Finite Group Databasebeta

← #29646766

Subgroups — #29646766

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3C2×#16839818C211yesmaximal, characteristic, complemented
4#21444290C212yesmaximal, complemented
5#21444286C212yesmaximal, complemented
6#21444252C212yesmaximal, complemented
7#21444250C212yesmaximal, complemented
8#21444233C211yesmaximal, characteristic, complemented
9#21444232C211yesmaximal, characteristic, complemented
10#21444230C211yesmaximal, characteristic, complemented
11C61×#1483C211yesmaximal, characteristic, complemented
12#16840318C411yescharacteristic
13#16840316C2211yescharacteristic
14#16840314C411yescharacteristic
15#16840311C411yescharacteristic
16#16840309C2211yescharacteristic
17#16840307C411yescharacteristic
18#16840297C411yescharacteristic
19#16840296C2211yescharacteristic
20#16840295—21no—
21#16840295—21no—
22#16840291C411yescharacteristic
23#16840290—21no—
24#16840289—21no—
25#16840275C411yescharacteristic
26#16840272C411yescharacteristic
27#16840271—21no—
28#16840270—21no—
29C4×#11758226C2211yescharacteristic
30#16840230—21no—
31C4×#11758224—21no—
32C4×#11758224C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839818—21no—
35#16839818—21no—
36#16839818C2212yes—
37#16839818C2212yes—
38#16839817—21no—
39#16839817—21no—
40#16839813C2212yes—
41#16839813C2212yes—
42#16839785—21no—
43C2×C4⋊#92418C2211yescharacteristic
44#16839725—21no—
45C2×#14519689—21no—
46C4×#11758194C2211yescharacteristic
47C2×#14519687—21no—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C61×#529C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C4×M16×C61C2211yescharacteristic
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
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—
67C22×#92418—21no—
68#14519776C2×C411yescharacteristic
69#14519776C2×C411yescharacteristic
70#14519775C2×C411yescharacteristic
71#14519773C2×C411yescharacteristic
72#14519772—21no—
73#14519771—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic
76#14519767—21no—
77#14519767—21no—
78#14519765C2×C411yescharacteristic
79#14519763—21no—
80#14519763—21no—
81#14519762—21no—
82#14519762—21no—
83#14519760—21no—
84#14519759—21no—
85#14519759—21no—
86#14519757C2×C411yescharacteristic
87#14519756C2×C411yescharacteristic
88#14519755—21no—
89#14519755—21no—
90#14519755—21no—
91#14519754—21no—
92#14519753C2×C411yescharacteristic
93#14519752C2×C411yescharacteristic
94#14519751C2×C411yescharacteristic
95#14519750—21no—
96#14519750—21no—
97#14519750—21no—
98#14519749—21no—
99#14519748C2×C411yescharacteristic
100#14519747—21no—
101#14519745—21no—
102Q8×Dic61C2×C411yescharacteristic
103C4×Dic122—21no—
104C4×Dic122C2311yescharacteristic
105#14519742—21no—
106#14519742—21no—
107#14519742—21no—
108#14519742C2×C411yescharacteristic
109C4×D244—21no—
110C4×D244C2311yescharacteristic
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic
113#14519739—21no—
114#14519739—21no—
115#14519739—21no—
116#14519739C2×C411yescharacteristic
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519735—21no—
128#14519735—21no—
129#14519735C2×C411yescharacteristic
130#14519735C2×C411yescharacteristic
131#14519734—21no—
132#14519734—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—21no—
136C2×C4×Dic61—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—
158#14519687—22no—
159#14519687—22no—
160C4×#92418C2312yes—
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×D61C22⋊C411yescharacteristic
179C2×Q8×C61C22×C411yescharacteristic
180C2×D4×C61—21no—
181C2×D4×C61C22×C411yescharacteristic
182C22×C4×C61—21no—
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61C22⋊C411yescharacteristic
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C22⋊C411yescharacteristic
196#11758226—42no—
197#11758224—42no—
198#11758224—44no—
199#11758222—42no—
200#11758222—42no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244C22×C411yescharacteristic
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—42no—
