Finite Group Databasebeta

← #30611389

Subgroups — #30611389

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#21461245C211yesmaximal, characteristic, complemented
4#21461244C211yesmaximal, characteristic, complemented
5#21461231C211yesmaximal, characteristic, complemented
6#21461230C211yesmaximal, characteristic, complemented
7#21461228C211yesmaximal, characteristic, complemented
8#21461224C211yesmaximal, characteristic, complemented
9#21461221C211yesmaximal, characteristic, complemented
10#21461220C211yesmaximal, characteristic, complemented
11#21461217C211yesmaximal, characteristic, complemented
12#21461215C211yesmaximal, characteristic, complemented
13#21461195C211yesmaximal, characteristic, complemented
14#21461194C211yesmaximal, characteristic, complemented
15#21459646C211yesmaximal, 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#16840615C2211yescharacteristic, complemented
41#16840615C2211yescharacteristic, complemented
42#16840615C2211yescharacteristic, complemented
43#16840615C2211yescharacteristic, complemented
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840462C411yescharacteristic, complemented
53#16840459—21no—
54#16840459C411yescharacteristic, complemented
55#16840457—21no—
56#16840454C411yescharacteristic, complemented
57#16840452C411yescharacteristic, complemented
58#16840443—21no—
59#16840438—21no—
60#16840420C411yescharacteristic, complemented
61#16840419C411yescharacteristic, complemented
62#16840406C411yescharacteristic, complemented
63#16840355—21no—
64#16840344—21no—
65#16840322—21no—
66#16840294C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840272C2211yescharacteristic
69#16840269C2211yescharacteristic
70C22⋊Q8×D61C2211yescharacteristic
71C2×#14519748C2211yescharacteristic
72#16840235—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic, 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×#11758224C2×C411yescharacteristic
108C2×Q8×D61C2×C411yescharacteristic
109C22×C22⋊D61—21no—
110C2×D4×D61D411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519772—21no—
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic
120#14519768—21no—
121#14519768C2×C411yescharacteristic
122#14519767—21no—
123#14519764—21no—
124#14519764C2×C411yescharacteristic
125#14519763—21no—
126#14519761—21no—
127#14519760—21no—
128#14519759—21no—
129#14519759—21no—
130#14519759—21no—
131#14519758—21no—
132#14519758—21no—
133#14519758—21no—
134#14519758—21no—
135#14519757C2311yescharacteristic
136#14519756—21no—
137#14519756C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519755—21no—
140#14519754—21no—
141#14519754—21no—
142#14519753C2×C411yescharacteristic
143#14519753C2311yescharacteristic
144#14519750—21no—
145#14519750—21no—
146#14519749—21no—
147#14519748—21no—
148#14519748—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748C2×C411yescharacteristic
152#14519748C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic
154#14519748C2311yescharacteristic
155#14519748C2311yescharacteristic
156#14519746—21no—
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61C2×C411yescharacteristic
160C4×Dic122C2×C411yescharacteristic
161C4×D244C2×C411yescharacteristic
162D4×Dic61—21no—
163D4×Dic61C2×C411yescharacteristic
164D4×Dic61D411yescharacteristic
165#14519739D411yescharacteristic
166C4×C22⋊D61—21no—
167C4×C22⋊D61—21no—
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#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519736—21no—
180#14519736C2×C411yescharacteristic
181#14519735C2×C411yescharacteristic
182#14519733—21no—
183#14519733—21no—
184#14519733—21no—
185C2×C4⋊Dic61C2×C411yescharacteristic
186C4⋊C4×D61—21no—
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61D411yescharacteristic
189C2×C22⋊Dic61—21no—
190C2×C22⋊Dic61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#124×C61C2×C411yescharacteristic
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C22⋊C4×C61—21no—
206C24×C61—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×C61C22×C411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—81no—
219C2×D4×C61C22⋊C411yescharacteristic
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⋊D61—21no—
232C2×C22⋊D61—42no—
233C2×C22⋊D61—42no—
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241Q8×D61—81no—
242#11758224—81no—
243D4×D61—41no—
244D4×D61—41no—
245C2×D244C22⋊C411yescharacteristic
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—81no—
249C2×C4×D61—81no—
250C2×C4×D61C22×C411yescharacteristic
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22×C411yescharacteristic
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×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C22⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61C22⋊C411yescharacteristic
301C22⋊Dic61C22⋊C411yescharacteristic
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61C22⋊C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318#11758196—21no—
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#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—42no—
339C23×C61—81no—
340C23×C61—81no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
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—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—81no—
371D4×C61—81no—
