Finite Group Databasebeta

← #29850939

Subgroups — #29850939

Order 15616.

1992 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451527C211yesmaximal, characteristic, complemented
2#21451506C212yesmaximal, complemented
3#21451309C211yesmaximal, characteristic, complemented
4#21451086C212yesmaximal, complemented
5#21450887C211yesmaximal, characteristic
6#21450663C212yesmaximal, complemented
7#21450633C212yesmaximal, complemented
8#21450002C212yesmaximal, complemented
9#21449972C212yesmaximal, complemented
10#21449111C211yesmaximal, characteristic, complemented
11#21449107C211yesmaximal, characteristic, complemented
12#21449064C212yesmaximal, complemented
13#21448360C212yesmaximal, complemented
14#21448358C211yesmaximal, characteristic, complemented
15#21448329C212yesmaximal, complemented
16#21448311C212yesmaximal, complemented
17#21448255C212yesmaximal, complemented
18#117×Dic61C212yesmaximal, complemented
19C61×#2609C211yesmaximal, characteristic, complemented
20C2×#14519765C2211yescharacteristic
21C2×#14519763C2212yes—
22C2×#14519749C2212yes—
23C2×#14519742C2211yescharacteristic
24C2×#14519742C2211yescharacteristic
25C2×D4×Dic61C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×#14519737C2212yes—
28C2×#14519737C2212yes—
29C2×#14519736C2212yes—
30C2×#14519735C2212yes—
31C22×C4×Dic61C2212yes—
32#16839702C2211yescharacteristic
33#16839701C2211yescharacteristic
34#16839696C2212yes—
35#16839695C2212yes—
36#16839693C2211yescharacteristic
37#16839691C2212yes—
38#16839690C2212yes—
39#16839684C2212yes—
40#16839683C2211yescharacteristic
41#16839682C2211yescharacteristic
42#16839682C2212yes—
43#16839679C2212yes—
44#16839678C2212yes—
45#16839678C2212yes—
46#16839676C2211yescharacteristic
47#16839674C2212yes—
48#16839671C2212yes—
49#16839667C2211yescharacteristic
50#16839666C2212yes—
51#16839663C2211yescharacteristic
52#16839662C2212yes—
53#16839662C2212yes—
54#16839659C2212yes—
55#16839656C2212yes—
56#16839654C2212yes—
57#16839654C2212yes—
58#16839654C2212yes—
59#16839653C2212yes—
60#16839653C2212yes—
61#16839652C2212yes—
62#16839652C2212yes—
63#16839652C2212yes—
64#16839651C2212yes—
65#16839651C2212yes—
66#16839651C2212yes—
67#16839650C2212yes—
68#16839649C2212yes—
69#16839648C2212yes—
70#16839647C2212yes—
71#16839645C2212yes—
72#16839643C2212yes—
73#16839641C2212yes—
74#16839641C2212yes—
75#16839639C2212yes—
76#16839637C2212yes—
77#16839626C2212yes—
78#16839620C2212yes—
79C4⋊C4×Dic61C2212yes—
80C4⋊C4×Dic61C2212yes—
81C4⋊C4×Dic61C2212yes—
82C4⋊C4×Dic61C2212yes—
83#16839613C2212yes—
84C22⋊C4×Dic61C2212yes—
85C22⋊C4×Dic61C2212yes—
86C22⋊C4×Dic61C2212yes—
87C22⋊C4×Dic61C2212yes—
88C22⋊C4×Dic61C2212yes—
89#16839609C2212yes—
90#16839609C2212yes—
91#16839609C2212yes—
92#16839608C2212yes—
93#16839608C2212yes—
94#16839607C2211yescharacteristic
95#16839607C2211yescharacteristic
96C42×Dic61C2212yes—
97C42×Dic61C2211yescharacteristic
98C2×#117×C61C2212yes—
99C61×#398C2211yescharacteristic
100C61×#396C2212yes—
101C61×#394C2211yescharacteristic
102C61×#388C2212yes—
103C61×#387C2212yes—
104C61×#386C2212yes—
105C61×#385C2212yes—
106C61×#382C2211yescharacteristic
107C22×Dic122C2311yescharacteristic
108C22×Dic122C2311yescharacteristic
