Finite Group Databasebeta

← #30552343

Subgroups — #30552343

Order 15616.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2#529×D61C211yesmaximal, characteristic
3#21457062C212yesmaximal, complemented
4#21457056C212yesmaximal, complemented
5#21457051C211yesmaximal, characteristic, complemented
6#21457046C211yesmaximal, characteristic, complemented
7#21457040C211yesmaximal, characteristic, complemented
8#21457003C212yesmaximal, complemented
9#21456997C212yesmaximal, complemented
10#21456990C212yesmaximal, complemented
11#21456984C212yesmaximal, complemented
12#21456370C212yesmaximal, complemented
13#21456204C212yesmaximal, complemented
14#21455762C212yesmaximal, complemented
15#21455754C212yesmaximal
16#21455625C212yesmaximal, complemented
17#21455617C212yesmaximal, complemented
18#21454449C211yesmaximal, characteristic, complemented
19C61×#3238C211yesmaximal, characteristic, complemented
20#16840317—21no—
21#16840317—21no—
22#16840317—21no—
23#16840317—21no—
24#16840317C2212yes—
25#16840317C2212yes—
26#16840317C2212yescomplemented
27#16840317C2212yescomplemented
28C2×#14519777C2211yescharacteristic, complemented
29#16840299C2211yescharacteristic
30#16840298C2211yescharacteristic
31#16840297C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840295—21no—
34#16840294C2211yescharacteristic
35#16840293C2211yescharacteristic
36#16840292—21no—
37#16840291C2211yescharacteristic
38#16840290—21no—
39#16840289—21no—
40#126×D61—21no—
41C2×#14519768C2212yescomplemented
42#125×D61C2211yescharacteristic
43#124×D61C2211yescharacteristic
44#123×D61—21no—
45C2×#14519757—21no—
46C2×#14519753—21no—
47C22⋊Q8×D61C2211yescharacteristic
48#121×D61C2211yescharacteristic
49C2×Q8×Dic61—21no—
50C2×#14519742—21no—
51C4×Q8×D61C2211yescharacteristic
52C4×D4×D61—21no—
53C4×D4×D61C2211yescharacteristic
54C2×#14519735C2212yes—
55#117×D61—21no—
56C2×C42×D61C2211yescharacteristic
57#16840172C2212yescomplemented
58#16840171C2212yescomplemented
59#16840168C2212yescomplemented
60#16840163C2214yescomplemented
61#16840162C2214yescomplemented
62#16840124C2212yescomplemented
63#16840122C2212yescomplemented
64#16840121C2212yescomplemented
65#16840118C2214yescomplemented
66#16840115C2214yescomplemented
67#16840106C2214yescomplemented
68#16840102C2214yescomplemented
69#16840098C2212yescomplemented
70#16840095C2212yescomplemented
71#16840092C2212yescomplemented
72#16840089C2214yes—
73#16840085C2214yes—
74#16840081C2212yes—
75#16840078C2212yes—
76#16840075C2212yes—
77#16840068C2214yescomplemented
78#16840067C2214yescomplemented
79#16840061C2214yescomplemented
80#16840060C2214yescomplemented
81#16840054C2212yescomplemented
82#16840049C2212yescomplemented
83#16840048C2212yescomplemented
84#16840047C2212yescomplemented
85#16840043C2212yescomplemented
86#16840042C2212yescomplemented
87#16839819C2211yescharacteristic, complemented
88#16839817C2212yescomplemented
89#16839814C2212yescomplemented
90#16839812C2212yescomplemented
91#16839803C2214yes—
