Finite Group Databasebeta

← #29852662

Subgroups — #29852662

Order 15616.

2834 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840359C211yesmaximal, characteristic, complemented
2#21454111C212yesmaximal, complemented
3#21454106C211yesmaximal, characteristic, complemented
4#21454101C211yesmaximal, characteristic
5#21451632C211yesmaximal, characteristic, complemented
6#21451599C212yesmaximal, complemented
7#21451561C211yesmaximal, characteristic, complemented
8#21450074C214yesmaximal, complemented
9#21449954C214yesmaximal, complemented
10#21449628C214yesmaximal, complemented
11#21449554C214yesmaximal, complemented
12#21448488C212yesmaximal, complemented
13#21448422C211yesmaximal, characteristic, complemented
14C4×#14519746C212yesmaximal, complemented
15C23×C4⋊C4×C61C211yesmaximal, characteristic, complemented
16#16840359—28no—
17C2×#14519772C2212yescomplemented
18C2×#14519767C2212yescomplemented
19C2×#14519762C2212yescomplemented
20C2×#14519760C2212yes—
21C2×#14519760C2212yes—
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2212yes—
24C2×#14519755C2212yescomplemented
25C2×#14519751C2211yescharacteristic
26C2×#14519751C2212yes—
27C2×#14519746C2212yes—
28C2×C4×C22⋊D61C2212yes—
29C2×C4×C22⋊D61C2214yes—
30#16839701C2212yescomplemented
31#16839700C2214yescomplemented
32#16839697C2214yescomplemented
33#16839695C2214yescomplemented
34#16839693C2214yescomplemented
35#16839692C2212yescomplemented
36#16839688C2214yescomplemented
37#16839684C2214yescomplemented
38#16839682C2212yescomplemented
39#16839679C2212yescomplemented
40#16839657C2214yescomplemented
41#16839652C2214yescomplemented
42#16839648C2214yescomplemented
43#16839648C2214yescomplemented
44#16839643C2214yescomplemented
45#16839641C2212yes—
46#16839641C2214yes—
47#16839641C2214yes—
48#16839641C2214yes—
49#16839641C2212yes—
50#16839641C2214yes—
51#16839635C2212yes—
52#16839635C2214yes—
53#16839635C2214yes—
54#16839635C2214yes—
55#16839635C2212yes—
56#16839635C2214yes—
57#16839633C2214yescomplemented
58#16839625C2212yes—
59#16839625C2212yes—
60#16839622C2211yescharacteristic
61#16839622C2212yes—
62#16839622C2211yescharacteristic
63#16839622C2212yes—
64#16839618C2212yes—
65C4×C22⋊Dic61C2212yes—
66C4×C22⋊Dic61C2214yes—
67C24×C4×C61C2211yescharacteristic
68C24×C4×C61C2211yescharacteristic
69C24×C4×C61C2211yescharacteristic
70C22×C4⋊C4×C61—28no—
71C22×C4⋊C4×C61C2211yescharacteristic
72C22×C4⋊C4×C61C2211yescharacteristic
73C22×C4⋊C4×C61C2211yescharacteristic
74C22×C4⋊C4×C61C2214yes—
75C22×C4⋊C4×C61C2214yes—
76C22×C4⋊C4×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61C2312yes—
80C22×C22⋊D61C2314yes—
81C22×C4×D61C2312yes—
82#14519772—28no—
83#14519767—28no—
84#14519762—28no—
85#14519760—28no—
86#14519760—28no—
87#14519756—24no—
88#14519756—44no—
89#14519755—28no—
90#14519751—24no—
91#14519751—44no—
92#14519746—28no—
93C4×C22⋊D61—28no—
94C4×C22⋊D61—48no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2312yes—
98C2×C4⋊Dic61C2312yes—
99C2×#11758196C2314yes—
100C2×#11758196C2312yes—
101C2×#11758196C2312yes—
102C2×#11758196C2312yes—
