Finite Group Databasebeta

← #30603008

Subgroups — #30603008

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#104C211yesmaximal, characteristic
2C2×#16840752C211yesmaximal, characteristic
3C22×#14519831C211yesmaximal, characteristic, complemented
4C2×#16840637C211yesmaximal, characteristic, complemented
5C2×#16840634C211yesmaximal, characteristic, complemented
6#21461484C211yesmaximal, characteristic, complemented
7#408×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2211yescharacteristic
9C22×D61⋊C8C2211yescharacteristic
10C2×#14519856C2211yescharacteristic
11C22×C4×#6923C2211yescharacteristic
12C2×#14519842C412yescomplemented
13D61⋊#104—22no—
14D61⋊#104—22no—
15C2×#14519841C412yescomplemented
16#16840752—22no—
17#16840752—22no—
18C2×#14519840C412yescomplemented
19C2×#14519839C412yescomplemented
20C2×#14519831—22no—
21C2×#14519831—22no—
22C2×#14519831—22no—
23#16840637—22no—
24#16840634—22no—
25(C2×#6923)⋊C8—22no—
26C2×#41×D61C2211yescharacteristic
27C2×M16×D61C2211yescharacteristic
28C22×C8×D61C2211yescharacteristic
29#16839730C411yescharacteristic, complemented
30#16839729C411yescharacteristic, complemented
31#16839728C411yescharacteristic, complemented
32#16839727—22no—
33C22⋊C8×D61—22no—
34C61×#408C411yescharacteristic, complemented
35C23×#6923—21no—
36C2×#11758213C2×C412yes—
37D61⋊M16—21no—
38D61⋊M16—21no—
39D61⋊M16—21no—
40D61⋊M16—21no—
41C2×#11758217—21no—
42C2×D61⋊C8—21no—
43C2×D61⋊C8—21no—
44C2×D61⋊C8—21no—
45C2×D61⋊C8—21no—
46C2×D61⋊C8C2×C412yes—
47C2×D61⋊C8D412yes—
48C2×D61⋊C8D412yes—
49C22×#92420—21no—
50#14519856—21no—
51#14519856—21no—
52#14519856—21no—
53#14519856—21no—
54C2×C4⋊#6923C2×C412yes—
55C2×C22⋊#6923—21no—
56C2×C4×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923—21no—
59C2×C4×#6923—21no—
60C2×C4×#6923C2×C412yes—
61C2×C4×#6923D412yes—
62C2×C4×#6923D412yes—
63#14519842—24no—
64#14519841—24no—
65#14519840—24no—
66#14519839—24no—
67#14519831—28no—
68C2×#11758226C2×C411yescharacteristic
69C2×#11758222—21no—
70C2×#11758222C2×C411yescharacteristic
71C2×#11758224—21no—
72C2×#11758224C2×C411yescharacteristic
73#41×D61—21no—
74#41×D61—21no—
75#41×D61—21no—
76#41×D61—21no—
77#41×D61—21no—
78#41×D61—21no—
79#41×D61—21no—
80#41×D61—21no—
81C2×Q8×D61C2×C411yescharacteristic
82C2×D4×D61—21no—
83C2×D4×D61C2×C411yescharacteristic
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758194C2×C411yescharacteristic
87C2×#11758189—21no—
88M16×D61—21no—
89M16×D61—21no—
90M16×D61—21no—
91M16×D61—21no—
92C22×#92418C2×C411yescharacteristic
93C2×C8×D61—21no—
94C2×C8×D61—21no—
95C2×C8×D61—21no—
96C2×C8×D61—21no—
97C2×C8×D61—21no—
98C2×C8×D61D412yes—
99C2×C8×D61D412yes—
100C22⋊#92418—22no—
101#14519689—22no—
102#14519689—22no—
103C2×#41×C61C2×C411yescharacteristic
104C2×M16×C61C2×C411yescharacteristic
105C22×C8×C61C2×C411yescharacteristic
106C22⋊C8×C61—22no—
107C23×D61—21no—
108C23×D61#4111yescharacteristic
