Finite Group Databasebeta

← #29646342

Subgroups — #29646342

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840495C211yesmaximal, characteristic
2#21454854C211yesmaximal, characteristic, complemented
3#21444172C211yesmaximal, characteristic, complemented
4#21444170C211yesmaximal, characteristic, complemented
5#21444168C212yesmaximal, complemented
6#21444165C212yesmaximal, complemented
7#21444162C211yesmaximal, characteristic, complemented
8#21444155C212yesmaximal, complemented
9#21444142C211yesmaximal, characteristic, complemented
10#21444135C212yesmaximal, complemented
11C61×#2974C211yesmaximal, characteristic, complemented
12#16840495—21no—
13#16840495—22no—
14#16840495—21no—
15#16840495—21no—
16#16840495—22no—
17#16840495—21no—
18C2×#14519773C411yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519764C411yescharacteristic
21C2×#14519763C412yes—
22C2×#14519760C2212yes—
23C2×#14519759C412yes—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742C411yescharacteristic
26C2×#14519739C411yescharacteristic
27C2×C4×C22⋊D61C2212yes—
28#16839840—21no—
29#16839834—22no—
30D4×#92418—21no—
31#16839819C2211yescharacteristic
32#16839815C2211yescharacteristic
33#16839726C2212yes—
34C2×C22⋊#92418C2212yes—
35#16839487C2211yescharacteristic
36#16839487C2212yes—
37#16839487C2211yescharacteristic
38#16839487C2211yescharacteristic
39#16839487C2211yescharacteristic
40#16839487C2212yes—
41#16839485C2212yes—
42#16839485C2212yes—
43#16839485C2212yes—
44#16839485C2212yes—
45C2×C4×D4×C61C2211yescharacteristic
46C61×#436—21no—
47C61×#435—22no—
48C8×D4×C61—21no—
49C61×#432C2211yescharacteristic
50C61×#431C2211yescharacteristic
51C61×#407C2212yes—
52C2×C22⋊C8×C61C2212yes—
53C22×Dic122C2×C411yescharacteristic
54C22×Dic122C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C22×C4×D61C2×C412yes—
59C2×#11758194—22no—
60C22×#92418—22no—
61#14519773—21no—
62#14519773—21no—
63#14519773—22no—
64#14519765—21no—
65#14519765—21no—
66#14519765—21no—
67#14519765—21no—
68#14519764—21no—
69#14519764—21no—
70#14519764—22no—
71#14519763—22no—
72#14519763—22no—
73#14519763—22no—
74#14519763—22no—
75#14519760—22no—
76#14519760—22no—
77#14519760—22no—
78#14519760—22no—
79#14519759—22no—
80#14519759—22no—
81#14519759—22no—
82#14519759—22no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86C4×Dic122—21no—
87#14519742—22no—
88#14519742—21no—
89#14519742—21no—
90#14519739—22no—
91#14519739—21no—
92#14519739—21no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196C2×C412yes—
99C2×#11758196C2311yescharacteristic
100C2×#11758196C2311yescharacteristic
101C2×C22⋊Dic61C2×C412yes—
102C2×C22⋊Dic61C2×C412yes—
103C2×#11758198C2×C412yes—
104C2×#11758198C2×C412yes—
105C2×#11758198C2312yes—
106C2×C4×Dic61C2×C412yes—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C4⋊#92418—21no—
110C4⋊#92418—21no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C22⋊#92418C2311yescharacteristic
114C22⋊#92418C2312yes—
115C22⋊#92418C2311yescharacteristic
116#14519688—21no—
117C4×#92418—21no—
118C22×D4×C61C2×C411yescharacteristic
119C23×C4×C61C2312yes—
120C2×M16×C61—22no—
121C22×C8×C61—22no—
122C4×D4×C61D411yescharacteristic
123C4×D4×C61D412yes—
124C4×D4×C61D411yescharacteristic
125C4×D4×C61D411yescharacteristic
126C4×D4×C61D412yes—
127C4×D4×C61D411yescharacteristic
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C412yes—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61—21no—
133C22⋊C8×C61—22no—
134C22⋊C8×C61—22no—
135C22⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2311yescharacteristic
138#97×C61—21no—
139C4×C8×C61—21no—
140C24×C61C22×C412yes—
141C23×D61C22×C412yes—
142C2×D4×C61—42no—
143C2×D4×C61C22⋊C411yescharacteristic
144C2×D4×C61C22⋊C411yescharacteristic
145C2×D4×C61C22⋊C412yes—
146C22×C4×C61—82no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—82no—
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C412yes—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—42no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—82no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—22no—
178C2×Dic122—41no—
179C2×Dic122—42no—
180M16×C61—82no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—22no—
184C2×C8×C61—82no—
185C4⋊C4×C61C22⋊C412yes—
186C4⋊C4×C61C22⋊C411yescharacteristic
187C4⋊C4×C61C22⋊C411yescharacteristic
