Finite Group Databasebeta

← #29658893

Subgroups — #29658893

Order 15616.

1322 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#21456734C211yesmaximal, characteristic, complemented
2#21455299C211yesmaximal, characteristic, complemented
3C2×#16839957C211yesmaximal, characteristic, complemented
4#21444922C212yesmaximal, complemented
5#21444908C212yesmaximal, complemented
6#21444884C212yesmaximal, complemented
7#21444873C212yesmaximal, complemented
8#21444496C211yesmaximal, characteristic, complemented
9#21444244C211yesmaximal, characteristic, complemented
10#21444206C211yesmaximal, characteristic, complemented
11D4×#41×C61C211yesmaximal, characteristic, complemented
12C2×#14519802—21no—
13C22×#11758199—21no—
14C2×#14519774C2211yescharacteristic, complemented
15#16840138C2212yescomplemented
16#16840110C2212yescomplemented
17#16839962—21no—
18#16839962C2212yescomplemented
19#16839957—22no—
20#16839957—21no—
21#16839957—21no—
22#16839957—21no—
23#16839957C2212yes—
24#16839957C2212yescomplemented
25#16839957C2212yescomplemented
26#16839895—22no—
27#16839815C2211yescharacteristic, complemented
28#16839786C2211yescharacteristic, complemented
29C2×C4⋊#92418C2211yescharacteristic, complemented
30#16839766—21no—
31C2×#14519697—21no—
32#16839508C2212yescomplemented
33#16839506C2212yescomplemented
34Q8⋊#92418C2212yescomplemented
35D4⋊#92418C2212yescomplemented
36D4⋊#92418C2212yescomplemented
37D4⋊#92418C2212yescomplemented
38C22×#41×C61—21no—
39C61×#550C2211yescharacteristic, complemented
40D4×Q8×C61C2211yescharacteristic, complemented
41C61×#548—21no—
42C61×#547—21no—
43C61×#547C2211yescharacteristic, complemented
44C61×#546—22no—
45C61×#546—21no—
46D42×C61—21no—
47D42×C61C2211yescharacteristic, complemented
48C61×#532—21no—
49C61×#532C2211yescharacteristic
50C61×#525—22no—
51C61×#525—21no—
52C4×#41×C61C2211yescharacteristic
53C2×C4×D4×C61—21no—
54C2×C4×D4×C61C2211yescharacteristic
55C22×D244—21no—
56C22×D244—21no—
57C22×D244—21no—
58#14519802—44no—
59C2×#11758201—22no—
60C2×#11758199—22no—
61C2×#11758199—22no—
62C2×#11758199—22no—
63C2×#11758199—24no—
64C2×#11758199—44no—
65C2×#11758194—21no—
66C22×#92418—21no—
67#14519774—21no—
68#14519774—21no—
69#14519774—21no—
70#14519774C2312yes—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75C4⋊#92418C2312yes—
76#14519697—22no—
77#14519697—22no—
78#14519697—22no—
79#14519697—24no—
80#14519697—22no—
81C22⋊#92418—21no—
82C4×#92418C2312yes—
83C2×#41×C61—22no—
84C2×#41×C61—22no—
85C2×#41×C61—21no—
86C2×#41×C61—21no—
87C2×#41×C61—21no—
88C2×#41×C61—44no—
89C2×#41×C61—44no—
90C2×#41×C61D411yescharacteristic
91C22×Q8×C61—21no—
92C22×D4×C61—22no—
93C22×D4×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61D411yescharacteristic
96C23×C4×C61—22no—
97C23×C4×C61—21no—
98C4⋊Q8×C61—21no—
99C4⋊Q8×C61C2311yescharacteristic
100#127×C61—21no—
101#127×C61C2311yescharacteristic
102#124×C61—22no—
103#124×C61—21no—
104#123×C61—22no—
105#123×C61—22no—
106#123×C61—22no—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61—21no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—21no—
111#121×C61—22no—
112#121×C61—22no—
113#121×C61—21no—
114#121×C61—22no—
115#121×C61—21no—
116#121×C61—21no—
117#121×C61—21no—
118#121×C61—21no—
119#121×C61D412yes—
120#120×C61—22no—
121#120×C61—22no—
122#120×C61—22no—
123C4×Q8×C61D411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61D411yescharacteristic
136C4×D4×C61D412yes—
137C4×D4×C61D411yescharacteristic
138C4×D4×C61D411yescharacteristic
139C4×D4×C61C2311yescharacteristic
140C4×D4×C61C2311yescharacteristic
141C4×D4×C61C2311yescharacteristic
142#117×C61—21no—
143#117×C61D411yescharacteristic
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—21no—
148C2×C42×C61—21no—
