Finite Group Databasebeta

← #29708021

Subgroups — #29708021

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic
2C2×#16839784C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic
4C2×#16839769C211yesmaximal, characteristic, complemented
5#21448306C211yesmaximal, characteristic
6#391×D61C211yesmaximal, characteristic, complemented
7#21447143C211yesmaximal, characteristic, complemented
8#21447142C211yesmaximal, characteristic, complemented
9#21447141C211yesmaximal, characteristic, complemented
10#21447140C211yesmaximal, characteristic, complemented
11#21447136C211yesmaximal, characteristic, complemented
12#21447135C211yesmaximal, characteristic, complemented
13#21447132C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#2055C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519806—24no—
19C2×#14519806—24no—
20C2×#14519806—24no—
21C22×Dic244C2211yescharacteristic
22C22×#11758202C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×#11758189C2211yescharacteristic
26C2×#14519735C2211yescharacteristic
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16839784—24no—
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33#16839769—24no—
34#16839760—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41#16839669C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839668C2211yescharacteristic
44#16839667C2211yescharacteristic
45#16839667C2211yescharacteristic
46#16839666—21no—
47#16839666—21no—
48#16839665C2211yescharacteristic
49#16839638—21no—
50#16839638—21no—
51C22⋊C4×Dic61—21no—
52C22⋊C4×Dic61—21no—
53#95×D61—21no—
54#95×D61—21no—
55#16839525C2211yescharacteristic
56#16839524C2211yescharacteristic
57#16839524C2211yescharacteristic
58C22×SD16×C61C2211yescharacteristic
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C61×#391C2211yescharacteristic
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224D414yes—
71C22×Dic122—21no—
72C22×Dic122C2311yescharacteristic
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61D414yes—
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87#14519806—232no—
88C2×Dic244—22no—
89C2×Dic244—22no—
90C2×Dic244—22no—
91C2×#11758202—22no—
92C2×#11758202—22no—
93C2×#11758202—22no—
94C2×#11758200—22no—
95C2×#11758200—22no—
96C2×#11758200—22no—
97C2×#11758189—22no—
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189—22no—
101C2×#11758189—22no—
102C2×#11758189D414yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519735—22no—
106#14519735—22no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C42×D61—22no—
120C42×D61—22no—
121C4⋊#92418—22no—
122#14519706—22no—
123#14519706—22no—
124#14519702—22no—
125#14519702—22no—
126#14519701—22no—
127#14519700—22no—
128#14519700—22no—
129#14519698—22no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140C22×Q8×C61C2311yescharacteristic
141C22×D4×C61C2311yescharacteristic
142C2×SD16×C61—22no—
143C2×SD16×C61—22no—
144C2×SD16×C61—22no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C42×C61C2311yescharacteristic
152C4⋊C8×C61—22no—
153#103×C61—22no—
154#102×C61—22no—
155#95×C61—21no—
156#95×C61—21no—
157C24×C61—21no—
158C23×D61C2×D411yescharacteristic
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C2×D412yes—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61C2×D412yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—24no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—24no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190Q8×D61—28no—
191Q8×D61—28no—
192Q8×D61—44no—
193Q8×D61—44no—
194#11758224—28no—
195#11758224—28no—
196#11758224—44no—
197#11758224—44no—
198C2×C4×D61—24no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—41no—
204C2×C4×D61—41no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61C2×D412yes—
211C2×C4×D61C2×D412yes—
212C2×C4×D61C2×D412yes—
213C2×C4×D61#4112yes—
214C2×C4×D61#4112yes—
215C2×C4×D61#4112yes—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—24no—
227C2×Dic122—42no—
228C2×Dic122—42no—
229C2×Dic122C2×D412yes—
230C2×Dic122C2×D412yes—
231SD16×C61—28no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61C2×D412yes—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C22⋊C4×C61—42no—
243C22⋊C4×C61—42no—
244C42×C61—21no—
245C42×C61—21no—
246C22⋊Dic61—42no—
247C22⋊Dic61—42no—
248#11758202—28no—
249#11758200—28no—
250#11758198—42no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255#11758196—42no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—22no—
