Finite Group Databasebeta

← #30616699

Subgroups — #30616699

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461997C212yesmaximal, complemented
4#21461986C212yesmaximal, complemented
5#21461807C214yesmaximal, complemented
6C4×#14519839C214yesmaximal, complemented
7#532×D61C211yesmaximal, characteristic
8C2×#14519856C2212yes—
9#16840781—21no—
10#16840780—21no—
11#16840779—21no—
12#16840778—21no—
13D61⋊(C4⋊C8)C2212yes—
14C2×#14519839C2218yes—
15D61⋊(C22⋊C8)C2212yes—
16C4×D61⋊C8C2212yes—
17C4×C4⋊#6923C2212yes—
18C4×C4⋊#6923C2212yes—
19C4×C22⋊#6923—21no—
20C4×C22⋊#6923—21no—
21#16840698—21no—
22C42×#6923—21no—
23#16840635C2218yes—
24C2×#41×D61—21no—
25#16840313C411yescharacteristic, complemented
26#16840312C411yescharacteristic, complemented
27#16840311—21no—
28#16840310C411yescharacteristic, complemented
29#16840309—21no—
30#16840309C412yescomplemented
31#16840308—21no—
32#16840307—21no—
33#16840307C412yescomplemented
34C4⋊Q8×D61C2211yescharacteristic
35#127×D61C2211yescharacteristic
36#124×D61—21no—
37#121×D61—21no—
38#121×D61C2212yes—
39C4×D4×D61—21no—
40C4×D4×D61C2212yes—
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic, complemented
43C2×D61⋊C8C2314yes—
44#14519856—28no—
45C2×C4⋊#6923C2314yes—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50#14519844—22no—
51C4⋊#92420—22no—
52#14519839—216no—
53#14519834—22no—
54C22⋊#92420—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59C2×#11758226—21no—
60C2×#11758222—21no—
61C2×#11758222—22no—
62C2×#11758224—22no—
63C2×#11758224—21no—
64#41×D61—48no—
65C2×Q8×D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61C2312yes—
70C22×C4×D61—22no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74#14519777C2×C411yescharacteristic
75#14519776—21no—
76#14519776C2×C412yes—
77#14519775—21no—
78#14519774C2×C411yescharacteristic
79#14519773—21no—
80#14519773—21no—
81#14519773C2×C412yes—
82#14519766—21no—
83#14519765—21no—
84#14519764—21no—
85#14519763—22no—
86#14519763—22no—
87#14519752—21no—
88#14519752C2×C412yes—
89#14519751—21no—
90#14519751C2×C412yes—
91#14519750—22no—
92#14519750—22no—
93#14519749—22no—
94#14519749—22no—
95#14519748—21no—
96#14519748C2×C412yes—
97C4×D244—21no—
98C4×D244C2×C412yes—
99D4×Dic61—21no—
100D4×Dic61C2×C412yes—
101#14519739—21no—
102#14519739C2×C412yes—
103C4×C22⋊D61—22no—
104C4×C22⋊D61—22no—
105#14519737—22no—
106#14519737—22no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61C2312yes—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—22no—
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61C2311yescharacteristic
121C42×D61C2311yescharacteristic
122C2×#41×C61—21no—
123C4⋊Q8×C61C2×C411yescharacteristic
124#127×C61C2×C411yescharacteristic
125#124×C61—21no—
126#121×C61—21no—
127#121×C61C2×C412yes—
128C4×D4×C61—21no—
129C4×D4×C61C2×C412yes—
130C2×C42×C61C2×C411yescharacteristic
131C23×D61—22no—
132C23×D61C2×D411yescharacteristic
133C22×#6923—24no—
134#41×C61—44no—
135C2×Q8×C61—21no—
136C2×D4×C61—22no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61C22×C412yes—
140C22×C4×C61—22no—
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C22×Dic61—22no—
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153#11758226—44no—
154Q8×D61—44no—
155#11758224—44no—
156#11758224—48no—
157D4×D61—28no—
158D4×D61—44no—
159D4×D61—48no—
160D4×D61—44no—
161#11758222—48no—
162#11758222—44no—
163C2×D244—22no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244C22×C412yes—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—48no—
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×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×C4×D61C2411yescharacteristic
186C2×Dic122—21no—
187C2×Dic122—22no—
188C22⋊#6923—28no—
189C2×#92420—24no—
190C4⋊#6923—24no—
191C4⋊#6923#4118yescomplemented
192C4×#6923—28no—
193C4×#6923—44no—
194C4×#6923—44no—
195D61⋊C8—28no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61C22×C412yes—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C42×C61C22⋊C411yescharacteristic
