Finite Group Databasebeta

← #29647606

Subgroups — #29647606

Order 15616.

1366 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459480C211yesmaximal, characteristic
2#21454265C211yesmaximal, characteristic, complemented
3#21448650C211yesmaximal, characteristic, complemented
4#21444388C211yesmaximal, characteristic, complemented
5#21444374C212yesmaximal, complemented
6#21444362C211yesmaximal, characteristic, complemented
7#21444346C212yesmaximal, complemented
8#21444334C211yesmaximal, characteristic, complemented
9#21444322C212yesmaximal, complemented
10#327×D61C212yesmaximal, complemented
11C61×#1501C211yesmaximal, characteristic, complemented
12C2×#14519823C411yescharacteristic, complemented
13C22×#11758222C2211yescharacteristic
14C2×#14519783—21no—
15#16840433—21no—
16#16840421—21no—
17#16840408—21no—
18#16840404—22no—
19D4×D244—21no—
20#16840394—22no—
21#16840342C412yescomplemented
22#16840340C411yescharacteristic, complemented
23#16840331C411yescharacteristic, complemented
24#16840328C412yescomplemented
25#16840275C2212yes—
26C2×#14519751C2211yescharacteristic
27#121×D61C2212yes—
28#16840242C411yescharacteristic, complemented
29C2×C4×D244—21no—
30#16839728—21no—
31#16839727—22no—
32#16839726C2211yescharacteristic, complemented
33#16839724C2212yescomplemented
34C22⋊C8×D61C2212yescomplemented
35#16839668—21no—
36#16839638—22no—
37#16839624C2212yescomplemented
38#16839622C2211yescharacteristic, complemented
39#95×D61C2212yescomplemented
40#16839499C2212yescomplemented
41#16839497C2212yescomplemented
42#16839497C2212yescomplemented
43#16839496C2212yescomplemented
44#16839495C2212yescomplemented
45#16839495C2212yescomplemented
46C61×#525C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic, complemented
48C4×C22⋊C4×C61C2211yescharacteristic, complemented
49C61×#328C2211yescharacteristic, complemented
50C61×#328C2211yescharacteristic, complemented
51C61×#327C2211yescharacteristic, complemented
52C61×#327C2211yescharacteristic, complemented
53#14519823—44no—
54C2×#11758226C2×C412yescomplemented
55C2×#11758222—21no—
56C2×#11758222—44no—
57C2×#11758222C2×C411yescharacteristic
58C2×#11758222C2×C412yes—
59C2×#11758222C2×C411yescharacteristic
60C2×#11758222D411yescharacteristic
61C2×#11758222D412yes—
62C2×#11758222D411yescharacteristic
63C22×Dic122D411yescharacteristic
64C22×D244—21no—
65C22×D244C2×C411yescharacteristic, complemented
66C22×D244D411yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61D412yes—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61C2×C412yescomplemented
72C22×C4×D61—22no—
73C22×C4×D61C2312yes—
74#14519783—44no—
75C2×#11758194—21no—
76C2×#11758189—22no—
77C2×C8×D61—22no—
78#14519774—21no—
79#14519773—22no—
80#14519765—21no—
81#14519763—22no—
82#14519762—22no—
83#14519756—21no—
84#14519755—22no—
85#14519753C2×C412yescomplemented
86#14519752—22no—
87#14519752C2×C412yescomplemented
88#14519752C2×C412yescomplemented
89#14519751—21no—
90#14519751—21no—
91#14519751—21no—
92#14519751C2×C412yescomplemented
93#14519751C2312yes—
94#14519750—22no—
95#14519750—22no—
96#14519750—22no—
97#14519749—22no—
98#14519749—22no—
99#14519748C2×C412yescomplemented
100#14519747—22no—
101#14519747—22no—
102#14519747—22no—
103#14519745—22no—
104C4×Dic122—21no—
105C4×D244—21no—
106C4×D244—44no—
107#14519739—22no—
108#14519737—22no—
109#14519737—22no—
110#14519735C2×C412yescomplemented
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2×C411yescharacteristic, complemented
113C4⋊C4×D61C2×C412yescomplemented
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—22no—
117C22⋊C4×D61—22no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120#14519689—22no—
121#14519689—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684C2312yes—
125C2×#41×C61C2×C411yescharacteristic, complemented
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61—21no—
128#123×C61—21no—
129C22⋊Q8×C61C2×C411yescharacteristic, complemented
130C22⋊Q8×C61C2311yescharacteristic
131#121×C61C2×C411yescharacteristic, complemented
132#121×C61C2311yescharacteristic
133#120×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136#117×C61C2×C411yescharacteristic, complemented
