Finite Group Databasebeta

← #30611245

Subgroups — #30611245

Order 15616.

1274 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840785C211yesmaximal, characteristic, complemented
2#21462266C211yesmaximal, characteristic, complemented
3#21461254C214yesmaximal, complemented
4#21461240C212yesmaximal, complemented
5#21461239C212yesmaximal, complemented
6#21461209C214yesmaximal, complemented
7#532×D61C211yesmaximal, characteristic
8#16840785—21no—
9#16840785—21no—
10#16840785C2212yescomplemented
11#16840785C2212yescomplemented
12C2×#14519844—21no—
13C2×#14519834C2212yes—
14C2×#14519832—21no—
15#16840707C2212yescomplemented
16#16840706—21no—
17#16840705—21no—
18#16840704C2212yes—
19C4×C4⋊#6923—21no—
20C4×C22⋊#6923—21no—
21#16840698C2212yescomplemented
22#16840614C2218yescomplemented
23#16840613C2218yescomplemented
24C2×#41×D61—21no—
25#16840313C2211yescharacteristic
26#16840312C411yescharacteristic, complemented
27#16840311—21no—
28#16840310C2211yescharacteristic
29#16840309—21no—
30#16840309C2212yes—
31#16840308—21no—
32#16840307—21no—
33#16840307C412yescomplemented
34C4⋊Q8×D61C411yescharacteristic, complemented
35#127×D61C411yescharacteristic, complemented
36#124×D61—21no—
37#121×D61—21no—
38#121×D61C2212yes—
39C4×D4×D61—21no—
40C4×D4×D61C412yescomplemented
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic, complemented
43C22×#92420—22no—
44C2×C4⋊#6923—22no—
45C2×C22⋊#6923—22no—
46C2×C4×#6923—22no—
47#14519844—22no—
48#14519844—22no—
49#14519834—22no—
50#14519834C2314yes—
51#14519832—22no—
52#14519832—22no—
53(C2×#6923)⋊C4—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4C2314yes—
57C2×#11758226—21no—
58C2×#11758222—21no—
59C2×#11758222—22no—
60C2×#11758224—22no—
61C2×#11758224—21no—
62#41×D61—48no—
63C2×Q8×D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—21no—
66C2×D4×D61—21no—
67C2×D4×D61C2×C412yes—
68C22×C4×D61—22no—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72#14519777C2×C411yescharacteristic
73#14519776—21no—
74#14519776C2×C412yes—
75#14519775—21no—
76#14519774C2×C411yescharacteristic
77#14519773—21no—
78#14519773—21no—
79#14519773C2×C412yes—
80#14519766—21no—
81#14519765—21no—
82#14519764—21no—
83#14519763—22no—
84#14519763—22no—
85#14519752—21no—
86#14519752C2312yes—
87#14519751—21no—
88#14519751C2×C412yes—
89#14519750—22no—
90#14519750—22no—
91#14519749—22no—
92#14519749—22no—
93#14519748—21no—
94#14519748C2312yes—
95C4×D244—21no—
96C4×D244C2×C412yes—
97D4×Dic61—21no—
98D4×Dic61C2×C412yes—
99#14519739—21no—
100#14519739C2×C412yes—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103#14519737—22no—
104#14519737—22no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61C2×C412yes—
107C22⋊C4×D61—22no—
108C22⋊C4×D61—22no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C2×#41×C61—21no—
121C4⋊Q8×C61C2×C411yescharacteristic
122#127×C61C2×C411yescharacteristic
123#124×C61—21no—
124#121×C61—21no—
125#121×C61C2×C412yes—
126C4×D4×C61—21no—
127C4×D4×C61C2×C412yes—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61—22no—
130C23×D61C2×D411yescharacteristic
131C22×#6923—24no—
132#41×C61—44no—
133C2×Q8×C61—21no—
134C2×D4×C61—22no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61C22×C412yes—
138C22×C4×C61—22no—
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—
147C22×Dic61—22no—
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151#11758226—44no—
152Q8×D61—44no—
153#11758224—44no—
154#11758224—48no—
155D4×D61—44no—
156D4×D61—44no—
157D4×D61—44no—
158D4×D61—48no—
159#11758222—48no—
160#11758222—44no—
161C2×D244—22no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244C22×C412yes—
165C2×C4×D61—24no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—48no—
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22×C411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2411yescharacteristic
184C2×Dic122—21no—
185C2×Dic122—22no—
186C22⋊#6923—44no—
187C2×#92420—24no—
188C2×#92420—44no—
189C4⋊#6923—44no—
