Finite Group Databasebeta

← #30623926

Subgroups — #30623926

Order 15616.

1410 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462429C211yesmaximal, characteristic, complemented
2#21462418C211yesmaximal, characteristic, complemented
3#21462078C212yesmaximal, complemented
4#21462074C214yesmaximal, complemented
5#21462070C212yesmaximal, complemented
6C2×#16840662C214yesmaximal, complemented
7#21459454C211yesmaximal, characteristic
8#16840840—21no—
9#16840829—21no—
10#16840749—22no—
11#16840748C2212yescomplemented
12D61⋊#100—21no—
13C2×#14519837C2214yescomplemented
14#16840742—21no—
15#16840741C2212yescomplemented
16D61⋊#99—22no—
17C2×#14519835C2214yescomplemented
18#16840664C2214yescomplemented
19#16840662C2214yescomplemented
20#16840662C2218yescomplemented
21C2×#14519822C2211yescharacteristic
22#16840406—21no—
23#16840406—21no—
24#16840406—22no—
25D4×C22⋊D61—22no—
26D4×C22⋊D61—21no—
27D4×C22⋊D61—21no—
28#16840329C411yescharacteristic, complemented
29#16840329C2211yescharacteristic
30#16840321C412yescomplemented
31#16840321C2212yes—
32#16840273C411yescharacteristic, complemented
33#16840273C2211yescharacteristic
34C2×#14519746C412yescomplemented
35C2×#14519746C2212yes—
36#16840237C411yescharacteristic, complemented
37C23×D4×C61C411yescharacteristic, complemented
38#14519864—44no—
39D61⋊M16—22no—
40C2×#11758217—24no—
41D4×#6923—44no—
42#14519856—22no—
43C2×C22⋊#6923—24no—
44#14519838—22no—
45#14519837—24no—
46#14519837C2314yes—
47#14519836—22no—
48#14519835—24no—
49#14519835C2314yes—
50#14519822—44no—
51C2×#11758222C2×C411yescharacteristic
52C2×#11758222C2311yescharacteristic
53C2×#11758224D411yescharacteristic
54C2×#11758224D411yescharacteristic
55C2×#11758224D412yes—
56C22×C22⋊D61—22no—
57C22×C22⋊D61—22no—
58C22×C22⋊D61C2×C412yes—
59C22×C22⋊D61C2312yes—
60C2×D4×D61D412yes—
61C2×D4×D61D411yescharacteristic
62C2×D4×D61D411yescharacteristic
63#14519773—21no—
64#14519773—21no—
65#14519764—21no—
66#14519764—21no—
67#14519760C2×C412yescomplemented
68#14519760C2×C411yescharacteristic, complemented
69#14519760C2311yescharacteristic
70#14519758—22no—
71#14519758—22no—
72#14519756—21no—
73#14519756—21no—
74#14519751—21no—
75#14519751—21no—
76#14519749—22no—
77#14519749—22no—
78#14519749—22no—
79#14519749—22no—
80#14519748—22no—
81#14519748—21no—
82#14519748—21no—
83#14519746—22no—
84#14519746—22no—
85#14519746—22no—
86#14519746—22no—
87#14519746C2×C411yescharacteristic, complemented
88#14519746C2×C412yescomplemented
89#14519746C2×C412yescomplemented
90#14519746C2×C412yescomplemented
91#14519746C2×C412yescomplemented
92#14519746C2311yescharacteristic
93#14519746C2312yes—
94#14519745—22no—
95#14519745—22no—
96D4×Dic61—22no—
97D4×Dic61—21no—
98D4×Dic61—21no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102#14519736C2×C411yescharacteristic, complemented
103#14519736C2×C411yescharacteristic, complemented
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61C2×C412yescomplemented
107C2×C22⋊Dic61C2×C412yescomplemented
108C25×C61C2×C412yescomplemented
109C22×D4×C61—22no—
110C22×D4×C61—21no—
111C22×D4×C61—21no—
112C22×D4×C61—44no—
113C22×D4×C61C2×C411yescharacteristic
114C22×D4×C61C2×C412yescomplemented
115C22×D4×C61C2×C411yescharacteristic, complemented
116C23×C4×C61C2×C411yescharacteristic, complemented
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—44no—
120C24×C61—84no—
121C24×C61C22×C412yes—
122C24×C61C22×C411yescharacteristic
123C24×C61C22×C412yes—
124C23×D61C22⋊C412yes—
125C23×D61C2×D412yes—
126C22×#6923—44no—
127C2×D4×C61—24no—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—42no—
133C2×D4×C61—48no—
134C2×D4×C61—44no—
135C2×D4×C61—44no—
