Finite Group Databasebeta

← #29611469

Subgroups — #29611469

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×#14519756C211yesmaximal, characteristic, complemented
2C2×#16839682C211yesmaximal, characteristic, complemented
3C2×#16839674C211yesmaximal, characteristic, complemented
4C2×#16839635C212yesmaximal, complemented
5#21444072C211yesmaximal, characteristic, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444062C212yesmaximal, complemented
8#21444060C212yesmaximal
9#21444052C212yesmaximal, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C22×C4×D4×C61C211yesmaximal, characteristic
12C23×Dic122C2211yescharacteristic
13C2×#14519756—28no—
14C2×#14519756—24no—
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758196C2212yes—
17C22×#11758196C2212yes—
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2212yes—
21C22×C22⋊Dic61C2212yes—
22#16839682—24no—
23#16839674—24no—
24#16839635—28no—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C23×D4×C61C2211yescharacteristic
34C24×C4×C61C2211yescharacteristic
35C24×C4×C61C2211yescharacteristic
36C2×C4×D4×C61—24no—
37C2×C4×D4×C61—24no—
38C2×C4×D4×C61—24no—
39C22×C4⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C22×C42×C61C2211yescharacteristic
43C22×Dic122—22no—
44C22×Dic122—24no—
45C22×Dic122—22no—
46C22×Dic122—22no—
47C22×Dic122—42no—
48C23×Dic61C2312yes—
49C23×Dic61C2312yes—
50C23×Dic61C2312yes—
51C23×Dic61C2312yes—
52#14519756—232no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—24no—
55C2×#11758196—24no—
56C2×#11758196—24no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—42no—
60C2×#11758196D418yescomplemented
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—24no—
68C2×C22⋊Dic61—24no—
69C2×C22⋊Dic61—24no—
70C2×C22⋊Dic61—24no—
71C2×C22⋊Dic61—42no—
72C2×C22⋊Dic61—42no—
73#14519684—24no—
74#14519684—22no—
75#14519684—24no—
76#14519684—24no—
77#14519684—22no—
78#14519684—24no—
79#14519684—24no—
80#14519684—24no—
81C25×C61C2311yescharacteristic
82C25×C61C2311yescharacteristic
83C22×D4×C61—22no—
84C22×D4×C61—22no—
85C22×D4×C61—22no—
86C22×D4×C61—22no—
87C22×D4×C61—22no—
88C22×D4×C61—22no—
89C22×D4×C61Q814yescomplemented
90C23×C4×C61—22no—
91C23×C4×C61—24no—
92C23×C4×C61—22no—
93C23×C4×C61—22no—
94C23×C4×C61—22no—
95C23×C4×C61—22no—
96C23×C4×C61—24no—
97C23×C4×C61—42no—
98C23×C4×C61—42no—
99C23×C4×C61D414yes—
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C4×D4×C61—232no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61D414yes—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61D414yes—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61—22no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—21no—
121C24×C61—21no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—21no—
125C24×C61—21no—
126C24×C61—21no—
127C24×C61—21no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—22no—
134C24×C61C2×D412yes—
135C24×C61C2×D412yes—
136C24×C61C2×Q812yes—
137C24×C61C2×Q812yes—
138C24×C61#4112yes—
139C24×C61#4112yes—
140C24×C61C2411yescharacteristic
141C2×D4×C61—28no—
142C2×D4×C61—28no—
143C2×D4×C61—28no—
144C2×D4×C61—28no—
145C2×D4×C61—28no—
146C2×D4×C61—28no—
147C2×D4×C61—28no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—28no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—28no—
167C22×C4×C61—28no—
168C22×C4×C61—44no—
169C22×C4×C61—48no—
170C22×C4×C61—48no—
171C22×C4×C61—48no—
172C22×C4×C61—48no—
173C22×C4×C61—44no—
174C22×C4×C61—44no—
175C22×C4×C61C2×D412yes—
176C22×C4×C61C2×D412yes—
177C22×C4×C61C2×D414yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×Q812yes—
184C22×C4×C61#4112yes—
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—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61C2×D414yes—
211C22×Dic61C2×D414yes—
212C22×Dic61#4114yes—
213C2×Dic122—28no—
214C2×Dic122—48no—
215C2×Dic122—48no—
216C2×Dic122—44no—
217C2×Dic122—44no—
218C4⋊C4×C61—28no—
219C22⋊C4×C61—28no—
220C22⋊C4×C61—28no—
221C42×C61—28no—
222C22⋊Dic61—216no—
223C22⋊Dic61—216no—
224C22⋊Dic61—48no—
225C22⋊Dic61—48no—
226C4⋊Dic61—28no—
227#11758196—216no—
228#11758196—48no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—24no—
247C23×C61—24no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—24no—