149C2×C42×C61C2311yescharacteristic
150C24×C61—22no—
151C24×C61—21no—
152C23×D61—41no—
153#41×C61—22no—
154#41×C61—48no—
155#41×C61—48no—
156#41×C61—42no—
157#41×C61—42no—
158#41×C61—42no—
159#41×C61—42no—
160#41×C61—42no—
161#41×C61—42no—
162#41×C61D814yescomplemented
163C2×Q8×C61—22no—
164C2×Q8×C61—21no—
165C2×Q8×C61—42no—
166C2×Q8×C61—42no—
167C2×Q8×C61C2×D411yescharacteristic
168C2×D4×C61—21no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—41no—
180C2×D4×C61—42no—
181C2×D4×C61—48no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61C2×D411yescharacteristic
186C2×D4×C61C2×D411yescharacteristic
187C2×D4×C61C2×D411yescharacteristic
188C2×D4×C61C2×D412yes—
189C22×C4×C61—21no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—48no—
202C22×C4×C61—42no—
203C22×C4×C61—42no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—42no—
211C2×D244—42no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244—41no—
215C2×D244—41no—
216C2×D244—41no—
217C2×D244—82no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61C2×D411yescharacteristic
225C4⋊C4×C61C2×D411yescharacteristic
226C4⋊C4×C61C2×D411yescharacteristic
227C4⋊C4×C61C2×D411yescharacteristic
228C4⋊C4×C61C2×D412yes—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C42×C61—21no—
243C42×C61—21no—
244C42×C61—21no—
245C42×C61C2×D411yescharacteristic
246C42×C61C2×D411yescharacteristic
247C42×C61C2×D411yescharacteristic
248C42×C61C2411yescharacteristic
249#11758201—44no—
250#11758199—44no—
251#11758199—44no—
252#11758199—44no—
253#11758199—84no—
254#11758194—42no—
255C2×#92418—22no—
256C2×#92418—22no—
257C2×#92418—22no—
258C2×#92418—42no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—42no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—42no—
267C23×C61—81no—
268C23×C61—82no—
269C23×C61#12011yescharacteristic
270C22×D61—42no—
271C22×D61—82no—
272C22×D61—82no—
273C22×D61—82no—
274Q8×C61—21no—
275Q8×C61—44no—
276Q8×C61—41no—
277Q8×C61—41no—
278Q8×C61C2×D812yescomplemented
279D4×C61—24no—
280D4×C61—21no—
281D4×C61—21no—
282D4×C61—21no—
283D4×C61—21no—
284D4×C61—42no—
285D4×C61—42no—
286D4×C61—44no—
287D4×C61—44no—
288D4×C61—44no—
289D4×C61—44no—
290D4×C61—44no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—82no—
296D4×C61C2×D812yescomplemented
297D4×C61AGL(1,ℤ/8)12yescomplemented
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—24no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—44no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61—42no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—44no—
320C2×C4×C61—42no—
321C2×C4×C61—81no—
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12011yescharacteristic
325C2×C4×C61C2×D812yes—
326C2×C4×C61AGL(1,ℤ/8)12yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330D244—44no—
331D244—42no—
332D244—42no—
333D244—42no—
334D244—42no—
335D244—82no—
336D244—82no—
337D244—82no—
338#92418—42no—
339#92418—42no—
340#92418—42no—
341#18786—611nomaximal, Sylow
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—42no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—41no—
356C22×C61—84no—
357C22×C61—88no—
358C22×C61#44712yes—
359C22×C61C2×#12011yescharacteristic
360C2×D61—82no—
361C2×D61—82no—
362C2×D61—82no—
363C2×D61—164no—
364C4×C61—22no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—41no—
369C4×C61—42no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61#44712yes—
374C4×C61C22×D811yescharacteristic
375C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
376C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
377C4×C61#57511yescharacteristic
378D4×#41D6111yescharacteristic, complemented
379#3205—611no—
380#3038—611no—
381C2×#459—611no—
382#1627—612no—
383#1625—612no—
384#1621—612no—
385#1619—612no—
386#1547—611no—
387#1486—611no—
