Finite Group Databasebeta

← #29651321

Subgroups — #29651321

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455820C211yesmaximal, characteristic
2#21454885C211yesmaximal, characteristic, complemented
3#21454853C211yesmaximal, characteristic, complemented
4#21444734C211yesmaximal, characteristic, complemented
5#21444705C211yesmaximal, characteristic, complemented
6#21444685C211yesmaximal, characteristic, complemented
7#21444685C211yesmaximal, characteristic, complemented
8#21444650C211yesmaximal, characteristic, complemented
9#21444650C211yesmaximal, characteristic, complemented
10#21444644C211yesmaximal, characteristic, complemented
11C8×D488C211yesmaximal, characteristic, complemented
12#21444599C211yesmaximal, characteristic, complemented
13#21444289C211yesmaximal, characteristic, complemented
14#21444211C211yesmaximal, characteristic, complemented
15C61×#1454C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840076C411yescharacteristic
19#16840076C411yescharacteristic
20#16840043C411yescharacteristic
21#16840043C411yescharacteristic
22#16839958C411yescharacteristic
23#16839958C411yescharacteristic
24#16839898C411yescharacteristic
25#16839898C411yescharacteristic
26C4×D488C2211yescharacteristic
27C4×D488C2211yescharacteristic
28C4×D488C2211yescharacteristic
29C4×D488C2211yescharacteristic
30#16839841C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839841C2211yescharacteristic, complemented
33#16839841C2211yescharacteristic, complemented
34#16839839—21no—
35#16839832—21no—
36#16839832—21no—
37C8×D244C2211yescharacteristic
38C8×D244C2211yescharacteristic
39C8×D244C2211yescharacteristic, complemented
40C8×D244C2211yescharacteristic, complemented
41#16839827—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839727—21no—
45#16839727—21no—
46#16839724—21no—
47C22⋊C8×D61—21no—
48#16839515C2211yescharacteristic, complemented
49#16839515C2211yescharacteristic, complemented
50#16839513C2211yescharacteristic, complemented
51#16839513C2211yescharacteristic, complemented
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839491C2211yescharacteristic, complemented
57#16839491C2211yescharacteristic, complemented
58#16839491C2211yescharacteristic, complemented
59#16839491C2211yescharacteristic, complemented
60C61×#431C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#322C2211yescharacteristic, complemented
64C61×#322C2211yescharacteristic, complemented
65C61×#322C2211yescharacteristic, complemented
66C82×C61C2211yescharacteristic, complemented
67C2×#11758222—21no—
68C22×D244C2×C411yescharacteristic
69C22×C4×D61—21no—
70C2×D488C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×D488C2×C411yescharacteristic
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C2×#11758189—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82#14519777C2×C411yescharacteristic
83#14519774C2×C411yescharacteristic
84#14519765—21no—
85#14519751—21no—
86#14519751C2×C411yescharacteristic
87#14519751C2×C411yescharacteristic
88C4×D244—21no—
89C4×D244—21no—
90C4×D244—21no—
91C4×D244C2×C411yescharacteristic
92C4×D244C2×C411yescharacteristic
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95C4×D244C2311yescharacteristic
96C4×D244C2311yescharacteristic
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758198—21no—
99#14519711C2×C411yescharacteristic
100#14519711C2×C411yescharacteristic
101#14519711C2×C411yescharacteristic
102#14519711C2×C411yescharacteristic
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519699C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114#14519699C2×C411yescharacteristic
115C22⋊#92418—21no—
116C22⋊#92418—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125#14519688—21no—
126C4×#92418—21no—
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61—21no—
129C4⋊C8×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61D411yescharacteristic
133C22⋊C8×C61—21no—
134C22⋊C8×C61C2×C411yescharacteristic
135C22⋊C8×C61C2×C411yescharacteristic
136C22⋊C8×C61D411yescharacteristic
137C22⋊C8×C61D411yescharacteristic
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61#4111yescharacteristic
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151#11758222—81no—