259C4×Dic61—22no—
260C4×Dic61—42no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418C2×D412yes—
267Dic244—28no—
268#11758189—28no—
269#11758189—44no—
270C23×C61—22no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61C22×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61#12112yes—
283C22×D61#12112yes—
284C22×D61#12112yes—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—41no—
288Q8×C61—41no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—41no—
292D4×C61—41no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61#13712yescomplemented
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C22⋊D61—48no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—48no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61#12112yes—
334C2×Dic61#12112yes—
335C2×Dic61#12112yes—
336C2×Dic61#13712yescomplemented
337C4×D61—44no—
338C4×D61—44no—
339C4×D61—48no—
340C4×D61—84no—
341C4×D61#12014yes—
342C4×D61#12314yes—
343C4×D61#12314yes—
344C4×D61#12414yes—
345Dic122—22no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—41no—
350Dic122—41no—
351Dic122—41no—
352Dic122—41no—
353Dic122—48no—
354C8×C61—22no—
355C8×C61—41no—
356#92418—22no—
357#92418—41no—
358#23547—611nomaximal, Sylow
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61C2×#12111yescharacteristic
367C22×C61C2×#12111yescharacteristic
368C22×C61C2×#12111yescharacteristic
369C22×C61C2×#13711yescharacteristic
370C22×C61C2×#13711yescharacteristic
371C22×C61#57511yescharacteristic
372C22×C61#57511yescharacteristic
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61#39414yes—
380C4×C61—22no—
381C4×C61—42no—
382C4×C61—41no—
383C4×C61—81no—
384C4×C61—81no—
385C4×C61C2×#12011yescharacteristic
386C4×C61C2×#12311yescharacteristic
387C4×C61C2×#12311yescharacteristic
388C4×C61C2×#12411yescharacteristic
389Dic61—22no—
390Dic61—42no—
391Dic61—42no—
392Dic61—41no—
393Dic61—81no—
394Dic61—81no—
395Dic61#39414yes—
396C22×#137—611no—
397C2×#423—611no—
398C2×#417—611no—
399C2×#419—611no—
400#2297—611no—
401C2×#391—611no—
402#2056—611no—
403#2056—611no—
404#2056—611no—
405#2056—611no—
406#2055—611no—
407#2055—611no—
408#2055—611no—
409#2055D6111yescharacteristic, complemented
410#1736—611no—
411C2×C61—82no—
412C2×C61C2×#39411yescharacteristic
413C2×C61#303711yescharacteristic
414C2×C61#303711yescharacteristic
415C2×C61#303911yescharacteristic
416C2×C61#304011yescharacteristic
417C2×C61#305611yescharacteristic
418C2×C61#305611yescharacteristic
419D61—24no—
420C22×#41—611no—
421C23×Q8—611no—
422C2×#137—1224no—
423C2×#137—1224no—
424C2×#137—1224no—
425C22×Q16—611no—
426C22×Q16—611no—
427C22×SD16—611no—
428C22×SD16C2×D6111yescharacteristic
429C22×M16—611no—
430C22×M16—611no—
431C2×#117—611no—
432C22×C4⋊C4—611no—
433C22×C42—611no—
434#423—1224no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8C2×D6111yescharacteristic
439#419—1224no—
440#417—1224no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#103C2×D6111yescharacteristic
447C2×#102—611no—
448C2×#102C2×D6111yescharacteristic
449#391—611no—
450#391—611no—
451#391—611no—
452#391—611no—
453#391—611no—
454#391—1221no—
455#391—1221no—
456#391C2×D6111yescharacteristic
457#390—611no—
458#390C2×D6111yescharacteristic
459#386—1221no—
460#386—1221no—
461C4×C22⋊C4—1221no—
462C4×C22⋊C4—1221no—
463C2×#95—1221no—
464C2×#95—1221no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340C2×D6111yescharacteristic
469C61#2354711yescharacteristic, complemented, Sylow
470C2×#41—614no—
471C2×#41—1222no—
472C2×#41—1222no—
473C2×#41—1222no—
474C2×#41—1222no—
475C2×#41—1222no—
476C22×Q8—614no—
477C22×Q8—611no—
478C22×Q8—611no—
479C22×Q8—1221no—
480C22×Q8—1222no—
481C22×Q8—1222no—
482C22×Q8—1222no—
483C22×Q8—1222no—
484C22×Q8—1222no—
485C22×Q8C22×D6111yescharacteristic
486C22×D4—1221no—
487C22×D4C22×D6111yescharacteristic
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494#137—12232no—
495C2×Q16—1222no—
496C2×Q16—1222no—
497C2×Q16—1222no—
498C2×Q16—1222no—
499C2×Q16—1222no—
500C2×Q16—1222no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—1222no—
505C2×SD16—1222no—
506C2×SD16—1222no—
507C2×M16—614no—
508C2×M16—1222no—
509C2×M16—1222no—
510C2×M16—1222no—
511C2×M16—1222no—
512C2×M16—1222no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517#117—1222no—
518#117—1222no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—611no—
534C2×C42—1222no—
535C2×C42—1222no—