92#16839801C2214yes—
93#16839784C2212yes—
94#16839769C2214yes—
95#16839765C2214yes—
96#16839724C2212yes—
97#16839714C2212yes—
98C2×C4⋊Q8×C61C2211yescharacteristic, complemented
99C61×#529C2211yescharacteristic
100C61×#501C2212yescomplemented
101C61×#489C2212yescomplemented
102C61×#483C2212yescomplemented
103C61×#480C2212yes—
104C61×#477C2212yescomplemented
105C61×#476C2212yescomplemented
106C61×#432C2211yescharacteristic, complemented
107C22×Dic122—21no—
108C2×Q8×D61C2311yescharacteristic
109C2×D4×D61—21no—
110C2×D4×D61C2311yescharacteristic
111C22×C4×D61—21no—
112C22×C4×D61D411yescharacteristic
113C22×C4×D61D411yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C2×#11758189C2314yes—
116#14519777—21no—
117#14519777—21no—
118#14519777C2312yes—
119#14519777C2312yes—
120#14519772—21no—
121#14519772—21no—
122#14519772—21no—
123#14519771—21no—
124#14519770—21no—
125#14519770—21no—
126#14519770—21no—
127#14519769C2311yescharacteristic
128#14519768—22no—
129#14519768—22no—
130#14519768C2311yescharacteristic
131#14519768C2311yescharacteristic
132#14519768C2314yes—
133#14519768C2314yes—
134#14519767—21no—
135#14519767—21no—
136#14519766C2311yescharacteristic
137#14519765C2311yescharacteristic
138#14519764C2311yescharacteristic
139#14519763—21no—
140#14519763—21no—
141#14519762—21no—
142#14519762—21no—
143#14519761—21no—
144#14519760—21no—
145#14519759—21no—
146#14519759—21no—
147#14519758—21no—
148#14519757—22no—
149#14519757—22no—
150#14519757—22no—
151#14519757—22no—
152#14519757C2311yescharacteristic
153#14519756C2311yescharacteristic
154#14519755—21no—
155#14519754—21no—
156#14519753—22no—
157#14519753—22no—
158#14519753—22no—
159#14519753—22no—
160#14519753C2311yescharacteristic
161#14519752C2311yescharacteristic
162#14519751C2311yescharacteristic
163#14519750—21no—
164#14519749—21no—
165#14519748C2311yescharacteristic
166Q8×Dic61—22no—
167Q8×Dic61—22no—
168Q8×Dic61—22no—
169Q8×Dic61—22no—
170Q8×Dic61C2311yescharacteristic
171C4×Dic122—21no—
172C4×Dic122C2311yescharacteristic
173#14519742—21no—
174#14519742—22no—
175#14519742—22no—
176#14519742—22no—
177#14519742—22no—
178#14519742C2311yescharacteristic
179C4×D244—21no—
180C4×D244C2311yescharacteristic
181D4×Dic61—21no—
182D4×Dic61C2311yescharacteristic
183#14519739—21no—
184#14519739C2311yescharacteristic
185C4×C22⋊D61—21no—
186C4×C22⋊D61—21no—
187C4×C22⋊D61—21no—
188#14519737—21no—
189#14519737—21no—
190#14519737—21no—
191#14519736—21no—
192#14519735—22no—
193#14519735—22no—
194#14519735—21no—
195#14519735—21no—
196#14519735C2314yes—
197#14519735C2314yes—
198#14519734—21no—
199#14519734—21no—
200#14519733—21no—
201#14519733—21no—
202C2×C4⋊Dic61—21no—
203C2×C4⋊Dic61—22no—
204C2×C4⋊Dic61C2312yes—
205C2×#11758196—22no—
206C4⋊C4×D61—21no—
207C4⋊C4×D61—21no—
208C4⋊C4×D61—21no—
209C4⋊C4×D61—21no—
210C4⋊C4×D61C2311yescharacteristic
211C4⋊C4×D61C2311yescharacteristic
212C2×#11758198—22no—
213C22⋊C4×D61—21no—
214C22⋊C4×D61—21no—
215C22⋊C4×D61—21no—
