Finite Group Databasebeta

← #29602253

Subgroups — #29602253

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839662C212yesmaximal
3C2×#16839631C211yesmaximal, characteristic, complemented
4C2×#16839621C212yesmaximal, complemented
5C2×#16839620C212yesmaximal, complemented
6C2×#16839613C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444047C212yesmaximal, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C2×#14519737—24no—
16C2×#14519737—24no—
17C2×#14519737C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2212yes—
20C22×#11758196C2212yes—
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2212yes—
23C22×C22⋊Dic61C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839662—28no—
30#16839631—24no—
31#16839621—28no—
32#16839620—28no—
33#16839613—24no—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C2×#95×C61C2211yescharacteristic
43C24×D61C2311yescharacteristic
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61C2×C414yes—
49C22×C22⋊D61D414yes—
50C22×C22⋊D61Q814yes—
51C23×Dic61—22no—
52C23×Dic61—22no—
53C23×Dic61—24no—
54C23×Dic61—24no—
55C23×Dic61C2×C414yes—
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—24no—
64C22×C4×D61—24no—
65C22×C4×D61C2×C414yes—
66#14519737—232no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—42no—
69C2×#11758196—22no—
70C2×#11758196—22no—
71C2×#11758196—24no—
72C2×#11758196—24no—
73C2×#11758196—24no—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196—24no—
77C2×#11758196—24no—
78C2×#11758196—24no—
79C2×#11758196C2×C414yes—
80C2×#11758196D418yescomplemented
81C2×C22⋊Dic61—24no—
82C2×C22⋊Dic61—24no—
83C2×C22⋊Dic61—42no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—42no—
91C2×#11758198—42no—
92C2×#11758198C2×C414yes—
93C2×C4×Dic61—24no—
94C2×C4×Dic61—24no—
95C2×C4×Dic61—24no—
96C2×C4×Dic61C2×C414yes—
97C2×C4×Dic61D414yes—
98C2×C4×Dic61D414yes—
99#14519684—22no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103C25×C61C2311yescharacteristic
104C23×C4×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—42no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—42no—
115C2×C22⋊C4×C61C2×C414yes—
116#95×C61—22no—
117#95×C61—24no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61C22×C412yes—
127C24×C61C2×D412yes—
128C24×C61C2×Q812yes—
129C24×C61C2411yescharacteristic
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61C22×C412yes—
139C23×D61C2×D412yes—
140C23×D61C2×Q812yes—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
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×C61—22no—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C2×D414yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
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⋊D61C4⋊C4116yescomplemented
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—28no—
183C22×Dic61—216no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—48no—
192C22×Dic61—44no—
193C22×Dic61—44no—
194C22×Dic61C22×C412yes—
195C22×Dic61C22×C412yes—
196C22×Dic61C22×C412yes—
197C22×Dic61C2×D414yes—
198C22×Dic61C2×D412yes—
199C22×Dic61C2×D412yes—
200C22×Dic61C2×D412yes—
201C22×Dic61C2×D412yes—
202C22×Dic61C2×D412yes—
203C22×Dic61C2×D414yes—
204C22×Dic61C2×Q812yes—
205C22×Dic61#4112yes—
206C22×Dic61#4112yes—
207C22×Dic61#4114yes—
208C2×C4×D61—28no—
209C2×C4×D61—216no—
210C2×C4×D61—48no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C4⋊C4×C61—44no—
214C22⋊C4×C61—28no—
215C22⋊C4×C61—48no—
216C22⋊Dic61—48no—
217#11758198—28no—
218#11758198—48no—
219#11758198—48no—
220C4⋊Dic61—44no—
221#11758196—28no—
222#11758196—216no—
223#11758196—48no—
224#11758196—48no—
225C4×Dic61—48no—
226C4×Dic61C22⋊C4116yescomplemented
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—24no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—42no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61C2×C4⋊C414yes—
250C23×C61C23×C411yescharacteristic
251C23×C61C22×D411yescharacteristic
252C23×C61C22×D411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D412yes—
