Finite Group Databasebeta

← #30611357

Subgroups — #30611357

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462667C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461261C211yesmaximal, characteristic, complemented
4#21461260C211yesmaximal, characteristic, complemented
5#21461257C211yesmaximal, characteristic, complemented
6#21461255C211yesmaximal, characteristic, complemented
7#21461245C211yesmaximal, characteristic, complemented
8#21461244C211yesmaximal, characteristic, complemented
9#21461195C211yesmaximal, characteristic, complemented
10#21461194C211yesmaximal, characteristic, complemented
11#21461191C211yesmaximal, characteristic, complemented
12#21461190C211yesmaximal, characteristic, complemented
13D61⋊#328C211yesmaximal, characteristic, complemented
14C2×#16840613C211yesmaximal, characteristic, complemented
15#21459646C211yesmaximal, characteristic
16#16840790—21no—
17#16840789—21no—
18#16840789—21no—
19D4×#92420—21no—
20#16840781C2211yescharacteristic, complemented
21#16840780C2211yescharacteristic, complemented
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic, complemented
24D61⋊(C22⋊C8)C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic, complemented
34#16840698C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic
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
75C23×#6923—21no—
76C2×D61⋊C8—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C4×#92420—21no—
97C4×#92420—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—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, complemented
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, complemented
120#14519768—21no—
121#14519768C2×C411yescharacteristic, complemented
122#14519767—21no—
123#14519764—21no—
124#14519764C2×C411yescharacteristic, complemented
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, complemented
139#14519755—21no—
140#14519754—21no—
141#14519754—21no—
142#14519753C2×C411yescharacteristic, complemented
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, complemented
154#14519748C2311yescharacteristic
155#14519748C2311yescharacteristic
156#14519746—21no—
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61C2×C411yescharacteristic, complemented
160C4×Dic122C2×C411yescharacteristic, complemented
161C4×D244C2×C411yescharacteristic
162D4×Dic61—21no—
163D4×Dic61C2×C411yescharacteristic, complemented
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, complemented
181#14519735C2×C411yescharacteristic, complemented
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, complemented
196C22×D4×C61C2×C411yescharacteristic
197#124×C61C2×C411yescharacteristic, complemented
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic, complemented
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic, complemented
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—
213C22×#6923—42no—
214C22×#6923—42no—
215C22×#6923—81no—
216#41×C61—81no—
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—81no—
222C2×D4×C61C22⋊C411yescharacteristic
223C2×D4×C61C22×C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61—42no—
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244Q8×D61—81no—
245#11758224—81no—
246D4×D61—22no—
247D4×D61—22no—
248C2×D244C22⋊C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—81no—
252C2×C4×D61—81no—
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2411yescharacteristic
262C2×Dic122—21no—
263C2×Dic122C22×C411yescharacteristic
264C22⋊#6923—42no—
265C22⋊#6923—42no—
266C22⋊#6923—81no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—81no—
272C2×#92420—81no—
273C4⋊#6923—81no—
274C4×#6923—42no—
275C4×#6923—81no—
276D61⋊C8—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—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61#13512yes—
352C22×D61#13512yes—
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—
366C2×#6923—84no—
367Q8×C61—41no—
368D4×C61—22no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—81no—
372D4×C61—81no—
373D4×C61—81no—
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—22no—
386C22⋊D61—22no—
387C22⋊D61—41no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61—41no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—81no—
394C22⋊D61—81no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—42no—
402C2×Dic61—81no—
403C2×Dic61—81no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C22×D411yescharacteristic
409D244—22no—
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—81no—
421C4×D61—81no—
422Dic122—41no—
423Dic122—81no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17615—611nomaximal, Sylow
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×C61#41612yes—
442C22×C61C22×C22⋊C411yescharacteristic
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61#41612yes—
455C2×D61C2×#13511yescharacteristic
456C2×D61C2×#13511yescharacteristic
457#6923—42no—
458#6923—81no—
459#6923—81no—
460#6923—81no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—41no—
467C4×C61—41no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—41no—
474Dic61—41no—
475Dic61—41no—
476Dic61—41no—
477#3505—611no—
478#2972—611no—
479#2353—611no—
480#1521—611no—
481#1521—611no—
482#1520—611no—
483#1519—611no—
484#1516—611no—
485#1516—611no—
486#1501—611no—
487#1501—611no—
488#1500—611no—
489#1500—611no—
490C2×#328—611no—
491C2×#327—611no—
492C2×C61—22no—
493C2×C61—41no—
494C2×C61—81no—
495C2×C61—81no—
496C2×C61#288311yescharacteristic
497C2×C61C2×#41611yescharacteristic
498C2×C61#290111yescharacteristic
499D61—21no—
500D61—21no—
501D61—22no—
502D61—41no—
503#553—611no—
504#553—611no—
505#553—1221no—
506#553—1221no—
507#552—611no—
508#552—611no—
509#551—1221no—
510#551—1221no—
511#548—611no—
512#548—611no—
513#546—611no—
514#546#692311yescharacteristic, complemented
515#539—1221no—
516#538—1221no—
517#534—1221no—
518#529—611no—
519#529—611no—
520#525—611no—
521#525—611no—
522C2×C22⋊Q8—611no—
523C2×#121—611no—
524#518—1221no—
525C2×C4×D4—611no—
526C8×D4—1221no—
527C8×D4—1221no—
528C8×D4—1221no—
529C8×D4—1221no—
530#431—611no—
531#431—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536#388—1221no—
537#387—1221no—
538#386—1221no—
539#383—611no—
540#381—611no—
541#380—611no—
542C4×C22⋊C4—611no—
543C4×C22⋊C4—1221no—
544#376—611no—
545C2×#95—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#328—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561#327—611no—
