42no—
556D4—1224no—
557D4—1222no—
558D4—4882no—
559D4—2444no—
560D4#1451978512yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—612no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—4882no—
583C2×C4—2442no—
584C2×C4—2444no—
585C2×C4C22⋊C4×D6111yescharacteristic
586C2×C4C22⋊C4×D6111yescharacteristic
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4#1451979612yes—
589C2×C4#1451979812yes—
590C2×C4C22×C4×D6111yescharacteristic
591C2×C4C2×D4×D6111yescharacteristic
592C2×C4C2×D4×D6111yescharacteristic
593C8—42no—
594C8—42no—
595C8—1222no—
596C8—2441no—
597C8—2441no—
598C8—2441no—
599C22—21no—
600C22—21no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—84no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22#1683975512yes—
612C22C2×C22⋊C4×D6111yescharacteristic
613C4—21no—
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—1222no—
619C4—1222no—
620C4—1222no—
621C4—2442no—
622C4—2442no—
623C4#1683975512yes—
624C4C2×#1451978511yescharacteristic
625C4#1684052811yescharacteristic
626C4C2×#1451979611yescharacteristic
627C4C2×#1451979811yescharacteristic
628C2—22no—
629C2—42no—
630C2—81no—
631C2—2442no—
632C2#2145426911yescharacteristic
633C2C2×#1683975511yescharacteristic
634C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1486C2
socleC22×C61C22×C22⋊C4
prime radical#21459377C2
cosocleC42×C61C24
hypercenter#1486D61
hypocenterC61#17508
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #21454775C2semidirect
3. #21454487C2semidirect
4. #21444276C2semidirect
5. #21444273C2semidirect
6. #21444250C2semidirect
7. #21444224C2semidirect
8. #21444223C2semidirect
9. #21444198C2semidirect
10. C2×D4⋊#92418C2semidirect
11. C61×#1486C2semidirect
32. #16839818C22semidirect
33. #16839814C22semidirect
34. #16839813C22semidirect
39. C4×C8×D61C22semidirect
40. #16839494C22semidirect
41. #16839494C22semidirect
42. #16839492C22semidirect
43. #16839492C22semidirect
317. #1486D61semidirect
370. C61#17508semidirect

Maximal subgroups

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

subgroupindex
#214593772
#214547752
#214544872
#214442762
#214442732
#214442502
#214442242
#214442232
#214441982
C2×D4⋊#924182
C61×#14862
#1750861