Finite Group Databasebeta

← #29646664

Subgroups — #29646664

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3C2×#16839813C211yesmaximal, characteristic, complemented
4#21444283C212yesmaximal, complemented
5#21444281C212yesmaximal, complemented
6#21444280C211yesmaximal, characteristic, complemented
7#21444279C211yesmaximal, characteristic, complemented
8#21444277C211yesmaximal, characteristic, complemented
9#21444212C212yesmaximal, complemented
10#21444208C212yesmaximal, complemented
11C61×#1494C211yesmaximal, 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#16839819C2211yescharacteristic, complemented
35#16839817—21no—
36#16839814C2212yes—
37#16839813—21no—
38#16839813—21no—
39#16839813C2212yes—
40#16839813C2212yescomplemented
41#16839812—21no—
42#16839784C2212yescomplemented
43C2×#14519706—21no—
44#16839724—21no—
45C2×#14519689—21no—
46#16839714—21no—
47C2×C4×#92418C2211yescharacteristic, complemented
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic, complemented
56C2×C4×C8×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×#11758189—22no—
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⋊#92418C2312yes—
150#14519706—22no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418—21no—
154#14519689—22no—
155#14519689—22no—
156#14519689—22no—
157#14519688—21no—
158C4×#92418—21no—
159C4×#92418C2312yes—
160C8×Dic61—22no—
161C22×C8×C61—21no—
162#126×C61—21no—
163#125×C61C2×C411yescharacteristic
164#124×C61C2×C411yescharacteristic
165#123×C61—21no—
166C22⋊Q8×C61C2×C411yescharacteristic
167#121×C61C2×C411yescharacteristic
168C4×Q8×C61C2311yescharacteristic
169C4×D4×C61—21no—
170C4×D4×C61C2311yescharacteristic
171#117×C61—21no—
172C2×C42×C61C2311yescharacteristic
173C4⋊C8×C61C2312yes—
174C22⋊C8×C61—21no—
175#97×C61—21no—
176C4×C8×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—42no—
206C2×C4×D61—44no—
207C2×C4×D61—42no—
208C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×Dic122—21no—
221C2×Dic122C22×C411yescharacteristic
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61—42no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C22×C411yescharacteristic
230C4⋊C4×C61C22×C411yescharacteristic
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C42×C61—21no—
237C42×C61C22×C411yescharacteristic
238C42×C61C2×D411yescharacteristic
239C42×C61C2×D411yescharacteristic
240C42×C61C2411yescharacteristic
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246#11758198—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—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C22×C411yescharacteristic
261C4⋊Dic61C22×C411yescharacteristic
262#11758196—21no—
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—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22×C411yescharacteristic
282C4×Dic61C22×C411yescharacteristic
283C4×Dic61C2×D411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418—42no—
290#11758189—44no—
291C23×C61—21no—
292C23×C61C2×C22⋊C411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—21no—
296C22×D61—41no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302Q8×C61—22no—
303D4×C61—22no—
304D4×C61—42no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—42no—
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C22⋊D61—42no—
319C22⋊D61—42no—
320C22⋊D61—42no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—41no—
327C2×Dic61—42no—
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334D244—22no—
335D244—42no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—42no—
348C4×D61—42no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61#13114yes—
353Dic122—22no—
354Dic122—42no—
355C8×C61—42no—
356C8×C61—42no—
357#92418—42no—
358#92418—42no—
359#17480—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61#42112yes—
366C22×C61C22×C22⋊C411yescharacteristic
367C2×D61—21no—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—44no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—84no—
377C2×D61#40812yes—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61C2×#13112yes—
386C4×C61#57512yes—
387Dic61—21no—
388Dic61—21no—
389Dic61—21no—
390Dic61—21no—
391Dic61—21no—
392Dic61—41no—
393Dic61—41no—
394Dic61—41no—
395Dic61#40812yes—
396C2×#529—611no—
397#2920—611no—
398C2×#431—611no—
399#1495—612no—
400#1495—612no—
401#1494—611no—
402#1494—611no—
403#1494—611no—
404#1494D6111yescharacteristic, complemented
405#1479—612no—
406#1478—612no—
407C2×C61—22no—
408C2×C61—81no—
409C2×C61C2×#40811yescharacteristic
410C2×C61#289611yescharacteristic
411C2×C61C2×#42111yescharacteristic
412D61—22no—
413D61—41no—
414D61—81no—
415#529—611no—
416#529—611no—
417#529—611no—
418#529—611no—
419#529—611no—
420#529—611no—
421#529—611no—
422#529—1221no—
423#529—1221no—
424#529—1221no—
425#529—1221no—
426#529C2×D6111yescharacteristic
427C2×#126—1221no—
428C2×#125—611no—
429C2×#124—611no—
430C2×#123—1221no—
431C2×C22⋊Q8—611no—
432C2×#121—611no—
433C2×C4×Q8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×#117—1221no—
437C22×C42—611no—
438#432—611no—
439#432—1221no—
440#432C2×D6111yescharacteristic, complemented
441#431—612no—
442#431—612no—
443#431—612no—
444#431—1221no—
445#431—1221no—
446#431—1221no—
447#423—612no—
448C2×C4⋊C8—1221no—
449#407—1221no—
450C2×C22⋊C8—1221no—
451C4×M16—1221no—
452C2×C4×C8—611no—
453C2×C4×C8C2×D6111yescharacteristic, complemented
454Q8⋊C8—612no—
455Q8⋊C8—612no—
456Q8⋊C8—612no—