188C22⋊C4×C61C22⋊C412yes—
189C22⋊C4×C61C22⋊C412yes—
190C22⋊C4×C61C22⋊C412yes—
191C22⋊C4×C61C22⋊C412yes—
192C42×C61C2×D411yescharacteristic
193C42×C61C2×D411yescharacteristic
194C42×C61C2×D411yescharacteristic
195C42×C61C2×D411yescharacteristic
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208#11758196—22no—
209#11758196—22no—
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213#11758196—21no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220#11758194—82no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—22no—
224C2×#92418—82no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61C2×C22⋊C412yes—
230C23×C61C2×C22⋊C412yes—
231C23×C61C23×C411yescharacteristic
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—42no—
236C22×D61—42no—
237D4×C61—22no—
238D4×C61—22no—
239D4×C61—42no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—22no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—41no—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C412yes—
251C2×C4×C61C2×C22⋊C412yes—
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C22⋊D61—44no—
258C22⋊D61—44no—
259C22⋊D61—82no—
260C22⋊D61—82no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—22no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—42no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61#13112yes—
273D244—42no—
274D244—42no—
275C4×D61—82no—
276C4×D61—82no—
277Dic122—42no—
278Dic122—42no—
279Dic122—42no—
280Dic122—42no—
281C8×C61—41no—
282C8×C61—42no—
283C8×C61—41no—
284#92418—41no—
285#92418—42no—
286#92418—41no—
287#17429—611nomaximal, Sylow
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—82no—
297C22×C61—82no—
298C22×C61C22×C22⋊C411yescharacteristic
299C22×C61C2×#13111yescharacteristic
300C22×C61#56811yescharacteristic
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—82no—
305C2×D61—82no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—22no—
311C4×C61—22no—
312C4×C61—21no—
313C4×C61#41312yes—
314Dic61—22no—
315Dic61—41no—
316Dic61—41no—
317Dic61—41no—
318Dic61—42no—
319C2×#559—611no—
320#2974—611no—
321#2974D6111yescharacteristic, complemented
322#1469—611no—
323#1469—611no—
324#1468—612no—
325#1468—612no—
326#1467—611no—
327#1465—612no—
328#1461—611no—
329#1459—612no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61—42no—
333C2×C61—42no—
334C2×C61#288011yescharacteristic
335C2×C61#288311yescharacteristic
336C2×C61C2×#41311yescharacteristic
337D61—82no—
338#559—1221no—
339#559—1222no—
340#559—1221no—
341#559—1221no—
342#559—1222no—
343#559—1221no—
344C2×#127—611no—
345C2×#124—611no—
346C2×#124—612no—
347C2×#124—611no—
348C2×#123—612no—
349C2×#123—612no—
350C2×C4×Q8—611no—
351C2×C4×Q8—611no—
352C2×C4×D4—612no—
353C2×C4×D4—611no—
354C2×C4×D4C2×D6111yescharacteristic
355#436—21no—
356#436—1221no—
357#435—22no—
358#435—1222no—
359C8×D4—21no—
360C8×D4—1221no—
361#432—611no—
362#432C2×D6111yescharacteristic
363#431—611no—
364#431C2×D6111yescharacteristic
365#407—612no—
366#407C2×D6112yes—
367C2×C22⋊C8—612no—
368C2×C22⋊C8C2×D6112yes—
369#324—611no—
370#324—612no—
371#324—611no—
372#324—611no—
373#324—611no—
374#324—612no—
375#323—612no—
376#323—612no—
377#323—612no—
378#323—612no—
379C61#1742911yescharacteristic, complemented, Sylow
380C22×Q8—611no—
381C22×Q8—611no—
382C22×D4—612no—
383C22×D4—612no—
384C22×D4—611no—
385C22×D4C4×D6111yescharacteristic
386C23×C4—612no—
387C23×C4C22×D6112yes—
388C2×M16—22no—
389C2×M16—1222no—
390C22×C8—22no—
391C22×C8—1222no—
392#127—1221no—
393#127—1221no—
394#127—1222no—
395#124—1221no—
396#124—1221no—
397#124—1222no—
398#124—1222no—
399#124—1222no—
400#124—1222no—
401#124—1222no—
402#124—1221no—
403#124—1221no—
404#124—1221no—
405#124—1221no—
406#123—1222no—
407#123—1222no—
408#123—1222no—
409#123—1222no—
410#123—1222no—
411#123—1222no—
412#123—1222no—
413#123—1222no—
414C4×Q8—1222no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×Q8—1221no—
419C4×Q8—1221no—
420C4×Q8—1221no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1221no—
427C4×D4—1221no—
428C4×D4D24411yescharacteristic
429C4×D4D24412yes—
430C4×D4D24411yescharacteristic
431C4×D4C22⋊D6111yescharacteristic
432C4×D4C22⋊D6112yes—
433C4×D4C22⋊D6111yescharacteristic
434C2×C4⋊C4—612no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4C4×D6111yescharacteristic
439C2×C22⋊C4—612no—
440C2×C22⋊C4—612no—