208C2×C4×D61—41no—
209C2×C4×D61—41no—
210C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122C22×C411yescharacteristic
226M16×C61—42no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61—42no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C411yescharacteristic
235C4⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C42×C61—21no—
242C42×C61C22×C411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2411yescharacteristic
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⋊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×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—21no—
298C22×D61—41no—
299C22×D61—41no—
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—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C22⋊D61—42no—
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—42no—
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—
341D244—42no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—21no—
345C4×D61—21no—
346C4×D61—21no—
347C4×D61—21no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—41no—
359C4×D61—41no—
360Dic122—22no—
361Dic122—42no—
362Dic122—42no—
363C8×C61—42no—
364C8×C61—42no—
365#92418—42no—
366#92418—42no—
367#17494—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—21no—
381C2×D61—44no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61#56812yes—
393C4×C61#57511yescharacteristic
394C4×C61#57511yescharacteristic
395Dic61—21no—
396Dic61—21no—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—41no—
402Dic61—41no—
403Dic61—41no—
404#3444—611no—
405#2920—611no—
406C2×#432—611no—
407#1497—612no—
408#1496—612no—
409#1488—612no—
410#1488—612no—
411#1483—611no—
412#1483—611no—
413#1483—611no—
414#1483D6111yescharacteristic, complemented
415C2×C61—22no—
416C2×C61—81no—
417C2×C61#287911yescharacteristic
418C2×C61#289611yescharacteristic
419C2×C61C2×#42111yescharacteristic
420D61—41no—
421D61—41no—
422D61—81no—
423#533—611no—
424#533—611no—
425#533—611no—
426#532—611no—
427#532—611no—
428#532—611no—
429#529—611no—
430#529—611no—
431#529—611no—
432#529—1221no—
433#529—1221no—
434#529—1221no—
435#529—1221no—
436#529C2×D6111yescharacteristic
437#525—611no—
438#525—611no—
439#525—1221no—
440#525—1221no—
441C4×#41—611no—
442C4×#41—611no—
443C4×#41—1221no—
444C4×#41—1221no—
445C22×C42—611no—
446#432—612no—
447#432—612no—
448#432—1221no—
449#432—1221no—
450#432—1221no—
451#432—1221no—
452#431—612no—
453#431—612no—
454#423—1221no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8C2×D6111yescharacteristic
457#407—1221no—
458C2×C22⋊C8—1221no—
459C4×M16—611no—
460C4×M16C2×D6111yescharacteristic
461C2×#97—1221no—
462Q8⋊C8—612no—
463Q8⋊C8—612no—
464Q8⋊C8—612no—
465Q8⋊C8C2×D6112yescomplemented
466D4⋊C8—612no—
467D4⋊C8—612no—
468D4⋊C8—612no—
469D4⋊C8C2×D6112yescomplemented
470C61#1749411yescharacteristic, complemented, Sylow
471C2×#41—611no—
472C2×#41—611no—
473C2×#41—1221no—
474C2×#41—1221no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C2×M16—21no—
479C2×M16—1221no—
480C22×C8—21no—
481C22×C8—1221no—
482C4⋊Q8—611no—
483C4⋊Q8—611no—
484C4⋊Q8—611no—
485#127—611no—
486#126—21no—
487#126—1221no—
488#126—1221no—
489#126—1221no—
490#125—611no—
491#125—1221no—
492#125—1221no—
493#125C4×D6111yescharacteristic
494#124—611no—
495#124—1221no—
496#124—1221no—
497#124C4×D6111yescharacteristic
498#123—21no—
499#123—1221no—
500#123—1221no—
501#123—1221no—
502#123—1221no—
503#123—1221no—
504C22⋊Q8—611no—
505C22⋊Q8—611no—
506C22⋊Q8—611no—
507C22⋊Q8—1221no—
508C22⋊Q8—1221no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8C4×D6111yescharacteristic
512#121—611no—
513#121—611no—
514#121—611no—
515#121—1221no—
516#121—1221no—
517#121—1221no—
518#121—1221no—
519#121C4×D6111yescharacteristic
520#120—1221no—
521#120—1221no—
522C4×Q8—611no—
523C4×Q8—611no—
524C4×Q8—611no—
525C4×Q8—1221no—
526C4×Q8—1221no—
527C4×Q8—1221no—
528C4×Q8—1221no—
529C4×Q8C22×D6111yescharacteristic
530C4×D4—21no—
531C4×D4—611no—
532C4×D4—611no—
533C4×D4—611no—
