Finite Group Databasebeta

← #29646197

Subgroups — #29646197

Order 15616.

1424 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
1C2×#16840409C211yesmaximal, characteristic
2#21454269C211yesmaximal, characteristic, complemented
3#21454265C211yesmaximal, characteristic, complemented
4#21444179C211yesmaximal, characteristic, complemented
5#21444164C212yesmaximal, complemented
6#21444164C212yesmaximal, complemented
7#21444155C211yesmaximal, characteristic, complemented
8#21444144C212yesmaximal, complemented
9#21444135C211yesmaximal, characteristic, complemented
10#323×D61C212yesmaximal, complemented
11C61×#1471C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C22×D4×D61C411yescharacteristic
14C2×#14519785—21no—
15C2×#14519783—21no—
16#16840409—21no—
17#16840409—21no—
18#16840409—22no—
19#16840409—22no—
20#16840409—21no—
21#16840409—21no—
22C2×#14519764C411yescharacteristic
23C2×#14519759C2212yes—
24C2×#14519757C411yescharacteristic
25C2×#14519748C412yes—
26C2×#14519745C412yes—
27C2×#14519739C411yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C22⋊C4×D61C2212yes—
30#16839730—21no—
31#16839728—21no—
32#16839727—22no—
33#16839727—22no—
34#16839726C2211yescharacteristic, complemented
35#16839724C2212yescomplemented
36#16839724C2212yescomplemented
37C2×C22⋊#92418C2211yescharacteristic, complemented
38C22⋊C8×D61C2212yescomplemented
39C22⋊C8×D61C2212yescomplemented
40#16839487C2211yescharacteristic, complemented
41#16839487C2211yescharacteristic, complemented
42#16839487C2212yescomplemented
43#16839486C2212yescomplemented
44#16839486C2212yescomplemented
45#16839485C2211yescharacteristic
46#16839485C2212yes—
47#16839485C2211yescharacteristic
48C2×#121×C61C2211yescharacteristic
49C61×#407C2211yescharacteristic, complemented
50C2×C22⋊C8×C61C2211yescharacteristic, complemented
51C61×#323C2212yescomplemented
52C61×#323C2212yescomplemented
53C24×D61C2×C412yes—
54C2×#11758222—44no—
55C2×#11758222D411yescharacteristic
56C2×#11758222D411yescharacteristic
57C2×#11758222D412yes—
58C2×#11758222D412yes—
59C2×#11758222D411yescharacteristic
60C2×#11758222D411yescharacteristic
61C22×Dic122C2×C411yescharacteristic
62C22×D244C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C412yes—
65C22×C22⋊D61C2×C412yes—
66C2×D4×D61—22no—
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—44no—
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C412yes—
72C22×C4×D61C2312yes—
73#14519785—44no—
74#14519783—44no—
75C2×#11758194—21no—
76C2×#11758189—22no—
77C2×#11758189—22no—
78C22×#92418—21no—
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81#14519764—21no—
82#14519764—21no—
83#14519764—22no—
84#14519759—22no—
85#14519759—22no—
86#14519759—22no—
87#14519759—22no—
88#14519757—21no—
89#14519757—21no—
90#14519757—22no—
91#14519748—22no—
92#14519748—22no—
93#14519748—22no—
94#14519748—22no—
95#14519745—22no—
96#14519745—22no—
97#14519745—22no—
98#14519745—22no—
99#14519739—22no—
100#14519739—21no—
101#14519739—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104C4×C22⋊D61—21no—
105C4×C22⋊D61—21no—
106C2×C4⋊Dic61C2×C412yes—
107C2×#11758196C2311yescharacteristic
108C2×C22⋊Dic61C2×C412yes—
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C412yes—
111C2×#11758198C2×C412yes—
112C2×#11758198C2×C412yes—
113C2×#11758198C2311yescharacteristic
114C22⋊C4×D61—22no—
115C22⋊C4×D61—22no—
116C22⋊C4×D61—22no—
117C22⋊C4×D61—22no—
118C2×C4×Dic61C2×C411yescharacteristic
119C22⋊#92418—21no—
120C22⋊#92418—21no—
121C22⋊#92418C2311yescharacteristic
122C22⋊#92418C2312yes—
123C22⋊#92418C2311yescharacteristic
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128C22×D4×C61C2×C411yescharacteristic
129C22×D4×C61C2×C412yes—
130C23×C4×C61C2311yescharacteristic