251C23×C61—24no—
252C23×C61—24no—
253C23×C61—24no—
254C23×C61—24no—
255C23×C61—41no—
256C23×C61—42no—
257C23×C61—41no—
258C23×C61—42no—
259C23×C61—42no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61—42no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61—42no—
273C23×C61C22⋊Q814yes—
274C23×C61C22⋊Q814yescomplemented
275C23×C61C22×D411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61C22×D412yes—
279C23×C61C22×Q811yescharacteristic
280C23×C61C2×#4111yescharacteristic
281C23×C61C2×#4111yescharacteristic
282C23×C61C2×#4111yescharacteristic
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C612−1+412yes—
286D4×C61—232no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—24no—
298C2×C4×C61—24no—
299C2×C4×C61—24no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—416no—
306C2×C4×C61—416no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61#12014yes—
314C2×C4×C61#12014yes—
315C2×C4×C61C22⋊Q814yescomplemented
316C2×Dic61—24no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
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—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344Dic122—416no—
345#14723—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—24no—
348C22×C61—24no—
349C22×C61—24no—
350C22×C61—28no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—44no—
362C22×C61—44no—
363C22×C61—44no—
364C22×C61—44no—
365C22×C61—44no—
366C22×C61—44no—
367C22×C61—44no—
368C22×C61C2×#12011yescharacteristic
369C22×C61C2×#12011yescharacteristic
370C22×C61C2×C22⋊Q811yescharacteristic
371C22×C61C2×C22⋊Q811yescharacteristic
372C22×C61C2×C22⋊Q811yescharacteristic
373C22×C61#52512yes—
374C22×C61#52511yescharacteristic
375C22×C61#52511yescharacteristic
376C22×C61#52511yescharacteristic
377C22×C61#53211yescharacteristic
378C22×C61#53212yes—
379C22×C61#53411yescharacteristic
380C22×C61#53611yescharacteristic
381C22×C61#53912yes—
382C22×C61#54212yes—
383C22×C61D4212yes—
384C22×C61D4212yes—
385C22×C61#54712yes—
386C22×C61#54812yes—
387C22×C61#54812yes—
388C22×C61D4×Q812yes—
389C22×C61#55112yes—
390C22×C61#55412yes—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395C4×C61—42no—
396Dic61—44no—
397Dic61—44no—
398Dic61—44no—
399Dic61—82no—
400C22×C22⋊Q8—611no—
401C22×C4×D4D6111yescharacteristic
402C2×#395—611no—
403C2×#393—611no—
404C2×#385—612no—
405#1441—611no—
406#1439—612no—
407#1439—611no—
408#1438—612no—
409#1436—612no—
410C22⋊#95—611no—
411C2×C61—44no—
412C2×C61—44no—
413C2×C61#238811yescharacteristic
414C2×C61#240311yescharacteristic
415C2×C61#240911yescharacteristic
416C2×C61#243211yescharacteristic
417C2×C61#244912yes—
418C2×C61#245212yes—
419C2×C61#246112yes—
420C2×C61#246312yes—
421C2×C61#256411yescharacteristic
422C2×C61#263811yescharacteristic
423C2×C61#284811yescharacteristic
424C23×Q8—611no—
425C23×D4C2×D6111yescharacteristic
426C24×C4C2×D6111yescharacteristic
427C24×C4C2×D6111yescharacteristic
428C2×C22⋊Q8—1228no—
429C2×C22⋊Q8—1224no—
430C2×C4×D4—24no—
431C2×C4×D4—24no—
432C2×C4×D4—24no—
433C22×C4⋊C4—612no—
434C22×C4⋊C4—611no—
435C22×C4⋊C4—612no—
436C22×C4⋊C4C2×D6111yescharacteristic
437C22×C22⋊C4—612no—
438C22×C22⋊C4—612no—
439C22×C22⋊C4—612no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4C2×D6111yescharacteristic
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C42C2×D6111yescharacteristic
444#395—1224no—
445#393—1224no—
446#385—1228no—
447C2×#95—611no—
448C2×#95—612no—
449C2×#95—611no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—612no—
454C2×#95—612no—
455C61#1472311yescharacteristic, complemented, Sylow
456C25C22×D6111yescharacteristic
457C25C22×D6111yescharacteristic
458C22×Q8—1224no—
459C22×Q8—1222no—
460C22×Q8—1222no—
461C22×Q8—1222no—
462C22×Q8—2442no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4Dic12214yescomplemented
470C23×C4—22no—
471C23×C4—24no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—24no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—612no—
480C23×C4—612no—
481C23×C4—612no—
482C23×C4—612no—
483C23×C4C22⋊D6114yes—
484C23×C4C22×D6111yescharacteristic
485C23×C4C22×D6111yescharacteristic
486C23×C4C22×D6111yescharacteristic