190C4×#6923—44no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61C22×C412yes—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C42×C61C22⋊C411yescharacteristic
196C42×C61C22⋊C411yescharacteristic
197C42×C61C22×C411yescharacteristic
198C42×C61C22×C411yescharacteristic
199C22⋊Dic61—22no—
200C22⋊Dic61—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205C4⋊Dic61—21no—
206C4⋊Dic61C22×C412yes—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C23×C61—22no—
222C23×C61C2×C22⋊C411yescharacteristic
223C22×D61—22no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—44no—
227C22×D61—44no—
228C22×D61—44no—
229C22×D61C2×C22⋊C411yescharacteristic
230C22×D61AGL(1,ℤ/8)14yes—
231C22×D61C22×D411yescharacteristic
232C2×#6923—44no—
233C2×#6923—44no—
234C2×#6923—44no—
235Q8×C61—42no—
236D4×C61—42no—
237D4×C61—42no—
238D4×C61—42no—
239D4×C61—44no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—44no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C23×C411yescharacteristic
251C22⋊D61—44no—
252C22⋊D61—44no—
253C22⋊D61—44no—
254C22⋊D61—44no—
255C22⋊D61—44no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—44no—
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C22×D411yescharacteristic
267D244—42no—
268D244—42no—
269D244—42no—
270D244—44no—
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—41no—
282C4×D61—41no—
283C4×D61—44no—
284C4×D61—44no—
285C4×D61—44no—
286Dic122—44no—
287Dic122—42no—
288#92420—44no—
289#17595—611nomaximal, Sylow
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61#41812yes—
296C22×C61C22×C22⋊C411yescharacteristic
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—44no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—88no—
306C2×D61#41812yes—
307C2×D61C2×AGL(1,ℤ/8)12yes—
308#6923—84no—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—42no—
316Dic61—21no—
317Dic61—21no—
318Dic61—21no—
319Dic61—21no—
320Dic61—42no—
321Dic61#41012yes—
322Dic61#42112yes—
323C2×#532—611no—
324C2×#432—611no—
325#2283—611no—
326#1519—614no—
327#1514—612no—
328#1514—612no—
329#1505—614no—
330C2×C61—22no—
331C2×C61—82no—
332C2×C61C2×#41011yescharacteristic
333C2×C61C2×#41811yescharacteristic
334C2×C61C2×#42111yescharacteristic
335D61—22no—
336D61—22no—
337D61—82no—
338C22×#41—1221no—
339#532—611no—
340#532—611no—
341#532—612no—
342#532—612no—
343#532—611no—
344#532—1221no—
345#532—1221no—
346#532—1221no—
347#532—1221no—
348#532#692311yescharacteristic, complemented
349C2×C4⋊Q8—611no—
350C2×#127—611no—
351C2×#124—1221no—
352C2×#121—612no—
353C2×#121—1221no—
354C2×C4×D4—612no—
355C2×C4×D4—1221no—
356C22×C42—611no—
357#432—612no—
358#432—612no—
359#432—1221no—
360#432—1221no—
361C2×C4⋊C8—1221no—
362C2×C22⋊C8—612no—
363C2×#97—1221no—
364#383—612no—
365#382—1221no—
366#381—1221no—
367#380—612no—
368C4×C4⋊C4—1221no—
369C4×C22⋊C4—1221no—
370#376—612no—
371#327—618no—
372#327—618no—
373C61#1759511yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C2×#41—1222no—
376C2×#41—1222no—
377C2×#41—1221no—
378C2×#41—1221no—
379C2×#41—1221no—
380C2×#41—2448no—
381C22×Q8—1221no—
382C22×D4—612no—
383C22×D4—1221no—
384C22×D4—1221no—
385C22×D4—1222no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—1222no—
390C22×C8—1222no—
391C4⋊Q8—612no—
392C4⋊Q8—611no—
393C4⋊Q8—1221no—
394C4⋊Q8—1221no—
395C4⋊Q8C2×#692311yescharacteristic
396#127—612no—
397#127—611no—
398#127—1221no—
399#127—1221no—
400#127C2×#692311yescharacteristic
401#124—21no—
402#124—1222no—
403#124—1222no—
404#124—1221no—
405#124—1221no—
406#124—1221no—
407#121—21no—
408#121—612no—
409#121—612no—
410#121—612no—
411#121—1222no—
412#121—1222no—
413#121—1221no—
414#121—1222no—
415#121—1221no—
416#121—1222no—
417#121—1221no—
418#121C2×#692312yes—
419C4×D4—21no—
420C4×D4—612no—
421C4×D4—612no—
422C4×D4—612no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1221no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1221no—
429C4×D4—1221no—
430C4×D4C2×#692312yes—
431C2×C4⋊C4—612no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1222no—
