Finite Group Databasebeta

← #29646565

Subgroups — #29646565

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3C2×#16839814C211yesmaximal, characteristic, complemented
4#21444233C211yesmaximal, characteristic, complemented
5#21444232C211yesmaximal, characteristic, complemented
6#21444230C211yesmaximal, characteristic, complemented
7#21444226C212yesmaximal, complemented
8#21444224C212yesmaximal, complemented
9#21444212C212yesmaximal, complemented
10#21444208C212yesmaximal, complemented
11C61×#1483C211yesmaximal, characteristic, complemented
12#16840299C2211yescharacteristic
13#16840298C411yescharacteristic
14#16840297C411yescharacteristic
15#16840296C2211yescharacteristic
16#16840295—21no—
17#16840294C2211yescharacteristic
18#16840293C411yescharacteristic
19#16840292—21no—
20#16840291C411yescharacteristic
21#16840290—21no—
22#16840289—21no—
23#126×D61—21no—
24#125×D61C411yescharacteristic
25#124×D61C411yescharacteristic
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic
28#121×D61C411yescharacteristic
29C4×Q8×D61C2211yescharacteristic
30C4×D4×D61—21no—
31C4×D4×D61C2211yescharacteristic
32#117×D61—21no—
33C2×C42×D61C2211yescharacteristic
34#16839817—21no—
35#16839817—21no—
36#16839814—21no—
37#16839814—21no—
38#16839814C2212yes—
39#16839814C2212yescomplemented
40#16839813C2212yes—
41#16839813C2212yescomplemented
42#16839785—21no—
43C2×C4⋊#92418C2211yescharacteristic, complemented
44#16839725—21no—
45C2×#14519689—21no—
46C4×#11758194C2211yescharacteristic, complemented
47C2×C8×Dic61—21no—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C61×#529C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic, complemented
56C4×M16×C61C2211yescharacteristic, complemented
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C2×#11758194—21no—
67C22×#92418—21no—
68#14519772—21no—
69#14519772—21no—
70#14519772—21no—
71#14519771—21no—
72#14519770—21no—
73#14519770—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic
76#14519768C2×C411yescharacteristic
77#14519768C2×C411yescharacteristic
78#14519767—21no—
79#14519767—21no—
80#14519766C2×C411yescharacteristic
81#14519765C2×C411yescharacteristic
82#14519764C2×C411yescharacteristic
83#14519763—21no—
84#14519763—21no—
85#14519762—21no—
86#14519762—21no—
87#14519761—21no—
88#14519760—21no—
89#14519759—21no—
90#14519759—21no—
91#14519758—21no—
92#14519757C2×C411yescharacteristic
93#14519756C2×C411yescharacteristic
94#14519755—21no—
95#14519754—21no—
96#14519753C2×C411yescharacteristic
97#14519752C2×C411yescharacteristic
98#14519751C2×C411yescharacteristic
99#14519750—21no—
100#14519749—21no—
101#14519748C2×C411yescharacteristic
102Q8×Dic61C2×C411yescharacteristic
103C4×Dic122—21no—
104C4×Dic122C2311yescharacteristic
105#14519742—21no—
106#14519742C2×C411yescharacteristic
107C4×D244—21no—
108C4×D244C2311yescharacteristic
109D4×Dic61—21no—
110D4×Dic61C2×C411yescharacteristic
111#14519739—21no—
112#14519739C2×C411yescharacteristic
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116#14519737—21no—
117#14519737—21no—
118#14519737—21no—
119#14519736—21no—
120#14519735—21no—
121#14519735—21no—
122#14519734—21no—
123#14519734—21no—
124#14519733—21no—
125#14519733—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61C2×C411yescharacteristic
131C4⋊C4×D61C2×C411yescharacteristic
132C22⋊C4×D61—21no—
133C22⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61D411yescharacteristic
140C42×D61—21no—
141C42×D61C2×C411yescharacteristic
142C42×D61C2×C411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61C2311yescharacteristic
148C42×D61C2311yescharacteristic
149C4⋊#92418—21no—
150C4⋊#92418C2312yes—
151#14519706—22no—
152#14519706—22no—
153#14519689—22no—
154#14519689—22no—
155#14519689—22no—
156#14519689—22no—
157#14519688—21no—
158C4×#92418C2312yes—
159C8×Dic61—22no—
160C8×Dic61—22no—
161C2×M16×C61—21no—
162C22×C8×C61—21no—
163#126×C61—21no—
164#125×C61C2×C411yescharacteristic
165#124×C61C2×C411yescharacteristic
166#123×C61—21no—
167C22⋊Q8×C61C2×C411yescharacteristic
168#121×C61C2×C411yescharacteristic
169C4×Q8×C61C2311yescharacteristic
170C4×D4×C61—21no—
171C4×D4×C61C2311yescharacteristic
172#117×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C4⋊C8×C61C2312yes—
176#97×C61—21no—
177C4×C8×C61C2312yes—
178C23×D61—21no—
179C23×D61C22⋊C411yescharacteristic
