Finite Group Databasebeta

← #29650128

Subgroups — #29650128

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455817C211yesmaximal, characteristic
2#21454896C211yesmaximal, characteristic, complemented
3#21454840C211yesmaximal, characteristic, complemented
4#21444685C211yesmaximal, characteristic, complemented
5#21444648C211yesmaximal, characteristic, complemented
6#21444646C211yesmaximal, characteristic, complemented
7#21444643C211yesmaximal, characteristic, complemented
8#21444642C211yesmaximal, characteristic, complemented
9#21444611C211yesmaximal, characteristic, complemented
10#21444611C211yesmaximal, characteristic, complemented
11#21444596C211yesmaximal, characteristic, complemented
12#21444260C211yesmaximal, characteristic, complemented
13#21444234C211yesmaximal, characteristic, complemented
14#21444117C211yesmaximal, characteristic, complemented
15C61×#1586C211yesmaximal, 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, complemented
30#16839831—21no—
31#16839830—21no—
32C8×D244C2211yescharacteristic
33D4×#92418C2211yescharacteristic
34D4×#92418C2211yescharacteristic, complemented
35#16839827C2211yescharacteristic
36#16839827C2211yescharacteristic, complemented
37C8×C22⋊D61—21no—
38#16839825—21no—
39#16839818C2211yescharacteristic
40#16839814C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839730—21no—
44#16839727—21no—
45C2×#14519689—21no—
46C22⋊C8×D61—21no—
47C4×#11758189C2211yescharacteristic
48#16839514C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839513C2211yescharacteristic, complemented
51#16839491C2211yescharacteristic
52#16839491C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic, complemented
57#16839483C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic, complemented
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic, complemented
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic, complemented
66C61×#322C2211yescharacteristic, complemented
67C2×#11758222—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C2×D488C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80#14519776C2×C411yescharacteristic
81#14519773C2×C411yescharacteristic
82#14519763—21no—
83#14519752C2×C411yescharacteristic
84#14519750—21no—
85#14519748C2×C411yescharacteristic
86C4×D244C2311yescharacteristic
87C4×D244C2311yescharacteristic
88D4×Dic61C2×C411yescharacteristic
89#14519739C2×C411yescharacteristic
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92#14519737—21no—
93C4⋊C4×D61C2×C411yescharacteristic
94C22⋊C4×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
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#14519689C2×C411yescharacteristic
120#14519689C2×C411yescharacteristic
121#14519689D411yescharacteristic
122#14519689D411yescharacteristic
123#14519687—21no—
124#14519687—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×D8×C61C2×C411yescharacteristic
130C2×M16×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—22no—
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—
172M16×C61—81no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
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—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
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—81no—
205C2×#92418—81no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210D488—22no—
211#11758189—42no—
212#11758189—81no—
213C8×D61—81no—
214C8×D61—81no—
215C8×D61—81no—
216C23×C61—21no—
217C23×C61—21no—
218C22×D61—21no—
219C22×D61—24no—
220C22×D61—21no—
221C22×D61—81no—
222C22×D61—81no—
223C22×D61C4×D411yescharacteristic
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61#13112yes—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61C23×C411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C22⋊D61—24no—
238C22⋊D61—81no—
239C22⋊D61—81no—
240C22⋊D61—81no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—81no—
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C4×D411yescharacteristic
246C2×Dic61C4×D411yescharacteristic
247D244—21no—
248D244—21no—
249D244—21no—
250D244—81no—
251D244#13112yes—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—81no—
262C4×D61—81no—
263Dic122—81no—
264C8×C61—22no—
265C8×C61—21no—
266C8×C61—21no—
267C8×C61—21no—
268C8×C61—21no—
269C8×C61—41no—
270C8×C61—41no—
271#92418—21no—
272#92418—21no—
273#92418—21no—
274#92418—21no—
275#92418—41no—
276#92418—41no—
277#92418—41no—
278#17922—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61C2×C4×D411yescharacteristic
286C2×D61—21no—
287C2×D61—22no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—84no—
296C4×C61—21no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61C2×#13111yescharacteristic
300C4×C61C2×#13111yescharacteristic
301C4×C61#57611yescharacteristic
302C4×C61#57611yescharacteristic
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—41no—
307Dic61—41no—
308#3100—611no—
309#2981—611no—
310#2972—611no—
311#1586—611no—
312#1586D6111yescharacteristic, complemented
313#1581—611no—
314#1581—611no—
315#1580—611no—
316#1580—611no—
317C8×D8—611no—
318C8×D8—611no—
319#1572—611no—
320#1490—611no—
321#1484—611no—
322#1453—611no—
323C2×C61—42no—
324C2×C61—81no—
325C2×C61#292911yescharacteristic
326C2×C61#294811yescharacteristic
327C2×C61#295611yescharacteristic
328D61—41no—
329D61—42no—
330D61—81no—
331#532—611no—
332C2×C4×D4—611no—
333#480—611no—
334#480—611no—
335#474—611no—
336#474—611no—
337#459—611no—
338#459—611no—
339#447—611no—
340#447—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344C4×D8C2×D6111yescharacteristic
345#436—611no—
