Finite Group Databasebeta

← #29656341

Subgroups — #29656341

Order 15616.

1244 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456553C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic, complemented
3#21455283C211yesmaximal, characteristic, complemented
4#21445103C211yesmaximal, characteristic, complemented
5#21445082C211yesmaximal, characteristic, complemented
6#21445019C211yesmaximal, characteristic, complemented
7#21444998C211yesmaximal, characteristic, complemented
8#21444922C211yesmaximal, characteristic, complemented
9#21444908C211yesmaximal, characteristic, complemented
10#21444884C211yesmaximal, characteristic, complemented
11#21444873C211yesmaximal, characteristic, complemented
12#21444541C211yesmaximal, characteristic, complemented
13#21444262C211yesmaximal, characteristic, complemented
14#21444258C211yesmaximal, characteristic, complemented
15D4×#41×C61C211yesmaximal, characteristic, complemented
16C2×#14519803—21no—
17#16840312C2211yescharacteristic, complemented
18#16840158C2211yescharacteristic, complemented
19#16840138C2211yescharacteristic, complemented
20#16840110C2211yescharacteristic, complemented
21#16840108C2211yescharacteristic, complemented
22#16840086—21no—
23#16840047C2211yescharacteristic, complemented
24#16840042C2211yescharacteristic, complemented
25#16840013—22no—
26#16839977—21no—
27#16839977—21no—
28#16839967C2211yescharacteristic
29#16839967C2211yescharacteristic, complemented
30#16839962C2211yescharacteristic, complemented
31#16839957C2211yescharacteristic
32#16839957C2211yescharacteristic, complemented
33#16839957C2211yescharacteristic, complemented
34#16839907—21no—
35#16839872—21no—
36#16839872—22no—
37#16839860—21no—
38#16839819C2211yescharacteristic, complemented
39#16839786C2211yescharacteristic, complemented
40#16839761—21no—
41C4×#11758194C2211yescharacteristic, complemented
42#16839508C2211yescharacteristic, complemented
43#16839508C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic, complemented
45#16839506C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C22×#41×C61—21no—
55C61×#550C2211yescharacteristic
56D4×Q8×C61C2211yescharacteristic
57C61×#548—21no—
58C61×#547—21no—
59C61×#547C2211yescharacteristic
60C61×#546—22no—
61C61×#546—21no—
62D42×C61—21no—
63D42×C61C2211yescharacteristic
64C61×#532—21no—
65C61×#532C2211yescharacteristic
66C61×#525—22no—
67C61×#525—21no—
68C4×#41×C61C2211yescharacteristic
69C2×C4×D4×C61—21no—
70C2×C4×D4×C61C2211yescharacteristic
71C2×#11758222—21no—
72#14519803—44no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758201—21no—
76C2×#11758199—21no—
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—22no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519765—21no—
85#14519751—21no—
86#14519751—21no—
87C4×D244—21no—
88C4×D244—21no—
89#14519710—21no—
90#14519708—22no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519700—21no—
99#14519700—21no—
100#14519698—22no—
101#14519698—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—22no—
107C22⋊#92418—21no—
108#14519688—21no—
109#14519688—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—44no—
118C2×#41×C61—44no—
119C2×#41×C61D411yescharacteristic
120C22×Q8×C61—21no—
121C22×D4×C61—22no—
122C22×D4×C61—21no—
123C22×D4×C61—21no—
124C22×D4×C61D411yescharacteristic
125C23×C4×C61—22no—
126C23×C4×C61—21no—
127C4⋊Q8×C61—21no—
128C4⋊Q8×C61C2311yescharacteristic
129#127×C61—21no—
130#127×C61C2311yescharacteristic
131#124×C61—22no—
132#124×C61—21no—
133#123×C61—22no—
134#123×C61—22no—
135#123×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61—21no—
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—21no—
143#121×C61—22no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61D412yes—
149#120×C61—22no—
150#120×C61—22no—
151#120×C61—22no—
152C4×Q8×C61D411yescharacteristic
153C4×Q8×C61C2311yescharacteristic
154C4×D4×C61—22no—
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61—21no—
164C4×D4×C61D411yescharacteristic
165C4×D4×C61D412yes—