109C22×D244C2311yescharacteristic
110C22×C22⋊D61C2312yes—
111C22×C22⋊D61C2312yes—
112C23×Dic61C2312yes—
113C23×Dic61C2312yes—
114C22×C4×D61C2312yes—
115#14519765—24no—
116#14519763—28no—
117#14519749—28no—
118#14519742—42no—
119#14519742—42no—
120D4×Dic61—42no—
121#14519739—42no—
122#14519737—28no—
123#14519737—44no—
124#14519736—28no—
125#14519735—28no—
126C2×C4⋊Dic61C2312yes—
127C2×C4⋊Dic61C2312yes—
128C2×C4⋊Dic61C2312yes—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2311yescharacteristic
135C2×#11758196C2312yes—
136C2×#11758196C2311yescharacteristic
137C2×C22⋊Dic61C2312yes—
138C2×C22⋊Dic61C2312yes—
139C2×C22⋊Dic61C2312yes—
140C2×C22⋊Dic61C2312yes—
141C2×#11758198C2312yes—
142C2×#11758198C2312yes—
143C2×#11758198C2312yes—
144C2×#11758198C2312yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×C4×Dic61—28no—
153C2×C4×Dic61C2312yes—
154C2×C4×Dic61C2312yes—
155C2×C4×Dic61C2312yes—
156C2×C4×Dic61C2312yes—
157C2×C4×Dic61C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2312yes—
160C2×C4×Dic61C2311yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C2×C4×Dic61C2311yescharacteristic
163C2×C4×Dic61C2312yes—
164C2×C4×Dic61C2311yescharacteristic
165C2×C4×Dic61C2312yes—
166C2×C4×Dic61C2312yes—
167#14519684C2312yes—
168#14519684C2312yes—
169#14519684C2311yescharacteristic
170#14519684C2312yes—
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2311yescharacteristic
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184#14519684C2312yes—
185C22×D4×C61C2311yescharacteristic
186C23×C4×C61C2312yes—
187#117×C61—28no—
188C2×C4⋊C4×C61C2312yes—
189C2×C4⋊C4×C61C2312yes—
190C2×C4⋊C4×C61C2312yes—
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C4⋊C4×C61C2311yescharacteristic
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61C2312yes—
195C2×C22⋊C4×C61C2312yes—
196C2×C22⋊C4×C61C2312yes—
197C2×C22⋊C4×C61C2312yes—
198C2×C22⋊C4×C61C2312yes—
199C2×C42×C61C2312yes—
200C2×C42×C61C2311yescharacteristic
201#95×C61C2311yescharacteristic
202#95×C61C2312yes—
203#95×C61C2312yes—
204#95×C61C2311yescharacteristic
205#95×C61C2312yes—
206#95×C61C2312yes—
207C24×C61C2412yes—
208C23×D61C2412yes—
209C2×D4×C61—24no—
210C2×D4×C61—41no—
211C22×C4×C61—24no—
212C22×C4×C61—24no—
213C22×C4×C61—24no—
214C22×C4×C61C2412yes—
215C22×C4×C61C2411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C22×C4×C61C2412yes—
218C22×C4×C61C2412yes—
219C22×C4×C61C2411yescharacteristic
220C22×C4×C61C2412yes—
221C22×C4×C61C2412yes—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—42no—
227C2×C22⋊D61—42no—
228C22×Dic61—24no—
229C22×Dic61—24no—
230C22×Dic61—24no—
231C22×Dic61—24no—
232C22×Dic61—24no—
233C22×Dic61—42no—
234C22×Dic61C2412yes—
235C22×Dic61C2411yescharacteristic
236C22×Dic61C2411yescharacteristic
237C22×Dic61C2412yes—
238C22×Dic61C2411yescharacteristic
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2411yescharacteristic
243C2×D244—22no—
244C2×D244—41no—
245C2×D244—41no—
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×Dic122—22no—
250C2×Dic122—24no—
251C2×Dic122—41no—
252C2×Dic122—41no—
253C2×Dic122—41no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—41no—
258C4⋊C4×C61—41no—