136C2×D4×C61—44no—
137C2×D4×C61C22⋊C412yes—
138C2×D4×C61C22⋊C411yescharacteristic
139C2×D4×C61C22⋊C411yescharacteristic
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—42no—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C2×C22⋊D61—22no—
146C2×C22⋊D61—21no—
147C2×C22⋊D61—21no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—44no—
153C2×C22⋊D61—44no—
154C2×C22⋊D61—84no—
155C2×C22⋊D61—84no—
156C2×C22⋊D61C22⋊C412yes—
157C2×C22⋊D61C22⋊C412yes—
158C2×C22⋊D61C22×C411yescharacteristic
159C2×C22⋊D61C22×C412yes—
160C2×C22⋊D61C2×D412yes—
161C2×C22⋊D61C2×D412yes—
162C2×C22⋊D61C2411yescharacteristic
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61C22⋊C412yes—
166C22×Dic61C2×D412yes—
167#11758224—24no—
168#11758224—42no—
169#11758224—44no—
170D4×D61—24no—
171D4×D61—42no—
172D4×D61—44no—
173#11758222—42no—
174#11758222—42no—
175C2×D244C22⋊C411yescharacteristic
176C2×D244C2×D411yescharacteristic
177C2×C4×D61C22⋊C412yes—
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×Dic122C22⋊C411yescharacteristic
181C2×Dic122C2×D411yescharacteristic
182C22⋊#6923—24no—
183C22⋊#6923—44no—
184#11758217—24no—
185#11758217—44no—
186C2×#92420—44no—
187C4⋊#6923—42no—
188C4×#6923—42no—
189#11758213—42no—
190D61⋊C8—42no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—21no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—21no—
199C22⋊Dic61—22no—
200C22⋊Dic61C22×C411yescharacteristic
201C22⋊Dic61C22×C412yes—
202C22⋊Dic61C22×C411yescharacteristic
203#11758198—22no—
204#11758198—21no—
205#11758198—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208#11758196—22no—
209#11758196—21no—
210#11758196—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C23×C61—21no—
214C23×C61—24no—
215C23×C61—22no—
216C23×C61—41no—
217C23×C61—42no—
218C23×C61—44no—
219C23×C61—44no—
220C23×C61—44no—
221C23×C61—42no—
222C23×C61—44no—
223C23×C61—82no—
224C23×C61—82no—
225C23×C61—82no—
226C23×C61—82no—
227C23×C61—88no—
228C23×C61—88no—
229C23×C61C2×C22⋊C412yes—
230C23×C61C2×C22⋊C412yes—
231C23×C61C23×C411yescharacteristic
232C22×D61—24no—
233C22×D61—42no—
234C22×D61—82no—
235C22×D61—82no—
236C22×D61C2×C22⋊C412yes—
237C22×D61C2×C22⋊C411yescharacteristic
238C22×D61C22×D411yescharacteristic
239C2×#6923—44no—
240C2×#6923—164no—
241D4×C61—24no—
242D4×C61—22no—
243D4×C61—42no—
244D4×C61—44no—
245D4×C61—44no—
246D4×C61—42no—
247D4×C61#9914yes—
248C2×C4×C61—22no—
249C2×C4×C61—21no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—41no—
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C22⋊D61—24no—
256C22⋊D61—24no—
257C22⋊D61—42no—
258C22⋊D61—41no—
259C22⋊D61—41no—
260C22⋊D61—42no—
261C22⋊D61—42no—
262C22⋊D61—44no—
263C22⋊D61—42no—
264C22⋊D61—42no—
265C22⋊D61—82no—
266C22⋊D61—82no—
267C22⋊D61—82no—
268C22⋊D61—82no—
269C2×Dic61—24no—
270C2×Dic61—22no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—42no—
274C2×Dic61—82no—
275C2×Dic61—82no—
276C2×Dic61C2×C22⋊C412yes—
277C2×Dic61C2×C22⋊C411yescharacteristic
278C2×Dic61C22×D411yescharacteristic
279D244—22no—
280D244—41no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—42no—
284Dic122—22no—
285Dic122—41no—
286#92420—44no—
287#33348—611nomaximal, Sylow
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—21no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—41no—
300C22×C61—42no—
301C22×C61—84no—
302C22×C61—88no—
303C22×C61—88no—
304C22×C61—84no—
305C22×C61C2×#9914yes—
306C22×C61C22×C22⋊C411yescharacteristic
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—22no—
310C2×D61—42no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—84no—
314C2×D61—162no—
315#6923—84no—
316C4×C61—21no—
317C4×C61—41no—
318C4×C61C2×#9912yes—
319Dic61—21no—
