Finite Group Databasebeta

← #29647615

Subgroups — #29647615

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#21459484C211yesmaximal, characteristic
2#21454265C211yesmaximal, characteristic, complemented
3#21448647C211yesmaximal, characteristic, complemented
4#21444372C212yesmaximal, complemented
5#21444360C211yesmaximal, characteristic, complemented
6#21444346C212yesmaximal, complemented
7#21444335C211yesmaximal, characteristic, complemented
8#21444320C212yesmaximal, complemented
9#21444311C211yesmaximal, characteristic, complemented
10#327×D61C212yesmaximal, complemented
11C61×#1519C211yesmaximal, characteristic, complemented
12C2×#14519822C411yescharacteristic, complemented
13C22×#11758222C2211yescharacteristic
14C2×#14519783—21no—
15#16840430—21no—
16#16840418—21no—
17#16840409—21no—
18#16840402—22no—
19#16840396—21no—
20D4×C22⋊D61—22no—
21#16840343C411yescharacteristic, complemented
22#16840341C412yescomplemented
23#16840329C411yescharacteristic, complemented
24#16840328C412yescomplemented
25#16840273C2211yescharacteristic
26#16840272C2212yes—
27#121×D61C2212yes—
28#16840243C411yescharacteristic, complemented
29C2×#14519739—21no—
30#16839728—21no—
31#16839727—22no—
32#16839726C2211yescharacteristic, complemented
33#16839724C2212yescomplemented
34C22⋊C8×D61C2212yescomplemented
35#16839667—21no—
36#16839638—22no—
37#16839624C2212yescomplemented
38C4×C22⋊Dic61C2211yescharacteristic, complemented
39#95×D61C2212yescomplemented
40#16839500C2211yescharacteristic, complemented
41#16839500C2211yescharacteristic, complemented
42#16839498C2212yescomplemented
43#16839497C2211yescharacteristic, complemented
44#16839497C2211yescharacteristic, complemented
45#16839496C2212yescomplemented
46#16839496C2212yescomplemented
47#16839495C2212yescomplemented
48C2×#121×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic, complemented
50C61×#380C2211yescharacteristic, complemented
51C61×#327C2212yescomplemented
52C61×#327C2212yescomplemented
53#14519822—44no—
54C2×#11758222—44no—
55C2×#11758222C2×C411yescharacteristic
56C2×#11758222C2×C412yes—
57C2×#11758222C2×C411yescharacteristic
58C2×#11758222C2×C411yescharacteristic, complemented
59C2×#11758222D411yescharacteristic
60C2×#11758222D412yes—
61C2×#11758222D411yescharacteristic
62C2×#11758224—21no—
63C2×#11758224C2×C412yescomplemented
64C22×Dic122D411yescharacteristic
65C22×D244D411yescharacteristic
66C22×C22⋊D61—22no—
67C22×C22⋊D61D412yes—
68C2×D4×D61—22no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C412yescomplemented
71C22×C4×D61—22no—
72C22×C4×D61C2312yes—
73#14519783—44no—
74C2×#11758194—21no—
75C2×#11758189—22no—
76C2×C8×D61—22no—
77#14519773—22no—
78#14519773—21no—
79#14519764—21no—
80#14519763—22no—
81#14519760—21no—
82#14519759—22no—
83#14519757—21no—
84#14519757C2×C412yescomplemented
85#14519756C2×C411yescharacteristic, complemented
86#14519756C2311yescharacteristic
87#14519754—22no—
88#14519752—21no—
89#14519752C2×C412yescomplemented
90#14519751—22no—
91#14519751C2×C411yescharacteristic, complemented
92#14519751C2311yescharacteristic
93#14519750—22no—
94#14519750—22no—
95#14519749—22no—
96#14519749—22no—
97#14519748—22no—
98#14519748C2×C412yescomplemented
99#14519748C2×C412yescomplemented
100#14519747—22no—
101#14519746—21no—
102#14519746—22no—
103#14519745—22no—
104#14519745—22no—
105#14519742—21no—
106D4×Dic61—22no—
107#14519739—21no—
108#14519739—44no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111C4×C22⋊D61—22no—
112#14519737—22no—
113#14519736C2×C411yescharacteristic, complemented
114#14519735C2×C412yescomplemented
115C4⋊C4×D61C2×C412yescomplemented
116C2×C22⋊Dic61—21no—
117C2×#11758198—22no—
118C22⋊C4×D61—22no—
119C2×C4×Dic61—21no—
120C22⋊#92418—21no—
121C22⋊#92418C2312yes—
122#14519689—22no—
123#14519689—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684C2311yescharacteristic
127#14519684C2311yescharacteristic