201C42×C61C22⋊C411yescharacteristic
202C42×C61C22×C411yescharacteristic
203C42×C61C22×C411yescharacteristic
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210C4⋊Dic61—21no—
211C4⋊Dic61C22×C412yes—
212#11758196—22no—
213#11758196—22no—
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C22×C411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C23×C61—22no—
227C23×C61C2×C22⋊C411yescharacteristic
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—44no—
233C22×D61—44no—
234C22×D61—44no—
235C22×D61C2×C22⋊C411yescharacteristic
236C22×D61C22×D411yescharacteristic
237C2×#6923—28no—
238C2×#6923—44no—
239C2×#6923—44no—
240Q8×C61—42no—
241D4×C61—24no—
242D4×C61—42no—
243D4×C61—44no—
244D4×C61—42no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—44no—
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C23×C411yescharacteristic
256C22⋊D61—44no—
257C22⋊D61—44no—
258C22⋊D61—44no—
259C22⋊D61—44no—
260C22⋊D61—44no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—44no—
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C22×D411yescharacteristic
272D244—24no—
273D244—42no—
274D244—44no—
275D244—42no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—44no—
286C4×D61—44no—
287C4×D61—44no—
288C4×D61#13514yes—
289C4×D61AGL(1,ℤ/8)14yes—
290C4×D61C2×#4114yes—
291Dic122—44no—
292Dic122—42no—
293#92420—44no—
294#21390—611nomaximal, Sylow
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61C22×C22⋊C411yescharacteristic
302C2×D61—21no—
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—44no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—88no—
310C2×D61#52512yes—
311C2×D61C2×#13512yes—
312C2×D61C2×AGL(1,ℤ/8)12yes—
313#6923—48no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—42no—
318C4×C61#41612yes—
319C4×C61#41812yes—
320C4×C61C4×#4112yes—
321Dic61—21no—
322Dic61—21no—
323Dic61—21no—
324Dic61—42no—
325Dic61#41612yes—
326Dic61#41812yes—
327Dic61#53212yes—
328C2×#532—611no—
329C2×#431—611no—
330C4×#117—611no—
331#1987—612no—
332#1982—612no—
333#1875—614no—
334C4×#102—614no—
335C2×C61—41no—
336C2×C61—82no—
337C2×C61#229711yescharacteristic
338C2×C61C2×#41611yescharacteristic
339C2×C61C2×#41811yescharacteristic
340D61—41no—
341D61—82no—
342D61#310614yes—
343C22×#41—1221no—
344#532—611no—
345#532—611no—
346#532—612no—
347#532—612no—
348#532—611no—
349#532—1221no—
350#532—1221no—
351#532—1221no—
352#532—1221no—
353#532#692311yescharacteristic, complemented
354C2×C4⋊Q8—611no—
355C2×#127—611no—
356C2×#124—1221no—
357C2×#121—612no—
358C2×#121—1221no—
359C2×C4×D4—612no—
360C2×C4×D4—1221no—
361C2×#117—612no—
362C22×C42—611no—
363#431—1221no—
364#431—1221no—
365#431—1221no—
366#431—1221no—
367C2×C4⋊C8—612no—
368C2×#102—618no—
369C2×C22⋊C8—612no—
370C2×C4×C8—612no—
371C4×C4⋊C4—612no—
372C4×C4⋊C4—612no—
373C4×C22⋊C4—1221no—
374C4×C22⋊C4—1221no—
375#376—1221no—
376C43—1221no—
377#340—618no—
378C61#2139011yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C2×#41—1222no—
381C2×#41—1222no—
382C2×#41—1221no—
383C2×#41—1221no—
384C2×#41—1221no—
385C2×#41—2448no—
386C22×Q8—1221no—
387C22×D4—612no—
388C22×D4—1221no—
389C22×D4—1221no—
390C22×D4—1222no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—1222no—
395C22×C8—614no—
396C4⋊Q8—612no—
397C4⋊Q8—611no—
398C4⋊Q8—1221no—
399C4⋊Q8—1221no—
400C4⋊Q8C2×#692311yescharacteristic
401#127—612no—
402#127—611no—
403#127—1221no—
404#127—1221no—
405#127C2×#692311yescharacteristic
406#124—21no—
407#124—1222no—
408#124—1222no—
409#124—1221no—
410#124—1221no—
411#124—1221no—
412#121—21no—
413#121—612no—
414#121—612no—
415#121—612no—
416#121—1222no—
417#121—1222no—
418#121—1221no—
419#121—1222no—
420#121—1221no—
421#121—1222no—
422#121—1221no—
423#121C2×#692312yes—
424C4×D4—21no—
425C4×D4—612no—
426C4×D4—612no—
427C4×D4—612no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1221no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4C2×#692312yes—
436#117—1228no—
437C2×C4⋊C4—614no—
438C2×C4⋊C4—612no—
