Finite Group Databasebeta

← #29851498

Subgroups — #29851498

Order 15616.

2570 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×#16840291C211yesmaximal, characteristic, complemented
2C2×C4×#11758224C211yesmaximal, characteristic, complemented
3#21451427C214yesmaximal, complemented
4#21451409C214yesmaximal, complemented
5#21451015C211yesmaximal, characteristic, complemented
6#21451010C211yesmaximal, characteristic, complemented
7#21450800C211yesmaximal, characteristic, complemented
8#21450280C211yesmaximal, characteristic, complemented
9#21450274C211yesmaximal, characteristic, complemented
10#21449450C211yesmaximal, characteristic, complemented
11#21449435C211yesmaximal, characteristic
12#21449058C214yesmaximal, complemented
13#21448388C211yesmaximal, characteristic, complemented
14#127×Dic61C211yesmaximal, characteristic, complemented
15#21448366C211yesmaximal, characteristic, complemented
16#124×Dic61C211yesmaximal, characteristic, complemented
17#21448259C214yesmaximal, complemented
18C4×#14519735C211yesmaximal, characteristic, complemented
19C61×#2544C211yesmaximal, characteristic, complemented
20C22×#11758224C2211yescharacteristic
21C2×#14519775C2211yescharacteristic
22#16840291—28no—
23C2×#14519770C2212yes—
24C2×#14519769C2211yescharacteristic
25C2×#14519764C2211yescharacteristic
26C2×#14519759C2212yes—
27C2×#14519753C2211yescharacteristic
28C2×#14519748C2211yescharacteristic
29C4×#11758224—28no—
30C2×Q8×Dic61C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×D4×Dic61C2211yescharacteristic
34C2×D4×Dic61C2214yes—
35C2×D4×Dic61C2211yescharacteristic
36C2×C4×C22⋊D61C2212yes—
37C2×#14519737C2212yes—
38C2×#14519737C2212yes—
39C2×#14519735C2211yescharacteristic
40C2×#14519735C2212yes—
41C2×#14519733C2212yes—
42C2×#14519733C2212yes—
43C22×C4×Dic61C2212yes—
44C2×C42×D61C2211yescharacteristic
45#16839692C2214yes—
46#16839689C2214yes—
47#16839685C2214yes—
48#16839685C2214yes—
49#16839677C2214yes—
50#16839677C2214yes—
51#16839670C2214yes—
52#16839669C2211yescharacteristic
53#16839668C2211yescharacteristic
54#16839668C2211yescharacteristic
55#16839665C2211yescharacteristic
56#16839665C2211yescharacteristic
57#16839665C2211yescharacteristic
58#16839665C2214yes—
59#16839659C2214yes—
60#16839656C2214yes—
61#16839655C2214yes—
62#16839650C2214yes—
63#16839650C2214yes—
64#16839647C2214yes—
65#16839645C2214yes—
66#16839642C2214yes—
67#16839635C2214yes—
68#16839634C2214yes—
69#16839632C2211yescharacteristic
70#16839631C2211yescharacteristic
71#16839628C2211yescharacteristic
72#16839627C2211yescharacteristic
73C4⋊C4×Dic61C2212yes—
74C4×C4⋊Dic61C2211yescharacteristic
75#16839613C2214yes—
76C22⋊C4×Dic61C2214yes—
77C22⋊C4×Dic61C2214yes—
78C4×#11758198C2211yescharacteristic
79C4×#11758198C2211yescharacteristic
80#16839609C2212yes—
81#16839607C2212yes—
82C42×Dic61C2211yescharacteristic
83C42×Dic61C2211yescharacteristic
84C2×#127×C61C2211yescharacteristic
85C2×#124×C61C2211yescharacteristic
86C2×#124×C61C2211yescharacteristic
87C2×C4×D4×C61C2211yescharacteristic
88C61×#394C2214yes—
89C61×#391C2211yescharacteristic
90C61×#390C2211yescharacteristic
91C61×#386C2214yes—
92C4×C4⋊C4×C61C2211yescharacteristic
93C2×#11758224—24no—
94C2×#11758224—24no—
95C2×#11758224—24no—
96C22×Dic122C2311yescharacteristic
97C22×C22⋊D61C2312yes—
98C22×C22⋊D61C2312yes—
99C23×Dic61C2312yes—
100C23×Dic61C2312yes—
101C23×Dic61C2312yes—