346#436C2×D6111yescharacteristic, complemented
347#435—1221no—
348#435—1221no—
349C8×D4—611no—
350C8×D4—611no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—1221no—
355C8×D4—1221no—
356C8×D4C2×D6111yescharacteristic
357#432—611no—
358#431—611no—
359#431—611no—
360#431—611no—
361#408—1221no—
362#408—1221no—
363C2×C22⋊C8—1221no—
364C2×C22⋊C8—1221no—
365C4×M16—611no—
366#335—611no—
367#335—611no—
368#334—611no—
369#334C2×D6111yescharacteristic, complemented
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8C2×D6111yescharacteristic
377D4⋊C8C2×D6111yescharacteristic, complemented
378#322—611no—
379#322—611no—
380#322C2×D6111yescharacteristic, complemented
381C82—611no—
382C61#1792211yescharacteristic, complemented, Sylow
383C2×#41—1221no—
384C22×D4—611no—
385C23×C4—1221no—
386C2×D8—611no—
387C2×D8—611no—
388C2×D8—611no—
389C2×D8C4×D6111yescharacteristic
390C2×M16—21no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—21no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C4⋊Q8—611no—
400#127—611no—
401#124—1221no—
402#121—611no—
403#121—611no—
404#121—1221no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4C22×D6111yescharacteristic
413C4×D4C22×D6111yescharacteristic
414C2×C4⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417#107—611no—
418#107—611no—
419#107—611no—
420#107C4×D6111yescharacteristic
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8C22×D6111yescharacteristic
428C4⋊C8C22×D6111yescharacteristic
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102C4×D6111yescharacteristic
436#102C4×D6111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—611no—
440C22⋊C8—611no—
441C22⋊C8—611no—
442C22⋊C8—611no—
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—
452#97—1221no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—1221no—
457C4×C8C22×D6111yescharacteristic
458C4×C8C22×D6111yescharacteristic
459C4×C8C22×D6111yescharacteristic
460C24—1221no—
461#41—4881no—
462#41—4881no—
463C2×Q8—1221no—
464C2×D4—611no—
465C2×D4—611no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1222no—
471C2×D4—1222no—
472C2×D4—1221no—
473C2×D4C2×C4×D6111yescharacteristic
474C2×D4C2×C4×D6111yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—4881no—
486C22×C4—4881no—
487D8—22no—
488D8—1222no—
489D8—1222no—
490D8—1222no—
491M16—81no—
492M16—4881no—
493M16—2442no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—4881no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8—4881no—
509C2×C8—4881no—
510C2×C8C2×C4×D6111yescharacteristic
511C2×C8C2×C4×D6111yescharacteristic
512C2×C8D4×D6111yescharacteristic
513C2×C8D4×D6111yescharacteristic
514C4⋊C4—611no—
515C4⋊C4—611no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4C2×C4×D6111yescharacteristic
519C4⋊C4C2×C4×D6111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42C23×D6111yescharacteristic
532C23—21no—
533C23—21no—
534C23—611no—
535C23—1224no—
536C23—1221no—
537C23—1221no—
538C23—4881no—
539C23—4881no—
540Q8—4881no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—612no—
545D4—1224no—
546D4—1221no—
547D4—1221no—
548D4—1221no—
549D4—4881no—
550D4—4881no—
551D4—4881no—
552D4—4881no—
553D4#1451978512yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—4881no—
570C2×C4—4881no—
571C2×C4—4881no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4C22×C4×D6111yescharacteristic
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4#41×D6111yescharacteristic
580C8—22no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—1221no—
588C8—1221no—
589C8—1221no—
590C8—1221no—
591C8—2441no—
592C8—2441no—
593C8—2441no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—1221no—
601C22—1221no—
602C22—1221no—
603C22—1222no—
604C22—4884no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22C4×D4×D6111yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—1221no—
615C4—1221no—
616C4—1221no—
617C4—2441no—
618C4—2441no—
619C4#131×D6111yescharacteristic
620C4C2×#1451978511yescharacteristic
621C4#1684056611yescharacteristic
622C4#1684056611yescharacteristic
623C2—42no—
624C2—81no—
625C2—4881no—
626C2—2441no—
627C2—2442no—
628C2#2145451011yescharacteristic
629C2#2145466811yescharacteristic
630C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1586C2
socleC22×C61C2×C4×D4
prime radical#21455817C2
cosocleC42×C61C24
hypercenter#1586D61
hypocenterC61#17922
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #21454896C2semidirect
3. #21454840C2semidirect
4. #21444685C2semidirect
5. #21444648C2semidirect
6. #21444646C2semidirect
7. #21444643C2semidirect
8. #21444642C2semidirect
9. #21444611C2semidirect
10. #21444611C2semidirect
11. #21444596C2semidirect
12. #21444260C2semidirect
13. #21444234C2semidirect
14. #21444117C2semidirect
15. C61×#1586C2semidirect
29. #16839841C22semidirect
34. D4×#92418C22semidirect
36. #16839827C22semidirect
48. #16839514C22semidirect
49. #16839514C22semidirect
50. #16839513C22semidirect
52. #16839491C22semidirect
54. D4⋊#92418C22semidirect
56. #16839489C22semidirect
57. #16839483C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
61. C61×#436C22semidirect
63. C61×#334C22semidirect
65. C61×D4⋊C8C22semidirect
66. C61×#322C22semidirect
312. #1586D61semidirect
346. #436C2×D61semidirect
369. #334C2×D61semidirect
377. D4⋊C8C2×D61semidirect
380. #322C2×D61semidirect
382. C61#17922semidirect

Maximal subgroups

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

subgroupindex
#214558172
#214548962
#214548402
#214446852
#214446482
#214446462
#214446432
#214446422
#214446112
#214445962
#214442602
#214442342
#214441172
C61×#15862
#1792261