Finite Group Databasebeta

← #29611470

Subgroups — #29611470

Order 15616.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519757C211yesmaximal, characteristic, complemented
2C22×#14519737C211yesmaximal, characteristic
3C2×#16839683C211yesmaximal, characteristic, complemented
4C2×#16839674C211yesmaximal, characteristic, complemented
5C2×#16839637C212yesmaximal, complemented
6#21444069C211yesmaximal, characteristic, complemented
7#21444065C212yesmaximal, complemented
8#21444058C212yesmaximal
9#21444053C212yesmaximal, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C22⋊D61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×#14519757—28no—
17C2×#14519757—24no—
18C2×#14519737—24no—
19C2×#14519737—24no—
20C2×#14519737—24no—
21C22×C4⋊Dic61C2212yes—
22C22×C4⋊Dic61C2212yes—
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2212yes—
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2212yes—
27C22×#11758198C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839683—24no—
30#16839674—24no—
31#16839637—28no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C22×Dic122—22no—
45C22×Dic122—24no—
46C22×Dic122—22no—
47C22×Dic122—22no—
48C22×Dic122—42no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61—22no—
52C22×C22⋊D61—22no—
53C22×C22⋊D61—22no—
54C22×C22⋊D61—22no—
55C22×C22⋊D61Q814yescomplemented
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—24no—
60C23×Dic61—42no—
61C23×Dic61C2312yes—
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—24no—
69C22×C4×D61—42no—
70C22×C4×D61D414yes—
71#14519757—232no—
72#14519737—232no—
73C2×C4⋊Dic61—24no—
74C2×C4⋊Dic61—24no—
75C2×C4⋊Dic61—24no—
76C2×C4⋊Dic61—24no—
77C2×C4⋊Dic61—42no—
78C2×C4⋊Dic61D418yescomplemented
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196D414yes—
82C2×C22⋊Dic61—24no—
83C2×C22⋊Dic61—24no—
84C2×C22⋊Dic61—42no—
85C2×#11758198—22no—
86C2×#11758198—24no—
87C2×#11758198—22no—
88C2×#11758198—24no—
89C2×#11758198—22no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198—42no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97#14519684—24no—
98#14519684—24no—
99#14519684—22no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103C25×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61—24no—
109C2×C4⋊C4×C61—22no—
110C2×C22⋊C4×C61—24no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61D414yes—
116#95×C61—22no—
117#95×C61—24no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—22no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61C2×D412yes—
127C24×C61C2×Q812yes—
128C24×C61#4112yes—
129C24×C61C2411yescharacteristic
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61C2×D412yes—
139C23×D61C2×Q812yes—
140C23×D61#4112yes—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D414yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61#4114yes—
165C2×C22⋊D61—28no—
166C2×C22⋊D61—28no—
167C2×C22⋊D61—28no—
168C2×C22⋊D61—28no—
169C2×C22⋊D61—28no—
170C2×C22⋊D61—28no—
171C2×C22⋊D61—28no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—22no—
179C22×Dic61—28no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—48no—
198C22×Dic61—48no—
199C22×Dic61—44no—
200C22×Dic61—44no—
201C22×Dic61C2×D412yes—
202C22×Dic61C2×D414yes—
203C22×Dic61C2×D414yes—
204C22×Dic61C2×D412yes—
205C22×Dic61C2×D412yes—
206C22×Dic61C2×Q812yes—
207C22×Dic61#4112yes—
208C2×C4×D61—28no—
209C2×C4×D61—28no—
210C2×C4×D61—44no—
211C2×C4×D61—48no—
212C2×C4×D61—48no—
213C2×Dic122—28no—
214C2×Dic122—48no—
215C2×Dic122—48no—
216C2×Dic122—44no—
217C2×Dic122—44no—
218C4⋊C4×C61—28no—
219C22⋊C4×C61—216no—
220C22⋊C4×C61—28no—
221C22⋊Dic61—48no—
222#11758198—28no—
223#11758198—216no—
224#11758198—48no—
225C4⋊Dic61—216no—
226C4⋊Dic61—48no—
227#11758196—28no—
228C4×Dic61—28no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—24no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—42no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61C22⋊Q814yescomplemented
252C23×C61C22×D411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×D412yes—
256C23×C61C22×Q811yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61C2×#4111yescharacteristic
260C23×C61C2×#4112yes—
261C23×C61H(5,𝔽2)12yes—
262C23×C612−1+412yes—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61C22⋊Q814yes—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61#12014yes—
