Finite Group Databasebeta

← #29719000

Subgroups — #29719000

Order 15616.

1182 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839914C211yesmaximal, characteristic
2C2×#102×D61C211yesmaximal, characteristic
3#21450301C211yesmaximal, characteristic, complemented
4D4×#11758198C211yesmaximal, characteristic
5#21447236C211yesmaximal, characteristic, complemented
6#21447233C211yesmaximal, characteristic, complemented
7#21447138C211yesmaximal, characteristic, complemented
8#21447137C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446151C211yesmaximal, characteristic, complemented
12#21445995C211yesmaximal, characteristic, complemented
13#21445904C211yesmaximal, characteristic, complemented
14#21445827C211yesmaximal, characteristic, complemented
15C61×#1804C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C22×#11758198—21no—
24#16839914—24no—
25C2×#14519706C2211yescharacteristic, complemented
26C2×#14519702C2211yescharacteristic, complemented
27C2×#14519700C2211yescharacteristic, complemented
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32#102×D61—24no—
33C2×#14519689C2211yescharacteristic
34#16839704—21no—
35#16839704—21no—
36#16839668C2211yescharacteristic, complemented
37#16839667C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839641—21no—
41#16839639—21no—
42#16839627C2211yescharacteristic, complemented
43#16839624—21no—
44#16839624—21no—
45#16839619C2211yescharacteristic
46#16839617—21no—
47C4×#11758198C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic, complemented
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#382C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×Dic122C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—41no—
69C2×D4×D61—41no—
70C2×D4×D61D414yes—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C2×#11758190—22no—
75C2×#11758190—41no—
76C2×#11758190—41no—
77C2×#11758200—22no—
78C2×#11758200—22no—
79C2×#11758200—22no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—41no—
84C2×C8×D61—41no—
85#14519757—22no—
86#14519757—22no—
87D4×Dic61—22no—
88D4×Dic61—41no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—44no—
103C2×#11758198D411yescharacteristic
104C2×#11758198D411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106#14519706—41no—
107#14519702—41no—
108#14519700—41no—
109#14519699—22no—
110#14519698—22no—
111#14519697—22no—
112#14519697—22no—
113#14519689—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684D411yescharacteristic
122#14519684D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C4×D4×C61—22no—
128C4×D4×C61—41no—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—41no—
135#102×C61—22no—
136#102×C61—22no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—81no—
147C23×D61—81no—
148C23×D61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C2×D412yes—
153C2×D4×C61#4112yes—
154C2×D4×C61#4112yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—81no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—24no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—42no—
171C22×Dic61—42no—
172C22×Dic61—81no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176D4×D61—28no—
177D4×D61—44no—
178D4×D61—44no—
179D4×D61—44no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244C2×D412yes—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61C2×D412yes—
194C2×C4×D61#4112yes—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C22⋊C4×C61—42no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—42no—
217#11758200—44no—
218#11758198—22no—
219#11758198—22no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224#11758198—81no—
225#11758198—81no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—42no—
231#11758196—42no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240#11758190—44no—
241C8×D61—44no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—22no—
255C22×D61—48no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—48no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—84no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61#12112yes—
269C22×D61#13512yes—
270C22×D61AGL(1,ℤ/8)12yes—
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61#12314yes—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
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×C61—41no—
290C2×C4×C61—84no—
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C22⋊D61—48no—
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—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—84no—
316C2×Dic61#12112yes—
317D244—22no—
318D244—22no—
319D244—41no—
320D244—41no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—84no—
326Dic122—41no—
327Dic122—41no—
328Dic122—41no—
329Dic122—41no—
330C8×C61—41no—
331C8×C61—41no—
332#92418—41no—
333#92418—41no—
334#24527—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61C2×#12111yescharacteristic
343C22×C61#54611yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61C2×#13511yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61#57711yescharacteristic
348C22×C61#57711yescharacteristic
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—816no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61#46314yes—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61C2×#12311yescharacteristic
370C4×C61#53411yescharacteristic
371C4×C61#55111yescharacteristic
372C4×C61#55111yescharacteristic
373Dic61—22no—
374Dic61—41no—
375Dic61—41no—
376Dic61—81no—
377Dic61—81no—
378Dic61—81no—
379C2×#450—611no—
380C22×#102—611no—
381#2503—611no—
382D4×C22⋊C4—611no—
383#2073—611no—
384#2073—611no—
385#2055—611no—
386#2055—611no—
387#1892—611no—
388#1877—611no—
389#1877—611no—
390#1850—611no—
391#1823—611no—
392#1804—611no—
393#1804D6111yescharacteristic, complemented
394C2×C61—44no—
395C2×C61#241211yescharacteristic
396C2×C61C2×#46311yescharacteristic
397C2×C61#304211yescharacteristic
398C2×C61#329611yescharacteristic
399C2×C61#329611yescharacteristic
400C2×C61#331011yescharacteristic
401C2×C61#331011yescharacteristic
402D61—24no—
403D61—82no—
