Finite Group Databasebeta

← #30611778

Subgroups — #30611778

Order 15616.

1252 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic, complemented
2D61⋊#431C211yesmaximal, characteristic, complemented
3#21461342C214yesmaximal, complemented
4#21461334C212yesmaximal, complemented
5#21461326C212yesmaximal, complemented
6#21461316C214yesmaximal, complemented
7C2×#16840309C211yesmaximal, characteristic
8#16840785C2212yescomplemented
9#16840784—21no—
10#16840781—21no—
11#16840781—21no—
12#16840780C2212yescomplemented
13#16840780C2212yescomplemented
14#16840779C2212yes—
15#16840778—21no—
16#16840765C2212yes—
17D61⋊(C4⋊C8)C2212yescomplemented
18#16840734—21no—
19D61⋊(C22⋊C8)—21no—
20C4×#11758217—21no—
21C4×D61⋊C8—21no—
22#16840621C2218yescomplemented
23#16840620C2218yescomplemented
24C22×#11758222—21no—
25#16840309—21no—
26#16840309—21no—
27#16840309—21no—
28#16840309—21no—
29#16840309C412yes—
30#16840309C412yes—
31#16840309C2212yes—
32#16840309C2212yes—
33C2×#14519776C2211yescharacteristic
34C2×#14519773C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519752C411yescharacteristic
37C2×#14519750—21no—
38C2×#14519748C411yescharacteristic
39C2×C4×D244C411yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic
43C2×#11758217—22no—
44C2×D61⋊C8—22no—
45#14519844C2314yes—
46#14519844C2314yes—
47C4⋊#92420—22no—
48C4⋊#92420—22no—
49#14519834—22no—
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54C4×#92420—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57C2×#11758222—22no—
58C2×#11758222—22no—
59C2×#11758222—22no—
60C2×#11758222—22no—
61C2×#11758222—48no—
62C22×Dic122—21no—
63C22×D244—21no—
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72#14519776—21no—
73#14519776—21no—
74#14519776C2×C412yes—
75#14519776C2312yes—
76#14519773—21no—
77#14519773—21no—
78#14519773C2×C412yes—
79#14519773C2312yes—
80#14519763—22no—
81#14519763—22no—
82#14519763—22no—
83#14519763—22no—
84#14519752—21no—
85#14519752—21no—
86#14519752C2×C412yes—
87#14519752C2×C412yes—
88#14519750—22no—
89#14519750—22no—
90#14519750—22no—
91#14519750—22no—
92#14519748—21no—
93#14519748—21no—
94#14519748C2×C412yes—
95#14519748C2×C412yes—
96C4×D244—21no—
97C4×D244—21no—
98C4×D244C2×C412yes—
99C4×D244C2×C412yes—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104C2×C4⋊Dic61C2×C411yescharacteristic
105C2×#11758196—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C22×D4×C61C2×C411yescharacteristic
121C23×C4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61C2×C412yes—
125C4×D4×C61C2×C412yes—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C24×C61—21no—
130C23×D61—21no—
131C23×D61C22⋊C411yescharacteristic
132C2×D4×C61—21no—
133C2×D4×C61—42no—
134C2×D4×C61C22×C412yes—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—44no—
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—44no—
149C2×C22⋊D61—44no—
150C2×C22⋊D61—44no—
151C22×Dic61—21no—
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155#11758222—48no—
156#11758222—48no—
157#11758222—48no—
158#11758222—48no—
159C2×D244—22no—
160C2×D244—22no—
161C2×D244—21no—
162C2×D244—44no—
163C2×D244—42no—
164C2×D244C22×C412yes—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—42no—
170C2×C4×D61—44no—
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22⋊C411yescharacteristic
177C2×C4×D61C22×C411yescharacteristic
178C2×C4×D61C22×C411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×Dic122—22no—
184C2×Dic122—22no—
185C2×Dic122—44no—
186#11758217—44no—
187C2×#92420—24no—
188C2×#92420—24no—
189D61⋊C8—44no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C22×C412yes—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C42×C61C22⋊C411yescharacteristic
195C42×C61C22⋊C411yescharacteristic
