Finite Group Databasebeta

← #29647930

Subgroups — #29647930

Order 15616.

1068 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444427C211yesmaximal, characteristic, complemented
5#21444426C211yesmaximal, characteristic, complemented
6#21444424C211yesmaximal, characteristic, complemented
7#21444419C212yesmaximal, complemented
8#21444415C212yesmaximal, complemented
9#21444406C212yesmaximal, complemented
10#21444404C212yesmaximal, complemented
11C61×#1529C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13#16840299C411yescharacteristic
14#16840298C411yescharacteristic
15#16840297C2211yescharacteristic
16#16840296C2211yescharacteristic
17#16840295—21no—
18#16840294C411yescharacteristic
19#16840293C411yescharacteristic
20#16840292—21no—
21#16840291C2211yescharacteristic
22#16840290—21no—
23#16840289—21no—
24#126×D61—21no—
25#125×D61C2211yescharacteristic
26#124×D61C2211yescharacteristic
27#123×D61—21no—
28C22⋊Q8×D61C411yescharacteristic
29#121×D61C411yescharacteristic
30C4×Q8×D61C411yescharacteristic
31C4×D4×D61—21no—
32C4×D4×D61C411yescharacteristic
33#117×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839819C2211yescharacteristic, complemented
36#16839817C2212yes—
37#16839814—21no—
38#16839812—21no—
39#16839784—21no—
40#16839724—21no—
41C4×#11758194C2211yescharacteristic, complemented
42#16839714C2212yes—
43#16839714C2212yescomplemented
44M16×Dic61—21no—
45C4×#11758189—21no—
46#97×D61C2212yescomplemented
47C4×C8×D61—21no—
48#16839504C2212yescomplemented
49#16839503C2212yescomplemented
50#16839503C2212yescomplemented
51#16839502C2212yescomplemented
52#16839501C2212yescomplemented
53#16839501C2212yescomplemented
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic, complemented
56C4×M16×C61C2211yescharacteristic, complemented
57C61×#330C2212yescomplemented
58C61×#329C2212yescomplemented
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—
67C2×#11758189—22no—
68C2×#11758189—22no—
69M16×D61—28no—
70C2×C8×D61—22no—
71#14519772—21no—
72#14519772—21no—
73#14519772—21no—
74#14519771—21no—
75#14519770—21no—
76#14519770—21no—
77#14519770—21no—
78#14519769C2311yescharacteristic
79#14519768C2×C411yescharacteristic
80#14519768C2×C411yescharacteristic
81#14519767—21no—
82#14519767—21no—
83#14519766C2×C411yescharacteristic
84#14519765C2311yescharacteristic
85#14519764C2×C411yescharacteristic
86#14519763—21no—
87#14519763—21no—
88#14519762—21no—
89#14519762—21no—
90#14519761—21no—
91#14519760—21no—
92#14519759—21no—
93#14519759—21no—
94#14519758—21no—
95#14519757C2×C411yescharacteristic
96#14519756C2×C411yescharacteristic
97#14519755—21no—
98#14519754—21no—
99#14519753C2×C411yescharacteristic
100#14519752C2×C411yescharacteristic
101#14519751C2×C411yescharacteristic
102#14519750—21no—
103#14519749—21no—
104#14519748C2×C411yescharacteristic
105Q8×Dic61C2×C411yescharacteristic
106C4×Dic122—21no—
107C4×Dic122C2×C411yescharacteristic
108#14519742—21no—
109#14519742C2×C411yescharacteristic
110C4×D244—21no—
111C4×D244C2×C411yescharacteristic
112D4×Dic61—21no—
113D4×Dic61C2×C411yescharacteristic
114#14519739—21no—
115#14519739C2×C411yescharacteristic
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519736—21no—
123#14519735—21no—
124#14519735—21no—
125#14519734—21no—
126#14519734—21no—
127#14519733—21no—
128#14519733—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61C2×C411yescharacteristic
134C4⋊C4×D61C2×C411yescharacteristic
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C42×D61—21no—
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61C2311yescharacteristic
151C42×D61C2311yescharacteristic
152C4⋊#92418—21no—
153#14519706—22no—
154C22⋊#92418—21no—
155#14519689—22no—
156#14519688C2312yes—
157#14519688C2312yes—
158#14519687—22no—
159C4×#92418—21no—
160C8×Dic61—22no—
161C8×Dic61—22no—
162C2×M16×C61—21no—
163#126×C61—21no—
164#125×C61C2311yescharacteristic
165#124×C61C2311yescharacteristic
166#123×C61—21no—
167C22⋊Q8×C61C2×C411yescharacteristic
168#121×C61C2×C411yescharacteristic
169C4×Q8×C61C2×C411yescharacteristic
170C4×D4×C61—21no—
171C4×D4×C61C2×C411yescharacteristic
172#117×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C22⋊C8×C61—21no—
176#97×C61C2312yes—
177#97×C61C2312yes—
178C4×C8×C61—21no—
179C23×D61—21no—
180C23×D61C22⋊C411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61—21no—
192C22×Dic61C22⋊C411yescharacteristic
193C22×Dic61C22⋊C411yescharacteristic
194C22×Dic61C22⋊C411yescharacteristic