404C23×D4—611no—
405C22×SD16—611no—
406C22×SD16—611no—
407C23×C8—611no—
408C2×C22⋊Q8—611no—
409C2×C4×D4—611no—
410C2×C4×D4C2×D6111yescharacteristic
411C22×C4⋊C4—611no—
412C22×C22⋊C4—1221no—
413#450—1224no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8C2×D6111yescharacteristic, complemented
416C2×#103—611no—
417C2×#103—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—1224no—
423C2×#102C2×D6111yescharacteristic
424C2×#102C2×D6111yescharacteristic
425C2×C22⋊C8—611no—
426#400—1221no—
427#400—1221no—
428#391—611no—
429#391—611no—
430#390—611no—
431#390—611no—
432#386—1221no—
433#386—1221no—
434#382—611no—
435#382C2×D6111yescharacteristic, complemented
436#381—1221no—
437#381—1221no—
438#380—611no—
439#379—1221no—
440C4×C22⋊C4—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic, complemented
446#340C2×D6111yescharacteristic, complemented
447#336—611no—
448#336—611no—
449C61#2452711yescharacteristic, complemented, Sylow
450C25—1221no—
451C22×Q8—611no—
452C22×D4—614no—
453C22×D4—611no—
454C22×D4—1222no—
455C22×D4—1221no—
456C22×D4—1222no—
457C22×D4—1222no—
458C22×D4—2441no—
459C22×D4—2441no—
460C22×D4C22×D6111yescharacteristic
461C23×C4—21no—
462C23×C4—611no—
463C23×C4—1221no—
464C23×C4—1221no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—2441no—
470C2×SD16—2441no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—1222no—
474C22×C8—2441no—
475C22×C8—2441no—
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478C22⋊Q8—1222no—
479C22⋊Q8—1222no—
480C4×D4—22no—
481C4×D4—41no—
482C4×D4—1222no—
483C4×D4—2441no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—2444no—
504C2×C42—611no—
505C2×C42C22×D6111yescharacteristic
506C4⋊C8—41no—
507C4⋊C8—2441no—
508#103—2441no—
509#103—2441no—
510#102—22no—
511#102—22no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516C22⋊C8—1222no—
517#95—21no—
518#95—21no—
519#95—611no—
520#95—611no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24—611no—
530C24—1224no—
531C24—1221no—
532C24—4881no—
533C24—4881no—
534C24—2442no—
535C24—2442no—
536C24—2442no—
537C24—2442no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—612no—
548C2×D4—1224no—
549C2×D4—1228no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—2444no—
556C2×D4—2444no—
557C2×D4—2444no—
558C2×D4—2442no—
559C2×D4—2442no—
560C2×D4#1175822212yes—
561C2×D4D4×D6112yes—
562C2×D4#1175822612yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—611no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—4881no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590SD16—2444no—
591SD16—2444no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—2444no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C22⋊C4—42no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—4881no—
621C22⋊C4—4881no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C42—21no—
628C42—21no—
629C42—1221no—
630C42—1221no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—612no—
639C23—612no—
640C23—612no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1222no—
646C23—4884no—
647C23—4884no—
648C23—4884no—
649C23—4884no—
650C23—4884no—
651C23—2448no—
652C23—2448no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C2×D4×D6111yescharacteristic
660Q8—2441no—
661Q8—2441no—
662Q8—2441no—
663Q8—2441no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—1222no—
668D4—1222no—
669D4—2448no—
670D4—2441no—
671D4—2441no—
672D4#1451976214yes—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—612no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4C2×#1175822211yescharacteristic
716C2×C4C2×#1175822611yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982311yescharacteristic
719C8—41no—
720C8—41no—
721C8—2441no—
722C8—2441no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—614no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—48816no—
738C22—4881no—
739C22—4881no—
740C22—4881no—
741C22—4881no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22#121×D6111yescharacteristic
746C22#1684040211yescharacteristic
747C22#1684040311yescharacteristic
748C22#135×D6111yescharacteristic
749C22AGL(1,ℤ/8)×D6111yescharacteristic
750C22#1684056911yescharacteristic
751C22#1684057211yescharacteristic
752C4—41no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—1222no—
758C4—4881no—
759C4—4881no—
760C4—4881no—
761C4—2441no—
762C4—2441no—
763C4C2×#1451976211yescharacteristic
764C4#1684032011yescharacteristic
765C4#1684043611yescharacteristic
766C4#1684043911yescharacteristic
767C2—44no—
768C2—1224no—
769C2—4882no—
770C2#2144921211yescharacteristic
771C2#463×D6111yescharacteristic
772C2#2145532911yescharacteristic
773C2#2145765111yescharacteristic
774C2#2145765511yescharacteristic
775C2#2145783711yescharacteristic
776C2#2145784111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1804C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#1804D61
hypocenterC61#24527
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
3. #21450301C2semidirect
5. #21447236C2semidirect
6. #21447233C2semidirect
7. #21447138C2semidirect
8. #21447137C2semidirect
9. #21446241C2semidirect
10. #21446153C2semidirect
11. #21446151C2semidirect
12. #21445995C2semidirect
13. #21445904C2semidirect
14. #21445827C2semidirect
15. C61×#1804C2semidirect
25. C2×#14519706C22semidirect
26. C2×#14519702C22semidirect
27. C2×#14519700C22semidirect
36. #16839668C22semidirect
37. #16839667C22semidirect
42. #16839627C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839516C22semidirect
55. C2×C4⋊C8×C61C22semidirect
58. C61×#382C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
393. #1804D61semidirect
415. C2×C4⋊C8C2×D61semidirect
435. #382C2×D61semidirect
445. #340C2×D61semidirect
446. #340C2×D61semidirect
449. C61#24527semidirect

Maximal subgroups

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

subgroupindex
C2×#168399142
C2×#102×D612
#214503012
D4×#117581982
#214472362
#214472332
#214471382
#214471372
#214462412
#214461532
#214461512
#214459952
#214459042
#214458272
C61×#18042
#2452761