196C42×C61C22×C411yescharacteristic
197C42×C61C22×C411yescharacteristic
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204C4⋊Dic61—21no—
205C4⋊Dic61C22×C412yes—
206#11758196—22no—
207#11758196—22no—
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22×C411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2411yescharacteristic
220C23×C61—22no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61C2×C22⋊C411yescharacteristic
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—41no—
229C22×D61—42no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234D4×C61—42no—
235D4×C61—42no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—44no—
241C2×C4×C61—42no—
242C2×C4×C61—44no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C23×C411yescharacteristic
249C22⋊D61—44no—
250C22⋊D61—44no—
251C22⋊D61—44no—
252C22⋊D61—44no—
253C22⋊D61—44no—
254C22⋊D61—44no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61#13514yes—
264C2×Dic61C22×D411yescharacteristic
265C2×Dic61C22×D411yescharacteristic
266D244—42no—
267D244—44no—
268D244—44no—
269D244—42no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—44no—
282C4×D61—44no—
283C4×D61AGL(1,ℤ/8)14yes—
284Dic122—44no—
285Dic122—44no—
286#92420—44no—
287#92420—44no—
288#17717—611nomaximal, Sylow
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—84no—
295C22×C61#41612yes—
296C22×C61C22×C22⋊C411yescharacteristic
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61—44no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—84no—
307C2×D61#41812yes—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—42no—
313C4×C61#41312yes—
314C4×C61#41812yes—
315Dic61—21no—
316Dic61—21no—
317Dic61—21no—
318Dic61—42no—
319Dic61#41612yes—
320Dic61C2×#13512yes—
321Dic61C2×AGL(1,ℤ/8)12yes—
322C2×#532—611no—
323#2920—611no—
324C2×#431—611no—
325#1553—614no—
326#1549—612no—
327#1545—612no—
328#1540—614no—
329C2×C61—22no—
330C2×C61—82no—
331C2×C61C2×#41311yescharacteristic
332C2×C61C2×#41611yescharacteristic
333C2×C61C2×#41811yescharacteristic
334D61—22no—
335D61—41no—
336D61—82no—
337C22×#41—1221no—
338#532—612no—
339#532—612no—
340#532—612no—
341#532—612no—
342#532—1221no—
343#532—1221no—
344#532—1221no—
345#532—1221no—
346C2×C4⋊Q8—611no—
347C2×#127—611no—
348C2×#124—1221no—
349C2×#121—611no—
350C2×#121—611no—
351C2×#121—1221no—
352C2×C4×D4—611no—
353C2×C4×D4—1221no—
354C2×C4×D4#692311yescharacteristic
355C22×C42—611no—
356#432—612no—
357#432—1221no—
358#431—612no—
359#431—612no—
360#431—612no—
361#431—1221no—
362#431—1221no—
363#431—1221no—
364#423—612no—
365C2×C4⋊C8—612no—
366#407—1221no—
367C2×C22⋊C8—1221no—
368C4×M16—1221no—
369C2×C4×C8—1221no—
370#332—618no—
371#331—618no—
372C61#1771711yescharacteristic, complemented, Sylow
373C2×#41—1222no—
374C2×#41—1222no—
375C2×#41—1222no—
376C2×#41—1222no—
377C2×#41—2448no—
378C22×Q8—1221no—
379C22×D4—611no—
380C22×D4—1221no—
381C22×D4—1221no—
382C22×D4—1221no—
383C22×D4—1221no—
384C22×D4C2×#692311yescharacteristic
385C23×C4—21no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—1221no—
390C2×M16—1222no—
391C22×C8—1222no—
392C4⋊Q8—612no—
393C4⋊Q8—612no—
394C4⋊Q8—1221no—
395C4⋊Q8—1221no—
396#127—612no—
397#127—612no—
398#127—1221no—
399#127—1221no—
400#124—1222no—
401#124—1222no—
402#124—1222no—
403#124—1222no—
404#121—612no—
405#121—612no—
406#121—612no—
407#121—612no—
408#121—1222no—
409#121—1222no—
410#121—1222no—
411#121—1222no—
412#121—1221no—
413#121—1221no—
414#121—1221no—
415#121—1221no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—612no—
419C4×D4—612no—
420C4×D4—1222no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1221no—
425C4×D4—1221no—
426C4×D4C2×#692312yes—