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2311yescharacteristic
141C22⋊C8×C61C2311yescharacteristic
142#95×C61C2311yescharacteristic
143#95×C61C2311yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61—22no—
147C23×D61C2×D412yes—
148#41×C61—42no—
149C2×Q8×C61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61C22×C411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—42no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—44no—
169C2×C22⋊D61—81no—
170C2×C22⋊D61—81no—
171C2×C22⋊D61C22⋊C412yes—
172C2×C22⋊D61C22⋊C412yes—
173C2×C22⋊D61C22⋊C412yes—
174C2×C22⋊D61C22⋊C412yes—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61C2×D412yes—
178#11758226—44no—
179D4×D61—44no—
180D4×D61—48no—
181D4×D61—82no—
182D4×D61—82no—
183#11758222—24no—
184#11758222—24no—
185#11758222—42no—
186#11758222—42no—
187#11758222—44no—
188#11758222—44no—
189#11758222—44no—
190C2×D244—24no—
191C2×D244—22no—
192C2×D244—21no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—44no—
196C2×D244—42no—
197C2×D244C22⋊C412yes—
198C2×D244C22⋊C411yescharacteristic
199C2×D244C22⋊C411yescharacteristic
200C2×D244C22×C412yes—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—44no—
204C2×C4×D61—44no—
205C2×C4×D61—44no—
206C2×C4×D61—82no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×D412yes—
211C2×Dic122—42no—
212C2×Dic122C22⋊C411yescharacteristic
213C2×Dic122C22⋊C411yescharacteristic
214C2×Dic122C22⋊C412yes—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—42no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C22×C411yescharacteristic
221C4⋊C4×C61C22×C411yescharacteristic
222C22⋊C4×C61—21no—
223C22⋊C4×C61—21no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—21no—
226C22⋊C4×C61—21no—
227C22⋊C4×C61—42no—
228C42×C61—21no—
229C42×C61—42no—
230C22⋊Dic61—22no—
231C22⋊Dic61—81no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—44no—
239C4⋊Dic61—21no—
240C4⋊Dic61—42no—
241C4⋊Dic61C22×C412yes—
242#11758196—22no—
243#11758196—22no—
244C4×Dic61—22no—
245#11758194—42no—
246C2×#92418—22no—
247#11758189—44no—
248C8×D61—44no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61C2×C22⋊C411yescharacteristic
255C23×C61C2×C22⋊C411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—24no—
260C22×D61—22no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—44no—
264C22×D61—82no—
265C22×D61—82no—
266C22×D61—81no—
267C22×D61—81no—
268C22×D61C2×C22⋊C412yes—
269C22×D61C2×C22⋊C412yes—
270Q8×C61—41no—
271D4×C61—41no—
272D4×C61—42no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—81no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—42no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C22⋊D61—24no—
297C22⋊D61—24no—
298C22⋊D61—42no—
299C22⋊D61—42no—
300C22⋊D61—44no—
301C22⋊D61—42no—
302C22⋊D61—42no—
303C22⋊D61—82no—
304C22⋊D61—82no—
305C2×Dic61—22no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—81no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313D244—24no—
314D244—22no—
315D244—42no—
316D244—44no—
317D244—42no—
318D244—82no—
319D244—82no—
320D244#9914yes—
321C4×D61—24no—
322C4×D61—24no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—44no—
326C4×D61—82no—
327C4×D61—88no—
328Dic122—22no—
329Dic122—22no—
330Dic122—42no—
331C8×C61—41no—
332C8×C61—41no—
333#92418—42no—
334#17603—611nomaximal, Sylow
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61C22×C22⋊C411yescharacteristic
349C22×C61#57611yescharacteristic
350C22×C61#57711yescharacteristic
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—44no—
357C2×D61—44no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—164no—
362C2×D61—162no—
363C2×D61C2×#9914yes—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—42no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61—81no—
372C4×C61C2×#9912yes—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—82no—
377#3488—611no—
378#2880—611no—
379#2339—611no—
380#1519—611no—
381#1516—612no—
382#1513—611no—
383#1510—612no—
384#1507—611no—
385#1504—612no—
386#1501D6111yescharacteristic, complemented
387C2×#327—612no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—41no—
