Finite Group Databasebeta

← #29646037

Subgroups — #29646037

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×#16840345C211yesmaximal, characteristic
2#21454845C211yesmaximal, characteristic, complemented
3#21454841C211yesmaximal, characteristic, complemented
4#21444187C212yesmaximal, complemented
5#21444177C212yesmaximal, complemented
6#21444169C212yesmaximal, complemented
7#21444166C212yesmaximal, complemented
8#21444137C211yesmaximal, characteristic, complemented
9C2×#16839485C211yesmaximal, characteristic, complemented
10C2×#16839485C211yesmaximal, characteristic, complemented
11C61×#1459C211yesmaximal, characteristic, complemented
12#16840345—22no—
13#16840345—22no—
14#16840345—22no—
15#16840345—22no—
16C2×#14519772C2211yescharacteristic
17C2×#14519771C411yescharacteristic
18C2×#14519765C411yescharacteristic
19C2×#14519763C2211yescharacteristic
20C2×#14519762C2211yescharacteristic
21C2×#14519760C411yescharacteristic
22C2×#14519754C411yescharacteristic
23C2×#14519751C411yescharacteristic
24C2×#14519750C2211yescharacteristic
25C2×#14519749C411yescharacteristic
26C2×#14519747C411yescharacteristic
27C2×#14519745C411yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30#16839833—22no—
31#16839830—22no—
32C8×C22⋊D61—22no—
33#16839825—22no—
34#16839816C2212yescomplemented
35#16839812C2212yescomplemented
36#16839724C2212yescomplemented
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C22⋊C8×D61C2212yescomplemented
40#16839488C2212yescomplemented
41#16839486C2212yescomplemented
42#16839485C2212yes—
43#16839485C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C61×#324C2212yescomplemented
50C61×#323C2212yescomplemented
51C24×D61C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2×C411yescharacteristic
59C23×Dic61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758189—22no—
62C22×#92418—21no—
63C22×#92418—21no—
64C2×C8×D61—22no—
65#14519772—22no—
66#14519772—22no—
67#14519771—22no—
68#14519771—22no—
69#14519765—22no—
70#14519765—22no—
71#14519763—22no—
72#14519763—22no—
73#14519762—22no—
74#14519762—22no—
75#14519760—22no—
76#14519760—22no—
77#14519754—22no—
78#14519754—22no—
79#14519751—22no—
80#14519751—22no—
81#14519750—22no—
82#14519750—22no—
83#14519749—22no—
84#14519749—22no—
85#14519747—22no—
86#14519747—22no—
87#14519745—22no—
88#14519745—22no—
89C4×C22⋊D61D412yes—
90C4×C22⋊D61D412yes—
91C4×C22⋊D61D412yes—
92C4×C22⋊D61D412yes—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×C22⋊Dic61C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2311yescharacteristic
113C2×#11758198C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—21no—
129C22×C8×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C42×C61C2×C411yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2312yes—
141C22⋊C8×C61C2312yes—
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—81no—
149C23×D61—81no—
150C23×D61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—81no—
160C22×C4×C61—81no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—81no—
176C2×C22⋊D61—81no—
177C2×C22⋊D61—81no—
178C2×C22⋊D61C22⋊C412yes—
179C2×C22⋊D61C22⋊C412yes—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—81no—
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—81no—
191C2×D244—81no—
192C2×C4×D61—81no—
193C2×C4×D61C2×D412yes—
194C2×C4×D61C2×D412yes—
195C2×Dic122—22no—
196C2×Dic122—81no—
197C2×C8×C61—22no—
198C2×C8×C61—22no—
199C2×C8×C61—81no—
200C2×C8×C61—81no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C22⋊Dic61—22no—
210C22⋊Dic61C22⋊C412yes—
211C22⋊Dic61C22⋊C412yes—
212#11758198—22no—
213#11758198—21no—
214#11758198—21no—
215#11758198—21no—
216#11758198—21no—
217#11758198—21no—
218#11758198—21no—
219#11758198—21no—
220#11758198—21no—
221#11758198—22no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198C22⋊C412yes—
226#11758198C22⋊C412yes—
227C4⋊Dic61—22no—
228#11758196—22no—
229#11758196—22no—
230#11758196—22no—
231#11758196C22⋊C412yes—
232#11758196C22⋊C412yes—
233C4×Dic61C2×D412yes—
234C4×Dic61C2×D412yes—
235C2×#92418—22no—
236C2×#92418—22no—
