Finite Group Databasebeta

← #30610996

Subgroups — #30610996

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic, complemented
3#21461222C211yesmaximal, characteristic, complemented
4#21461218C211yesmaximal, characteristic, complemented
5#21461217C211yesmaximal, characteristic, complemented
6#21461212C211yesmaximal, characteristic, complemented
7#21461207C211yesmaximal, characteristic, complemented
8#21461206C211yesmaximal, characteristic, complemented
9#21461201C211yesmaximal, characteristic, complemented
10#21461197C211yesmaximal, characteristic, complemented
11#21461196C211yesmaximal, characteristic, complemented
12#21461193C211yesmaximal, characteristic, complemented
13D61⋊#328C211yesmaximal, characteristic, complemented
14C2×#16840615C211yesmaximal, characteristic, complemented
15#21459865C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17#16840795—21no—
18#16840793—21no—
19#16840792—21no—
20#16840789—21no—
21#16840785C2211yescharacteristic
22#16840780C2211yescharacteristic
23#16840734C2211yescharacteristic
24#16840733C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26D61⋊(C22⋊C8)C2211yescharacteristic
27C4⋊C4×#6923—21no—
28C4×C4⋊#6923C2211yescharacteristic
29C22⋊C4×#6923—21no—
30C22⋊C4×#6923—21no—
31C4×C22⋊#6923C2211yescharacteristic
32C4×C22⋊#6923C2211yescharacteristic
33#16840698C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840615C2211yescharacteristic
45#16840615C2211yescharacteristic
46#16840615C2211yescharacteristic
47#16840615C2211yescharacteristic
48#16840614C2211yescharacteristic
49#16840614C2211yescharacteristic
50#16840614C2211yescharacteristic
51#16840614C2211yescharacteristic
52#16840480C411yescharacteristic, complemented
53#16840468—21no—
54#16840450C411yescharacteristic, complemented
55#16840437—21no—
56#16840436—21no—
57#16840425C411yescharacteristic, complemented
58#16840424C411yescharacteristic, complemented
59#16840421C411yescharacteristic, complemented
60#16840414C411yescharacteristic, complemented
61#16840413C411yescharacteristic, complemented
62#16840404—21no—
63#16840378—21no—
64#16840360—21no—
65#16840356—21no—
66#16840316C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840274C2211yescharacteristic
70C2×#14519757C2211yescharacteristic
71C22⋊Q8×D61C2211yescharacteristic
72#16840242—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#552C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81D4×#6923—28no—
82C2×C4⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89#14519844—21no—
90#14519844—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99#14519832—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108C2×#11758226C2×C411yescharacteristic, complemented
109C2×#11758222—21no—
110C2×#11758222C2×C411yescharacteristic, complemented
111C22×Dic122C2×C411yescharacteristic, complemented
112C2×Q8×D61C2×C411yescharacteristic, complemented
113C2×D4×D61D411yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116#14519776—21no—
117#14519776C2×C411yescharacteristic, complemented
118#14519775C2×C411yescharacteristic, complemented
119#14519772—21no—
120#14519772—21no—
121#14519771—21no—
122#14519770—21no—
123#14519768—21no—
124#14519767—21no—
125#14519765—21no—
126#14519765C2×C411yescharacteristic, complemented
127#14519763—21no—
128#14519763—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519762—21no—
134#14519761—21no—
135#14519760—21no—
136#14519759—21no—
137#14519757—21no—
138#14519757—21no—
139#14519757—21no—
140#14519757C2×C411yescharacteristic, complemented
141#14519757C2×C411yescharacteristic, complemented
142#14519757C2×C411yescharacteristic, complemented
143#14519757C2311yescharacteristic
144#14519757C2311yescharacteristic
145#14519756C2×C411yescharacteristic, complemented
146#14519755—21no—
147#14519755—21no—
148#14519755—21no—
149#14519755—21no—
150#14519755—21no—
151#14519754—21no—
152#14519754—21no—
153#14519753C2311yescharacteristic
154#14519752—21no—
155#14519752C2×C411yescharacteristic, complemented
156#14519752C2311yescharacteristic
157#14519751C2×C411yescharacteristic, complemented
158#14519750—21no—
159#14519749—21no—
160#14519747—21no—
161#14519747—21no—
162C4×Dic122—21no—
163C4×Dic122—21no—
164C4×Dic122C2×C411yescharacteristic, complemented
165#14519742C2×C411yescharacteristic, complemented
166C4×D244—21no—
167C4×D244—21no—
168C4×D244—21no—
