Finite Group Databasebeta

← #29843349

Subgroups — #29843349

Order 15616.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic
2#21449002C212yesmaximal, complemented
3#21448989C212yesmaximal, complemented
4#21448940C212yesmaximal, complemented
5#21448936C212yesmaximal, complemented
6#21448781C212yesmaximal, complemented
7#21448757C212yesmaximal, complemented
8#21448709C212yesmaximal, complemented
9#21448673C212yesmaximal, complemented
10#21448610C212yesmaximal, complemented
11#21448606C212yesmaximal, complemented
12#21448586C211yesmaximal, characteristic
13#21448575C211yesmaximal, characteristic, complemented
14#21448572C211yesmaximal, characteristic, complemented
15#21448456C212yesmaximal, complemented
16#21448445C212yesmaximal, complemented
17#21448213C211yesmaximal, characteristic, complemented
18#21448210C211yesmaximal, characteristic, complemented
19C61×#2333C211yesmaximal, characteristic
20#16840293C4116yescomplemented
21C2×#14519770C2212yes—
22C2×#14519768C2211yescharacteristic
23C2×#14519764C2211yescharacteristic
24C2×#14519758C2212yes—
25C2×#14519756C2211yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×D4×Dic61C2212yes—
29C2×#14519733C2212yes—
30C22×C4×Dic61C2211yescharacteristic
31#16839666C2212yes—
32#16839666C2212yes—
33#16839665C2212yes—
34#16839660C2212yes—
35#16839659C2212yes—
36#16839658C2212yes—
37#16839657C2212yes—
38#16839656C2212yes—
39#16839656C2212yes—
40#16839656C2212yes—
41#16839656C2212yes—
42#16839656C2212yes—
43#16839655C2212yes—
44#16839650C2212yes—
45#16839650C2212yes—
46#16839650C2212yes—
47#16839650C2212yes—
48#16839650C2212yes—
49#16839649C2212yes—
50#16839648C2212yes—
51#16839647C2212yes—
52#16839647C2212yes—
53#16839646C2212yes—
54#16839646C2212yes—
55#16839645C2212yes—
56#16839645C2212yes—
57#16839644C2212yes—
58#16839644C2212yes—
59#16839643C2212yes—
60#16839642C2212yes—
61#16839642C2212yes—
62#16839635C2212yes—
63#16839635C2212yes—
64#16839634C2212yes—
65#16839634C2212yes—
66#16839629C2212yes—
67#16839629C2212yes—
68#16839629C2212yes—
69#16839626C2212yes—
70#16839626C2212yes—
71#16839626C2212yes—
72#16839625C2211yescharacteristic
73#16839623C2212yes—
74#16839623C2212yes—
75#16839620C2212yes—
76#16839620C2211yescharacteristic
77#16839620C2211yescharacteristic
78#16839620C2212yes—
79C4⋊C4×Dic61C2212yes—
80C4×#11758196C2211yescharacteristic
81C4×#11758196C2212yes—
82C4×#11758196C2211yescharacteristic
83C4×#11758196C2212yes—
84#16839613C2212yes—
85#16839613C2212yes—
86#16839613C2212yes—
87C22⋊C4×Dic61C2212yes—
88C22⋊C4×Dic61C2211yescharacteristic
89C22⋊C4×Dic61C2211yescharacteristic
90C22⋊C4×Dic61C2212yes—
91C22⋊C4×Dic61C2212yes—
92C4×C22⋊Dic61C2211yescharacteristic
93C4×C22⋊Dic61C2212yes—
94#16839608C2212yes—
95#16839608C2211yescharacteristic
96#16839608C2211yescharacteristic
97#16839607C2212yes—
98C2×#14519684C2212yes—
99C2×#121×C61C2211yescharacteristic
100C61×#390C2212yes—
101C61×#388C2212yes—
102C61×#387C2212yes—
103C61×#386C2212yes—
104C61×#386C2212yes—
105C61×#381C2211yescharacteristic
106C4×C22⋊C4×C61C2211yescharacteristic
107C4×C22⋊C4×C61C2212yes—
108C22×Dic122C2311yescharacteristic
109C23×Dic61C2312yes—
110C23×Dic61C2311yescharacteristic
111C23×Dic61C2311yescharacteristic
112C23×Dic61C2312yes—