320Dic61—22no—
321Dic61—21no—
322Dic61—42no—
323Dic61—41no—
324Dic61—41no—
325#3484—611no—
326#2888—611no—
327#2883—611no—
328#2122—612no—
329#2121—614no—
330#2120—612no—
331C2×AΣL(1,𝔽16)—614no—
332C2×C61—21no—
333C2×C61—24no—
334C2×C61—42no—
335C2×C61—42no—
336C2×C61—41no—
337C2×C61—82no—
338C2×C61C22×#9911yescharacteristic
339D61—41no—
340D61—42no—
341D61—41no—
342C2×H(5,𝔽2)—611no—
343C23×D4#692311yescharacteristic, complemented
344#568—1221no—
345#546—1221no—
346#546—1222no—
347#546—1221no—
348D42—1222no—
349D42—1221no—
350D42—1221no—
351#535—611no—
352#535—611no—
353#534—612no—
354#534—612no—
355#525—611no—
356#525—611no—
357C2×#120—612no—
358C2×#120—612no—
359#518—611no—
360#518—1221no—
361#413—612no—
362#413—1222no—
363C2×#100—614no—
364C2×#100—1221no—
365#410—612no—
366#410—1221no—
367C2×#99—614no—
368C2×#99—1222no—
369#352—614no—
370AΣL(1,𝔽16)—614no—
371AΣL(1,𝔽16)—618no—
372C61#3334811yescharacteristic, complemented, Sylow
373C25C2×#692312yescomplemented
374H(5,𝔽2)—2444no—
375C2×#41—611no—
376C2×#41—612no—
377C2×#41—611no—
378C2×#41—611no—
379C2×#41—611no—
380C22×D4—22no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—44no—
384C22×D4—612no—
385C22×D4—612no—
386C22×D4—611no—
387C22×D4—612no—
388C22×D4—611no—
389C22×D4—1222no—
390C22×D4—1222no—
391C22×D4C2×#692311yescharacteristic
392C22×D4C2×#692312yescomplemented
393C22×D4C2×#692311yescharacteristic, complemented
394C23×C4C2×#692311yescharacteristic, complemented
395#131—2444no—
396C2×M16—1224no—
397C2×M16—1222no—
398#127—1221no—
399#127—1221no—
400#124—1221no—
401#124—1221no—
402#123—611no—
403#123—611no—
404#123—612no—
405#123—1222no—
406#123—1222no—
407C22⋊Q8—1221no—
408C22⋊Q8—1221no—
409#121—1221no—
410#121—1221no—
411#121—1221no—
412#121—1221no—
413#121—1222no—
414#121—1222no—
415#121—1222no—
416#121—1222no—
417#121—1222no—
418#120—611no—
419#120—611no—
420#120—612no—
421#120—612no—
422#120—612no—
423#120—612no—
424#120—612no—
425#120—1222no—
426#120—1222no—
427#120—1222no—
428#120—1222no—
429#120—1222no—
430#120—1222no—
431C4×D4—1221no—
432C4×D4—1221no—
433C4×D4—1222no—
434C4×D4—1222no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4—2444no—
438#117—611no—
439#117—611no—
440#117—1222no—
441C2×C22⋊C4—612no—
442C2×C22⋊C4—612no—
443C2×C22⋊C4—1222no—
444C2×C22⋊C4—1222no—
445C2×C22⋊C4—1224no—
446#101—1222no—
447#100—614no—
448#100—1224no—
449#99—614no—
450#99—1224no—
451#99—1222no—
452C24—22no—
453C24—22no—
454C24—44no—
455C24—84no—
456C24—612no—
457C24—612no—
458C24C22×#692312yes—
459C24C22×#692311yescharacteristic
460C24C22×#692312yes—
461#41—1224no—
462#41—2442no—
463#41—2442no—
464#41—2444no—
465#41—2442no—
466C2×Q8—611no—
467C2×Q8—611no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—612no—
479C2×D4—612no—
480C2×D4—612no—
481C2×D4—612no—
482C2×D4—611no—
483C2×D4—611no—
484C2×D4—612no—
485C2×D4—611no—
486C2×D4—611no—
487C2×D4—1224no—
488C2×D4—1222no—
489C2×D4—1222no—
490C2×D4—1222no—
491C2×D4—1222no—
492C2×D4—1221no—
493C2×D4—1222no—
494C2×D4—1221no—
495C2×D4—4884no—
496C2×D4—4884no—
497C2×D4—2442no—
498C2×D4—2444no—
499C2×D4—2444no—
500C2×D4—2444no—
501C2×D4C22⋊#692312yes—
502C2×D4C22⋊#692311yescharacteristic
503C2×D4C22⋊#692311yescharacteristic
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—612no—
508C22×C4—612no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—612no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—2444no—
515C22×C4C22×#692311yescharacteristic
516C22×C4C22×#692311yescharacteristic
517M16—1224no—
518M16—2442no—
519M16—2444no—
520C2×C8—2442no—
521C2×C8—2444no—
522C4⋊C4—1221no—
523C4⋊C4—1222no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2442no—