216C22⋊C4×D61—21no—
217C22⋊C4×D61—21no—
218C2×C4×Dic61—22no—
219C2×C4×Dic61D411yescharacteristic
220C2×C4×Dic61D411yescharacteristic
221C2×C4×Dic61C2311yescharacteristic
222C42×D61—21no—
223C42×D61D411yescharacteristic
224C42×D61D411yescharacteristic
225C42×D61D411yescharacteristic
226C42×D61D411yescharacteristic
227C42×D61C2311yescharacteristic
228C42×D61C2311yescharacteristic
229C42×D61C2311yescharacteristic
230C42×D61C2311yescharacteristic
231#14519711C2314yes—
232#14519710C2314yes—
233#14519710C2314yes—
234#14519709C2314yes—
235#14519708C2314yes—
236#14519708C2314yes—
237C4⋊#92418C2312yes—
238#14519706C2314yes—
239#14519702C2314yes—
240#14519701C2314yes—
241#14519700C2314yes—
242#14519699C2314yes—
243#14519698C2314yes—
244#14519697C2314yes—
245C22⋊#92418C2312yes—
246#14519689C2314yes—
247#14519688C2312yes—
248C8×Dic61C2314yes—
249C22×Q8×C61—21no—
250C4⋊Q8×C61—21no—
251C4⋊Q8×C61—21no—
252C4⋊Q8×C61C2312yes—
253C4⋊Q8×C61C2312yes—
254#126×C61—21no—
255#125×C61C2311yescharacteristic
256#124×C61C2311yescharacteristic
257#123×C61—21no—
258C22⋊Q8×C61C2311yescharacteristic
259#121×C61C2311yescharacteristic
260C4×Q8×C61C2311yescharacteristic
261C4×D4×C61—21no—
262C4×D4×C61C2311yescharacteristic
263#117×C61—21no—
264C2×C4⋊C4×C61—21no—
265C2×C4⋊C4×C61C2312yes—
266C2×C42×C61C2311yescharacteristic
267#107×C61C2314yes—
268#106×C61C2314yes—
269C4⋊C8×C61C2312yes—
270#103×C61C2314yes—
271#102×C61C2314yes—
272C22⋊C8×C61C2312yes—
273#97×C61C2312yes—
274C23×D61—21no—
275C23×D61C2×D411yescharacteristic
276C2×Q8×C61—22no—
277C2×Q8×C61—22no—
278C2×Q8×C61—44no—
279C2×Q8×C61C2411yescharacteristic
280C2×D4×C61—21no—
281C2×D4×C61C2411yescharacteristic
282C22×C4×C61—22no—
283C22×C4×C61—21no—
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2411yescharacteristic
287C2×C22⋊D61—21no—
288C2×C22⋊D61—21no—
289C2×C22⋊D61—21no—
290C22×Dic61—22no—
291C22×Dic61—21no—
292C22×Dic61C2×D411yescharacteristic
293C22×Dic61C2×D411yescharacteristic
294C22×Dic61C2×D411yescharacteristic
295Q8×D61—24no—
296D4×D61—24no—
297D4×D61—44no—
298C2×D244—21no—
299C2×D244C2411yescharacteristic
300C2×C4×D61—24no—
301C2×C4×D61—21no—
302C2×C4×D61—21no—
303C2×C4×D61—21no—
304C2×C4×D61—21no—
305C2×C4×D61—21no—
306C2×C4×D61—42no—
307C2×C4×D61—44no—
308C2×C4×D61—42no—
309C2×C4×D61C2×D411yescharacteristic
310C2×C4×D61C2×D411yescharacteristic
311C2×C4×D61C2×D411yescharacteristic
312C2×C4×D61C2×D411yescharacteristic
313C2×C4×D61C2×D411yescharacteristic
314C2×C4×D61C2×D411yescharacteristic
315C2×C4×D61C2×D411yescharacteristic
316C2×C4×D61C2×D411yescharacteristic
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2411yescharacteristic
320C2×C4×D61C2411yescharacteristic
321C2×Dic122—22no—
322C2×Dic122—22no—
323C2×Dic122—21no—
324C2×Dic122—44no—
325C2×Dic122C2411yescharacteristic
326C2×C8×C61C2414yes—
327C4⋊C4×C61—22no—
328C4⋊C4×C61—22no—
329C4⋊C4×C61—22no—
330C4⋊C4×C61—21no—
331C4⋊C4×C61—21no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61C2414yes—