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—22no—
112C22×#6923—22no—
113C22×#6923—44no—
114#41×C61—21no—
115#41×C61—21no—
116#41×C61—21no—
117#41×C61—21no—
118C2×Q8×C61C4211yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61C4211yescharacteristic
121C22×C4×C61—21no—
122C22×C4×C61C22×C411yescharacteristic
123C2×C22⋊D61—21no—
124C2×C22⋊D61—21no—
125C2×C22⋊D61—21no—
126C22×Dic61—21no—
127C22×Dic61#4111yescharacteristic
128#11758226—21no—
129#11758226—21no—
130#11758226—21no—
131#11758226—21no—
132Q8×D61—21no—
133Q8×D61—21no—
134Q8×D61—21no—
135Q8×D61—21no—
136#11758224—21no—
137#11758224—21no—
138#11758224—21no—
139#11758224—21no—
140#11758224—41no—
141#11758224—41no—
142#11758224—41no—
143#11758224—41no—
144D4×D61—21no—
145D4×D61—21no—
146D4×D61—21no—
147D4×D61—21no—
148D4×D61—41no—
149D4×D61—41no—
150D4×D61—41no—
151D4×D61—41no—
152#11758222—21no—
153#11758222—21no—
154#11758222—21no—
155#11758222—21no—
156#11758222—41no—
157#11758222—41no—
158#11758222—41no—
159#11758222—41no—
160C2×D244—21no—
161C2×D244C4211yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—41no—
166C2×C4×D61—41no—
167C2×C4×D61—41no—
168C2×C4×D61—41no—
169C2×C4×D61C22×C411yescharacteristic
170C2×C4×D61C22×C411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61#4111yescharacteristic
178C2×C4×D61#4111yescharacteristic
179C2×C4×D61#4111yescharacteristic
180C2×C4×D61#4111yescharacteristic
181C2×Dic122—21no—
182C2×Dic122C4211yescharacteristic
183C22⋊#6923—41no—
184C22⋊#6923—41no—
185#11758217—41no—
186#11758217—41no—
187C2×#92420—22no—
188C2×#92420—22no—
189C2×#92420—22no—
190C2×#92420—22no—
191C4⋊#6923—22no—
192C4⋊#6923—22no—
193C4×#6923—22no—
194C4×#6923—22no—
195C4×#6923—22no—
196C4×#6923—41no—
197C4×#6923—41no—
198C4×#6923C22⋊C414yes—
199#11758213—22no—
200#11758213—22no—
201D61⋊C8—22no—
202D61⋊C8—22no—
203D61⋊C8—22no—
204D61⋊C8—41no—
205D61⋊C8—41no—
206D61⋊C8C22⋊C414yes—
207M16×C61—21no—
208M16×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61C22⋊C412yes—
213#11758194—21no—
214#11758194—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418C22⋊C412yes—
219#11758189—41no—
220#11758189—41no—
221C8×D61—22no—
222C8×D61—22no—
223C8×D61—22no—
224C8×D61—22no—
225C8×D61—41no—
226C8×D61—41no—
227C23×C61—21no—
228C23×C61#11711yescharacteristic
229C22×D61—24no—
230C22×D61—21no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—44no—
234C22×D61C4×D411yescharacteristic
235C22×D61C4×D411yescharacteristic
236C22×D61#12111yescharacteristic
237C22×D61#12311yescharacteristic
238C22×D61#12411yescharacteristic
239C22×D61#12611yescharacteristic
240C2×#6923—24no—
241C2×#6923—44no—
242C2×#6923—44no—
243C2×#6923—44no—
244C2×#6923—42no—
245C2×#6923—44no—
246Q8×C61—21no—
247Q8×C61—21no—
248D4×C61—21no—
249D4×C61—21no—
250D4×C61—41no—
251D4×C61—41no—
252C2×C4×C61—21no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61C2×C4211yescharacteristic
