Finite Group Databasebeta

← #29647984

Subgroups — #29647984

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#432×D61C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444432C212yesmaximal, complemented
5#21444428C212yesmaximal, complemented
6#21444427C211yesmaximal, characteristic, complemented
7#21444426C211yesmaximal, characteristic, complemented
8#21444424C211yesmaximal, characteristic, complemented
9#21444406C212yesmaximal, complemented
10#21444404C212yesmaximal, complemented
11C61×#1529C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13#16840318C2211yescharacteristic
14#16840316C411yescharacteristic
15#16840314C411yescharacteristic
16#16840311C2211yescharacteristic
17#16840309C411yescharacteristic
18#16840307C411yescharacteristic
19#16840297C2211yescharacteristic
20#16840296C2211yescharacteristic
21#16840295—21no—
22#16840295—21no—
23#16840291C2211yescharacteristic
24#16840290—21no—
25#16840289—21no—
26#16840275C411yescharacteristic
27#16840272C411yescharacteristic
28#16840271—21no—
29#16840270—21no—
30C4×#11758226C411yescharacteristic
31#16840230—21no—
32C4×#11758224—21no—
33C4×#11758224C411yescharacteristic
34C2×C42×D61C2211yescharacteristic
35#16839819C2211yescharacteristic
36#16839818—21no—
37#16839817C2212yes—
38#16839816—21no—
39C4⋊C8×D61—21no—
40C22⋊C8×D61—21no—
41C4×#11758194C2211yescharacteristic
42#16839714C2212yes—
43M16×Dic61—21no—
44C4×#11758189—21no—
45#97×D61C2212yes—
46#97×D61C2212yes—
47C4×C8×D61—21no—
48#16839504C2212yescomplemented
49#16839503C2212yescomplemented
50#16839503C2212yescomplemented
51#16839502C2212yescomplemented
52#16839501C2212yescomplemented
53#16839501C2212yescomplemented
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic
56C4×M16×C61C2211yescharacteristic
57C61×#330C2212yescomplemented
58C61×#329C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C2×#11758194—21no—
67C2×#11758189—22no—
68M16×D61—28no—
69C2×C8×D61—22no—
70C2×C8×D61—22no—
71#14519776C2×C411yescharacteristic
72#14519776C2×C411yescharacteristic
73#14519775C2×C411yescharacteristic
74#14519773C2×C411yescharacteristic
75#14519772—21no—
76#14519771—21no—
77#14519770—21no—
78#14519769C2311yescharacteristic
79#14519767—21no—
80#14519767—21no—
81#14519765C2311yescharacteristic
82#14519763—21no—
83#14519763—21no—
84#14519762—21no—
85#14519762—21no—
86#14519760—21no—
87#14519759—21no—
88#14519759—21no—
89#14519757C2×C411yescharacteristic
90#14519756C2×C411yescharacteristic
91#14519755—21no—
92#14519755—21no—
93#14519755—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519752C2×C411yescharacteristic
97#14519751C2×C411yescharacteristic
98#14519750—21no—
99#14519750—21no—
100#14519750—21no—
101#14519749—21no—
102#14519748C2×C411yescharacteristic
103#14519747—21no—
104#14519745—21no—
105Q8×Dic61C2×C411yescharacteristic
106C4×Dic122—21no—
107C4×Dic122C2×C411yescharacteristic
108#14519742—21no—
109#14519742—21no—
110#14519742—21no—
111#14519742C2×C411yescharacteristic
112C4×D244—21no—
113C4×D244C2×C411yescharacteristic
114D4×Dic61—21no—
115D4×Dic61C2×C411yescharacteristic
116#14519739—21no—
117#14519739—21no—
118#14519739—21no—
119#14519739C2×C411yescharacteristic
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519735—21no—
131#14519735—21no—
132#14519735C2×C411yescharacteristic
133#14519735C2×C411yescharacteristic
134#14519734—21no—
135#14519734—21no—
136#14519733—21no—
137#14519733—21no—
138#14519733—21no—
139C2×C4×Dic61—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—
159#14519687—22no—
160C4×#92418—21no—
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×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—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197#11758226—42no—
198#11758224—42no—
199#11758224—44no—
200#11758222—44no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244C22×C411yescharacteristic
204C2×C4×D61—24no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
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×Dic122—21no—
224C2×Dic122C22×C411yescharacteristic