102C22×C4×D61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519775—24no—
106#14519770—28no—
107#14519769—24no—
108#14519764—24no—
109#14519759—28no—
110#14519753—24no—
111#14519748—24no—
112Q8×Dic61—24no—
113C4×Dic122—24no—
114#14519742—24no—
115D4×Dic61—24no—
116D4×Dic61—24no—
117D4×Dic61—216no—
118C4×C22⋊D61—28no—
119#14519737—28no—
120#14519737—28no—
121#14519735—24no—
122#14519735—28no—
123#14519733—28no—
124#14519733—28no—
125C2×C4⋊Dic61C2312yes—
126C2×C4⋊Dic61C2314yes—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2314yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2314yes—
138C2×C22⋊Dic61C2314yes—
139C2×C22⋊Dic61C2314yes—
140C2×C22⋊Dic61C2314yes—
141C2×C22⋊Dic61C2312yes—
142C2×C22⋊Dic61C2312yes—
143C2×C22⋊Dic61C2312yes—
144C2×C22⋊Dic61C2314yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×C4×Dic61—28no—
150C2×C4×Dic61C2312yes—
151C2×C4×Dic61C2312yes—
152C2×C4×Dic61C2312yes—
153C2×C4×Dic61C2312yes—
154C2×C4×Dic61C2312yes—
155C2×C4×Dic61C2311yescharacteristic
156C2×C4×Dic61C2311yescharacteristic
157C2×C4×Dic61C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2311yescharacteristic
160C2×C4×Dic61C2311yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C2×C4×Dic61C2312yes—
163C42×D61D418yescomplemented
164#14519684C2314yes—
165#14519684C2314yes—
166#14519684C2314yes—
167#14519684C2314yes—
168#14519684C2314yes—
169#14519684C2312yes—
170#14519684C2312yes—
171#14519684C2312yes—
172C22×Q8×C61C2311yescharacteristic
173C22×D4×C61C2311yescharacteristic
174C22×D4×C61C2314yes—
175C22×D4×C61C2311yescharacteristic
176C23×C4×C61C2312yes—
177#127×C61—24no—
178#124×C61—24no—
179#124×C61—24no—
180C4×D4×C61—24no—
181C2×C4⋊C4×C61C2312yes—
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C22⋊C4×C61C2312yes—
184C2×C22⋊C4×C61C2312yes—
185C2×C22⋊C4×C61C2312yes—
186C2×C22⋊C4×C61C2314yes—
187C2×C22⋊C4×C61C2314yes—
188C2×C42×C61C2311yescharacteristic
189C2×C42×C61C2311yescharacteristic
190C2×C42×C61C2311yescharacteristic
191#95×C61C2314yes—
192#95×C61C2312yes—
193C24×C61C2412yes—
194C24×C61C2412yes—
195C23×D61C2411yescharacteristic
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×D4×C61—28no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—28no—
205C2×D4×C61—22no—
206C2×D4×C61—44no—
207C2×D4×C61#4114yes—
208C22×C4×C61—24no—
209C22×C4×C61—44no—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—44no—
222C22×Dic61—24no—
223C22×Dic61—24no—
224C22×Dic61—24no—
225C22×Dic61—24no—
226C22×Dic61—24no—
227C22×Dic61—28no—
228C22×Dic61—28no—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2411yescharacteristic
234C22×Dic61C2411yescharacteristic
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2411yescharacteristic
238#11758224—232no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—24no—
242C2×C4×D61—42no—
243C2×C4×D61C2×D414yes—
244C2×C4×D61C2×D414yes—
245C2×C4×D61C2×D414yes—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122#4114yes—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—24no—
251C22⋊C4×C61—28no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—44no—
256C42×C61—22no—
257C42×C61—22no—
258C42×C61C2×D414yes—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262C22⋊Dic61—28no—
263C22⋊Dic61—28no—
264C22⋊Dic61—28no—
265C22⋊Dic61—44no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270C4⋊Dic61—22no—
271C4⋊Dic61—22no—
272C4⋊Dic61—22no—
273C4⋊Dic61—28no—
274C4⋊Dic61—24no—
