Finite Group Databasebeta

← #29651768

Subgroups — #29651768

Order 15616.

722 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#21456395C211yesmaximal, characteristic
2#21454564C211yesmaximal, characteristic, complemented
3#21454558C211yesmaximal, characteristic, complemented
4#21444702C211yesmaximal, characteristic, complemented
5#21444701C211yesmaximal, characteristic, complemented
6#21444650C211yesmaximal, characteristic, complemented
7#21444649C211yesmaximal, characteristic, complemented
8#21444647C211yesmaximal, characteristic, complemented
9C8×#11758199C211yesmaximal, characteristic, complemented
10#21444611C211yesmaximal, characteristic, complemented
11#335×D61C211yesmaximal, characteristic, complemented
12#21444216C211yesmaximal, characteristic, complemented
13#21444216C211yesmaximal, characteristic, complemented
14#21444098C211yesmaximal, characteristic, complemented
15C61×#1581C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17C2×#14519783—21no—
18#16840309C2211yescharacteristic
19#16840309C2211yescharacteristic
20#16840166C411yescharacteristic
21#16840137C411yescharacteristic
22#16840107C411yescharacteristic
23#16840107C411yescharacteristic
24#16839999C411yescharacteristic
25#16839997C411yescharacteristic
26#16839997C411yescharacteristic
27#16839995C411yescharacteristic
28C4×D488C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839840C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839836—21no—
35#16839833—21no—
36#16839831—21no—
37#16839830—21no—
38C8×D244C2211yescharacteristic
39D4×#92418C2211yescharacteristic
40#16839827C2211yescharacteristic
41#16839813C2211yescharacteristic
42C4⋊C8×D61C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44#16839727—21no—
45#16839727—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839491C2211yescharacteristic
52#16839491C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758222—21no—
69C2×D488C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72#14519785—44no—
73#14519783—44no—
74C2×#11758194—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C2×#11758189D411yescharacteristic
78C2×#11758189D411yescharacteristic
79C22×#92418—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84C2×C8×D61C2×C411yescharacteristic
85C2×C8×D61C2×C411yescharacteristic
86#14519776C2×C411yescharacteristic
87#14519776C2×C411yescharacteristic
88#14519773C2×C411yescharacteristic
89#14519773C2×C411yescharacteristic
90#14519763—21no—
91#14519763—21no—
92#14519752C2×C411yescharacteristic
93#14519752C2×C411yescharacteristic
94#14519750—21no—
95#14519750—21no—
96#14519748C2×C411yescharacteristic
97#14519748C2×C411yescharacteristic
98C4×D244C2311yescharacteristic
99C4×D244C2311yescharacteristic
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C42×D61C2311yescharacteristic
103#14519711C2×C411yescharacteristic
104#14519710C2×C411yescharacteristic
105#14519710C2×C411yescharacteristic
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519697C2×C411yescharacteristic
116#14519697C2×C411yescharacteristic
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519687D411yescharacteristic
125#14519687D411yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C4×#92418C2311yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C8×Dic61C2×C411yescharacteristic
131C2×D8×C61C2×C411yescharacteristic
132C2×M16×C61—21no—
133C22×C8×C61—21no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136#107×C61C2×C411yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#102×C61C2×C411yescharacteristic
140#102×C61C2×C411yescharacteristic
141C22⋊C8×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C4×C8×C61C2311yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156#11758222—42no—
157#11758222—42no—
158#11758222—42no—
159#11758222—42no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244C22×C411yescharacteristic
163C2×D244C22×C411yescharacteristic
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61#4111yescharacteristic
169C2×Dic122—21no—
170C2×Dic122—21no—
171D8×C61—41no—
172M16×C61—42no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—42no—
