Finite Group Databasebeta

← #30611390

Subgroups — #30611390

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462340C211yesmaximal, characteristic, complemented
3#21461246C211yesmaximal, characteristic, complemented
4#21461245C211yesmaximal, characteristic, complemented
5#21461232C211yesmaximal, characteristic, complemented
6#21461231C211yesmaximal, characteristic, complemented
7#21461229C211yesmaximal, characteristic, complemented
8#21461225C211yesmaximal, characteristic, complemented
9#21461223C211yesmaximal, characteristic, complemented
10#21461220C211yesmaximal, characteristic, complemented
11#21461219C211yesmaximal, characteristic, complemented
12#21461214C211yesmaximal, characteristic, complemented
13#21461197C211yesmaximal, characteristic, complemented
14#21461194C211yesmaximal, characteristic, complemented
15#21459655C211yesmaximal, characteristic
16#16840794—21no—
17#16840793—21no—
18#16840792—21no—
19#16840791—21no—
20#16840785C2211yescharacteristic, complemented
21#16840784C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840714—21no—
27#16840712—21no—
28#16840712—21no—
29#16840706C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic
31#16840705C2211yescharacteristic, complemented
32C4⋊C4×#6923—21no—
33C4×C4⋊#6923C2211yescharacteristic, complemented
34C4×C22⋊#6923C2211yescharacteristic
35C4×C22⋊#6923C2211yescharacteristic, complemented
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840616C2211yescharacteristic, complemented
41#16840616C2211yescharacteristic, complemented
42#16840616C2211yescharacteristic, complemented
43#16840616C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840464C411yescharacteristic, complemented
53#16840461—21no—
54#16840458C411yescharacteristic, complemented
55#16840455—21no—
56#16840453C411yescharacteristic, complemented
57#16840446C411yescharacteristic, complemented
58#16840442—21no—
59#16840439—21no—
60#16840423C411yescharacteristic, complemented
61#16840405C411yescharacteristic, complemented
62#16840400C411yescharacteristic, complemented
63#16840358—21no—
64#16840346—21no—
65#16840320—21no—
66#16840299C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519753C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#548C411yescharacteristic, complemented
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88#14519844—21no—
89C4⋊#92420—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99#14519832—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758226C2×C411yescharacteristic
108C2×D4×D61—21no—
109C2×D4×D61C2×C411yescharacteristic
110C2×D4×D61D411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519772—21no—
114#14519772—21no—
115#14519771—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic
120#14519768C2×C411yescharacteristic
121#14519767—21no—
122#14519767—21no—
123#14519766—21no—
124#14519766C2×C411yescharacteristic
125#14519762—21no—
126#14519762—21no—
127#14519762—21no—
128#14519761—21no—
129#14519760—21no—
130#14519759—21no—
131#14519759—21no—
132#14519759—21no—
133#14519759—21no—
134#14519758—21no—
135#14519753—21no—
136#14519753—21no—
137#14519753—21no—
138#14519753C2×C411yescharacteristic
139#14519753C2×C411yescharacteristic
140#14519753C2×C411yescharacteristic
141#14519753C2311yescharacteristic
142#14519753C2311yescharacteristic
143#14519752C2311yescharacteristic
144#14519751—21no—
145#14519751C2×C411yescharacteristic
146#14519751C2×C411yescharacteristic
147#14519750—21no—
148#14519750—21no—
149#14519749—21no—
150#14519749—21no—
151#14519749—21no—
152#14519749—21no—
153#14519748C2×C411yescharacteristic
154#14519748C2311yescharacteristic
155#14519747—21no—
156#14519747—21no—
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61C2×C411yescharacteristic
160C4×D244—21no—
161C4×D244C2×C411yescharacteristic
162C4×D244C2×C411yescharacteristic
163D4×Dic61—21no—
164D4×Dic61C2×C411yescharacteristic
165D4×Dic61D411yescharacteristic
166#14519739—21no—
167#14519739D411yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61C2×C411yescharacteristic
172C4×C22⋊D61C2×C411yescharacteristic
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737D411yescharacteristic
177#14519737D411yescharacteristic
178#14519736C2×C411yescharacteristic
179#14519735—21no—
180#14519735C2×C411yescharacteristic
181#14519734—21no—
182#14519734—21no—
183#14519733—21no—
184C2×C4⋊Dic61C2×C411yescharacteristic
185C2×#11758196—21no—
186C4⋊C4×D61C2×C411yescharacteristic
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×Q8×C61C2×C411yescharacteristic
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213#41×C61—81no—
214C2×Q8×C61—21no—
215C2×Q8×C61—81no—
216C2×Q8×C61C22×C411yescharacteristic
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61C22⋊C411yescharacteristic
