Finite Group Databasebeta

← #30611960

Subgroups — #30611960

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462748C211yesmaximal, characteristic, complemented
2#21462746C211yesmaximal, characteristic, complemented
3#21461351C211yesmaximal, characteristic, complemented
4#21461350C211yesmaximal, characteristic, complemented
5#21461347C211yesmaximal, characteristic, complemented
6#21461343C211yesmaximal, characteristic, complemented
7#21461342C211yesmaximal, characteristic, complemented
8#21461341C211yesmaximal, characteristic, complemented
9#21461341C211yesmaximal, characteristic, complemented
10#21461331C211yesmaximal, characteristic, complemented
11#21461330C211yesmaximal, characteristic, complemented
12#21461317C211yesmaximal, characteristic, complemented
13#21461316C211yesmaximal, characteristic, complemented
14D61⋊#331C211yesmaximal, characteristic, complemented
15#21459691C211yesmaximal, characteristic
16#16840814—21no—
17#16840812—21no—
18#16840794—21no—
19#16840794—21no—
20#16840792—21no—
21#16840791—21no—
22#16840790—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840785C2211yescharacteristic
26#16840785C2211yescharacteristic, complemented
27#16840782C2211yescharacteristic, complemented
28#16840780C2211yescharacteristic, complemented
29#16840779C2211yescharacteristic, complemented
30#16840767C2211yescharacteristic, complemented
31#16840765C2211yescharacteristic, complemented
32C2×#14519844C2211yescharacteristic, complemented
33D61⋊(C4⋊C8)C2211yescharacteristic
34D61⋊(C4⋊C8)C2211yescharacteristic
35D61⋊(C4⋊C8)C2211yescharacteristic, complemented
36#16840621C2211yescharacteristic, complemented
37#16840621C2211yescharacteristic, complemented
38#16840621C2211yescharacteristic, complemented
39#16840621C2211yescharacteristic, complemented
40#16840621C2211yescharacteristic, complemented
41#16840621C2211yescharacteristic, complemented
42#16840621C2211yescharacteristic, complemented
43#16840621C2211yescharacteristic, complemented
44#16840620C2211yescharacteristic
45#16840620C2211yescharacteristic
46#16840620C2211yescharacteristic
47#16840620C2211yescharacteristic
48#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52#16840496—21no—
53#16840496—21no—
54#16840430—21no—
55#16840430—21no—
56#16840404—21no—
57#16840404—21no—
58#16840401—21no—
59#16840401—21no—
60#16840368C411yescharacteristic
61#16840367C411yescharacteristic
62#16840366C411yescharacteristic
63#16840328C411yescharacteristic
64#16840328C411yescharacteristic
65#16840318C2211yescharacteristic
66#16840309C2211yescharacteristic
67#16840309C2211yescharacteristic
68#16840307C2211yescharacteristic
69#16840307C2211yescharacteristic
70#127×D61C2211yescharacteristic
71#16840234C411yescharacteristic
72#16840234C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#540C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844C2311yescharacteristic
84#14519844C2311yescharacteristic
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94C4⋊#92420—21no—
95#14519834—21no—
96#14519834—21no—
97#14519834—21no—
98#14519834—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104#14519832—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222—21no—
108C2×#11758222—21no—
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224—21no—
111C2×#11758224—21no—
112C2×D4×D61—21no—
113C2×D4×D61—21no—
114C2×D4×D61C2×C411yescharacteristic
115C2×D4×D61C2×C411yescharacteristic
116#14519776C2311yescharacteristic
117#14519776C2311yescharacteristic
118#14519774C2×C411yescharacteristic
119#14519773—21no—
120#14519773—21no—
121#14519773—21no—
122#14519773—21no—
123#14519773C2311yescharacteristic
124#14519773C2311yescharacteristic
125#14519769C2×C411yescharacteristic
126#14519763—21no—
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519763—21no—
131#14519763—21no—
132#14519762—21no—
133#14519762—21no—
134#14519762—21no—
135#14519762—21no—
136#14519758—21no—
137#14519758—21no—
138#14519755—21no—
139#14519755—21no—
140#14519752—21no—
141#14519752—21no—
142#14519752C2×C411yescharacteristic
143#14519752C2×C411yescharacteristic