275C4⋊Dic61—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—28no—
282#11758196—44no—
283C4×Dic61—24no—
284C4×Dic61—22no—
285C4×Dic61—22no—
286C4×Dic61—24no—
287C4×Dic61—24no—
288C4×Dic61—24no—
289C4×Dic61—24no—
290C4×Dic61—42no—
291C4×Dic61—42no—
292C4×Dic61C2×D414yes—
293C4×Dic61C2×D414yes—
294C4×Dic61C2×D414yes—
295C4×Dic61#4118yescomplemented
296C23×C61—22no—
297C23×C61—24no—
298C23×C61—22no—
299C23×C61—24no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—24no—
303C23×C61—22no—
304C23×C61—24no—
305C23×C61C2×#4114yes—
306C23×C61C2511yescharacteristic
307C22×D61—22no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—22no—
311C22×D61C22×D412yes—
312Q8×C61—44no—
313D4×C61—28no—
314D4×C61—416no—
315D4×C61—44no—
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—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—24no—
328C2×C4×C61—48no—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D412yes—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C2×#4114yes—
333C2×C4×C61C2×#4112yes—
334C2×C4×C61C2×#4112yes—
335C22⋊D61—216no—
336C22⋊D61—48no—
337C2×Dic61—216no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—22no—
353C2×Dic61—24no—
354C2×Dic61—48no—
355C2×Dic61—48no—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C2×#4114yes—
360C2×Dic61C2×#4114yes—
361C2×Dic61C2×#4114yes—
362C4×D61—28no—
363C4×D61—28no—
364C4×D61—44no—
365Dic122—28no—
366#34910—611nomaximal, Sylow
367C22×C61—24no—
368C22×C61—28no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—44no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—44no—
376C22×C61—44no—
377C22×C61C23×D411yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4112yes—
380C22×C61C22×#4111yescharacteristic
381C22×C61#58512yes—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—42no—
386C2×D61—42no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—24no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61#52514yes—
394Dic61—24no—
395Dic61—22no—
396Dic61—22no—
397Dic61—24no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61—42no—
402Dic61#53214yes—
403C2×#529—611no—
404C2×C4×#41—611no—
405#2602—614no—
406#2601—614no—
407#2566—611no—
408#2565—611no—
409#2545—611no—
410#2544D6111yescharacteristic, complemented
411#2500—611no—
412#2499—611no—
413#2432—611no—
414#2431—611no—
415#2392—614no—
416C4×C4⋊Q8—611no—
417C4×#127—611no—
418C4×#124—611no—
419C4×#124—611no—
420#2290—614no—
421C4×#117—611no—
422C2×C61—44no—
423C2×C61—82no—
424C2×C61C2×#52511yescharacteristic
425C2×C61C2×#53211yescharacteristic
426C2×C61#344911yescharacteristic
427C2×C61#347512yes—
428C2×C61#348012yes—
429D61—42no—
430C22×#41—611no—
431C2×C4⋊Q8—611no—
432C2×#127C2×D6111yescharacteristic
433#529—1228no—
434C2×#126—612no—
435C2×#125—611no—
436C2×#124—611no—
437C2×#124C2×D6111yescharacteristic
438C2×#124C2×D6111yescharacteristic
439C2×#123—612no—
440C2×C22⋊Q8—611no—
441C2×#121—611no—
442C4×#41—1228no—
443C2×C4×Q8—611no—
444C2×C4×Q8—611no—
445C2×C4×Q8—611no—
446C2×C4×D4—614no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—612no—
450C2×C4×D4—612no—
451C2×C4×D4—612no—
452C2×C4×D4C2×D6111yescharacteristic
453C2×#117—612no—
454C2×#117—611no—
455C2×#117—612no—
456C2×#117—612no—
457C22×C42—611no—
458C22×C42—612no—
459#398—614no—
460#397—614no—
461#396—614no—
462#396—614no—
463#394—614no—
464#394—614no—
465#394C2×D6114yes—
466#392—614no—
467#391—611no—
468#391—611no—
469#391—611no—
