Finite Group Databasebeta

← #29647697

Subgroups — #29647697

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459480C211yesmaximal, characteristic
2#21454265C211yesmaximal, characteristic, complemented
3#21448659C211yesmaximal, characteristic, complemented
4#21444388C211yesmaximal, characteristic, complemented
5#21444385C212yesmaximal, complemented
6#21444362C211yesmaximal, characteristic, complemented
7#21444361C212yesmaximal, complemented
8#21444334C211yesmaximal, characteristic, complemented
9#21444333C212yesmaximal, complemented
10#21444309C212yesmaximal, 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×Dic122—21no—
30#16839728—21no—
31#16839727—22no—
32#16839726C2211yescharacteristic, complemented
33#16839724C2212yescomplemented
34C22⋊C8×D61C2212yescomplemented
35#16839664—21no—
36#16839662—22no—
37#16839622C2211yescharacteristic, complemented
38#16839621C2212yescomplemented
39#16839609C2212yescomplemented
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×C412yes—
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
66C22×D244D411yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61D412yes—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61C2×C412yes—
72C22×C4×D61C2312yes—
73#14519783—44no—
74C2×#11758194—21no—
75C2×#11758189—22no—
76C2×C8×D61—22no—
77#14519774—21no—
78#14519773—22no—
79#14519765—21no—
80#14519763—22no—
81#14519762—22no—
82#14519756—21no—
83#14519755—22no—
84#14519753C2×C412yes—
85#14519752—22no—
86#14519752C2×C412yes—
87#14519752C2×C412yes—
88#14519751—21no—
89#14519751—21no—
90#14519751—21no—
91#14519751C2×C412yes—
92#14519751C2312yes—
93#14519750—22no—
94#14519750—22no—
95#14519750—22no—
96#14519749—22no—
97#14519749—22no—
98#14519748C2×C412yes—
99#14519747—22no—
100#14519747—22no—
101#14519747—22no—
102#14519745—22no—
103C4×Dic122—21no—
104C4×Dic122—44no—
105C4×D244—21no—
106#14519739—22no—
107#14519737—22no—
108#14519737—22no—
109#14519735C2×C412yes—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61C2×C411yescharacteristic
112C2×#11758196—22no—
113C4⋊C4×D61C2×C412yes—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C22⋊C4×D61—22no—
119C2×C4×Dic61—22no—
120C22⋊#92418—21no—
121C22⋊#92418C2312yes—
122#14519689—22no—
123#14519689—22no—
124#14519684C2312yes—
125C2×#41×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61—21no—
128#123×C61—21no—
129C22⋊Q8×C61C2×C411yescharacteristic
130C22⋊Q8×C61C2311yescharacteristic
131#121×C61C2×C411yescharacteristic
132#121×C61C2311yescharacteristic
133#120×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136#117×C61C2×C411yescharacteristic
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—44no—
186#11758222—44no—
187#11758222—42no—
188#11758222—42no—
189#11758222—44no—
190C2×D244—22no—
191C2×D244—21no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—42no—
195C2×D244—44no—
196C2×D244—42no—
197C2×D244C22⋊C411yescharacteristic
198C2×D244C22⋊C411yescharacteristic
199C2×D244C22⋊C412yes—
200C2×D244C22×C412yes—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—44no—
204C2×C4×D61C22×C412yes—
205C2×C4×D61C22×C412yes—
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2×D412yes—
208C2×Dic122—24no—
209C2×Dic122C22⋊C412yes—
210C2×Dic122C22⋊C411yescharacteristic
211C2×Dic122C22⋊C411yescharacteristic
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—42no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C22×C411yescharacteristic
218C4⋊C4×C61C22×C411yescharacteristic
219C22⋊C4×C61—21no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—21no—
223C22⋊C4×C61—21no—
224C22⋊C4×C61—42no—
225C42×C61—21no—
226C42×C61—42no—
227C22⋊Dic61—22no—
228C22⋊Dic61—81no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—44no—
236#11758198—82no—
237C4⋊Dic61—21no—
238C4⋊Dic61—42no—
239C4⋊Dic61C22×C412yes—
240#11758196—22no—
241#11758196—22no—
242#11758196—44no—
243C4×Dic61—22no—
244C4×Dic61—44no—
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—22no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—44no—
263C22×D61—42no—
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—42no—
301C22⋊D61—42no—
302C22⋊D61—44no—
303C22⋊D61—82no—
