Finite Group Databasebeta

← #30611942

Subgroups — #30611942

Order 15616.

982 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#21462739C211yesmaximal, characteristic, complemented
2#21462517C211yesmaximal, characteristic, complemented
3#21461356C211yesmaximal, characteristic, complemented
4#21461354C211yesmaximal, characteristic, complemented
5#21461351C211yesmaximal, characteristic, complemented
6#21461347C211yesmaximal, characteristic, complemented
7#21461344C211yesmaximal, characteristic, complemented
8#21461343C211yesmaximal, characteristic, complemented
9#21461338C211yesmaximal, characteristic, complemented
10#21461338C211yesmaximal, characteristic, complemented
11#21461331C211yesmaximal, characteristic, complemented
12#21461327C211yesmaximal, characteristic, complemented
13#21461322C211yesmaximal, characteristic, complemented
14#21461317C211yesmaximal, characteristic, complemented
15#21459689C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic
23#16840785C2211yescharacteristic
24#16840782C2211yescharacteristic, complemented
25#16840782C2211yescharacteristic, complemented
26#16840780C2211yescharacteristic
27#16840779C2211yescharacteristic, complemented
28#16840779C2211yescharacteristic, complemented
29#16840767C2211yescharacteristic
30#16840765C2211yescharacteristic, complemented
31#16840765C2211yescharacteristic, complemented
32C2×#14519844C2211yescharacteristic, complemented
33C2×#14519844C2211yescharacteristic, complemented
34#16840735—21no—
35#16840726—21no—
36#16840622C2211yescharacteristic, complemented
37#16840622C2211yescharacteristic, complemented
38#16840622C2211yescharacteristic, complemented
39#16840622C2211yescharacteristic, 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#16840498C411yescharacteristic
53#16840497C411yescharacteristic
54#16840495—21no—
55#16840433C411yescharacteristic
56#16840432—21no—
57#16840409C411yescharacteristic
58#16840409C411yescharacteristic
59#16840401—21no—
60#16840401—21no—
61#16840400C411yescharacteristic
62#16840400C411yescharacteristic
63#16840362—21no—
64#16840362—21no—
65#16840325—21no—
66#16840316C2211yescharacteristic
67#16840308C2211yescharacteristic
68#16840308C2211yescharacteristic
69#16840307C2211yescharacteristic
70#16840307C2211yescharacteristic
71#127×D61C2211yescharacteristic
72#16840234—21no—
73C4×#11758224C2211yescharacteristic
74C61×#550C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—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—
93#14519834—21no—
94#14519834—21no—
95#14519834—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99C22⋊#92420—21no—
100#14519832—21no—
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222C2×C411yescharacteristic
108C2×#11758222C2×C411yescharacteristic
109C2×#11758224—21no—
110C2×#11758224—21no—
111C2×#11758224D411yescharacteristic
112C2×D4×D61—21no—
113C2×D4×D61—21no—
114C2×D4×D61C2×C411yescharacteristic
115C2×D4×D61C2×C411yescharacteristic
116#14519776C2311yescharacteristic
117#14519775C2311yescharacteristic
118#14519774C2×C411yescharacteristic
119#14519773—21no—
120#14519773—21no—
121#14519773—21no—
122#14519773C2311yescharacteristic
123#14519773C2311yescharacteristic
124#14519767—21no—
125#14519766C2×C411yescharacteristic
126#14519766C2×C411yescharacteristic
127#14519765—21no—
128#14519764—21no—
129#14519764C2×C411yescharacteristic
130#14519764C2×C411yescharacteristic
131#14519763—21no—
132#14519763—21no—
133#14519762—21no—
134#14519762—21no—
135#14519760—21no—
136#14519760—21no—
137#14519759—21no—
138#14519759—21no—
139#14519758—21no—
140#14519758—21no—
141#14519757C2×C411yescharacteristic
142#14519755—21no—
143#14519753C2×C411yescharacteristic