103C2×#11758196C2312yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×C22⋊Dic61C2312yes—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2312yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2312yes—
111C2×C22⋊Dic61C2314yes—
112C2×#11758198C2312yes—
113C2×#11758198C2314yes—
114C2×#11758198C2312yes—
115C2×#11758198C2312yes—
116C2×#11758198C2312yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×C4×Dic61C2312yes—
120C2×C4×Dic61C2314yes—
121#14519684C2314yes—
122#14519684C2312yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2312yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132C25×C61C2311yescharacteristic
133C23×C4×C61—24no—
134C23×C4×C61—24no—
135C23×C4×C61—24no—
136C23×C4×C61—24no—
137C23×C4×C61—24no—
138C23×C4×C61—44no—
139C23×C4×C61—44no—
140C23×C4×C61C2314yes—
141C23×C4×C61C2314yes—
142C23×C4×C61C2312yes—
143C23×C4×C61C2312yes—
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61—24no—
151C2×C4⋊C4×C61—24no—
152C2×C4⋊C4×C61—24no—
153C2×C4⋊C4×C61—216no—
154C2×C4⋊C4×C61—216no—
155C2×C4⋊C4×C61D418yescomplemented
156C2×C4⋊C4×C61C2312yes—
157C2×C4⋊C4×C61C2314yes—
158C2×C4⋊C4×C61C2312yes—
159C2×C4⋊C4×C61C2314yes—
160C2×C4⋊C4×C61C2312yes—
161C2×C4⋊C4×C61C2312yes—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—24no—
165C24×C61—24no—
166C24×C61#4114yes—
167C24×C61C2411yescharacteristic
168C24×C61C2412yes—
169C23×D61C2412yes—
170C22×C4×C61—232no—
171C22×C4×C61—22no—
172C22×C4×C61—28no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—28no—
177C22×C4×C61—28no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—28no—
181C22×C4×C61—24no—
182C22×C4×C61—24no—
183C22×C4×C61—28no—
184C22×C4×C61—24no—
185C22×C4×C61—24no—
186C22×C4×C61—42no—
187C22×C4×C61—44no—
188C22×C4×C61—42no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61—416no—
194C22×C4×C61—416no—
195C22×C4×C61C2×D414yes—
196C22×C4×C61C2×D414yes—
197C22×C4×C61C2×D414yes—
198C22×C4×C61#4114yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C22×C4×C61C2412yes—
205C22×C4×C61C2412yes—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—28no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—28no—
211C2×C22⋊D61—28no—
212C22×Dic61C2412yes—
213C22×Dic61C2414yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2414yes—
217C2×D244—22no—
218C2×D244—42no—
219C2×C4×D61—24no—
220C2×C4×D61—44no—
221C2×Dic122—22no—
222C2×Dic122—42no—
223C4⋊C4×C61—28no—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—28no—
227C4⋊C4×C61C2×D418yes—
228C4⋊C4×C61C2×D418yes—
229C22⋊Dic61—24no—
230C22⋊Dic61—24no—
231C22⋊Dic61—28no—
232C22⋊Dic61—24no—
233C22⋊Dic61—28no—
234C22⋊Dic61—28no—
235#11758198—24no—
236#11758198—24no—
237#11758198—24no—
238#11758198—24no—
239#11758198—28no—
240#11758198—44no—
241#11758198—44no—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61—42no—
245C4⋊Dic61—42no—
246#11758196—24no—
247#11758196—24no—
248#11758196—24no—
249#11758196—24no—
250#11758196—28no—
251#11758196—44no—
252#11758196—44no—
253C4×Dic61—24no—
254C4×Dic61—44no—
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—216no—
258C23×C61—28no—
259C23×C61—216no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61C22×D412yes—
267C23×C61C2×#4112yes—
268C23×C61C2×#4112yes—
