Finite Group Databasebeta

← #29648000

Subgroups — #29648000

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459768C211yesmaximal, characteristic
2#21454830C211yesmaximal, characteristic, complemented
3#21454248C211yesmaximal, characteristic, complemented
4#21444439C211yesmaximal, characteristic, complemented
5#21444438C211yesmaximal, characteristic, complemented
6#21444428C211yesmaximal, characteristic, complemented
7#21444425C211yesmaximal, characteristic, complemented
8#21444416C211yesmaximal, characteristic, complemented
9#21444415C211yesmaximal, characteristic, complemented
10#21444409C211yesmaximal, characteristic, complemented
11#21444406C211yesmaximal, characteristic, complemented
12#21444406C211yesmaximal, characteristic, complemented
13C2×#16839501C211yesmaximal, characteristic, complemented
14#329×D61C211yesmaximal, characteristic, complemented
15C61×#1524C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840495C411yescharacteristic
18#16840484C411yescharacteristic
19#16840475—21no—
20#16840436—21no—
21#16840435—21no—
22#16840425C411yescharacteristic
23#16840424C411yescharacteristic
24#16840418C411yescharacteristic
25#16840407C411yescharacteristic
26#16840404—21no—
27#16840403C411yescharacteristic
28#16840396C411yescharacteristic
29#16840378—21no—
30#16840351—21no—
31#16840345—21no—
32#16840311C2211yescharacteristic
33#16840297C2211yescharacteristic
34#16840297C2211yescharacteristic
35C2×#14519765C2211yescharacteristic
36#124×D61C2211yescharacteristic
37#16840234—21no—
38C4×#11758222C2211yescharacteristic
39#16839890—21no—
40#16839835—21no—
41#16839833—21no—
42C8×C22⋊D61—21no—
43#16839819C2211yescharacteristic, complemented
44#16839817C2211yescharacteristic, complemented
45#16839817C2211yescharacteristic, complemented
46#16839720—21no—
47#16839716—21no—
48#16839716—21no—
49#16839714C2211yescharacteristic, complemented
50#16839714C2211yescharacteristic, complemented
51#16839714C2211yescharacteristic, complemented
52C2×#14519688C2211yescharacteristic, complemented
53#97×D61C2211yescharacteristic, complemented
54#97×D61C2211yescharacteristic, complemented
55#97×D61C2211yescharacteristic, complemented
56#16839504C2211yescharacteristic, complemented
57#16839504C2211yescharacteristic, complemented
58#16839502C2211yescharacteristic, complemented
59#16839502C2211yescharacteristic, complemented
60#16839501C2211yescharacteristic
61#16839501C2211yescharacteristic
62#16839501C2211yescharacteristic
63#16839501C2211yescharacteristic
64#16839501C2211yescharacteristic, complemented
65#16839501C2211yescharacteristic, complemented
66#16839501C2211yescharacteristic, complemented
67#16839501C2211yescharacteristic, complemented
68C61×#529C2211yescharacteristic
69C4×M16×C61C2211yescharacteristic, complemented
70C2×#97×C61C2211yescharacteristic, complemented
71C61×#330C2211yescharacteristic, complemented
72C61×#330C2211yescharacteristic, complemented
73C61×#329C2211yescharacteristic, complemented
74C61×#329C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222D411yescharacteristic
77C2×#11758224C2×C411yescharacteristic
78C22×Dic122C2×C411yescharacteristic
79C2×Q8×D61C2×C411yescharacteristic
80C22×D244C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83#14519785—28no—
84C2×#11758189—21no—
85C2×#11758189—21no—
86C2×#11758189—21no—
87C22×#92418—21no—
88C2×C8×D61—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91#14519776—21no—
92#14519775C2×C411yescharacteristic
93#14519773C2×C411yescharacteristic
94#14519772—21no—
95#14519772—21no—
96#14519772—21no—
97#14519771—21no—
98#14519766C2×C411yescharacteristic
99#14519765—21no—
100#14519765—21no—
101#14519765—21no—
102#14519765C2×C411yescharacteristic
103#14519765C2×C411yescharacteristic
104#14519765C2311yescharacteristic
105#14519765C2311yescharacteristic
106#14519764C2×C411yescharacteristic
107#14519763—21no—
108#14519763—21no—
109#14519763—21no—
110#14519763—21no—
111#14519762—21no—
112#14519762—21no—
113#14519762—21no—
114#14519761—21no—
115#14519760—21no—
116#14519759—21no—
117#14519757—21no—
118#14519757C2×C411yescharacteristic
119#14519757C2×C411yescharacteristic
120#14519755—21no—
121#14519755—21no—
122#14519754—21no—
123#14519754—21no—
124#14519752—21no—