144#14519751C2×C411yescharacteristic
145#14519751C2×C411yescharacteristic
146#14519750—21no—
147#14519750—21no—
148#14519749—21no—
149#14519749—21no—
150#14519749—21no—
151#14519749—21no—
152#14519749—21no—
153#14519749—21no—
154#14519749—21no—
155#14519749—21no—
156#14519748—21no—
157#14519748—21no—
158#14519745—21no—
159#14519745—21no—
160#14519745—21no—
161#14519745—21no—
162C4×Dic122—21no—
163C4×Dic122C2×C411yescharacteristic
164C4×Dic122C2×C411yescharacteristic
165#14519742D411yescharacteristic
166C4×D244—21no—
167D4×Dic61—21no—
168D4×Dic61C2×C411yescharacteristic
169D4×Dic61C2×C411yescharacteristic
170D4×Dic61D411yescharacteristic
171#14519739—21no—
172#14519739C2×C411yescharacteristic
173#14519739C2×C411yescharacteristic
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61—21no—
177C4×C22⋊D61—21no—
178C4×C22⋊D61C2×C411yescharacteristic
179C4×C22⋊D61C2×C411yescharacteristic
180#14519737—21no—
181#14519737—21no—
182#14519737D411yescharacteristic
183#14519737D411yescharacteristic
184#14519735D411yescharacteristic
185#14519734—21no—
186#14519733D411yescharacteristic
187#14519733D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197#127×C61—21no—
198#127×C61C2×C411yescharacteristic
199#121×C61—21no—
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208#41×C61—81no—
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61C22⋊C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242#11758224—41no—
243#11758224—41no—
244#11758224—81no—
245#11758224—81no—
246#11758224—81no—
247#11758224—81no—
248D4×D61—42no—
249D4×D61—42no—
250D4×D61—81no—
251D4×D61—81no—
252D4×D61—81no—
253D4×D61—81no—
254#11758222—81no—
255#11758222—81no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244C22×C411yescharacteristic
259C2×D244C22×C411yescharacteristic
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×Dic122—21no—
268C2×Dic122C22⋊C411yescharacteristic
269C2×Dic122C22×C411yescharacteristic
270#11758217—42no—
271#11758217—81no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—42no—
281C2×#92420—81no—
282#11758213—81no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61C22⋊C411yescharacteristic
289C22⋊C4×C61C22⋊C411yescharacteristic
290C42×C61—21no—
291C42×C61C22×C411yescharacteristic
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61C22⋊C411yescharacteristic
299C22⋊Dic61C22⋊C411yescharacteristic
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
312C4⋊Dic61—21no—
313C4⋊Dic61C22⋊C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
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×Dic61C22×C411yescharacteristic
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
337C23×C61C2×C22⋊C411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—81no—
343C22×D61—81no—
344C22×D61—81no—
345C22×D61—81no—
346C22×D61C2×C22⋊C411yescharacteristic
347Q8×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—42no—
352D4×C61—81no—
353D4×C61—81no—
354D4×C61—81no—
355D4×C61—81no—
356D4×C61—81no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—81no—
362C2×C4×C61—81no—
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C23×C411yescharacteristic
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—41no—
377C22⋊D61—41no—
378C22⋊D61—81no—
379C22⋊D61—81no—
380C22⋊D61—81no—
381C22⋊D61—81no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—81no—
395C2×Dic61—81no—
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C22×D411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403D244—41no—
404D244—41no—
405D244—42no—
406D244—81no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—41no—
412C4×D61—81no—
413C4×D61—81no—
414C4×D61—81no—
415C4×D61—81no—