225M16×C61—24no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
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—
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⋊Dic61C22×C411yescharacteristic
260C4⋊Dic61C22×C411yescharacteristic
261#11758196—21no—
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—
271C4×Dic61—21no—
272C4×Dic61—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—
292C8×D61—28no—
293C8×D61—44no—
294C23×C61—21no—
295C23×C61C2×C22⋊C411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—21no—
299C22×D61—41no—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302Q8×C61—41no—
303D4×C61—41no—
304D4×C61—42no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
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—
321C22⋊D61—42no—
322C22⋊D61—42no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—41no—
329C2×Dic61—42no—
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—
339D244—42no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61#10414yes—
355Dic122—42no—
356Dic122—42no—
357Dic122—41no—
358C8×C61—24no—
359C8×C61—42no—
360#92418—24no—
361#92418—42no—
362#17651—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#41312yes—
379C2×D61C2×#10412yes—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61C2×#10412yes—
389Dic61—21no—
390Dic61—21no—
391Dic61—21no—
392Dic61—21no—
393Dic61—41no—
394Dic61—41no—
395Dic61—41no—
396Dic61C2×#10412yes—
397Dic61#42112yes—
398#3444—611no—
399C2×#432—611no—
400C2×C4×M16—611no—
401#1531—612no—
402#1530—612no—
403#1529—611no—
404#1529—611no—
405#1529—611no—
406#1529D6111yescharacteristic, complemented
407#1524—612no—
408#1524—612no—
409C2×C61—41no—
410C2×C61—81no—
411C2×C61C2×#41311yescharacteristic
412C2×C61C22×#10411yescharacteristic
413C2×C61C2×#42111yescharacteristic
414D61—22no—
415D61—22no—
416D61—81no—
417C22×M16—1221no—
418#533—611no—
419#533—611no—
420#533—611no—
421#532—611no—
422#532—611no—
423#532—611no—
424#529—611no—
425#529—611no—
426#529—611no—
427#529—1221no—
428#529—1221no—
429#529—1221no—
430#529—1221no—
431#529C2×D6111yescharacteristic
432#525—611no—
433#525—611no—
434#525—1221no—
435#525—1221no—
436C4×#41—611no—
437C4×#41—611no—
438C4×#41—1221no—
439C4×#41—1221no—
440C22×C42—611no—
441#432—611no—
442#432—612no—
443#432—1221no—
444#432—1221no—
445#432C2×D6111yescharacteristic
446C2×C4⋊C8—1221no—
447C2×C22⋊C8—1221no—
448C4×M16—611no—
449C4×M16—612no—
450C4×M16—1221no—
451C4×M16—1221no—
452C4×M16C2×D6111yescharacteristic
453C2×#97—612no—
454C2×#97—612no—
455C2×C4×C8—1221no—
456#330—612no—
457#330—612no—
458#330—612no—
459#330C2×D6112yescomplemented
460#329—612no—
461#329—612no—
462#329—612no—
463#329C2×D6112yescomplemented
464C61#1765111yescharacteristic, complemented, Sylow
465C2×#41—611no—
466C2×#41—611no—
467C2×#41—1221no—
468C2×#41—1221no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C2×M16—21no—
473C2×M16—1222no—
474C2×M16—1228no—
475C2×M16—1221no—
476C22×C8—1222no—
477C22×C8—1222no—
478C4⋊Q8—611no—
479C4⋊Q8—611no—
480C4⋊Q8—611no—
481#127—611no—
482#126—21no—
483#126—1221no—
484#126—1221no—
485#126—1221no—
486#125—611no—
487#125—1221no—
488#125—1221no—
489#125C22×D6111yescharacteristic
490#124—611no—
491#124—1221no—
492#124—1221no—
493#124C22×D6111yescharacteristic
494#123—21no—
495#123—1221no—
496#123—1221no—
497#123—1221no—
498#123—1221no—
499#123—1221no—
500C22⋊Q8—611no—
501C22⋊Q8—611no—
502C22⋊Q8—611no—
503C22⋊Q8—1221no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8C4×D6111yescharacteristic
508#121—611no—
509#121—611no—
510#121—611no—
511#121—1221no—
512#121—1221no—
513#121—1221no—
514#121—1221no—
515#121C4×D6111yescharacteristic
516#120—1221no—
517#120—1221no—
518C4×Q8—611no—
519C4×Q8—611no—
520C4×Q8—611no—
521C4×Q8—1221no—
522C4×Q8—1221no—
523C4×Q8—1221no—
524C4×Q8—1221no—
525C4×Q8C4×D6111yescharacteristic
526C4×D4—21no—
527C4×D4—611no—
528C4×D4—611no—
529C4×D4—611no—
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×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4C4×D6111yescharacteristic
