Finite Group Databasebeta

← #30611358

Subgroups — #30611358

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#21461262C211yesmaximal, characteristic, complemented
4#21461261C211yesmaximal, characteristic, complemented
5#21461258C211yesmaximal, characteristic, complemented
6#21461254C211yesmaximal, characteristic, complemented
7#21461247C211yesmaximal, characteristic, complemented
8#21461244C211yesmaximal, characteristic, complemented
9#21461196C211yesmaximal, characteristic, complemented
10#21461195C211yesmaximal, characteristic, complemented
11#21461193C211yesmaximal, characteristic, complemented
12#21461190C211yesmaximal, characteristic, complemented
13C2×#16840615C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459648C211yesmaximal, 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#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840615C2211yescharacteristic, complemented
41#16840615C2211yescharacteristic, complemented
42#16840615C2211yescharacteristic, complemented
43#16840615C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840464—21no—
53#16840460C411yescharacteristic, complemented
54#16840458—21no—
55#16840451C411yescharacteristic, complemented
56#16840450C411yescharacteristic, complemented
57#16840437—21no—
58#16840435—21no—
59#16840421C411yescharacteristic, complemented
60#16840418C411yescharacteristic, complemented
61#16840409C411yescharacteristic, complemented
62#16840407C411yescharacteristic, complemented
63#16840353—21no—
64#16840348—21no—
65#16840320—21no—
66#16840297C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840272C2211yescharacteristic
70C2×#14519757C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, 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×#11758222C2×C411yescharacteristic, complemented
108C2×#11758224C2×C411yescharacteristic, complemented
109C22×Dic122C2×C411yescharacteristic
110C2×D4×D61—21no—
111C2×D4×D61C2×C411yescharacteristic
112C2×D4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769—21no—
121#14519768—21no—
122#14519768C2×C411yescharacteristic, complemented
123#14519765C2×C411yescharacteristic, complemented
124#14519764C2×C411yescharacteristic, complemented
125#14519763—21no—
126#14519763—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519761—21no—
131#14519761—21no—
132#14519759—21no—
133#14519759—21no—
134#14519759—21no—
135#14519759—21no—
136#14519757—21no—
137#14519757—21no—
138#14519757C2×C411yescharacteristic
139#14519757C2×C411yescharacteristic
140#14519757C2×C411yescharacteristic, complemented
141#14519757C2311yescharacteristic
142#14519757C2311yescharacteristic
143#14519756C2×C411yescharacteristic, complemented
144#14519755—21no—
145#14519754—21no—
146#14519752C2×C411yescharacteristic, complemented
147#14519752C2311yescharacteristic
148#14519751—21no—
149#14519751—21no—
150#14519751C2×C411yescharacteristic
151#14519750—21no—
152#14519749—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748—21no—
156#14519748C2311yescharacteristic
157#14519747—21no—
158#14519747—21no—
159#14519745—21no—
160#14519745—21no—
161C4×Dic122C2×C411yescharacteristic, complemented
162#14519742C2×C411yescharacteristic, complemented
163C4×D244—21no—
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61D411yescharacteristic
169#14519739—21no—
170#14519739C2×C411yescharacteristic, complemented
171#14519739D411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519736—21no—
181#14519735—21no—
182#14519735—21no—
183#14519735C2×C411yescharacteristic, complemented
184#14519734—21no—
185C2×C4⋊Dic61—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
195#126×C61—21no—
196#125×C61C2×C411yescharacteristic, complemented
197#123×C61—21no—
198#121×C61—21no—
199#121×C61C2×C411yescharacteristic
200#121×C61C2×C411yescharacteristic, complemented
201C4×D4×C61—21no—
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic, complemented
204#117×C61C2×C411yescharacteristic, complemented
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61—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—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
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⋊D61C22⋊C411yescharacteristic
230C2×C22⋊D61C22⋊C411yescharacteristic
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235#11758224—81no—
236D4×D61—22no—
237D4×D61—22no—
238D4×D61—42no—
239D4×D61—42no—
240D4×D61—81no—
241#11758222—81no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244C22⋊C411yescharacteristic
245C2×D244C22×C411yescharacteristic
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—81no—
250C2×C4×D61—81no—
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C22×C411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2411yescharacteristic
260C2×Dic122—21no—
261C2×Dic122—81no—
262C2×Dic122C22×C411yescharacteristic
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×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61C22⋊C411yescharacteristic
290C22⋊C4×C61C22⋊C411yescharacteristic
291C42×C61—21no—
292C42×C61C22×C411yescharacteristic
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
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#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61C22⋊C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
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—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—42no—
347C22×D61—81no—
348C22×D61—81no—
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—
367D4×C61—22no—
368D4×C61—41no—
369D4×C61—42no—
370D4×C61—81no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—81no—
377C2×C4×C61—81no—
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C23×C411yescharacteristic
383C22⋊D61—22no—
384C22⋊D61—22no—
385C22⋊D61—42no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C22⋊D61—81no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403D244—22no—
404D244—41no—
405D244—41no—
406D244—41no—
407D244—81no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—42no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—41no—
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#41612yes—
438C22×C61C22×C22⋊C411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—162no—
