Finite Group Databasebeta

← #29646014

Subgroups — #29646014

Order 15616.

1020 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
1C2×#16840294C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444185C214yesmaximal, complemented
5#21444164C214yesmaximal, complemented
6#21444142C211yesmaximal, characteristic, complemented
7#21444142C211yesmaximal, characteristic, complemented
8#21444140C211yesmaximal, characteristic, complemented
9C61×#1460C211yesmaximal, characteristic, complemented
10#16840294—21no—
11#16840294—21no—
12#16840294—21no—
13#16840294—21no—
14#16840294—21no—
15#16840294—21no—
16#16840294—21no—
17#16840294—21no—
18C2×#14519770C2212yes—
19C2×#14519768C411yescharacteristic
20C2×#14519764C411yescharacteristic
21C2×#14519759C2212yes—
22C2×#14519757C411yescharacteristic
23C2×#14519748C411yescharacteristic
24C2×C4×Dic122C2211yescharacteristic
25C2×C4×C22⋊D61C412yes—
26C2×#14519736C412yes—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839816C2212yes—
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839814—21no—
33#16839813—21no—
34#16839813—21no—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40C4×#11758189—21no—
41C4×C8×D61—21no—
42#16839487C2214yes—
43#16839487C2214yes—
44#16839486C2214yes—
45C2×C4×D4×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×#323C2214yes—
49C22×Dic122C2×C411yescharacteristic
50C22×C22⋊D61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519770—22no—
57#14519770—22no—
58#14519770—22no—
59#14519770—22no—
60#14519768—21no—
61#14519768—21no—
62#14519768—21no—
63#14519768—21no—
64#14519764—21no—
65#14519764—21no—
66#14519764—21no—
67#14519764—21no—
68#14519759—22no—
69#14519759—22no—
70#14519759—22no—
71#14519759—22no—
72#14519757—21no—
73#14519757—21no—
74#14519757—21no—
75#14519757—21no—
76#14519748—21no—
77#14519748—21no—
78#14519748—21no—
79#14519748—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88#14519736—22no—
89#14519736—22no—
90#14519736—22no—
91#14519736—22no—
92C2×C4⋊Dic61C2×C412yes—
93C2×C4⋊Dic61C2×C412yes—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196C2×C412yes—
96C2×#11758196C2312yes—
97C2×C22⋊Dic61C2×C412yes—
98C2×C22⋊Dic61C2×C412yes—
99C2×C22⋊Dic61C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×C4×Dic61C2×C412yes—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61D411yescharacteristic
106C42×D61D411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122C4×#92418—21no—
123C4×#92418—21no—
124C8×Dic61—22no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C412yes—
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2312yes—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138C4×C8×C61—21no—
139C4×C8×C61—21no—
140C24×C61C22×C412yes—
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—44no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C412yes—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—44no—
156C22×Dic61C22×C412yes—
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C412yes—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×C8×C61—22no—
182C2×C8×C61—22no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197#11758198—22no—
198#11758198—22no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204C4⋊Dic61—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C2×#92418—22no—
224C2×#92418—22no—
225#11758189—44no—
226C8×D61—44no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61C23×C411yescharacteristic
233C22×D61—21no—
234C22×D61—21no—
235C22×D61—22no—
236C22×D61—41no—
237C22×D61C2×C22⋊C411yescharacteristic
238C22×D61C2×C22⋊C411yescharacteristic
239D4×C61—42no—
240D4×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—41no—
244C2×C4×C61—44no—
245C2×C4×C61—44no—
246C2×C4×C61—42no—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61#13112yes—
252C2×C4×C61#13112yes—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—44no—
256C22⋊D61—44no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—42no—
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284Dic122—42no—
285Dic122—42no—
286C8×C61—42no—
287C8×C61—42no—
288#92418—42no—
289#92418—42no—
290#17383—611nomaximal, Sylow
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—82no—
297C22×C61—82no—
298C22×C61C22×C22⋊C411yescharacteristic
299C22×C61C2×#13111yescharacteristic
300C22×C61C2×#13111yescharacteristic
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—21no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61#41012yes—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—42no—
313C4×C61#40812yes—
314C4×C61#40812yes—
315C4×C61#41312yes—
316Dic61—21no—
317Dic61—21no—
318Dic61—21no—
319Dic61—21no—
320Dic61—21no—
321Dic61—21no—
322Dic61—42no—
323Dic61—42no—
324C2×#529—611no—
325#2920—611no—
326C2×#431—611no—
327#1473—614no—
328#1468—614no—
329#1461—611no—
330#1461—611no—
331#1460—611no—
332#1460D6111yescharacteristic, complemented
333C2×C61—21no—
334C2×C61—21no—
335C2×C61—82no—
336C2×C61C2×#40811yescharacteristic
337C2×C61C2×#41011yescharacteristic
338C2×C61C2×#41311yescharacteristic
339D61—22no—
340D61—41no—
