Finite Group Databasebeta

← #30611504

Subgroups — #30611504

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#21462659C211yesmaximal, characteristic, complemented
2#21462390C211yesmaximal, characteristic, complemented
3#21461296C211yesmaximal, characteristic, complemented
4#21461295C211yesmaximal, characteristic, complemented
5#21461288C211yesmaximal, characteristic, complemented
6#21461287C211yesmaximal, characteristic, complemented
7#21461280C211yesmaximal, characteristic, complemented
8#21461279C211yesmaximal, characteristic, complemented
9#21461273C211yesmaximal, characteristic, complemented
10#21461272C211yesmaximal, characteristic, complemented
11#21461271C211yesmaximal, characteristic, complemented
12#21461270C211yesmaximal, characteristic, complemented
13C2×#16840618C211yesmaximal, characteristic, complemented
14D61⋊#329C211yesmaximal, characteristic, complemented
15#21459773C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840794—21no—
19#16840793—21no—
20#16840789—21no—
21#16840785C2211yescharacteristic, complemented
22#16840783C2211yescharacteristic, complemented
23#16840782C2211yescharacteristic, complemented
24#16840727—21no—
25#16840726—21no—
26#16840726—21no—
27C4×#11758213C2211yescharacteristic, complemented
28C4×#11758217C2211yescharacteristic, complemented
29C4×#11758217C2211yescharacteristic, complemented
30C4×#11758217C2211yescharacteristic, complemented
31#16840721C2211yescharacteristic, complemented
32#16840721C2211yescharacteristic, complemented
33C2×#14519832C2211yescharacteristic, complemented
34C2×#14519832C2211yescharacteristic, complemented
35C2×#14519832C2211yescharacteristic, complemented
36#16840619C2211yescharacteristic, complemented
37#16840619C2211yescharacteristic, complemented
38#16840619C2211yescharacteristic, complemented
39#16840619C2211yescharacteristic, complemented
40#16840618C2211yescharacteristic
41#16840618C2211yescharacteristic
42#16840618C2211yescharacteristic
43#16840618C2211yescharacteristic
44#16840618C2211yescharacteristic, complemented
45#16840618C2211yescharacteristic, complemented
46#16840618C2211yescharacteristic, complemented
47#16840618C2211yescharacteristic, complemented
48#16840617C2211yescharacteristic, complemented
49#16840617C2211yescharacteristic, complemented
50#16840617C2211yescharacteristic, complemented
51#16840617C2211yescharacteristic, complemented
52#16840494C411yescharacteristic
53#16840484C411yescharacteristic
54#16840474—21no—
55#16840441—21no—
56#16840439—21no—
57Q8×C22⋊D61C411yescharacteristic
58#16840422C411yescharacteristic
59#16840408C411yescharacteristic
60#16840401—21no—
61#16840400C411yescharacteristic
62#16840396C411yescharacteristic
63#16840382—21no—
64#16840349—21no—
65#16840346—21no—
66#16840308C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840298C2211yescharacteristic
69#16840293C2211yescharacteristic
70C2×#14519766C2211yescharacteristic
71#124×D61C2211yescharacteristic
72#16840234—21no—
73C4×#11758224C2211yescharacteristic
74C61×#548C411yescharacteristic
75#14519864—28no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×D61⋊C8—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832C2311yescharacteristic
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C4×#92420—21no—
108C2×#11758222C2×C411yescharacteristic
109C2×#11758224D411yescharacteristic
110C2×Q8×D61C2×C411yescharacteristic
111C22×D244C2×C411yescharacteristic
112C2×D4×D61—21no—
113C2×D4×D61C2×C411yescharacteristic
114#14519775—21no—
115#14519775C2×C411yescharacteristic
116#14519773C2×C411yescharacteristic
117#14519772—21no—
118#14519772—21no—
119#14519772—21no—
120#14519771—21no—
121#14519770—21no—
122#14519768C2311yescharacteristic
123#14519766—21no—
124#14519766—21no—
125#14519766C2×C411yescharacteristic
126#14519766C2×C411yescharacteristic
127#14519766C2311yescharacteristic
128#14519766C2311yescharacteristic
129#14519765C2×C411yescharacteristic
130#14519764C2311yescharacteristic
131#14519763—21no—
132#14519763—21no—
133#14519763—21no—
134#14519763—21no—
135#14519762—21no—
136#14519762—21no—
137#14519761—21no—
138#14519761—21no—
139#14519760—21no—
140#14519759—21no—
141#14519758—21no—
142#14519756—21no—
143#14519756C2×C411yescharacteristic
144#14519755—21no—
145#14519755—21no—
146#14519753—21no—
147#14519753C2×C411yescharacteristic
148#14519752C2×C411yescharacteristic
149#14519751C2×C411yescharacteristic
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519749—21no—
156#14519747—21no—
157#14519745—21no—
158#14519745—21no—
159#14519745—21no—
160Q8×Dic61C2×C411yescharacteristic
161C4×Dic122C2×C411yescharacteristic
162#14519742C2×C411yescharacteristic
163#14519742D411yescharacteristic
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166D4×Dic61—21no—
167D4×Dic61C2×C411yescharacteristic
168D4×Dic61D411yescharacteristic
169#14519739—21no—