335C4⋊C4×C61C2411yescharacteristic
336C4⋊C4×C61C2411yescharacteristic
337C22⋊C4×C61—21no—
338C22⋊C4×C61—21no—
339C22⋊C4×C61—21no—
340C22⋊C4×C61—21no—
341C22⋊C4×C61—21no—
342C42×C61—21no—
343C42×C61C2×D411yescharacteristic
344C42×C61C2×D411yescharacteristic
345C42×C61C2411yescharacteristic
346C42×C61C2411yescharacteristic
347C22⋊Dic61—21no—
348C22⋊Dic61—21no—
349C22⋊Dic61—21no—
350C22⋊Dic61—21no—
351C22⋊Dic61—21no—
352#11758198—21no—
353#11758198—21no—
354#11758198—24no—
355#11758198—24no—
356#11758198—21no—
357#11758198—21no—
358#11758198—21no—
359#11758198—21no—
360#11758198—21no—
361#11758198—21no—
362#11758198—21no—
363#11758198—21no—
364C4⋊Dic61—22no—
365C4⋊Dic61—22no—
366C4⋊Dic61—22no—
367C4⋊Dic61—21no—
368C4⋊Dic61—21no—
369C4⋊Dic61—21no—
370C4⋊Dic61—21no—
371C4⋊Dic61—24no—
372C4⋊Dic61—24no—
373C4⋊Dic61C2414yes—
374C4⋊Dic61C2411yescharacteristic
375C4⋊Dic61C2411yescharacteristic
376#11758196—21no—
377#11758196—21no—
378#11758196—21no—
379#11758196—21no—
380#11758196—21no—
381#11758196—21no—
382#11758196—21no—
383#11758196—21no—
384#11758196—21no—
385#11758196—21no—
386#11758196—24no—
387#11758196—24no—
388C4×Dic61—21no—
389C4×Dic61—21no—
390C4×Dic61—21no—
391C4×Dic61—24no—
392C4×Dic61—24no—
393C4×Dic61C2×D411yescharacteristic
394C4×Dic61C2×D411yescharacteristic
395C4×Dic61C2×D411yescharacteristic
396C4×Dic61C2×D411yescharacteristic
397C4×Dic61C2×D411yescharacteristic
398C4×Dic61C2×D411yescharacteristic
399C4×Dic61C2×D411yescharacteristic
400C4×Dic61C2×D411yescharacteristic
401C4×Dic61C2×D411yescharacteristic
402C4×Dic61C2×D411yescharacteristic
403C4×Dic61C2411yescharacteristic
404C4×Dic61C2411yescharacteristic
405C2×#92418C2414yes—
406#11758189—28no—
407C23×C61—21no—
408C23×C61C22×D411yescharacteristic
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—21no—
412C22×D61—41no—
413C22×D61—42no—
414C22×D61—42no—
415C22×D61—42no—
416C22×D61C22×D411yescharacteristic
417C22×D61C22×D411yescharacteristic
418Q8×C61—22no—
419Q8×C61—44no—
420Q8×C61—44no—
421D4×C61—22no—
422D4×C61—42no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—24no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—44no—
431C2×C4×C61—42no—
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C22×D411yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C22×D411yescharacteristic
437C2×C4×C61C2511yescharacteristic
438C22⋊D61—42no—
439C22⋊D61—42no—
440C22⋊D61—42no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—24no—
446C2×Dic61—21no—
447C2×Dic61—41no—
448C2×Dic61—42no—
449C2×Dic61—44no—
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452C2×Dic61C22×D411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454C2×Dic61C22×D411yescharacteristic
455C2×Dic61C22×D411yescharacteristic
456D244—22no—
457D244—42no—
458C4×D61—22no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—41no—
464C4×D61—41no—
465C4×D61—41no—
466C4×D61—41no—
467C4×D61—41no—
468C4×D61—41no—
469C4×D61—42no—
470C4×D61—42no—
471C4×D61—42no—
472C4×D61—42no—
473C4×D61—42no—