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C4×D411yescharacteristic
258C2×C4×C61C4×D411yescharacteristic
259C2×C4×C61C4×D411yescharacteristic
260C2×C4×C61C4×D411yescharacteristic
261C22⋊D61—41no—
262C22⋊D61—41no—
263C22⋊D61—41no—
264C22⋊D61—41no—
265C22⋊D61—41no—
266C22⋊D61—41no—
267C2×Dic61—21no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61C4×D411yescharacteristic
271C2×Dic61C4×D411yescharacteristic
272C2×Dic61#12111yescharacteristic
273C2×Dic61#12311yescharacteristic
274C2×Dic61#12411yescharacteristic
275C2×Dic61#12611yescharacteristic
276D244—21no—
277D244—21no—
278D244—41no—
279D244—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61C2×C22⋊C411yescharacteristic
287C4×D61C2×C22⋊C411yescharacteristic
288C4×D61#11711yescharacteristic
289C4×D61#11711yescharacteristic
290C4×D61C4×D411yescharacteristic
291C4×D61C4×D411yescharacteristic
292C4×D61C4×D411yescharacteristic
293C4×D61C4×D411yescharacteristic
294C4×D61#12011yescharacteristic
295C4×D61#12111yescharacteristic
296C4×D61#12111yescharacteristic
297C4×D61#12111yescharacteristic
298C4×D61#12111yescharacteristic
299C4×D61#12311yescharacteristic
300C4×D61#12411yescharacteristic
301C4×D61#12711yescharacteristic
302Dic122—21no—
303Dic122—21no—
304Dic122—41no—
305Dic122—41no—
306#92420—24no—
307#92420—42no—
308C8×C61—22no—
309C8×C61—41no—
310#92418—22no—
311#92418—41no—
312#10930—611nomaximal, Sylow
313C22×C61—22no—
314C22×C61—41no—
315C22×C61—42no—
316C22×C61C4×C22⋊C411yescharacteristic
317C22×C61#38811yescharacteristic
318C22×C61#38811yescharacteristic
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—41no—
325C2×D61—42no—
326C2×D61—82no—
327C2×D61—82no—
328C2×D61#38611yescharacteristic
329C2×D61#38811yescharacteristic
330C2×D61#38811yescharacteristic
331C2×D61#39011yescharacteristic
332C2×D61#44414yes—
333#6923—44no—
334#6923—82no—
335C4×C61—41no—
336C4×C61C4×C22⋊C411yescharacteristic
337C4×C61C4×C22⋊C411yescharacteristic
338C4×C61#38611yescharacteristic
339C4×C61#39011yescharacteristic
340Dic61—41no—
341Dic61#38611yescharacteristic
342Dic61#38811yescharacteristic
343Dic61#38811yescharacteristic
344Dic61#39011yescharacteristic
345C22×#104—611no—
346C2×#416—611no—
347C2×#408—611no—
348C22×#97—611no—
349C2×#341—611no—
350C2×#339—611no—
351#1729—611no—
352C2×C61—21no—
353C2×C61—21no—
354C2×C61—81no—
355C2×C61#143711yescharacteristic
356C2×C61#176512yes—
357D61—21no—
358D61—21no—
359D61—81no—
360D61#193812yes—
361D61#197512yes—
362C22×#41—611no—
363C22×M16—611no—
364C22×M16—611no—
365C23×C8—611no—
366C23×C8—611no—
367C2×#117—611no—
368C22×C42—611no—
369C2×#104—612no—
370C2×#104—612no—
371C2×#104—1222no—
372C2×#104—1222no—
373#416—1222no—
374#416—1222no—
375C2×#103—612no—
376C2×#102—612no—
377#408—611no—
378#408—611no—
379#408—611no—
380#408—1222no—
381#408#692311yescharacteristic, complemented
382C2×C22⋊C8—1222no—
383C2×#97—1222no—
384C2×#97—1222no—
385C2×#97—1222no—
386#341—1222no—