113#14519770C2×C4116yescomplemented
114#14519768C2×C418yescomplemented
115#14519764C2×C418yes—
116#14519758C2×C4116yescomplemented
117#14519756C2×C418yescomplemented
118#14519742C2×C418yescomplemented
119D4×Dic61C2×C418yes—
120D4×Dic61C2×C4116yescomplemented
121#14519733C2×C4116yescomplemented
122C2×C4⋊Dic61C2312yes—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2312yes—
125C2×#11758196C2312yes—
126C2×#11758196C2312yes—
127C2×#11758196C2312yes—
128C2×#11758196C2312yes—
129C2×#11758196C2312yes—
130C2×#11758196C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×C22⋊Dic61C2312yes—
137C2×C22⋊Dic61C2312yes—
138C2×C22⋊Dic61C2311yescharacteristic
139C2×C22⋊Dic61C2311yescharacteristic
140C2×C22⋊Dic61C2312yes—
141C2×C22⋊Dic61C2312yes—
142C2×C22⋊Dic61C2312yes—
143C2×C22⋊Dic61C2312yes—
144C2×C22⋊Dic61C2312yes—
145C2×C22⋊Dic61C2312yes—
146C2×C4×Dic61C2×C418yescomplemented
147C2×C4×Dic61C2312yes—
148C2×C4×Dic61C2312yes—
149C2×C4×Dic61C2311yescharacteristic
150C2×C4×Dic61C2311yescharacteristic
151C2×C4×Dic61C2312yes—
152C2×C4×Dic61C2312yes—
153C2×C4×Dic61C2312yes—
154C2×C4×Dic61C2312yes—
155C2×C4×Dic61C2312yes—
156C2×C4×Dic61C2311yescharacteristic
157C2×C4×Dic61C2311yescharacteristic
158C2×C4×Dic61C2311yescharacteristic
159C2×C4×Dic61C2311yescharacteristic
160C2×C4×Dic61C2312yes—
161#14519684C2312yes—
162#14519684C2312yes—
163#14519684C2312yes—
164#14519684C2312yes—
165#14519684C2312yes—
166#14519684C2312yes—
167#14519684C2312yes—
168#14519684C2312yes—
169#14519684C2312yes—
170#14519684C2312yes—
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184C22×D4×C61C2312yes—
185C22×D4×C61C2311yescharacteristic
186C23×C4×C61C2312yes—
187C23×C4×C61C2311yescharacteristic
188#121×C61C2×C418yes—
189C2×C4⋊C4×C61C2312yes—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61C2312yes—
192C2×C22⋊C4×C61C2312yes—
193C2×C22⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61C2312yes—
196C2×C22⋊C4×C61C2312yes—
197C2×C22⋊C4×C61C2312yes—
198C2×C42×C61C2311yescharacteristic
199C2×C42×C61C2312yes—
200C2×C42×C61C2311yescharacteristic
201#95×C61C2312yes—
202#95×C61C2312yes—
203#95×C61C2312yes—
204#95×C61C2312yes—
205#95×C61C2312yes—
206C24×C61C2411yescharacteristic
207C24×C61C2412yes—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—41no—
211C2×D4×C61—41no—
212C2×D4×C61C22×C414yes—
213C2×D4×C61C22×C418yes—
214C22×C4×C61—41no—
215C22×C4×C61—41no—
216C22×C4×C61—42no—
217C22×C4×C61—42no—
218C22×C4×C61—42no—
219C22×C4×C61C22×C414yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C22×C4×C61C2412yes—
227C22×Dic61—42no—
228C22×Dic61—42no—
229C22×Dic61—42no—
230C22×Dic61—42no—
231C22×Dic61—42no—
232C22×Dic61—42no—
233C22×Dic61—42no—
234C22×Dic61C22×C414yes—
235C22×Dic61C22×C414yes—
236C22×Dic61C22×C418yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C22×Dic61C2411yescharacteristic
242C22×Dic61C2411yescharacteristic
243C22×Dic61C2411yescharacteristic
244C22×Dic61C2412yes—
245C22×Dic61C2411yescharacteristic
246C22×Dic61C2412yes—
247C2×Dic122—41no—
248C2×Dic122—41no—
249C2×Dic122C22×C414yes—
250C4⋊C4×C61—42no—
251C4⋊C4×C61C22×C414yes—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—41no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—41no—
258C22⋊C4×C61C22×C418yes—
259C42×C61—41no—