391C2×C61—41no—
392C2×C61—81no—
393C2×C61C22×#9911yescharacteristic
394C2×C61#289711yescharacteristic
395C2×C61#290111yescharacteristic
396D61—24no—
397D61—42no—
398D61—82no—
399C2×H(5,𝔽2)—611no—
400C22×#41—611no—
401C2×#131—1221no—
402#550—1221no—
403#548—1221no—
404#546—1221no—
405#546—1222no—
406D42—1221no—
407D42—1222no—
408#537—611no—
409#537—612no—
410#535—612no—
411#535—611no—
412#525—612no—
413#525C2×D6111yescharacteristic
414C2×#121—611no—
415C2×#121—612no—
416#520—611no—
417C2×C4×D4—1221no—
418#408—1222no—
419#408—1221no—
420#407—611no—
421#407—612no—
422C2×C22⋊C8—612no—
423C2×C22⋊C8C2×D6111yescharacteristic, complemented
424#391—1221no—
425#386—1222no—
426#381—612no—
427#380—611no—
428C4×C22⋊C4C2×D6111yescharacteristic, complemented
429C2×#95—612no—
430#328—612no—
431#328C2×D6111yescharacteristic, complemented
432#328C2×D6111yescharacteristic, complemented
433#327—612no—
434#327—612no—
435#327—612no—
436#327—612no—
437#327—612no—
438#327C2×D6111yescharacteristic, complemented
439#327C2×D6111yescharacteristic, complemented
440C61#1760311yescharacteristic, complemented, Sylow
441H(5,𝔽2)—2444no—
442C2×#41—611no—
443C2×#41—612no—
444C2×#41—611no—
445C2×#41—611no—
446C2×#41—612no—
447C2×#41—611no—
448C2×#41—612no—
449C2×#41—1221no—
450C2×#41—2444no—
451C2×#41C4×D6111yescharacteristic, complemented
452C22×Q8—611no—
453C22×D4—612no—
454C22×D4—612no—
455C22×D4—611no—
456C22×D4—611no—
457C22×D4—1221no—
458C22×D4—1222no—
459C22×D4—1222no—
460C22×D4—1221no—
461C23×C4—612no—
462C23×C4—1222no—
463C23×C4C22×D6111yescharacteristic
464#131—2444no—
465C2×M16—1222no—
466C2×M16—1221no—
467C22×C8—21no—
468C22×C8—1222no—
469#127—1221no—
470#127—1222no—
471#124—1221no—
472#124—1222no—
473#123—21no—
474#123—1222no—
475C22⋊Q8—612no—
476C22⋊Q8—1222no—
477C22⋊Q8—1221no—
478C22⋊Q8C4×D6111yescharacteristic, complemented
479C22⋊Q8C22×D6111yescharacteristic
480#121—612no—
481#121—612no—
482#121—612no—
483#121—612no—
484#121—612no—
485#121—1222no—
486#121—1222no—
487#121—1222no—
488#121—1222no—
489#121—1221no—
490#121—1222no—
491#121—1222no—
492#121—1221no—
493#121—1221no—
494#121C4×D6111yescharacteristic, complemented
495#121C22×D6111yescharacteristic
496#120—21no—
497#120—1222no—
498#120—1222no—
499#120—1222no—
500#120—1222no—
501C4×Q8—1221no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—1221no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—2444no—
509#117—612no—
510#117C4×D6111yescharacteristic, complemented
511C2×C4⋊C4—611no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4—1221no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1222no—
519C2×C42—21no—
520C22⋊C8—21no—
521C22⋊C8—612no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524C22⋊C8—1221no—
525C22⋊C8C22×D6111yescharacteristic
526C22⋊C8C22×D6111yescharacteristic
527#95—612no—
528#95—1222no—
529#95—1222no—
530#95C22×D6111yescharacteristic
531#95C22×D6111yescharacteristic
532C24—612no—
533C24—1222no—
534C24—1221no—
535C24D4×D6111yescharacteristic
536#41—42no—
537#41—1224no—
538#41—1224no—
539#41—2442no—
540#41—2442no—
541#41—2444no—
542#41—2444no—
543#41—2444no—
544#41—2444no—
545C2×Q8—611no—
546C2×Q8—611no—
547C2×Q8—612no—
548C2×Q8—2442no—
549C2×Q8C2×C4×D6111yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—612no—
554C2×D4—612no—
555C2×D4—612no—
556C2×D4—612no—
557C2×D4—612no—
558C2×D4—611no—
559C2×D4—612no—
560C2×D4—611no—
561C2×D4—1224no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—4882no—
571C2×D4—4882no—
572C2×D4—4881no—
573C2×D4—4881no—
574C2×D4—2442no—
575C2×D4—2444no—
576C2×D4—2444no—
577C2×D4—2448no—
578C2×D4—2444no—
579C2×D4C2×C4×D6111yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1221no—
592C22×C4—1222no—
593C22×C4—4882no—
594C22×C4—2444no—
595C22×C4—2444no—
596C22×C4—2444no—
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603M16—2444no—
604M16—2442no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—42no—
608C2×C8—1222no—
609C2×C8—2444no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—612no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1221no—
616C4⋊C4—2442no—