170#14519739C2×C411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519735—21no—
181#14519735D411yescharacteristic
182#14519734—21no—
183#14519734—21no—
184#14519733—21no—
185#14519733D411yescharacteristic
186#14519733D411yescharacteristic
187C2×#11758198—21no—
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22×Q8×C61C2×C411yescharacteristic
198#124×C61—21no—
199#124×C61C2×C411yescharacteristic
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61—21no—
203#121×C61C2×C411yescharacteristic
204C4×Q8×C61C2×C411yescharacteristic
205C4×D4×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209#41×C61—81no—
210C2×Q8×C61—21no—
211C2×Q8×C61—81no—
212C2×Q8×C61C22×C411yescharacteristic
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61C22⋊C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61C22⋊C411yescharacteristic
228C2×C22⋊D61C22⋊C411yescharacteristic
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234Q8×D61—81no—
235#11758224—24no—
236D4×D61—44no—
237D4×D61—81no—
238#11758222—81no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—81no—
242C2×D244C22×C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×Dic122—21no—
252C2×Dic122C22⋊C411yescharacteristic
253C2×Dic122C22×C411yescharacteristic
254#11758217—24no—
255#11758217—24no—
256#11758217—42no—
257C2×#92420—24no—
258C2×#92420—24no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—42no—
268#11758213—24no—
269D61⋊C8—24no—
270D61⋊C8—42no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61C22⋊C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61C22⋊C411yescharacteristic
280C22⋊C4×C61C22⋊C411yescharacteristic
281C42×C61—21no—
282C42×C61C22×C411yescharacteristic
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61C22×C411yescharacteristic
323C4×Dic61C22×C411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2411yescharacteristic
331C23×C61—21no—
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—81no—
339C22×D61—81no—
340C22×D61—81no—
341C22×D61—81no—
342C22×D61C2×C22⋊C411yescharacteristic
343Q8×C61—41no—
344Q8×C61—41no—
345Q8×C61—81no—
346D4×C61—22no—
347D4×C61—41no—
348D4×C61—42no—
349D4×C61—81no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—81no—
356C2×C4×C61—81no—
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C23×C411yescharacteristic
362C22⋊D61—22no—
363C22⋊D61—42no—
364C22⋊D61—81no—
365C22⋊D61—81no—
366C22⋊D61—81no—
367C22⋊D61—81no—
368C22⋊D61#10414yes—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—81no—
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C22×D411yescharacteristic
382C2×Dic61C22×D411yescharacteristic
383D244—41no—
384D244—41no—
385D244—42no—
386D244—81no—
387C4×D61—22no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—42no—
391C4×D61—81no—
392C4×D61—81no—
393C4×D61—81no—
394Dic122—22no—
395Dic122—41no—
396Dic122—81no—
397#92420—22no—
398#92420—22no—
399#92420—22no—
400#92420—22no—
401#92420—22no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#17652—611nomaximal, Sylow
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61C2×#10412yes—
415C22×C61C22×C22⋊C411yescharacteristic
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—41no—
433C4×C61—41no—
434C4×C61—41no—
435Dic61—21no—
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#1524—611no—
457C2×#329—611no—
458C2×#329—611no—
459C2×C61—22no—
460C2×C61—41no—
461C2×C61—81no—
462C2×C61#288811yescharacteristic
463C2×C61C22×#10411yescharacteristic
464C2×C61#290111yescharacteristic
465D61—22no—
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#692311yescharacteristic
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#529—611no—
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×M16—611no—
506C2×#97—611no—
507C2×#97—611no—
508C2×#97—611no—
509C2×#97—611no—
510C2×#97—611no—
511#330—611no—
512#330—611no—
513#330—611no—
514#330—611no—
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#329—611no—
526#329—611no—
527C61#1765211yescharacteristic, complemented, Sylow
528C2×#41—611no—
529C2×#41—611no—
530C2×#41C2×#692311yescharacteristic
531C22×Q8—611no—
532C22×Q8C2×#692311yescharacteristic
533C22×D4—611no—
534C22×D4—611no—
535C22×D4—1221no—
536#131—1228no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C22×C8—1221no—
542C22×C8—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C4⋊Q8—611no—
547C4⋊Q8—1221no—
548#127—611no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#125—611no—
555#124—21no—
556#124—611no—
557#124—611no—
558#124—611no—
559#124—611no—
560#124—611no—
561#124—611no—
562#124—1221no—
563#124—1221no—
564#124—1221no—
565#124—1221no—
566#124—1221no—
567#124—1221no—
568#124C2×#692311yescharacteristic
569#123—1221no—
570#123—1221no—
571#123—1221no—
572#123—1221no—
573#123—1221no—
574#123—1221no—
575#123—1221no—
576C22⋊Q8—21no—
577C22⋊Q8—611no—
578C22⋊Q8—611no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8C2×#692311yescharacteristic
584#121—21no—
