Finite Group Databasebeta

← #30622187

Subgroups — #30622187

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C212yesmaximal, complemented
2#21462349C211yesmaximal, characteristic
3Q8×C4⋊#6923C211yesmaximal, characteristic, complemented
4#21461947C211yesmaximal, characteristic
5#21461931C211yesmaximal, characteristic, complemented
6#21461909C212yesmaximal, complemented
7#21461815C212yesmaximal, complemented
8#21461784C212yesmaximal, complemented
9#21461612C211yesmaximal, characteristic, complemented
10C4×#14519840C211yesmaximal, characteristic, complemented
11#460×D61C211yesmaximal, characteristic
12C2×Q8×#6923C2212yes—
13C2×D4×#6923—21no—
14C2×D4×#6923C2212yes—
15SD16×#6923—28no—
16C2×#14519845C2212yes—
17C2×#14519840C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519839C2212yes—
20C2×#14519839C2212yes—
21C4×D61⋊C8C2211yescharacteristic
22C2×C8×#6923C2212yes—
23#16840714—21no—
24#16840714C2212yes—
25#16840713—22no—
26#16840713C2212yes—
27#16840710—22no—
28#16840708—21no—
29#16840708C2211yescharacteristic
30C4×C4⋊#6923—21no—
31C4×C4⋊#6923C2211yescharacteristic
32C4×C4⋊#6923C2211yescharacteristic
33#16840636C2212yes—
34#16840635C2211yescharacteristic
35#16840635C2211yescharacteristic
36(C2×#6923)⋊C8C2212yes—
37C2×SD16×D61C2212yes—
38#127×D61C2211yescharacteristic
39C4×Q8×D61C2211yescharacteristic
40#16839963C411yescharacteristic, complemented
41#16839962C411yescharacteristic, complemented
42#16839961C412yescomplemented
43#16839960C412yescomplemented
44#16839959C411yescharacteristic, complemented
45C4⋊C8×D61C2211yescharacteristic
46#102×D61C2212yes—
47C61×#460C411yescharacteristic, complemented
48C23×#6923—22no—
49C2×D61⋊C8C2311yescharacteristic
50C2×D61⋊C8C2311yescharacteristic
51Q8×#6923—24no—
52Q8×#6923—42no—
53D4×#6923—24no—
54D4×#6923—42no—
55D4×#6923—44no—
56C2×C4⋊#6923—22no—
57C2×C4⋊#6923—21no—
58C2×C4⋊#6923—22no—
59C2×C4⋊#6923—21no—
60C2×C4⋊#6923D411yescharacteristic
61C2×C4⋊#6923D411yescharacteristic
62C2×C4⋊#6923C2312yes—
63C2×C4⋊#6923C2311yescharacteristic
64C2×C4⋊#6923C2311yescharacteristic
65C2×C22⋊#6923—22no—
66C2×C22⋊#6923—22no—
67C2×C22⋊#6923—22no—
68C2×C4×#6923—22no—
69C2×C4×#6923—21no—
70C2×C4×#6923C2312yes—
71#14519845—24no—
72#14519840—22no—
73#14519840D414yescomplemented
74#14519839—24no—
75#14519839—42no—
76C4×#92420—21no—
77C4×#92420—21no—
78C8×#6923—24no—
79(C2×#6923)⋊C4—22no—
80(C2×#6923)⋊C4—21no—
81(C2×#6923)⋊C4D412yes—
82C2×Q8×D61C2311yescharacteristic
83C2×D4×D61—21no—
84C2×D4×D61—21no—
85C2×D4×D61C2312yes—
86C2×#11758190C2×C412yescomplemented
87C2×#11758200C2×C412yescomplemented
88C2×#11758201C2×C412yescomplemented
89SD16×D61—24no—
90SD16×D61—24no—
91C2×C8×D61C2312yes—
92#14519774C2×C411yescharacteristic
93#14519773—21no—
94#14519773—21no—
95#14519773C2×C412yes—
96Q8×Dic61C2×C411yescharacteristic, complemented
97C4×Dic122—21no—
98C4×Dic122C2×C411yescharacteristic, complemented
99#14519742—21no—
100#14519742C2×C411yescharacteristic, complemented
101C4⋊C4×D61—21no—
102C4⋊C4×D61C2311yescharacteristic
103C42×D61—21no—
104C42×D61C2311yescharacteristic
105C4⋊#92418C2×C411yescharacteristic, complemented
106#14519706C2×C412yescomplemented
107#14519699C2×C412yescomplemented
108#14519698C2×C412yescomplemented
109#14519697C2×C412yescomplemented
110C2×SD16×C61C2×C412yescomplemented
111#127×C61C2×C411yescharacteristic
112C4×Q8×C61C2×C411yescharacteristic, complemented
113C4⋊C8×C61C2×C411yescharacteristic, complemented
114#102×C61C2×C412yescomplemented
115C23×D61—22no—
