Finite Group Databasebeta

← #30617839

Subgroups — #30617839

Order 15616.

1444 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461984C214yesmaximal, complemented
4#21461953C212yesmaximal, complemented
5#21461952C212yesmaximal, complemented
6#21461661C214yesmaximal, complemented
7#532×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840784—21no—
10#16840783—21no—
11#16840781—21no—
12#16840778—21no—
13#16840766C2212yescomplemented
14C2×#14519842C2218yescomplemented
15C2×#14519841C2218yescomplemented
16#16840733C2212yes—
17C4×#11758213C2212yescomplemented
18C4×C4⋊#6923—21no—
19C4×C4⋊#6923C2212yescomplemented
20C4×C22⋊#6923—21no—
21C4×C22⋊#6923C2212yes—
22#16840698—21no—
23C42×#6923C2212yescomplemented
24C2×#41×D61C2212yes—
25#16840313C2211yescharacteristic
26#16840312C411yescharacteristic, complemented
27#16840311C2212yes—
28#16840310C2211yescharacteristic
29#16840309—21no—
30#16840309—21no—
31#16840308C412yescomplemented
32#16840307—21no—
33#16840307—21no—
34C4⋊Q8×D61C411yescharacteristic, complemented
35#127×D61C411yescharacteristic, complemented
36#124×D61C412yescomplemented
37#121×D61—21no—
38#121×D61—21no—
39C4×D4×D61—21no—
40C4×D4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic, complemented
43C2×#11758213C2314yes—
44#14519856—28no—
45C2×C4⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923C2314yes—
50C4⋊#92420—22no—
51C4⋊#92420—22no—
52#14519842—48no—
53#14519841—48no—
54#14519834—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60C2×#11758226C2312yes—
61C2×#11758222—22no—
62C2×#11758222C2×C412yes—
63C2×#11758224—22no—
64C2×#11758224C2312yes—
65#41×D61—48no—
66C2×Q8×D61C2×C412yes—
67C2×D4×D61—22no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C412yes—
71C22×C4×D61—22no—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75#14519777C2×C411yescharacteristic
76#14519776—21no—
77#14519776—21no—
78#14519775C2×C412yes—
79#14519774C2×C411yescharacteristic
80#14519773—21no—
81#14519773—21no—
82#14519773C2×C412yes—
83#14519766C2×C412yes—
84#14519765C2×C412yes—
85#14519764C2×C412yes—
86#14519763—22no—
87#14519763—22no—
88#14519752—21no—
89#14519752—21no—
90#14519751—21no—
91#14519751—21no—
92#14519750—22no—
93#14519750—22no—
94#14519749—22no—
95#14519749—22no—
96#14519748—21no—
97#14519748—21no—
98C4×D244—21no—
99C4×D244—21no—
100D4×Dic61—21no—
101D4×Dic61—21no—
102#14519739—21no—
103#14519739—21no—
104C4×C22⋊D61—22no—
105C4×C22⋊D61—22no—
106#14519737—22no—
107#14519737—22no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61C2×C411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61C2311yescharacteristic
122C42×D61C2311yescharacteristic
123C2×#41×C61C2×C412yes—
124C4⋊Q8×C61C2×C411yescharacteristic
125#127×C61C2×C411yescharacteristic
126#124×C61C2×C412yes—
127#121×C61—21no—
128#121×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C2×C42×C61C2×C411yescharacteristic
132C23×D61—22no—
133C23×D61C2×D411yescharacteristic
134C22×#6923—24no—
135#41×C61—44no—
136C2×Q8×C61C22×C412yes—
137C2×D4×C61—22no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61C22×C412yes—
141C22×C4×C61—22no—
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22⋊C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C22×Dic61—22no—
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154#11758226—28no—
155Q8×D61—44no—
156#11758224—28no—
157#11758224—48no—
158D4×D61—44no—
159D4×D61—44no—
160D4×D61—48no—
161D4×D61—44no—
162#11758222—44no—
163#11758222—48no—
164C2×D244—22no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244C22×C412yes—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—42no—
174C2×C4×D61—48no—
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22⋊C411yescharacteristic
177C2×C4×D61C22⋊C411yescharacteristic
178C2×C4×D61C22⋊C411yescharacteristic
179C2×C4×D61C22×C411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×C4×D61C2×D411yescharacteristic
186C2×C4×D61C2411yescharacteristic
187C2×Dic122—22no—
188C2×Dic122C22×C412yes—
189C22⋊#6923—28no—
190C2×#92420—24no—
191C4⋊#6923—28no—
192C4×#6923—28no—
193C4×#6923—24no—
194C4×#6923—24no—
195C4×#6923—44no—