144#14519751C2×C411yescharacteristic
145#14519751C2×C411yescharacteristic
146#14519750—21no—
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519749—21no—
151#14519749—21no—
152#14519749—21no—
153#14519749—21no—
154#14519748C2×C411yescharacteristic
155#14519748C2×C411yescharacteristic
156#14519747—21no—
157#14519747—21no—
158#14519745—21no—
159#14519745—21no—
160#14519742—21no—
161#14519742—21no—
162#14519742D411yescharacteristic
163#14519742D411yescharacteristic
164C4×D244C2×C411yescharacteristic
165C4×D244C2×C411yescharacteristic
166D4×Dic61C2×C411yescharacteristic
167D4×Dic61C2×C411yescharacteristic
168#14519739C2×C411yescharacteristic
169#14519739C2×C411yescharacteristic
170#14519739D411yescharacteristic
171#14519739D411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519737D411yescharacteristic
183#14519737D411yescharacteristic
184#14519735C2×C411yescharacteristic
185#14519735C2×C411yescharacteristic
186#14519734C2×C411yescharacteristic
187#14519734C2×C411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195#127×C61C2×C411yescharacteristic
196#125×C61C2×C411yescharacteristic
197#123×C61—21no—
198#123×C61—21no—
199#121×C61—21no—
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C22×C411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
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×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233#11758224—81no—
234#11758224—81no—
235#11758224—81no—
236#11758224—81no—
237D4×D61—42no—
238D4×D61—42no—
239D4×D61—81no—
240D4×D61—81no—
241D4×D61—81no—
242D4×D61—81no—
243#11758222—42no—
244#11758222—81no—
245#11758222—81no—
246#11758222—81no—
247#11758222—81no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244C22⋊C411yescharacteristic
253C2×D244C22×C411yescharacteristic
254C2×D244C22×C411yescharacteristic
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61C22×C411yescharacteristic
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×Dic122—21no—
266C2×Dic122—21no—
267C2×Dic122C22⋊C411yescharacteristic
268#11758217—81no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—81no—
278#11758213—81no—
279D61⋊C8—81no—
280D61⋊C8—81no—
281D61⋊C8—81no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22⋊C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61C22⋊C411yescharacteristic
293C22⋊C4×C61C22⋊C411yescharacteristic
294C42×C61C22×C411yescharacteristic
295C42×C61C22×C411yescharacteristic
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61C22×C411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2411yescharacteristic
334C23×C61—21no—
335C23×C61—21no—
336C23×C61C2×C22⋊C411yescharacteristic
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61—81no—
344C22×D61—81no—
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—81no—
350D4×C61—81no—
351D4×C61—81no—
352D4×C61—81no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—41no—
356C2×C4×C61—81no—
357C2×C4×C61—81no—
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C23×C411yescharacteristic
364C22⋊D61—22no—
365C22⋊D61—41no—
366C22⋊D61—42no—
367C22⋊D61—42no—
368C22⋊D61—41no—
369C22⋊D61—41no—
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—41no—
375C22⋊D61—41no—
376C22⋊D61—81no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C22⋊D61—81no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—81no—
387C2×Dic61—81no—
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C22×D411yescharacteristic
393C2×Dic61C22×D411yescharacteristic
394D244—22no—
395D244—41no—
396D244—41no—
397D244—81no—
398D244—81no—
399D244—81no—
400D244—81no—
401C4×D61—22no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—41no—
411C4×D61—81no—
412C4×D61—81no—
413C4×D61—81no—
414C4×D61—81no—
415Dic122—41no—
416Dic122—41no—
417Dic122—41no—
418Dic122—41no—
419Dic122—41no—
420#92420—41no—
421#92420—41no—
422#92420—41no—
423#92420—41no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17771—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61C22×C22⋊C411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—162no—
451C2×D61—162no—