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C22×Dic61—21no—
191C22×Dic61C22⋊C411yescharacteristic
192C22×Dic61C22⋊C411yescharacteristic
193C22×Dic61C22⋊C411yescharacteristic
194Q8×D61—24no—
195D4×D61—24no—
196D4×D61—44no—
197C2×D244—21no—
198C2×D244C22×C411yescharacteristic
199C2×C4×D61—24no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—41no—
206C2×C4×D61—41no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22×C411yescharacteristic
217C2×C4×D61C22×C411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×Dic122—21no—
223C2×Dic122C22×C411yescharacteristic
224M16×C61—42no—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C2×C8×C61—42no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61C22×C411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2411yescharacteristic
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22×C411yescharacteristic
285C4×Dic61C22×C411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290#11758194—42no—
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418—42no—
294C23×C61—21no—
295C23×C61C2×C22⋊C411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—21no—
299C22×D61—41no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C2×C22⋊C411yescharacteristic
305Q8×C61—22no—
306D4×C61—22no—
307D4×C61—42no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C22⋊D61—42no—
324C22⋊D61—42no—
325C22⋊D61—42no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—41no—
332C2×Dic61—42no—
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339D244—22no—
340D244—42no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—21no—
344C4×D61—21no—
345C4×D61—21no—
346C4×D61—21no—
347C4×D61—22no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61#13114yes—
361Dic122—22no—
362Dic122—42no—
363C8×C61—42no—
364C8×C61—42no—
365#92418—42no—
366#92418—42no—
367#17465—611nomaximal, Sylow
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61#42112yes—
374C22×C61C22×C22⋊C411yescharacteristic
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—44no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—84no—
385C2×D61#40812yes—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61C2×#13112yes—
394C4×C61#57511yescharacteristic
395C4×C61#57511yescharacteristic
396Dic61—21no—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—41no—
402Dic61—41no—
403Dic61—41no—
404Dic61#40812yes—
405C2×#529—611no—
406#2920—611no—
407C2×#431—611no—
408#1483—611no—
409#1483—611no—
410#1483—611no—
411#1483D6111yescharacteristic, complemented
412#1482—612no—
413#1482—612no—
414#1479—612no—
415#1478—612no—
416C2×C61—22no—
417C2×C61—81no—
418C2×C61C2×#40811yescharacteristic
419C2×C61#289611yescharacteristic
420C2×C61C2×#42111yescharacteristic
421D61—22no—
422D61—41no—
423D61—81no—
424#529—611no—
425#529—611no—
426#529—611no—
427#529—611no—
428#529—611no—
429#529—611no—
430#529—611no—
431#529—1221no—
432#529—1221no—
433#529—1221no—
434#529—1221no—
435#529C2×D6111yescharacteristic
436C2×#126—1221no—
437C2×#125—611no—
438C2×#124—611no—
439C2×#123—1221no—
440C2×C22⋊Q8—611no—
441C2×#121—611no—
442C2×C4×Q8—611no—
443C2×C4×D4—611no—
444C2×C4×D4—1221no—
445C2×#117—1221no—
446C22×C42—611no—
447#432—1221no—
448#432—1221no—
449#431—612no—
450#431—612no—
451#431—612no—
452#431—612no—
453#431—1221no—
454#431—1221no—
455#423—1221no—
456C2×C4⋊C8—611no—
457C2×C4⋊C8C2×D6111yescharacteristic, complemented
458#407—1221no—
459C2×C22⋊C8—1221no—
460C4×M16—611no—
461C4×M16C2×D6111yescharacteristic, complemented
462C2×C4×C8—1221no—
463Q8⋊C8—612no—
464Q8⋊C8—612no—
465Q8⋊C8—612no—
466Q8⋊C8C2×D6112yescomplemented
467D4⋊C8—612no—
468D4⋊C8—612no—
469D4⋊C8—612no—
470D4⋊C8C2×D6112yescomplemented
471C61#1746511yescharacteristic, complemented, Sylow
472C22×Q8—611no—
473C22×D4—611no—
474C22×D4—1221no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—1221no—
479C2×M16—21no—
480C2×M16—1221no—
481C22×C8—21no—
482C22×C8—1221no—
483#126—21no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#126—1221no—
489#126—1221no—
490#126—1221no—
491#125—611no—
492#125—611no—
493#125—611no—
494#125—1221no—
495#125—1221no—
496#125C4×D6111yescharacteristic
497#124—611no—
498#124—611no—
499#124—611no—
500#124—1221no—
501#124—1221no—
502#124C4×D6111yescharacteristic
503#123—21no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508#123—1221no—
509#123—1221no—
510#123—1221no—