196#11758213—28no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C42×C61C22⋊C411yescharacteristic
202C42×C61C22⋊C411yescharacteristic
203C42×C61C22×C411yescharacteristic
204C42×C61C22×C411yescharacteristic
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213#11758196—22no—
214#11758196—22no—
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22×C411yescharacteristic
222C4×Dic61C22×C411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C23×C61—22no—
228C23×C61C2×C22⋊C411yescharacteristic
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—41no—
233C22×D61—44no—
234C22×D61—44no—
235C22×D61—44no—
236C22×D61C2×C22⋊C411yescharacteristic
237C22×D61C22×D411yescharacteristic
238C2×#6923—28no—
239C2×#6923—44no—
240C2×#6923—44no—
241Q8×C61—24no—
242D4×C61—24no—
243D4×C61—44no—
244D4×C61—42no—
245D4×C61—42no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—44no—
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C23×C411yescharacteristic
257C22⋊D61—44no—
258C22⋊D61—44no—
259C22⋊D61—44no—
260C22⋊D61—44no—
261C22⋊D61—44no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—41no—
266C2×Dic61—44no—
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C22×D411yescharacteristic
273D244—24no—
274D244—44no—
275D244—42no—
276D244—42no—
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—41no—
286C4×D61—41no—
287C4×D61—44no—
288C4×D61—44no—
289C4×D61—44no—
290C4×D61#10414yescomplemented
291C4×D61H(5,𝔽2)14yes—
292Dic122—24no—
293Dic122—44no—
294#92420—44no—
295#21815—611nomaximal, Sylow
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—21no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61—42no—
302C22×C61C22×C22⋊C411yescharacteristic
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—21no—
306C2×D61—21no—
307C2×D61—44no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—88no—
312C2×D61C2×#10412yes—
313C2×D61#53512yes—
314#6923—48no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—42no—
319C4×C61C2×#10412yes—
320C4×C61#42112yes—
321C4×C61#51812yes—
322Dic61—21no—
323Dic61—21no—
324Dic61—21no—
325Dic61—21no—
326Dic61—42no—
327Dic61C2×#10412yes—
328Dic61#53512yes—
329C2×#532—611no—
330#2920—611no—
331C4×#117—611no—
332#1980—614no—
333#1962—612no—
334#1962—612no—
335#1789—614no—
336C2×C61—41no—
337C2×C61—82no—
338C2×C61#230911yescharacteristic
339C2×C61C22×#10411yescharacteristic
340C2×C61C2×#42111yescharacteristic
341D61—22no—
342D61—22no—
343D61—82no—
344C22×#41—612no—
345#532—612no—
346#532—611no—
347#532—611no—
348#532—612no—
349#532—611no—
350#532—1221no—
351#532—1221no—
352#532—1221no—
353#532—1221no—
354#532#692311yescharacteristic, complemented
355C2×C4⋊Q8—611no—
356C2×#127—611no—
357C2×#124—612no—
358C2×#121—1221no—
359C2×#121—1221no—
360C2×C4×D4—1221no—
361C2×C4×D4—1221no—
362C2×#117—1221no—
363C22×C42—611no—
364#432—1221no—
365#432—1221no—
366#431—1221no—
367#431—1221no—
368#423—612no—
369C2×#104—618no—
370C2×#104—618no—
371#407—612no—
372C4×M16—612no—
373C4×C4⋊C4—612no—
374C4×C4⋊C4—1221no—
375C4×C22⋊C4—612no—
376C4×C22⋊C4—1221no—
377#376—1221no—
378C43—612no—
379C61#2181511yescharacteristic, complemented, Sylow
380C2×#41—612no—
381C2×#41—612no—
382C2×#41—612no—
383C2×#41—1222no—
384C2×#41—1222no—
385C2×#41—2448no—
386C2×#41C2×#692312yes—
387C22×Q8—612no—
388C22×D4—612no—
389C22×D4—1221no—
390C22×D4—1221no—
391C22×D4—1222no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—1222no—
396C2×M16—614no—
397C4⋊Q8—612no—
398C4⋊Q8—611no—
399C4⋊Q8—1221no—
400C4⋊Q8—1221no—
401C4⋊Q8C2×#692311yescharacteristic
402#127—612no—
403#127—611no—
404#127—1221no—
405#127—1221no—
406#127C2×#692311yescharacteristic
407#124—612no—
408#124—612no—
409#124—612no—
410#124—1222no—
411#124—1222no—
412#124C2×#692312yes—
413#121—21no—
414#121—21no—
415#121—1222no—
416#121—1222no—
417#121—1221no—
418#121—1221no—
419#121—1221no—
420#121—1221no—
421#121—1222no—
422#121—1222no—
423#121—1221no—
424#121—1221no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1221no—
430C4×D4—1221no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437#117—1228no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C22⋊C4—1222no—