169C4×D244C2×C411yescharacteristic
170D4×Dic61D411yescharacteristic
171#14519739—21no—
172#14519739—21no—
173#14519739C2×C411yescharacteristic, complemented
174#14519739D411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519735—21no—
183#14519735—21no—
184#14519735C2×C411yescharacteristic, complemented
185#14519734—21no—
186C2×C4⋊Dic61—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61C2×C411yescharacteristic, complemented
190C4⋊C4×D61D411yescharacteristic
191C2×#11758198—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61D411yescharacteristic
194C22⋊C4×D61D411yescharacteristic
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61—21no—
198#125×C61C2×C411yescharacteristic, complemented
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201C22⋊Q8×C61C2×C411yescharacteristic, complemented
202C4×Q8×C61C2×C411yescharacteristic, complemented
203C4×D4×C61C2×C411yescharacteristic
204#117×C61—21no—
205#117×C61C2×C411yescharacteristic, complemented
206C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—24no—
214C22×#6923—24no—
215C22×#6923—81no—
216C22×#6923—81no—
217C22×#6923—81no—
218C22×#6923—81no—
219C2×Q8×C61C22×C411yescharacteristic
220C2×D4×C61C22⋊C411yescharacteristic
221C22×C4×C61—21no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61C22⋊C411yescharacteristic
227C2×C22⋊D61C22⋊C411yescharacteristic
228C22×Dic61—21no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758226—81no—
232Q8×D61—81no—
233D4×D61—24no—
234#11758222—44no—
235#11758222—81no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C22⋊C411yescharacteristic
240C2×D244C22×C411yescharacteristic
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—81no—
247C2×C4×D61—81no—
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C22×C411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2411yescharacteristic
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122—21no—
260C2×Dic122—81no—
261C2×Dic122C22×C411yescharacteristic
262C2×Dic122C22×C411yescharacteristic
263C22⋊#6923—24no—
264C22⋊#6923—24no—
265#11758217—81no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—81no—
271C4⋊#6923—24no—
272C4×#6923—24no—
273C4×#6923—81no—
274C4×#6923—81no—
275C4×#6923—81no—
276#11758213—81no—
277D61⋊C8—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61C22⋊C411yescharacteristic
292C22⋊C4×C61C22⋊C411yescharacteristic
293C42×C61—21no—
294C42×C61—21no—
295C42×C61C22×C411yescharacteristic
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#11758198—21no—
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
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#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333C4×Dic61—21no—
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61C22×C411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C23×C61C2×C22⋊C411yescharacteristic
340C23×C61C2×C22⋊C411yescharacteristic
341C22×D61—22no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—22no—
347C22×D61—21no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61C22×D411yescharacteristic
353C2×#6923—22no—
354C2×#6923—22no—
355C2×#6923—22no—
356C2×#6923—22no—
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—84no—
366C2×#6923—84no—
367Q8×C61—41no—
368D4×C61—22no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—42no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C23×C411yescharacteristic
381C22⋊D61—22no—
382C22⋊D61—42no—
383C22⋊D61—81no—
384C22⋊D61#10414yes—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—81no—
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C22×D411yescharacteristic
396D244—22no—
397D244—41no—
398D244—41no—
399D244—41no—
400D244—42no—
401D244—81no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—22no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—42no—
413C4×D61—42no—
414C4×D61—81no—
415C4×D61—81no—
416C4×D61—81no—
417Dic122—42no—
418Dic122—41no—
419Dic122—41no—
420Dic122—81no—
421Dic122—81no—
422#92420—41no—
423#92420—41no—
424#92420—41no—
425#92420—41no—
426#17548—611nomaximal, Sylow
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61C2×#10412yes—
433C22×C61C22×C22⋊C411yescharacteristic
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61C2×#10412yes—
449C2×D61#57711yescharacteristic
450C2×D61#57811yescharacteristic
451#6923—42no—
452#6923—42no—
453#6923—42no—
454#6923—42no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—41no—