116C22×#6923—21no—
117C22×#6923—21no—
118C22×#6923—22no—
119C22×#6923—44no—
120C22×#6923—44no—
121C22×#6923—82no—
122C22×#6923C2×D412yes—
123C22×#6923C2×D412yes—
124C2×Q8×C61C22×C411yescharacteristic
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61C22×C412yes—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—22no—
131Q8×D61—21no—
132Q8×D61—21no—
133Q8×D61C2×D412yes—
134Q8×D61#4112yes—
135D4×D61—22no—
136D4×D61—22no—
137D4×D61—22no—
138D4×D61—22no—
139D4×D61—42no—
140D4×D61—42no—
141D4×D61—81no—
142D4×D61—81no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244C22×C412yes—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61C2×D411yescharacteristic
149C2×C4×D61C2×D411yescharacteristic
150C2×C4×D61C2411yescharacteristic
151C2×Dic122—21no—
152C2×Dic122C22×C411yescharacteristic
153C22⋊#6923—44no—
154C22⋊#6923—44no—
155C22⋊#6923—82no—
156C2×#92420—21no—
157C2×#92420—21no—
158C4⋊#6923—22no—
159C4⋊#6923—22no—
160C4⋊#6923—21no—
161C4⋊#6923—21no—
162C4⋊#6923—22no—
163C4⋊#6923—21no—
164C4⋊#6923—44no—
165C4⋊#6923—42no—
166C4⋊#6923—81no—
167C4⋊#6923—82no—
168C4⋊#6923SD1614yescomplemented
169C4⋊#6923C2×D412yes—
170C4×#6923—22no—
171C4×#6923—22no—
172C4×#6923—44no—
173C4×#6923—42no—
174D61⋊C8—21no—
175D61⋊C8—21no—
176D61⋊C8—21no—
177D61⋊C8C2×D412yes—
178SD16×C61—24no—
179C2×C8×C61C22×C412yes—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C411yescharacteristic
182C42×C61—21no—
183C42×C61C22×C411yescharacteristic
184#11758201—24no—
185#11758200—24no—
186C4⋊Dic61—21no—
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61#4111yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418C22×C412yes—
198#11758190—24no—
199C8×D61—22no—
200C8×D61—22no—
201C23×C61—22no—
202C22×D61—22no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61C22×D411yescharacteristic
210C2×#6923—22no—
211C2×#6923—22no—
212C2×#6923—22no—
213C2×#6923—22no—
214C2×#6923—22no—
215C2×#6923—22no—
216C2×#6923—41no—
217C2×#6923—41no—
218C2×#6923—42no—
219C2×#6923—41no—
220C2×#6923—41no—
221C2×#6923—42no—
222C2×#6923—42no—
223C2×#6923—41no—
224C2×#6923—88no—
225C2×#6923C2×SD1614yes—
226Q8×C61—21no—
227Q8×C61C4×D412yescomplemented
228D4×C61—22no—
229D4×C61—22no—
230D4×C61—42no—
231D4×C61—81no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—44no—
240C22⋊D61—82no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61C4×D411yescharacteristic
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C2×#4111yescharacteristic
246D244—22no—
247D244—22no—
248D244—42no—
249D244—81no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61C2×SD1612yes—
257C4×D61#13512yes—
258C4×D61C22×D411yescharacteristic
259C4×D61C2×#4111yescharacteristic
260C4×D61H(5,𝔽2)11yescharacteristic
261C4×D612−1+411yescharacteristic
262Dic122—21no—
263Dic122—22no—
264Dic122—22no—
265Dic122C4×D412yescomplemented
266#92420—22no—
267#92420—41no—
268C8×C61—22no—
269#92418—22no—
270#22997—611nomaximal, Sylow
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61C2×C4×D411yescharacteristic
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—82no—
279C2×D61—82no—
280C2×D61—82no—
281C2×D61—82no—
282C2×D61D4211yescharacteristic
283C2×D61#54811yescharacteristic
284C2×D61C22×SD1611yescharacteristic
285C2×D61C2×#13511yescharacteristic
286C2×D61#57611yescharacteristic
287C2×D61#57711yescharacteristic
288#6923—24no—
289#6923—42no—
290#6923—42no—
291#6923—81no—
292#6923—82no—
293C4×C61—22no—
294C4×C61—21no—
295C4×C61—41no—
296C4×C61C4×SD1612yescomplemented