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—
468C4×C61—41no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
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#288311yescharacteristic
496C2×C61C2×#41611yescharacteristic
497C2×C61#290111yescharacteristic
498D61—21no—
499D61—21no—
500D61—22no—
501D61—41no—
502D61—81no—
503#553—611no—
504#553—1221no—
505#553—1221no—
506#553#692311yescharacteristic, complemented
507#552—611no—
508#552—611no—
509#551—1221no—
510#551—1221no—
511#548—611no—
512#548—611no—
513#546—611no—
514#546—611no—
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×#41—611no—
565C22×Q8—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C22×C8—1221no—
576#126—21no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#126—1221no—
581#126—1221no—
582#125—611no—
583#125—1221no—
584#125—1221no—
585#125C2×#692311yescharacteristic, complemented
586#124—611no—
587#124—611no—
588#124—1221no—
589#124—1221no—
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—611no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610#121—21no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—611no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121C2×#692311yescharacteristic
623#121C2×#692311yescharacteristic, complemented
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×Q8—611no—
629C4×Q8—611no—
630C4×D4—21no—
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
649C4×D4C2×#692311yescharacteristic, complemented
650#117—611no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655#117C2×#692311yescharacteristic, complemented
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4C2×#692311yescharacteristic
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—
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—611no—
695C24—611no—
696C24—1221no—
697#41—4881no—
698#41—4881no—
699C2×Q8—611no—
700C2×Q8—611no—
701C2×Q8—1221no—
702C2×Q8—4881no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1222no—
713C2×D4—1222no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—4881no—
719C2×D4—2442no—
720C2×D4—2442no—
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—21no—
762C4⋊C4—21no—
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—4881no—
779C4⋊C4C22⋊#692311yescharacteristic
780C4⋊C4C22×#692311yescharacteristic
781C4⋊C4C22×#692311yescharacteristic
782C4⋊C4C22×#692311yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
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—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—4881no—
810C22⋊C4—2442no—
811C22⋊C4—2442no—
812C22⋊C4C22⋊#692311yescharacteristic
813C22⋊C4C22⋊#692311yescharacteristic
814C42—21no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—4881no—
822C42—2442no—
823C42C22×#692311yescharacteristic
824C23—21no—
825C23—611no—
826C23—611no—
827C23—612no—
828C23—612no—
829C23—611no—
830C23—1221no—
831C23—1221no—
832C23—1221no—
833C23—4881no—
834C23—4881no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23C2×C22⋊#692311yescharacteristic
841C23C2×C22⋊#692311yescharacteristic
842Q8—4881no—
843Q8—2441no—
844Q8—2441no—
845D4—22no—
846D4—41no—
847D4—42no—
848D4—81no—
849D4—1222no—
850D4—1222no—
851D4—1222no—
852D4—4881no—
853D4—4881no—
854D4—4881no—
855D4—4881no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2442no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1222no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4884no—
884C2×C4—4881no—
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—2442no—
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—2441no—
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—611no—
925C22—611no—
926C22—612no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—9762no—
935C22—4881no—
936C22—4881no—
937C22—2442no—
938C22—2442no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22#1684075212yes—
943C22C22×C22⋊#692311yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—4881no—
958C4—4881no—
959C4—4881no—
960C4—2442no—
961C4—2441no—
962C4—2441no—
963C4—2441no—
964C2—22no—
965C2—41no—
966C2—81no—
967C2—1221no—
968C2—1221no—
969C2—1222no—
970C2—4881no—
971C2—2441no—
972C2#2146241911yescharacteristic
973C2C2×#1684075211yescharacteristic
974C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459648C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#17615
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462667C2semidirect
2. #21462336C2semidirect
3. #21461262C2semidirect
4. #21461261C2semidirect
5. #21461258C2semidirect
6. #21461254C2semidirect
7. #21461247C2semidirect
8. #21461244C2semidirect
9. #21461196C2semidirect
10. #21461195C2semidirect
11. #21461193C2semidirect
12. #21461190C2semidirect
13. C2×#16840615C2semidirect
14. D61⋊#327C2semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
23. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840707C22semidirect
30. #16840705C22semidirect
33. C4×C22⋊#6923C22semidirect
34. #16840698C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
40. #16840615C22semidirect
41. #16840615C22semidirect
42. #16840615C22semidirect
43. #16840615C22semidirect
53. #16840460C4semidirect
55. #16840451C4semidirect
56. #16840450C4semidirect
59. #16840421C4semidirect
60. #16840418C4semidirect
61. #16840409C4semidirect
62. #16840407C4semidirect
74. C61×#553C4semidirect
107. C2×#11758222C2×C4semidirect
108. C2×#11758224C2×C4semidirect
122. #14519768C2×C4semidirect
123. #14519765C2×C4semidirect
124. #14519764C2×C4semidirect
140. #14519757C2×C4semidirect
143. #14519756C2×C4semidirect
146. #14519752C2×C4semidirect
161. C4×Dic122C2×C4semidirect
162. #14519742C2×C4semidirect
170. #14519739C2×C4semidirect
183. #14519735C2×C4semidirect
196. #125×C61C2×C4semidirect
200. #121×C61C2×C4semidirect
203. C4×D4×C61C2×C4semidirect
204. #117×C61C2×C4semidirect
506. #553#6923semidirect
562. C61#17615semidirect
585. #125C2×#6923semidirect
623. #121C2×#6923semidirect
649. C4×D4C2×#6923semidirect
655. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626672
#214623362
#214612622
#214612612
#214612582
#214612542
#214612472
#214612442
#214611962
#214611952
#214611932
#214611902
C2×#168406152
D61⋊#3272
#214596482
#1761561