Finite Group Databasebeta

← #29647359

Subgroups — #29647359

Order 15616.

1036 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#21459111C211yesmaximal, characteristic
2C2×#16839812C211yesmaximal, characteristic, complemented
3#21448210C211yesmaximal, characteristic, complemented
4#21444381C212yesmaximal, complemented
5#21444377C212yesmaximal, complemented
6#21444376C211yesmaximal, characteristic, complemented
7#21444375C211yesmaximal, characteristic, complemented
8#21444373C211yesmaximal, characteristic, complemented
9#21444304C212yesmaximal, complemented
10#21444302C212yesmaximal, complemented
11C61×#1516C211yesmaximal, characteristic, complemented
12#16840315C411yescharacteristic, complemented
13#16840314C411yescharacteristic, complemented
14#16840314C2211yescharacteristic
15#16840308C411yescharacteristic, complemented
16#16840307C411yescharacteristic, complemented
17#16840307C2211yescharacteristic
18#16840298C411yescharacteristic, complemented
19#16840298C2211yescharacteristic
20#16840293C411yescharacteristic, complemented
21#16840293C2211yescharacteristic
22#16840292—21no—
23#16840292—21no—
24#16840289—21no—
25#16840289—21no—
26#16840273C2211yescharacteristic
27#16840268—21no—
28#16840268—21no—
29#41×Dic61C411yescharacteristic, complemented
30#16840230C411yescharacteristic, complemented
31C4×#11758224—21no—
32C4×#11758224—21no—
33C22×C4×Dic61C2211yescharacteristic
34#16839812—21no—
35#16839812—21no—
36#16839812C2212yes—
37#16839812C2212yes—
38C2×#14519706—21no—
39C2×C22⋊#92418C2211yescharacteristic
40C2×C8×Dic61—21no—
41#16839629—21no—
42#16839626C2212yes—
43#16839625C2211yescharacteristic
44#16839620—21no—
45#16839613—21no—
46C22⋊C4×Dic61—21no—
47#16839607C2212yes—
48#16839500C2212yes—
49#16839499C2212yes—
50#16839498C2212yes—
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#525C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C61×#381C2211yescharacteristic
57C61×#328C2212yes—
58C61×#327C2212yes—
59C2×#11758222C2×C411yescharacteristic
60C2×#11758224—21no—
61C2×#11758224—21no—
62C23×Dic61D411yescharacteristic
63C23×Dic61D411yescharacteristic
64C22×#92418—21no—
65#14519776C2×C411yescharacteristic
66#14519776C2×C411yescharacteristic
67#14519775C2×C411yescharacteristic
68#14519773C2×C411yescharacteristic
69#14519772—21no—
70#14519772—21no—
71#14519770—21no—
72#14519770—21no—
73#14519768C2×C411yescharacteristic
74#14519768C2×C411yescharacteristic
75#14519767—21no—
76#14519767—21no—
77#14519766C2×C411yescharacteristic
78#14519764C2×C411yescharacteristic
79#14519763—21no—
80#14519763—21no—
81#14519761—21no—
82#14519761—21no—
83#14519760—21no—
84#14519758—21no—
85#14519758—21no—
86#14519756C2×C411yescharacteristic
87#14519756C2311yescharacteristic
88#14519754—21no—
89#14519754—21no—
90#14519754—21no—
91#14519754—21no—
92#14519751C2×C411yescharacteristic
93#14519751C2311yescharacteristic
94#14519749—21no—
95#14519749—21no—
96#14519749—21no—
97#14519749—21no—
98#14519746—21no—
99Q8×Dic61C2×C411yescharacteristic
100Q8×Dic61C2×C411yescharacteristic
101C4×Dic122—21no—
102C4×Dic122—21no—
103#14519742—21no—
104#14519742—21no—
105#14519742C2×C411yescharacteristic
106#14519742C2×C411yescharacteristic
107D4×Dic61—21no—
108D4×Dic61—21no—
109D4×Dic61—21no—
110D4×Dic61—21no—
111D4×Dic61C2×C411yescharacteristic
112D4×Dic61C2×C411yescharacteristic
113#14519739C2×C411yescharacteristic
114#14519739C2×C411yescharacteristic
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519736—21no—
126#14519736C2×C411yescharacteristic
127#14519735—21no—
128#14519735—21no—
129#14519734—21no—
130#14519733—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134C2×#11758196—22no—
135C2×C22⋊Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—22no—
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61C2×C411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150C42×D61—21no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418—21no—
154C22⋊#92418C2312yes—
155C8×Dic61—22no—
156C8×Dic61—22no—
157#14519684—21no—
158#14519684—22no—
159#14519684—22no—
160#14519684C2312yes—
161C2×#41×C61C2×C411yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C22×C8×C61—21no—
164#123×C61—21no—
165C22⋊Q8×C61C2×C411yescharacteristic
166C22⋊Q8×C61C2311yescharacteristic
167#121×C61C2×C411yescharacteristic
168#121×C61C2311yescharacteristic
169#120×C61—21no—
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172#117×C61C2×C411yescharacteristic
173C2×C22⋊C4×C61—21no—
174C22⋊C8×C61—21no—