297C4×C61C2×C4×D411yescharacteristic
298C4×C61#52011yescharacteristic
299Dic61—22no—
300Dic61—21no—
301Dic61—41no—
302Dic61C4×SD1612yescomplemented
303Dic61#54711yescharacteristic
304Dic61#55311yescharacteristic
305C2×#460—611no—
306C2×C4×SD16—612no—
307#2366—611no—
308Q8×C4⋊C4—611no—
309#1957—611no—
310#1948—611no—
311#1934—612no—
312#1880—612no—
313#1864—612no—
314C8×C4⋊C4—611no—
315C4×#103—611no—
316C2×C61—82no—
317C2×C61#236111yescharacteristic
318C2×C61C2×C4×SD1611yescharacteristic
319C2×C61#294611yescharacteristic
320D61—82no—
321D61D4×SD1611yescharacteristic
322D61#328711yescharacteristic
323D61#336211yescharacteristic
324D61#336511yescharacteristic
325C22×SD16—612no—
326C2×#127—611no—
327C2×C4×Q8—611no—
328C2×C4×Q8—612no—
329C2×C4×D4—612no—
330C2×C4×D4—1221no—
331#460—612no—
332#460—611no—
333#460—611no—
334#460—611no—
335#460—612no—
336#460#692311yescharacteristic, complemented
337C4×SD16—1228no—
338C2×#106—612no—
339C2×C4⋊C8—611no—
340C2×#103—611no—
341C2×#103—611no—
342C2×#102—612no—
343C2×#102—612no—
344C2×#102—612no—
345C2×C4×C8—612no—
346C2×C4×C8—611no—
347#390—612no—
348#390—1221no—
349#389—612no—
350#389—1222no—
351#386—1222no—
352#384—611no—
353#384—1221no—
354C4×C4⋊C4—611no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—1221no—
357#340—611no—
358#340—612no—
359#340—611no—
360#336—612no—
361C61#2299711yescharacteristic, complemented, Sylow
362C22×Q8—611no—
363C22×D4—612no—
364C22×D4—1221no—
365C22×D4—1221no—
366C23×C4—1222no—
367C2×SD16—612no—
368C2×SD16—612no—
369C2×SD16—612no—
370C2×SD16—1224no—
371C2×SD16—1224no—
372C2×SD16C2×#692312yescomplemented
373C22×C8—611no—
374C22×C8—612no—
375C22×C8—611no—
376#127—612no—
377#127—611no—
378#127—1221no—
379#127—1221no—
380#127C2×#692311yescharacteristic
381C4×Q8—611no—
382C4×Q8—611no—
383C4×Q8—611no—
384C4×Q8—1221no—
385C4×Q8—1221no—
386C4×Q8—1224no—
387C4×Q8—2442no—
388C4×Q8C2×#692311yescharacteristic, complemented
389C4×D4—1224no—
390C4×D4—2442no—
391C4×D4—2444no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1221no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1222no—
405C2×C22⋊C4—1222no—
406C2×C42—611no—
407C2×C42—612no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42—1222no—
411#106—1224no—
412C4⋊C8—612no—
413C4⋊C8—611no—
414C4⋊C8C2×#692311yescharacteristic, complemented
415#103—614no—
416#103—1222no—
417#102—612no—
418#102—612no—
419#102—612no—
420#102—1224no—
421#102—2442no—
422#102C2×#692312yescomplemented
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8—1224no—
426#95—612no—
427#95—1221no—
428#95—1222no—
429C24—1222no—
430C2×Q8—612no—
431C2×Q8—612no—
432C2×Q8—611no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8C22×#692311yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—612no—
440C2×D4—1222no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1222no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—4881no—
450C2×D4—4881no—
451C2×D4—2442no—
452C2×D4—2442no—
453C2×D4C22×#692312yes—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—611no—
458C22×C4—612no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—4882no—
465C22×C4—2444no—
466C22×C4—2444no—
467SD16—24no—
468SD16—1224no—
469SD16—1224no—
470SD16—1224no—
471C2×C8—612no—
472C2×C8—612no—
473C2×C8—1222no—
474C2×C8—1222no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8C22×#692312yes—
481C4⋊C4—21no—
482C4⋊C4—614no—
483C4⋊C4—612no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—4881no—
496C4⋊C4—4882no—
497C4⋊C4—2442no—