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C22⋊Q8—12232no—
490C4×D4—232no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—618no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1224no—
499C2×C4⋊C4—1224no—
500C2×C4⋊C4—2442no—
501C2×C4⋊C4C22⋊D6114yes—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1224no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
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⋊C4C22⋊D6114yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523#95—1224no—
524#95—1224no—
525#95—1224no—
526#95—1224no—
527#95—1224no—
528#95—1222no—
529#95—1222no—
530#95—1224no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24C2×Dic12212yes—
548C24C2×Dic12212yes—
549C24#1175822212yes—
550C24#1175822212yes—
551C24C2×C22⋊D6112yes—
552C24C2×C22⋊D6112yes—
553C24C23×D6111yescharacteristic
554C2×Q8—1228no—
555C2×Q8—2448no—
556C2×Q8—2448no—
557C2×Q8—2444no—
558C2×Q8—2444no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—614no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4C2×Dic12212yes—
622C22×C4#1175822212yes—
623C22×C4D4×D6114yes—
624C22×C4C2×C22⋊D6112yes—
625C22×C4C2×C22⋊D6112yes—
626C22×C4C2×C22⋊D6112yes—
627C22×C4C2×C22⋊D6112yes—
628C22×C4C2×C22⋊D6112yes—
629C22×C4C2×C22⋊D6112yes—
630C22×C4C2×C22⋊D6112yes—
631C4⋊C4—28no—
632C4⋊C4—1228no—
633C4⋊C4—12216no—
634C4⋊C4—2448no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—12216no—
638C22⋊C4—12216no—
639C22⋊C4—2448no—
640C22⋊C4—2448no—
641C42—28no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23#1451975614yes—
687C23#1451975614yescomplemented
688C23C2×D4×D6112yes—
689C23C22×C22⋊D6111yescharacteristic
690C23C22×C22⋊D6111yescharacteristic
691C23C22×C22⋊D6111yescharacteristic
692C23C22×Dic12211yescharacteristic
693C23#41×D6112yes—
694C23C2×#1175822211yescharacteristic
695C23C2×#1175822211yescharacteristic
696C23C2×#1175822211yescharacteristic
697C23#1451982212yes—
698C23#1451982412yes—
699Q8—24416no—
700D4—232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4#1451974514yes—
756C2×C4#1451974614yes—
757C2×C4#1451975614yescomplemented
758C22—24no—
759C22—24no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22C2×#1451974511yescharacteristic
781C22C2×#1451974611yescharacteristic
782C22C2×#1451975611yescharacteristic
783C22C2×#1451975611yescharacteristic
784C22C2×#1451975611yescharacteristic
785C22#1684027112yes—
786C22#1684027311yescharacteristic
787C22#1684027311yescharacteristic
788C22#1684027311yescharacteristic
789C22#1684030811yescharacteristic
790C22#1684030912yes—
791C22#1684032111yescharacteristic
792C22#1684033311yescharacteristic
793C22#1684035412yes—
794C22#1684037712yes—
795C22D4×C22⋊D6112yes—
796C22D4×C22⋊D6112yes—
797C22#1684041112yes—
798C22#1684041912yes—
799C22#1684042112yes—
800C22D4×Dic12212yes—
801C22#1684044112yes—
802C22#1684047112yes—
803C4—24no—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—4882no—
809C4—2444no—
810C4—2444no—
811C4—2444no—
812C2—44no—
813C2—44no—
814C2#2144903411yescharacteristic
815C2#2144912911yescharacteristic
816C2#2144918411yescharacteristic
817C2#2144944311yescharacteristic
818C2#2144962212yes—
819C2#2144966312yes—
820C2#2144978012yes—
821C2#2144981012yes—
822C2#2145099511yescharacteristic
823C2#2145173611yescharacteristic
824C2#2145410611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC22×C4×D4×C61C2
prime radicalC23×D4×C61C22
hypercenterC22×C4×D4D61
hypocenterC61#14723
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14519756C2semidirect
2. C2×#16839682C2semidirect
3. C2×#16839674C2semidirect
4. C2×#16839635C2semidirect
5. #21444072C2semidirect
6. #21444064C2semidirect
7. #21444062C2semidirect
9. #21444052C2semidirect
10. #21444042C2semidirect
60. C2×#11758196D4semidirect
89. C22×D4×C61Q8semidirect
274. C23×C61C22⋊Q8semidirect
315. C2×C4×C61C22⋊Q8semidirect
455. C61#14723semidirect
469. C22×D4Dic122semidirect
687. C23#14519756semidirect
757. C2×C4#14519756semidirect

Maximal subgroups

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

subgroupindex
C22×#145197562
C2×#168396822
C2×#168396742
C2×#168396352
#214440722
#214440642
#214440622
#214440602
#214440522
#214440422
C22×C4×D4×C612
#1472361