Finite Group Databasebeta

← #29646567

Subgroups — #29646567

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840299C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444231C214yesmaximal, complemented
5#21444226C214yesmaximal, complemented
6#21444214C211yesmaximal, characteristic, complemented
7#21444211C211yesmaximal, characteristic, complemented
8#21444209C211yesmaximal, characteristic, complemented
9C61×#1479C211yesmaximal, characteristic, complemented
10#16840299—21no—
11#16840299—21no—
12#16840299—21no—
13#16840299—21no—
14#16840299C412yes—
15#16840299C412yes—
16#16840299C2212yes—
17#16840299C2212yes—
18C2×#14519772—21no—
19C2×#14519768C411yescharacteristic
20C2×#14519766C411yescharacteristic
21C2×#14519762—21no—
22C2×#14519753C411yescharacteristic
23C2×#14519752C411yescharacteristic
24C2×C4×D244—21no—
25C2×C4×D244C2211yescharacteristic
26C2×#14519734—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839816—21no—
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839814C2212yescomplemented
33#16839813—21no—
34#16839813C2212yescomplemented
35#16839812—21no—
36#16839784—21no—
37C4⋊C8×D61C2212yescomplemented
38#16839724—21no—
39C22⋊C8×D61—21no—
40C4×#11758189C2212yescomplemented
41C4×C8×D61—21no—
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C22×D244—21no—
50C22×D244C2×C411yescharacteristic
51C22×C4×D61—21no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C2×#11758189—22no—
56C2×C8×D61—22no—
57#14519772—22no—
58#14519772—22no—
59#14519772—22no—
60#14519772—22no—
61#14519768—21no—
62#14519768—21no—
63#14519768C2×C412yes—
64#14519768C2×C412yes—
65#14519766—21no—
66#14519766—21no—
67#14519766C2×C412yes—
68#14519766C2×C412yes—
69#14519762—22no—
70#14519762—22no—
71#14519762—22no—
72#14519762—22no—
73#14519753—21no—
74#14519753—21no—
75#14519753C2×C412yes—
76#14519753C2×C412yes—
77#14519752—21no—
78#14519752—21no—
79#14519752C2×C412yes—
80#14519752C2×C412yes—
81C4×D244—22no—
82C4×D244—22no—
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—21no—
86C4×D244—21no—
87C4×D244C2×C412yes—
88C4×D244C2312yes—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92#14519734—22no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122C4×#92418—21no—
123C4×#92418C2312yes—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2×C412yes—
129C4×Q8×C61C2312yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2312yes—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C4×C8×C61—21no—
139C4×C8×C61C2312yes—
140C23×D61—21no—
141C23×D61C22⋊C411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—22no—
144C2×Q8×C61—22no—
145C2×Q8×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—21no—
160C2×D244—44no—
161C2×D244C22×C412yes—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
168C2×C4×D61—44no—
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22×C411yescharacteristic
176C2×C4×D61C22×C411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C8×C61—22no—
182C2×C8×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61C22×C412yes—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61C22×C411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61C2×D411yescharacteristic
192C42×C61C2411yescharacteristic
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203C4⋊Dic61—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61C22×C412yes—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—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×C61C2×C22⋊C411yescharacteristic
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—41no—
232C22×D61—42no—
233C22×D61—42no—
234C22×D61—42no—
235C22×D61C2×C22⋊C411yescharacteristic
236C22×D61C2×C22⋊C411yescharacteristic
237Q8×C61—22no—
238Q8×C61—22no—
239Q8×C61—42no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—41no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61#13112yes—
250C2×C4×C61#13112yes—
251C2×C4×C61C23×C411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265D244—22no—
266D244—22no—
267D244—44no—
268D244—44no—
269D244—42no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—21no—
273C4×D61—21no—
274C4×D61—21no—
275C4×D61—21no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—44no—
285C4×D61—44no—
286C8×C61—42no—
287C8×C61—42no—
288#92418—42no—
289#92418—42no—
290#17465—611nomaximal, Sylow
291C22×C61—21no—
292C22×C61—21no—
293C22×C61#40812yes—
294C22×C61C22×C22⋊C411yescharacteristic
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—44no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—84no—
305C2×D61#42112yes—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—42no—
310C4×C61—42no—
311C4×C61#40812yes—
312C4×C61C2×#13111yescharacteristic
313C4×C61C2×#13111yescharacteristic
314C4×C61#57512yes—
315Dic61—21no—
316Dic61—21no—
317Dic61—21no—
318Dic61—21no—
319Dic61—21no—
320Dic61—21no—
321Dic61—42no—
322C2×#529—611no—
323#2920—611no—
324C2×#431—611no—
325#1483—614no—
326#1482—614no—
327#1479—611no—
328#1479D6111yescharacteristic, complemented
329#1478—611no—
330#1478—611no—
331C2×C61—22no—
332C2×C61C2×#40811yescharacteristic
333C2×C61#289611yescharacteristic
334C2×C61C2×#42111yescharacteristic
335D61—22no—
336D61—41no—
337D61—82no—
338#529—612no—
339#529—612no—
340#529—612no—
341#529—612no—
342#529—1221no—
343#529—1221no—
344#529—1221no—
345#529—1221no—
346C2×#126—1221no—
347C2×#125—611no—
348C2×#124—611no—
349C2×#123—1221no—
350C2×C22⋊Q8—611no—