498C4⋊C4—2444no—
499C4⋊C4C22×#692311yescharacteristic
500C22⋊C4—4882no—
501C22⋊C4—2444no—
502C22⋊C4—2444no—
503C42—21no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—1221no—
508C42—1221no—
509C42—1222no—
510C42—1222no—
511C42—1221no—
512C42—2442no—
513C42—2444no—
514C42C22×#692311yescharacteristic
515C23—22no—
516C23—611no—
517C23—1222no—
518C23—2442no—
519C23—2442no—
520C23—2442no—
521C23—2442no—
522C23—2442no—
523C23—2442no—
524Q8—21no—
525Q8—612no—
526Q8—1222no—
527Q8—1222no—
528Q8—1221no—
529Q8D4×#692312yescomplemented
530D4—22no—
531D4—22no—
532D4—42no—
533D4—81no—
534D4—1222no—
535D4—1222no—
536D4—4881no—
537D4—4882no—
538D4—2442no—
539D4—2442no—
540D4—2444no—
541D4—2442no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—614no—
553C2×C4—611no—
554C2×C4—1222no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1221no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1221no—
566C2×C4—4888no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2442no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4D4×#692311yescharacteristic
578C2×C4D4×#692311yescharacteristic
579C2×C4C23×#692311yescharacteristic
580C8—22no—
581C8—1222no—
582C8—1222no—
583C8—2441no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—611no—
588C22—611no—
589C22—611no—
590C22—611no—
591C22—611no—
592C22—611no—
593C22—4882no—
594C22—4882no—
595C22—4882no—
596C22—4882no—
597C22—2442no—
598C22—2442no—
599C22—2442no—
600C22C2×D4×#692311yescharacteristic
601C4—21no—
602C4—22no—
603C4—41no—
604C4—612no—
605C4—611no—
606C4—611no—
607C4—1224no—
608C4—1221no—
609C4—1222no—
610C4—4882no—
611C4—4881no—
612C4—2442no—
613C4—2442no—
614C4—2441no—
615C4SD16×#692312yescomplemented
616C4C2×D4×#692311yescharacteristic
617C4#1684083111yescharacteristic
618C2—82no—
619C2—611no—
620C2—611no—
621C2—611no—
622C2—611no—
623C2—4882no—
624C2#2146234411yescharacteristic
625C2C2×SD16×#692311yescharacteristic
626C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#460C4
socleC22×C61C2×C4×D4
prime radical#127×D61C22
cosocleC2×C4×D61C24
hypercenter#460#6923
hypocenterC61#22997
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
3. Q8×C4⋊#6923C2semidirect
5. #21461931C2semidirect
6. #21461909C2semidirect
7. #21461815C2semidirect
8. #21461784C2semidirect
9. #21461612C2semidirect
10. C4×#14519840C2semidirect
40. #16839963C4semidirect
41. #16839962C4semidirect
42. #16839961C4semidirect
43. #16839960C4semidirect
44. #16839959C4semidirect
47. C61×#460C4semidirect
73. #14519840D4semidirect
86. C2×#11758190C2×C4semidirect
87. C2×#11758200C2×C4semidirect
88. C2×#11758201C2×C4semidirect
96. Q8×Dic61C2×C4semidirect
98. C4×Dic122C2×C4semidirect
100. #14519742C2×C4semidirect
105. C4⋊#92418C2×C4semidirect
106. #14519706C2×C4semidirect
107. #14519699C2×C4semidirect
108. #14519698C2×C4semidirect
109. #14519697C2×C4semidirect
110. C2×SD16×C61C2×C4semidirect
112. C4×Q8×C61C2×C4semidirect
113. C4⋊C8×C61C2×C4semidirect
114. #102×C61C2×C4semidirect
168. C4⋊#6923SD16semidirect
227. Q8×C61C4×D4semidirect
265. Dic122C4×D4semidirect
296. C4×C61C4×SD16semidirect
302. Dic61C4×SD16semidirect
336. #460#6923semidirect
361. C61#22997semidirect
372. C2×SD16C2×#6923semidirect
388. C4×Q8C2×#6923semidirect
414. C4⋊C8C2×#6923semidirect
422. #102C2×#6923semidirect
529. Q8D4×#6923semidirect
615. C4SD16×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
#214623492
Q8×C4⋊#69232
#214619472
#214619312
#214619092
#214618152
#214617842
#214616122
C4×#145198402
#460×D612
#2299761