221C2×D4×C61C22×C411yescharacteristic
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61C22⋊C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237#11758226—81no—
238D4×D61—41no—
239D4×D61—41no—
240D4×D61—42no—
241D4×D61—42no—
242D4×D61—81no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244C22⋊C411yescharacteristic
246C2×D244C22×C411yescharacteristic
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—81no—
251C2×C4×D61—81no—
252C2×C4×D61C22×C411yescharacteristic
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2411yescharacteristic
261C22⋊#6923—42no—
262C22⋊#6923—42no—
263C22⋊#6923—81no—
264C22⋊#6923—81no—
265#11758217—81no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—81no—
271C4⋊#6923—42no—
272C4⋊#6923—42no—
273C4×#6923—42no—
274C4×#6923—81no—
275C4×#6923—81no—
276#11758213—81no—
277D61⋊C8—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61C22⋊C411yescharacteristic
287C22⋊C4×C61C22⋊C411yescharacteristic
288C42×C61—21no—
289C42×C61C22×C411yescharacteristic
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61C22⋊C411yescharacteristic
295C22⋊Dic61C22⋊C411yescharacteristic
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#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61C22⋊C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61—21no—
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C2×C22⋊C411yescharacteristic
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—42no—
349C22×D61—81no—
350C22×D61—81no—
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C22×D411yescharacteristic
354C2×#6923—22no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366Q8×C61—41no—
367Q8×C61—41no—
368Q8×C61—81no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—42no—
372D4×C61—81no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—81no—
379C2×C4×C61—81no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C23×C411yescharacteristic
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—42no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61—81no—
391C22⋊D61—81no—
392C22⋊D61—81no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—81no—
399C2×Dic61—81no—
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C22×D411yescharacteristic
405D244—41no—
406D244—41no—
407D244—41no—
408D244—41no—
409D244—81no—
410C4×D61—21no—
411C4×D61—21no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—42no—
421C4×D61—81no—
422C4×D61—81no—
423#92420—41no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#17625—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61C22×C22⋊C411yescharacteristic
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—162no—
454C2×D61#57511yescharacteristic
455C2×D61#57511yescharacteristic
456#6923—42no—
457#6923—81no—
458#6923—81no—
459#6923—81no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—41no—
474Dic61—41no—
475Dic61—41no—
476#3505—611no—
477#2973—611no—
478#2357—611no—
479#1516—611no—
480#1516—611no—
481#1512—611no—
482#1512—611no—
483#1511—611no—
484#1510—611no—
485#1509—611no—
486#1509—611no—
487#1508—611no—
488#1507—611no—
489#1501—611no—
490#1501—611no—
491C2×C61—41no—
492C2×C61—41no—
493C2×C61—81no—
494C2×C61#288311yescharacteristic
495C2×C61#289611yescharacteristic
496C2×C61#290111yescharacteristic
497D61—21no—
498D61—21no—
499D61—41no—
500D61—41no—
501D61—81no—
502#553—611no—
503#553—611no—
504#553—1221no—
505#553—1221no—
506#552—611no—
507#552—611no—
508#551—1221no—
509#551—1221no—
510#548—611no—
511#548#692311yescharacteristic, complemented
512#546—611no—
513#546—611no—
514#539—1221no—
515#538—1221no—
516#534—1221no—
517#529—611no—
518#529—611no—
519#525—611no—
520#525—611no—
521C2×C22⋊Q8—611no—
522C2×#121—611no—
523#518—1221no—
524C2×C4×D4—611no—
525#435—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432—611no—
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535#390—1221no—
536#388—1221no—
537#388—1221no—
538#382—611no—
539#381—611no—
540#381—611no—
541C4×C4⋊C4—611no—
542C4×C4⋊C4—1221no—
543C4×C22⋊C4—611no—
544C4×C22⋊C4—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#327—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561C61#1762511yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41C2×#692311yescharacteristic
564C22×Q8C2×#692311yescharacteristic
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—1221no—
568C23×C4—611no—
569C23×C4—611no—
570C2×M16—1221no—
571C2×M16—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574#126—1221no—
575#126—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#125—611no—
581#125—611no—
582#125—1221no—
583#125—1221no—
584#124—21no—
585#124—611no—
586#124—1221no—
587#124C2×#692311yescharacteristic
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598C22⋊Q8—21no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8C2×#692311yescharacteristic