546#117—21no—
547#117—611no—
548#117—611no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555#117—1221no—
556C2×C42—611no—
557C2×C42—611no—
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—1221no—
568C2×C42—1221no—
569C2×C42C22×D6111yescharacteristic
570C4⋊C8—21no—
571C4⋊C8—1222no—
572C4⋊C8—1221no—
573C22⋊C8—21no—
574C22⋊C8—1222no—
575C22⋊C8—1221no—
576#97—612no—
577#97—612no—
578#97—1222no—
579#97—1222no—
580#97C22×D6112yes—
581#97C22×D6112yes—
582C4×C8—21no—
583C4×C8—1222no—
584C4×C8—1221no—
585C24—611no—
586#41—2444no—
587#41—2444no—
588#41—2442no—
589#41—2442no—
590C2×Q8—611no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8C2×C4×D6111yescharacteristic
594C2×D4—21no—
595C2×D4—611no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4C2×C4×D6111yescharacteristic
604C22×C4—21no—
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—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—1224no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631M16—24no—
632M16—1228no—
633M16—1224no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—1228no—
637C2×C8—1222no—
638C2×C8—1222no—
639C2×C8—2444no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—611no—
645C4⋊C4—611no—
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⋊C4C2×C4×D6111yescharacteristic
659C4⋊C4C2×C4×D6111yescharacteristic
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
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—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C42—21no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—1221no—
692C42—1221no—
693C42—1221no—
694C42—1221no—
695C42—1221no—
696C42C2×C4×D6111yescharacteristic
697C42D4×D6111yescharacteristic
698C42D4×D6111yescharacteristic
699C42C23×D6111yescharacteristic
700C23—21no—
701C23—611no—
702C23—611no—
703C23—1222no—
704C23—1222no—
705C23—1221no—
706C23—2441no—
707C23C22⋊C4×D6111yescharacteristic
708Q8—41no—
709Q8—2441no—
710Q8—2442no—
711Q8—2442no—
712D4—41no—
713D4—42no—
714D4—2441no—
715D4—2442no—
716D4—2442no—
717D4—2442no—
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—2441no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4C22⋊C4×D6111yescharacteristic
759C2×C4C22⋊C4×D6111yescharacteristic
760C2×C4C22⋊C4×D6111yescharacteristic
761C2×C4C22×C4×D6111yescharacteristic
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4C2×D4×D6111yescharacteristic
764C8—24no—
765C8—42no—
766C8—1224no—
767C8—2442no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—612no—
775C22—612no—
776C22—1221no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—2444no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22C2×C22⋊C4×D6111yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—612no—
794C4—612no—
795C4—1221no—
796C4—1221no—
797C4—1221no—
798C4—1221no—
799C4—2441no—
800C4—2441no—
801C4—2441no—
802C4#104×D6112yes—
803C2—41no—
804C2—81no—
805C2—1222no—
806C2—1222no—
807C2—4881no—
808C2#413×D6111yescharacteristic
809C2C2×#104×D6111yescharacteristic
810C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1529C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC42×C61C24
hypercenter#1529D61
hypocenterC61#17651
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. #432×D61C2semidirect
3. C4×M16×D61C2semidirect
4. #21444432C2semidirect
5. #21444428C2semidirect
6. #21444427C2semidirect
7. #21444426C2semidirect
8. #21444424C2semidirect
9. #21444406C2semidirect
10. #21444404C2semidirect
11. C61×#1529C2semidirect
48. #16839504C22semidirect
49. #16839503C22semidirect
50. #16839503C22semidirect
51. #16839502C22semidirect
52. #16839501C22semidirect
53. #16839501C22semidirect
57. C61×#330C22semidirect
58. C61×#329C22semidirect
406. #1529D61semidirect
459. #330C2×D61semidirect
463. #329C2×D61semidirect
464. C61#17651semidirect

Maximal subgroups

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

subgroupindex
#214591132
#432×D612
C4×M16×D612
#214444322
#214444282
#214444272
#214444262
#214444242
#214444062
#214444042
C61×#15292
#1765161