Finite Group Databasebeta

← #29840883

Subgroups — #29840883

Order 15616.

2186 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic
2#21448951C212yesmaximal, complemented
3#21448948C212yesmaximal, complemented
4#21448929C211yesmaximal, characteristic, complemented
5#21448929C211yesmaximal, characteristic, complemented
6#21448925C211yesmaximal, characteristic, complemented
7#21448773C212yesmaximal, complemented
8#21448764C212yesmaximal, complemented
9#21448743C212yesmaximal, complemented
10#21448743C212yesmaximal, complemented
11#21448583C212yesmaximal
12#21448571C212yesmaximal, complemented
13#21448425C212yesmaximal, complemented
14C4×#14519772C212yesmaximal, complemented
15#21448369C212yesmaximal, complemented
16#21448211C211yesmaximal, characteristic, complemented
17#21448173C212yesmaximal, complemented
18#21448158C211yesmaximal, characteristic, complemented
19C61×#2371C211yesmaximal, characteristic, complemented
20#16840297C4116yescomplemented
21C2×#14519772C2212yes—
22C2×#14519765C2211yescharacteristic
23C2×#14519762C2212yes—
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C2×#14519739C2212yes—
29C2×#14519735C2212yes—
30C2×#14519734C2212yes—
31C2×#14519734C2212yes—
32C2×C4⋊C4×D61C2212yes—
33C2×C42×D61C2211yescharacteristic
34#16839666C2212yes—
35#16839666C2212yes—
36#16839664C2212yes—
37#16839663C2212yes—
38#16839654C2212yes—
39#16839654C2212yes—
40#16839654C2212yes—
41#16839653C2212yes—
42#16839653C2212yes—
43#16839653C2212yes—
44#16839652C2212yes—
45#16839652C2212yes—
46#16839652C2212yes—
47#16839651C2212yes—
48#16839651C2212yes—
49#16839651C2212yes—
50#16839649C2212yes—
51#16839648C2212yes—
52#16839648C2212yes—
53#16839648C2212yes—
54#16839648C2212yes—
55#16839647C2212yes—
56#16839645C2212yes—
57#16839643C2212yes—
58#16839640C2212yes—
59#16839640C2212yes—
60#16839640C2212yes—
61#16839640C2212yes—
62#16839631C2212yes—
63#16839629C2211yescharacteristic
64#16839629C2211yescharacteristic
65#16839626C2212yes—
66#16839626C2212yes—
67#16839624C2212yes—
68#16839621C2211yescharacteristic
69#16839621C2211yescharacteristic
70#16839621C2212yes—
71#16839621C2212yes—
72C4⋊C4×Dic61C2212yes—
73C4⋊C4×Dic61C2212yes—
74C4⋊C4×Dic61C2212yes—
75C4×#11758196C2212yes—
76C4×#11758196C2212yes—
77C4×#11758196C2212yes—
78C4×C4⋊Dic61C2212yes—
79#16839613C2212yes—
80#16839613C2212yes—
81#16839613C2212yes—
82#16839613C2211yescharacteristic
83#16839613C2211yescharacteristic
84C4×#11758198C2212yes—
85C4×#11758198C2212yes—
86C4×#11758198C2212yes—
87C4×#11758198C2212yes—
88C4×#11758198C2212yes—
89#16839609C2212yes—
90#16839609C2212yes—
91#16839609C2212yes—
92#16839609C2212yes—
93#16839609C2211yescharacteristic
94#16839609C2211yescharacteristic
95#16839609C2212yes—
96#16839608C2211yescharacteristic
97#16839608C2211yescharacteristic
98C42×Dic61C2212yes—
99C2×#125×C61C2211yescharacteristic
100C61×#387C2212yes—
101C61×#387C2212yes—
102C61×#387C2212yes—
103C61×#387C2212yes—
104C4×C4⋊C4×C61C2212yes—
105C4×C4⋊C4×C61C2212yes—
106C61×#376C2211yescharacteristic
107C61×#376C2211yescharacteristic
108C22×Dic122C2311yescharacteristic
109C22×D244C2312yes—
110C22×D244C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2312yes—
113C22×C4×D61C2312yes—
114C22×C4×D61C2312yes—