131C2×M16×C61—21no—
132C22×C8×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2312yes—
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C22⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61C2312yes—
143C22⋊C8×C61C2311yescharacteristic
144C24×C61C22×C412yes—
145C24×C61C22×C411yescharacteristic
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61—44no—
151C23×D61—82no—
152C23×D61C22×C412yes—
153C23×D61C22×C411yescharacteristic
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—82no—
160C22×C4×C61—42no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—21no—
169C2×C22⋊D61—21no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61—44no—
175C2×C22⋊D61—44no—
176C2×C22⋊D61C22⋊C412yes—
177C2×C22⋊D61C22⋊C412yes—
178C2×C22⋊D61C22⋊C412yes—
179C2×C22⋊D61C22⋊C412yes—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C412yes—
184D4×D61—48no—
185D4×D61—44no—
186D4×D61—44no—
187#11758222—24no—
188#11758222—24no—
189#11758222—42no—
190#11758222—42no—
191#11758222—44no—
192#11758222—44no—
193C2×D244—24no—
194C2×D244C22⋊C412yes—
195C2×D244C22⋊C411yescharacteristic
196C2×D244C22⋊C411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—44no—
202C2×C4×D61—42no—
203C2×C4×D61—82no—
204C2×C4×D61C2×D412yes—
205C2×C4×D61C2×D412yes—
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2×D412yes—
208C2×Dic122—42no—
209C2×Dic122C22⋊C411yescharacteristic
210C2×Dic122C22⋊C411yescharacteristic
211C2×Dic122C22⋊C412yes—
212M16×C61—42no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—22no—
216C2×C8×C61—42no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊Dic61—21no—
222C22⋊Dic61—21no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—21no—
230#11758198—21no—
231#11758198—22no—
232#11758198—22no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235#11758196—21no—
236#11758196—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239#11758194—42no—
240C2×#92418—21no—
241C2×#92418—22no—
242C2×#92418—21no—
243C2×#92418—42no—
244#11758189—44no—
245#11758189—44no—
246C8×D61—44no—
247C8×D61—44no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61C2×C22⋊C411yescharacteristic
258C23×C61C2×C22⋊C411yescharacteristic
259C23×C61C23×C411yescharacteristic
260C22×D61—21no—
261C22×D61—22no—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—24no—
265C22×D61—42no—
266C22×D61—44no—
267C22×D61—44no—
268C22×D61—44no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—44no—
272C22×D61—82no—
273C22×D61—82no—
274C22×D61—88no—
275C22×D61—88no—
276C22×D61C2×C22⋊C412yes—
277C22×D61C2×C22⋊C412yes—
278C22×D61#13112yescomplemented
279D4×C61—42no—
280D4×C61—42no—
281D4×C61—82no—
282D4×C61—82no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C22⋊D61—24no—
296C22⋊D61—24no—
297C22⋊D61—42no—
298C22⋊D61—42no—
299C22⋊D61—42no—
300C22⋊D61—42no—
301C22⋊D61—44no—
302C22⋊D61—44no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—42no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313D244—24no—
314D244—22no—
315D244#9914yes—
316C4×D61—24no—
317C4×D61—24no—
318C4×D61—42no—
319C4×D61—42no—
320C4×D61—42no—
321C4×D61—42no—
322C4×D61—82no—
323C4×D61—82no—
324Dic122—22no—
325Dic122—22no—
326Dic122—42no—
327C8×C61—41no—
328C8×C61—42no—
329C8×C61—41no—
330#92418—41no—
331#92418—42no—
332#92418—41no—
333#17411—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—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—82no—
348C22×C61—82no—
349C22×C61C22×C22⋊C411yescharacteristic
350C22×C61C2×#13111yescharacteristic
351C22×C61#56811yescharacteristic
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—42no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—42no—
364C2×D61—88no—
365C2×D61—88no—