166C4×D4×C61D411yescharacteristic
167C4×D4×C61D411yescharacteristic
168C4×D4×C61C2311yescharacteristic
169C4×D4×C61C2311yescharacteristic
170C4×D4×C61C2311yescharacteristic
171#117×C61—21no—
172#117×C61D411yescharacteristic
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61D411yescharacteristic
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C24×C61—22no—
180C24×C61—21no—
181#41×C61—22no—
182#41×C61—22no—
183#41×C61—48no—
184#41×C61—42no—
185#41×C61—42no—
186#41×C61—48no—
187#41×C61—42no—
188#41×C61—42no—
189#41×C61—42no—
190#41×C61—42no—
191C2×Q8×C61—22no—
192C2×Q8×C61—21no—
193C2×Q8×C61—42no—
194C2×Q8×C61—42no—
195C2×Q8×C61C2×D411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—41no—
208C2×D4×C61—42no—
209C2×D4×C61—48no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61C2×D411yescharacteristic
214C2×D4×C61C2×D411yescharacteristic
215C2×D4×C61C2×D411yescharacteristic
216C2×D4×C61C2×D412yes—
217C22×C4×C61—21no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—22no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—22no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—48no—
230C22×C4×C61—42no—
231C22×C4×C61—42no—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C2×C22⋊D61—41no—
236#11758222—42no—
237#11758222—42no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×C4×D61—41no—
242C2×Dic122—21no—
243C4⋊C4×C61—22no—
244C4⋊C4×C61—22no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2×D411yescharacteristic
250C4⋊C4×C61C2×D411yescharacteristic
251C4⋊C4×C61C2×D411yescharacteristic
252C4⋊C4×C61C2×D411yescharacteristic
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C42×C61—21no—
268C42×C61—21no—
269C42×C61—21no—
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2411yescharacteristic
274#11758201—42no—
275#11758200—42no—
276#11758200—42no—
277#11758199—44no—
278#11758199—42no—
279#11758199—42no—
280#11758199—42no—
281#11758198—41no—
282#11758198—41no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285#11758194—42no—
286#11758194—42no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—44no—
300C23×C61—44no—
301C23×C61—81no—
302C23×C61—82no—
303C23×C61#12011yescharacteristic
304C22×D61—41no—
305Q8×C61—21no—
306Q8×C61—44no—
307Q8×C61—41no—
308Q8×C61—41no—
309Q8×C61AGL(1,ℤ/8)12yescomplemented
310D4×C61—24no—
311D4×C61—21no—
312D4×C61—21no—
313D4×C61—21no—
314D4×C61—21no—
315D4×C61—42no—
316D4×C61—42no—
317D4×C61—44no—
318D4×C61—44no—
319D4×C61—44no—
320D4×C61—44no—
321D4×C61—44no—
322D4×C61—41no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—82no—
327D4×C61AGL(1,ℤ/8)12yes—
328D4×C61AGL(1,ℤ/8)12yescomplemented
329C2×C4×C61—24no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—22no—
339C2×C4×C61—21no—
340C2×C4×C61—41no—
341C2×C4×C61—42no—
342C2×C4×C61—44no—
343C2×C4×C61—44no—
344C2×C4×C61—42no—
345C2×C4×C61—44no—
346C2×C4×C61—42no—
347C2×C4×C61—44no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—81no—
355C2×C4×C61#12011yescharacteristic
356C2×C4×C61#12011yescharacteristic
357C2×C4×C61#12011yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C22⋊D61—82no—
362C2×Dic61—41no—
363D244—42no—
364D244—41no—
365D244—41no—
366D244—41no—
367D244—41no—
368C4×D61—82no—
369Dic122—41no—
370Dic122—41no—
371#92418—22no—
372#92418—41no—
373#92418—41no—
374#92418—41no—
375#92418—41no—
376#92418—41no—
377#18554—611nomaximal, Sylow
378C22×C61—21no—
379C22×C61—22no—
380C22×C61—21no—
381C22×C61—22no—
382C22×C61—21no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—84no—
394C22×C61—88no—
395C22×C61C2×#12011yescharacteristic
396C2×D61—81no—
397C2×D61—81no—
398C2×D61—81no—
399C4×C61—21no—
400C4×C61—22no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—41no—
405C4×C61—42no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
410C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
411C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
412C4×C61#57511yescharacteristic
413Dic61—81no—
414D4×#41D6111yescharacteristic, complemented
415#3184—611no—
416#3115—611no—