260C42×C61—41no—
261C42×C61—42no—
262C22⋊Dic61—42no—
263C22⋊Dic61—42no—
264C22⋊Dic61—41no—
265C22⋊Dic61—42no—
266C22⋊Dic61—42no—
267C22⋊Dic61—41no—
268C22⋊Dic61C22×C418yes—
269C22⋊Dic61C22×C418yes—
270C22⋊Dic61C22×C418yes—
271C22⋊Dic61C22×C418yes—
272C4⋊Dic61—42no—
273C4⋊Dic61C22×C414yes—
274C4⋊Dic61C22×C418yes—
275#11758196—42no—
276#11758196—42no—
277#11758196—42no—
278#11758196—42no—
279#11758196—42no—
280#11758196—42no—
281#11758196—42no—
282#11758196—42no—
283#11758196C22×C418yes—
284#11758196C22×C418yes—
285#11758196C22×C418yes—
286C4×Dic61—42no—
287C4×Dic61—42no—
288C4×Dic61—42no—
289C4×Dic61—42no—
290C4×Dic61—42no—
291C4×Dic61—42no—
292C4×Dic61—42no—
293C4×Dic61—41no—
294C4×Dic61—41no—
295C4×Dic61C22×C414yes—
296C4×Dic61C22×C414yes—
297C4×Dic61C22×C414yes—
298C4×Dic61C22×C414yes—
299C4×Dic61C22×C418yes—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61C23×C414yes—
311C23×C61C23×C412yes—
312C23×C61C2511yescharacteristic
313D4×C61—44no—
314D4×C61—48no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—44no—
334C2×C4×C61—84no—
335C2×C4×C61C23×C412yes—
336C2×C4×C61C23×C412yes—
337C2×C4×C61C23×C414yes—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—44no—
359C2×Dic61—48no—
360C2×Dic61—44no—
361C2×Dic61—84no—
362C2×Dic61C23×C412yes—
363C2×Dic61C23×C412yes—
364C2×Dic61C23×C412yes—
365C2×Dic61C23×C412yes—
366C2×Dic61C23×C414yes—
367C2×Dic61C23×C414yes—
368Dic122—44no—
369#34405—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—24no—
373C22×C61—22no—
374C22×C61—24no—
375C22×C61—24no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61C24×C411yescharacteristic
383C22×C61#58511yescharacteristic
384C22×C61#58512yes—
385C22×C61#58511yescharacteristic
386C22×C61#58512yes—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—24no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61—42no—
394Dic61—24no—
395Dic61—22no—
396Dic61—22no—
397Dic61—22no—
398Dic61—24no—
399Dic61—22no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C2×#529—611no—
405#2382—612no—
406#2379—612no—
407#2373—612no—
408#2373—612no—
409#2356—612no—
410#2353—612no—
411#2347—612no—
412#2343—612no—
413#2335—612no—
414#2335—612no—
415#2333—611no—
416#2333D6111yescharacteristic
417#2332—611no—
418#2332—611no—
419#2319—612no—
420#2318—612no—
421#2283—611no—
422#2283—611no—
423C2×C61—42no—
424C2×C61—44no—
425C2×C61#342811yescharacteristic
426C2×C61#342811yescharacteristic
427C2×C61#342811yescharacteristic
428C2×C61#356712yes—
429C2×C61#356812yes—
430#529—6116no—
431C2×#126—612no—
432C2×#125—611no—
433C2×#124—611no—
434C2×#123—612no—
435C2×C22⋊Q8—611no—
436C2×#121C2×D6111yescharacteristic
437C2×C4×Q8—611no—
438C2×C4×D4—612no—
439C2×C4×D4—611no—
440C2×#117—612no—
441C22×C42—611no—
442#391—612no—
443#391—612no—
444#390—612no—
445#390C2×D6112yes—
446#389—612no—
447#389—612no—
448#389—612no—
449#389—612no—
450#388—612no—
451#388—612no—
452#388—612no—
453#388—612no—
454#388—612no—
455#388—612no—
456#388—612no—
457#388—612no—
458#388—612no—
459#388—612no—
460#388—612no—
461#388C2×D6112yes—
462#387—612no—
463#387—612no—
464#387—612no—
465#387—612no—
466#387—612no—
467#387—612no—
468#387—612no—
469#387—612no—
470#387—612no—
471#387—612no—
472#387—612no—
473#387C2×D6112yes—