269C23×C61C2×#4114yes—
270C23×C61H(5,𝔽2)14yes—
271C23×C612−1+414yes—
272C23×C61C2511yescharacteristic
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—24no—
277C22×D61—24no—
278C2×C4×C61—232no—
279C2×C4×C61—28no—
280C2×C4×C61—28no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—44no—
294C2×C4×C61—44no—
295C2×C4×C61—48no—
296C2×C4×C61—416no—
297C2×C4×C61—48no—
298C2×C4×C61—44no—
299C2×C4×C61—44no—
300C2×C4×C61C22×D414yes—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D414yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C2×#4114yes—
305C22⋊D61—48no—
306C22⋊D61—416no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—22no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—24no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320D244—82no—
321C4×D61—84no—
322Dic122—82no—
323#34989—611nomaximal, Sylow
324C22×C61—232no—
325C22×C61—24no—
326C22×C61—24no—
327C22×C61—24no—
328C22×C61—22no—
329C22×C61—24no—
330C22×C61—22no—
331C22×C61—24no—
332C22×C61—24no—
333C22×C61—24no—
334C22×C61—24no—
335C22×C61#52514yes—
336C22×C61#53918yescomplemented
337C22×C61C23×D411yescharacteristic
338C22×C61C22×#4111yescharacteristic
339C22×C61C22×#4111yescharacteristic
340C22×C61C2×H(5,𝔽2)12yes—
341C22×C61C2×2−1+412yes—
342C2×D61—42no—
343C2×D61—44no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—44no—
347C4×C61—24no—
348C4×C61—24no—
349C4×C61—22no—
350C4×C61—24no—
351C4×C61—22no—
352C4×C61—42no—
353C4×C61—42no—
354Dic61—42no—
355Dic61—44no—
356Dic61—42no—
357Dic61—42no—
358Dic61—44no—
359C2×#539—611no—
360C23×C4⋊C4D6111yescharacteristic, complemented
361#2849—612no—
362#2848—611no—
363#2847—611no—
364#2627—611no—
365#2623—612no—
366#2618—611no—
367#2481—614no—
368#2473—614no—
369#2449—614no—
370#2443—614no—
371#2322—612no—
372#2313—611no—
373C4×#120—612no—
374C2×C61—24no—
375C2×C61—28no—
376C2×C61C2×#52511yescharacteristic
377C2×C61C2×#53912yes—
378C2×C61#348411yescharacteristic
379C2×C61#348611yescharacteristic
380C2×C61#349212yes—
381D61—82no—
382C24×C4C2×D6111yescharacteristic
383C24×C4C2×D6111yescharacteristic
384C24×C4C2×D6111yescharacteristic
385#539—1228no—
386C2×#126—612no—
387C2×#125—612no—
388C2×#123—612no—
389C2×#123—612no—
390C2×#123—612no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—612no—
393C2×C22⋊Q8—612no—
394C2×#121—611no—
395C2×#121—612no—
396C2×#120—612no—
397C2×C4×D4—612no—
398C2×C4×D4—614no—
399C22×C4⋊C4—28no—
400C22×C4⋊C4C2×D6111yescharacteristic
401C22×C4⋊C4C2×D6111yescharacteristic
402C22×C4⋊C4C2×D6111yescharacteristic
403C22×C4⋊C4C2×D6114yes—
404C22×C4⋊C4C2×D6114yes—
405C22×C4⋊C4C2×D6111yescharacteristic
406#400—614no—
407#400—612no—
408#399—614no—
409#398—612no—
410#398—614no—
411#398—614no—
412#397—614no—
413#396—614no—
414#395—612no—
415#394—612no—
416#389—614no—
417#388—614no—
418#387—614no—
419#387—614no—
420#387—614no—
421#386—612no—
422#386—614no—
423#386—614no—
424#386—614no—
425#386—612no—
426#386—614no—
427#385—612no—
428#385—614no—
429#385—614no—
430#385—614no—
431#385—612no—
432#385—614no—
433#385—614no—
434#381—612no—
435#381—612no—
436#380—611no—
437#380—611no—
438#380—612no—
439#380—612no—
440#379—612no—