457Q8⋊C8C2×D6112yescomplemented
458D4⋊C8—612no—
459D4⋊C8—612no—
460D4⋊C8—612no—
461D4⋊C8C2×D6112yescomplemented
462C61#1748011yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×D4—611no—
465C22×D4—1221no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—1221no—
470C2×M16—1222no—
471C22×C8—21no—
472C22×C8—1221no—
473#126—21no—
474#126—1221no—
475#126—1221no—
476#126—1221no—
477#126—1221no—
478#126—1221no—
479#126—1221no—
480#126—1221no—
481#125—611no—
482#125—611no—
483#125—611no—
484#125—1221no—
485#125—1221no—
486#125C4×D6111yescharacteristic
487#124—611no—
488#124—611no—
489#124—611no—
490#124—1221no—
491#124—1221no—
492#124C4×D6111yescharacteristic
493#123—21no—
494#123—1221no—
495#123—1221no—
496#123—1221no—
497#123—1221no—
498#123—1221no—
499#123—1221no—
500#123—1221no—
501C22⋊Q8—611no—
502C22⋊Q8—611no—
503C22⋊Q8—611no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8C4×D6111yescharacteristic
507#121—611no—
508#121—611no—
509#121—611no—
510#121—1221no—
511#121—1221no—
512#121C4×D6111yescharacteristic
513C4×Q8—611no—
514C4×Q8—611no—
515C4×Q8—611no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8C22×D6111yescharacteristic
519C4×D4—21no—
520C4×D4—611no—
521C4×D4—611no—
522C4×D4—611no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4C22×D6111yescharacteristic
533#117—21no—
534#117—1221no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C42—611no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—1221no—
564C2×C42C22×D6111yescharacteristic
565C4⋊C8—612no—
566C4⋊C8—1222no—
567C4⋊C8—1222no—
568C4⋊C8—1222no—
569C4⋊C8C22×D6112yes—
570C22⋊C8—21no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C22⋊C8—1221no—
575#97—21no—
576#97—1221no—
577C4×C8—21no—
578C4×C8—612no—
579C4×C8—1222no—
580C4×C8—1221no—
581C4×C8C22×D6112yes—
582C24—611no—
583C24—1221no—
584C2×Q8—611no—
585C2×Q8—1221no—
586C2×Q8—1224no—
587C2×Q8C2×C4×D6111yescharacteristic
588C2×D4—21no—
589C2×D4—611no—
590C2×D4—1221no—
591C2×D4—1224no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—2444no—
596C2×D4C2×C4×D6111yescharacteristic
597C22×C4—21no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
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—1224no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2444no—
623C22×C4C2×C4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626M16—2444no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—42no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—2442no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—611no—
638C4⋊C4—611no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
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⋊C4C2×C4×D6111yescharacteristic
654C4⋊C4C2×C4×D6111yescharacteristic
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
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—
675C42—21no—
676C42—611no—
677C42—611no—
678C42—611no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—1221no—
689C42—1221no—
690C42—1221no—
691C42C2×C4×D6111yescharacteristic
692C42D4×D6111yescharacteristic
693C42D4×D6111yescharacteristic
694C42C23×D6111yescharacteristic
695C23—21no—
696C23—611no—
697C23—611no—
698C23—1222no—
699C23—1222no—
700C23—1221no—
701C23—2441no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23C22⋊C4×D6111yescharacteristic
706Q8—22no—
707Q8—1222no—
708Q8—2442no—
709D4—22no—
710D4—42no—
711D4—1222no—
712D4—2442no—
713D4—2442no—
714D4—2442no—
715D4—2442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—42no—
723C2×C4—611no—
724C2×C4—614no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4C22⋊C4×D6111yescharacteristic
754C2×C4C22⋊C4×D6111yescharacteristic
755C2×C4C22⋊C4×D6111yescharacteristic
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C8—42no—
760C8—42no—
761C8—2442no—
762C8—2442no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—612no—
769C22—1221no—
770C22—1221no—
771C22—1221no—
772C22—1221no—
773C22—1221no—
774C22—4884no—
775C22—2444no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22#1683977712yes—
780C22C2×C22⋊C4×D6111yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—612no—
789C4—1221no—
790C4—1221no—
791C4—1221no—
792C4—1221no—
793C4—1221no—
794C4—2441no—
795C4—2441no—
796C4—2441no—
797C4#131×D6112yes—
798C4#1684055912yes—
799C2—22no—
800C2—81no—
801C2—1222no—
802C2—4881no—
803C2—2441no—
804C2#408×D6111yescharacteristic
805C2#2145433411yescharacteristic
806C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C4
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#17480
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. C2×#16839813C2semidirect
4. #21444283C2semidirect
5. #21444281C2semidirect
6. #21444280C2semidirect
7. #21444279C2semidirect
8. #21444277C2semidirect
9. #21444212C2semidirect
10. #21444208C2semidirect
11. C61×#1494C2semidirect
34. #16839819C22semidirect
40. #16839813C22semidirect
42. #16839784C22semidirect
47. C2×C4×#92418C22semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
55. C61×#432C22semidirect
56. C2×C4×C8×C61C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
404. #1494D61semidirect
440. #432C2×D61semidirect
453. C2×C4×C8C2×D61semidirect
457. Q8⋊C8C2×D61semidirect
461. D4⋊C8C2×D61semidirect
462. C61#17480semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#214544492
C2×#168398132
#214442832
#214442812
#214442802
#214442792
#214442772
#214442122
#214442082
C61×#14942
#1748061