585#121—611no—
586#121—611no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121C2×#692311yescharacteristic
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×Q8C2×#692311yescharacteristic
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×D4C2×#692311yescharacteristic
621#117—611no—
622#117—611no—
623#117—611no—
624#117—1221no—
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×C42—611no—
637C4⋊C8—1221no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643#97—611no—
644#97—611no—
645#97—611no—
646#97—611no—
647#97—611no—
648#97—611no—
649#97—611no—
650#97—611no—
651#97—1221no—
652#97—1221no—
653#97—1221no—
654#97—1221no—
655#97—1221no—
656C4×C8—1221no—
657C4×C8—1221no—
658C4×C8—1221no—
659C4×C8—1221no—
660C24—1221no—
661C24—1221no—
662#41—81no—
663#41—1224no—
664#41—4881no—
665C2×Q8—21no—
666C2×Q8—81no—
667C2×Q8—611no—
668C2×Q8—611no—
669C2×Q8—1221no—
670C2×Q8—4881no—
671C2×Q8C22×#692311yescharacteristic
672C2×Q8C22×#692311yescharacteristic
673C2×D4—21no—
674C2×D4—21no—
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—4881no—
687C2×D4—4881no—
688C2×D4—2444no—
689C2×D4C22⋊#692311yescharacteristic
690C2×D4C22×#692311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4C22×#692311yescharacteristic
706C22×C4C22×#692311yescharacteristic
707M16—1224no—
708M16—1224no—
709M16—1224no—
710M16—2442no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1224no—
717C2×C8—1224no—
718C2×C8—1224no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—2442no—
723C2×C8—2442no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4C22⋊#692311yescharacteristic
741C4⋊C4C22×#692311yescharacteristic
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—611no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
770C22⋊C4C22⋊#692311yescharacteristic
771C42—21no—
772C42—611no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—1221no—
782C42—1221no—
783C42C22×#692311yescharacteristic
784C23—21no—
785C23—611no—
786C23—1221no—
787C23—1221no—
788C23—4881no—
789C23—4881no—
790C23—4881no—
791C23—4881no—
792C23—2442no—
793C23—2442no—
794C23C2×C22⋊#692311yescharacteristic
795C23C2×C22⋊#692311yescharacteristic
796Q8—41no—
797Q8—41no—
798Q8—81no—
799Q8—1222no—
800Q8—4881no—
801Q8—2441no—
802D4—22no—
803D4—41no—
804D4—42no—
805D4—81no—
806D4—614no—
807D4—1222no—
808D4—4881no—
809D4—4881no—
810D4—4881no—
811D4—4881no—
812D4—4881no—
813D4—2441no—
814D4—2441no—
815D4—2442no—
816D4—2442no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—4881no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2442no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4C2×C22⋊#692311yescharacteristic
849C2×C4C23×#692311yescharacteristic
850C8—1222no—
851C8—1222no—
852C8—1222no—
853C8—1222no—
854C8—1222no—
855C8—2441no—
856C8—2441no—
857C8—2441no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—612no—
867C22—1221no—
868C22—1221no—
869C22—9762no—
870C22—9762no—
871C22—2441no—
872C22—2441no—
873C22—2441no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22D61⋊#10412yes—
878C22C22×C22⋊#692311yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—612no—
888C4—1221no—
889C4—1221no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—1221no—
894C4—2441no—
895C4—2441no—
896C2—22no—
897C2—41no—
898C2—81no—
899C2—1222no—
900C2—4881no—
901C2—4881no—
902C2#2146242911yescharacteristic
903C2C2×D61⋊#10411yescharacteristic
904C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459773C2
cosocleC4×Dic61C24
hypercenter#548#6923
hypocenterC61#17652
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #21462659C2semidirect
2. #21462390C2semidirect
3. #21461296C2semidirect
4. #21461295C2semidirect
5. #21461288C2semidirect
6. #21461287C2semidirect
7. #21461280C2semidirect
8. #21461279C2semidirect
9. #21461273C2semidirect
10. #21461272C2semidirect
11. #21461271C2semidirect
12. #21461270C2semidirect
13. C2×#16840618C2semidirect
14. D61⋊#329C2semidirect
21. #16840785C22semidirect
22. #16840783C22semidirect
23. #16840782C22semidirect
27. C4×#11758213C22semidirect
28. C4×#11758217C22semidirect
29. C4×#11758217C22semidirect
30. C4×#11758217C22semidirect
31. #16840721C22semidirect
32. #16840721C22semidirect
33. C2×#14519832C22semidirect
34. C2×#14519832C22semidirect
35. C2×#14519832C22semidirect
36. #16840619C22semidirect
37. #16840619C22semidirect
38. #16840619C22semidirect
39. #16840619C22semidirect
44. #16840618C22semidirect
45. #16840618C22semidirect
46. #16840618C22semidirect
47. #16840618C22semidirect
48. #16840617C22semidirect
49. #16840617C22semidirect
50. #16840617C22semidirect
51. #16840617C22semidirect
527. C61#17652semidirect

Maximal subgroups

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

subgroupindex
#214626592
#214623902
#214612962
#214612952
#214612882
#214612872
#214612802
#214612792
#214612732
#214612722
#214612712
#214612702
C2×#168406182
D61⋊#3292
#214597732
#1765261