536C2×C42—1221no—
537C2×C42C22×D6111yescharacteristic
538C4⋊C8—22no—
539C4⋊C8—1222no—
540C4⋊C8—1222no—
541C4⋊C8—1222no—
542#103—22no—
543#103—1222no—
544#103—1222no—
545#103—1222no—
546#103—1222no—
547#103—1222no—
548#102—22no—
549#102—1222no—
550#95—21no—
551#95—21no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561#95—1221no—
562C24—21no—
563C24—611no—
564#41—1228no—
565#41—1228no—
566#41—2444no—
567#41—2444no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—612no—
574C2×Q8—612no—
575C2×Q8—1224no—
576C2×Q8—1228no—
577C2×Q8—1228no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—2442no—
589C2×Q8—2442no—
590C2×Q8—2444no—
591C2×Q8—2444no—
592C2×Q8D4×D6112yes—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—1224no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4D4×D6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—611no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1224no—
618C22×C4—1224no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1222no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—2441no—
625C22×C4—2441no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636Q16—1228no—
637Q16—1228no—
638SD16—28no—
639SD16—1228no—
640M16—1228no—
641M16—2444no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—612no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8D4×D6112yes—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—2442no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C42—21no—
669C42—21no—
670C42—1222no—
671C42—1222no—
672C42—1221no—
673C42—1221no—
674C42—2442no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—612no—
683C23—612no—
684C23—612no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23C2×D4×D6111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—41no—
693Q8—41no—
694Q8—1222no—
695Q8—1222no—
696Q8—1222no—
697Q8—1222no—
698Q8—2448no—
699Q8—2441no—
700Q8—2441no—
701Q8—2441no—
702Q8—2441no—
703D4—22no—
704D4—22no—
705D4—41no—
706D4—41no—
707D4—2448no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—612no—
723C2×C4—612no—
724C2×C4—612no—
725C2×C4—614no—
726C2×C4—614no—
727C2×C4—614no—
728C2×C4—614no—
729C2×C4—612no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—4884no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2448no—
741C2×C4—2448no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4#1451980612yescomplemented
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4#41×D6111yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C8—22no—
760C8—41no—
761C8—1222no—
762C8—2441no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—614no—
771C22—1222no—
772C22—1222no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—1222no—
777C22#121×D6111yescharacteristic
778C22#121×D6111yescharacteristic
779C22#121×D6111yescharacteristic
780C22#137×D6111yescharacteristic
781C22C2×#1451980611yescharacteristic
782C22#1684055811yescharacteristic
783C22#1684055911yescharacteristic
784C4—22no—
785C4—42no—
786C4—41no—
787C4—81no—
788C4—81no—
789C4—614no—
790C4—1222no—
791C4—4881no—
792C4—4881no—
793C4—2442no—
794C4—2442no—
795C4—2441no—
796C4#120×D6111yescharacteristic
797C4#123×D6111yescharacteristic
798C4#123×D6111yescharacteristic
799C4#124×D6111yescharacteristic
800C2—82no—
801C2—1224no—
802C2#394×D6111yescharacteristic
803C2#2145528611yescharacteristic
804C2#2145528911yescharacteristic
805C2#2145530111yescharacteristic
806C2#2145530811yescharacteristic
807C2#2145544211yescharacteristic
808C2#2145544411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2055C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenter#2055D61
hypocenterC61#23547
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×#16839784C2semidirect
4. C2×#16839769C2semidirect
6. #391×D61C2semidirect
7. #21447143C2semidirect
8. #21447142C2semidirect
9. #21447141C2semidirect
10. #21447140C2semidirect
11. #21447136C2semidirect
12. #21447135C2semidirect
13. #21447132C2semidirect
14. #21445537C2semidirect
15. C61×#2055C2semidirect
307. C2×C4×C61#137semidirect
336. C2×Dic61#137semidirect
409. #2055D61semidirect
469. C61#23547semidirect
752. C2×C4#14519806semidirect

Maximal subgroups

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

subgroupindex
C22×#145198062
C2×#168397842
C2×#168397602
C2×#168397692
#214483062
#391×D612
#214471432
#214471422
#214471412
#214471402
#214471362
#214471352
#214471322
#214455372
C61×#20552
#2354761