175C22⋊C8×C61C2312yes—
176#95×C61—21no—
177#95×C61C2312yes—
178C24×C61C2×D411yescharacteristic
179#41×C61—42no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—22no—
187C22×C4×C61—42no—
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C22×Dic61—24no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—22no—
203C22×Dic61—42no—
204C22×Dic61C22⋊C411yescharacteristic
205C22×Dic61C22⋊C411yescharacteristic
206C22×Dic61C22⋊C411yescharacteristic
207C22×Dic61C22⋊C411yescharacteristic
208C22×Dic61C22⋊C411yescharacteristic
209C22×Dic61C22⋊C411yescharacteristic
210C22×Dic61C22⋊C411yescharacteristic
211C22×Dic61C22⋊C411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216#11758224—44no—
217#11758224—44no—
218#11758222—42no—
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122C22×C411yescharacteristic
226C2×C8×C61—22no—
227C2×C8×C61—42no—
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—
237C22⋊C4×C61—42no—
238C42×C61—21no—
239C22⋊Dic61—21no—
240C22⋊Dic61—21no—
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—42no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C411yescharacteristic
258C4⋊Dic61C22×C411yescharacteristic
259#11758196—21no—
260#11758196—21no—
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—44no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—44no—
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×Dic61C22×C411yescharacteristic
285C4×Dic61C22×C411yescharacteristic
286C4×Dic61C22×C411yescharacteristic
287C4×Dic61C22×C411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292C2×#92418—22no—
293C2×#92418—42no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—21no—
297C23×C61—41no—
298C23×C61C2×C22⋊C411yescharacteristic
299C23×C61C2×C22⋊C411yescharacteristic
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302Q8×C61—41no—
303D4×C61—41no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307C2×C4×C61—22no—
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—41no—
315C2×C4×C61—41no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C22⋊D61—42no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61#13514yes—
357D244—41no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361Dic122—42no—
362Dic122—42no—
363Dic122—41no—
364C8×C61—42no—
365#92418—42no—
366#17571—611nomaximal, Sylow
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—44no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61#41012yes—
379C22×C61C22×C22⋊C411yescharacteristic
380C22×C61C2×#13512yes—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—82no—
392Dic61—21no—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—41no—
398Dic61—41no—
399Dic61—41no—
400Dic61—82no—
401Dic61#41612yes—
402Dic61#41612yes—
403Dic61#42112yes—
404#3444—611no—
405C2×#431—611no—
406#2283—611no—
407#1518—612no—
408#1517—612no—
409#1516—611no—
410#1516—611no—
411#1516—611no—
412#1516D6111yescharacteristic, complemented
413#1500—612no—
414#1500—612no—
415C2×C61—22no—
416C2×C61—22no—
417C2×C61—41no—
418C2×C61—81no—
419C2×C61C2×#41011yescharacteristic
420C2×C61C2×#41611yescharacteristic
421C2×C61C2×#42111yescharacteristic
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—611no—
433#529—1221no—
434#529—1221no—
435#529—1221no—
436#529—1221no—
437#525—611no—
438#525—1221no—
439#525—1221no—
440#525C2×D6111yescharacteristic
441C4×#41—611no—
442C4×#41—611no—
443C4×#41—1221no—
444C4×#41—1221no—
445C22×C42—611no—
446#431—612no—
447#431—612no—
448#431—1221no—
449#431—1221no—
450C2×C4⋊C8—1221no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8C2×D6111yescharacteristic
453C2×C4×C8—1221no—
454#383—1221no—
455#382—612no—
456#381—611no—
457#381C2×D6111yescharacteristic
458#380—1221no—
459C4×C4⋊C4—1221no—
460C4×C22⋊C4—1221no—
461#376—612no—
462#328—612no—
463#328—612no—
464#328—612no—
465#328C2×D6112yes—
466#327—612no—
467#327—612no—
468#327—612no—
469#327C2×D6112yes—
470C61#1757111yescharacteristic, complemented, Sylow
471C2×#41—611no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41C4×D6111yescharacteristic
475C23×C4—611no—
476C23×C4—611no—
477C23×C4C22×D6111yescharacteristic
478C22×C8—21no—
479C22×C8—1221no—
480C4⋊Q8—611no—
481C4⋊Q8—611no—
482C4⋊Q8—611no—
483#127—611no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#125—611no—
489#125—611no—
490#125—1221no—
491#125—1221no—
492#124—611no—
493#124—611no—
494#124—1221no—
495#124—1221no—
496#123—21no—
497#123—1221no—
498#123—1221no—
499#123—1221no—
500#123—1221no—
501#123—1221no—
502C22⋊Q8—611no—