608#121—21no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121C2×#692311yescharacteristic
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626C4×Q8—611no—
627C4×Q8C2×#692311yescharacteristic
628C4×D4—21no—
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—1221no—
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
648#117—611no—
649#117—611no—
650#117—1221no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654C2×C4⋊C4—611no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C42—611no—
671C2×C42—1221no—
672C2×C42—1221no—
673C2×C42—1221no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—611no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684#97—1221no—
685#97—1221no—
686#95—611no—
687#95—611no—
688#95—611no—
689#95—611no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693C24—611no—
694C24—611no—
695C24—1221no—
696#41—81no—
697#41—4881no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C22×#692311yescharacteristic
701C2×Q8C22×#692311yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—4881no—
716C2×D4—2441no—
717C2×D4—2441no—
718C2×D4—2442no—
719C2×D4—2442no—
720C2×D4C22⋊#692311yescharacteristic
721C2×D4C22×#692311yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—4881no—
745C22×C4—4881no—
746C22×C4C22×#692311yescharacteristic
747C22×C4C22×#692311yescharacteristic
748M16—4881no—
749M16—4881no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—4881no—
755C2×C8—4881no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—2442no—
777C4⋊C4—2442no—
778C4⋊C4C22⋊#692311yescharacteristic
779C4⋊C4C22×#692311yescharacteristic
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
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⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—4881no—
807C22⋊C4—4881no—
808C22⋊C4—2442no—
809C22⋊C4—2442no—
810C22⋊C4C22⋊#692311yescharacteristic
811C22⋊C4C22⋊#692311yescharacteristic
812C42—21no—
813C42—611no—
814C42—611no—
815C42—611no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—4881no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—21no—
824C23—611no—
825C23—611no—
826C23—611no—
827C23—1221no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—4881no—
833C23—4881no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2442no—
839C23C2×C22⋊#692311yescharacteristic
840C23C2×C22⋊#692311yescharacteristic
841Q8—41no—
842Q8—41no—
843Q8—81no—
844D4—41no—
845D4—41no—
846D4—42no—
847D4—81no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2442no—
859D4—2441no—
860D4—2441no—
861C2×C4—21no—
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—1221no—
874C2×C4—1221no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2442no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4C2×C22⋊#692311yescharacteristic
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C23×#692311yescharacteristic
910C8—2441no—
911C8—2441no—
912C8—2441no—
913C8—2441no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—611no—
924C22—611no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—9762no—
934C22—4881no—
935C22—4881no—
936C22—4881no—
937C22—4881no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C22×C22⋊#692311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—4881no—
956C4—4881no—
957C4—4881no—
958C4—2442no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—1221no—
966C2—1221no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2146241811yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459655C2
cosocleC2×C4×D61C24
hypercenter#548#6923
hypocenterC61#17625
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. #21462671C2semidirect
2. #21462340C2semidirect
3. #21461246C2semidirect
4. #21461245C2semidirect
5. #21461232C2semidirect
6. #21461231C2semidirect
7. #21461229C2semidirect
8. #21461225C2semidirect
9. #21461223C2semidirect
10. #21461220C2semidirect
11. #21461219C2semidirect
12. #21461214C2semidirect
13. #21461197C2semidirect
14. #21461194C2semidirect
20. #16840785C22semidirect
21. #16840784C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840706C22semidirect
31. #16840705C22semidirect
33. C4×C4⋊#6923C22semidirect
35. C4×C22⋊#6923C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840616C22semidirect
41. #16840616C22semidirect
42. #16840616C22semidirect
43. #16840616C22semidirect
52. #16840464C4semidirect
54. #16840458C4semidirect
56. #16840453C4semidirect
57. #16840446C4semidirect
60. #16840423C4semidirect
61. #16840405C4semidirect
62. #16840400C4semidirect
74. C61×#548C4semidirect
511. #548#6923semidirect
561. C61#17625semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623402
#214612462
#214612452
#214612322
#214612312
#214612292
#214612252
#214612232
#214612202
#214612192
#214612142
#214611972
#214611942
#214596552
#1762561