128C22×D4×C61—21no—
129C22×D4×C61C2×C411yescharacteristic, complemented
130C23×C4×C61C2311yescharacteristic
131C22×C8×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134#121×C61C2×C412yescomplemented
135#121×C61C2312yes—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C22⋊C8×C61—21no—
141C22⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61C2311yescharacteristic
143#95×C61C2312yes—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61—22no—
147C23×D61C2×D412yes—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—21no—
151C2×D4×C61—42no—
152C2×D4×C61—81no—
153C2×D4×C61—81no—
154C2×D4×C61C22×C412yes—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
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—21no—
165C2×C22⋊D61—21no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—21no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—44no—
172C2×C22⋊D61—48no—
173C2×C22⋊D61C22⋊C412yes—
174C2×C22⋊D61C22⋊C412yes—
175C2×C22⋊D61C22⋊C412yes—
176C2×C22⋊D61C22⋊C412yes—
177C22×Dic61—21no—
178C22×Dic61—22no—
179C22×Dic61—21no—
180C22×Dic61C2×D412yes—
181#11758224—44no—
182#11758224—44no—
183D4×D61—44no—
184D4×D61—44no—
185D4×D61—82no—
186D4×D61—82no—
187#11758222—24no—
188#11758222—24no—
189#11758222—42no—
190#11758222—42no—
191#11758222—44no—
192#11758222—44no—
193#11758222—42no—
194C2×D244—24no—
195C2×D244—22no—
196C2×D244C22⋊C412yes—
197C2×D244C22⋊C411yescharacteristic
198C2×D244C22⋊C411yescharacteristic
199C2×D244C22×C411yescharacteristic
200C2×C4×D61—21no—
201C2×C4×D61—22no—
202C2×C4×D61—44no—
203C2×C4×D61—44no—
204C2×C4×D61—44no—
205C2×C4×D61—82no—
206C2×C4×D61C22×C412yes—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×Dic122—42no—
211C2×Dic122C22⋊C411yescharacteristic
212C2×Dic122C22⋊C411yescharacteristic
213C2×Dic122C22⋊C412yes—
214C2×Dic122C22×C411yescharacteristic
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—42no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61C22×C412yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—81no—
224C22⋊Dic61—21no—
225C22⋊Dic61—21no—
226C22⋊Dic61—21no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—42no—
230#11758198—22no—
231#11758198—22no—
232#11758198—21no—
233#11758198—21no—
234#11758198—22no—
235#11758198—44no—
236C4⋊Dic61—22no—
237C4⋊Dic61C22×C411yescharacteristic
238C4⋊Dic61C22×C411yescharacteristic
239#11758196—21no—
240#11758196—21no—
241#11758196—22no—
242C4×Dic61—21no—
243C4×Dic61—22no—
244C4×Dic61—42no—
245#11758194—42no—
246C2×#92418—22no—
247#11758189—44no—
248C8×D61—44no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—42no—
255C23×C61—81no—
256C23×C61—81no—
257C23×C61C2×C22⋊C411yescharacteristic
258C23×C61C2×C22⋊C411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—24no—
263C22×D61—21no—
264C22×D61—42no—
265C22×D61—44no—
266C22×D61—82no—
267C22×D61—82no—
268C22×D61C2×C22⋊C412yes—
269C22×D61C2×C22⋊C412yes—
270D4×C61—42no—
271D4×C61—42no—
272D4×C61—42no—
273D4×C61—42no—
274D4×C61—82no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—81no—
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C23×C411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C22⋊D61—24no—
291C22⋊D61—24no—
292C22⋊D61—42no—
293C22⋊D61—42no—
294C22⋊D61—44no—
295C22⋊D61—42no—
296C22⋊D61—41no—
297C22⋊D61—41no—
298C22⋊D61—44no—
299C22⋊D61—82no—
300C22⋊D61—82no—
301C22⋊D61—81no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—42no—
307C2×Dic61—44no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×C22⋊C412yes—
315D244—24no—
316D244—22no—
317D244—41no—
318D244—82no—
319D244#9914yes—
320C4×D61—24no—
321C4×D61—24no—
322C4×D61—42no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—82no—
326C4×D61—88no—
327Dic122—22no—
328Dic122—22no—
329Dic122—42no—
330Dic122—41no—
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—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—162no—
349C22×C61C22×C22⋊C411yescharacteristic