388#1477—611no—
389C2×C61—22no—
390C2×C61—42no—
391C2×C61—42no—
392C2×C61—81no—
393C2×C61—82no—
394C2×C61C2×#44711yescharacteristic
395C2×C61#300611yescharacteristic
396C2×C61#302111yescharacteristic
397D61—162no—
398C22×#41—21no—
399C2×AGL(1,ℤ/8)—1221no—
400C22×D8—1221no—
401#550C2×D6111yescharacteristic, complemented
402D4×Q8C2×D6111yescharacteristic, complemented
403#548—21no—
404#547—21no—
405#547C2×D6111yescharacteristic, complemented
406#546—22no—
407#546—21no—
408D42—21no—
409D42C2×D6111yescharacteristic, complemented
410#532—21no—
411#532C2×D6111yescharacteristic
412C2×#127—611no—
413#525—22no—
414#525—21no—
415C4×#41C2×D6111yescharacteristic
416C2×C4×D4—21no—
417C2×C4×D4C2×D6111yescharacteristic
418#493—612no—
419#486—612no—
420#460—612no—
421#460—1221no—
422#459—612no—
423#459—612no—
424#459—612no—
425#459—1222no—
426#459—1221no—
427#459—1221no—
428#459—1221no—
429#447—1222no—
430#431—611no—
431#423—611no—
432C2×C4⋊C8—611no—
433#418—1221no—
434C2×#102—1221no—
435#332—612no—
436#331—612no—
437Q8⋊C8—612no—
438D4⋊C8—612no—
439D4⋊C8—612no—
440D4⋊C8—612no—
441C61#1878611yescharacteristic, complemented, Sylow
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—44no—
448C2×#41—44no—
449C2×#41C22⋊D6111yescharacteristic
450C22×Q8—21no—
451C22×D4—22no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—1221no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4C22⋊D6111yescharacteristic
458C23×C4—22no—
459C23×C4—21no—
460AGL(1,ℤ/8)—2444no—
461C2×SD16—1222no—
462C2×D8—1224no—
463C2×D8—1222no—
464C2×D8—1222no—
465C2×D8—1222no—
466C2×D8—2444no—
467C2×M16—1221no—
468C22×C8—1221no—
469C4⋊Q8—21no—
470C4⋊Q8C22×D6111yescharacteristic
471#127—21no—
472#127—612no—
473#127—1221no—
474#127—1221no—
475#127—1221no—
476#127C22×D6111yescharacteristic
477#124—22no—
478#124—21no—
479#123—22no—
480#123—22no—
481#123—22no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—21no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121C22⋊D6112yes—
495#120—22no—
496#120—22no—
497#120—22no—
498C4×Q8C22⋊D6111yescharacteristic
499C4×Q8C22×D6111yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4C22⋊D6111yescharacteristic
511C4×D4C22⋊D6111yescharacteristic
512C4×D4C22⋊D6111yescharacteristic
513C4×D4C22⋊D6112yes—
514C4×D4C22×D6111yescharacteristic
515C4×D4C22×D6111yescharacteristic
516C4×D4C22×D6111yescharacteristic
517#117—21no—
518#117C22⋊D6111yescharacteristic
519C2×C4⋊C4—21no—
520C2×C4⋊C4C22⋊D6111yescharacteristic
521C2×C22⋊C4—22no—
522C2×C22⋊C4—21no—
523C2×C42—21no—
524C2×C42C22×D6111yescharacteristic
525C4⋊C8—612no—
526C4⋊C8—612no—
527C4⋊C8—1221no—
528C4⋊C8—1221no—
529C4⋊C8—1221no—
530#102—1222no—
531#102—1222no—
532#102—1222no—
533#102—1222no—
534#102—1224no—
535C22⋊C8—1221no—
536C4×C8—612no—
537C24—22no—
538C24—21no—
539C24—2441no—
540#41—22no—
541#41—48no—
542#41—48no—
543#41—42no—
544#41—42no—
545#41—42no—
546#41—42no—
547#41—42no—
548#41—42no—
549#41#1175819914yescomplemented
550C2×Q8—22no—
551C2×Q8—21no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8C2×C22⋊D6111yescharacteristic
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—41no—
567C2×D4—48no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—4882no—
576C2×D4—2442no—
577C2×D4—2442no—
578C2×D4—2441no—
579C2×D4—2441no—
580C2×D4—2441no—
581C2×D4—2442no—
582C2×D4—2442no—
583C2×D4C2×C22⋊D6111yescharacteristic
584C2×D4C2×C22⋊D6111yescharacteristic
585C2×D4C2×C22⋊D6111yescharacteristic
586C2×D4C2×C22⋊D6112yes—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—48no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605SD16—2444no—
606D8—4884no—
607D8—2444no—
608D8—2444no—
609D8—2444no—
610M16—2442no—
611C2×C8—1222no—
612C2×C8—1222no—
613C2×C8—1222no—