452C2×D61#41312yes—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—41no—
460C4×C61—41no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—41no—
466Dic61—41no—
467Dic61#57611yescharacteristic
468Dic61#57611yescharacteristic
469Dic61#57711yescharacteristic
470Dic61#57711yescharacteristic
471#3508—611no—
472#2990—611no—
473#2990—611no—
474#1557—611no—
475#1557—611no—
476#1555—611no—
477#1553—611no—
478#1553—611no—
479#1552—611no—
480#1552—611no—
481#1547—611no—
482#1547—611no—
483#1540—611no—
484#1540—611no—
485C2×#331—611no—
486C2×C61—41no—
487C2×C61—81no—
488C2×C61—81no—
489C2×C61C2×#41311yescharacteristic
490C2×C61#289711yescharacteristic
491C2×C61#289711yescharacteristic
492D61—22no—
493D61—41no—
494D61—81no—
495D61—81no—
496#559—1221no—
497#559—1221no—
498#550—1221no—
499#550—1221no—
500#546—1221no—
501#546—1221no—
502#546—1221no—
503#546—1221no—
504#540—611no—
505#540—611no—
506#540—611no—
507#540#692311yescharacteristic
508#535—611no—
509#535—611no—
510#533—611no—
511#532—611no—
512#532—611no—
513#532—611no—
514#532—611no—
515C2×#127—611no—
516#518—611no—
517#518—611no—
518C4×#41—611no—
519#446—1221no—
520#446—1221no—
521#435—1221no—
522#435—1221no—
523#435—1221no—
524#435—1221no—
525C8×D4—1221no—
526C8×D4—1221no—
527#432—611no—
528#432—611no—
529#432—611no—
530#432—611no—
531#431—611no—
532#431—611no—
533#423—611no—
534#423—611no—
535C2×C4⋊C8—611no—
536C2×C4⋊C8—611no—
537C2×C4⋊C8—611no—
538C2×C4⋊C8—611no—
539#332—611no—
540#332—611no—
541#332—611no—
542#332—611no—
543#332—611no—
544#332—611no—
545#332—611no—
546#332—611no—
547#331—611no—
548#331—611no—
549#331—611no—
550#331—611no—
551#331—611no—
552#331—611no—
553#331—611no—
554#331—611no—
555C61#1777111yescharacteristic, complemented, Sylow
556C2×#41—611no—
557C2×#41—1221no—
558C2×#41—1221no—
559C2×#41—1221no—
560C2×#41—1221no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—1221no—
564C22×D4—1221no—
565C2×M16—1221no—
566C2×M16—1221no—
567C22×C8—1221no—
568C22×C8—1221no—
569C22×C8—1221no—
570C22×C8—1221no—
571C4⋊Q8—611no—
572C4⋊Q8—611no—
573#127—611no—
574#127—611no—
575#127—611no—
576#127—1221no—
577#127—1221no—
578#127—1221no—
579#127—1221no—
580#127C2×#692311yescharacteristic
581#125—611no—
582#125C2×#692311yescharacteristic
583#124—1221no—
584#124—1221no—
585#124—1221no—
586#124—1221no—
587#124—1221no—
588#124—1221no—
589#123—21no—
590#123—21no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599#121—21no—
600#121—21no—
601#121—611no—
602#121—611no—
603#121—611no—
604#121—611no—
605#121—611no—
606#121—611no—
607#121—1221no—
608#121—1221no—
609#121—1221no—
610#121—1221no—
611#121—1221no—
612#121—1221no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121C2×#692311yescharacteristic
618#121C2×#692311yescharacteristic
619#120—1221no—
620#120—1221no—
621#120—1221no—
622#120—1221no—
623C4×Q8—611no—
624C4×Q8—611no—
625C4×Q8—1221no—
626C4×Q8—1221no—
627C4×D4—611no—
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4C2×#692311yescharacteristic
648C4×D4C2×#692311yescharacteristic
649#117—611no—
650#117—611no—
651#117—611no—
652#117—611no—
653#117C2×#692311yescharacteristic
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C42—611no—
659C2×C42—611no—
660C2×C42—611no—
661C4⋊C8—611no—
662C4⋊C8—611no—
663C4⋊C8—611no—
664C4⋊C8—611no—
665C4⋊C8—611no—
666C4⋊C8—611no—
667C4⋊C8—611no—
668C4⋊C8—611no—
669C4⋊C8—1221no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C4⋊C8—1221no—
673C4⋊C8—1221no—
674C4⋊C8—1221no—
675C22⋊C8—1221no—
676C22⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681#97—1221no—
682#97—1221no—
683#97—1221no—
684#97—1221no—
685C4×C8—1221no—
686C4×C8—1221no—
687C24—1221no—
688C24—1221no—
689#41—4881no—
690#41—4881no—
691#41—4881no—
692#41—4881no—
693#41—4881no—
694#41—4881no—
695#41—4881no—
696#41—4881no—
697#41—2442no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—1221no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—4881no—
725C2×D4—4881no—
726C2×D4—4881no—
727C2×D4—4881no—
728C2×D4—2442no—
729C2×D4—2442no—
730C2×D4C22×#692311yescharacteristic