464Dic61—21no—
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—41no—
469Dic61—41no—
470Dic61—41no—
471Dic61C2×#10412yes—
472#3520—611no—
473#2974—611no—
474#2275—611no—
475#1509—611no—
476#1508—611no—
477#1508—611no—
478#1506—611no—
479#1504—611no—
480#1504—611no—
481#1503—611no—
482#1501—611no—
483#1501—611no—
484#1500—611no—
485C2×#328—611no—
486C2×#328—611no—
487C2×C61—22no—
488C2×C61—41no—
489C2×C61#288311yescharacteristic
490C2×C61#289811yescharacteristic
491C2×C61C22×#10411yescharacteristic
492D61—21no—
493D61—21no—
494D61—22no—
495D61—41no—
496D61—81no—
497#556—611no—
498#554—1221no—
499#552—611no—
500#552#692311yescharacteristic, complemented
501#551—1221no—
502#551—1221no—
503D4×Q8—611no—
504#548—611no—
505#548—611no—
506#547—611no—
507#547—611no—
508#546—1221no—
509#542—1221no—
510#539—1221no—
511#539—1221no—
512#533—611no—
513#529—611no—
514#525—611no—
515#525—611no—
516C2×C22⋊Q8—611no—
517C2×C22⋊Q8—611no—
518#520—1221no—
519C2×C4×D4—611no—
520C2×C4×D4—1221no—
521#436—1221no—
522#435—1221no—
523#435—1221no—
524C8×D4—1221no—
525#432—611no—
526#431—611no—
527#407—611no—
528#407—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C4×C4⋊C4—611no—
532C4×C4⋊C4—1221no—
533C4×C22⋊C4—611no—
534C4×C22⋊C4—611no—
535C4×C22⋊C4—1221no—
536C4×C22⋊C4—1221no—
537#376—611no—
538C2×#95—611no—
539C2×#95—611no—
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#327—611no—
553#327—611no—
554#327—611no—
555#327—611no—
556C61#1754811yescharacteristic, complemented, Sylow
557C2×#41—611no—
558C2×#41—611no—
559C2×#41—1221no—
560C22×Q8—611no—
561C22×Q8—611no—
562C22×D4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—1221no—
566C23×C4—1221no—
567C2×M16—1221no—
568C2×M16—1221no—
569C22×C8—1221no—
570C22×C8—1221no—
571C4⋊Q8—611no—
572C4⋊Q8—611no—
573C4⋊Q8—1221no—
574#126—21no—
575#126—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#125—21no—
580#125—1221no—
581#125—1221no—
582#125C2×#692311yescharacteristic, complemented
583#124—611no—
584#124—1221no—
585#124—1221no—
586#124—1221no—
587#123—21no—
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596C22⋊Q8—611no—
597C22⋊Q8—611no—
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⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8C2×#692311yescharacteristic, complemented
614C22⋊Q8C2×#692311yescharacteristic, complemented
615#121—611no—
616#121—611no—
617#121—611no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#120—1221no—
622#120—1221no—
623C4×Q8—611no—
624C4×Q8—611no—
625C4×Q8—1221no—
626C4×Q8—1221no—
627C4×Q8C2×#692311yescharacteristic, complemented
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—1228no—
644C4×D4—1221no—
645C4×D4C2×#692311yescharacteristic
646#117—21no—
647#117—611no—
648#117—1221no—
649#117—1221no—
650#117—1221no—
651#117C2×#692311yescharacteristic, complemented
652C2×C4⋊C4—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4C2×#692311yescharacteristic, complemented
659C2×C22⋊C4—611no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C42—611no—
666C2×C42—1221no—
667C2×C42—1221no—
668C2×C42—1221no—
669C2×C42—1221no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C22⋊C8—611no—
673C22⋊C8—611no—
674C22⋊C8—611no—
675C22⋊C8—611no—
676C22⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680#97—1221no—
681C4×C8—1221no—
682#95—611no—
683#95—611no—
684#95—611no—
685#95—611no—
686#95—1221no—
687#95—1221no—
688#95—1221no—
689C24—611no—
690C24—611no—
691#41—4881no—
692#41—4881no—
693#41—2444no—
694C2×Q8—611no—
695C2×Q8—611no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—4881no—
700C2×Q8—4881no—
701C2×Q8C22×#692311yescharacteristic
702C2×D4—611no—
703C2×D4—611no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1224no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4C22⋊#692311yescharacteristic
713C22×C4—21no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1224no—
730C22×C4—1224no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—4881no—
738C22×C4—4881no—
739C22×C4—4881no—
740C22×C4—4881no—
741C22×C4—4881no—
742C22×C4—4881no—
743C22×C4C22×#692311yescharacteristic
744C22×C4C22×#692311yescharacteristic
745M16—4881no—
746M16—4881no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—4881no—
752C2×C8—4881no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