387#339—1222no—
388#336—1222no—
389C61#1093011yescharacteristic, complemented, Sylow
390C2×#41—611no—
391C2×#41—611no—
392C2×#41—611no—
393C2×#41—1221no—
394C2×#41—1221no—
395C2×#41—1221no—
396C2×#41—1221no—
397C2×#41—1221no—
398C2×#41—1221no—
399C2×#41—1221no—
400C2×#41—1221no—
401C2×#41—1221no—
402C2×#41—1221no—
403C2×#41C2×#692311yescharacteristic
404C22×Q8—611no—
405C22×D4—611no—
406C22×D4—1221no—
407C23×C4—611no—
408C23×C4—1221no—
409C23×C4—1221no—
410C2×M16—612no—
411C2×M16—611no—
412C2×M16—1221no—
413C2×M16—1221no—
414C2×M16—1221no—
415C2×M16—1221no—
416C2×M16—1221no—
417C2×M16—1221no—
418C2×M16—1221no—
419C2×M16—1221no—
420C2×M16—1221no—
421C2×M16—1221no—
422C2×M16C2×#692311yescharacteristic
423C22×C8—612no—
424C22×C8—612no—
425C22×C8—612no—
426C22×C8—611no—
427C22×C8—612no—
428C22×C8—612no—
429C22×C8—1221no—
430C22×C8—1221no—
431C22×C8—1221no—
432C22×C8—1221no—
433C22×C8—1221no—
434C22×C8—1221no—
435C22×C8—1221no—
436C22×C8—1221no—
437C22×C8—1221no—
438C22×C8—1221no—
439C22×C8C2×#692311yescharacteristic
440#117—1221no—
441#117—1221no—
442#117—1221no—
443#117—1221no—
444C2×C4⋊C4—612no—
445C2×C22⋊C4—1221no—
446C2×C42—612no—
447C2×C42—612no—
448C2×C42—612no—
449C2×C42—1221no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42—1221no—
453#104—1224no—
454#104—1224no—
455#103—1224no—
456#102—1224no—
457C22⋊C8—22no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460C22⋊C8—1222no—
461#97—1228no—
462C24—611no—
463C24—1221no—
464#41—21no—
465#41—21no—
466#41—21no—
467#41—21no—
468#41—1221no—
469#41—1221no—
470#41—1221no—
471#41—1221no—
472#41—1221no—
473#41—1221no—
474#41—1221no—
475#41—1221no—
476#41—1221no—
477#41—1221no—
478#41—1221no—
479#41—1221no—
480#41—2441no—
481#41—2441no—
482#41—2441no—
483#41—2441no—
484#41—2441no—
485#41—2441no—
486#41—2441no—
487#41—2441no—
488C2×Q8—611no—
489C2×Q8—1221no—
490C2×Q8—1221no—
491C2×Q8—1221no—
492C2×Q8—1221no—
493C2×Q8—1221no—
494C2×Q8C4×#692311yescharacteristic
495C2×D4—21no—
496C2×D4—611no—
497C2×D4—1221no—
498C2×D4—1221no—
499C2×D4—1221no—
500C2×D4—1221no—
501C2×D4—1221no—
502C2×D4—1221no—
503C2×D4—1221no—
504C2×D4—1221no—
505C2×D4—2441no—
506C2×D4—2441no—
507C2×D4—2441no—
508C2×D4—2441no—
509C2×D4C4×#692311yescharacteristic
510C22×C4—21no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1221no—
531C22×C4—1222no—
532C22×C4—2441no—
533C22×C4—2441no—
534C22×C4—2441no—
535C22×C4—2441no—
536C22×C4—2444no—
537C22×C4C22×#692311yescharacteristic
538M16—21no—
539M16—21no—
540M16—1222no—
541M16—1222no—
542M16—1221no—
543M16—1221no—
544M16—2441no—
545M16—2441no—
546M16—2441no—
547M16—2441no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—614no—
552C2×C8—612no—
553C2×C8—1222no—
554C2×C8—1222no—
555C2×C8—1222no—
556C2×C8—1222no—
557C2×C8—1222no—
558C2×C8—1222no—
559C2×C8—1222no—
560C2×C8—1222no—
561C2×C8—1222no—
562C2×C8—1222no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1222no—