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117#14519772C2×C4116yescomplemented
118#14519765C2×C418yes—
119#14519762C2×C4116yescomplemented
120#14519757C2×C418yescomplemented
121#14519752C2×C418yes—
122#14519742C2×C418yescomplemented
123#14519739C2×C418yes—
124#14519739C2×C4116yescomplemented
125#14519735C2×C4116yescomplemented
126#14519734—28no—
127#14519734—28no—
128C2×C4⋊Dic61C2312yes—
129C2×C4⋊Dic61C2312yes—
130C2×C4⋊Dic61C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2312yes—
138C4⋊C4×D61—28no—
139C2×#11758198C2312yes—
140C2×#11758198C2312yes—
141C2×#11758198C2312yes—
142C2×#11758198C2312yes—
143C2×#11758198C2312yes—
144C2×#11758198C2312yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×C4×Dic61C2312yes—
155C2×C4×Dic61C2312yes—
156C2×C4×Dic61C2312yes—
157C2×C4×Dic61C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2312yes—
160C2×C4×Dic61C2312yes—
161C2×C4×Dic61C2312yes—
162C2×C4×Dic61C2312yes—
163C2×C4×Dic61C2312yes—
164C2×C4×Dic61C2311yescharacteristic
165C2×C4×Dic61C2311yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2312yes—
168C42×D61C2×C418yescomplemented
169#14519684C2311yescharacteristic
170#14519684C2312yes—
171#14519684C2311yescharacteristic
172#14519684C2311yescharacteristic
173#14519684C2311yescharacteristic
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184#14519684C2312yes—
185#14519684C2312yes—
186#14519684C2312yes—
187#125×C61C2×C418yescomplemented
188C2×C4⋊C4×C61C2312yes—
189C2×C4⋊C4×C61C2312yes—
190C2×C4⋊C4×C61C2312yes—
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C4⋊C4×C61C2312yes—
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C42×C61C2312yes—
195C2×C42×C61C2312yes—
196C2×C42×C61C2312yes—
197C2×C42×C61C2312yes—
198C2×C42×C61C2311yescharacteristic
199#95×C61C2311yescharacteristic
200#95×C61C2311yescharacteristic
201#95×C61C2311yescharacteristic
202#95×C61C2312yes—
203#95×C61C2311yescharacteristic
204#95×C61C2312yes—
205#95×C61C2312yes—
206#95×C61C2312yes—
207#95×C61C2312yes—
208#95×C61C2312yes—
209C23×D61C2411yescharacteristic
210C23×D61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C22×C4×C61C2412yes—
218C22×C4×C61C2412yes—
219C22×C4×C61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2411yescharacteristic
224C22×Dic61C2411yescharacteristic
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2411yescharacteristic
228C2×D244—42no—
229C2×D244—42no—
230C2×D244—41no—
231C2×D244—41no—
232C2×D244C22×C414yes—
233C2×D244C22×C418yes—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—42no—
240C2×C4×D61—41no—
241C2×C4×D61—41no—
242C2×C4×D61—42no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×C4×D61—42no—
246C2×C4×D61C22×C414yes—
247C2×C4×D61C22×C418yes—
248C2×C4×D61C22×C414yes—
249C2×C4×D61C22×C414yes—
250C2×Dic122—41no—
251C2×Dic122—41no—
252C2×Dic122C22×C414yes—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61C22×C418yes—
256C4⋊C4×C61C22×C414yes—
257C4⋊C4×C61C22×C418yes—
258C4⋊C4×C61C22×C414yes—
259C42×C61—24no—
260C42×C61—24no—
261C42×C61—42no—
262C42×C61—42no—
263C42×C61C22×C414yes—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—42no—
269#11758198—42no—
270#11758198—42no—
271#11758198—42no—
272#11758198—42no—
273#11758198—42no—
274#11758198C22×C418yes—
275#11758198C22×C418yes—
276#11758198C22×C418yes—
277#11758198C22×C418yes—