366C2×D61C2×#9914yes—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—42no—
371C4×C61C2×#9912yes—
372Dic61—22no—
373Dic61—22no—
374Dic61—41no—
375Dic61—41no—
376Dic61—41no—
377C2×#546—611no—
378#2880—611no—
379#2880—611no—
380#1471—611no—
381#1471D6111yescharacteristic, complemented
382#1468—612no—
383#1468—612no—
384#1465—611no—
385#1462—612no—
386#1459—611no—
387C2×#323—612no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—41no—
391C2×C61—41no—
392C2×C61—82no—
393C2×C61#288011yescharacteristic
394C2×C61C22×#9911yescharacteristic
395C2×C61#288811yescharacteristic
396D61—24no—
397D61—42no—
398D61—42no—
399C22×#41—611no—
400C23×D4—611no—
401C2×#131—1221no—
402C2×#131—1221no—
403#546—1221no—
404#546—1221no—
405#546—1222no—
406#546—1222no—
407#546—1221no—
408#546—1221no—
409C2×#124—611no—
410C2×#123—612no—
411C2×C22⋊Q8—611no—
412C2×#121—612no—
413C2×#121C2×D6111yescharacteristic
414C2×#120—612no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C22×C22⋊C4—612no—
418#408—1222no—
419#408—1222no—
420#408—1221no—
421#408—1221no—
422#407—611no—
423#407—612no—
424#407—612no—
425#407C2×D6111yescharacteristic, complemented
426C2×C22⋊C8—611no—
427C2×C22⋊C8—612no—
428C2×C22⋊C8—612no—
429C2×C22⋊C8C2×D6111yescharacteristic, complemented
430#324—611no—
431#324—611no—
432#324—612no—
433#323—612no—
434#323—612no—
435#323—611no—
436#323—612no—
437#323—611no—
438#323C2×D6112yescomplemented
439#323C2×D6112yescomplemented
440C61#1741111yescharacteristic, complemented, Sylow
441C25—612no—
442C2×#41—611no—
443C2×#41—611no—
444C2×#41—612no—
445C2×#41—612no—
446C2×#41—611no—
447C2×#41—611no—
448C2×#41—2444no—
449C22×Q8—611no—
450C22×D4—612no—
451C22×D4—611no—
452C22×D4—612no—
453C22×D4—611no—
454C22×D4—1221no—
455C22×D4—1222no—
456C22×D4—1221no—
457C22×D4—2444no—
458C22×D4C4×D6111yescharacteristic
459C22×D4C4×D6112yes—
460C23×C4—612no—
461C23×C4—612no—
462C23×C4—611no—
463C23×C4C22×D6111yescharacteristic
464#131—2444no—
465#131—2444no—
466C2×M16—21no—
467C2×M16—1222no—
468C2×M16—1222no—
469C2×M16—1221no—
470C22×C8—21no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1221no—
474#124—1221no—
475#124—1221no—
476#124—1222no—
477#123—1222no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481C22⋊Q8—1221no—
482C22⋊Q8—1221no—
483C22⋊Q8—1222no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492#120—1222no—
493#120—1222no—
494#120—1222no—
495#120—1222no—
496C4×D4—1221no—
497C4×D4—1222no—
498C4×D4—1221no—
499C4×D4—1221no—
500C4×D4—1221no—
501C4×D4—1221no—
502C4×D4—1221no—
503C2×C4⋊C4—612no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4C4×D6111yescharacteristic
506C2×C22⋊C4—612no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—612no—
509C2×C22⋊C4—612no—
510C2×C22⋊C4—612no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—1222no—
513C2×C22⋊C4—1222no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4C22×D6112yes—
517C2×C42—611no—
518C22⋊C8—21no—
519C22⋊C8—21no—
520C22⋊C8—611no—
521C22⋊C8—612no—
522C22⋊C8—611no—
523C22⋊C8—1222no—
524C22⋊C8—1222no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527C22⋊C8—1221no—
528C22⋊C8—1221no—
529C22⋊C8C22×D6111yescharacteristic
530C22⋊C8C22×D6112yes—
531C22⋊C8C22×D6111yescharacteristic
532C24—612no—
533C24—611no—
534C24—1224no—
535C24—1222no—
536C24—1222no—
537C24—4882no—
538C24—2442no—
539C24—2444no—
540C24C2×C4×D6112yes—
541C24C2×C4×D6111yescharacteristic
542#41—1224no—
543#41—1224no—
544#41—2442no—
545#41—2442no—
546#41—2444no—
547#41—2444no—
548C2×Q8—611no—
549C2×Q8—611no—
550C2×Q8—612no—
551C2×Q8—2442no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—82no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—611no—
563C2×D4—612no—
564C2×D4—611no—
565C2×D4—1224no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—2441no—