195Q8×D61—42no—
196D4×D61—42no—
197D4×D61—44no—
198C2×D244—21no—
199C2×D244C22×C411yescharacteristic
200C2×C4×D61—24no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—44no—
209C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122C22×C411yescharacteristic
223M16×C61—24no—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C22×C411yescharacteristic
231C4⋊C4×C61C22×C411yescharacteristic
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—21no—
238C42×C61C22×C411yescharacteristic
239C42×C61C2×D411yescharacteristic
240C42×C61C2×D411yescharacteristic
241C42×C61C2411yescharacteristic
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247#11758198—21no—
248#11758198—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—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C22×C411yescharacteristic
262C4⋊Dic61C22×C411yescharacteristic
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22×C411yescharacteristic
283C4×Dic61C22×C411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288#11758194—24no—
289C2×#92418—22no—
290C2×#92418—22no—
291#11758189—28no—
292#11758189—44no—
293C8×D61—28no—
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—41no—
306D4×C61—41no—
307D4×C61—42no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—42no—
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—42no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—41no—
330C2×Dic61—42no—
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337D244—41no—
338D244—42no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61—42no—
355C4×D61#10414yes—
356Dic122—42no—
357Dic122—41no—
358C8×C61—24no—
359C8×C61—42no—
360#92418—24no—
361#92418—42no—
362#17642—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61C22×C22⋊C411yescharacteristic
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—44no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—84no—
379C2×D61C2×#10412yes—
380C2×D61#42112yes—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61C2×#10412yes—
390Dic61—21no—
391Dic61—21no—
392Dic61—21no—
393Dic61—21no—
394Dic61—41no—
395Dic61—41no—
396Dic61—41no—
397Dic61#41312yes—
398Dic61C2×#10412yes—
399C2×#529—611no—
400#2920—611no—
401C2×C4×M16—611no—
402#1529—611no—
403#1529—611no—
404#1529—611no—
405#1529D6111yescharacteristic, complemented
406#1528—612no—
407#1527—612no—
408#1524—612no—
409#1524—612no—
410C2×C61—41no—
411C2×C61—81no—
412C2×C61C2×#41311yescharacteristic
413C2×C61C22×#10411yescharacteristic
414C2×C61C2×#42111yescharacteristic
415D61—22no—
416D61—22no—
417D61—81no—
418C22×M16—1221no—
419#529—611no—
420#529—611no—
421#529—611no—
422#529—611no—
423#529—611no—
424#529—611no—
425#529—611no—
426#529—1221no—
427#529—1221no—
428#529—1221no—
429#529—1221no—
430#529C2×D6111yescharacteristic
431C2×#126—1221no—
432C2×#125—611no—
433C2×#124—611no—
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×#121—611no—
437C2×C4×Q8—611no—
438C2×C4×D4—611no—
439C2×C4×D4—1221no—
440C2×#117—1221no—
441C22×C42—611no—
442#432—611no—
443#432—612no—
444#432C2×D6111yescharacteristic, complemented
445#431—1221no—
446#431—1221no—
447#423—1221no—
448#407—1221no—
449C4×M16—611no—
450C4×M16—612no—
451C4×M16—612no—
452C4×M16—1221no—
453C4×M16—1221no—
454C4×M16C2×D6111yescharacteristic, complemented
455C2×#97—612no—
456C2×C4×C8—1221no—
457#330—612no—
458#330—612no—
459#330—612no—
460#330C2×D6112yescomplemented
461#329—612no—
462#329—612no—
463#329—612no—
464#329C2×D6112yescomplemented
465C61#1764211yescharacteristic, complemented, Sylow
466C22×Q8—611no—
467C22×D4—611no—
468C22×D4—1221no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—1221no—
473C2×M16—21no—
474C2×M16—1222no—
475C2×M16—1222no—
476C2×M16—1228no—
477C2×M16—1221no—
478C22×C8—1222no—
479#126—21no—
480#126—1221no—
481#126—1221no—
482#126—1221no—
483#126—1221no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#125—611no—
488#125—611no—
489#125—611no—
490#125—1221no—
491#125—1221no—
492#125C22×D6111yescharacteristic
493#124—611no—
494#124—611no—
495#124—611no—
496#124—1221no—
497#124—1221no—
498#124C22×D6111yescharacteristic
499#123—21no—
500#123—1221no—
501#123—1221no—
502#123—1221no—
503#123—1221no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507C22⋊Q8—611no—
508C22⋊Q8—611no—
509C22⋊Q8—611no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8C4×D6111yescharacteristic
513#121—611no—
514#121—611no—
515#121—611no—
516#121—1221no—
517#121—1221no—
518#121C4×D6111yescharacteristic
519C4×Q8—611no—