152#11758222—81no—
153C2×D244—22no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—41no—
158C2×D244C22×C411yescharacteristic
159C2×D244C22×C411yescharacteristic
160C2×D244C22×C411yescharacteristic
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×Dic122—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C22×C411yescharacteristic
175C2×C8×C61C22×C411yescharacteristic
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61#4111yescharacteristic
184C42×C61C2411yescharacteristic
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C22×C411yescharacteristic
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203D488—22no—
204D488—22no—
205D488—41no—
206D488—41no—
207#11758189—81no—
208#11758189—81no—
209#11758189—81no—
210#11758189—81no—
211C8×D61—81no—
212C8×D61—81no—
213C8×D61—81no—
214C8×D61—81no—
215C23×C61C4×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—81no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—81no—
235C22⋊D61—81no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—81no—
241D244—21no—
242D244—21no—
243D244—21no—
244D244—21no—
245D244—21no—
246D244—21no—
247D244—21no—
248D244—42no—
249D244—42no—
250D244—81no—
251D244#13112yes—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—81no—
261C4×D61—81no—
262Dic122—81no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—21no—
266C8×C61—21no—
267C8×C61—21no—
268C8×C61—21no—
269C8×C61—21no—
270C8×C61—21no—
271C8×C61—41no—
272C8×C61—41no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#18026—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61C2×C4×D411yescharacteristic
282C2×D61—22no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—84no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61C2×#13111yescharacteristic
300C4×C61#56811yescharacteristic
301C4×C61#57611yescharacteristic
302C4×C61#57611yescharacteristic
303Dic61—41no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307#3100—611no—
308#2979—611no—
309#2974—611no—
310#1594—611no—
311#1589—611no—
312#1586—611no—
313#1586—611no—
314#1581—611no—
315#1581—611no—
316#1580—611no—
317C8×D8—611no—
318#1572—611no—
319#1496—611no—
320#1478—611no—
321#1454D6111yescharacteristic, complemented
322C2×C61—41no—
323C2×C61#293311yescharacteristic
324C2×C61#294811yescharacteristic
325C2×C61#295511yescharacteristic
326D61—42no—
327D61—81no—
328D61—81no—
329D61—81no—
330#532—611no—
331C2×C4×D4—611no—
332#480—611no—
333#480—611no—
334#474—611no—
335#474—611no—
336#459—611no—
337#459—611no—
338#447—611no—
339#447—611no—
340C4×D8—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344#436—611no—
345#436—611no—
346#436—611no—
347#436—611no—
348#436—1221no—
349#435—1221no—
350#435—1221no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—1221no—
356#432—611no—
357#431—611no—
358#431C2×D6111yescharacteristic
359#431C2×D6111yescharacteristic
360#431C2×D6111yescharacteristic
361#408—1221no—
362#408—1221no—
363#407—1221no—
364C2×C22⋊C8—1221no—
365#335—611no—
366#335—611no—
367#334—611no—
368#334—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377#322C2×D6111yescharacteristic, complemented
378#322C2×D6111yescharacteristic, complemented
379#322C2×D6111yescharacteristic, complemented
380C82C2×D6111yescharacteristic, complemented
381C61#1802611yescharacteristic, complemented, Sylow
382C2×#41—1221no—
383C22×D4—611no—
384C23×C4—1221no—
385C2×D8—611no—
386C2×D8—611no—
387C2×D8—611no—
388C2×D8—611no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C4⋊Q8—611no—
398#127—611no—
399#124—1221no—
400#121—611no—
401#121—611no—
402#121—1221no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C2×C4⋊C4—611no—
413C2×C22⋊C4—1221no—
414C2×C42C22×D6111yescharacteristic
415#107—611no—
416#107—611no—
417#107—611no—
418#107—611no—
419C4⋊C8—21no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8C4×D6111yescharacteristic
425C4⋊C8C4×D6111yescharacteristic
426C4⋊C8D24411yescharacteristic
427C4⋊C8D24411yescharacteristic
428#102—611no—
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102—611no—
436C22⋊C8—21no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8C4×D6111yescharacteristic
448C22⋊C8C4×D6111yescharacteristic