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#17766—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61C22×C22⋊C411yescharacteristic
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—162no—
452C2×D61—162no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—41no—
459C4×C61—41no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—41no—
466Dic61—41no—
467Dic61#57511yescharacteristic
468Dic61#57511yescharacteristic
469Dic61#57611yescharacteristic
470Dic61#57711yescharacteristic
471#3508—611no—
472#2989—611no—
473#2925—611no—
474#1560—611no—
475#1559—611no—
476#1557—611no—
477#1555—611no—
478#1554—611no—
479#1553—611no—
480#1551—611no—
481#1551—611no—
482#1547—611no—
483#1545—611no—
484#1543—611no—
485#1540—611no—
486C2×C61—41no—
487C2×C61—41no—
488C2×C61—81no—
489C2×C61—81no—
490C2×C61#288811yescharacteristic
491C2×C61#289611yescharacteristic
492C2×C61#289711yescharacteristic
493D61—41no—
494D61—81no—
495D61—81no—
496#559—611no—
497#559—611no—
498#559—1221no—
499#550—611no—
500#550—1221no—
501#550#692311yescharacteristic
502#546—611no—
503#546—611no—
504#546—611no—
505#546—611no—
506#546—1221no—
507#546—1221no—
508#540—1221no—
509#540—1221no—
510#535—1221no—
511#533—611no—
512#532—611no—
513#532—611no—
514#532—611no—
515#532—611no—
516C2×#127—611no—
517#518—1221no—
518C4×#41—611no—
519#446—1221no—
520#436—1221no—
521#435—1221no—
522#435—1221no—
523#433—1221no—
524#433—1221no—
525#432—611no—
526#432—611no—
527#432—611no—
528#432—611no—
529#431—611no—
530#431—611no—
531#431—611no—
532#423—611no—
533#423—611no—
534#423—611no—
535C2×C4⋊C8—611no—
536C2×C4⋊C8—611no—
537#408—1221no—
538#405—1221no—
539#333—611no—
540#333—611no—
541#333—611no—
542#333—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#1776611yescharacteristic, complemented, Sylow
556C2×#41—611no—
557C2×#41—611no—
558C2×#41—611no—
559C2×#41—1221no—
560C2×#41—1221no—
561C2×#41C2×#692311yescharacteristic
562C2×#41C2×#692311yescharacteristic
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—1221no—
566C22×D4—1221no—
567C2×M16—1221no—
568C2×M16—1221no—
569C2×M16—1221no—
570C22×C8—1221no—
571C22×C8—1221no—
572C4⋊Q8—611no—
573C4⋊Q8—611no—
574#127—21no—
575#127—611no—
576#127—611no—
577#127—611no—
578#127—1221no—
579#127—1221no—
580#127—1221no—
581#127C2×#692311yescharacteristic
582#125—1221no—
583#124—611no—
584#124—611no—
585#124—611no—
586#124—611no—
587#124—1221no—
588#124—1221no—
589#124—1221no—
590#124—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—1221no—
602#121—21no—
603#121—21no—
604#121—611no—
605#121—611no—
606#121—1221no—
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#121—1221no—
618#121C2×#692311yescharacteristic
619#121C2×#692311yescharacteristic
620#120—1221no—
621#120—1221no—
622#120—1221no—
623#120—1221no—
624C4×Q8—611no—
625C4×Q8—611no—
626C4×Q8—611no—
627C4×Q8—1221no—
628C4×Q8C2×#692311yescharacteristic
629C4×D4—21no—
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×D4—1221no—
648C4×D4C2×#692311yescharacteristic
649#117—611no—
650#117—611no—
651#117—611no—
652#117—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C42—611no—
658C2×C42—611no—
659C2×C42—611no—
660C4⋊C8—611no—
661C4⋊C8—611no—
662C4⋊C8—611no—
663C4⋊C8—611no—
664C4⋊C8—611no—
665C4⋊C8—611no—
666C4⋊C8—611no—
667C4⋊C8—611no—
668C4⋊C8—1221no—
669C4⋊C8—1221no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C4⋊C8—1221no—
673C22⋊C8—1221no—
674C22⋊C8—1221no—
675C22⋊C8—1221no—
676C22⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680#97—1221no—
681#97—1221no—
682#97—1221no—
683#97—1221no—
684C4×C8—1221no—
685C4×C8—1221no—
686C4×C8—1221no—
687C24—1221no—
688C24—1221no—
689#41—81no—
690#41—81no—
691#41—4881no—
692#41—4881no—
693#41—4881no—