278#11758198C22×C418yes—
279C4⋊Dic61—24no—
280C4⋊Dic61—42no—
281C4⋊Dic61C22×C418yes—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196—42no—
286#11758196—42no—
287#11758196C22×C418yes—
288#11758196#4118yes—
289C4×Dic61—24no—
290C4×Dic61—24no—
291C4×Dic61—42no—
292C4×Dic61—42no—
293C4×Dic61—42no—
294C4×Dic61—42no—
295C4×Dic61—42no—
296C4×Dic61—42no—
297C4×Dic61—42no—
298C4×Dic61—42no—
299C4×Dic61C22×C414yes—
300C4×Dic61C22×C414yes—
301C4×Dic61C22×C414yes—
302C4×Dic61C22×C418yes—
303C23×C61C2511yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61C23×C414yes—
315C22×D61C23×C412yes—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
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—22no—
334C2×C4×C61—22no—
335C2×C4×C61C23×C414yes—
336C2×C4×C61C23×C412yes—
337C2×C4×C61C23×C412yes—
338C2×C4×C61C23×C412yes—
339C2×C4×C61C23×C414yes—
340C2×C4×C61C2×#4114yes—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—21no—
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×Dic61C23×C412yes—
358C2×Dic61C23×C412yes—
359C2×Dic61C23×C414yes—
360C2×Dic61C23×C412yes—
361C2×Dic61C2×#4114yes—
362C2×Dic61C2×#4114yes—
363D244—44no—
364D244—48no—
365C4×D61—216no—
366C4×D61—28no—
367C4×D61—44no—
368C4×D61—44no—
369C4×D61—84no—
370C4×D61—84no—
371Dic122—44no—
372#34244—611nomaximal, Sylow
373C22×C61C24×C411yescharacteristic
374C22×C61C22×#4112yes—
375C22×C61#58512yes—
376C22×C61#58511yescharacteristic
377C22×C61#58511yescharacteristic
378C2×D61—22no—
379C2×D61—24no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C4×C61—22no—
391C4×C61—24no—
392C4×C61—22no—
393C4×C61—22no—
394C4×C61—24no—
395C4×C61—24no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—42no—
399Dic61—24no—
400Dic61—22no—
401Dic61—22no—
402Dic61—24no—
403Dic61—42no—
404Dic61—42no—
405Dic61—42no—
406Dic61C4×#4114yes—
407C2×#529—611no—
408#2374—612no—
409#2374—612no—
410#2372—611no—
411#2372—611no—
412#2371—611no—
413#2371D6111yescharacteristic, complemented
414#2355—612no—
415#2354—612no—
416#2352—612no—
417#2352—612no—
418#2333—612no—
419#2332—612no—
420#2314—612no—
421C4×#126—612no—
422C4×#126—612no—
423#2283—611no—
424#2274—612no—
425C4×#117—611no—
426C2×C61C2×C4×#4111yescharacteristic
427C2×C61#342811yescharacteristic
428C2×C61#342811yescharacteristic
429C2×C61#352112yes—
430C2×C61#352412yes—
431D61—42no—
432D61—44no—
433#529—6116no—
434C2×#126—612no—
435C2×#125C2×D6111yescharacteristic
436C2×#124—611no—
437C2×#123—612no—
438C2×C22⋊Q8—611no—
439C2×#121—611no—
440C2×C4×Q8—611no—
441C2×C4×D4—611no—
442C2×C4×D4—612no—
443C2×#117—612no—
444C2×#117—612no—
445C2×#117—612no—
446C22×C4⋊C4—612no—
447C22×C42—611no—
448#391—612no—
449#391—612no—
450#390—612no—
451#390—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#388—612no—
462#388—612no—
463#388—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#387C2×D6112yes—
473#387C2×D6112yes—
474#387C2×D6112yes—
475#387C2×D6112yes—
476#386—612no—
477#386—612no—
478#386—612no—
479#386—612no—
480#384—612no—
481#383—611no—
482#383—611no—
483#382—612no—
484#382—612no—
485#381—612no—
486#380—612no—
487#380—612no—
488#380—611no—
489#380—611no—
490C4×C4⋊C4—612no—
491C4×C4⋊C4—612no—
492C4×C4⋊C4—612no—
493C4×C4⋊C4—612no—
494C4×C4⋊C4—612no—
495C4×C4⋊C4—612no—
496C4×C4⋊C4—612no—
