Finite Group Databasebeta

← #29691290

Subgroups — #29691290

Order 15616.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2#21448497C211yesmaximal, characteristic, complemented
3#21448401C211yesmaximal, characteristic
4#21446701C211yesmaximal, characteristic, complemented
5#21446674C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446499C211yesmaximal, characteristic, complemented
8#21446449C211yesmaximal, characteristic, complemented
9#21446442C211yesmaximal, characteristic, complemented
10#21446171C211yesmaximal, characteristic, complemented
11#21446171C211yesmaximal, characteristic, complemented
12#21446129C211yesmaximal, characteristic, complemented
13#21446016C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519742C2211yescharacteristic, complemented
20C2×#14519736C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16839913C418yescomplemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519702C2211yescharacteristic, complemented
26C2×#14519702C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519687C2211yescharacteristic, complemented
31C2×C8×Dic61C2211yescharacteristic, complemented
32#16839667C2211yescharacteristic, complemented
33#16839665—21no—
34#16839665—21no—
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839659—21no—
40#16839658C2211yescharacteristic, complemented
41#16839656—21no—
42#16839650—21no—
43#16839649—21no—
44#16839618—21no—
45#16839618—21no—
46C4⋊C4×Dic61C2211yescharacteristic, complemented
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C23×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C2×#11758200—41no—
62C2×#11758200—41no—
63C2×#11758200—41no—
64C2×#11758200—41no—
65C2×#11758200C2×C414yes—
66C2×#11758200C2×C414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519756—22no—
70#14519756C2×C414yes—
71#14519742—41no—
72#14519742—41no—
73#14519736—41no—
74#14519736—41no—
75#14519736—41no—
76#14519736—41no—
77C2×C4⋊Dic61D411yescharacteristic
78C2×C4⋊Dic61D411yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61D411yescharacteristic
96C2×C22⋊Dic61D411yescharacteristic
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519710—41no—
103#14519708—41no—
104#14519702—41no—
105#14519702—41no—
106#14519698C2×C414yes—
107#14519698C2×C414yes—
108C22⋊#92418C2×C414yes—
109#14519687—41no—
110C8×Dic61—41no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C25×C61—21no—
116C22×D4×C61—21no—
117C22×D4×C61—22no—
118C22×D4×C61—41no—
119C22×D4×C61—41no—
120C22×D4×C61—41no—
121C22×D4×C61—41no—
122C22×D4×C61C2×C414yes—
123C22×D4×C61C2311yescharacteristic
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131#102×C61—41no—
132#102×C61—41no—
133#102×C61—41no—
134#102×C61—41no—
135C22⋊C8×C61—22no—
136#95×C61—21no—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—24no—
140C24×C61—42no—
141C24×C61—42no—
142C24×C61—81no—
143C24×C61—81no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61C2×D411yescharacteristic
147C2×D4×C61—24no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—44no—
159C2×D4×C61—44no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C22×C412yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C22×C412yes—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61#4112yes—
175C22×C4×C61C2411yescharacteristic
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122C22×C412yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C22⋊C4×C61—81no—
201C22⋊Dic61—24no—
202C22⋊Dic61—41no—
203C22⋊Dic61—41no—
204C22⋊Dic61—42no—
205C22⋊Dic61—81no—
206C22⋊Dic61—81no—
207C22⋊Dic61—81no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211C22⋊Dic61—81no—
212C22⋊Dic61—81no—
213#11758200—44no—
214#11758200—44no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—41no—
221C4⋊Dic61—41no—
222C4⋊Dic61C22×C412yes—
223#11758196—24no—
224#11758196—42no—
225#11758196—81no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—42no—
231C4×Dic61—42no—
232C4×Dic61—81no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C22×C412yes—
238C2×#92418C22×C412yes—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—48no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—84no—
261C23×C61—84no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61C4×D412yes—
267C23×C61C22×D411yescharacteristic
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—48no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—41no—
276D4×C61—41no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C4×D412yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320Dic122—22no—
321Dic122—22no—
322Dic122—41no—
323Dic122—41no—
324C8×C61—41no—
325C8×C61—41no—
326#92418—22no—
327#92418—22no—
328#22052—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—816no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61C2×C4×D411yescharacteristic
352C22×C61#53411yescharacteristic
353C22×C61#53511yescharacteristic
354C22×C61#57611yescharacteristic
355C22×C61#57711yescharacteristic
356C22×C61#57711yescharacteristic
357C22×C61#57711yescharacteristic
358C4×C61—22no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61#51811yescharacteristic
362C4×C61#51811yescharacteristic
363C4×C61#53811yescharacteristic
364C4×C61#53811yescharacteristic
365Dic61—42no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61—42no—
371Dic61—81no—
372Dic61—81no—
373C2×#450—611no—
374#2323—611no—