614C2×C8—2442no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4C2×C22⋊D6111yescharacteristic
622C4⋊C4C2×C22⋊D6111yescharacteristic
623C4⋊C4C2×C22⋊D6111yescharacteristic
624C4⋊C4C2×C22⋊D6111yescharacteristic
625C4⋊C4C2×C22⋊D6112yes—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42C2×C22⋊D6111yescharacteristic
643C42C2×C22⋊D6111yescharacteristic
644C42C2×C22⋊D6111yescharacteristic
645C42C23×D6111yescharacteristic
646C23—21no—
647C23—21no—
648C23—22no—
649C23—21no—
650C23—42no—
651C23—44no—
652C23—44no—
653C23—42no—
654C23—81no—
655C23—82no—
656C23—4882no—
657C23—4882no—
658C23—4882no—
659C23—2442no—
660C23#1451974611yescharacteristic
661Q8—21no—
662Q8—44no—
663Q8—41no—
664Q8—41no—
665Q8C2×#1175819912yescomplemented
666D4—24no—
667D4—21no—
668D4—21no—
669D4—21no—
670D4—21no—
671D4—42no—
672D4—42no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—44no—
677D4—44no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—4882no—
684D4—4882no—
685D4—4882no—
686D4—2444no—
687D4—2442no—
688D4—2442no—
689D4—2442no—
690D4—2442no—
691D4C2×#1175819912yescomplemented
692D4#1451980212yescomplemented
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—24no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—81no—
717C2×C4#1451974611yescharacteristic
718C2×C4#1451974611yescharacteristic
719C2×C4#1451974611yescharacteristic
720C2×C4C2×#1175819912yes—
721C2×C4#1451980312yes—
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C22×C22⋊D6111yescharacteristic
724C2×C4C22×C22⋊D6111yescharacteristic
725C8—2442no—
726C8—2442no—
727C8—2442no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—84no—
743C22—88no—
744C22—9764no—
745C22—4882no—
746C22—4882no—
747C22—4882no—
748C22#1683989612yes—
749C22C2×#1451974611yescharacteristic
750C4—21no—
751C4—21no—
752C4—22no—
753C4—21no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4#1683989612yes—
760C4C22×#1175819911yescharacteristic
761C4C2×#1451980211yescharacteristic
762C4C2×#1451980311yescharacteristic
763C4#1684056011yescharacteristic
764C2—22no—
765C2—42no—
766C2—42no—
767C2—82no—
768C2—81no—
769C2—9762no—
770C2C2×#1683989611yescharacteristic
771C2#2145507111yescharacteristic
772C2#2145519111yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingD4×#41×C61C2
socleC22×C61C2×#120
hypercenterD4×#41D61
hypocenterC61#18786
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. #21456734C2semidirect
2. #21455299C2semidirect
3. C2×#16839957C2semidirect
4. #21444922C2semidirect
5. #21444908C2semidirect
6. #21444884C2semidirect
7. #21444873C2semidirect
8. #21444496C2semidirect
9. #21444244C2semidirect
10. #21444206C2semidirect
11. D4×#41×C61C2semidirect
14. C2×#14519774C22semidirect
15. #16840138C22semidirect
16. #16840110C22semidirect
18. #16839962C22semidirect
24. #16839957C22semidirect
25. #16839957C22semidirect
27. #16839815C22semidirect
28. #16839786C22semidirect
29. C2×C4⋊#92418C22semidirect
32. #16839508C22semidirect
33. #16839506C22semidirect
34. Q8⋊#92418C22semidirect
35. D4⋊#92418C22semidirect
36. D4⋊#92418C22semidirect
37. D4⋊#92418C22semidirect
39. C61×#550C22semidirect
40. D4×Q8×C61C22semidirect
43. C61×#547C22semidirect
47. D42×C61C22semidirect
162. #41×C61D8semidirect
278. Q8×C61C2×D8semidirect
296. D4×C61C2×D8semidirect
297. D4×C61AGL(1,ℤ/8)semidirect
378. D4×#41D61semidirect
401. #550C2×D61semidirect
402. D4×Q8C2×D61semidirect
405. #547C2×D61semidirect
409. D42C2×D61semidirect
441. C61#18786semidirect
549. #41#11758199semidirect
665. Q8C2×#11758199semidirect
691. D4C2×#11758199semidirect
692. D4#14519802semidirect

Maximal subgroups

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

subgroupindex
#214567342
#214552992
C2×#168399572
#214449222
#214449082
#214448842
#214448732
#214444962
#214442442
#214442062
D4×#41×C612
#1878661