497C4×C4⋊C4—612no—
498C4×C4⋊C4—611no—
499C4×C4⋊C4—612no—
500C4×C4⋊C4—612no—
501C4×C4⋊C4—611no—
502C4×C4⋊C4C2×D6112yes—
503C4×C4⋊C4C2×D6112yes—
504C4×C22⋊C4—612no—
505C4×C22⋊C4—612no—
506C4×C22⋊C4—612no—
507C4×C22⋊C4—612no—
508C4×C22⋊C4—612no—
509C4×C22⋊C4—612no—
510C4×C22⋊C4—612no—
511C4×C22⋊C4—612no—
512C4×C22⋊C4—612no—
513C4×C22⋊C4—612no—
514C4×C22⋊C4—611no—
515C4×C22⋊C4—611no—
516#376—611no—
517#376—611no—
518#376C2×D6111yescharacteristic
519#376C2×D6111yescharacteristic
520C43—612no—
521C61#3424411yescharacteristic, complemented, Sylow
522C22×Q8—611no—
523C22×D4—612no—
524C22×D4—611no—
525C23×C4—612no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—611no—
529C23×C4—612no—
530C23×C4—612no—
531#126—6116no—
532#125C4×D6118yescomplemented
533#124—618no—
534#123—6116no—
535C22⋊Q8—618no—
536#121—618no—
537C4×Q8—618no—
538C4×D4—618no—
539C4×D4—6116no—
540#117—6116no—
541#117—1228no—
542#117—1228no—
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⋊C4—612no—
553C2×C4⋊C4—1228no—
554C2×C4⋊C4C22×D6112yes—
555C2×C4⋊C4C22×D6112yes—
556C2×C4⋊C4C22×D6112yes—
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C4⋊C4C22×D6112yes—
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C22⋊C4—612no—
561C2×C22⋊C4—612no—
562C2×C22⋊C4—612no—
563C2×C22⋊C4—612no—
564C2×C22⋊C4—612no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—612no—
567C2×C22⋊C4—612no—
568C2×C22⋊C4—612no—
569C2×C22⋊C4—612no—
570C2×C22⋊C4—612no—
571C2×C22⋊C4—612no—
572C2×C22⋊C4—612no—
573C2×C22⋊C4—612no—
574C2×C22⋊C4—612no—
575C2×C42—611no—
576C2×C42—612no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—618no—
580C2×C42—612no—
581C2×C42—612no—
582C2×C42—612no—
583C2×C42—612no—
584C2×C42—612no—
585C2×C42—612no—
586C2×C42—612no—
587C2×C42—612no—
588C2×C42—612no—
589C2×C42—612no—
590C2×C42C22×D6112yes—
591C2×C42C22×D6112yes—
592C2×C42C22×D6112yes—
593C2×C42C22×D6112yes—
594C2×C42C22×D6111yescharacteristic
595#95—611no—
596#95—611no—
597#95—612no—
598#95—611no—
599#95—611no—
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#95—612no—
613#95C22×D6111yescharacteristic
614#95C22×D6111yescharacteristic
615#95C22×D6112yes—
616#95C22×D6111yescharacteristic
617#95C22×D6111yescharacteristic
618#95C22×D6112yes—
619#95C22×D6112yes—
620#95C22×D6112yes—
621#95C22×D6112yes—
622#95C22×D6112yes—
623C24—612no—
624C24—611no—
625C2×Q8—614no—
626C2×Q8—2441no—
627C2×Q8—2441no—
628C2×D4—618no—
629C2×D4—614no—
630C2×D4—2442no—
631C2×D4—2442no—
632C2×D4—2441no—
633C2×D4—2441no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—614no—
640C22×C4—618no—
641C22×C4—614no—
642C22×C4—614no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1224no—
650C22×C4—1224no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2441no—
657C22×C4—2441no—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6111yescharacteristic
662C22×C4C23×D6111yescharacteristic
663C22×C4C23×D6111yescharacteristic
664C22×C4C23×D6112yes—
665C22×C4C23×D6112yes—
666C22×C4C23×D6112yes—
667C4⋊C4—24no—
668C4⋊C4—42no—
669C4⋊C4—618no—
670C4⋊C4—618no—
671C4⋊C4—618no—
672C4⋊C4—1224no—
673C4⋊C4—1224no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—2442no—
677C4⋊C4—2442no—
678C4⋊C4—2442no—
679C4⋊C4C2×C4×D6118yes—
680C4⋊C4C2×C4×D6114yes—
681C4⋊C4C2×C4×D6118yes—
682C4⋊C4C2×C4×D6114yes—