441C2×C22⋊C4—612no—
442C2×C22⋊C4—612no—
443C2×C22⋊C4—612no—
444C2×C22⋊C4C4×D6112yes—
445C2×C42—612no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42C22×D6111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—1221no—
452C4⋊C8—1221no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—611no—
456C22⋊C8—612no—
457C22⋊C8—611no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460C22⋊C8C22×D6111yescharacteristic
461C22⋊C8C22×D6112yes—
462C22⋊C8C22×D6111yescharacteristic
463#97—21no—
464#97—1221no—
465C4×C8—21no—
466C4×C8—1221no—
467C24—612no—
468C24C2×C4×D6112yes—
469C2×Q8—1222no—
470C2×Q8—1221no—
471C2×Q8—1221no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×Q8—2441no—
475C2×Q8—2442no—
476C2×D4—42no—
477C2×D4—1224no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—4882no—
485C2×D4—2442no—
486C2×D4—2442no—
487C2×D4#1175819811yescharacteristic
488C2×D4#1175819811yescharacteristic
489C2×D4#1175819812yes—
490C22×C4—82no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—612no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—4882no—
499C22×C4C2×C4×D6111yescharacteristic
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4C2×C4×D6112yes—
502C22×C4C2×D24412yes—
503C22×C4C2×D24412yes—
504C22×C4C2×C22⋊D6112yes—
505C22×C4C2×C22⋊D6112yes—
506C22×C4C23×D6111yescharacteristic
507M16—82no—
508M16—4882no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—22no—
512C2×C8—82no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1222no—
516C2×C8—4882no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4#1175819812yes—
526C4⋊C4#1175819811yescharacteristic
527C4⋊C4#1175819811yescharacteristic
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4#1175819812yes—
539C22⋊C4#1175819812yes—
540C22⋊C4#1175819812yes—
541C22⋊C4#1175819812yes—
542C42—1222no—
543C42—1222no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42C2×D24411yescharacteristic
549C42C2×D24411yescharacteristic
550C42C2×C22⋊D6111yescharacteristic
551C42C2×C22⋊D6111yescharacteristic
552C23—22no—
553C23—22no—
554C23—42no—
555C23—42no—
556C23—1222no—
557C23—1222no—
558C23—1222no—
559C23—2442no—
560C23—2442no—
561C23C2×#1175819812yes—
562C23C2×#1175819812yes—
563C23C22×C4×D6111yescharacteristic
564Q8—2442no—
565Q8—2442no—
566Q8—2442no—
567Q8—2442no—
568D4—22no—
569D4—22no—
570D4—42no—
571D4—4882no—
572D4—4882no—
573D4—2442no—
574D4—2444no—
575D4—2444no—
576D4—2442no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—612no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1222no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—4882no—
596C2×C4—4882no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2442no—
600C2×C4C2×#1175819811yescharacteristic
601C2×C4C2×#1175819812yes—
602C2×C4C2×#1175819812yes—
603C2×C4C2×#1175819811yescharacteristic
604C2×C4C2×#1175819811yescharacteristic
605C2×C4C2×#1175819811yescharacteristic
606C2×C4C22×C22⋊D6111yescharacteristic
607C2×C4C22×D24411yescharacteristic
608C8—41no—
609C8—42no—
610C8—41no—
611C8—2441no—
612C8—2442no—
613C8—2441no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—82no—
623C22—82no—
624C22—4882no—
625C22—4882no—
626C22—2442no—
627C22—2442no—
628C22—2442no—
629C22C22×#1175819811yescharacteristic
630C22#131×D6111yescharacteristic
631C22#1684052711yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—22no—
637C4—22no—
638C4—21no—
639C4—1222no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C4—2442no—
644C4#1683974412yes—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—4882no—
650C2#2145426611yescharacteristic
651C2#2145427911yescharacteristic
652C2C2×#1683974411yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2974C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519773C4
cosocleC22×C4×C61C24
hypercenter#2974D61
hypocenterC61#17429
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #21454854C2semidirect
3. #21444172C2semidirect
4. #21444170C2semidirect
5. #21444168C2semidirect
6. #21444165C2semidirect
7. #21444162C2semidirect
8. #21444155C2semidirect
9. #21444142C2semidirect
10. #21444135C2semidirect
11. C61×#2974C2semidirect
321. #2974D61semidirect
379. C61#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#168404952
#214548542
#214441722
#214441702
#214441682
#214441652
#214441622
#214441552
#214441422
#214441352
C61×#29742
#1742961