375#2309—611no—
376#1973—611no—
377#1968—611no—
378#1936—611no—
379#1934—611no—
380#1926—611no—
381#1925—611no—
382#1880—611no—
383#1880—611no—
384#1873—611no—
385#1854—611no—
386#1786D6111yescharacteristic
387#1750—611no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61—82no—
391C2×C61#232111yescharacteristic
392C2×C61#294611yescharacteristic
393C2×C61#294911yescharacteristic
394C2×C61#319811yescharacteristic
395C2×C61#320011yescharacteristic
396C2×C61#322211yescharacteristic
397C2×C61#322411yescharacteristic
398C23×D4C2×D6111yescharacteristic
399C22×SD16—611no—
400C22×SD16—611no—
401C2×C22⋊Q8—611no—
402C2×C4×Q8—611no—
403C2×#117—611no—
404C2×#117—611no—
405#450—618no—
406C2×#107—611no—
407C2×#106—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102C2×D6111yescharacteristic
413C2×#102C2×D6111yescharacteristic
414C2×#102C2×D6111yescharacteristic
415C2×#102C2×D6111yescharacteristic
416C2×C22⋊C8—611no—
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×C4×C8—611no—
420#391—611no—
421#390—611no—
422#390—611no—
423#390—611no—
424#390—611no—
425#390—1221no—
426#390—1221no—
427#389—611no—
428#389—1221no—
429#388—1221no—
430#388—1221no—
431#387—1221no—
432#380C2×D6111yescharacteristic
433#379—1221no—
434#379—1221no—
435C4×C4⋊C4—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2205211yescharacteristic, complemented, Sylow
443C25—21no—
444C22×Q8—611no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C4×D6114yes—
452C22×D4C22×D6111yescharacteristic
453C22×D4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—614no—
457C2×SD16—2441no—
458C2×SD16—2441no—
459C2×SD16—2441no—
460C2×SD16—2441no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22⋊Q8—614no—
466C22⋊Q8—1222no—
467C4×Q8—2441no—
468C4×Q8—2441no—
469#117—2441no—
470#117—2441no—
471#117—2441no—
472#117—2441no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501#107—2441no—
502#106—2441no—
503#103—2441no—
504#103—2441no—
505#102—41no—
506#102—41no—
507#102—41no—
508#102—41no—
509#102—614no—
510#102—614no—
511C22⋊C8—22no—
512C22⋊C8—614no—
513#97—2441no—
514C4×C8—2441no—
515#95—21no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—21no—
521C24—21no—
522C24—24no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24D4×D6111yescharacteristic
530C2×Q8—612no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C2×C4×D6112yes—
554C2×D4C2×C4×D6112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4C2×C4×D6112yes—
570C22×C4D4×D6111yescharacteristic
571C22×C4#1175822412yes—
572C22×C4C23×D6111yescharacteristic
573SD16—2444no—
574SD16—2444no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—612no—
592C4⋊C4—1221no—
593C4⋊C4—1224no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—4881no—
599C4⋊C4—2441no—
600C4⋊C4—2441no—
601C4⋊C4—2442no—
602C22⋊C4—81no—
603C22⋊C4—1224no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C22⋊C4—4881no—
612C22⋊C4—2441no—
613C22⋊C4—2441no—
614C22⋊C4—2442no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—4881no—
620C42—2442no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23#1451973712yes—
650C23C2×D4×D6111yescharacteristic
651Q8—1222no—
652Q8—1222no—
653Q8—2441no—
654Q8—2441no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4#1451973712yes—
701C2×C4C22×C4×D6111yescharacteristic
702C2×C4C2×#1175822411yescharacteristic
703C2×C4#1451982211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982211yescharacteristic
707C8—41no—
708C8—41no—
709C8—1222no—
710C8—1222no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×#1451973711yescharacteristic
734C22#1684032211yescharacteristic
735C22#1684032711yescharacteristic
736C22#1684056311yescharacteristic
737C22#1684056811yescharacteristic
738C22#1684057211yescharacteristic
739C22#1684057211yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—4881no—
744C4—4881no—
745C4—2442no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C4—2441no—
750C4—2442no—
751C4#1684023511yescharacteristic
752C4#1684023511yescharacteristic
753C4#1684034711yescharacteristic
754C4#1684034711yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#2144847411yescharacteristic
759C2#2145464511yescharacteristic
760C2#2145468111yescharacteristic
761C2#2145666711yescharacteristic
762C2#2145668811yescharacteristic
763C2#2145688711yescharacteristic
764C2#2145690911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#22052
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #21448497C2semidirect
4. #21446701C2semidirect
5. #21446674C2semidirect
6. #21446513C2semidirect
7. #21446499C2semidirect
8. #21446449C2semidirect
9. #21446442C2semidirect
10. #21446171C2semidirect
11. #21446171C2semidirect
12. #21446129C2semidirect
13. #21446016C2semidirect
14. #21445587C2semidirect
19. C2×#14519742C22semidirect
22. #16839913C4semidirect
23. C2×#14519710C22semidirect
24. C2×#14519708C22semidirect
25. C2×#14519702C22semidirect
26. C2×#14519702C22semidirect
30. C2×#14519687C22semidirect
31. C2×C8×Dic61C22semidirect
32. #16839667C22semidirect
40. #16839658C22semidirect
46. C4⋊C4×Dic61C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
442. C61#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
#214484972
#214484012
#214467012
#214466742
#214465132
#214464992
#214464492
#214464422
#214461712
#214461292
#214460162
#214455872
C61×#17862
#2205261