304C22⋊D61—82no—
305C2×Dic61—24no—
306C2×Dic61—22no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—81no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313D244—22no—
314D244—22no—
315D244—42no—
316D244—42no—
317D244—44no—
318D244—42no—
319D244—82no—
320D244—82no—
321C4×D61—24no—
322C4×D61—24no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—44no—
326C4×D61—82no—
327Dic122—22no—
328Dic122—24no—
329Dic122#9914yes—
330C8×C61—41no—
331C8×C61—41no—
332#92418—42no—
333#17611—611nomaximal, Sylow
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61C22×C22⋊C411yescharacteristic
348C22×C61#57611yescharacteristic
349C22×C61#57711yescharacteristic
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—82no—
360C2×D61—82no—
361C2×D61—164no—
362C2×D61—162no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—42no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—81no—
371C4×C61C2×#9912yes—
372Dic61—22no—
373Dic61—42no—
374Dic61—82no—
375Dic61C2×#9914yes—
376#3488—611no—
377#2880—611no—
378#2341—611no—
379#1519—611no—
380#1519—612no—
381#1513—612no—
382#1513—611no—
383#1507—611no—
384#1507—612no—
385#1501—612no—
386#1501D6111yescharacteristic, complemented
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—41no—
390C2×C61—41no—
391C2×C61—81no—
392C2×C61C22×#9911yescharacteristic
393C2×C61#289711yescharacteristic
394C2×C61#290111yescharacteristic
395D61—42no—
396D61—42no—
397D61—82no—
398C2×H(5,𝔽2)—611no—
399C22×#41—611no—
400C2×#131—1221no—
401#550—1221no—
402#548—1221no—
403#546—1221no—
404#546—1222no—
405D42—1221no—
406D42—1222no—
407#537—611no—
408#537—612no—
409#535—612no—
410#535—611no—
411#525—612no—
412#525C2×D6111yescharacteristic
413C2×#121—611no—
414C2×#121—612no—
415#520—611no—
416C2×C4×Q8—1221no—
417#408—1222no—
418#408—1221no—
419#407—611no—
420#407—612no—
421C2×C22⋊C8—612no—
422C2×C22⋊C8C2×D6111yescharacteristic, complemented
423#390—1221no—
424#390—1222no—
425#380—611no—
426#380—612no—
427C4×C22⋊C4—612no—
428C4×C22⋊C4C2×D6111yescharacteristic, complemented
429#328—612no—
430#328C2×D6111yescharacteristic, complemented
431#328C2×D6111yescharacteristic, complemented
432#327—612no—
433#327—612no—
434#327—612no—
435#327—612no—
436#327—612no—
437#327C2×D6111yescharacteristic, complemented
438#327C2×D6111yescharacteristic, complemented
439C61#1761111yescharacteristic, complemented, Sylow
440H(5,𝔽2)—2444no—
441C2×#41—611no—
442C2×#41—612no—
443C2×#41—611no—
444C2×#41—611no—
445C2×#41—612no—
446C2×#41—611no—
447C2×#41—612no—
448C2×#41—1221no—
449C2×#41—2444no—
450C2×#41C4×D6111yescharacteristic
451C22×Q8—611no—
452C22×D4—612no—
453C22×D4—612no—
454C22×D4—611no—
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4—1222no—
458C22×D4—1222no—
459C22×D4—1221no—
460C23×C4—612no—
461C23×C4C22×D6111yescharacteristic
462#131—2444no—
463C2×M16—1222no—
464C2×M16—1221no—
465C22×C8—21no—
466C22×C8—1222no—
467#127—1221no—
468#127—1222no—
469#124—1221no—
470#124—1222no—
471#123—21no—
472#123—1222no—
473C22⋊Q8—612no—
474C22⋊Q8—1222no—
475C22⋊Q8—1221no—
476C22⋊Q8C4×D6111yescharacteristic
477C22⋊Q8C22×D6111yescharacteristic
478#121—612no—
479#121—612no—
480#121—612no—
481#121—612no—
482#121—612no—
483#121—1222no—
484#121—1222no—
485#121—1222no—
486#121—1222no—
487#121—1221no—
488#121—1222no—
489#121—1222no—
490#121—1221no—
491#121—1221no—
492#121C4×D6111yescharacteristic
493#121C22×D6111yescharacteristic
494#120—21no—
495#120—1222no—
496#120—1222no—
497#120—1222no—
498#120—1222no—
499C4×Q8—1221no—
500C4×Q8—2444no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—1221no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507#117—612no—
508#117C4×D6111yescharacteristic
509C2×C4⋊C4—611no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1221no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1222no—
519C2×C42—21no—
520C2×C42—1222no—
521C22⋊C8—21no—
522C22⋊C8—612no—
523C22⋊C8—1222no—
524C22⋊C8—1222no—
525C22⋊C8—1221no—
526C22⋊C8C22×D6111yescharacteristic
527C22⋊C8C22×D6111yescharacteristic
528#95—612no—
529#95C22×D6111yescharacteristic
530#95C22×D6111yescharacteristic
531C24—612no—
532C24—1222no—
533C24—1221no—