341#529—1221no—
342#529—1221no—
343#529—1221no—
344#529—1221no—
345#529—1221no—
346#529—1221no—
347#529—1221no—
348#529—1221no—
349C2×#126—612no—
350C2×#125—611no—
351C2×#124—611no—
352C2×#123—612no—
353C2×C22⋊Q8—611no—
354C2×#121—611no—
355C2×C4×Q8—611no—
356C2×C4×D4—612no—
357C2×C4×D4C2×D6111yescharacteristic
358C2×#117—612no—
359C22×C42—611no—
360#432—612no—
361#432—1221no—
362#431—611no—
363#431—611no—
364#431—612no—
365#431—1221no—
366#431—1221no—
367#431—1221no—
368#431C2×D6111yescharacteristic
369#431C2×D6111yescharacteristic
370#423—1221no—
371C2×C4⋊C8—1221no—
372#407—612no—
373C2×C22⋊C8—612no—
374C4×M16—1221no—
375C2×C4×C8—1221no—
376#324—614no—
377#324—614no—
378#323—614no—
379#323C2×D6114yes—
380C61#1738311yescharacteristic, complemented, Sylow
381C22×Q8—611no—
382C22×D4—612no—
383C22×D4C4×D6111yescharacteristic
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—611no—
387C23×C4C4×D6112yes—
388C2×M16—1222no—
389C22×C8—1222no—
390#126—1222no—
391#126—1222no—
392#126—1222no—
393#126—1222no—
394#125—1221no—
395#125—1221no—
396#125—1221no—
397#125—1221no—
398#124—1221no—
399#124—1221no—
400#124—1221no—
401#124—1221no—
402#123—1222no—
403#123—1222no—
404#123—1222no—
405#123—1222no—
406C22⋊Q8—1221no—
407C22⋊Q8—1221no—
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410#121—1221no—
411#121—1221no—
412#121—1221no—
413#121—1221no—
414C4×Q8—1221no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1222no—
426#117—1222no—
427#117—1222no—
428#117—1222no—
429#117—1222no—
430C2×C4⋊C4—612no—
431C2×C4⋊C4—612no—
432C2×C4⋊C4—612no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—612no—
435C2×C4⋊C4C4×D6111yescharacteristic
436C2×C22⋊C4—612no—
437C2×C22⋊C4—612no—
438C2×C22⋊C4—612no—
439C2×C22⋊C4—612no—
440C2×C22⋊C4C22×D6112yes—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—612no—
453C2×C42C22×D6111yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—1222no—
457C4⋊C8—1222no—
458C4⋊C8—1221no—
459C4⋊C8—1221no—
460C22⋊C8—612no—
461C22⋊C8—612no—
462C22⋊C8—1222no—
463C22⋊C8—1222no—
464C22⋊C8C22×D6112yes—
465C22⋊C8C22×D6112yes—
466#97—1222no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—1222no—
470C4×C8—1221no—
471C4×C8—1221no—
472C24—611no—
473C24C2×C4×D6112yes—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1222no—
477C2×Q8—1222no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—1222no—
483C2×D4—1222no—
484C2×D4—2444no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—612no—
504C22×C4—612no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—2442no—
508C22×C4—2442no—
509C22×C4C2×C4×D6111yescharacteristic
510C22×C4C2×C4×D6112yes—
511C22×C4C2×C4×D6111yescharacteristic
512C22×C4C23×D6111yescharacteristic
513M16—2444no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—1222no—
517C2×C8—1222no—
518C2×C8—2444no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—1222no—
554C42—1222no—
555C42D4×D6111yescharacteristic
556C42D4×D6111yescharacteristic
557C42D4×D6111yescharacteristic
558C42D4×D6111yescharacteristic
559C23—22no—
560C23—22no—
561C23—22no—
562C23—42no—
563C23—42no—
564C23—611no—
565C23—611no—
566C23—1222no—
567C23—1221no—
568C23—1221no—
569C23—2441no—
570C23C22×C4×D6111yescharacteristic
571Q8—2442no—
572Q8—2442no—
573D4—42no—
574D4—42no—
575D4—2444no—
576D4—2444no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2442no—
610C2×C4C22⋊C4×D6111yescharacteristic
611C2×C4C22⋊C4×D6111yescharacteristic
612C2×C4C22⋊C4×D6111yescharacteristic
613C2×C4C22⋊C4×D6111yescharacteristic
614C2×C4#1451978312yes—
615C2×C4#1451978512yes—
616C2×C4C2×D4×D6111yescharacteristic
617C2×C4C2×D4×D6111yescharacteristic
618C8—42no—
619C8—42no—
620C8—2442no—
621C8—2442no—
622C22—21no—
623C22—21no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—82no—
628C22—82no—
629C22—612no—
630C22—1221no—
631C22—1221no—
632C22—1221no—
633C22—1221no—
634C22—1221no—
635C22—2442no—
636C22—2442no—
637C22C2×C22⋊C4×D6111yescharacteristic
638C22C2×#1451978311yescharacteristic
639C22C2×#1451978511yescharacteristic
640C4—21no—
641C4—21no—
642C4—21no—
643C4—42no—
644C4—1221no—
645C4—1221no—
646C4—1221no—
647C4—1221no—
648C4—1221no—
649C4—1221no—
650C4—2442no—
651C4—2442no—
652C4#1683972712yes—
653C4#1683972712yes—
654C4#1683974312yes—
655C2—21no—
656C2—21no—
657C2—82no—
658C2—1222no—
659C2—2441no—
660C2C2×#1683972711yescharacteristic
661C2#410×D6111yescharacteristic
662C2C2×#1683974311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1460C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C4
cosocleC22×C4×C61C24
hypercenter#1460D61
hypocenterC61#17383
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #431×D61C2semidirect
4. #21444185C2semidirect
5. #21444164C2semidirect
6. #21444142C2semidirect
7. #21444142C2semidirect
8. #21444140C2semidirect
9. C61×#1460C2semidirect
332. #1460D61semidirect
380. C61#17383semidirect

Maximal subgroups

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

subgroupindex
C2×#168402942
#214544472
#431×D612
#214441852
#214441642
#214441422
#214441402
C61×#14602
#1738361