310C22⋊D61—232no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—22no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—416no—
327C2×Dic61—42no—
328C2×Dic61—41no—
329C2×Dic61—42no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61#12014yes—
342C2×Dic61C22⋊Q814yescomplemented
343C4×D61—416no—
344Dic122—416no—
345#14723—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—44no—
355C22×C61—44no—
356C22×C61—44no—
357C22×C61C2×#12011yescharacteristic
358C22×C61C2×#12011yescharacteristic
359C22×C61C2×C22⋊Q811yescharacteristic
360C22×C61C2×C22⋊Q811yescharacteristic
361C22×C61C2×C22⋊Q811yescharacteristic
362C22×C61#52512yes—
363C22×C61#52511yescharacteristic
364C22×C61#52511yescharacteristic
365C22×C61#52511yescharacteristic
366C22×C61#53212yes—
367C22×C61#53211yescharacteristic
368C22×C61#53411yescharacteristic
369C22×C61#53611yescharacteristic
370C22×C61#53912yes—
371C22×C61#54212yes—
372C22×C61D4212yes—
373C22×C61D4212yes—
374C22×C61#54712yes—
375C22×C61#54812yes—
376C22×C61#54812yes—
377C22×C61D4×Q812yes—
378C22×C61#55112yes—
379C22×C61#55412yes—
380C2×D61—24no—
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C4×C61—24no—
392C4×C61—44no—
393C4×C61—42no—
394C4×C61—44no—
395Dic61—24no—
396Dic61—24no—
397Dic61—44no—
398Dic61—42no—
399Dic61—82no—
400C22×C22⋊Q8—611no—
401C22×C4×D4—611no—
402C2×#395—611no—
403C2×#393—611no—
404C2×#385—612no—
405#1441—611no—
406#1439—612no—
407#1439D6111yescharacteristic, complemented
408#1438—612no—
409#1436—612no—
410C22⋊#95—611no—
411C2×C61—44no—
412C2×C61#238811yescharacteristic
413C2×C61#240311yescharacteristic
414C2×C61#240911yescharacteristic
415C2×C61#243211yescharacteristic
416C2×C61#244912yes—
417C2×C61#245212yes—
418C2×C61#246112yes—
419C2×C61#246312yes—
420C2×C61#256411yescharacteristic
421C2×C61#263811yescharacteristic
422C2×C61#284811yescharacteristic
423D61—44no—
424C23×Q8—611no—
425C23×D4—611no—
426C24×C4—611no—
427C24×C4—611no—
428C2×C22⋊Q8—1228no—
429C2×C22⋊Q8—1224no—
430C2×C4×D4—1224no—
431C2×C4×D4—1224no—
432C2×C4×D4—1224no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4—612no—
435C22×C4⋊C4—612no—
436C22×C4⋊C4C2×D6111yescharacteristic
437C22×C22⋊C4—611no—
438C22×C22⋊C4—612no—
439C22×C22⋊C4—612no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4C2×D6112yes—
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C42—611no—
444#395—1224no—
445#393—1224no—
446#385—1228no—
447C2×#95—611no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95C2×D6111yescharacteristic
454C2×#95C2×D6112yes—
455C61#1472311yescharacteristic, complemented, Sylow
456C25—611no—
457C25C22×D6111yescharacteristic
458C22×Q8—1224no—
459C22×Q8—1222no—
460C22×Q8—1222no—
461C22×Q8—1222no—
462C22×Q8—2442no—
463C22×D4—614no—
464C22×D4—1222no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—1222no—
469C22×D4—1222no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—612no—
473C23×C4—611no—
474C23×C4—614no—
475C23×C4—612no—
476C23×C4—1224no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1224no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—2442no—
484C23×C4—2442no—
485C23×C4C22×D6111yescharacteristic
486C23×C4C22×D6112yes—
487C23×C4C22×D6112yes—
488C23×C4C22×D6111yescharacteristic
489C22⋊Q8—12232no—
490C4×D4—12232no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—614no—
494C2×C4⋊C4—618no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1224no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—2442no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—1222no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1224no—
515C2×C22⋊C4—1224no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—2442no—
518C2×C22⋊C4—2442no—
519C2×C22⋊C4D24414yes—
520C2×C42—1222no—
521C2×C42—1222no—
522C2×C42—1222no—
523#95—22no—
524#95—24no—
525#95—1224no—
526#95—1224no—
527#95—1224no—
528#95—1224no—
529#95—1222no—
530#95—1224no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—612no—
540C24—612no—
541C24—612no—
542C24—1222no—
543C24—1221no—
544C24—1221no—
545C24—1221no—
546C24—1222no—
547C24—1221no—
548C24—1222no—
549C24—1222no—
550C24C2×D24412yes—
551C24#1175822412yes—
552C24Q8×D6112yes—
553C24C23×D6111yescharacteristic
554C2×Q8—1228no—
555C2×Q8—2448no—
556C2×Q8—2448no—
557C2×Q8—2444no—
