Finite Group Databasebeta

← #29649681

Subgroups — #29649681

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454857C211yesmaximal, characteristic, complemented
2#21454840C211yesmaximal, characteristic, complemented
3C4×D8×D61C211yesmaximal, characteristic
4#21444685C211yesmaximal, characteristic, complemented
5#21444684C211yesmaximal, characteristic, complemented
6#21444682C211yesmaximal, characteristic, complemented
7#21444651C211yesmaximal, characteristic, complemented
8#21444648C211yesmaximal, characteristic, complemented
9#21444646C211yesmaximal, characteristic, complemented
10#21444645C211yesmaximal, characteristic, complemented
11#21444564C211yesmaximal, characteristic, complemented
12#21444208C211yesmaximal, characteristic, complemented
13#21444208C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1586C211yesmaximal, characteristic, complemented
16C2×D8×D61C411yescharacteristic
17C4×D4×D61C2211yescharacteristic
18C4×D4×D61C2211yescharacteristic
19C4×D488C2211yescharacteristic
20D8×Dic61C411yescharacteristic
21#16839844C411yescharacteristic
22C4×#11758199C2211yescharacteristic
23C4×#11758199C2211yescharacteristic
24#16839842C411yescharacteristic
25#16839842C411yescharacteristic
26#16839841C2211yescharacteristic, complemented
27#16839840C2211yescharacteristic, complemented
28#16839839C2211yescharacteristic, complemented
29#16839838—21no—
30#16839837—21no—
31C8×D244C2211yescharacteristic, complemented
32D4×#92418C2211yescharacteristic, complemented
33#16839827C2211yescharacteristic, complemented
34C8×C22⋊D61—21no—
35#16839825—21no—
36#16839814C2211yescharacteristic
37#16839814C2211yescharacteristic
38#16839813C2211yescharacteristic
39#16839813C2211yescharacteristic
40#107×D61C411yescharacteristic
41#102×D61C411yescharacteristic
42#102×D61C411yescharacteristic
43#16839725—21no—
44#16839724—21no—
45C2×#14519689—21no—
46C22⋊C8×D61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839513C2211yescharacteristic, complemented
51#16839491C2211yescharacteristic, complemented
52#16839491C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54D4⋊#92418C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic, complemented
56#16839489C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839484C2211yescharacteristic, complemented
59#16839483C2211yescharacteristic, complemented
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic, complemented
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#334C2211yescharacteristic, complemented
64C61×D4⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic, complemented
66C61×#322C2211yescharacteristic, complemented
67C2×D4×D61C2×C411yescharacteristic
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C2×D488C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74D8×D61—24no—
75C2×#11758194—21no—
76C2×#11758189—21no—
77C2×#11758189—21no—
78C22×#92418—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61C2×C411yescharacteristic
82C2×C8×D61C2×C411yescharacteristic
83C4×D244C2311yescharacteristic
84C4×D244C2311yescharacteristic
85D4×Dic61C2×C411yescharacteristic
86D4×Dic61C2×C411yescharacteristic
87#14519739C2×C411yescharacteristic
88#14519739C2×C411yescharacteristic
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91#14519737—21no—
92#14519737—21no—
93C4⋊C4×D61C2×C411yescharacteristic
94C4⋊C4×D61C2×C411yescharacteristic
95C22⋊C4×D61—21no—
96C22⋊C4×D61—21no—
97C42×D61C2311yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519710C2×C411yescharacteristic
100#14519710C2×C411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706D411yescharacteristic
105#14519706D411yescharacteristic
106#14519699C2×C411yescharacteristic
107#14519699C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109#14519698C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112C22⋊#92418—21no—
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689D411yescharacteristic
122#14519689D411yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C2×D8×C61C2×C411yescharacteristic
131C2×M16×C61—21no—
132C22×C8×C61—21no—
133C4×D4×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#107×C61C2×C411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#102×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155D4×D61—22no—
156D4×D61—22no—
157D4×D61—22no—
158D4×D61M1614yescomplemented
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—21no—
166C2×C4×D61—21no—
167C2×C4×D61—81no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×C4×D61—81no—
171C2×C4×D61C22×C411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61#4111yescharacteristic
