Finite Group Databasebeta

← #29721418

Subgroups — #29721418

Order 15616.

794 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×#16840064C211yesmaximal, characteristic, complemented
2C2×#16839820C211yesmaximal, characteristic, complemented
3#21451653C211yesmaximal, characteristic, complemented
4#21448514C211yesmaximal, characteristic
5#21447252C211yesmaximal, characteristic, complemented
6#21447245C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic
8#21446775C211yesmaximal, characteristic, complemented
9#21446579C211yesmaximal, characteristic, complemented
10#21446561C211yesmaximal, characteristic, complemented
11#21446548C211yesmaximal, characteristic, complemented
12#21446518C211yesmaximal, characteristic, complemented
13#21446499C211yesmaximal, characteristic, complemented
14#21445817C211yesmaximal, characteristic, complemented
15C61×#2034C211yesmaximal, characteristic
16C2×#14519768C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19#16840064—24no—
20#16839820—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31#16839696—21no—
32#16839694—21no—
33#16839685—21no—
34#16839685—21no—
35#16839665—21no—
36#16839665C2211yescharacteristic
37#16839661C2211yescharacteristic
38#16839661C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839655—21no—
41#16839642—21no—
42#16839637—21no—
43#16839631C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C23×Dic61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519768—22no—
65#14519768—22no—
66D4×Dic61—22no—
67D4×Dic61—22no—
68#14519736—22no—
69#14519736—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61D411yescharacteristic
89C2×C22⋊Dic61D411yescharacteristic
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519710—22no—
94#14519709—22no—
95#14519708—22no—
96#14519706—22no—
97#14519706D414yescomplemented
98#14519698—22no—
99#14519698—22no—
100C22⋊#92418—22no—
101#14519687—22no—
102C8×Dic61—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114#121×C61—22no—
115#121×C61—22no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121#106×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124C22⋊C8×C61—22no—
125#95×C61—21no—
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128C2×D4×C61—24no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—81no—
135C2×D4×C61—81no—
136C2×D4×C61#4112yes—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—42no—
153C22×Dic61—81no—
154C22×Dic61—81no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D412yes—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61#4112yes—
171C22⋊C4×C61—24no—
172C22⋊C4×C61—81no—
173C22⋊Dic61—22no—
174C22⋊Dic61—22no—
175C22⋊Dic61—42no—
176C22⋊Dic61—81no—
177C22⋊Dic61—81no—
178C22⋊Dic61—81no—
179C22⋊Dic61—81no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—42no—
191C4⋊Dic61—81no—
192C4⋊Dic61—81no—
193#11758196—42no—
194#11758196—81no—
195#11758196—81no—
196#11758196—81no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—81no—
200C4×Dic61C2×D412yes—
201C4×Dic61#4112yes—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C2×D412yes—
208C23×C61—21no—
209C23×C61—22no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61C22×D411yescharacteristic
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—84no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C612−1+411yescharacteristic
249C2×C4×C612−1+411yescharacteristic
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—84no—
273C2×Dic61#12112yes—
274C2×Dic61#12112yes—
275C8×C61—22no—
276C8×C61—41no—
277#92418—22no—
278#92418—41no—
279#24717—611nomaximal, Sylow
280C22×C61—41no—
281C22×C61—42no—
282C22×C61—41no—
283C22×C61—42no—
284C22×C61—41no—
285C22×C61—42no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61—81no—
293C22×C61—81no—
294C22×C61C2×#12111yescharacteristic
295C22×C61#52511yescharacteristic
296C22×C61#53611yescharacteristic
297C22×C61#57611yescharacteristic
298C22×C61#57711yescharacteristic
299C22×C61#57711yescharacteristic
300C22×C61#57711yescharacteristic
301C4×C61—42no—
302C4×C61—41no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61#54711yescharacteristic
306C4×C61#54811yescharacteristic
307C4×C61#55211yescharacteristic
308C4×C61#55611yescharacteristic
309Dic61—22no—
310Dic61—22no—
311Dic61—41no—
312Dic61—41no—
313Dic61—81no—
314Dic61—81no—
315Dic61—81no—
316Dic61—81no—
317C2×#478—611no—
318C2×#433—611no—
319#2629—611no—
320#2324—611no—
321#2077—611no—
322#2075—611no—
323#2034—611no—
324#2034D6111yescharacteristic
325#1989—611no—
326#1948—611no—
327#1944—611no—
328#1941—611no—
329#1936—611no—
330#1934—611no—
331#1802—611no—
332C2×C61—81no—
333C2×C61—82no—
334C2×C61#241511yescharacteristic
335C2×C61#306011yescharacteristic
336C2×C61#306211yescharacteristic
337C2×C61#311911yescharacteristic