441C4×C22⋊C4—612no—
442C4×C22⋊C4—614no—
443C61#3498911yescharacteristic, complemented, Sylow
444C25C22×D6111yescharacteristic
445C22×Q8—611no—
446C22×D4—612no—
447C22×D4—614no—
448C22×D4—611no—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—44no—
455C23×C4—44no—
456C23×C4—612no—
457C23×C4C22×D6114yes—
458C23×C4C22×D6114yes—
459C23×C4C22×D6112yes—
460C23×C4C22×D6112yes—
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467#126—1228no—
468#125—1228no—
469#123—1228no—
470#123—1228no—
471#123—1228no—
472C22⋊Q8—1224no—
473C22⋊Q8—1228no—
474C22⋊Q8—2444no—
475#121—1224no—
476#121—2444no—
477#120—1228no—
478C4×D4—1228no—
479C4×D4—2448no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—216no—
484C2×C4⋊C4—216no—
485C2×C4⋊C4—612no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—612no—
488C2×C4⋊C4—612no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—612no—
491C2×C4⋊C4—614no—
492C2×C4⋊C4—614no—
493C2×C4⋊C4—612no—
494C2×C4⋊C4—612no—
495C2×C4⋊C4—614no—
496C2×C4⋊C4C22⋊D6118yescomplemented
497C2×C4⋊C4C22×D6114yes—
498C2×C4⋊C4C22×D6112yes—
499C2×C4⋊C4C22×D6112yes—
500C2×C4⋊C4C22×D6114yes—
501C2×C4⋊C4C22×D6112yes—
502C2×C4⋊C4C22×D6112yes—
503C2×C22⋊C4—612no—
504C2×C22⋊C4—614no—
505C2×C22⋊C4—612no—
506C2×C22⋊C4—614no—
507C2×C22⋊C4—612no—
508C2×C22⋊C4—614no—
509C2×C22⋊C4—612no—
510C2×C22⋊C4—612no—
511C2×C22⋊C4—612no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—614no—
516C2×C42—612no—
517C2×C42—614no—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—612no—
522#95—614no—
523#95—612no—
524#95—614no—
525#95—614no—
526#95—614no—
527#95—614no—
528#95—614no—
529C24—22no—
530C24—22no—
531C24—24no—
532C24—24no—
533C24—612no—
534C24#1175822214yes—
535C24C23×D6111yescharacteristic
536C24C23×D6112yes—
537C2×Q8—1222no—
538C2×Q8—2442no—
539C2×D4—1224no—
540C2×D4—1224no—
541C2×D4—1228no—
542C2×D4—1224no—
543C2×D4—1228no—
544C2×D4—1228no—
545C2×D4—1222no—
546C2×D4—2442no—
547C22×C4—232no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—28no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—42no—
564C22×C4—44no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—416no—
571C22×C4—416no—
572C22×C4—614no—
573C22×C4—612no—
574C22×C4—614no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—1224no—
578C22×C4—2444no—
579C22×C4#1175822214yes—
580C22×C4C2×C22⋊D6114yes—
581C22×C4C2×C22⋊D6114yes—
582C22×C4C2×C22⋊D6114yes—
583C22×C4C23×D6112yes—
584C22×C4C23×D6112yes—
585C22×C4C23×D6112yes—
586C22×C4C23×D6112yes—
587C22×C4C23×D6111yescharacteristic
588C22×C4C23×D6111yescharacteristic
589C22×C4C23×D6112yes—
590C4⋊C4—28no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—28no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—1228no—
601C4⋊C4—2444no—
602C4⋊C4—2444no—
603C4⋊C4—2442no—
604C4⋊C4—2442no—
605C4⋊C4C2×C22⋊D6118yes—
606C4⋊C4C2×C22⋊D6118yes—
607C22⋊C4—1224no—
608C22⋊C4—1224no—
609C22⋊C4—1228no—
610C22⋊C4—1224no—
611C22⋊C4—1228no—
612C22⋊C4—1228no—
613C22⋊C4—1224no—
614C22⋊C4—1224no—
615C22⋊C4—1224no—
616C22⋊C4—1224no—
617C22⋊C4—1228no—
618C22⋊C4—2444no—
619C22⋊C4—2444no—
620C42—1224no—
621C42—2444no—
622C23—28no—
623C23—28no—