174D8×C61—22no—
175M16×C61—81no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—81no—
180C2×C8×C61C22×C411yescharacteristic
181C2×C8×C61C22×C411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C42×C61C2411yescharacteristic
189C22⋊Dic61—21no—
190C22⋊Dic61—21no—
191#11758199—22no—
192#11758199—22no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200#11758196—21no—
201C4×Dic61C22×C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204#11758194—81no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—81no—
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213D488—22no—
214#11758189—81no—
215#11758189—81no—
216C8×D61—22no—
217C8×D61—22no—
218C8×D61—81no—
219C8×D61—81no—
220C23×C61—21no—
221C23×C61—21no—
222C22×D61—21no—
223C22×D61—24no—
224C22×D61—21no—
225C22×D61—42no—
226C22×D61—81no—
227C22×D61—81no—
228C22×D61—81no—
229C22×D61—81no—
230C22×D61C4×D411yescharacteristic
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61C2×M1612yes—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—24no—
245C22⋊D61—42no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—81no—
249C2×Dic61—81no—
250C2×Dic61C4×D411yescharacteristic
251C2×Dic61C4×D411yescharacteristic
252C2×Dic61C4×D411yescharacteristic
253D244—21no—
254D244—21no—
255D244—21no—
256D244C2×M1612yes—
257C4×D61—21no—
258C4×D61—21no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—81no—
265C4×D61—81no—
266C4×D61—81no—
267C4×D61—81no—
268C4×D61C2×M1612yes—
269C4×D61#13112yes—
270C8×C61—21no—
271C8×C61—21no—
272C8×C61—21no—
273C8×C61—21no—
274C8×C61—41no—
275C8×C61—41no—
276C8×C61—41no—
277#92418—21no—
278#92418—21no—
279#92418—21no—
280#92418—21no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#17877—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61C2×C4×D411yescharacteristic
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—22no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—84no—
301C2×D61—84no—
302C2×D61#43512yes—
303C4×C61—21no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61C22×M1611yescharacteristic
307C4×C61C2×#13111yescharacteristic
308C4×C61#57611yescharacteristic
309C4×C61#57611yescharacteristic
310Dic61—21no—
311Dic61—21no—
312Dic61—41no—
313Dic61—41no—
314Dic61#43512yes—
315#2975—611no—
316#2972—611no—
317C2×C4×D8—611no—
318#1586—611no—
319#1586—611no—
320#1586—611no—
321#1586D6111yescharacteristic, complemented
322#1581—611no—
323#1581—611no—
324#1581—611no—
325#1581—611no—
326#1564—611no—
327#1478—611no—
328#1478—611no—
329#1452—611no—
330C2×C61—42no—
331C2×C61—81no—
332C2×C61C2×#43511yescharacteristic
333C2×C61#294811yescharacteristic
334C2×C61#295711yescharacteristic
335D61—22no—
336D61—42no—
337D61—81no—
338C22×D8—611no—
339C2×C4×D4—611no—
340C2×C4×D4—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344C4×D8—611no—
345C4×D8—611no—
346C4×D8—611no—
347C4×D8—611no—
348C4×D8C2×D6111yescharacteristic
349#436—611no—
350#436—611no—
351#436—611no—
352#436—1221no—
353#436—1221no—
354#436C2×D6111yescharacteristic, complemented
355C8×D4—611no—
356C8×D4—611no—
357C8×D4—611no—
358C8×D4—1221no—
359C8×D4—1221no—
360C8×D4C2×D6111yescharacteristic, complemented
361#431—611no—
362#431—611no—
363#431—611no—
364#431—611no—
365C2×#107—611no—
366C2×#102—611no—
367C2×#102—611no—
368#407—1221no—
369#407—1221no—
370C2×C22⋊C8—1221no—
371C2×C22⋊C8—1221no—
372C2×C4×C8—611no—
373#335—611no—
374#335—611no—
375#334—611no—
376#334C2×D6111yescharacteristic, complemented
377D4⋊C8—611no—
378D4⋊C8—611no—
379D4⋊C8—611no—
380D4⋊C8—611no—
381D4⋊C8—611no—
382D4⋊C8—611no—
383D4⋊C8C2×D6111yescharacteristic, complemented
384D4⋊C8C2×D6111yescharacteristic, complemented
385#322—611no—
386#322—611no—
387#322—611no—
388#322C2×D6111yescharacteristic, complemented
389C61#1787711yescharacteristic, complemented, Sylow
390C22×D4—611no—
391C22×D4—611no—
392C23×C4—1221no—
393C23×C4—1221no—
394C2×D8—611no—
395C2×D8—611no—
396C2×D8—611no—
397C2×D8—1224no—
398C2×D8C4×D6111yescharacteristic
399C2×M16—21no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16—1221no—
403C22×C8—21no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—1221no—
407C22×C8—1221no—
408C22×C8—1221no—
409C4×D4—611no—
410C4×D4—611no—
411C4×D4—611no—
412C4×D4—611no—
413C4×D4—611no—
414C4×D4—611no—
415C4×D4—1221no—
416C4×D4—1221no—
417C4×D4—1221no—
418C4×D4—1221no—
419C4×D4C22×D6111yescharacteristic
420C4×D4C22×D6111yescharacteristic
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C42—611no—
426#107—611no—
427#107—611no—
428#107—611no—
429#107C4×D6111yescharacteristic