443C2×C22⋊C4—1222no—
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—611no—
455C2×C42—614no—
456C2×C42—1222no—
457C2×C42—1222no—
458C2×C42C2×#692311yescharacteristic
459C4⋊C8—1222no—
460C4⋊C8—1222no—
461#104—2448no—
462#104—2448no—
463C22⋊C8—1222no—
464C22⋊C8—1222no—
465#97—1222no—
466C4×C8—1222no—
467#95—1222no—
468#95—1222no—
469C24—611no—
470C24—1222no—
471#41—44no—
472#41—1228no—
473#41—1228no—
474#41—2444no—
475#41—2448no—
476#41—2448no—
477C2×Q8—612no—
478C2×Q8—1222no—
479C2×Q8—2444no—
480C2×Q8C22×#692312yes—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—612no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1222no—
489C2×D4—1222no—
490C2×D4—1222no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4—2444no—
494C2×D4—2444no—
495C2×D4—2444no—
496C2×D4—2448no—
497C2×D4C22×#692312yes—
498C22×C4—22no—
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—611no—
513C22×C4—611no—
514C22×C4—1224no—
515C22×C4—1224no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1224no—
520C22×C4—1222no—
521C22×C4—2442no—
522C22×C4—2448no—
523C22×C4C22⋊#692311yescharacteristic
524C22×C4C22⋊#692311yescharacteristic
525C22×C4C22×#692311yescharacteristic
526M16—1228no—
527C2×C8—1224no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1228no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1228no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—1224no—
557C42—1224no—
558C42—1228no—
559C42—2444no—
560C42C22⋊#692311yescharacteristic
561C42C22⋊#692311yescharacteristic
562C42C22×#692311yescharacteristic
563C42C22×#692311yescharacteristic
564C23—22no—
565C23—611no—
566C23—611no—
567C23—1222no—
568C23—1222no—
569C23—1222no—
570C23—2441no—
571C23—2444no—
572C23—2444no—
573C23—2444no—
574C23C2×C22⋊#692311yescharacteristic
575Q8—24no—
576Q8—1224no—
577Q8—2444no—
578D4—24no—
579D4—44no—
580D4—42no—
581D4—42no—
582D4—1224no—
583D4—2444no—
584D4—2444no—
585D4—2444no—
586D4—2444no—
587D4—2444no—
588D4—2444no—
589D4—2442no—
590D4—2442no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—614no—
599C2×C4—614no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
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—1228no—
615C2×C4—1222no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2444no—
619C2×C4—2444no—
620C2×C4—2444no—
621C2×C4—2444no—
622C2×C4—2441no—
623C2×C4—2444no—
624C2×C4—2444no—
625C2×C4C2×C22⋊#692311yescharacteristic
626C2×C4C2×C22⋊#692311yescharacteristic
627C2×C4C2×C22⋊#692311yescharacteristic
628C2×C4C2×C22⋊#692311yescharacteristic
629C2×C4C2×C22⋊#692311yescharacteristic
630C2×C4C23×#692311yescharacteristic
631C8—2444no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—612no—
639C22—612no—
640C22—1221no—
641C22—1221no—
642C22—1221no—
643C22—1221no—
644C22—4888no—
645C22—2444no—
646C22—2442no—
647C22—2442no—
648C22—2442no—
649C22C22×C22⋊#692311yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—42no—
654C4—612no—
655C4—612no—
656C4—1221no—
657C4—1221no—
658C4—1221no—
659C4—1221no—
660C4—2448no—
661C4—2442no—
662C4D61⋊#10412yes—
663C4#1684075912yes—
664C4#1684082912yes—
665C2—41no—
666C2—82no—
667C2—1222no—
668C2—1222no—
669C2—4882no—
670C2#2146229211yescharacteristic
671C2C2×D61⋊#10411yescharacteristic
672C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×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#21815
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462496C2semidirect
2. C4×#14519856C2semidirect
3. #21461984C2semidirect
4. #21461953C2semidirect
5. #21461952C2semidirect
6. #21461661C2semidirect
13. #16840766C22semidirect
14. C2×#14519842C22semidirect
15. C2×#14519841C22semidirect
17. C4×#11758213C22semidirect
19. C4×C4⋊#6923C22semidirect
23. C42×#6923C22semidirect
26. #16840312C4semidirect
31. #16840308C4semidirect
34. C4⋊Q8×D61C4semidirect
35. #127×D61C4semidirect
36. #124×D61C4semidirect
42. C61×#532C4semidirect
290. C4×D61#104semidirect
354. #532#6923semidirect
379. C61#21815semidirect

Maximal subgroups

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

subgroupindex
#214624962
C4×#145198562
#214619842
#214619532
#214619522
#214616612
#532×D612
#2181561