125#14519752—21no—
126#14519752C2×C411yescharacteristic
127#14519752C2×C411yescharacteristic
128#14519751—21no—
129#14519750—21no—
130#14519750—21no—
131#14519750—21no—
132#14519749—21no—
133#14519747—21no—
134#14519747—21no—
135#14519747—21no—
136#14519745—21no—
137C4×Dic122C2×C411yescharacteristic
138C4×Dic122D411yescharacteristic
139#14519742C2×C411yescharacteristic
140#14519742C2×C411yescharacteristic
141C4×D244—21no—
142C4×D244C2×C411yescharacteristic
143C4×D244D411yescharacteristic
144D4×Dic61—21no—
145#14519739—21no—
146#14519739—21no—
147#14519739C2×C411yescharacteristic
148#14519739C2×C411yescharacteristic
149C4×C22⋊D61—21no—
150C4×C22⋊D61C2×C411yescharacteristic
151C4×C22⋊D61C2×C411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154#14519737—21no—
155#14519737—21no—
156#14519737—21no—
157#14519736D411yescharacteristic
158#14519735—21no—
159#14519735—21no—
160#14519734—21no—
161#14519734D411yescharacteristic
162#14519734D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C42×D61C2311yescharacteristic
170C42×D61C2311yescharacteristic
171C4⋊#92418—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519688—21no—
178#14519688C2311yescharacteristic
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519687—21no—
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C8×Dic61—21no—
188C2×M16×C61—21no—
189C22×C8×C61—21no—
190#126×C61—21no—
191#125×C61C2311yescharacteristic
192#124×C61C2311yescharacteristic
193#123×C61—21no—
194C22⋊Q8×C61C2×C411yescharacteristic
195#121×C61C2×C411yescharacteristic
196C4×Q8×C61C2×C411yescharacteristic
197C4×D4×C61—21no—
198C4×D4×C61C2×C411yescharacteristic
199#117×C61—21no—
200C2×C42×C61C2311yescharacteristic
201#97×C61—21no—
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C4×C8×C61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61—21no—
224#11758226—81no—
225Q8×D61—81no—
226#11758224—81no—
227D4×D61—44no—
228D4×D61—81no—
229#11758222—24no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—81no—
235C2×D244C22⋊C411yescharacteristic
236C2×D244C22×C411yescharacteristic
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—81no—
251C2×Dic122C22⋊C411yescharacteristic
252C2×Dic122C22×C411yescharacteristic
253C2×Dic122C22×C411yescharacteristic
254M16×C61—24no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—42no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C22×C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C42×C61—21no—
272C42×C61C22×C411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2×D411yescharacteristic
275C42×C61C2411yescharacteristic
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61C22⋊C411yescharacteristic
279C22⋊Dic61C22⋊C411yescharacteristic
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22⋊C411yescharacteristic
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C2×#92418—24no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325#11758189—24no—
326#11758189—24no—
327#11758189—42no—
328C8×D61—24no—
329C8×D61—24no—
330C8×D61—42no—
331C23×C61—21no—
332C23×C61C2×C22⋊C411yescharacteristic
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—81no—
338C22×D61—81no—
339C22×D61—81no—
340C22×D61—81no—
341C22×D61C2×C22⋊C411yescharacteristic
342C22×D61C2×C22⋊C411yescharacteristic
343Q8×C61—41no—
344D4×C61—41no—
345D4×C61—42no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—81no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C22⋊D61—22no—
360C22⋊D61—42no—
361C22⋊D61—81no—
362C22⋊D61—81no—
363C22⋊D61—81no—
364C22⋊D61#10414yes—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—81no—
368C2×Dic61—81no—
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375D244—22no—
376D244—41no—
377D244—41no—
378D244—42no—
379D244—81no—
380D244—81no—
381D244—81no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—41no—
387C4×D61—41no—
388C4×D61—42no—
389C4×D61—81no—
390C4×D61—81no—
391C4×D61—81no—
392Dic122—22no—
393Dic122—41no—
394Dic122—41no—
395Dic122—81no—
396Dic122—81no—
397C8×C61—22no—
398C8×C61—22no—
399C8×C61—22no—
400C8×C61—41no—
401#92418—22no—
402#92418—22no—
403#92418—41no—
404#92418—41no—
405#17652—611nomaximal, Sylow
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61C2×#10412yes—
412C22×C61C22×C22⋊C411yescharacteristic