449C22⋊C8D24411yescharacteristic
450C22⋊C8D24411yescharacteristic
451#97—1221no—
452C4×C8—1221no—
453C4×C8C22×D6111yescharacteristic
454C4×C8C22×D6111yescharacteristic
455C4×C8C22×D6111yescharacteristic
456C4×C8C22×D6111yescharacteristic
457C4×C8C22×D6111yescharacteristic
458C4×C8C22×D6111yescharacteristic
459C24—1221no—
460#41—4881no—
461#41—4881no—
462C2×Q8—1221no—
463C2×D4—611no—
464C2×D4—611no—
465C2×D4—611no—
466C2×D4—611no—
467C2×D4—1222no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C2×D4—2441no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—4881no—
482C22×C4—4881no—
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4C2×D24411yescharacteristic
485C22×C4#1175822211yescharacteristic
486D8—1222no—
487D8—1222no—
488D8—2441no—
489D8—2441no—
490M16—4881no—
491M16—4881no—
492M16—4881no—
493M16—4881no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—4881no—
501C2×C8—4881no—
502C2×C8—4881no—
503C2×C8—4881no—
504C2×C8C2×C4×D6111yescharacteristic
505C2×C8C2×C4×D6111yescharacteristic
506C2×C8C2×C4×D6111yescharacteristic
507C2×C8C2×C4×D6111yescharacteristic
508C2×C8C2×D24411yescharacteristic
509C2×C8C2×D24411yescharacteristic
510C2×C8C2×D24411yescharacteristic
511C2×C8C2×D24411yescharacteristic
512C4⋊C4—611no—
513C4⋊C4—611no—
514C4⋊C4—611no—
515C4⋊C4—611no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42C2×C4×D6111yescharacteristic
527C42C2×D24411yescharacteristic
528C42#1175822211yescharacteristic
529C42C23×D6111yescharacteristic
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—4881no—
535C23—2442no—
536C23—2442no—
537C23C4×D24411yescharacteristic
538Q8—4881no—
539D4—612no—
540D4—1221no—
541D4—1221no—
542D4—1221no—
543D4—1221no—
544D4—1221no—
545D4—1221no—
546D4—1221no—
547D4—4881no—
548D4—4881no—
549D4—4881no—
550D4—2442no—
551D4—2442no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—4881no—
562C2×C4—4881no—
563C2×C4—4881no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4C4×D24411yescharacteristic
573C2×C4C4×D24411yescharacteristic
574C2×C4C4×D24411yescharacteristic
575C2×C4C22×C4×D6111yescharacteristic
576C2×C4C22×D24411yescharacteristic
577C2×C4C2×#1175822211yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—1222no—
596C22—4884no—
597C22—2441no—
598C22—2441no—
599C22—2441no—
600C22—2441no—
601C22—2441no—
602C22—2441no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22C2×C4×D24411yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—2441no—
614C4—2441no—
615C4—2441no—
616C4—2441no—
617C4#131×D6111yescharacteristic
618C4#1684052711yescharacteristic
619C4#1684056711yescharacteristic
620C4#1684056711yescharacteristic
621C2—41no—
622C2—4881no—
623C2—4881no—
624C2—4881no—
625C2—2442no—
626C2#2145454711yescharacteristic
627C2#2145467211yescharacteristic
628C2#2145472311yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1454C2
socleC22×C61C2×C4×D4
prime radical#21455820C2
cosocleC42×C61C24
hypercenter#1454D61
hypocenterC61#18026
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #21454885C2semidirect
3. #21454853C2semidirect
4. #21444734C2semidirect
5. #21444705C2semidirect
6. #21444685C2semidirect
7. #21444685C2semidirect
8. #21444650C2semidirect
9. #21444650C2semidirect
10. #21444644C2semidirect
11. C8×D488C2semidirect
12. #21444599C2semidirect
13. #21444289C2semidirect
14. #21444211C2semidirect
15. C61×#1454C2semidirect
32. #16839841C22semidirect
33. #16839841C22semidirect
39. C8×D244C22semidirect
40. C8×D244C22semidirect
48. #16839515C22semidirect
49. #16839515C22semidirect
50. #16839513C22semidirect
51. #16839513C22semidirect
56. #16839491C22semidirect
57. #16839491C22semidirect
58. #16839491C22semidirect
59. #16839491C22semidirect
63. C61×#322C22semidirect
64. C61×#322C22semidirect
65. C61×#322C22semidirect
66. C82×C61C22semidirect
321. #1454D61semidirect
377. #322C2×D61semidirect
378. #322C2×D61semidirect
379. #322C2×D61semidirect
380. C82C2×D61semidirect
381. C61#18026semidirect

Maximal subgroups

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

subgroupindex
#214558202
#214548852
#214548532
#214447342
#214447052
#214446852
#214446502
#214446442
C8×D4882
#214445992
#214442892
#214442112
C61×#14542
#1802661