351C2×#121—611no—
352C2×C4×Q8C2×D6111yescharacteristic
353C2×C4×D4—611no—
354C2×C4×D4—1221no—
355C2×#117—1221no—
356C22×C42—611no—
357#432—1221no—
358#432—1221no—
359#431—611no—
360#431—612no—
361#431—611no—
362#431—612no—
363#431—1221no—
364#431—1221no—
365#431C2×D6111yescharacteristic
366#431C2×D6111yescharacteristic
367#423—1221no—
368C2×C4⋊C8—612no—
369#407—1221no—
370C2×C22⋊C8—1221no—
371C4×M16—612no—
372C2×C4×C8—1221no—
373Q8⋊C8—614no—
374Q8⋊C8C2×D6114yescomplemented
375D4⋊C8—614no—
376D4⋊C8—614no—
377C61#1746511yescharacteristic, complemented, Sylow
378C22×Q8C4×D6111yescharacteristic
379C22×D4—611no—
380C22×D4—1221no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—1221no—
385C2×M16—1222no—
386C22×C8—1222no—
387#126—1222no—
388#126—1222no—
389#126—1222no—
390#126—1222no—
391#125—612no—
392#125—612no—
393#125—1221no—
394#125—1221no—
395#124—612no—
396#124—612no—
397#124—1221no—
398#124—1221no—
399#123—1222no—
400#123—1222no—
401#123—1222no—
402#123—1222no—
403C22⋊Q8—612no—
404C22⋊Q8—612no—
405C22⋊Q8—1221no—
406C22⋊Q8—1221no—
407#121—612no—
408#121—612no—
409#121—1221no—
410#121—1221no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C4×D6112yes—
414C4×Q8C22×D6112yes—
415C4×D4—612no—
416C4×D4—612no—
417C4×D4—1222no—
418C4×D4—1222no—
419C4×D4—1222no—
420C4×D4—1222no—
421C4×D4—1221no—
422C4×D4—1221no—
423#117—1222no—
424#117—1222no—
425#117—1222no—
426#117—1222no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4C4×D6111yescharacteristic
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C22⋊C4—1221no—
438C2×C42—21no—
439C2×C42—611no—
440C2×C42—611no—
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×C42C22×D6111yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—612no—
453C4⋊C8—1222no—
454C4⋊C8—1222no—
455C4⋊C8—1221no—
456C4⋊C8C22×D6112yes—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—1222no—
460C22⋊C8—1222no—
461C22⋊C8—1221no—
462C22⋊C8—1221no—
463#97—1222no—
464C4×C8—21no—
465C4×C8—612no—
466C4×C8—1222no—
467C4×C8—1221no—
468C4×C8C22×D6112yes—
469C24—611no—
470C24—1221no—
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8C2×C4×D6112yes—
475C2×D4—612no—
476C2×D4—1222no—
477C2×D4—1222no—
478C2×D4—1221no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—2444no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
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—1222no—
500C22×C4—1222no—
501C22×C4—1221no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—2442no—
505C22×C4—2444no—
506C22×C4—2442no—
507C22×C4C2×C4×D6111yescharacteristic
508C22×C4D4×D6111yescharacteristic
509C22×C4D4×D6111yescharacteristic
510M16—2444no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—1222no—
514C2×C8—1222no—
515C2×C8—2444no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—612no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1221no—
527C4⋊C4C2×C4×D6112yes—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C42—22no—
539C42—22no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42C2×C4×D6111yescharacteristic
553C42D4×D6111yescharacteristic
554C42D4×D6111yescharacteristic
555C42C23×D6111yescharacteristic
556C23—611no—
557C23—611no—
558C23—1222no—
559C23—1222no—
560C23—1222no—
561C23—2441no—
562C23—2442no—
563C23—2442no—
564C23—2442no—
565C23C22⋊C4×D6111yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—42no—
569D4—1222no—
570D4—1222no—
571D4—2444no—
572D4—2444no—
573D4—2442no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2444no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2442no—
606C2×C4—2444no—
607C2×C4C22⋊C4×D6111yescharacteristic
608C2×C4C22⋊C4×D6111yescharacteristic
609C2×C4C22⋊C4×D6111yescharacteristic
610C2×C4#1451978312yes—
611C2×C4#1451978512yes—
612C2×C4C22×C4×D6111yescharacteristic
613C2×C4C2×D4×D6111yescharacteristic
614C2×C4C2×D4×D6111yescharacteristic
615C8—42no—
616C8—42no—
617C8—2442no—
618C8—2442no—
619C22—21no—
620C22—21no—
621C22—612no—
622C22—1221no—
623C22—1221no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22—4884no—
628C22—2444no—
629C22—2442no—
630C22—2442no—
631C22—2442no—
632C22#1683972712yes—
633C22C2×C22⋊C4×D6111yescharacteristic
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—42no—
639C4—1221no—
640C4—1221no—
641C4—1221no—
642C4—1221no—
643C4—1221no—
644C4—1221no—
645C4—2442no—
646C4#1683972712yes—
647C4C2×#1451978311yescharacteristic
648C4C2×#1451978511yescharacteristic
649C4#1684056112yes—
650C2—22no—
651C2—1222no—
652C2—4882no—
653C2—2441no—
654C2C2×#1683972711yescharacteristic
655C2#2145433711yescharacteristic
656C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1479C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519752C4
cosocleC42×C61C24
hypercenter#1479D61
hypocenterC61#17465
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #431×D61C2semidirect
4. #21444231C2semidirect
5. #21444226C2semidirect
6. #21444214C2semidirect
7. #21444211C2semidirect
8. #21444209C2semidirect
9. C61×#1479C2semidirect
32. #16839814C22semidirect
34. #16839813C22semidirect
37. C4⋊C8×D61C22semidirect
40. C4×#11758189C22semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
328. #1479D61semidirect
374. Q8⋊C8C2×D61semidirect
377. C61#17465semidirect

Maximal subgroups

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

subgroupindex
C2×#168402992
#214544472
#431×D612
#214442312
#214442262
#214442142
#214442112
#214442092
C61×#14792
#1746561