520C4×Q8—611no—
521C4×Q8—611no—
522C4×Q8—1221no—
523C4×Q8—1221no—
524C4×Q8C4×D6111yescharacteristic
525C4×D4—21no—
526C4×D4—611no—
527C4×D4—611no—
528C4×D4—611no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4C4×D6111yescharacteristic
539#117—21no—
540#117—1221no—
541#117—1221no—
542#117—1221no—
543#117—1221no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—1221no—
570C2×C42C22×D6111yescharacteristic
571C4⋊C8—21no—
572C4⋊C8—1222no—
573C4⋊C8—1221no—
574C22⋊C8—21no—
575C22⋊C8—1222no—
576C22⋊C8—1221no—
577#97—612no—
578#97—612no—
579#97—1222no—
580#97C22×D6112yes—
581#97C22×D6112yes—
582C4×C8—21no—
583C4×C8—1222no—
584C4×C8—1222no—
585C4×C8—1221no—
586C24—611no—
587C24—1221no—
588C2×Q8—611no—
589C2×Q8—1221no—
590C2×Q8—2442no—
591C2×Q8C2×C4×D6111yescharacteristic
592C2×D4—21no—
593C2×D4—611no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—2442no—
599C2×D4—2444no—
600C2×D4C2×C4×D6111yescharacteristic
601C22×C4—21no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
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—1224no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—2444no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4C2×C4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630M16—24no—
631M16—1228no—
632M16—1224no—
633M16—2444no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—1228no—
637C2×C8—1222no—
638C2×C8—1222no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—611no—
644C4⋊C4—611no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
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⋊C4C2×C4×D6111yescharacteristic
660C4⋊C4C2×C4×D6111yescharacteristic
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
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—
681C42—21no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—1221no—
695C42—1221no—
696C42—1221no—
697C42C2×C4×D6111yescharacteristic
698C42D4×D6111yescharacteristic
699C42D4×D6111yescharacteristic
700C42C23×D6111yescharacteristic
701C23—21no—
702C23—611no—
703C23—611no—
704C23—1222no—
705C23—1222no—
706C23—1221no—
707C23—2441no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23C22⋊C4×D6111yescharacteristic
712Q8—41no—
713Q8—2441no—
714Q8—2442no—
715D4—41no—
716D4—42no—
717D4—2441no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—614no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4C22⋊C4×D6111yescharacteristic
760C2×C4C22⋊C4×D6111yescharacteristic
761C2×C4C22⋊C4×D6111yescharacteristic
762C2×C4C22×C4×D6111yescharacteristic
763C2×C4C2×D4×D6111yescharacteristic
764C2×C4C2×D4×D6111yescharacteristic
765C8—24no—
766C8—42no—
767C8—1224no—
768C8—2442no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—612no—
776C22—612no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—1221no—
781C22—4884no—
782C22—2444no—
783C22—2441no—
784C22—2441no—
785C22—2441no—
786C22C2×C22⋊C4×D6111yescharacteristic
787C4—21no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—612no—
796C4—612no—
797C4—1221no—
798C4—1221no—
799C4—1221no—
800C4—1221no—
801C4—2441no—
802C4—2441no—
803C4—2441no—
804C4#104×D6112yes—
805C2—41no—
806C2—81no—
807C2—1222no—
808C2—1222no—
809C2—4881no—
810C2#413×D6111yescharacteristic
811C2C2×#104×D6111yescharacteristic
812C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1529C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C4
cosocleC42×C61C24
hypercenter#1529D61
hypocenterC61#17642
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1529

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. C4×M16×D61C2semidirect
4. #21444427C2semidirect
5. #21444426C2semidirect
6. #21444424C2semidirect
7. #21444419C2semidirect
8. #21444415C2semidirect
9. #21444406C2semidirect
10. #21444404C2semidirect
11. C61×#1529C2semidirect
35. #16839819C22semidirect
41. C4×#11758194C22semidirect
43. #16839714C22semidirect
46. #97×D61C22semidirect
48. #16839504C22semidirect
49. #16839503C22semidirect
50. #16839503C22semidirect
51. #16839502C22semidirect
52. #16839501C22semidirect
53. #16839501C22semidirect
55. C61×#432C22semidirect
56. C4×M16×C61C22semidirect
57. C61×#330C22semidirect
58. C61×#329C22semidirect
405. #1529D61semidirect
444. #432C2×D61semidirect
454. C4×M16C2×D61semidirect
460. #330C2×D61semidirect
464. #329C2×D61semidirect
465. C61#17642semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#214544492
C4×M16×D612
#214444272
#214444262
#214444242
#214444192
#214444152
#214444062
#214444042
C61×#15292
#1764261