562C61#1761511yescharacteristic, complemented, Sylow
563C2×#41—611no—
564C2×#41C2×#692311yescharacteristic, complemented
565C22×Q8—611no—
566C22×D4—611no—
567C22×D4—1221no—
568C22×D4C2×#692311yescharacteristic
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C22×C8—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#126—1221no—
581#126—1221no—
582#125—611no—
583#125—611no—
584#125—1221no—
585#125—1221no—
586#124—611no—
587#124—1221no—
588#124—1221no—
589#124C2×#692311yescharacteristic, complemented
590#123—21no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8C2×#692311yescharacteristic
610#121—21no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—611no—
615#121—611no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#121C2×#692311yescharacteristic, complemented
624#120—21no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×Q8—611no—
629C4×Q8—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×D4—1221no—
648C4×D4C2×#692311yescharacteristic
649C4×D4C2×#692311yescharacteristic, complemented
650#117—611no—
651#117—611no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655#117—1221no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4—1221no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—611no—
663C2×C22⋊C4—611no—
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—
673C4⋊C8—1221no—
674C4⋊C8—1221no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685#95—611no—
686#95—611no—
687#95—611no—
688#95—611no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693#95—1221no—
694C24—21no—
695C24—611no—
696C24—611no—
697#41—81no—
698#41—4881no—
699C2×Q8—611no—
700C2×Q8—1221no—
701C2×Q8—4881no—
702C2×Q8C22×#692311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—81no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—1222no—
711C2×D4—1222no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—2442no—
719C2×D4—2442no—
720C2×D4C22⋊#692311yescharacteristic
721C2×D4C22×#692311yescharacteristic
722C2×D4C22×#692311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
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—611no—
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—1221no—
745C22×C4—4881no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4C22×#692311yescharacteristic
751C22×C4C22×#692311yescharacteristic
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—4881no—
757C2×C8—4881no—
758C2×C8—4881no—
759C2×C8—4881no—
760C4⋊C4—21no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
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—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—4881no—
781C4⋊C4C22⋊#692311yescharacteristic
782C4⋊C4C22×#692311yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
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—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—4881no—
810C22⋊C4—2442no—
811C22⋊C4—2442no—
812C22⋊C4C22⋊#692311yescharacteristic
813C22⋊C4C22⋊#692311yescharacteristic
814C42—611no—
815C42—611no—
816C42—611no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—4881no—
822C42—2442no—
823C42C22×#692311yescharacteristic
824C23—21no—
825C23—21no—
826C23—42no—
827C23—81no—
828C23—81no—
829C23—611no—
830C23—611no—
831C23—612no—
832C23—612no—
833C23—611no—
834C23—1221no—
835C23—1221no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2441no—
840C23C2×C22⋊#692311yescharacteristic
841C23C2×C22⋊#692311yescharacteristic
842Q8—41no—
843Q8—4881no—
844Q8—2441no—
845D4—22no—
846D4—41no—
847D4—41no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—1222no—
852D4—1222no—
853D4—1222no—
854D4—4881no—
855D4—4881no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2442no—
861D4—2442no—
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—1221no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4881no—
884C2×C4—4884no—
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—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2442no—
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C2×C22⋊#692311yescharacteristic
910C2×C4C2×C22⋊#692311yescharacteristic
911C2×C4C23×#692311yescharacteristic
912C8—2441no—
913C8—2441no—
914C8—2441no—
915C8—2441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—162no—
928C22—611no—
929C22—611no—
930C22—612no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—1221no—
938C22—4881no—
939C22—4881no—
940C22—2442no—
941C22—2442no—
942C22#1684075212yes—
943C22C22×C22⋊#692311yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—41no—
950C4—41no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—4881no—
957C4—4881no—
958C4—4881no—
959C4—2442no—
960C4—2441no—
961C4—2441no—
962C4—2441no—
963C4—2441no—
964C2—22no—
965C2—41no—
966C2—81no—
967C2—81no—
968C2—1221no—
969C2—1221no—
970C2—1222no—
971C2—2441no—
972C2#2146241811yescharacteristic
973C2C2×#1684075211yescharacteristic
974C2#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#17615
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. #21462667C2semidirect
2. #21462336C2semidirect
3. #21461261C2semidirect
4. #21461260C2semidirect
5. #21461257C2semidirect
6. #21461255C2semidirect
7. #21461245C2semidirect
8. #21461244C2semidirect
9. #21461195C2semidirect
10. #21461194C2semidirect
11. #21461191C2semidirect
12. #21461190C2semidirect
13. D61⋊#328C2semidirect
14. C2×#16840613C2semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
23. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840707C22semidirect
30. #16840705C22semidirect
33. C4×C22⋊#6923C22semidirect
34. #16840698C22semidirect
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
107. C2×#11758224C2×C4semidirect
119. #14519769C2×C4semidirect
121. #14519768C2×C4semidirect
124. #14519764C2×C4semidirect
138. #14519756C2×C4semidirect
142. #14519753C2×C4semidirect
153. #14519748C2×C4semidirect
159. Q8×Dic61C2×C4semidirect
160. C4×Dic122C2×C4semidirect
163. D4×Dic61C2×C4semidirect
180. #14519736C2×C4semidirect
181. #14519735C2×C4semidirect
195. C2×#41×C61C2×C4semidirect
197. #124×C61C2×C4semidirect
201. #121×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
514. #546#6923semidirect
562. C61#17615semidirect
564. C2×#41C2×#6923semidirect
589. #124C2×#6923semidirect
623. #121C2×#6923semidirect
649. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626672
#214623362
#214612612
#214612602
#214612572
#214612552
#214612452
#214612442
#214611952
#214611942
#214611912
#214611902
D61⋊#3282
C2×#168406132
#214596462
#1761561