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C42×C61C2411yescharacteristic
186C22⋊Dic61—21no—
187C22⋊Dic61—21no—
188#11758199—22no—
189#11758199—22no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198C4×Dic61C22×C411yescharacteristic
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61#4111yescharacteristic
201#11758194—42no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—42no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210D488—41no—
211#11758189—22no—
212#11758189—42no—
213#11758189—42no—
214#11758189D814yescomplemented
215C8×D61—22no—
216C8×D61—41no—
217C8×D61—42no—
218C8×D61—42no—
219C8×D61—42no—
220C8×D61—42no—
221C23×C61—21no—
222C23×C61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61C4×D411yescharacteristic
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C23×C411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C22⋊D61—42no—
240C22⋊D61—42no—
241C22⋊D61—42no—
242C22⋊D61—42no—
243C22⋊D61—81no—
244C22⋊D61—81no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61C4×D411yescharacteristic
248C2×Dic61C4×D411yescharacteristic
249C2×Dic61C4×D411yescharacteristic
250D244—21no—
251D244—21no—
252D244—21no—
253D244—21no—
254D244—42no—
255D244—42no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61C2×D812yes—
264C4×D61#13512yes—
265Dic122—42no—
266Dic122—42no—
267C8×C61—21no—
268C8×C61—21no—
269C8×C61—21no—
270C8×C61—41no—
271C8×C61—41no—
272C8×C61—41no—
273C8×C61C2×D812yes—
274#92418—21no—
275#92418—21no—
276#92418—41no—
277#92418—41no—
278#92418—41no—
279#92418#13112yescomplemented
280#92418C2×D812yes—
281#18066—611nomaximal, Sylow
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61C2×C4×D411yescharacteristic
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61C4×D812yes—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61C2×#13111yescharacteristic
302C4×C61#56811yescharacteristic
303C4×C61C22×D811yescharacteristic
304C4×C61C2×#13511yescharacteristic
305Dic61—21no—
306Dic61—21no—
307Dic61—41no—
308Dic61—41no—
309Dic61C4×D812yes—
310#3169—611no—
311#2935—611no—
312#2935—611no—
313#1589—611no—
314#1589—611no—
315#1581—611no—
316#1581—611no—
317#1581—611no—
318#1581D6111yescharacteristic, complemented
319C8×D8—611no—
320C8×D8—611no—
321C2×#335—611no—
322#1480—611no—
323#1480—611no—
324C8×M16—611no—
325C2×C61—81no—
326C2×C61—81no—
327C2×C61#293511yescharacteristic
328C2×C61C2×C4×D811yescharacteristic
329C2×C61#295711yescharacteristic
330D61—22no—
331D61—81no—
332D61—81no—
333C2×#131—1221no—
334C2×#131—1221no—
335#532—611no—
336#532—611no—
337#500—611no—
338#493—611no—
339#486—611no—
340#486—611no—
341#466—611no—
342#466—611no—
343#466—611no—
344#466—611no—
345C4×D8—611no—
346C4×D8—611no—
347C4×D8—611no—
348C4×D8C2×D6111yescharacteristic
349#436—611no—
350#436—611no—
351#436—611no—
352#436C2×D6111yescharacteristic
353#435—1221no—
354#435—1221no—
355#435—1221no—
356#435—1221no—
357C8×D4—611no—
358C8×D4—611no—
359C8×D4—611no—
360C8×D4C2×D6111yescharacteristic
361#431—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—611no—
364#408—1221no—
365#408—1221no—
366C4×M16—611no—
367C2×C4×C8—611no—
368#335—611no—
369#335—611no—
370#335—611no—
371#335C2×D6111yescharacteristic
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8C2×D6111yescharacteristic
379D4⋊C8C2×D6111yescharacteristic
380#322—611no—
381#322C2×D6111yescharacteristic
382C82—611no—
383C82—611no—
384C61#1806611yescharacteristic, complemented, Sylow
385C2×#41—1221no—
386C2×#41—1221no—
387C2×D8—611no—
388C2×D8—611no—
389C2×D8—611no—
390C2×D8C4×D6111yescharacteristic
391#131—2444no—
392#131—2444no—
393C2×M16—21no—
394C2×M16—611no—
395C2×M16—611no—
396C2×M16—1221no—
397C2×M16—1221no—
398C2×M16—1221no—
399C22×C8—21no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—1221no—
403C22×C8—1221no—
404C22×C8—1221no—
405C22×C8—1221no—
406C22×C8—1221no—
407C4⋊Q8—611no—
408C4⋊Q8—611no—
409#127—611no—
410#127—611no—
411#124—1221no—
412#124—1221no—
413#121—611no—
414#121—611no—
415#121—611no—
416#121—611no—
417#121—1221no—
418#121—1221no—
419C4×D4—611no—
420C4×D4—611no—
421C4×D4—1221no—
422C4×D4—1221no—
423C4×D4C22×D6111yescharacteristic