237C2×#92418—81no—
238C2×#92418—81no—
239#11758189—82no—
240C8×D61—82no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61C2×C22⋊C411yescharacteristic
249C23×C61C2×C22⋊C411yescharacteristic
250C23×C61#13112yes—
251C23×C61#13112yes—
252C23×C61C23×C411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—81no—
270C22×D61—81no—
271C22×D61—81no—
272C22×D61—81no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61C2×C22⋊C412yes—
276D4×C61—42no—
277D4×C61—42no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
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—41no—
291C2×C4×C61—81no—
292C2×C4×C61—81no—
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C22⋊D61—24no—
298C22⋊D61—24no—
299C22⋊D61—82no—
300C22⋊D61—82no—
301C22⋊D61—82no—
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—81no—
311C2×Dic61—81no—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×C22⋊C412yes—
315D244—82no—
316D244—82no—
317C4×D61—42no—
318C4×D61—42no—
319Dic122—82no—
320C8×C61—42no—
321C8×C61—42no—
322#92418—42no—
323#92418—42no—
324#17386—611nomaximal, Sylow
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61#40812yes—
339C22×C61#40812yes—
340C22×C61C22×C22⋊C411yescharacteristic
341C22×C61C2×#13111yescharacteristic
342C22×C61C2×#13111yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—84no—
355C2×D61—84no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—21no—
361C4×C61—21no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367Dic61—22no—
368Dic61—22no—
369Dic61—22no—
370Dic61—41no—
371Dic61—41no—
372C2×#538—611no—
373#2973—611no—
374#2972—611no—
375#1473—612no—
376#1471—612no—
377#1469—612no—
378#1468—612no—
379#1459—611no—
380#1459D6111yescharacteristic, complemented
381C2×#323—611no—
382C2×#323—611no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—22no—
386C2×C61—22no—
387C2×C61—81no—
388C2×C61C2×#40811yescharacteristic
389C2×C61#288311yescharacteristic
390C2×C61#288811yescharacteristic
391D61—42no—
392D61—81no—
393D61—81no—
394#538—1222no—
395#538—1222no—
396#538—1222no—
397#538—1222no—
398C2×#126—611no—
399C2×#126—611no—
400C2×#124—611no—
401C2×#124—611no—
402C2×#123—611no—
403C2×#123—611no—
404C2×C22⋊Q8—611no—
405C2×#121—611no—
406C2×#121—611no—
407C2×#121—611no—
408C2×#120—611no—
409C2×#120—611no—
410C2×C4×D4—611no—
411C2×C4×D4C2×D6111yescharacteristic
412C22×C22⋊C4—611no—
413#435—1222no—
414#435—1222no—
415C8×D4—1222no—
416C8×D4—1222no—
417#432—612no—
418#431—612no—
419#407—612no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—612no—
423C2×C22⋊C8C2×D6111yescharacteristic
424C2×C22⋊C8C2×D6111yescharacteristic
425#324—612no—
426#324C2×D6112yescomplemented
427#323—612no—
428#323—612no—
429#323—612no—
430#323—612no—
431#323—612no—
432#323C2×D6112yescomplemented
433C61#1738611yescharacteristic, complemented, Sylow
434C25—611no—
435C22×Q8—611no—
436C22×D4—611no—
437C22×D4—611no—
438C22×D4—611no—
439C22×D4—611no—
440C22×D4—611no—
441C22×D4—611no—
442C22×D4C4×D6111yescharacteristic
443C23×C4—611no—
444C23×C4—611no—
445C23×C4C4×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C2×M16—1222no—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—1222no—
451C22×C8—1221no—
452C22×C8—1221no—
453#126—1222no—
454#126—1222no—
455#126—1222no—
456#126—1222no—
457#124—1222no—
458#124—1222no—
459#124—1222no—
460#124—1222no—
461#123—1222no—
462#123—1222no—
463#123—1222no—
464#123—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467#121—1222no—
468#121—1222no—
469#121—1222no—
470#121—1222no—
471#121—1222no—
472#121—1222no—
473#120—1222no—
474#120—1222no—
475#120—1222no—
476#120—1222no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—612no—
482C4×D4—612no—
483C4×D4—612no—
484C4×D4—612no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4C4×D6111yescharacteristic
508C2×C22⋊C4C22×D6111yescharacteristic
509C2×C42—611no—
510C2×C42C4×D6111yescharacteristic
511C4⋊C8—1222no—
512C4⋊C8—1222no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—612no—
516C22⋊C8—612no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519C22⋊C8—1221no—