694#41—4881no—
695#41—4881no—
696#41—4881no—
697#41—2441no—
698#41—2441no—
699C2×Q8—611no—
700C2×Q8—611no—
701C2×Q8—1221no—
702C2×Q8C22×#692311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—611no—
712C2×D4—611no—
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—1221no—
725C2×D4—4881no—
726C2×D4—4881no—
727C2×D4—4881no—
728C2×D4—4881no—
729C2×D4—2442no—
730C2×D4—2442no—
731C2×D4C22⋊#692311yescharacteristic
732C2×D4C22×#692311yescharacteristic
733C2×D4C22×#692311yescharacteristic
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4C22×#692311yescharacteristic
750C22×C4C22×#692311yescharacteristic
751M16—4881no—
752M16—4881no—
753M16—2442no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—4881no—
763C2×C8—2442no—
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⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4C22⋊#692311yescharacteristic
778C4⋊C4C22×#692311yescharacteristic
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
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—21no—
804C42—611no—
805C42—611no—
806C42—611no—
807C42—611no—
808C42—611no—
809C42—611no—
810C42—611no—
811C42—611no—
812C42—611no—
813C42—1221no—
814C42C22×#692311yescharacteristic
815C23—21no—
816C23—21no—
817C23—611no—
818C23—1221no—
819C23—1221no—
820C23—4881no—
821C23—4881no—
822C23—4881no—
823C23—4881no—
824C23—2442no—
825C23—2442no—
826C23C2×C22⋊#692311yescharacteristic
827C23C2×C22⋊#692311yescharacteristic
828Q8—41no—
829Q8—2441no—
830Q8—2441no—
831Q8—2441no—
832Q8—2441no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—42no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841D4—81no—
842D4—4881no—
843D4—4881no—
844D4—4881no—
845D4—4881no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—2441no—
850D4—2441no—
851D4—2442no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—4881no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—4881no—
895C2×C4—2441no—
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—21no—
913C22—21no—
914C22—21no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
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—41no—
939C4—41no—
940C4—611no—
941C4—611no—
942C4—611no—
943C4—611no—
944C4—1221no—
945C4—1221no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—2441no—
950C4—2441no—
951C2—41no—
952C2—41no—
953C2—81no—
954C2—81no—
955C2—4881no—
956C2—4881no—
957C2—2441no—
958C2#2146242911yescharacteristic
959C2#2146243911yescharacteristic
960C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#550C4
socleC22×C61C22×C22⋊C4
prime radical#21459689C2
cosocleC4×Dic61C24
hypercenter#550#6923
hypocenterC61#17766
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462517C2semidirect
3. #21461356C2semidirect
4. #21461354C2semidirect
5. #21461351C2semidirect
6. #21461347C2semidirect
7. #21461344C2semidirect
8. #21461343C2semidirect
9. #21461338C2semidirect
10. #21461338C2semidirect
11. #21461331C2semidirect
12. #21461327C2semidirect
13. #21461322C2semidirect
14. #21461317C2semidirect
24. #16840782C22semidirect
25. #16840782C22semidirect
27. #16840779C22semidirect
28. #16840779C22semidirect
30. #16840765C22semidirect
31. #16840765C22semidirect
32. C2×#14519844C22semidirect
33. C2×#14519844C22semidirect
36. #16840622C22semidirect
37. #16840622C22semidirect
38. #16840622C22semidirect
39. #16840622C22semidirect
40. #16840621C22semidirect
41. #16840621C22semidirect
42. #16840621C22semidirect
43. #16840621C22semidirect
555. C61#17766semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214625172
#214613562
#214613542
#214613512
#214613472
#214613442
#214613432
#214613382
#214613312
#214613272
#214613222
#214613172
#214596892
#1776661