474#386—612no—
475#386—612no—
476#386C2×D6112yes—
477#386C2×D6112yes—
478#385—612no—
479#385—612no—
480#385—612no—
481#385—612no—
482#383—612no—
483#383—612no—
484#383—612no—
485#382—612no—
486#382—612no—
487#382—612no—
488#381—611no—
489#381—612no—
490#381—612no—
491#381C2×D6111yescharacteristic
492#380—611no—
493#380—611no—
494#380—612no—
495#380—612no—
496C4×C4⋊C4—612no—
497C4×C4⋊C4—612no—
498C4×C4⋊C4—612no—
499C4×C4⋊C4—611no—
500C4×C4⋊C4—611no—
501C4×C4⋊C4—612no—
502C4×C4⋊C4—612no—
503C4×C4⋊C4—612no—
504C4×C22⋊C4—611no—
505C4×C22⋊C4—612no—
506C4×C22⋊C4—612no—
507C4×C22⋊C4—612no—
508C4×C22⋊C4—611no—
509C4×C22⋊C4—611no—
510C4×C22⋊C4—612no—
511C4×C22⋊C4C2×D6111yescharacteristic
512C4×C22⋊C4C2×D6112yes—
513#376—612no—
514#376—611no—
515#376—611no—
516#376—612no—
517C2×#95—612no—
518C61#3440511yescharacteristic, complemented, Sylow
519C22×Q8—611no—
520C22×D4C22×D6112yes—
521C22×D4C22×D6111yescharacteristic
522C23×C4—612no—
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—612no—
526C23×C4C22×D6112yes—
527C23×C4C22×D6111yescharacteristic
528#126—6116no—
529#125—618no—
530#124—618no—
531#123—6116no—
532C22⋊Q8—618no—
533#121C4×D6118yes—
534C4×Q8—618no—
535C4×D4—618no—
536C4×D4—6116no—
537#117—6116no—
538C2×C4⋊C4—612no—
539C2×C4⋊C4—612no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—612no—
542C2×C4⋊C4—612no—
543C2×C4⋊C4—612no—
544C2×C4⋊C4—612no—
545C2×C4⋊C4—612no—
546C2×C4⋊C4—612no—
547C2×C4⋊C4—612no—
548C2×C4⋊C4—612no—
549C2×C4⋊C4—612no—
550C2×C4⋊C4—612no—
551C2×C4⋊C4—612no—
552C2×C4⋊C4C22×D6112yes—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C22⋊C4—612no—
555C2×C22⋊C4—612no—
556C2×C22⋊C4—612no—
557C2×C22⋊C4—612no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—612no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—612no—
562C2×C22⋊C4—612no—
563C2×C22⋊C4—612no—
564C2×C22⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4C22×D6111yescharacteristic
566C2×C22⋊C4C22×D6112yes—
567C2×C22⋊C4C22×D6112yes—
568C2×C22⋊C4C22×D6112yes—
569C2×C22⋊C4C22×D6112yes—
570C2×C22⋊C4C22×D6112yes—
571C2×C42—618no—
572C2×C42—611no—
573C2×C42—612no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—612no—
579C2×C42—612no—
580C2×C42—611no—
581C2×C42—612no—
582C2×C42—612no—
583C2×C42—612no—
584C2×C42—612no—
585C2×C42—612no—
586C2×C42C22×D6111yescharacteristic
587C2×C42C22×D6111yescharacteristic
588C2×C42C22×D6112yes—
589#95—612no—
590#95—612no—
591#95—612no—
592#95—612no—
593#95—612no—
594#95—612no—
595#95—612no—
596#95—612no—
597#95—612no—
598#95—612no—
599#95—612no—
600#95—612no—
601#95—612no—
602#95—612no—
603#95—612no—
604#95—612no—
605#95—612no—
606#95—612no—
607#95—612no—
608#95—612no—
609#95—612no—
610#95—612no—
611#95—612no—
612#95C22×D6112yes—
613#95C22×D6112yes—
614#95C22×D6112yes—
615#95C22×D6112yes—
616#95C22×D6112yes—
617C24C23×D6111yescharacteristic
618C24C23×D6112yes—
619C2×Q8—614no—
620C2×Q8—2441no—
621C2×Q8—2441no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D6118yes—
627C2×D4C2×C4×D6114yes—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—612no—
639C22×C4—614no—
640C22×C4—614no—
641C22×C4—618no—
642C22×C4—612no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4—2442no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4C2×C4×D6114yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6111yescharacteristic