474C4×D612−1+414yes—
475Dic122—22no—
476Dic122—44no—
477Dic122—44no—
478Dic122—42no—
479C8×C61—24no—
480#92418—24no—
481#60866—611nomaximal, Sylow
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61#57512yes—
488C22×C61C23×D411yescharacteristic
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—44no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61—84no—
499C2×D61#53612yes—
500C4×C61—21no—
501C4×C61—21no—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61—41no—
505C4×C61—41no—
506C4×C61—41no—
507C4×C61—44no—
508C4×C61#57512yes—
509C4×C61C2×2−1+412yes—
510Dic61—21no—
511Dic61—21no—
512Dic61—21no—
513Dic61—21no—
514Dic61—21no—
515Dic61—41no—
516Dic61—44no—
517Dic61—41no—
518Dic61—41no—
519Dic61#53612yes—
520C2×#533—611no—
521C2×#529—611no—
522#3240—612no—
523#3240—612no—
524#3239—611no—
525#3239—611no—
526#3238—611no—
527#3238D6111yescharacteristic, complemented
528#3233—612no—
529#3233—612no—
530#3232—612no—
531#3232—612no—
532#3166—612no—
533#3140—612no—
534#3095—612no—
535#3094—612no—
536#3078—612no—
537#3077—612no—
538#2920—611no—
539C2×C61—22no—
540C2×C61—81no—
541C2×C61C2×#53611yescharacteristic
542C2×C61C2×#57511yescharacteristic
543C2×C61C2×#57511yescharacteristic
544D61—22no—
545D61—41no—
546D61—81no—
547#533—612no—
548#533—612no—
549#533—612no—
550#533—612no—
551#533—1221no—
552#533—1221no—
553#533—1221no—
554#533—1221no—
555C2×C4⋊Q8—611no—
556C2×C4⋊Q8C2×D6111yescharacteristic, complemented
557#529—611no—
558#529—611no—
559#529—611no—
560#529—611no—
561#529—611no—
562#529—611no—
563#529—611no—
564#529—1221no—
565#529—1221no—
566#529—1221no—
567#529—1221no—
568#529C2×D6111yescharacteristic
569C2×#126—1221no—
570C2×#125—611no—
571C2×#125—612no—
572C2×#124—611no—
573C2×#123—1221no—
574C2×C22⋊Q8—611no—
575C2×C22⋊Q8—1221no—
576C2×C22⋊Q8—1221no—
577C2×#121—611no—
578C2×C4×Q8—611no—
579C2×C4×Q8—1221no—
580C2×C4×Q8—1221no—
581C2×C4×D4—611no—
582C2×C4×D4—1221no—
583C2×#117—612no—
584C2×#117—1221no—
585C22×C42—611no—
586#501—612no—
587#501—612no—
588#501—612no—
589#501C2×D6112yescomplemented
590#499—614no—
591#499—614no—
592#489—612no—
593#489—612no—
594#489—612no—
595#489C2×D6112yescomplemented
596#488—614no—
597#488—614no—
598#485—614no—
599#485—614no—
600#484—612no—
601#484—612no—
602#483—612no—
603#483C2×D6112yescomplemented
604#482—614no—
605#482—614no—
606#481—612no—
607#481—612no—
608#480—612no—
609#480C2×D6112yes—
610#479—614no—
611#479—614no—
612#478—614no—
613#478—614no—
614#477—612no—
615#477C2×D6112yescomplemented
616#476—612no—
617#476C2×D6112yescomplemented
618#475—612no—
619#475—612no—
620#474—612no—
621#474—612no—
622#432—611no—
623#432—612no—
624#432C2×D6111yescharacteristic, complemented
625#431—612no—
626#431—612no—
627#428—614no—
628#428—614no—
629#423—612no—
630#419—614no—
631#418—614no—
632#407—612no—
633C4×M16—612no—
634C61#6086611yescharacteristic, complemented, Sylow
635C22×Q8—21no—
636C22×Q8—611no—
637C22×Q8—1221no—
638C22×D4—611no—
639C22×D4—1221no—