259C4⋊C4×C61—41no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—42no—
265C42×C61—24no—
266C42×C61#4114yes—
267C22⋊Dic61—24no—
268C22⋊Dic61—42no—
269C22⋊Dic61—42no—
270C22⋊Dic61#4118yes—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—42no—
280#11758198—42no—
281#11758198—42no—
282C4⋊Dic61—24no—
283C4⋊Dic61—24no—
284C4⋊Dic61—24no—
285C4⋊Dic61—41no—
286#11758196—24no—
287#11758196—24no—
288#11758196—42no—
289#11758196—42no—
290#11758196—42no—
291#11758196—41no—
292#11758196—41no—
293C4×Dic61—24no—
294C4×Dic61—24no—
295C4×Dic61—24no—
296C4×Dic61—24no—
297C4×Dic61—24no—
298C4×Dic61—24no—
299C4×Dic61—24no—
300C4×Dic61—24no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—41no—
305C4×Dic61—42no—
306C4×Dic61#4118yes—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61C2×#4114yes—
314C23×C61C2511yescharacteristic
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322D4×C61—44no—
323C2×C4×C61—216no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—22no—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61C2×#4114yes—
344C2×C4×C61C2×#4114yes—
345C2×C4×C61C2×#4112yes—
346C22⋊D61—48no—
347C22⋊D61—48no—
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—22no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—48no—
369C2×Dic61—48no—
370C2×Dic61C2×#4114yes—
371C2×Dic61C2×#4114yes—
372C2×Dic61C2×#4114yes—
373C2×Dic61C2×#4114yes—
374C2×Dic61H(5,𝔽2)12yes—
375D244—44no—
376C4×D61—48no—
377Dic122—44no—
378Dic122—44no—
379#34874—611nomaximal, Sylow
380C22×C61—24no—
381C22×C61—24no—
382C22×C61—24no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61C22×#4112yes—
388C22×C61C22×#4112yes—
389C22×C61C22×#4111yescharacteristic
390C22×C61C2×H(5,𝔽2)11yescharacteristic
391C22×C61#58511yescharacteristic
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C4×C61—24no—
400C4×C61—24no—
401C4×C61—22no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—41no—
406C4×C61—41no—
407Dic61—24no—
408Dic61—24no—
409Dic61—24no—
410Dic61—41no—
411Dic61—41no—
412Dic61—42no—
413Dic61—42no—
414Dic61—41no—
415Dic61#55514yes—
416#2612—611no—
417#2610—612no—
418#2609D6111yescharacteristic, complemented
419#2593—611no—
420#2574—612no—
421#2555—611no—
422#2531—612no—
423#2529—612no—
424#2476—612no—
425#2474—612no—
426#2399—611no—
427#2398—611no—
428#2392—612no—
429C4×#124—612no—
430C4×#124—611no—
431C4×#121—612no—
432#2298—612no—
433#2290—612no—
434C4×#117—612no—
435C2×C61—44no—
436C2×C61#344412yes—
437C2×C61#346011yescharacteristic
438C2×C61C2×#55511yescharacteristic
439C2×C61#347512yes—
440C2×C61#348111yescharacteristic
441D61—82no—
442C2×#124—612no—
443C2×#124—611no—
444C2×#121—612no—
445C2×C4×Q8—611no—
446C2×C4×Q8—611no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—612no—
450C2×C4×D4—612no—
451C2×#117—612no—
452C2×#117—612no—
453C2×#117C2×D6112yes—
454C22×C42—612no—
455#400—611no—
456#400—611no—
457#398—611no—
458#398—612no—
459#398—612no—
460#398C2×D6111yescharacteristic
461#397—612no—
462#397—612no—
463#396—612no—
464#396C2×D6112yes—
465#395—612no—
466#395—611no—
467#395—611no—
468#394—611no—
469#394—612no—
470#394—612no—
471#394—612no—
472#394C2×D6111yescharacteristic
473#393—612no—
474#392—612no—
475#391—611no—
476#391—612no—