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—162no—
425C2×D61—162no—
426C2×D61C2×#10412yes—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—41no—
442Dic61—41no—
443Dic61C2×#10412yes—
444#3514—611no—
445#2970—611no—
446#2875—611no—
447#1532—611no—
448#1532—611no—
449#1530—611no—
450#1529—611no—
451#1527—611no—
452#1527—611no—
453#1525—611no—
454#1524—611no—
455#1524—611no—
456#1524D6111yescharacteristic, complemented
457C2×#329—611no—
458C2×#329—611no—
459C2×C61—22no—
460C2×C61—81no—
461C2×C61#288811yescharacteristic
462C2×C61C22×#10411yescharacteristic
463C2×C61#290111yescharacteristic
464D61—22no—
465D61—41no—
466D61—81no—
467D61—81no—
468C2×#131—1221no—
469#559—611no—
470#556—611no—
471#555—1221no—
472#551—1221no—
473#551—1221no—
474D4×Q8—611no—
475#548—611no—
476#548—611no—
477#546—611no—
478#546—611no—
479#546—1221no—
480D42—611no—
481#542—1221no—
482#538—1221no—
483#538—1221no—
484#532—611no—
485#529—611no—
486#529—611no—
487#529C2×D6111yescharacteristic
488C2×#124—611no—
489C2×#124—611no—
490#518—1221no—
491C4×#41—611no—
492#446—1221no—
493#435—1221no—
494#435—1221no—
495C8×D4—1221no—
496#432—611no—
497#432—611no—
498#432—611no—
499#405—1221no—
500#405—1221no—
501#405—1221no—
502C4×M16—611no—
503C4×M16—611no—
504C4×M16—611no—
505C4×M16C2×D6111yescharacteristic, complemented
506C2×#97—611no—
507C2×#97—611no—
508C2×#97—611no—
509C2×#97—611no—
510C2×#97C2×D6111yescharacteristic, complemented
511#330—611no—
512#330—611no—
513#330C2×D6111yescharacteristic, complemented
514#330C2×D6111yescharacteristic, complemented
515#329—611no—
516#329—611no—
517#329—611no—
518#329—611no—
519#329—611no—
520#329—611no—
521#329—611no—
522#329—611no—
523#329—611no—
524#329—611no—
525#329C2×D6111yescharacteristic, complemented
526#329C2×D6111yescharacteristic, complemented
527C61#1765211yescharacteristic, complemented, Sylow
528C2×#41—611no—
529C2×#41—611no—
530C2×#41—611no—
531C22×Q8—611no—
532C22×Q8—611no—
533C22×D4—611no—
534C22×D4—611no—
535C22×D4—1221no—
536#131—1228no—
537C2×M16—21no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C22×C8—21no—
542C22×C8—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C4⋊Q8—611no—
547C4⋊Q8—1221no—
548#127—611no—
549#126—21no—
550#126—1221no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#125C22×D6111yescharacteristic
555#124—611no—
556#124—611no—
557#124—611no—
558#124—611no—
559#124—611no—
560#124—611no—
561#124—1221no—
562#124—1221no—
563#124—1221no—
564#124—1221no—
565#124—1221no—
566#124—1221no—
567#124—1221no—
568#124C22×D6111yescharacteristic
569#123—21no—
570#123—1221no—
571#123—1221no—
572#123—1221no—
573#123—1221no—
574#123—1221no—
575#123—1221no—
576C22⋊Q8—611no—
577C22⋊Q8—611no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8C4×D6111yescharacteristic
584#121—611no—
585#121—611no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121C4×D6111yescharacteristic
594#120—1221no—
595#120—1221no—
596#120—1221no—
597#120—1221no—
598C4×Q8—611no—
599C4×Q8—611no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×Q8C4×D6111yescharacteristic
603C4×D4—21no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4C4×D6111yescharacteristic
621#117—21no—
622#117—611no—
623#117—611no—
624#117—611no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42C22×D6111yescharacteristic
637C4⋊C8—1221no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643#97—21no—
644#97—611no—
645#97—611no—
646#97—611no—
647#97—611no—
648#97—1221no—
649#97—1221no—
650#97—1221no—
651#97—1221no—
652#97C22×D6111yescharacteristic
653#97C22×D6111yescharacteristic
654#97C22×D6111yescharacteristic
655#97C22×D6111yescharacteristic
656C4×C8—21no—
657C4×C8—1221no—
658C4×C8—1221no—
659C4×C8—1221no—
660C24—1221no—
661C24—1221no—
662#41—1224no—
663#41—4881no—
664#41—4881no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—611no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—4881no—
671C2×Q8—4881no—
672C2×Q8C2×C4×D6111yescharacteristic
673C2×D4—21no—
674C2×D4—611no—
675C2×D4—611no—
676C2×D4—611no—
677C2×D4—611no—
678C2×D4—611no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—4881no—
688C2×D4—4881no—
689C2×D4—2444no—
690C2×D4C2×C4×D6111yescharacteristic