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—1224no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4C22⋊#692311yescharacteristic
778C4⋊C4C22×#692311yescharacteristic
779C4⋊C4C22×#692311yescharacteristic
780C4⋊C4C22×#692311yescharacteristic
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—1224no—
801C22⋊C4—1224no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4C22⋊#692311yescharacteristic
807C22⋊C4C22⋊#692311yescharacteristic
808C42—21no—
809C42—21no—
810C42—611no—
811C42—611no—
812C42—611no—
813C42—1221no—
814C42—1221no—
815C42—1224no—
816C42—1221no—
817C42—4881no—
818C42—4881no—
819C42—4881no—
820C42C22×#692311yescharacteristic
821C23—611no—
822C23—611no—
823C23—611no—
824C23—1222no—
825C23—1221no—
826C23—1221no—
827C23—1221no—
828C23—1221no—
829C23—1222no—
830C23—1221no—
831C23—2441no—
832C23—2441no—
833C23C2×C22⋊#692311yescharacteristic
834C23C2×C22⋊#692311yescharacteristic
835Q8—41no—
836Q8—4881no—
837Q8—4881no—
838Q8—2441no—
839Q8—2441no—
840Q8—2442no—
841D4—22no—
842D4—614no—
843D4—1222no—
844D4—1222no—
845D4—4881no—
846D4—4881no—
847D4—2441no—
848D4—2441no—
849D4—2441no—
850D4—2442no—
851D4—2442no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—1222no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—4881no—
875C2×C4—4881no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—4884no—
879C2×C4—4884no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2442no—
888C2×C4—2442no—
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×C4C2×C22⋊#692311yescharacteristic
900C2×C4C2×C22⋊#692311yescharacteristic
901C2×C4C2×C22⋊#692311yescharacteristic
902C2×C4C2×C22⋊#692311yescharacteristic
903C2×C4C23×#692311yescharacteristic
904C8—2441no—
905C8—2441no—
906C8—2441no—
907C8—2441no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—611no—
914C22—611no—
915C22—612no—
916C22—1221no—
917C22—1221no—
918C22—1221no—
919C22—1221no—
920C22—1221no—
921C22—1221no—
922C22—1221no—
923C22—2442no—
924C22—2442no—
925C22—2442no—
926C22—2442no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22D61⋊#10412yes—
931C22C22×C22⋊#692311yescharacteristic
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—612no—
942C4—1221no—
943C4—1221no—
944C4—1221no—
945C4—1221no—
946C4—2442no—
947C4—2442no—
948C4—2442no—
949C4—2442no—
950C4—2441no—
951C4—2441no—
952C4—2441no—
953C2—22no—
954C2—41no—
955C2—1221no—
956C2—1221no—
957C2—1222no—
958C2—4881no—
959C2—2441no—
960C2#2146241911yescharacteristic
961C2#2146244111yescharacteristic
962C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#552C4
socleC22×C61C22×C22⋊C4
prime radical#21459865C2
cosocleC2×C4×D61C24
hypercenter#552#6923
hypocenterC61#17548
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462258C2semidirect
3. #21461222C2semidirect
4. #21461218C2semidirect
5. #21461217C2semidirect
6. #21461212C2semidirect
7. #21461207C2semidirect
8. #21461206C2semidirect
9. #21461201C2semidirect
10. #21461197C2semidirect
11. #21461196C2semidirect
12. #21461193C2semidirect
13. D61⋊#328C2semidirect
14. C2×#16840615C2semidirect
52. #16840480C4semidirect
54. #16840450C4semidirect
57. #16840425C4semidirect
58. #16840424C4semidirect
59. #16840421C4semidirect
60. #16840414C4semidirect
61. #16840413C4semidirect
74. C61×#552C4semidirect
108. C2×#11758226C2×C4semidirect
110. C2×#11758222C2×C4semidirect
111. C22×Dic122C2×C4semidirect
112. C2×Q8×D61C2×C4semidirect
117. #14519776C2×C4semidirect
118. #14519775C2×C4semidirect
126. #14519765C2×C4semidirect
140. #14519757C2×C4semidirect
141. #14519757C2×C4semidirect
142. #14519757C2×C4semidirect
145. #14519756C2×C4semidirect
155. #14519752C2×C4semidirect
157. #14519751C2×C4semidirect
164. C4×Dic122C2×C4semidirect
165. #14519742C2×C4semidirect
173. #14519739C2×C4semidirect
184. #14519735C2×C4semidirect
189. C4⋊C4×D61C2×C4semidirect
198. #125×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
201. C22⋊Q8×C61C2×C4semidirect
202. C4×Q8×C61C2×C4semidirect
205. #117×C61C2×C4semidirect
206. C2×C4⋊C4×C61C2×C4semidirect
500. #552#6923semidirect
556. C61#17548semidirect
582. #125C2×#6923semidirect
613. C22⋊Q8C2×#6923semidirect
614. C22⋊Q8C2×#6923semidirect
627. C4×Q8C2×#6923semidirect
651. #117C2×#6923semidirect
658. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214622582
#214612222
#214612182
#214612172
#214612122
#214612072
#214612062
#214612012
#214611972
#214611962
#214611932
D61⋊#3282
C2×#168406152
#214598652
#1754861