477#390—611no—
478#390—612no—
479#390—612no—
480#389—612no—
481#388—612no—
482#388—612no—
483#388—612no—
484#388—612no—
485#388—612no—
486#388—612no—
487#388—612no—
488#388—612no—
489#388—612no—
490#388—612no—
491#388—612no—
492#388—612no—
493#388—612no—
494#388C2×D6112yes—
495#387—612no—
496#387—612no—
497#387—612no—
498#387—612no—
499#387—612no—
500#387C2×D6112yes—
501#386—612no—
502#386—612no—
503#386—612no—
504#386C2×D6112yes—
505#385—612no—
506#385C2×D6112yes—
507#382—612no—
508#382C2×D6111yescharacteristic
509#380—612no—
510C4×C4⋊C4—612no—
511C4×C4⋊C4—612no—
512C4×C4⋊C4—612no—
513C4×C4⋊C4—612no—
514C4×C4⋊C4—612no—
515C4×C22⋊C4—612no—
516C4×C22⋊C4—612no—
517C4×C22⋊C4—612no—
518C4×C22⋊C4—612no—
519C4×C22⋊C4—612no—
520C4×C22⋊C4—612no—
521C4×C22⋊C4—612no—
522C4×C22⋊C4—612no—
523#376—612no—
524#376—612no—
525#376—611no—
526#376—611no—
527C43—611no—
528C43—612no—
529C61#3487411yescharacteristic, complemented, Sylow
530C22×Q8—611no—
531C22×Q8—611no—
532C22×D4—612no—
533C22×D4—612no—
534C22×D4—611no—
535C22×D4C22×D6111yescharacteristic
536C23×C4—612no—
537C23×C4—612no—
538C23×C4—612no—
539C23×C4C22×D6112yes—
540#124—1228no—
541#124—1224no—
542#121—1228no—
543C4×Q8—2442no—
544C4×Q8—2442no—
545C4×D4—1228no—
546C4×D4—2444no—
547C4×D4—2442no—
548C4×D4—2442no—
549#117—28no—
550#117—1228no—
551#117—1228no—
552C2×C4⋊C4—612no—
553C2×C4⋊C4—612no—
554C2×C4⋊C4—612no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—612no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—612no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—612no—
563C2×C4⋊C4C22×D6112yes—
564C2×C4⋊C4C22×D6112yes—
565C2×C4⋊C4C22×D6112yes—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
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×C22⋊C4—612no—
576C2×C22⋊C4—612no—
577C2×C22⋊C4—612no—
578C2×C22⋊C4—612no—
579C2×C22⋊C4—612no—
580C2×C22⋊C4—612no—
581C2×C22⋊C4—612no—
582C2×C22⋊C4—612no—
583C2×C22⋊C4—612no—
584C2×C22⋊C4C22×D6112yes—
585C2×C22⋊C4C22×D6112yes—
586C2×C22⋊C4C22×D6112yes—
587C2×C22⋊C4C22×D6112yes—
588C2×C22⋊C4C22×D6112yes—
589C2×C42—612no—
590C2×C42—612no—
591C2×C42—612no—
592C2×C42—612no—
593C2×C42—612no—
594C2×C42—611no—
595C2×C42—611no—
596C2×C42—611no—
597C2×C42—612no—
598C2×C42—612no—
599C2×C42—612no—
600C2×C42—612no—
601C2×C42—611no—
602C2×C42—612no—
603C2×C42—1228no—
604C2×C42C22×D6112yes—
605C2×C42C22×D6111yescharacteristic
606#95—612no—
607#95—612no—
608#95—612no—
609#95—612no—
610#95—612no—
611#95—612no—
612#95—612no—
613#95—612no—
614#95—612no—
615#95—611no—
616#95—612no—
617#95—611no—
618#95—612no—
619#95—612no—
620#95—612no—
621#95—612no—
622#95—612no—
623#95—612no—
624#95C22×D6111yescharacteristic
625#95C22×D6111yescharacteristic
626#95C22×D6112yes—
627#95C22×D6112yes—
628#95C22×D6112yes—
629#95C22×D6112yes—
630C24—612no—
631C24C23×D6112yes—
632C2×Q8—1224no—
633C2×Q8—1222no—
634C2×Q8—2441no—
635C2×Q8—2441no—
636C2×Q8—2441no—
637C2×D4—24no—
638C2×D4—41no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1222no—
644C2×D4—2441no—
645C2×D4—2441no—
646C2×D4—2442no—
647C2×D4—2442no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—611no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4—1224no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1224no—