566C2×C8—1221no—
567C2×C8—2441no—
568C2×C8—2441no—
569C2×C8—2441no—
570C2×C8—2441no—
571C2×C8C22⋊#692312yes—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C22⋊C4—2441no—
575C22⋊C4—2441no—
576C42—614no—
577C42—1222no—
578C42—1222no—
579C42—1222no—
580C42—2441no—
581C42—2441no—
582C23—21no—
583C23—611no—
584C23—611no—
585C23—611no—
586C23—611no—
587C23—611no—
588C23—611no—
589C23—1224no—
590C23—1221no—
591C23—2441no—
592C23—2441no—
593C23—2444no—
594C23#1451985611yescharacteristic
595Q8—21no—
596Q8—21no—
597Q8—1221no—
598Q8—1221no—
599Q8—2441no—
600Q8—2441no—
601D4—21no—
602D4—21no—
603D4—41no—
604D4—41no—
605D4—1221no—
606D4—1221no—
607D4—2441no—
608D4—2441no—
609D4—2441no—
610D4—2441no—
611D4—2441no—
612D4—2441no—
613D4—2441no—
614D4—2441no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—611no—
625C2×C4—611no—
626C2×C4—611no—
627C2×C4—611no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—611no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—1224no—
641C2×C4—1221no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2442no—
649C2×C4—2444no—
650C2×C4—2444no—
651C2×C4—2444no—
652C2×C4—2444no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4C2×C4×#692311yescharacteristic
656C2×C4C2×C22⋊#692311yescharacteristic
657C2×C4D4×#692311yescharacteristic
658C2×C4D4×#692311yescharacteristic
659C2×C4D4×#692311yescharacteristic
660C2×C4D4×#692311yescharacteristic
661C8—22no—
662C8—41no—
663C8—1224no—
664C8—1222no—
665C8—2442no—
666C8—2441no—
667C22—22no—
668C22—41no—
669C22—42no—
670C22—611no—
671C22—611no—
672C22—614no—
673C22—611no—
674C22—611no—
675C22—1222no—
676C22—1222no—
677C22—1222no—
678C22—1222no—
679C22—1222no—
680C22—4882no—
681C22—4882no—
682C22—2441no—
683C22—2442no—
684C22C4×C22⋊#692311yescharacteristic
685C22#1684071211yescharacteristic
686C22#1684071211yescharacteristic
687C4—41no—
688C4—611no—
689C4—611no—
690C4—611no—
691C4—611no—
692C4—4882no—
693C4—2444no—
694C4—2441no—
695C4C22⋊C4×#692311yescharacteristic
696C4C22⋊C4×#692311yescharacteristic
697C4#1684071011yescharacteristic
698C4#1684071411yescharacteristic
699C2—21no—
700C2—21no—
701C2—81no—
702C2—612no—
703C2—612no—
704C2—1221no—
705C2—1221no—
706C2—4881no—
707C2#2146100011yescharacteristic
708C2#2146159712yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenter#408#6923
hypocenterC61#10930
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
3. C22×#14519831C2semidirect
4. C2×#16840637C2semidirect
5. C2×#16840634C2semidirect
6. #21461484C2semidirect
12. C2×#14519842C4semidirect
15. C2×#14519841C4semidirect
18. C2×#14519840C4semidirect
19. C2×#14519839C4semidirect
29. #16839730C4semidirect
30. #16839729C4semidirect
31. #16839728C4semidirect
34. C61×#408C4semidirect
381. #408#6923semidirect
389. C61#10930semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1042
C2×#168407522
C22×#145198312
C2×#168406372
C2×#168406342
#214614842
#408×D612
#1093061