470#391C2×D6111yescharacteristic
471#390—611no—
472#390—614no—
473#390—611no—
474#390—611no—
475#390C2×D6111yescharacteristic
476#389—614no—
477#388—614no—
478#388—614no—
479#388—614no—
480#388—614no—
481#387—614no—
482#387—614no—
483#386—614no—
484#386C2×D6114yes—
485#385—614no—
486#385—614no—
487#384—611no—
488#384—611no—
489#382—611no—
490#382—611no—
491C4×C4⋊C4—612no—
492C4×C4⋊C4—611no—
493C4×C4⋊C4—614no—
494C4×C4⋊C4C2×D6111yescharacteristic
495C4×C22⋊C4—614no—
496C4×C22⋊C4—614no—
497C4×C22⋊C4—611no—
498C4×C22⋊C4—611no—
499C4×C22⋊C4—612no—
500#376—612no—
501C43—611no—
502C43—611no—
503C61#3491011yescharacteristic, complemented, Sylow
504C2×#41—1224no—
505C2×#41—1224no—
506C2×#41—1224no—
507C22×Q8—611no—
508C22×Q8C22×D6111yescharacteristic
509C22×D4—612no—
510C22×D4—612no—
511C22×D4C22×D6111yescharacteristic
512C22×D4C22×D6114yes—
513C22×D4C22×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—612no—
518C23×C4—612no—
519C23×C4—612no—
520C23×C4C22×D6112yes—
521C4⋊Q8—1224no—
522#127—24no—
523#126—1228no—
524#125—1224no—
525#124—24no—
526#124—24no—
527#124—1224no—
528#123—1228no—
529C22⋊Q8—1224no—
530#121—1224no—
531C4×Q8—1224no—
532C4×Q8—1224no—
533C4×Q8—1224no—
534C4×D4—24no—
535C4×D4—1224no—
536C4×D4—1224no—
537C4×D4—12216no—
538C4×D4—1228no—
539C4×D4—1228no—
540C4×D4—1228no—
541#117—1228no—
542#117—1228no—
543#117—1228no—
544#117—1224no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—612no—
547C2×C4⋊C4—612no—
548C2×C4⋊C4—612no—
549C2×C4⋊C4—612no—
550C2×C4⋊C4—612no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—612no—
553C2×C4⋊C4—614no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—614no—
557C2×C4⋊C4—614no—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6112yes—
560C2×C22⋊C4—612no—
561C2×C22⋊C4—612no—
562C2×C22⋊C4—612no—
563C2×C22⋊C4—614no—
564C2×C22⋊C4—614no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—612no—
567C2×C22⋊C4—612no—
568C2×C22⋊C4—612no—
569C2×C22⋊C4—612no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4C22×D6112yes—
572C2×C22⋊C4C22×D6112yes—
573C2×C22⋊C4C22×D6112yes—
574C2×C22⋊C4C22×D6114yes—
575C2×C22⋊C4C22×D6114yes—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—612no—
579C2×C42—611no—
580C2×C42—618no—
581C2×C42—612no—
582C2×C42—612no—
583C2×C42—612no—
584C2×C42—612no—
585C2×C42—612no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—612no—
589C2×C42—612no—
590C2×C42—1228no—
591C2×C42C22×D6111yescharacteristic
592C2×C42C22×D6111yescharacteristic
593C2×C42C22×D6111yescharacteristic
594#95—612no—
595#95—612no—
596#95—612no—
597#95—614no—
598#95—614no—
599#95—614no—
600#95—614no—
601#95—614no—
602#95C22×D6112yes—
603#95C22×D6114yes—
604C24—611no—
605C24C23×D6112yes—
606C24C23×D6112yes—
607#41—12232no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—614no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×D4—28no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—28no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—2444no—
627C2×D4#1175822414yes—
628C22×C4—24no—
629C22×C4—44no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—611no—
635C22×C4—614no—
636C22×C4—614no—
637C22×C4—614no—
638C22×C4—612no—
639C22×C4—612no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1224no—
646C22×C4—1224no—
647C22×C4—1228no—
648C22×C4—1228no—
649C22×C4—1224no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—2442no—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6111yescharacteristic