668C22×C4—2442no—
669C22×C4C23×D6112yes—
670C22×C4C23×D6111yescharacteristic
671C22×C4C23×D6112yes—
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674C22×C4C23×D6112yes—
675C22×C4C23×D6111yescharacteristic
676C22×C4C23×D6112yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—1224no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—2442no—
689C4⋊C4—2442no—
690C4⋊C4—2442no—
691C4⋊C4—2441no—
692C4⋊C4—2441no—
693C4⋊C4—2441no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—42no—
699C22⋊C4—618no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C22⋊C4—2442no—
712C22⋊C4—2442no—
713C22⋊C4—2442no—
714C42—24no—
715C42—618no—
716C42—1224no—
717C42—1224no—
718C42—1224no—
719C42—1224no—
720C42—1224no—
721C42—1222no—
722C42—1224no—
723C42—1222no—
724C42—1222no—
725C42—1224no—
726C42—1224no—
727C42—2441no—
728C42—2442no—
729C42#1175822414yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—1222no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—1222no—
741C23—1222no—
742C23—1222no—
743C23#41×D6114yes—
744C23C24×D6111yescharacteristic
745Q8—2444no—
746Q8—2444no—
747D4—44no—
748D4—2444no—
749D4—2448no—
750D4—2448no—
751C2×C4—216no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—614no—
772C2×C4—612no—
773C2×C4—614no—
774C2×C4—614no—
775C2×C4—614no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—2448no—
797C2×C4—2448no—
798C2×C4—2448no—
799C2×C4#41×D6114yes—
800C2×C4C2×#1175822414yes—
801C2×C4C2×#1175822412yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22—2442no—
815C22—2442no—
816C22C2×#41×D6112yes—
817C22C2×#41×D6112yes—
818C22C22×#1175822411yescharacteristic
819C22H(5,𝔽2)×D6111yescharacteristic
820C22#1684059911yescharacteristic
821C4—22no—
822C4—24no—
823C4—24no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—614no—
830C4—1224no—
831C4—1224no—
832C4—1224no—
833C4—2441no—
834C4—2441no—
835C4—2442no—
836C4—2442no—
837C4—2441no—
838C2—44no—
839C2—4882no—
840C2#2145911112yes—
841C2#2145923611yescharacteristic
842C2#555×D6111yescharacteristic
843C2#2145937212yes—
844C2#2145942211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2609C2
prime radical#21450887C2
hypercenter#2609D61
hypocenterC61#34874
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2609

Complements

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

NH ≅ G/Ntype
1. #21451527C2semidirect
2. #21451506C2semidirect
3. #21451309C2semidirect
4. #21451086C2semidirect
6. #21450663C2semidirect
7. #21450633C2semidirect
8. #21450002C2semidirect
9. #21449972C2semidirect
10. #21449111C2semidirect
11. #21449107C2semidirect
12. #21449064C2semidirect
13. #21448360C2semidirect
14. #21448358C2semidirect
15. #21448329C2semidirect
16. #21448311C2semidirect
17. #21448255C2semidirect
18. #117×Dic61C2semidirect
19. C61×#2609C2semidirect
418. #2609D61semidirect
529. C61#34874semidirect

Maximal subgroups

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

subgroupindex
#214515272
#214515062
#214513092
#214510862
#214508872
#214506632
#214506332
#214500022
#214499722
#214491112
#214491072
#214490642
#214483602
#214483582
#214483292
#214483112
#214482552
#117×Dic612
C61×#26092
#3487461