Finite Group Databasebeta

← #29651310

Subgroups — #29651310

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#21455817C211yesmaximal, characteristic
2#21454882C211yesmaximal, characteristic, complemented
3#21454852C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444705C211yesmaximal, characteristic, complemented
6#21444683C211yesmaximal, characteristic, complemented
7#21444683C211yesmaximal, characteristic, complemented
8#21444649C211yesmaximal, characteristic, complemented
9#21444647C211yesmaximal, characteristic, complemented
10#21444640C211yesmaximal, characteristic, complemented
11#21444598C211yesmaximal, characteristic, complemented
12#21444286C211yesmaximal, characteristic, complemented
13#21444208C211yesmaximal, characteristic, complemented
14#21444118C211yesmaximal, characteristic, complemented
15C8×D8×C61C211yesmaximal, characteristic, complemented
16#16840309C2211yescharacteristic
17C4×D4×D61C2211yescharacteristic
18#16840077C411yescharacteristic
19#16840074C411yescharacteristic
20#16840041C411yescharacteristic
21#16840040C411yescharacteristic
22#16839956C411yescharacteristic
23#16839955C411yescharacteristic
24#16839897C411yescharacteristic
25#16839894C411yescharacteristic
26C4×D488C2211yescharacteristic
27C4×#11758199C2211yescharacteristic
28C4×#11758199C2211yescharacteristic
29#16839841C2211yescharacteristic
30#16839841C2211yescharacteristic, complemented
31#16839840C2211yescharacteristic, complemented
32#16839839C2211yescharacteristic
33#16839837—21no—
34#16839833—21no—
35#16839830—21no—
36D4×#92418C2211yescharacteristic
37#16839827C2211yescharacteristic, complemented
38C8×C22⋊D61—21no—
39#16839818C2211yescharacteristic
40#16839814C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839728—21no—
45#16839727—21no—
46#16839724—21no—
47C2×#14519689—21no—
48#16839515C2211yescharacteristic, complemented
49#16839512C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839491C2211yescharacteristic
52#16839491C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839484C2211yescharacteristic, complemented
59#16839484C2211yescharacteristic, complemented
60C4×D8×C61C2211yescharacteristic
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#335C2211yescharacteristic, complemented
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic, complemented
66C82×C61C2211yescharacteristic, complemented
67C2×#11758222—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C2×D488C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758194—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C22×#92418—21no—
78C2×C8×D61—21no—
79#14519776C2×C411yescharacteristic
80#14519773C2×C411yescharacteristic
81#14519763—21no—
82#14519752C2×C411yescharacteristic
83#14519750—21no—
84#14519748C2×C411yescharacteristic
85C4×D244C2311yescharacteristic
86C4×D244C2311yescharacteristic
87D4×Dic61C2×C411yescharacteristic
88#14519739C2×C411yescharacteristic
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91#14519737—21no—
92C4⋊C4×D61C2×C411yescharacteristic
93C22⋊C4×D61—21no—
94C42×D61C2311yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519706C2×C411yescharacteristic
102#14519706C2×C411yescharacteristic
103#14519706D411yescharacteristic
104#14519706D411yescharacteristic
105#14519699C2×C411yescharacteristic
106#14519699C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109#14519697C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689C2×C411yescharacteristic
121#14519689C2×C411yescharacteristic
122#14519689D411yescharacteristic
123#14519689D411yescharacteristic
124#14519687—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×D8×C61C2×C411yescharacteristic
130C22×C8×C61—21no—
131C22×C8×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#107×C61C2×C411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#102×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C2×D4×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154D4×D61—22no—
155D4×D61—41no—
156#11758222—81no—
157#11758222—81no—
158C2×D244—21no—
159C2×D244C22×C411yescharacteristic
160C2×D244C22×C411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—81no—
166C2×C4×D61—81no—
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61#4111yescharacteristic
170C2×Dic122—21no—
171D8×C61—22no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—81no—
176C2×C8×C61—81no—
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—41no—
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—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—81no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210D488—41no—
211#11758189—81no—
212#11758189—81no—
213#11758189—81no—
214C8×D61—81no—
215C23×C61—21no—
216C23×C61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—81no—
222C22×D61C4×D411yescharacteristic
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61#13112yes—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61C23×C411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C22⋊D61—42no—
237C22⋊D61—42no—
238C22⋊D61—81no—
239C22⋊D61—81no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—81no—
243C2×Dic61C4×D411yescharacteristic
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C4×D411yescharacteristic
246D244—21no—
247D244—21no—
248D244—21no—
249D244—21no—
250D244—81no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
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—41no—
268C8×C61—41no—
269C8×C61—41no—
270#92418—21no—
271#92418—21no—
272#92418—21no—
273#92418—21no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#18026—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61C2×C4×D411yescharacteristic
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