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×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4C22×D6111yescharacteristic
550#117—21no—
551#117—611no—
552#117—611no—
553#117—1221no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
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—611no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574C4⋊C8—21no—
575C4⋊C8—612no—
576C4⋊C8—1222no—
577C4⋊C8—1222no—
578C4⋊C8—1221no—
579C4⋊C8C22×D6112yes—
580C22⋊C8—1222no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584#97—21no—
585#97—1222no—
586#97—1222no—
587#97—1221no—
588C4×C8—612no—
589C4×C8C22×D6112yes—
590C24—611no—
591#41—2442no—
592#41—2442no—
593#41—2442no—
594#41—2444no—
595#41—2442no—
596C2×Q8—611no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8C2×C4×D6111yescharacteristic
600C2×D4—21no—
601C2×D4—611no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4C2×C4×D6111yescharacteristic
610C22×C4—21no—
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—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—2442no—
632C22×C4—2441no—
633C22×C4—2441no—
634C22×C4—2442no—
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4D4×D6111yescharacteristic
638M16—42no—
639M16—2442no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—42no—
643C2×C8—1222no—
644C2×C8—1222no—
645C2×C8—2442no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—611no—
651C4⋊C4—611no—
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⋊C4C2×C4×D6111yescharacteristic
665C4⋊C4C2×C4×D6111yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
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—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C42—21no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C42—1221no—
701C42—1221no—
702C42C2×C4×D6111yescharacteristic
703C42D4×D6111yescharacteristic
704C42D4×D6111yescharacteristic
705C42C23×D6111yescharacteristic
706C23—21no—
707C23—611no—
708C23—611no—
709C23—1222no—
710C23—1221no—
711C23—2441no—
712C23—2441no—
713C23C22⋊C4×D6111yescharacteristic
714Q8—22no—
715Q8—1222no—
716Q8—2442no—
717Q8—2442no—
718D4—22no—
719D4—42no—
720D4—1222no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
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—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4C22⋊C4×D6111yescharacteristic
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C22×C4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C8—42no—
776C8—42no—
777C8—2442no—
778C8—2442no—
779C22—21no—
780C22—21no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—1221no—
785C22—1221no—
786C22—1221no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—2444no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22#1683977712yes—
795C22C2×C22⋊C4×D6111yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—1221no—
804C4—1221no—
805C4—1221no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—2441no—
810C4—2441no—
811C4—2441no—
812C4#1684052712yes—
813C4#1684055811yescharacteristic
814C4#1684056111yescharacteristic
815C2—22no—
816C2—81no—
817C2—4881no—
818C2—2441no—
819C2—2441no—
820C2#2145426111yescharacteristic
821C2#2145433511yescharacteristic
822C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1483C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC42×C61C24
hypercenter#1483D61
hypocenterC61#17494
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×#16839818C2semidirect
4. #21444290C2semidirect
5. #21444286C2semidirect
6. #21444252C2semidirect
7. #21444250C2semidirect
8. #21444233C2semidirect
9. #21444232C2semidirect
10. #21444230C2semidirect
11. C61×#1483C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
414. #1483D61semidirect
465. Q8⋊C8C2×D61semidirect
469. D4⋊C8C2×D61semidirect
470. C61#17494semidirect

Maximal subgroups

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

subgroupindex
#214591132
#214544502
C2×#168398182
#214442902
#214442862
#214442522
#214442502
#214442332
#214442322
#214442302
C61×#14832
#1749461