659C22×C4C23×D6111yescharacteristic
660C22×C4C23×D6112yes—
661C4⋊C4—42no—
662C4⋊C4—618no—
663C4⋊C4—618no—
664C4⋊C4—618no—
665C4⋊C4—614no—
666C4⋊C4—618no—
667C4⋊C4—2442no—
668C4⋊C4—2442no—
669C4⋊C4—2442no—
670C4⋊C4—2442no—
671C4⋊C4—2442no—
672C4⋊C4—2442no—
673C4⋊C4—2442no—
674C4⋊C4—2442no—
675C4⋊C4—2442no—
676C4⋊C4C2×C4×D6114yes—
677C22⋊C4—42no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—41no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—618no—
684C22⋊C4—618no—
685C22⋊C4—618no—
686C22⋊C4—618no—
687C22⋊C4—2442no—
688C22⋊C4—2441no—
689C22⋊C4—2442no—
690C22⋊C4—2441no—
691C22⋊C4—2442no—
692C22⋊C4—2442no—
693C22⋊C4C2×C4×D6118yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—614no—
698C42—614no—
699C42—614no—
700C42—614no—
701C42—618no—
702C42—2441no—
703C42—2441no—
704C42—2442no—
705C42—2442no—
706C42—2442no—
707C42—2442no—
708C42—2442no—
709C42—2442no—
710C42—2442no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23C22×C4×D6114yes—
722C23C22×C4×D6112yes—
723C23C24×D6111yescharacteristic
724Q8—2444no—
725D4—44no—
726D4—48no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—84no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—614no—
752C2×C4—614no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—4884no—
774C2×C4—2444no—
775C2×C4—2444no—
776C2×C4—2448no—
777C2×C4C22×C4×D6112yes—
778C2×C4C22×C4×D6112yes—
779C2×C4C22×C4×D6114yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C23×C4×D6111yescharacteristic
793C22#1684059711yescharacteristic
794C22#1684059712yes—
795C22#1684059711yescharacteristic
796C22#1684059812yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—1222no—
805C4—1222no—
806C4—1224no—
807C4—1222no—
808C4—1224no—
809C4—1222no—
810C4—2442no—
811C4—2442no—
812C4—2442no—
813C4—2442no—
814C2—42no—
815C2—44no—
816C2#2145901711yescharacteristic
817C2#2145901711yescharacteristic
818C2#2145901811yescharacteristic
819C2#2146050412yes—
820C2#2146051212yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2333C2
socle, cosocleC23×C61C25
prime radicalC2×#121×C61C22
hypercenter#2333D61
hypocenterC61#34405
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #21449002C2semidirect
3. #21448989C2semidirect
4. #21448940C2semidirect
5. #21448936C2semidirect
6. #21448781C2semidirect
7. #21448757C2semidirect
8. #21448709C2semidirect
9. #21448673C2semidirect
10. #21448610C2semidirect
11. #21448606C2semidirect
13. #21448575C2semidirect
14. #21448572C2semidirect
15. #21448456C2semidirect
16. #21448445C2semidirect
17. #21448213C2semidirect
18. #21448210C2semidirect
20. #16840293C4semidirect
113. #14519770C2×C4semidirect
114. #14519768C2×C4semidirect
116. #14519758C2×C4semidirect
117. #14519756C2×C4semidirect
118. #14519742C2×C4semidirect
120. D4×Dic61C2×C4semidirect
121. #14519733C2×C4semidirect
146. C2×C4×Dic61C2×C4semidirect
518. C61#34405semidirect

Maximal subgroups

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

subgroupindex
C2×#168402932
#214490022
#214489892
#214489402
#214489362
#214487812
#214487572
#214487092
#214486732
#214486102
#214486062
#214485862
#214485752
#214485722
#214484562
#214484452
#214482132
#214482102
C61×#23332
#3440561