503C22⋊Q8—611no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8—1221no—
508C22⋊Q8C4×D6111yescharacteristic
509C22⋊Q8C22×D6111yescharacteristic
510#121—611no—
511#121—611no—
512#121—1221no—
513#121—1221no—
514#121—1221no—
515#121—1221no—
516#121C4×D6111yescharacteristic
517#121C22×D6111yescharacteristic
518#120—21no—
519#120—1221no—
520C4×Q8—611no—
521C4×Q8—611no—
522C4×Q8—611no—
523C4×Q8—611no—
524C4×Q8—1221no—
525C4×Q8—1221no—
526C4×Q8—1221no—
527C4×Q8—1221no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—611no—
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—
548#117—611no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
557#117C4×D6111yescharacteristic
558C2×C4⋊C4—1222no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—1221no—
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—611no—
572C2×C42—611no—
573C2×C42—1221no—
574C2×C42—1221no—
575C2×C42—1222no—
576C4⋊C8—1222no—
577C4⋊C8—1222no—
578C22⋊C8—21no—
579C22⋊C8—612no—
580C22⋊C8—1221no—
581C22⋊C8C22×D6112yes—
582C4×C8—1222no—
583C4×C8—1222no—
584#95—21no—
585#95—612no—
586#95—1222no—
587#95—1222no—
588#95—1221no—
589#95C22×D6112yes—
590C24D4×D6111yescharacteristic
591#41—42no—
592#41—2442no—
593#41—2444no—
594#41—2444no—
595C2×Q8—611no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8C2×C4×D6111yescharacteristic
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—611no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4C2×C4×D6111yescharacteristic
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—42no—
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—1221no—
625C22×C4—1221no—
626C22×C4—1224no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—2442no—
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638C2×C8—22no—
639C2×C8—42no—
640C2×C8—1222no—
641C2×C8—2442no—
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⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—2444no—
661C4⋊C4C2×C4×D6111yescharacteristic
662C4⋊C4C2×C4×D6111yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—42no—
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—
681C22⋊C4—1221no—
682C22⋊C4—2442no—
683C42—21no—
684C42—611no—
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—611no—
698C42—611no—
699C42—611no—
700C42—1221no—
701C42—1221no—
702C42—1221no—
703C42—1221no—
704C42—1221no—
705C42—2444no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—41no—
710C23—1221no—
711C23C22⋊C4×D6111yescharacteristic
712C23C22⋊C4×D6111yescharacteristic
713C23C2×D4×D6111yescharacteristic
714Q8—41no—
715Q8—2441no—
716Q8—2442no—
717Q8—2442no—
718D4—41no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—2441no—
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—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—614no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4C22⋊C4×D6111yescharacteristic
773C2×C4C22⋊C4×D6111yescharacteristic
774C2×C4C22×C4×D6111yescharacteristic
775C2×C4C2×D4×D6111yescharacteristic
776C8—42no—
777C8—2442no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—44no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22#1683973412yes—
793C22C2×C22⋊C4×D6111yescharacteristic
794C22#135×D6112yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—612no—
804C4—612no—
805C4—612no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—1221no—
810C4—1221no—
811C4—4882no—
812C4—2441no—
813C4—2441no—
814C4—2441no—
815C2—22no—
816C2—22no—
817C2—41no—
818C2—81no—
819C2—4881no—
820C2C2×#1683973411yescharacteristic
821C2#416×D6111yescharacteristic
822C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radical#21459111C2
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61#17571
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. C2×#16839812C2semidirect
3. #21448210C2semidirect
4. #21444381C2semidirect
5. #21444377C2semidirect
6. #21444376C2semidirect
7. #21444375C2semidirect
8. #21444373C2semidirect
9. #21444304C2semidirect
10. #21444302C2semidirect
11. C61×#1516C2semidirect
12. #16840315C4semidirect
13. #16840314C4semidirect
15. #16840308C4semidirect
16. #16840307C4semidirect
18. #16840298C4semidirect
20. #16840293C4semidirect
29. #41×Dic61C4semidirect
30. #16840230C4semidirect
412. #1516D61semidirect
470. C61#17571semidirect

Maximal subgroups

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

subgroupindex
#214591112
C2×#168398122
#214482102
#214443812
#214443772
#214443762
#214443752
#214443732
#214443042
#214443022
C61×#15162
#1757161