430C4⋊C8—611no—
431C4⋊C8—611no—
432C4⋊C8—611no—
433C4⋊C8—611no—
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—611no—
448C22⋊C8—611no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457C22⋊C8—1221no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—611no—
461C4×C8—611no—
462C4×C8—611no—
463C4×C8—1221no—
464C4×C8—1221no—
465C4×C8C22×D6111yescharacteristic
466C4×C8C22×D6111yescharacteristic
467C4×C8C22×D6111yescharacteristic
468C24—1221no—
469C24—1221no—
470C2×D4—614no—
471C2×D4—611no—
472C2×D4—611no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4C2×C4×D6111yescharacteristic
479C2×D4C2×C4×D6111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—4881no—
494C22×C4—4881no—
495C22×C4—4881no—
496C22×C4—4881no—
497D8—22no—
498D8—1222no—
499D8—1222no—
500D8—1222no—
501M16—81no—
502M16—4881no—
503M16—4881no—
504M16—4881no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—611no—
512C2×C8—611no—
513C2×C8—1222no—
514C2×C8—1222no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—4881no—
519C2×C8—4881no—
520C2×C8—4881no—
521C2×C8C2×C4×D6111yescharacteristic
522C2×C8C2×C4×D6111yescharacteristic
523C2×C8D4×D6111yescharacteristic
524C2×C8D4×D6111yescharacteristic
525C4⋊C4—611no—
526C4⋊C4—611no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4C2×C4×D6111yescharacteristic
530C4⋊C4C2×C4×D6111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42C23×D6111yescharacteristic
543C23—21no—
544C23—21no—
545C23—611no—
546C23—1224no—
547C23—1221no—
548C23—1221no—
549C23—4881no—
550C23—4881no—
551C23—4881no—
552C23—4881no—
553C23—2442no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—612no—
558D4—1224no—
559D4—1221no—
560D4—1221no—
561D4—1221no—
562D4—2442no—
563D4M16×D6112yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—611no—
571C2×C4—612no—
572C2×C4—612no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—4881no—
580C2×C4—4881no—
581C2×C4—4881no—
582C2×C4—4881no—
583C2×C4—4881no—
584C2×C4—4881no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4C22×C4×D6111yescharacteristic
591C2×C4C2×D4×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—1221no—
601C8—1221no—
602C8—1221no—
603C8—1221no—
604C8—2441no—
605C8—2441no—
606C8—2441no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—612no—
614C22—1221no—
615C22—1221no—
616C22—1222no—
617C22—4884no—
618C22—4884no—
619C22—2441no—
620C22—2441no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22C4×D4×D6111yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—612no—
629C4—1221no—
630C4—1221no—
631C4—2441no—
632C4—2441no—
633C4C2×M16×D6111yescharacteristic
634C4#131×D6111yescharacteristic
635C4#1684056611yescharacteristic
636C4#1684056611yescharacteristic
637C2—42no—
638C2—81no—
639C2—1222no—
640C2—4881no—
641C2—2442no—
642C2#435×D6111yescharacteristic
643C2#2145466811yescharacteristic
644C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1586C2
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C4
cosocleC42×C61C24
hypercenter#1586D61
hypocenterC61#17877
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
1. #21454857C2semidirect
2. #21454840C2semidirect
4. #21444685C2semidirect
5. #21444684C2semidirect
6. #21444682C2semidirect
7. #21444651C2semidirect
8. #21444648C2semidirect
9. #21444646C2semidirect
10. #21444645C2semidirect
11. #21444564C2semidirect
12. #21444208C2semidirect
13. #21444208C2semidirect
14. #21444110C2semidirect
15. C61×#1586C2semidirect
26. #16839841C22semidirect
27. #16839840C22semidirect
28. #16839839C22semidirect
31. C8×D244C22semidirect
32. D4×#92418C22semidirect
33. #16839827C22semidirect
48. #16839514C22semidirect
49. #16839514C22semidirect
50. #16839513C22semidirect
51. #16839491C22semidirect
52. #16839491C22semidirect
53. D4⋊#92418C22semidirect
54. D4⋊#92418C22semidirect
55. #16839489C22semidirect
56. #16839489C22semidirect
57. #16839484C22semidirect
58. #16839484C22semidirect
59. #16839483C22semidirect
61. C61×#436C22semidirect
62. C8×D4×C61C22semidirect
63. C61×#334C22semidirect
64. C61×D4⋊C8C22semidirect
65. C61×D4⋊C8C22semidirect
66. C61×#322C22semidirect
158. D4×D61M16semidirect
321. #1586D61semidirect
354. #436C2×D61semidirect
360. C8×D4C2×D61semidirect
376. #334C2×D61semidirect
383. D4⋊C8C2×D61semidirect
384. D4⋊C8C2×D61semidirect
388. #322C2×D61semidirect
389. C61#17877semidirect

Maximal subgroups

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

subgroupindex
#214548572
#214548402
C4×D8×D612
#214446852
#214446842
#214446822
#214446512
#214446482
#214446462
#214446452
#214445642
#214442082
#214441102
C61×#15862
#1787761