657C22×C4C23×D6111yescharacteristic
658C22×C4C23×D6112yes—
659C22×C4C23×D6111yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—24no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1228no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1228no—
674C4⋊C4—2444no—
675C22⋊C4—28no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—44no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1228no—
687C22⋊C4—1228no—
688C22⋊C4—1228no—
689C22⋊C4—1224no—
690C22⋊C4—2444no—
691C42—22no—
692C42—22no—
693C42—614no—
694C42—614no—
695C42—614no—
696C42—618no—
697C42—1224no—
698C42—1224no—
699C42—1224no—
700C42—1224no—
701C42—1224no—
702C42—1222no—
703C42—1222no—
704C42—2442no—
705C42—2442no—
706C42D4×D6114yes—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—24no—
716C23—612no—
717C23—1222no—
718C23—1221no—
719C23—1221no—
720C23—1222no—
721C23C2×#1175822414yes—
722C23C24×D6111yescharacteristic
723Q8—44no—
724Q8—1228no—
725D4—28no—
726D4—416no—
727D4—44no—
728D4—12216no—
729D4—2448no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—24no—
742C2×C4—48no—
743C2×C4—612no—
744C2×C4—614no—
745C2×C4—612no—
746C2×C4—612no—
747C2×C4—614no—
748C2×C4—614no—
749C2×C4—1228no—
750C2×C4—12216no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1228no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1224no—
765C2×C4—1224no—
766C2×C4—1222no—
767C2×C4—1224no—
768C2×C4—2444no—
769C2×C4—2448no—
770C2×C4—2448no—
771C2×C4C2×D4×D6112yes—
772C2×C4C2×D4×D6112yes—
773C2×C4C2×D4×D6112yes—
774C2×C4#41×D6114yes—
775C2×C4#41×D6112yes—
776C2×C4C2×#1175822412yes—
777C22—24no—
778C22—28no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—1222no—
788C22—1222no—
789C22—1222no—
790C22—2442no—
791C22—2442no—
792C22C22×D4×D6111yescharacteristic
793C22C2×#41×D6111yescharacteristic
794C22C2×#41×D6112yes—
795C22C22×#1175822411yescharacteristic
796C22#1684059712yes—
797C4—22no—
798C4—24no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—614no—
804C4—1222no—
805C4—1224no—
806C4—1222no—
807C4—1224no—
808C4—2442no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C4#1684027214yes—
813C2—44no—
814C2—82no—
815C2—2442no—
816C2C2×#1684027211yescharacteristic
817C2#532×D6111yescharacteristic
818C2#2145915011yescharacteristic
819C2#2145937012yes—
820C2#2145941512yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2544C2
prime radical#21449435C2
hypercenter#2544D61
hypocenterC61#34910
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. C2×#16840291C2semidirect
2. C2×C4×#11758224C2semidirect
3. #21451427C2semidirect
4. #21451409C2semidirect
5. #21451015C2semidirect
6. #21451010C2semidirect
7. #21450800C2semidirect
8. #21450280C2semidirect
9. #21450274C2semidirect
10. #21449450C2semidirect
12. #21449058C2semidirect
13. #21448388C2semidirect
14. #127×Dic61C2semidirect
15. #21448366C2semidirect
16. #124×Dic61C2semidirect
17. #21448259C2semidirect
18. C4×#14519735C2semidirect
19. C61×#2544C2semidirect
163. C42×D61D4semidirect
295. C4×Dic61#41semidirect
410. #2544D61semidirect
503. C61#34910semidirect

Maximal subgroups

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

subgroupindex
C2×#168402912
C2×C4×#117582242
#214514272
#214514092
#214510152
#214510102
#214508002
#214502802
#214502742
#214494502
#214494352
#214490582
#214483882
#127×Dic612
#214483662
#124×Dic612
#214482592
C4×#145197352
C61×#25442
#3491061