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C23×C4—1221no—
644C2×M16—614no—
645C4⋊Q8—21no—
646C4⋊Q8—21no—
647C4⋊Q8—612no—
648C4⋊Q8—612no—
649C4⋊Q8—1221no—
650C4⋊Q8—1221no—
651C4⋊Q8C22×D6112yes—
652C4⋊Q8C22×D6112yes—
653#126—21no—
654#126—1221no—
655#126—1221no—
656#126—1221no—
657#126—1221no—
658#126—1221no—
659#126—1221no—
660#126—1221no—
661#125—611no—
662#125—611no—
663#125—614no—
664#125—614no—
665#125—611no—
666#125—1221no—
667#125—1221no—
668#125—1222no—
669#125—1222no—
670#125C22×D6111yescharacteristic
671#124—611no—
672#124—611no—
673#124—611no—
674#124—1221no—
675#124—1221no—
676#124C22×D6111yescharacteristic
677#123—21no—
678#123—1221no—
679#123—1221no—
680#123—1221no—
681#123—1221no—
682#123—1221no—
683#123—1221no—
684#123—1221no—
685C22⋊Q8—611no—
686C22⋊Q8—611no—
687C22⋊Q8—611no—
688C22⋊Q8—1221no—
689C22⋊Q8—1221no—
690C22⋊Q8—1222no—
691C22⋊Q8—1222no—
692C22⋊Q8—1222no—
693C22⋊Q8—1222no—
694C22⋊Q8—1222no—
695C22⋊Q8—1222no—
696C22⋊Q8—1222no—
697C22⋊Q8—1222no—
698C22⋊Q8C22×D6111yescharacteristic
699#121—611no—
700#121—611no—
701#121—611no—
702#121—1221no—
703#121—1221no—
704#121C22×D6111yescharacteristic
705C4×Q8—611no—
706C4×Q8—611no—
707C4×Q8—611no—
708C4×Q8—1221no—
709C4×Q8—1221no—
710C4×Q8—1222no—
711C4×Q8—1222no—
712C4×Q8—1222no—
713C4×Q8—1222no—
714C4×Q8—1222no—
715C4×Q8—1222no—
716C4×Q8—1222no—
717C4×Q8—1222no—
718C4×Q8C22×D6111yescharacteristic
719C4×D4—21no—
720C4×D4—611no—
721C4×D4—611no—
722C4×D4—611no—
723C4×D4—1221no—
724C4×D4—1221no—
725C4×D4—1221no—
726C4×D4—1221no—
727C4×D4—1221no—
728C4×D4—1221no—
729C4×D4—1221no—
730C4×D4—1221no—
731C4×D4—1221no—
732C4×D4C22×D6111yescharacteristic
733#117—21no—
734#117—614no—
735#117—614no—
736#117—1221no—
737#117—1221no—
738#117—1221no—
739#117—1221no—
740#117—1221no—
741#117—1221no—
742#117—1222no—
743#117—1222no—
744#117—1221no—
745C2×C4⋊C4—21no—
746C2×C4⋊C4—612no—
747C2×C4⋊C4—611no—
748C2×C4⋊C4—611no—
749C2×C4⋊C4—1221no—
750C2×C4⋊C4—1221no—
751C2×C4⋊C4—1221no—
752C2×C4⋊C4—1221no—
753C2×C4⋊C4—1222no—
754C2×C4⋊C4—1222no—
755C2×C4⋊C4—1221no—
756C2×C4⋊C4C22×D6112yes—
757C2×C22⋊C4—1221no—
758C2×C22⋊C4—1221no—
759C2×C22⋊C4—1221no—
760C2×C22⋊C4—1221no—
761C2×C22⋊C4—1221no—
762C2×C22⋊C4—1222no—
763C2×C42—611no—
764C2×C42—611no—
765C2×C42—611no—
766C2×C42—611no—
767C2×C42—611no—
768C2×C42—611no—
769C2×C42—611no—
770C2×C42—611no—
771C2×C42—611no—
772C2×C42—611no—
773C2×C42—611no—
774C2×C42—1221no—
775C2×C42—1222no—
776C2×C42C22×D6111yescharacteristic
777#107—614no—
778#107—614no—
779#107—614no—
780#107C22×D6114yes—
781#106—614no—
782#106—614no—
783#106—614no—
784#106C22×D6114yes—
785C4⋊C8—614no—
786C4⋊C8—612no—
787C4⋊C8C22×D6112yes—
788#103—614no—
789#103—614no—
790#103—614no—
791#103C22×D6114yes—
792#102—614no—
793#102—614no—
794#102—614no—
795#102C22×D6114yes—
796C22⋊C8—612no—
797C22⋊C8—614no—
798C22⋊C8C22×D6112yes—
799#97—612no—
800#97C22×D6112yes—
801C4×C8—614no—
802C24—611no—
803C24—1221no—
804C2×Q8—22no—
805C2×Q8—22no—
806C2×Q8—44no—