572C2×D4—2444no—
573C2×D4—2448no—
574C2×D4—2444no—
575C2×D4—2444no—
576C2×D4—2444no—
577C22×C4—42no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—4882no—
591C22×C4—2442no—
592C22×C4—2444no—
593C22×C4C2×C4×D6111yescharacteristic
594C22×C4C2×C4×D6112yes—
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600M16—42no—
601M16—2444no—
602M16—2444no—
603M16—2442no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—22no—
607C2×C8—42no—
608C2×C8—1221no—
609C2×C8—1222no—
610C2×C8—1221no—
611C2×C8—2444no—
612C2×C8—2444no—
613C2×C8—2442no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1221no—
631C22⋊C4—1221no—
632C22⋊C4—1221no—
633C22⋊C4—1221no—
634C42—1221no—
635C42—1221no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—612no—
646C23—612no—
647C23—612no—
648C23—1224no—
649C23—1221no—
650C23—1222no—
651C23—1221no—
652C23—1222no—
653C23—4882no—
654C23—4882no—
655C23—4888no—
656C23—4888no—
657C23—2442no—
658C23—2441no—
659C23—2441no—
660C23—2444no—
661C23—2444no—
662C23—2444no—
663C23—2444no—
664C23C22⋊C4×D6111yescharacteristic
665C23C22⋊C4×D6111yescharacteristic
666C23C22×C4×D6111yescharacteristic
667Q8—1222no—
668Q8—1222no—
669Q8—2442no—
670D4—42no—
671D4—42no—
672D4—82no—
673D4—82no—
674D4—614no—
675D4—1224no—
676D4—1224no—
677D4—1224no—
678D4—1222no—
679D4—2442no—
680D4—2442no—
681D4—2442no—
682D4—2442no—
683D4—2444no—
684D4—2444no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—4882no—
703C2×C4—4882no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4C22⋊C4×D6111yescharacteristic
712C2×C4C22⋊C4×D6111yescharacteristic
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C8—41no—
716C8—41no—
717C8—42no—
718C8—2441no—
719C8—2442no—
720C8—2441no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—82no—
735C22—82no—
736C22—614no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—1222no—
742C22—1222no—
743C22—4888no—
744C22—4888no—
745C22—2444no—
746C22—2444no—
747C22—2442no—
748C22—2442no—
749C22—2441no—
750C22—2441no—
751C22C2×C22⋊C4×D6111yescharacteristic
752C22#131×D6111yescharacteristic
753C22#1684052711yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—1222no—
759C4—1222no—
760C4—2441no—
761C4—2441no—
762C4—2441no—
763C4#99×D6112yes—
764C2—21no—
765C2—21no—
766C2—41no—
767C2—41no—
768C2—82no—
769C2—1224no—
770C2—2442no—
771C2—2442no—
772C2#2145426711yescharacteristic
773C2C2×#99×D6111yescharacteristic
774C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1471C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840409C2
cosocleC22×C4×C61C24
hypercenter#1471D61
hypocenterC61#17411
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #21454269C2semidirect
3. #21454265C2semidirect
4. #21444179C2semidirect
5. #21444164C2semidirect
6. #21444164C2semidirect
7. #21444155C2semidirect
8. #21444144C2semidirect
9. #21444135C2semidirect
10. #323×D61C2semidirect
11. C61×#1471C2semidirect
34. #16839726C22semidirect
35. #16839724C22semidirect
36. #16839724C22semidirect
37. C2×C22⋊#92418C22semidirect
38. C22⋊C8×D61C22semidirect
39. C22⋊C8×D61C22semidirect
40. #16839487C22semidirect
41. #16839487C22semidirect
42. #16839487C22semidirect
43. #16839486C22semidirect
44. #16839486C22semidirect
49. C61×#407C22semidirect
50. C2×C22⋊C8×C61C22semidirect
51. C61×#323C22semidirect
52. C61×#323C22semidirect
278. C22×D61#131semidirect
381. #1471D61semidirect
425. #407C2×D61semidirect
429. C2×C22⋊C8C2×D61semidirect
438. #323C2×D61semidirect
439. #323C2×D61semidirect
440. C61#17411semidirect

Maximal subgroups

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

subgroupindex
C2×#168404092
#214542692
#214542652
#214441792
#214441642
#214441552
#214441442
#214441352
#323×D612
C61×#14712
#1741161