511C22⋊Q8—611no—
512C22⋊Q8—611no—
513C22⋊Q8—611no—
514C22⋊Q8—1221no—
515C22⋊Q8—1221no—
516C22⋊Q8C4×D6111yescharacteristic
517#121—611no—
518#121—611no—
519#121—611no—
520#121—1221no—
521#121—1221no—
522#121C4×D6111yescharacteristic
523C4×Q8—611no—
524C4×Q8—611no—
525C4×Q8—611no—
526C4×Q8—1221no—
527C4×Q8—1221no—
528C4×Q8C22×D6111yescharacteristic
529C4×D4—21no—
530C4×D4—611no—
531C4×D4—611no—
532C4×D4—611no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4C22×D6111yescharacteristic
543#117—21no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—1221no—
574C2×C42C22×D6111yescharacteristic
575C4⋊C8—21no—
576C4⋊C8—612no—
577C4⋊C8—1222no—
578C4⋊C8—1222no—
579C4⋊C8—1221no—
580C4⋊C8C22×D6112yes—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1222no—
585#97—21no—
586#97—1221no—
587C4×C8—612no—
588C4×C8—1222no—
589C4×C8—1222no—
590C4×C8C22×D6112yes—
591C24—611no—
592C24—1221no—
593C2×Q8—611no—
594C2×Q8—1221no—
595C2×Q8—1224no—
596C2×Q8C2×C4×D6111yescharacteristic
597C2×D4—21no—
598C2×D4—611no—
599C2×D4—1221no—
600C2×D4—1224no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—2444no—
605C2×D4C2×C4×D6111yescharacteristic
606C22×C4—21no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—1224no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—2441no—
630C22×C4—2441no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637M16—42no—
638M16—2442no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—42no—
642C2×C8—1222no—
643C2×C8—1222no—
644C2×C8—2442no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—611no—
650C4⋊C4—611no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4C2×C4×D6111yescharacteristic
666C4⋊C4C2×C4×D6111yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C42—21no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—1221no—
701C42—1221no—
702C42—1221no—
703C42C2×C4×D6111yescharacteristic
704C42D4×D6111yescharacteristic
705C42D4×D6111yescharacteristic
706C42C23×D6111yescharacteristic
707C23—21no—
708C23—611no—
709C23—611no—
710C23—1222no—
711C23—1222no—
712C23—1221no—
713C23—2441no—
714C23—2442no—
715C23—2442no—
716C23—2442no—
717C23C22⋊C4×D6111yescharacteristic
718Q8—22no—
719Q8—1222no—
720Q8—2442no—
721D4—22no—
722D4—42no—
723D4—1222no—
724D4—2442no—
725D4—2442no—
726D4—2442no—
727D4—2442no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—611no—
738C2×C4—614no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C22⋊C4×D6111yescharacteristic
773C2×C4C22×C4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C2×D4×D6111yescharacteristic
776C8—42no—
777C8—42no—
778C8—2442no—
779C8—2442no—
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—612no—
786C22—1221no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—4884no—
792C22—2444no—
793C22—2441no—
794C22—2441no—
795C22—2441no—
796C22#1683977712yes—
797C22C2×C22⋊C4×D6111yescharacteristic
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—612no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—1221no—
810C4—1221no—
811C4—2441no—
812C4—2441no—
813C4—2441no—
814C4#131×D6112yes—
815C4#1684055811yescharacteristic
816C4#1684056111yescharacteristic
817C2—22no—
818C2—81no—
819C2—1222no—
820C2—4881no—
821C2—2441no—
822C2#408×D6111yescharacteristic
823C2#2145433511yescharacteristic
824C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1483C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C4
cosocleC42×C61C24
hypercenter#1483D61
hypocenterC61#17465
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #21454450C2semidirect
3. C2×#16839814C2semidirect
4. #21444233C2semidirect
5. #21444232C2semidirect
6. #21444230C2semidirect
7. #21444226C2semidirect
8. #21444224C2semidirect
9. #21444212C2semidirect
10. #21444208C2semidirect
11. C61×#1483C2semidirect
39. #16839814C22semidirect
41. #16839813C22semidirect
43. C2×C4⋊#92418C22semidirect
46. C4×#11758194C22semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
55. C2×C4⋊C8×C61C22semidirect
56. C4×M16×C61C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
411. #1483D61semidirect
457. C2×C4⋊C8C2×D61semidirect
461. C4×M16C2×D61semidirect
466. Q8⋊C8C2×D61semidirect
470. D4⋊C8C2×D61semidirect
471. C61#17465semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#214544502
C2×#168398142
#214442332
#214442322
#214442302
#214442262
#214442242
#214442122
#214442082
C61×#14832
#1746561