691C22×C4—21no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4C2×C4×D6111yescharacteristic
705C22×C4D4×D6111yescharacteristic
706C22×C4D4×D6111yescharacteristic
707M16—24no—
708M16—1224no—
709M16—1224no—
710M16—2442no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—42no—
716C2×C8—1224no—
717C2×C8—1224no—
718C2×C8—1224no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—2442no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4C2×C4×D6111yescharacteristic
741C4⋊C4C2×C4×D6111yescharacteristic
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—611no—
750C22⋊C4—611no—
751C22⋊C4—611no—
752C22⋊C4—611no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C42—21no—
772C42—611no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—1221no—
779C42—1221no—
780C42C2×C4×D6111yescharacteristic
781C42D4×D6111yescharacteristic
782C42D4×D6111yescharacteristic
783C42C23×D6111yescharacteristic
784C23—21no—
785C23—611no—
786C23—611no—
787C23—1221no—
788C23—1221no—
789C23—4881no—
790C23—4881no—
791C23—4881no—
792C23—4881no—
793C23—2442no—
794C23—2442no—
795C23C22⋊C4×D6111yescharacteristic
796Q8—41no—
797Q8—1222no—
798Q8—4881no—
799Q8—4881no—
800Q8—2441no—
801Q8—2441no—
802D4—41no—
803D4—42no—
804D4—614no—
805D4—1222no—
806D4—1222no—
807D4—4881no—
808D4—4881no—
809D4—4881no—
810D4—4881no—
811D4—4881no—
812D4—4881no—
813D4—2441no—
814D4—2441no—
815D4—2442no—
816D4—2442no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—81no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—4881no—
835C2×C4—4881no—
836C2×C4—4881no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2442no—
844C2×C4C22⋊C4×D6111yescharacteristic
845C2×C4C22⋊C4×D6111yescharacteristic
846C2×C4C22⋊C4×D6111yescharacteristic
847C2×C4C22×C4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C2×D4×D6111yescharacteristic
850C8—22no—
851C8—22no—
852C8—22no—
853C8—41no—
854C8—1222no—
855C8—1222no—
856C8—2441no—
857C8—2441no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—612no—
864C22—1221no—
865C22—1221no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—9762no—
870C22—9762no—
871C22—2441no—
872C22—2441no—
873C22—2441no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22#104×D6112yes—
878C22C2×C22⋊C4×D6111yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—612no—
889C4—1221no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—1221no—
894C4—2441no—
895C4—2441no—
896C2—22no—
897C2—81no—
898C2—1222no—
899C2—4881no—
900C2—4881no—
901C2—2441no—
902C2#2145429611yescharacteristic
903C2C2×#104×D6111yescharacteristic
904C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1524C2
socleC22×C61C22×C22⋊C4
prime radical#21459768C2
cosocleC42×C61C24
hypercenter#1524D61
hypocenterC61#17652
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. #21454830C2semidirect
3. #21454248C2semidirect
4. #21444439C2semidirect
5. #21444438C2semidirect
6. #21444428C2semidirect
7. #21444425C2semidirect
8. #21444416C2semidirect
9. #21444415C2semidirect
10. #21444409C2semidirect
11. #21444406C2semidirect
12. #21444406C2semidirect
13. C2×#16839501C2semidirect
14. #329×D61C2semidirect
15. C61×#1524C2semidirect
43. #16839819C22semidirect
44. #16839817C22semidirect
45. #16839817C22semidirect
49. #16839714C22semidirect
50. #16839714C22semidirect
51. #16839714C22semidirect
52. C2×#14519688C22semidirect
53. #97×D61C22semidirect
54. #97×D61C22semidirect
55. #97×D61C22semidirect
56. #16839504C22semidirect
57. #16839504C22semidirect
58. #16839502C22semidirect
59. #16839502C22semidirect
64. #16839501C22semidirect
65. #16839501C22semidirect
66. #16839501C22semidirect
67. #16839501C22semidirect
69. C4×M16×C61C22semidirect
70. C2×#97×C61C22semidirect
71. C61×#330C22semidirect
72. C61×#330C22semidirect
73. C61×#329C22semidirect
74. C61×#329C22semidirect
456. #1524D61semidirect
505. C4×M16C2×D61semidirect
510. C2×#97C2×D61semidirect
513. #330C2×D61semidirect
514. #330C2×D61semidirect
525. #329C2×D61semidirect
526. #329C2×D61semidirect
527. C61#17652semidirect

Maximal subgroups

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

subgroupindex
#214597682
#214548302
#214542482
#214444392
#214444382
#214444282
#214444252
#214444162
#214444152
#214444092
#214444062
C2×#168395012
#329×D612
C61×#15242
#1765261