520C22⋊C8—1221no—
521C22⋊C8C22×D6112yes—
522C22⋊C8C22×D6112yes—
523#97—1222no—
524C4×C8—1222no—
525C24—611no—
526C24—611no—
527C24—611no—
528C24—1221no—
529C24—1221no—
530C24—1222no—
531C24—1222no—
532C24—4881no—
533C24—4881no—
534C24C2×C4×D6111yescharacteristic
535C24C2×C4×D6111yescharacteristic
536C2×Q8—1222no—
537C2×Q8—4881no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—612no—
543C2×D4—612no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—4881no—
552C2×D4—4881no—
553C2×D4—4881no—
554C2×D4—4881no—
555C2×D4—4881no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4C2×C4×D6111yescharacteristic
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4D4×D6111yescharacteristic
576C22×C4D4×D6111yescharacteristic
577C22×C4D4×D6111yescharacteristic
578C22×C4D4×D6111yescharacteristic
579C22×C4C23×D6111yescharacteristic
580M16—4882no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—81no—
584C2×C8—81no—
585C2×C8—1222no—
586C2×C8—1222no—
587C2×C8—4882no—
588C2×C8—4881no—
589C2×C8—4881no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—612no—
593C4⋊C4—612no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—612no—
603C22⋊C4—612no—
604C22⋊C4—612no—
605C22⋊C4—612no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1221no—
613C22⋊C4—1221no—
614C22⋊C4—1221no—
615C22⋊C4—1221no—
616C22⋊C4—1221no—
617C22⋊C4—1221no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C42—21no—
621C42—21no—
622C42—612no—
623C42—612no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—612no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—4881no—
641C23—4881no—
642C23—4881no—
643C23—4881no—
644C23—4884no—
645C23—4884no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2442no—
653C23—2442no—
654C23C22⋊C4×D6111yescharacteristic
655C23C22⋊C4×D6111yescharacteristic
656C23#1451978312yes—
657C23#1451978512yes—
658C23C22×C4×D6111yescharacteristic
659Q8—4882no—
660D4—42no—
661D4—42no—
662D4—1224no—
663D4—1224no—
664D4—4882no—
665D4—4882no—
666D4—4882no—
667D4—4882no—
668D4—4882no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—4881no—
692C2×C4—4881no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4C22⋊C4×D6111yescharacteristic
700C2×C4C22⋊C4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C2×D4×D6111yescharacteristic
703C8—42no—
704C8—42no—
705C8—2442no—
706C8—2442no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—81no—
719C22—81no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—4884no—
728C22—4884no—
729C22—4881no—
730C22—4881no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22#1683972712yes—
738C22#1683972712yes—
739C22C2×C22⋊C4×D6111yescharacteristic
740C22C2×#1451978311yescharacteristic
741C22C2×#1451978511yescharacteristic
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—1222no—
750C4—1222no—
751C4—1222no—
752C4—2441no—
753C4—2441no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—22no—
758C2—81no—
759C2—4881no—
760C2—4881no—
761C2—2442no—
762C2C2×#1683972711yescharacteristic
763C2#2145427711yescharacteristic
764C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1459C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840345C2
cosocleC22×C4×C61C24
hypercenter#1459D61
hypocenterC61#17386
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #21454845C2semidirect
3. #21454841C2semidirect
4. #21444187C2semidirect
5. #21444177C2semidirect
6. #21444169C2semidirect
7. #21444166C2semidirect
8. #21444137C2semidirect
9. C2×#16839485C2semidirect
10. C2×#16839485C2semidirect
11. C61×#1459C2semidirect
34. #16839816C22semidirect
35. #16839812C22semidirect
36. #16839724C22semidirect
39. C22⋊C8×D61C22semidirect
40. #16839488C22semidirect
41. #16839486C22semidirect
49. C61×#324C22semidirect
50. C61×#323C22semidirect
380. #1459D61semidirect
426. #324C2×D61semidirect
432. #323C2×D61semidirect
433. C61#17386semidirect

Maximal subgroups

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

subgroupindex
C2×#168403452
#214548452
#214548412
#214441872
#214441772
#214441692
#214441662
#214441372
C2×#168394852
C61×#14592
#1738661