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—41no—
297C4×C61—41no—
298C4×C61C2×#13111yescharacteristic
299C4×C61#56811yescharacteristic
300C4×C61#57611yescharacteristic
301C4×C61#57611yescharacteristic
302Dic61—21no—
303Dic61—21no—
304Dic61—21no—
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×D8D6111yescharacteristic, complemented
318#1572—611no—
319#1496—611no—
320#1478—611no—
321#1454—611no—
322C2×C61—42no—
323C2×C61—81no—
324C2×C61#293311yescharacteristic
325C2×C61#294811yescharacteristic
326C2×C61#295511yescharacteristic
327D61—41no—
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×D8C2×D6111yescharacteristic
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—1221no—
354C8×D4C2×D6111yescharacteristic
355C8×D4C2×D6111yescharacteristic, complemented
356#432—611no—
357#431—611no—
358#431—611no—
359#431—611no—
360#431—611no—
361#408—1221no—
362#408—1221no—
363#407—1221no—
364C2×C22⋊C8—1221no—
365#335—611no—
366#335C2×D6111yescharacteristic, complemented
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⋊C8C2×D6111yescharacteristic
376D4⋊C8C2×D6111yescharacteristic, complemented
377#322—611no—
378#322—611no—
379#322—611no—
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×D8C4×D6111yescharacteristic
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—21no—
394C22×C8—21no—
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—1221no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4C22×D6111yescharacteristic
411C4×D4C22×D6111yescharacteristic
412C2×C4⋊C4—611no—
413C2×C22⋊C4—1221no—
414C2×C42—611no—
415#107—611no—
416#107—611no—
417#107—611no—
418#107C4×D6111yescharacteristic
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—1221no—
426C4⋊C8C22×D6111yescharacteristic
427C4⋊C8C22×D6111yescharacteristic
428#102—611no—
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102C4×D6111yescharacteristic
435#102C4×D6111yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—611no—
439C22⋊C8—611no—
440C22⋊C8—611no—
441C22⋊C8—611no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451#97—1221no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—1221no—
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—1221no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1222no—
470C2×D4—1221no—
471C2×D4—2441no—
472C2×D4C2×C4×D6111yescharacteristic
473C2×D4C2×C4×D6111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—4881no—
485C22×C4—4881no—
486D8—22no—
487D8—1222no—
488D8—2441no—
489D8—2441no—
490M16—4881no—
491M16—4881no—
492M16—4881no—
493M16—4881no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—81no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—611no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8C2×C4×D6111yescharacteristic
509C2×C8C2×C4×D6111yescharacteristic
510C2×C8D4×D6111yescharacteristic
511C2×C8D4×D6111yescharacteristic
512C4⋊C4—611no—
513C4⋊C4—611no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4C2×C4×D6111yescharacteristic
517C4⋊C4C2×C4×D6111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42C23×D6111yescharacteristic
530C23—21no—
531C23—21no—
532C23—611no—
533C23—1221no—
534C23—1221no—
535C23—4881no—
536C23—2442no—
537C23—2442no—
538Q8—4881no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—1221no—
543D4—1221no—
544D4—1221no—
545D4—1221no—
546D4—4881no—
547D4—4881no—
548D4—4881no—
549D4—2442no—
550D4—2442no—
551D4#1451978312yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—4881no—
568C2×C4—4881no—
569C2×C4—4881no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4C22×C4×D6111yescharacteristic
576C2×C4C2×D4×D6111yescharacteristic
577C2×C4#41×D6111yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—1221no—
586C8—1221no—
587C8—1221no—
588C8—1221no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—1221no—
599C22—1221no—
600C22—1221no—
601C22—4884no—
602C22—2441no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22C4×D4×D6111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—1221no—
613C4—1221no—
614C4—1221no—
615C4—2441no—
616C4—2441no—
617C4C2×#1451978311yescharacteristic
618C4#1684052711yescharacteristic
619C4#1684056311yescharacteristic
620C4#1684056411yescharacteristic
621C2—42no—
622C2—81no—
623C2—4881no—
624C2—4881no—
625C2—2441no—
626C2#2145453911yescharacteristic
627C2#2145466611yescharacteristic
628C2#2145471711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×D8×C61C2
socleC22×C61C2×C4×D4
prime radical#21455817C2
cosocleC42×C61C24
hypercenterC8×D8D61
hypocenterC61#18026
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #21454882C2semidirect
3. #21454852C2semidirect
4. #21444730C2semidirect
5. #21444705C2semidirect
6. #21444683C2semidirect
7. #21444683C2semidirect
8. #21444649C2semidirect
9. #21444647C2semidirect
10. #21444640C2semidirect
11. #21444598C2semidirect
12. #21444286C2semidirect
13. #21444208C2semidirect
14. #21444118C2semidirect
15. C8×D8×C61C2semidirect
30. #16839841C22semidirect
31. #16839840C22semidirect
37. #16839827C22semidirect
48. #16839515C22semidirect
49. #16839512C22semidirect
50. #16839512C22semidirect
52. #16839491C22semidirect
54. D4⋊#92418C22semidirect
56. #16839489C22semidirect
57. #16839484C22semidirect
58. #16839484C22semidirect
59. #16839484C22semidirect
62. C8×D4×C61C22semidirect
63. C61×#335C22semidirect
65. C61×D4⋊C8C22semidirect
66. C82×C61C22semidirect
317. C8×D8D61semidirect
355. C8×D4C2×D61semidirect
366. #335C2×D61semidirect
376. D4⋊C8C2×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
#214558172
#214548822
#214548522
#214447302
#214447052
#214446832
#214446492
#214446472
#214446402
#214445982
#214442862
#214442082
#214441182
C8×D8×C612
#1802661