558C2×Q8—2444no—
559C2×D4—1228no—
560C2×D4—1228no—
561C2×D4—1228no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—1228no—
565C2×D4—1228no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—612no—
585C22×C4—614no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—614no—
590C22×C4—612no—
591C22×C4—1228no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1222no—
599C22×C4—1228no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1221no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1221no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1228no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—2444no—
619C22×C4—2448no—
620C22×C4—2448no—
621C22×C4—2444no—
622C22×C4—2448no—
623C22×C4—2448no—
624C22×C4—2444no—
625C22×C4C2×D24412yes—
626C22×C4C2×D24412yes—
627C22×C4D4×D6114yes—
628C22×C4D4×D6112yes—
629C22×C4D4×D6112yes—
630C22×C4#1175822414yes—
631C4⋊C4—28no—
632C4⋊C4—12216no—
633C4⋊C4—1228no—
634C4⋊C4—2448no—
635C22⋊C4—216no—
636C22⋊C4—28no—
637C22⋊C4—1228no—
638C22⋊C4—12216no—
639C22⋊C4—2448no—
640C22⋊C4—2448no—
641C42—1228no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—614no—
665C23—1224no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1224no—
677C23—1224no—
678C23—1224no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23#1451975714yescomplemented
688C23C2×D4×D6111yescharacteristic
689C23C2×D4×D6112yes—
690C23C2×D4×D6111yescharacteristic
691C23C22×D24411yescharacteristic
692C23C2×Q8×D6111yescharacteristic
693C23#41×D6111yescharacteristic
694C23#41×D6111yescharacteristic
695C23C2×#1175822412yes—
696C23C2×#1175822411yescharacteristic
697C23#1451982312yes—
698C23#1451982412yes—
699Q8—24416no—
700D4—12232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—614no—
725C2×C4—614no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1222no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—24416no—
742C2×C4—24416no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4—2441no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4#1451974714yes—
758C22—24no—
759C22—28no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—42no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—1224no—
770C22—1224no—
771C22—1224no—
772C22—2444no—
773C22—2442no—
774C22—2444no—
775C22—2444no—
776C22—2442no—
777C22—2444no—
778C22—2442no—
779C22—2442no—
780C22#120×D6111yescharacteristic
781C22C2×#1451974711yescharacteristic
782C22C22⋊Q8×D6111yescharacteristic
783C22C22⋊Q8×D6111yescharacteristic
784C22C2×#1451975711yescharacteristic
785C22#1684026812yes—
786C22#1684027211yescharacteristic
787C22#1684027211yescharacteristic
788C22#1684027411yescharacteristic
789C22#1684030712yes—
790C22#1684031011yescharacteristic
791C22#1684032311yescharacteristic
792C22#1684033211yescharacteristic
793C22#1684035612yes—
794C22#1684037812yes—
795C22#1684039612yes—
796C22D4×D24412yes—
797C22#1684041612yes—
798C22#1684041812yes—
799C22#1684042012yes—
800C22#1684042512yes—
801C22#1684043512yes—
802C22#1684047012yes—
803C4—24no—
804C4—44no—
805C4—44no—
806C4—42no—
807C4—1224no—
808C4—1224no—
809C4—4882no—
810C4—2442no—
811C4—2444no—
812C2—44no—
813C2—2444no—
814C2#2144903111yescharacteristic
815C2#2144913111yescharacteristic
816C2#2144917711yescharacteristic
817C2#2144944911yescharacteristic
818C2#2144962612yes—
819C2#2144966212yes—
820C2#2144978412yes—
821C2#2144981112yes—
822C2#2145099411yescharacteristic
823C2#2145174111yescharacteristic
824C2#2145410711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC61×#1439C2
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14723
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#14519757C2semidirect
3. C2×#16839683C2semidirect
4. C2×#16839674C2semidirect
5. C2×#16839637C2semidirect
6. #21444069C2semidirect
7. #21444065C2semidirect
9. #21444053C2semidirect
10. #21444040C2semidirect
11. C61×#1439C2semidirect
55. C22×C22⋊D61Q8semidirect
78. C2×C4⋊Dic61D4semidirect
251. C23×C61C22⋊Q8semidirect
342. C2×Dic61C22⋊Q8semidirect
407. #1439D61semidirect
455. C61#14723semidirect
687. C23#14519757semidirect

Maximal subgroups

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

subgroupindex
C22×#145197572
C22×#145197372
C2×#168396832
C2×#168396742
C2×#168396372
#214440692
#214440652
#214440582
#214440532
#214440402
C61×#14392
#1472361