528C22⋊C4—611no—
529C22⋊C4—612no—
530C22⋊C4—611no—
531C22⋊C4—1221no—
532C22⋊C4—1222no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C22⋊C4—1222no—
536C22⋊C4—1221no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C22⋊C4—1224no—
544C22⋊C4—2444no—
545C42—1221no—
546C42—1221no—
547C42—2442no—
548C23—21no—
549C23—24no—
550C23—22no—
551C23—41no—
552C23—42no—
553C23—44no—
554C23—44no—
555C23—44no—
556C23—42no—
557C23—44no—
558C23—82no—
559C23—82no—
560C23—82no—
561C23—82no—
562C23—88no—
563C23—88no—
564C23—611no—
565C23—612no—
566C23—611no—
567C23—1224no—
568C23—4882no—
569C23—4882no—
570C23—2442no—
571C23C2×C22⋊#692312yes—
572C23C2×C22⋊#692312yes—
573C23C23×#692311yescharacteristic
574Q8—1222no—
575Q8—2441no—
576D4—24no—
577D4—22no—
578D4—42no—
579D4—44no—
580D4—44no—
581D4—42no—
582D4—1224no—
583D4—1224no—
584D4—1222no—
585D4—4882no—
586D4—4882no—
587D4—4882no—
588D4—4882no—
589D4—2441no—
590D4—2441no—
591D4—2442no—
592D4—2441no—
593D4—2442no—
594D4—2442no—
595D4—2442no—
596D4—2442no—
597D4—2444no—
598D4#1451983514yes—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—611no—
605C2×C4—612no—
606C2×C4—611no—
607C2×C4—1224no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—9764no—
614C2×C4—4882no—
615C2×C4—4882no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2444no—
619C2×C4C2×C22⋊#692311yescharacteristic
620C2×C4C2×C22⋊#692311yescharacteristic
621C8—2444no—
622C22—22no—
623C22—21no—
624C22—22no—
625C22—42no—
626C22—42no—
627C22—41no—
628C22—41no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—84no—
636C22—88no—
637C22—88no—
638C22—84no—
639C22—1221no—
640C22—1221no—
641C22—1222no—
642C22—9762no—
643C22—4884no—
644C22—2441no—
645C22—2441no—
646C22—2442no—
647C22C2×#1451983514yes—
648C22C22×C22⋊#692311yescharacteristic
649C4—21no—
650C4—41no—
651C4—1221no—
652C4—1221no—
653C4—1222no—
654C4—4884no—
655C4—2441no—
656C4—2442no—
657C4—2441no—
658C4C2×#1451983512yes—
659C2—21no—
660C2—24no—
661C2—42no—
662C2—41no—
663C2—42no—
664C2—82no—
665C2—2441no—
666C2—2441no—
667C2—2442no—
668C2C22×#1451983511yescharacteristic
subgroupG/H
centerC2C22×#14519835
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC23×D4×C61C4
socleC2×C61C22×#99
prime radical#21459454C2
cosocleC2×C22⋊D61C24
hypercenterC23×D4#6923
hypocenterC61#33348
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×D4 ◁ C22×D4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #21462429C2semidirect
2. #21462418C2semidirect
3. #21462078C2semidirect
4. #21462074C2semidirect
5. #21462070C2semidirect
6. C2×#16840662C2semidirect
11. #16840748C22semidirect
13. C2×#14519837C22semidirect
15. #16840741C22semidirect
17. C2×#14519835C22semidirect
18. #16840664C22semidirect
19. #16840662C22semidirect
20. #16840662C22semidirect
28. #16840329C4semidirect
30. #16840321C4semidirect
32. #16840273C4semidirect
34. C2×#14519746C4semidirect
36. #16840237C4semidirect
37. C23×D4×C61C4semidirect
67. #14519760C2×C4semidirect
68. #14519760C2×C4semidirect
87. #14519746C2×C4semidirect
88. #14519746C2×C4semidirect
89. #14519746C2×C4semidirect
90. #14519746C2×C4semidirect
91. #14519746C2×C4semidirect
102. #14519736C2×C4semidirect
103. #14519736C2×C4semidirect
106. C2×C22⋊Dic61C2×C4semidirect
107. C2×C22⋊Dic61C2×C4semidirect
108. C25×C61C2×C4semidirect
114. C22×D4×C61C2×C4semidirect
115. C22×D4×C61C2×C4semidirect
116. C23×C4×C61C2×C4semidirect
343. C23×D4#6923semidirect
372. C61#33348semidirect
373. C25C2×#6923semidirect
392. C22×D4C2×#6923semidirect
393. C22×D4C2×#6923semidirect
394. C23×C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624292
#214624182
#214620782
#214620742
#214620702
C2×#168406622
#214594542
#3334861