683C22⋊C4—618no—
684C22⋊C4—618no—
685C22⋊C4—618no—
686C22⋊C4—618no—
687C22⋊C4—618no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—2442no—
693C22⋊C4—2442no—
694C22⋊C4—2442no—
695C22⋊C4—2442no—
696C22⋊C4—2442no—
697C22⋊C4—2442no—
698C42—24no—
699C42—24no—
700C42—42no—
701C42—42no—
702C42—614no—
703C42—614no—
704C42—614no—
705C42—618no—
706C42—1224no—
707C42—1224no—
708C42—2442no—
709C42—2442no—
710C42—2442no—
711C42—2442no—
712C42—2442no—
713C42—2442no—
714C42—2442no—
715C42—2442no—
716C42C2×C4×D6114yes—
717C23—614no—
718C23—612no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1221no—
726C23—1221no—
727C23—1222no—
728C23—1222no—
729C23C24×D6111yescharacteristic
730Q8—2444no—
731D4—2448no—
732D4—2444no—
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—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—612no—
753C2×C4—614no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—614no—
757C2×C4—614no—
758C2×C4—1228no—
759C2×C4—12216no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1221no—
763C2×C4—1221no—
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—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—4884no—
777C2×C4—4884no—
778C2×C4—2444no—
779C2×C4—2444no—
780C2×C4C22×C4×D6112yes—
781C2×C4C22×C4×D6112yes—
782C2×C4C22×C4×D6112yes—
783C2×C4C22×C4×D6114yes—
784C2×C4C22×C4×D6114yes—
785C2×C4#41×D6114yes—
786C22—1224no—
787C22—1222no—
788C22—1222no—
789C22—1224no—
790C22—1222no—
791C22—1224no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22C23×C4×D6111yescharacteristic
799C22C2×#41×D6112yes—
800C22#1684059812yes—
801C22#1684059911yescharacteristic
802C22#1684059911yescharacteristic
803C4—22no—
804C4—24no—
805C4—22no—
806C4—24no—
807C4—22no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—614no—
813C4—1222no—
814C4—1222no—
815C4—1224no—
816C4—1224no—
817C4—2442no—
818C4—2442no—
819C4—2442no—
820C2—2442no—
821C2—2444no—
822C2C4×#41×D6111yescharacteristic
823C2#2145901811yescharacteristic
824C2#2145902111yescharacteristic
825C2#2145987412yes—
826C2#2145992512yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2371C2
socle, cosocleC23×C61C25
prime radicalC2×#14519752C22
hypercenter#2371D61
hypocenterC61#34244
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #21448951C2semidirect
3. #21448948C2semidirect
4. #21448929C2semidirect
5. #21448929C2semidirect
6. #21448925C2semidirect
7. #21448773C2semidirect
8. #21448764C2semidirect
9. #21448743C2semidirect
10. #21448743C2semidirect
12. #21448571C2semidirect
13. #21448425C2semidirect
14. C4×#14519772C2semidirect
15. #21448369C2semidirect
16. #21448211C2semidirect
17. #21448173C2semidirect
18. #21448158C2semidirect
19. C61×#2371C2semidirect
20. #16840297C4semidirect
117. #14519772C2×C4semidirect
119. #14519762C2×C4semidirect
120. #14519757C2×C4semidirect
122. #14519742C2×C4semidirect
124. #14519739C2×C4semidirect
125. #14519735C2×C4semidirect
168. C42×D61C2×C4semidirect
187. #125×C61C2×C4semidirect
413. #2371D61semidirect
521. C61#34244semidirect
532. #125C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402972
#214489512
#214489482
#214489292
#214489252
#214487732
#214487642
#214487432
#214485832
#214485712
#214484252
C4×#145197722
#214483692
#214482112
#214481732
#214481582
C61×#23712
#3424461