427C4×D4C2×#692312yes—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4C2×#692311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42C2×#692311yescharacteristic
447C4⋊C8—614no—
448C4⋊C8—614no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455#97—1222no—
456C4×C8—1222no—
457C4×C8—1222no—
458C4×C8—1222no—
459C24—21no—
460C24—611no—
461C24—1221no—
462#41—2448no—
463#41—2448no—
464#41—2448no—
465#41—2448no—
466C2×Q8—1222no—
467C2×Q8—1222no—
468C2×Q8—2444no—
469C2×D4—21no—
470C2×D4—42no—
471C2×D4—612no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1222no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1221no—
481C2×D4—2442no—
482C2×D4—2444no—
483C2×D4—2444no—
484C2×D4—2444no—
485C2×D4—2444no—
486C2×D4C22×#692312yes—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—44no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1224no—
507C22×C4—1224no—
508C22×C4—1221no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—2442no—
512C22×C4—2444no—
513C22×C4C22⋊#692311yescharacteristic
514C22×C4C22⋊#692311yescharacteristic
515C22×C4C22×#692311yescharacteristic
516M16—2444no—
517C2×C8—1224no—
518C2×C8—1224no—
519C2×C8—2444no—
520C4⋊C4—21no—
521C4⋊C4—612no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1221no—
525C4⋊C4C22×#692312yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42C22⋊#692311yescharacteristic
547C42C22⋊#692311yescharacteristic
548C42C22×#692311yescharacteristic
549C42C22×#692311yescharacteristic
550C23—22no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—611no—
555C23—611no—
556C23—1222no—
557C23—1222no—
558C23—1222no—
559C23—2441no—
560C23—2442no—
561C23—2442no—
562C23—2442no—
563C23C2×C22⋊#692311yescharacteristic
564Q8—2444no—
565Q8—2444no—
566D4—42no—
567D4—42no—
568D4—2442no—
569D4—2444no—
570D4—2444no—
571D4—2444no—
572D4—2444no—
573D4—2444no—
574D4—2444no—
575D4—2444no—
576D4—2444no—
577D4—2442no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—44no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—614no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—614no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2444no—
607C2×C4—2441no—
608C2×C4—2442no—
609C2×C4—2444no—
610C2×C4C2×C22⋊#692311yescharacteristic
611C2×C4C2×C22⋊#692311yescharacteristic
612C2×C4C2×C22⋊#692311yescharacteristic
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C2×C22⋊#692311yescharacteristic
615C2×C4C23×#692311yescharacteristic
616C8—2444no—
617C8—2444no—
618C22—21no—
619C22—21no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—84no—
624C22—612no—
625C22—1221no—
626C22—1221no—
627C22—1221no—
628C22—1221no—
629C22—1221no—
630C22—4884no—
631C22—2444no—
632C22—2442no—
633C22—2442no—
634C22—2442no—
635C22#1684075212yes—
636C22C22×C22⋊#692311yescharacteristic
637C4—21no—
638C4—21no—
639C4—21no—
640C4—21no—
641C4—42no—
642C4—612no—
643C4—612no—
644C4—612no—
645C4—1221no—
646C4—1221no—
647C4—1221no—
648C4—2442no—
649C4#1684074812yes—
650C4#1684075412yes—
651C2—22no—
652C2—82no—
653C2—1222no—
654C2—4882no—
655C2—2441no—
656C2C2×#1684074811yescharacteristic
657C2C2×#1684075211yescharacteristic
658C2C2×#1684075411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC4×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17717
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462497C2semidirect
2. D61⋊#431C2semidirect
3. #21461342C2semidirect
4. #21461334C2semidirect
5. #21461326C2semidirect
6. #21461316C2semidirect
8. #16840785C22semidirect
12. #16840780C22semidirect
13. #16840780C22semidirect
17. D61⋊(C4⋊C8)C22semidirect
22. #16840621C22semidirect
23. #16840620C22semidirect
372. C61#17717semidirect

Maximal subgroups

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

subgroupindex
#214624972
D61⋊#4312
#214613422
#214613342
#214613262
#214613162
C2×#168403092
#1771761