439C2×C4⋊C4—1221no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C22⋊C4—1222no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—1222no—
455C2×C42—1222no—
456C2×C42—1222no—
457C2×C42C2×#692311yescharacteristic
458C4⋊C8—1222no—
459C4⋊C8—1222no—
460#102—12216no—
461C22⋊C8—1222no—
462C22⋊C8—1222no—
463C4×C8—1222no—
464C4×C8—1222no—
465#95—1222no—
466#95—1222no—
467C24—611no—
468C24—1222no—
469#41—44no—
470#41—2444no—
471#41—2448no—
472#41—2444no—
473#41—2448no—
474#41—2444no—
475C2×Q8—21no—
476C2×Q8—1222no—
477C2×Q8—1221no—
478C2×Q8—2444no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—612no—
483C2×D4—1222no—
484C2×D4—1228no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1222no—
489C2×D4—1222no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—2444no—
493C2×D4—2444no—
494C2×D4—2448no—
495C2×D4C22×#692312yes—
496C22×C4—22no—
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—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—1224no—
513C22×C4—1224no—
514C22×C4—1224no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1224no—
519C22×C4—1222no—
520C22×C4—2448no—
521C22×C4C22⋊#692311yescharacteristic
522C22×C4C22⋊#692311yescharacteristic
523C22×C4C22×#692311yescharacteristic
524C2×C8—1224no—
525C2×C8—1228no—
526C4⋊C4—21no—
527C4⋊C4—618no—
528C4⋊C4—612no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1224no—
532C4⋊C4—1221no—
533C4⋊C4C22×#692312yes—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1228no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—1228no—
556C42—2444no—
557C42—2444no—
558C42C22⋊#692311yescharacteristic
559C42C22⋊#692311yescharacteristic
560C42C22×#692311yescharacteristic
561C42C22×#692311yescharacteristic
562C23—22no—
563C23—611no—
564C23—611no—
565C23—1222no—
566C23—1222no—
567C23—1222no—
568C23—1222no—
569C23—2444no—
570C23—2444no—
571C23—2444no—
572C23C2×C22⋊#692311yescharacteristic
573Q8—42no—
574Q8—2442no—
575Q8—2444no—
576D4—24no—
577D4—42no—
578D4—44no—
579D4—42no—
580D4—1224no—
581D4—2442no—
582D4—2444no—
583D4—2444no—
584D4—2444no—
585D4—2444no—
586D4—2444no—
587D4—2444no—
588D4—2442no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—44no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—614no—
598C2×C4—614no—
599C2×C4—614no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1228no—
616C2×C4—1222no—
617C2×C4—2444no—
618C2×C4—2444no—
619C2×C4—2444no—
620C2×C4—2444no—
621C2×C4—2444no—
622C2×C4—2444no—
623C2×C4C2×C22⋊#692311yescharacteristic
624C2×C4C2×C22⋊#692311yescharacteristic
625C2×C4C2×C22⋊#692311yescharacteristic
626C2×C4C2×C22⋊#692311yescharacteristic
627C2×C4C2×C22⋊#692311yescharacteristic
628C2×C4C23×#692311yescharacteristic
629C8—2444no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—612no—
637C22—612no—
638C22—612no—
639C22—1221no—
640C22—1221no—
641C22—1221no—
642C22—4888no—
643C22—2444no—
644C22—2442no—
645C22—2442no—
646C22—2442no—
647C22C22×C22⋊#692311yescharacteristic
648C4—21no—
649C4—21no—
650C4—21no—
651C4—42no—
652C4—612no—
653C4—612no—
654C4—612no—
655C4—1221no—
656C4—1221no—
657C4—1221no—
658C4—2448no—
659C4—2442no—
660C4#1684075212yes—
661C4#1684075412yes—
662C4#41×#692312yes—
663C2—41no—
664C2—82no—
665C2—614no—
666C2—4882no—
667C2—2441no—
668C2#2146228011yescharacteristic
669C2C2×#1684075211yescharacteristic
670C2C2×#1684075411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#532C4
socleC22×C61C22×C22⋊C4
prime radical#532×D61C2
cosocleC2×C4×D61C24
hypercenter#532#6923
hypocenterC61#21390
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. D61⋊#431C2semidirect
2. C4×#14519856C2semidirect
3. #21461997C2semidirect
4. #21461986C2semidirect
5. #21461807C2semidirect
6. C4×#14519839C2semidirect
25. #16840313C4semidirect
26. #16840312C4semidirect
28. #16840310C4semidirect
30. #16840309C4semidirect
33. #16840307C4semidirect
42. C61×#532C4semidirect
191. C4⋊#6923#41semidirect
353. #532#6923semidirect
378. C61#21390semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
C4×#145198562
#214619972
#214619862
#214618072
C4×#145198392
#532×D612
#2139061