534C24D4×D6111yescharacteristic
535#41—42no—
536#41—1224no—
537#41—1224no—
538#41—2442no—
539#41—2442no—
540#41—2444no—
541#41—2444no—
542#41—2444no—
543#41—2444no—
544C2×Q8—611no—
545C2×Q8—612no—
546C2×Q8—611no—
547C2×Q8—1224no—
548C2×Q8C2×C4×D6111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—612no—
553C2×D4—612no—
554C2×D4—612no—
555C2×D4—612no—
556C2×D4—612no—
557C2×D4—611no—
558C2×D4—611no—
559C2×D4—612no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1221no—
568C2×D4—4882no—
569C2×D4—4882no—
570C2×D4—4881no—
571C2×D4—4881no—
572C2×D4—2442no—
573C2×D4—2442no—
574C2×D4—2444no—
575C2×D4—2444no—
576C2×D4—2444no—
577C2×D4—2448no—
578C2×D4C2×C4×D6111yescharacteristic
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—2444no—
593C22×C4C2×C4×D6111yescharacteristic
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4C23×D6111yescharacteristic
599M16—2444no—
600M16—2442no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C2×C8—1222no—
605C2×C8—2444no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—612no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1221no—
612C4⋊C4—2442no—
613C4⋊C4—2444no—
614C4⋊C4C2×C4×D6111yescharacteristic
615C4⋊C4C2×C4×D6111yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—42no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—4882no—
630C22⋊C4—4881no—
631C22⋊C4—2444no—
632C42—21no—
633C42—42no—
634C42—1222no—
635C42—2444no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—612no—
642C23—612no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—4881no—
647C23—4881no—
648C23—4882no—
649C23—4882no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2444no—
654C23C22⋊C4×D6111yescharacteristic
655C23C22⋊C4×D6111yescharacteristic
656C23C2×D4×D6111yescharacteristic
657Q8—41no—
658Q8—614no—
659Q8—1224no—
660Q8—1222no—
661D4—41no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—1224no—
667D4—1224no—
668D4—1222no—
669D4—1222no—
670D4—4882no—
671D4—4882no—
672D4—4882no—
673D4—4882no—
674D4—2442no—
675D4—2442no—
676D4—2444no—
677D4—2444no—
678D4—2442no—
679D4—2442no—
680D4—2442no—
681D4—2442no—
682D4—2442no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—1224no—
702C2×C4—1224no—
703C2×C4—1224no—
704C2×C4—1222no—
705C2×C4—4882no—
706C2×C4—4881no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2444no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4C22⋊C4×D6111yescharacteristic
714C2×C4C22⋊C4×D6111yescharacteristic
715C2×C4C22×C4×D6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C8—41no—
718C8—41no—
719C8—2442no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—1222no—
738C22—1222no—
739C22—9762no—
740C22—9764no—
741C22—4882no—
742C22—4882no—
743C22—2442no—
744C22—2442no—
745C22—2442no—
746C22C2×C22⋊C4×D6111yescharacteristic
747C22#1684056411yescharacteristic
748C22#1684056911yescharacteristic
749C4—21no—
750C4—21no—
751C4—21no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—81no—
757C4—614no—
758C4—1222no—
759C4—4882no—
760C4—2442no—
761C4#99×D6112yes—
762C2—21no—
763C2—21no—
764C2—41no—
765C2—41no—
766C2—81no—
767C2—4882no—
768C2—2442no—
769C2—2442no—
770C2C2×#99×D6111yescharacteristic
771C2#2145434111yescharacteristic
772C2#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#17611
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. #21448659C2semidirect
4. #21444388C2semidirect
5. #21444385C2semidirect
6. #21444362C2semidirect
7. #21444361C2semidirect
8. #21444334C2semidirect
9. #21444333C2semidirect
10. #21444309C2semidirect
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. #16839622C22semidirect
38. #16839621C22semidirect
39. #16839609C22semidirect
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
386. #1501D61semidirect
422. C2×C22⋊C8C2×D61semidirect
428. C4×C22⋊C4C2×D61semidirect
430. #328C2×D61semidirect
431. #328C2×D61semidirect
437. #327C2×D61semidirect
438. #327C2×D61semidirect
439. C61#17611semidirect

Maximal subgroups

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

subgroupindex
#214594802
#214542652
#214486592
#214443882
#214443852
#214443622
#214443612
#214443342
#214443332
#214443092
C61×#15012
#1761161