807C2×Q8—611no—
808C2×Q8—1221no—
809C2×Q8—1224no—
810C2×Q8—1222no—
811C2×Q8—1222no—
812C2×Q8—2444no—
813C2×Q8C23×D6111yescharacteristic
814C2×D4—21no—
815C2×D4—611no—
816C2×D4—1221no—
817C2×D4—1224no—
818C2×D4—1221no—
819C2×D4—1221no—
820C2×D4—1221no—
821C2×D4—2444no—
822C2×D4C23×D6111yescharacteristic
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—611no—
834C22×C4—611no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—1224no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1222no—
847C22×C4—1221no—
848C22×C4—2442no—
849C22×C4—2442no—
850C22×C4—2444no—
851C22×C4D4×D6111yescharacteristic
852C22×C4D4×D6111yescharacteristic
853C22×C4C23×D6111yescharacteristic
854M16—1228no—
855C2×C8—614no—
856C2×C8C23×D6114yes—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—22no—
864C4⋊C4—614no—
865C4⋊C4—611no—
866C4⋊C4—611no—
867C4⋊C4—1221no—
868C4⋊C4—1221no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—1224no—
874C4⋊C4—1224no—
875C4⋊C4—1221no—
876C4⋊C4—1221no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1224no—
880C4⋊C4—1224no—
881C4⋊C4—1222no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—1222no—
887C4⋊C4—1222no—
888C4⋊C4C23×D6114yes—
889C4⋊C4C23×D6111yescharacteristic
890C4⋊C4C23×D6111yescharacteristic
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—1221no—
897C22⋊C4—1221no—
898C22⋊C4—1221no—
899C22⋊C4—1221no—
900C22⋊C4—1224no—
901C22⋊C4—1224no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—1221no—
905C22⋊C4—1221no—
906C22⋊C4—1221no—
907C22⋊C4—1221no—
908C22⋊C4—1221no—
909C22⋊C4—1221no—
910C22⋊C4—1221no—
911C22⋊C4—1221no—
912C22⋊C4—1221no—
913C42—21no—
914C42—611no—
915C42—611no—
916C42—611no—
917C42—611no—
918C42—611no—
919C42—611no—
920C42—611no—
921C42—611no—
922C42—611no—
923C42—611no—
924C42—611no—
925C42—611no—
926C42—1224no—
927C42—1224no—
928C42—1221no—
929C42—1221no—
930C42—1221no—
931C42D4×D6111yescharacteristic
932C42D4×D6111yescharacteristic
933C42C23×D6111yescharacteristic
934C42C23×D6111yescharacteristic
935C23—21no—
936C23—611no—
937C23—611no—
938C23—1222no—
939C23—1222no—
940C23—1221no—
941C23—2441no—
942C23—2442no—
943C23—2442no—
944C23—2442no—
945C23C2×D4×D6111yescharacteristic
946Q8—22no—
947Q8—44no—
948Q8—44no—
949Q8—1222no—
950Q8—2444no—
951Q8—2442no—
952Q8—2444no—
953D4—22no—
954D4—42no—
955D4—1222no—
956D4—2442no—
957D4—2442no—
958D4—2442no—
959D4—2442no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—24no—
966C2×C4—21no—
967C2×C4—44no—
968C2×C4—42no—
969C2×C4—611no—
970C2×C4—614no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1224no—
986C2×C4—1221no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2442no—
994C2×C4—2442no—
995C2×C4—2442no—
996C2×C4—2442no—
997C2×C4—2441no—
998C2×C4—2442no—
999C2×C4—2444no—
1000C2×C4—2442no—
1001C2×C4C2×D4×D6111yescharacteristic
1002C2×C4C2×D4×D6111yescharacteristic
1003C2×C4C2×D4×D6111yescharacteristic
1004C2×C4C2×D4×D6111yescharacteristic
1005C2×C4C2×D4×D6111yescharacteristic
1006C2×C4C24×D6111yescharacteristic