350C22×C61#57611yescharacteristic
351C22×C61#57711yescharacteristic
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—44no—
358C2×D61—44no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—164no—
363C2×D61C2×#9914yes—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—42no—
368C4×C61—82no—
369C4×C61C2×#9912yes—
370Dic61—22no—
371Dic61—22no—
372Dic61—42no—
373Dic61—41no—
374Dic61—41no—
375Dic61—41no—
376Dic61—81no—
377#3488—611no—
378#2880—611no—
379#2339—611no—
380#1519D6111yescharacteristic, complemented
381#1516—612no—
382#1513—611no—
383#1510—612no—
384#1507—611no—
385#1504—612no—
386#1501—611no—
387C2×#327—612no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—41no—
391C2×C61—41no—
392C2×C61—82no—
393C2×C61C22×#9911yescharacteristic
394C2×C61#289711yescharacteristic
395C2×C61#290111yescharacteristic
396D61—24no—
397D61—42no—
398D61—81no—
399C2×H(5,𝔽2)—611no—
400C22×#41—611no—
401C2×#131—1221no—
402#550—1221no—
403#548—1221no—
404#546—1222no—
405#546—1221no—
406D42—1221no—
407D42—1222no—
408#537—612no—
409#537—611no—
410#535—611no—
411#535—612no—
412#525—611no—
413#525—612no—
414C2×#121—612no—
415C2×#121C2×D6111yescharacteristic
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#380C2×D6111yescharacteristic, complemented
428C4×C22⋊C4—611no—
429C2×#95—612no—
430#328—611no—
431#328—611no—
432#328—612no—
433#327—612no—
434#327—612no—
435#327—611no—
436#327—611no—
437#327—612no—
438#327C2×D6112yescomplemented
439#327C2×D6112yescomplemented
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—611no—
450C2×#41—1221no—
451C2×#41—2444no—
452C22×Q8—611no—
453C22×D4—21no—
454C22×D4—612no—
455C22×D4—612no—
456C22×D4—611no—
457C22×D4—1221no—
458C22×D4—1222no—
459C22×D4—1222no—
460C22×D4C4×D6111yescharacteristic, complemented
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—1222no—
470#127—1221no—
471#124—1222no—
472#124—1221no—
473#123—1222no—
474#123—1221no—
475C22⋊Q8—611no—
476C22⋊Q8—611no—
477C22⋊Q8—612no—
478C22⋊Q8—1222no—
479C22⋊Q8—1221no—
480#121—21no—
481#121—21no—
482#121—612no—
483#121—612no—
484#121—611no—
485#121—611no—
486#121—612no—
487#121—1222no—
488#121—1222no—
489#121—1221no—
490#121—1222no—
491#121—1222no—
492#121—1222no—
493#121—1222no—
494#121C4×D6112yescomplemented
495#121C22×D6112yes—
496#120—1222no—
497#120—1222no—
498#120—1222no—
499#120—1222no—
500#120—1221no—
501C4×Q8—1221no—
502C4×D4—1222no—
503C4×D4—1221no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1221no—
507C4×D4—1221no—
508C4×D4—2444no—
509#117—611no—
510#117—612no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4C4×D6111yescharacteristic, complemented
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1221no—
519C2×C42—1221no—
520C22⋊C8—21no—
521C22⋊C8—612no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524C22⋊C8—1221no—
525C22⋊C8C22×D6111yescharacteristic
526C22⋊C8C22×D6111yescharacteristic
527#95—611no—
528#95—611no—
529#95—1222no—
530#95—1222no—
531#95C22×D6112yes—
532C24—21no—
533C24—612no—
534C24—1222no—
535C24D4×D6111yescharacteristic
536#41—1224no—
537#41—1224no—
538#41—2442no—
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—611no—
549C2×Q8—2442no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—612no—
557C2×D4—612no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—611no—
561C2×D4—611no—
562C2×D4—612no—
563C2×D4—611no—
564C2×D4—1224no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1222no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—4882no—
574C2×D4—4882no—
575C2×D4—2444no—
576C2×D4—2444no—
577C2×D4—2444no—
578C2×D4—2448no—
579C2×D4C2×C4×D6112yes—
580C22×C4—21no—
581C22×C4—22no—
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—1221no—
592C22×C4—1221no—
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—42no—
612C4⋊C4—611no—
613C4⋊C4—611no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4C2×C4×D6112yes—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—81no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1221no—