372D4×C61—81no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—81no—
378C2×C4×C61—81no—
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C23×C411yescharacteristic
384C22⋊D61—41no—
385C22⋊D61—41no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61—41no—
391C22⋊D61—41no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—42no—
401C2×Dic61—81no—
402C2×Dic61—81no—
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C22×D411yescharacteristic
408D244—41no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—41no—
422Dic122—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×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—162no—
441C22×C61C22×C22⋊C411yescharacteristic
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
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—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—41no—
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—81no—
495C2×C61#288311yescharacteristic
496C2×C61#289611yescharacteristic
497C2×C61#290111yescharacteristic
498D61—21no—
499D61—21no—
500D61—41no—
501D61—41no—
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—611no—
512#546—611no—
513#546#692311yescharacteristic, complemented
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×Q8—611no—
565C22×D4—611no—
566C22×D4—1221no—
567C22×D4C2×#692311yescharacteristic
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—611no—
585#124—1221no—
586#124—1221no—
587#124C2×#692311yescharacteristic
588#123—21no—
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—611no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—1221no—
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—21no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626C4×Q8—611no—
627C4×Q8—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—1221no—
637C4×D4—1221no—
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×D4C2×#692311yescharacteristic
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—21no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—611no—
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—21no—
694C24—611no—
695C24—611no—
696#41—81no—
697#41—4881no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—4881no—
701C2×Q8C22×#692311yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—81no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—2441no—
716C2×D4—2441no—
717C2×D4—2442no—
718C2×D4—2442no—
719C2×D4C22⋊#692311yescharacteristic
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—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—1221no—
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—21no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
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—611no—
813C42—611no—
814C42—611no—
815C42—1221no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—4881no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—21no—
824C23—21no—
825C23—42no—
826C23—81no—
827C23—81no—
828C23—611no—
829C23—611no—
830C23—611no—
831C23—1221no—
832C23—1221no—
833C23—1221no—
834C23—1221no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23C2×C22⋊#692311yescharacteristic
840C23C2×C22⋊#692311yescharacteristic
841Q8—41no—
842Q8—4881no—
843Q8—2441no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2441no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2442no—
860D4—2442no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
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—1221no—
873C2×C4—1221no—
874C2×C4—1222no—
875C2×C4—1221no—
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—2441no—
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—2442no—
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—41no—
924C22—41no—
925C22—41no—
926C22—162no—
927C22—611no—
928C22—611no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—4881no—
938C22—4881no—
939C22—4881no—
940C22—4881no—
941C22C22×C22⋊#692311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—41no—
948C4—41no—
949C4—1221no—
950C4—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—4881no—
955C4—4881no—
956C4—4881no—
957C4—2442no—
958C4—2441no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—81no—
966C2—1221no—
967C2—1221no—
968C2—2441no—
969C2—2441no—
970C2#2146241811yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459646C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#17625
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462340C2semidirect
3. #21461245C2semidirect
4. #21461244C2semidirect
5. #21461231C2semidirect
6. #21461230C2semidirect
7. #21461228C2semidirect
8. #21461224C2semidirect
9. #21461221C2semidirect
10. #21461220C2semidirect
11. #21461217C2semidirect
12. #21461215C2semidirect
13. #21461195C2semidirect
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. #16840615C22semidirect
41. #16840615C22semidirect
42. #16840615C22semidirect
43. #16840615C22semidirect
52. #16840462C4semidirect
54. #16840459C4semidirect
56. #16840454C4semidirect
57. #16840452C4semidirect
60. #16840420C4semidirect
61. #16840419C4semidirect
62. #16840406C4semidirect
74. C61×#546C4semidirect
513. #546#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
#214612452
#214612442
#214612312
#214612302
#214612282
#214612242
#214612212
#214612202
#214612172
#214612152
#214611952
#214611942
#214596462
#1762561