434C2×C22⋊C4—1222no—
435C2×C22⋊C4—1222no—
436C2×C22⋊C4—1222no—
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×C42—611no—
447C2×C42—611no—
448C2×C42—1222no—
449C2×C42C2×#692311yescharacteristic
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C22⋊C8—614no—
453C22⋊C8—1222no—
454#97—1222no—
455#97—1222no—
456#95—614no—
457#95—1222no—
458#95—1222no—
459#95—1222no—
460C24—611no—
461C24—1222no—
462#41—44no—
463#41—2444no—
464#41—2448no—
465#41—2444no—
466#41—2448no—
467#41—2444no—
468C2×Q8—21no—
469C2×Q8—1222no—
470C2×Q8—1221no—
471C2×Q8—2444no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—612no—
476C2×D4—1222no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—2444no—
485C2×D4—2444no—
486C2×D4—2444no—
487C2×D4—2448no—
488C2×D4C22×#692312yes—
489C22×C4—22no—
490C22×C4—611no—
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—1222no—
506C22×C4—1224no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1224no—
511C22×C4—2442no—
512C22×C4—2442no—
513C22×C4—2448no—
514C22×C4C22⋊#692311yescharacteristic
515C22×C4C22⋊#692311yescharacteristic
516C22×C4C22×#692311yescharacteristic
517C2×C8—1224no—
518C2×C8—2444no—
519C4⋊C4—21no—
520C4⋊C4—612no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1221no—
524C4⋊C4—2444no—
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—
534C22⋊C4—2444no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—2444no—
548C42C22⋊#692311yescharacteristic
549C42C22⋊#692311yescharacteristic
550C42C22×#692311yescharacteristic
551C42C22×#692311yescharacteristic
552C23—22no—
553C23—611no—
554C23—611no—
555C23—614no—
556C23—1222no—
557C23—2441no—
558C23—2441no—
559C23—2444no—
560C23—2444no—
561C23—2444no—
562C23C2×C22⋊#692311yescharacteristic
563Q8—42no—
564Q8—2442no—
565Q8—2444no—
566D4—42no—
567D4—42no—
568D4—42no—
569D4—44no—
570D4—2442no—
571D4—2442no—
572D4—2442no—
573D4—2444no—
574D4—2444no—
575D4—2444no—
576D4—2444no—
577D4—2444no—
578D4—2444no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—44no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
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—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2444no—
607C2×C4—2444no—
608C2×C4—2444no—
609C2×C4—2444no—
610C2×C4—2444no—
611C2×C4—2444no—
612C2×C4—2444no—
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C2×C22⋊#692311yescharacteristic
615C2×C4C2×C22⋊#692311yescharacteristic
616C2×C4C2×C22⋊#692311yescharacteristic
617C2×C4C2×C22⋊#692311yescharacteristic
618C2×C4C23×#692311yescharacteristic
619C8—2444no—
620C22—21no—
621C22—21no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—612no—
626C22—612no—
627C22—1221no—
628C22—1221no—
629C22—1221no—
630C22—1221no—
631C22—4888no—
632C22—2444no—
633C22—2442no—
634C22—2442no—
635C22—2442no—
636C22#1684075412yes—
637C22C22×C22⋊#692311yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—21no—
642C4—21no—
643C4—21no—
644C4—42no—
645C4—612no—
646C4—612no—
647C4—1221no—
648C4—1221no—
649C4—1221no—
650C4—1221no—
651C4—4884no—
652C4—2442no—
653C2—22no—
654C2—82no—
655C2—1222no—
656C2—1222no—
657C2—4882no—
658C2D61⋊#41011yescharacteristic
659C2C2×#1684075411yescharacteristic
660C2D61⋊#42111yescharacteristic
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#17595
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#16840785C2semidirect
2. #21462266C2semidirect
3. #21461254C2semidirect
4. #21461240C2semidirect
5. #21461239C2semidirect
6. #21461209C2semidirect
10. #16840785C22semidirect
11. #16840785C22semidirect
15. #16840707C22semidirect
21. #16840698C22semidirect
22. #16840614C22semidirect
23. #16840613C22semidirect
26. #16840312C4semidirect
33. #16840307C4semidirect
34. C4⋊Q8×D61C4semidirect
35. #127×D61C4semidirect
40. C4×D4×D61C4semidirect
42. C61×#532C4semidirect
348. #532#6923semidirect
373. C61#17595semidirect

Maximal subgroups

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

subgroupindex
C2×#168407852
#214622662
#214612542
#214612402
#214612392
#214612092
#532×D612
#1759561