731C2×D4C22×#692311yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4C22×#692311yescharacteristic
749M16—4881no—
750M16—4881no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—4881no—
760C2×C8—4881no—
761C2×C8—4881no—
762C2×C8—4881no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—611no—
770C4⋊C4—611no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4C22⋊#692311yescharacteristic
776C4⋊C4C22⋊#692311yescharacteristic
777C4⋊C4C22×#692311yescharacteristic
778C4⋊C4C22×#692311yescharacteristic
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4C22⋊#692311yescharacteristic
802C22⋊C4C22⋊#692311yescharacteristic
803C42—611no—
804C42—611no—
805C42—611no—
806C42—611no—
807C42—611no—
808C42—611no—
809C42—611no—
810C42—611no—
811C42—1221no—
812C42—1221no—
813C42C22×#692311yescharacteristic
814C42C22×#692311yescharacteristic
815C23—21no—
816C23—21no—
817C23—611no—
818C23—611no—
819C23—1221no—
820C23—1221no—
821C23—4881no—
822C23—4881no—
823C23—4881no—
824C23—4881no—
825C23—2442no—
826C23—2442no—
827C23C2×C22⋊#692311yescharacteristic
828Q8—2441no—
829Q8—2441no—
830Q8—2441no—
831Q8—2441no—
832Q8—2441no—
833D4—41no—
834D4—41no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—1222no—
840D4—1222no—
841D4—4881no—
842D4—4881no—
843D4—4881no—
844D4—4881no—
845D4—4881no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—2441no—
850D4—2441no—
851D4—2441no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2442no—
861D4—2442no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—611no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1222no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—4881no—
889C2×C4—4881no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—2441no—
895C2×C4C2×C22⋊#692311yescharacteristic
896C2×C4C2×C22⋊#692311yescharacteristic
897C2×C4C2×C22⋊#692311yescharacteristic
898C2×C4C2×C22⋊#692311yescharacteristic
899C2×C4C2×C22⋊#692311yescharacteristic
900C2×C4C23×#692311yescharacteristic
901C8—2441no—
902C8—2441no—
903C8—2441no—
904C8—2441no—
905C8—2441no—
906C8—2441no—
907C8—2441no—
908C8—2441no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—612no—
919C22—1221no—
920C22—1221no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—9762no—
925C22—9762no—
926C22—2441no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22—2441no—
931C22—2441no—
932C22C22×C22⋊#692311yescharacteristic
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—41no—
940C4—41no—
941C4—611no—
942C4—611no—
943C4—611no—
944C4—611no—
945C4—1221no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—2441no—
950C4—2441no—
951C2—41no—
952C2—81no—
953C2—81no—
954C2—1222no—
955C2—4881no—
956C2—4881no—
957C2—2441no—
958C2D61⋊#41311yescharacteristic
959C2#2146244011yescharacteristic
960C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#540C4
socleC22×C61C22×C22⋊C4
prime radical#21459691C2
cosocleC4×Dic61C24
hypercenter#540#6923
hypocenterC61#17771
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #21462748C2semidirect
2. #21462746C2semidirect
3. #21461351C2semidirect
4. #21461350C2semidirect
5. #21461347C2semidirect
6. #21461343C2semidirect
7. #21461342C2semidirect
8. #21461341C2semidirect
9. #21461341C2semidirect
10. #21461331C2semidirect
11. #21461330C2semidirect
12. #21461317C2semidirect
13. #21461316C2semidirect
14. D61⋊#331C2semidirect
26. #16840785C22semidirect
27. #16840782C22semidirect
28. #16840780C22semidirect
29. #16840779C22semidirect
30. #16840767C22semidirect
31. #16840765C22semidirect
32. C2×#14519844C22semidirect
35. D61⋊(C4⋊C8)C22semidirect
36. #16840621C22semidirect
37. #16840621C22semidirect
38. #16840621C22semidirect
39. #16840621C22semidirect
40. #16840621C22semidirect
41. #16840621C22semidirect
42. #16840621C22semidirect
43. #16840621C22semidirect
555. C61#17771semidirect

Maximal subgroups

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

subgroupindex
#214627482
#214627462
#214613512
#214613502
#214613472
#214613432
#214613422
#214613412
#214613312
#214613302
#214613172
#214613162
D61⋊#3312
#214596912
#1777161