417#3036—611no—
418#1654—611no—
419#1651—611no—
420#1642—611no—
421#1639—611no—
422#1627—611no—
423#1625—611no—
424#1621—611no—
425#1619—611no—
426#1557—611no—
427#1490—611no—
428#1489—611no—
429C2×C61—41no—
430C2×C61—42no—
431C2×C61—42no—
432C2×C61—81no—
433C2×C61—82no—
434C2×C61#300311yescharacteristic
435C2×C61#300611yescharacteristic
436C2×C61#301811yescharacteristic
437D61—161no—
438C22×#41—21no—
439C2×AGL(1,ℤ/8)—1221no—
440#550C2×D6111yescharacteristic
441D4×Q8C2×D6111yescharacteristic
442#548—21no—
443#547—21no—
444#547C2×D6111yescharacteristic
445#546—22no—
446#546—21no—
447D42—21no—
448D42C2×D6111yescharacteristic
449#532—21no—
450#532—611no—
451#532C2×D6111yescharacteristic
452#525—22no—
453#525—21no—
454C4×#41C2×D6111yescharacteristic
455C2×C4×D4—21no—
456C2×C4×D4C2×D6111yescharacteristic
457#498—611no—
458#493—611no—
459#486—611no—
460#486—611no—
461#482—1221no—
462#475—611no—
463#474—611no—
464#469—1222no—
465#463—1221no—
466#463—1221no—
467#461—611no—
468#461—611no—
469#460—611no—
470#459—611no—
471#459—611no—
472#459—611no—
473#449—1221no—
474#442—1221no—
475#442—1222no—
476#440—1221no—
477#432—611no—
478#423—611no—
479#417—1221no—
480C4×M16—611no—
481#332—611no—
482#332—611no—
483#331—611no—
484#331—611no—
485Q8⋊C8—611no—
486Q8⋊C8—611no—
487D4⋊C8—611no—
488D4⋊C8—611no—
489D4⋊C8—611no—
490D4⋊C8—611no—
491D4⋊C8—611no—
492D4⋊C8—611no—
493C61#1855411yescharacteristic, complemented, Sylow
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—44no—
500C2×#41—44no—
501C2×#41—1221no—
502C2×#41C22⋊D6111yescharacteristic
503C22×Q8—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C22⋊D6111yescharacteristic
508C23×C4—22no—
509C23×C4—21no—
510AGL(1,ℤ/8)—2444no—
511C2×SD16—1221no—
512C2×SD16—1221no—
513C2×SD16—1221no—
514C2×D8—1221no—
515C2×D8—1221no—
516C2×D8—1221no—
517C2×D8—1222no—
518C2×M16—1221no—
519C2×M16—1221no—
520C4⋊Q8—21no—
521C4⋊Q8—611no—
522C4⋊Q8C22×D6111yescharacteristic
523#127—21no—
524#127—611no—
525#127C22×D6111yescharacteristic
526#124—22no—
527#124—21no—
528#124—1221no—
529#123—22no—
530#123—22no—
531#123—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—22no—
535C22⋊Q8—21no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—1221no—
545#121—1221no—
546#121C22⋊D6112yes—
547#120—22no—
548#120—22no—
549#120—22no—
550C4×Q8C22⋊D6111yescharacteristic
551C4×Q8C22×D6111yescharacteristic
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4C22⋊D6111yescharacteristic
565C4×D4C22⋊D6111yescharacteristic
566C4×D4C22⋊D6111yescharacteristic
567C4×D4C22⋊D6112yes—
568C4×D4C22×D6111yescharacteristic
569C4×D4C22×D6111yescharacteristic
570C4×D4C22×D6111yescharacteristic
571#117—21no—
572#117C22⋊D6111yescharacteristic
573C2×C4⋊C4—21no—
574C2×C4⋊C4C22⋊D6111yescharacteristic
575C2×C22⋊C4—22no—
576C2×C22⋊C4—21no—
577C2×C42—21no—
578C2×C42C22×D6111yescharacteristic
579#107—1221no—
580#106—1222no—
581#106—1221no—
582C4⋊C8—611no—
583C4⋊C8—611no—
584C4⋊C8—611no—
585C4⋊C8—611no—
586C4⋊C8—1221no—
587#103—1221no—
588#103—1221no—
589#103—1221no—
590#102—1221no—
591#102—1222no—
592#102—1221no—
593#102—1221no—
594#102—1221no—
595#102—1221no—
596#102—1222no—
597C22⋊C8—1221no—
598#97—1221no—
599#97—1221no—
600C4×C8—611no—
601C4×C8—611no—
602C24—22no—
603C24—21no—
604#41—22no—
605#41—22no—
606#41—48no—
607#41—42no—
608#41—42no—
609#41—48no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614#41—2442no—
615#41—2442no—
616C2×Q8—22no—
617C2×Q8—21no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—1221no—
621C2×Q8C2×C22⋊D6111yescharacteristic
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—41no—
634C2×D4—48no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—2441no—
643C2×D4C2×C22⋊D6111yescharacteristic
644C2×D4C2×C22⋊D6111yescharacteristic
645C2×D4C2×C22⋊D6111yescharacteristic
646C2×D4C2×C22⋊D6112yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—48no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—2441no—
663C22×C4C2×C22⋊D6111yescharacteristic
664C22×C4C2×C22⋊D6111yescharacteristic