617C4⋊C4C2×C4×D6111yescharacteristic
618C4⋊C4C2×C4×D6111yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—42no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—4881no—
633C22⋊C4—2444no—
634C42—21no—
635C42—42no—
636C42—1222no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—612no—
643C23—612no—
644C23—1224no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—4881no—
649C23—4881no—
650C23—4882no—
651C23—4882no—
652C23—2442no—
653C23—2442no—
654C23—2444no—
655C23C22⋊C4×D6111yescharacteristic
656C23C22⋊C4×D6111yescharacteristic
657C23C2×D4×D6111yescharacteristic
658Q8—41no—
659Q8—1222no—
660Q8—1222no—
661Q8—2442no—
662D4—41no—
663D4—42no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—614no—
668D4—1224no—
669D4—1224no—
670D4—1224no—
671D4—1222no—
672D4—4882no—
673D4—4882no—
674D4—4882no—
675D4—4882no—
676D4—2442no—
677D4—2444no—
678D4—2442no—
679D4—2442no—
680D4—2444no—
681D4—2442no—
682D4—2442no—
683D4—2442no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—1224no—
703C2×C4—1224no—
704C2×C4—1222no—
705C2×C4—4888no—
706C2×C4—4882no—
707C2×C4—4881no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2444no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4C22⋊C4×D6111yescharacteristic
716C2×C4C22⋊C4×D6111yescharacteristic
717C2×C4C22×C4×D6111yescharacteristic
718C2×C4C2×D4×D6111yescharacteristic
719C8—41no—
720C8—41no—
721C8—2442no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—81no—
734C22—81no—
735C22—614no—
736C22—1222no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—9762no—
742C22—9764no—
743C22—2444no—
744C22—2444no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22C2×C22⋊C4×D6111yescharacteristic
749C22#1684056411yescharacteristic
750C22#1684056911yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—42no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—1222no—
760C4—1222no—
761C4—4882no—
762C4—2442no—
763C4#99×D6112yes—
764C2—21no—
765C2—21no—
766C2—41no—
767C2—41no—
768C2—81no—
769C2—1224no—
770C2—4882no—
771C2—2442no—
772C2C2×#99×D6111yescharacteristic
773C2#2145434111yescharacteristic
774C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1501C2
socleC22×C61C22×C22⋊C4
prime radical#21459480C2
cosocleC22×C4×C61C24
hypercenter#1501D61
hypocenterC61#17603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21448650C2semidirect
4. #21444388C2semidirect
5. #21444374C2semidirect
6. #21444362C2semidirect
7. #21444346C2semidirect
8. #21444334C2semidirect
9. #21444322C2semidirect
10. #327×D61C2semidirect
11. C61×#1501C2semidirect
12. C2×#14519823C4semidirect
21. #16840342C4semidirect
22. #16840340C4semidirect
23. #16840331C4semidirect
24. #16840328C4semidirect
28. #16840242C4semidirect
32. #16839726C22semidirect
33. #16839724C22semidirect
34. C22⋊C8×D61C22semidirect
37. #16839624C22semidirect
38. #16839622C22semidirect
39. #95×D61C22semidirect
40. #16839499C22semidirect
41. #16839497C22semidirect
42. #16839497C22semidirect
43. #16839496C22semidirect
44. #16839495C22semidirect
45. #16839495C22semidirect
47. C2×C22⋊C8×C61C22semidirect
48. C4×C22⋊C4×C61C22semidirect
49. C61×#328C22semidirect
50. C61×#328C22semidirect
51. C61×#327C22semidirect
52. C61×#327C22semidirect
54. C2×#11758226C2×C4semidirect
65. C22×D244C2×C4semidirect
71. C2×D4×D61C2×C4semidirect
85. #14519753C2×C4semidirect
87. #14519752C2×C4semidirect
88. #14519752C2×C4semidirect
92. #14519751C2×C4semidirect
99. #14519748C2×C4semidirect
110. #14519735C2×C4semidirect
112. C2×C4⋊Dic61C2×C4semidirect
113. C4⋊C4×D61C2×C4semidirect
125. C2×#41×C61C2×C4semidirect
129. C22⋊Q8×C61C2×C4semidirect
131. #121×C61C2×C4semidirect
136. #117×C61C2×C4semidirect
386. #1501D61semidirect
423. C2×C22⋊C8C2×D61semidirect
428. C4×C22⋊C4C2×D61semidirect
431. #328C2×D61semidirect
432. #328C2×D61semidirect
438. #327C2×D61semidirect
439. #327C2×D61semidirect
440. C61#17603semidirect
451. C2×#41C4×D61semidirect
478. C22⋊Q8C4×D61semidirect
494. #121C4×D61semidirect
510. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214594802
#214542652
#214486502
#214443882
#214443742
#214443622
#214443462
#214443342
#214443222
#327×D612
C61×#15012
#1760361