628C22⋊C4—1221no—
629C22⋊C4—1221no—
630C22⋊C4—1221no—
631C22⋊C4—1221no—
632C22⋊C4—2444no—
633C22⋊C4—2442no—
634C42—1222no—
635C42—1221no—
636C42—2442no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—81no—
644C23—81no—
645C23—612no—
646C23—612no—
647C23—1224no—
648C23—1222no—
649C23—1222no—
650C23—1221no—
651C23—4882no—
652C23—4882no—
653C23—2442no—
654C23—2444no—
655C23C22⋊C4×D6111yescharacteristic
656C23C22⋊C4×D6111yescharacteristic
657C23C2×D4×D6111yescharacteristic
658Q8—1222no—
659Q8—1222no—
660Q8—2442no—
661Q8—2441no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—82no—
667D4—614no—
668D4—1224no—
669D4—1224no—
670D4—1224no—
671D4—1222no—
672D4—4882no—
673D4—4881no—
674D4—4882no—
675D4—4882no—
676D4—2441no—
677D4—2442no—
678D4—2442no—
679D4—2444no—
680D4—2442no—
681D4—2444no—
682D4—2441no—
683D4—2441no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—81no—
695C2×C4—612no—
696C2×C4—612no—
697C2×C4—1224no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—4882no—
704C2×C4—4888no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2444no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
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—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—162no—
736C22—614no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—1222no—
742C22—9764no—
743C22—2444no—
744C22—2444no—
745C22—2441no—
746C22—2441no—
747C22—2441no—
748C22C2×C22⋊C4×D6111yescharacteristic
749C22#1684056311yescharacteristic
750C22#1684056811yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—42no—
755C4—82no—
756C4—1222no—
757C4—1222no—
758C4—4881no—
759C4—2442no—
760C4—2441no—
761C4—2441no—
762C4—2441no—
763C4#99×D6112yes—
764C2—21no—
765C2—21no—
766C2—41no—
767C2—41no—
768C2—82no—
769C2—1224no—
770C2—4881no—
771C2—2442no—
772C2C2×#99×D6111yescharacteristic
773C2#2145434011yescharacteristic
774C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1519C2
socleC22×C61C22×C22⋊C4
prime radical#21459484C2
cosocleC22×C4×C61C24
hypercenter#1519D61
hypocenterC61#17603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21448647C2semidirect
4. #21444372C2semidirect
5. #21444360C2semidirect
6. #21444346C2semidirect
7. #21444335C2semidirect
8. #21444320C2semidirect
9. #21444311C2semidirect
10. #327×D61C2semidirect
11. C61×#1519C2semidirect
12. C2×#14519822C4semidirect
21. #16840343C4semidirect
22. #16840341C4semidirect
23. #16840329C4semidirect
24. #16840328C4semidirect
28. #16840243C4semidirect
32. #16839726C22semidirect
33. #16839724C22semidirect
34. C22⋊C8×D61C22semidirect
37. #16839624C22semidirect
38. C4×C22⋊Dic61C22semidirect
39. #95×D61C22semidirect
40. #16839500C22semidirect
41. #16839500C22semidirect
42. #16839498C22semidirect
43. #16839497C22semidirect
44. #16839497C22semidirect
45. #16839496C22semidirect
46. #16839496C22semidirect
47. #16839495C22semidirect
49. C2×C22⋊C8×C61C22semidirect
50. C61×#380C22semidirect
51. C61×#327C22semidirect
52. C61×#327C22semidirect
58. C2×#11758222C2×C4semidirect
63. C2×#11758224C2×C4semidirect
70. C2×D4×D61C2×C4semidirect
84. #14519757C2×C4semidirect
85. #14519756C2×C4semidirect
89. #14519752C2×C4semidirect
91. #14519751C2×C4semidirect
98. #14519748C2×C4semidirect
99. #14519748C2×C4semidirect
113. #14519736C2×C4semidirect
114. #14519735C2×C4semidirect
115. C4⋊C4×D61C2×C4semidirect
129. C22×D4×C61C2×C4semidirect
134. #121×C61C2×C4semidirect
137. C2×C4⋊C4×C61C2×C4semidirect
380. #1519D61semidirect
423. C2×C22⋊C8C2×D61semidirect
427. #380C2×D61semidirect
438. #327C2×D61semidirect
439. #327C2×D61semidirect
440. C61#17603semidirect
460. C22×D4C4×D61semidirect
494. #121C4×D61semidirect
513. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214594842
#214542652
#214486472
#214443722
#214443602
#214443462
#214443352
#214443202
#214443112
#327×D612
C61×#15192
#1760361