665C22×C4C2×C22⋊D6111yescharacteristic
666SD16—2442no—
667SD16—2442no—
668SD16—2442no—
669D8—2444no—
670D8—2442no—
671D8—2442no—
672D8—2442no—
673M16—2442no—
674M16—2442no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4C2×C22⋊D6111yescharacteristic
690C4⋊C4C2×C22⋊D6111yescharacteristic
691C4⋊C4C2×C22⋊D6111yescharacteristic
692C4⋊C4C2×C22⋊D6112yes—
693C4⋊C4C2×C22⋊D6111yescharacteristic
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—22no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—22no—
707C22⋊C4—2441no—
708C22⋊C4—2441no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42C2×C22⋊D6111yescharacteristic
713C42C2×C22⋊D6111yescharacteristic
714C42C2×C22⋊D6111yescharacteristic
715C42C23×D6111yescharacteristic
716C23—21no—
717C23—21no—
718C23—22no—
719C23—21no—
720C23—42no—
721C23—42no—
722C23—44no—
723C23—44no—
724C23—81no—
725C23—82no—
726C23—2441no—
727C23#1451974611yescharacteristic
728Q8—21no—
729Q8—44no—
730Q8—41no—
731Q8—41no—
732Q8—2441no—
733Q8—2441no—
734Q8#1451980312yescomplemented
735D4—24no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—44no—
743D4—44no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—82no—
752D4—4882no—
753D4—2442no—
754D4—2441no—
755D4—2441no—
756D4—2441no—
757D4—2441no—
758D4#1451980212yes—
759D4#1451980312yescomplemented
760C2×C4—24no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—81no—
786C2×C4—4882no—
787C2×C4—2441no—
788C2×C4#1451974611yescharacteristic
789C2×C4#1451974611yescharacteristic
790C2×C4#1451974611yescharacteristic
791C2×C4C22×C22⋊D6111yescharacteristic
792C2×C4C22×C22⋊D6111yescharacteristic
793C2×C4C22×C22⋊D6111yescharacteristic
794C8—1222no—
795C8—2441no—
796C8—2441no—
797C8—2441no—
798C8—2441no—
799C8—2441no—
800C22—21no—
801C22—21no—
802C22—22no—
803C22—21no—
804C22—22no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—84no—
816C22—88no—
817C22—4881no—
818C22—4881no—
819C22—4881no—
820C22C2×#1451974611yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—22no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—41no—
831C4—4881no—
832C4C2×#1451980211yescharacteristic
833C4C2×#1451980311yescharacteristic
834C4C2×#1451980311yescharacteristic
835C4#1684056011yescharacteristic
836C2—41no—
837C2—42no—
838C2—42no—
839C2—82no—
840C2—81no—
841C2—9761no—
842C2#2145504611yescharacteristic
843C2#2145507111yescharacteristic
844C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingD4×#41×C61C2
socleC22×C61C2×#120
hypercenterD4×#41D61
hypocenterC61#18554
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. #21456553C2semidirect
2. #21455970C2semidirect
3. #21455283C2semidirect
4. #21445103C2semidirect
5. #21445082C2semidirect
6. #21445019C2semidirect
7. #21444998C2semidirect
8. #21444922C2semidirect
9. #21444908C2semidirect
10. #21444884C2semidirect
11. #21444873C2semidirect
12. #21444541C2semidirect
13. #21444262C2semidirect
14. #21444258C2semidirect
15. D4×#41×C61C2semidirect
17. #16840312C22semidirect
18. #16840158C22semidirect
19. #16840138C22semidirect
20. #16840110C22semidirect
21. #16840108C22semidirect
23. #16840047C22semidirect
24. #16840042C22semidirect
29. #16839967C22semidirect
30. #16839962C22semidirect
32. #16839957C22semidirect
33. #16839957C22semidirect
38. #16839819C22semidirect
39. #16839786C22semidirect
41. C4×#11758194C22semidirect
42. #16839508C22semidirect
43. #16839508C22semidirect
44. #16839506C22semidirect
45. #16839506C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
50. D4⋊#92418C22semidirect
51. D4⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
309. Q8×C61AGL(1,ℤ/8)semidirect
328. D4×C61AGL(1,ℤ/8)semidirect
414. D4×#41D61semidirect
493. C61#18554semidirect
734. Q8#14519803semidirect
759. D4#14519803semidirect

Maximal subgroups

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

subgroupindex
#214565532
#214559702
#214552832
#214451032
#214450822
#214450192
#214449982
#214449222
#214449082
#214448842
#214448732
#214445412
#214442622
#214442582
D4×#41×C612
#1855461