338C2×C61#312311yescharacteristic
339C2×C61#324111yescharacteristic
340C2×C61#324411yescharacteristic
341C2×#125—611no—
342C2×#121C2×D6111yescharacteristic
343C2×C4×D4—611no—
344C2×#117—611no—
345#478—1224no—
346#433—1224no—
347C2×#107—611no—
348C2×#106—611no—
349C2×#106—611no—
350C2×#106C2×D6111yescharacteristic
351C2×C4⋊C8—611no—
352C2×C4⋊C8—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102C2×D6111yescharacteristic
356C2×#102C2×D6111yescharacteristic
357C2×C22⋊C8—611no—
358C2×C22⋊C8C2×D6111yescharacteristic
359C2×#97—611no—
360C2×C4×C8—611no—
361#398—1221no—
362#398—1221no—
363#396—1221no—
364#396—1221no—
365#390—611no—
366#390—1221no—
367#389—611no—
368#389—611no—
369#389—611no—
370#388—1221no—
371#386—1221no—
372#385—1221no—
373#384—611no—
374#380—611no—
375#380—611no—
376#380C2×D6111yescharacteristic
377C4×C4⋊C4—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340C2×D6111yescharacteristic
386C61#2471711yescharacteristic, complemented, Sylow
387C22×D4—21no—
388C22×D4C22×D6111yescharacteristic
389C23×C4—1221no—
390C23×C4C22×D6111yescharacteristic
391C22×C8—611no—
392C22×C8—611no—
393C22×C8C22×D6111yescharacteristic
394C22×C8C22×D6111yescharacteristic
395#125—1222no—
396#125—1222no—
397#121—22no—
398#121—22no—
399C4×D4—1222no—
400C4×D4—1222no—
401#117—1222no—
402#117—1222no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—1221no—
431#107—1222no—
432#106—22no—
433#106—1222no—
434#106—1222no—
435C4⋊C8—614no—
436C4⋊C8—1222no—
437#102—22no—
438#102—22no—
439#102—1222no—
440#102—1222no—
441C22⋊C8—22no—
442C22⋊C8—1222no—
443#97—1222no—
444C4×C8—1222no—
445#95—21no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452C24—21no—
453C24D4×D6111yescharacteristic
454C2×D4—24no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4#1175822412yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—4881no—
481C22×C4—4881no—
482C22×C4—2442no—
483C22×C4D4×D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—612no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8D4×D6112yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—4881no—
513C4⋊C4—4881no—
514C4⋊C4—4881no—
515C4⋊C4—4881no—
516C4⋊C4—4881no—
517C4⋊C4—2442no—
518C4⋊C4—2442no—
519C4⋊C4#1175822412yes—
520C22⋊C4—24no—
521C22⋊C4—81no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—4881no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—2442no—
529C42—612no—
530C42—612no—
531C42—1221no—
532C42—1221no—
533C42—4881no—
534C23—21no—
535C23—22no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23C2×D4×D6111yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—84no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—612no—
571C2×C4—612no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—4884no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4C2×D4×D6111yescharacteristic
596C2×C4#41×D6111yescharacteristic
597C2×C4C2×#1175822411yescharacteristic
598C2×C4C2×#1175822411yescharacteristic
599C2×C4#1451982411yescharacteristic
600C2×C4#1451982411yescharacteristic
601C8—22no—
602C8—41no—
603C8—1222no—
604C8—2441no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#121×D6111yescharacteristic
620C22#1684026811yescharacteristic
621C22#1684033411yescharacteristic
622C22#1684056611yescharacteristic
623C22#1684056811yescharacteristic
624C22#1684056911yescharacteristic
625C22#1684057211yescharacteristic
626C4—41no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—1222no—
631C4—1222no—
632C4—4881no—
633C4—4881no—
634C4—4881no—
635C4—4881no—
636C4—2441no—
637C4—2441no—
638C4#1684041211yescharacteristic
639C4#1684041811yescharacteristic
640C4#1684044911yescharacteristic
641C4#1684048111yescharacteristic
642C2—81no—
643C2—82no—
644C2#2144924111yescharacteristic
645C2#2145547611yescharacteristic
646C2#2145549611yescharacteristic
647C2#2145601911yescharacteristic
648C2#2145606511yescharacteristic
649C2#2145707611yescharacteristic
650C2#2145711511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2034C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenter#2034D61
hypocenterC61#24717
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. C2×#16840064C2semidirect
2. C2×#16839820C2semidirect
3. #21451653C2semidirect
5. #21447252C2semidirect
6. #21447245C2semidirect
8. #21446775C2semidirect
9. #21446579C2semidirect
10. #21446561C2semidirect
11. #21446548C2semidirect
12. #21446518C2semidirect
13. #21446499C2semidirect
14. #21445817C2semidirect
97. #14519706D4semidirect
386. C61#24717semidirect

Maximal subgroups

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

subgroupindex
C2×#168400642
C2×#168398202
#214516532
#214485142
#214472522
#214472452
#214470052
#214467752
#214465792
#214465612
#214465482
#214465182
#214464992
#214458172
C61×#20342
#2471761