624C23—216no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—216no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1224no—
637C23—1224no—
638C23C22×C22⋊D6112yes—
639C23C2×#1175822212yes—
640C23C2×#1175822212yes—
641C23C2×#1175822214yes—
642C23#1451982214yes—
643C23#1451982514yes—
644C23C24×D6111yescharacteristic
645Q8—4882no—
646D4—4882no—
647D4—2448no—
648D4—24416no—
649C2×C4—232no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—416no—
667C2×C4—48no—
668C2×C4—48no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1224no—
675C2×C4—1222no—
676C2×C4—1224no—
677C2×C4—1222no—
678C2×C4—1224no—
679C2×C4—1224no—
680C2×C4—1224no—
681C2×C4—1224no—
682C2×C4—1224no—
683C2×C4—1224no—
684C2×C4—4884no—
685C2×C4C22×C22⋊D6114yes—
686C2×C4C22×C22⋊D6114yes—
687C2×C4C22×C22⋊D6112yes—
688C2×C4C22×C22⋊D6112yes—
689C2×C4C2×#1175822214yes—
690C22—232no—
691C22—22no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—24no—
698C22—24no—
699C22—22no—
700C22—24no—
701C22—2442no—
702C22—2444no—
703C22—2442no—
704C22—2444no—
705C22—2442no—
706C22#1684027314yes—
707C22#1684035918yescomplemented
708C22C23×C22⋊D6111yescharacteristic
709C22C22×#1175822211yescharacteristic
710C22C22×#1175822211yescharacteristic
711C22C2×#1451982212yes—
712C22C2×#1451982512yes—
713C4—24no—
714C4—24no—
715C4—24no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—2442no—
721C4—2444no—
722C4—2442no—
723C4—2444no—
724C4—2442no—
725C2—24no—
726C2—28no—
727C2—4882no—
728C2C2×#1684027311yescharacteristic
729C2C2×#1684035912yes—
730C2#2145945411yescharacteristic
731C2#2145947011yescharacteristic
732C2#2145952812yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC23×C4⋊C4×C61C2
prime radical#21454101C2
hypercenterC23×C4⋊C4D61
hypocenterC61#34989
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840359C2semidirect
2. #21454111C2semidirect
3. #21454106C2semidirect
5. #21451632C2semidirect
6. #21451599C2semidirect
7. #21451561C2semidirect
8. #21450074C2semidirect
9. #21449954C2semidirect
10. #21449628C2semidirect
11. #21449554C2semidirect
12. #21448488C2semidirect
13. #21448422C2semidirect
14. C4×#14519746C2semidirect
15. C23×C4⋊C4×C61C2semidirect
17. C2×#14519772C22semidirect
18. C2×#14519767C22semidirect
19. C2×#14519762C22semidirect
24. C2×#14519755C22semidirect
30. #16839701C22semidirect
31. #16839700C22semidirect
32. #16839697C22semidirect
33. #16839695C22semidirect
34. #16839693C22semidirect
35. #16839692C22semidirect
36. #16839688C22semidirect
37. #16839684C22semidirect
38. #16839682C22semidirect
39. #16839679C22semidirect
40. #16839657C22semidirect
41. #16839652C22semidirect
42. #16839648C22semidirect
43. #16839648C22semidirect
44. #16839643C22semidirect
57. #16839633C22semidirect
155. C2×C4⋊C4×C61D4semidirect
336. C22×C61#539semidirect
360. C23×C4⋊C4D61semidirect
443. C61#34989semidirect
496. C2×C4⋊C4C22⋊D61semidirect
707. C22#16840359semidirect

Maximal subgroups

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

subgroupindex
C2×#168403592
#214541112
#214541062
#214541012
#214516322
#214515992
#214515612
#214500742
#214499542
#214496282
#214495542
#214484882
#214484222
C4×#145197462
C23×C4⋊C4×C612
#3498961