424C4×D4C22×D6111yescharacteristic
425C2×C42—611no—
426#107—611no—
427#107—611no—
428#107—611no—
429#107C4×D6111yescharacteristic
430C4⋊C8—611no—
431C4⋊C8—611no—
432C4⋊C8—1221no—
433C4⋊C8—1221no—
434C4⋊C8—1221no—
435C4⋊C8C22×D6111yescharacteristic
436C4⋊C8C22×D6111yescharacteristic
437#102—611no—
438#102—611no—
439#102—611no—
440#102—611no—
441#102—611no—
442#102—611no—
443#102C4×D6111yescharacteristic
444#102C4×D6111yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454#97—611no—
455#97—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—611no—
461C4×C8C22×D6111yescharacteristic
462C4×C8C22×D6111yescharacteristic
463C4×C8C22×D6111yescharacteristic
464#41—2442no—
465#41—2442no—
466#41—2442no—
467#41—2442no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×D4—611no—
471C2×D4—611no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4C2×C4×D6111yescharacteristic
481C2×D4C2×C4×D6111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1221no—
488C22×C4—1221no—
489D8—41no—
490D8—1222no—
491D8—1222no—
492D8—2441no—
493M16—42no—
494M16—614no—
495M16—1222no—
496M16—2442no—
497M16—2442no—
498M16—2442no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—42no—
503C2×C8—611no—
504C2×C8—611no—
505C2×C8—611no—
506C2×C8—611no—
507C2×C8—1222no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—2441no—
512C2×C8—2442no—
513C2×C8—2442no—
514C2×C8—2442no—
515C2×C8—2442no—
516C2×C8—2442no—
517C2×C8C2×C4×D6111yescharacteristic
518C2×C8C2×C4×D6111yescharacteristic
519C2×C8D4×D6111yescharacteristic
520C2×C8D4×D6111yescharacteristic
521C4⋊C4—611no—
522C4⋊C4—611no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4C2×C4×D6111yescharacteristic
526C4⋊C4C2×C4×D6111yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—1221no—
530C22⋊C4—1221no—
531C22⋊C4—1221no—
532C22⋊C4—1221no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42C23×D6111yescharacteristic
539C23—21no—
540C23—21no—
541C23—611no—
542C23—1221no—
543C23—1221no—
544Q8—2442no—
545Q8—2442no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—1221no—
551D4—1221no—
552D4—1221no—
553D4—1221no—
554D4—4881no—
555D4—4881no—
556D4—2442no—
557D4—2442no—
558D4—2442no—
559D4—2442no—
560D4—2442no—
561D4—2442no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—611no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4C22×C4×D6111yescharacteristic
583C2×C4C2×D4×D6111yescharacteristic
584C2×C4#41×D6111yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—612no—
592C8—612no—
593C8—1221no—
594C8—1221no—
595C8—2441no—
596C8—2441no—
597C8—2441no—
598C8D8×D6112yes—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—612no—
606C22—1221no—
607C22—1221no—
608C22—2441no—
609C22—2441no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22—2441no—
614C22C4×D4×D6111yescharacteristic
615C4—21no—
616C4—41no—
617C4—41no—
618C4—612no—
619C4—1221no—
620C4—1221no—
621C4—2441no—
622C4—2441no—
623C4#131×D6111yescharacteristic
624C4#1684052811yescharacteristic
625C4C2×D8×D6111yescharacteristic
626C4#135×D6111yescharacteristic
627C2—81no—
628C2—81no—
629C2—1222no—
630C2—4881no—
631C2—4881no—
632C2#2145456011yescharacteristic
633C2C4×D8×D6111yescharacteristic
634C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1581C2
socleC22×C61C2×C4×D4
prime radical#21456395C2
cosocleC42×C61C24
hypercenter#1581D61
hypocenterC61#18066
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #21454564C2semidirect
3. #21454558C2semidirect
4. #21444702C2semidirect
5. #21444701C2semidirect
6. #21444650C2semidirect
7. #21444649C2semidirect
8. #21444647C2semidirect
9. C8×#11758199C2semidirect
10. #21444611C2semidirect
11. #335×D61C2semidirect
12. #21444216C2semidirect
13. #21444216C2semidirect
14. #21444098C2semidirect
15. C61×#1581C2semidirect
214. #11758189D8semidirect
279. #92418#131semidirect
318. #1581D61semidirect
384. C61#18066semidirect

Maximal subgroups

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

subgroupindex
#214563952
#214545642
#214545582
#214447022
#214447012
#214446502
#214446492
#214446472
C8×#117581992
#214446112
#335×D612
#214442162
#214440982
C61×#15812
#1806661