1007C8—24no—
1008C8—1224no—
1009C22—21no—
1010C22—21no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—612no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—4884no—
1021C22—2444no—
1022C22—2441no—
1023C22—2441no—
1024C22—2441no—
1025C22#1684055812yes—
1026C22C22×D4×D6111yescharacteristic
1027C4—21no—
1028C4—21no—
1029C4—21no—
1030C4—21no—
1031C4—44no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—612no—
1036C4—1221no—
1037C4—1221no—
1038C4—1221no—
1039C4—1221no—
1040C4—1221no—
1041C4—2441no—
1042C4—2441no—
1043C4—2444no—
1044C4—2441no—
1045C4#1684056112yes—
1046C42−1+4×D6112yes—
1047C2—22no—
1048C2—81no—
1049C2—1222no—
1050C2—4881no—
1051C2—2441no—
1052C2#536×D6111yescharacteristic
1053C2C2×#1684055811yescharacteristic
1054C2C2×#1684056111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3238C2
socleC22×C61C23×D4
prime radical#121×D61C22
hypercenter#3238D61
hypocenterC61#60866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21457062C2semidirect
4. #21457056C2semidirect
5. #21457051C2semidirect
6. #21457046C2semidirect
7. #21457040C2semidirect
8. #21457003C2semidirect
9. #21456997C2semidirect
10. #21456990C2semidirect
11. #21456984C2semidirect
12. #21456370C2semidirect
13. #21456204C2semidirect
14. #21455762C2semidirect
16. #21455625C2semidirect
17. #21455617C2semidirect
18. #21454449C2semidirect
19. C61×#3238C2semidirect
26. #16840317C22semidirect
27. #16840317C22semidirect
28. C2×#14519777C22semidirect
41. C2×#14519768C22semidirect
57. #16840172C22semidirect
58. #16840171C22semidirect
59. #16840168C22semidirect
60. #16840163C22semidirect
61. #16840162C22semidirect
62. #16840124C22semidirect
63. #16840122C22semidirect
64. #16840121C22semidirect
65. #16840118C22semidirect
66. #16840115C22semidirect
67. #16840106C22semidirect
68. #16840102C22semidirect
69. #16840098C22semidirect
70. #16840095C22semidirect
71. #16840092C22semidirect
77. #16840068C22semidirect
78. #16840067C22semidirect
79. #16840061C22semidirect
80. #16840060C22semidirect
81. #16840054C22semidirect
82. #16840049C22semidirect
83. #16840048C22semidirect
84. #16840047C22semidirect
85. #16840043C22semidirect
86. #16840042C22semidirect
87. #16839819C22semidirect
88. #16839817C22semidirect
89. #16839814C22semidirect
90. #16839812C22semidirect
98. C2×C4⋊Q8×C61C22semidirect
100. C61×#501C22semidirect
101. C61×#489C22semidirect
102. C61×#483C22semidirect
104. C61×#477C22semidirect
105. C61×#476C22semidirect
106. C61×#432C22semidirect
527. #3238D61semidirect
556. C2×C4⋊Q8C2×D61semidirect
589. #501C2×D61semidirect
595. #489C2×D61semidirect
603. #483C2×D61semidirect
615. #477C2×D61semidirect
617. #476C2×D61semidirect
624. #432C2×D61semidirect
634. C61#60866semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
#529×D612
#214570622
#214570562
#214570512
#214570462
#214570402
#214570032
#214569972
#214569902
#214569842
#214563702
#214562042
#214557622
#214557542
#214556252
#214556172
#214544492
C61×#32382
#6086661