255C23×C61C22×Q811yescharacteristic
256C23×C61C2×#4111yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4112yes—
259C23×C61H(5,𝔽2)12yes—
260C23×C612−1+412yes—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61C2×C4⋊C414yes—
284C2×C4×C61—24no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—24no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61C2×C22⋊C414yes—
308C22⋊D61—232no—
309C2×Dic61—22no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—416no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61C2×C22⋊C414yes—
330C2×Dic61C2×C22⋊C414yes—
331C2×Dic61C2×C4⋊C414yes—
332C2×Dic61#11714yes—
333C2×Dic61C4×D418yes—
334C2×Dic61#12114yes—
335C2×Dic61#12114yes—
336C2×Dic61#12118yes—
337C2×Dic61C22⋊Q814yes—
338C2×Dic61C22⋊Q814yes—
339C2×Dic61#12414yes—
340C2×Dic61#12714yes—
341C4×D61—416no—
342#13906—611nomaximal, Sylow
343C22×C61—28no—
344C22×C61—24no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—44no—
348C22×C61—44no—
349C22×C61—44no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61C22×C22⋊C411yescharacteristic
355C22×C61C22×C4⋊C411yescharacteristic
356C22×C61C2×#11711yescharacteristic
357C22×C61C2×C4×D412yes—
358C22×C61#52012yes—
359C22×C61C2×#12111yescharacteristic
360C22×C61C2×#12111yescharacteristic
361C22×C61C2×#12112yes—
362C22×C61C2×C22⋊Q811yescharacteristic
363C22×C61C2×C22⋊Q811yescharacteristic
364C22×C61C2×#12411yescharacteristic
365C22×C61C2×#12711yescharacteristic
366C22×C61#53511yescharacteristic
367C22×C61#53611yescharacteristic
368C22×C61#53712yes—
369C22×C61D4212yes—
370C22×C61#54712yes—
371C22×C61#54712yes—
372C22×C61D4×Q812yes—
373C22×C61#55012yes—
374C22×C61#55412yes—
375C22×C61#55512yes—
376C22×C61#55612yes—
377C2×D61—28no—
378C2×D61—24no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C4×C61—24no—
389C4×C61—44no—
390C4×C61—42no—
391C4×C61—82no—
392Dic61—44no—
393Dic61—42no—
394Dic61—82no—
395Dic61#38018yescomplemented
396Dic61#39018yescomplemented
397C22×C4×D4—611no—
398C2×#390—612no—
399C2×#384—611no—
400C2×#380—612no—
401C2×#380—612no—
402C2×C4×C4⋊C4—611no—
403#1439—611no—
404#1439—611no—
405#1439—611no—
406#1439D6111yescharacteristic, complemented
407C4⋊#95—612no—
408C2×C61—44no—
409C2×C61C2×#38011yescharacteristic
410C2×C61C2×#39011yescharacteristic
411C2×C61#231111yescharacteristic
412C2×C61D4×C4⋊C412yes—
413C2×C61#235412yes—
414C2×C61#253712yes—
415C2×C61#253812yes—
416C2×C61#254111yescharacteristic
417C2×C61#254211yescharacteristic
418C2×C61#254711yescharacteristic
419C2×C61#256311yescharacteristic
420D61—44no—
421C23×D4—611no—
422C24×C4—611no—
423C24×C4—611no—
424C2×C4×D4—618no—
425C2×C4×D4—1224no—
426C2×C4×D4—1224no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—612no—
429C22×C4⋊C4—612no—
430C22×C4⋊C4—612no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4C2×D6111yescharacteristic
433C22×C22⋊C4—611no—
434C22×C22⋊C4—612no—
435C22×C22⋊C4—612no—
436C22×C22⋊C4—612no—
437C22×C22⋊C4C2×D6112yes—
438C22×C22⋊C4C2×D6111yescharacteristic
439C22×C42—611no—
440C22×C42—612no—
441#390—1228no—
442#384—1224no—
443#380—1228no—
444#380—1228no—
445C4×C4⋊C4—1224no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—611no—
450C2×#95C2×D6112yes—
451C2×#95C2×D6111yescharacteristic
452C61#1390611yescharacteristic, complemented, Sylow
453C25—611no—
454C25C22×D6111yescharacteristic
455C22×D4—614no—
456C22×D4—614no—
457C22×D4—614no—
458C22×D4—1222no—
459C22×D4—1222no—
460C22×D4—1222no—
461C22×D4—1222no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—614no—
465C23×C4—612no—
466C23×C4—611no—
467C23×C4—614no—
468C23×C4—612no—
469C23×C4—1222no—
470C23×C4—1222no—
471C23×C4—1224no—
472C23×C4—1224no—
473C23×C4—1222no—
474C23×C4—1222no—
475C23×C4—1224no—
476C23×C4—1224no—
477C23×C4C22×D6112yes—
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6112yes—
480C23×C4C22×D6111yescharacteristic
481C4×D4—12232no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—618no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1224no—
489C2×C4⋊C4—1224no—
490C2×C4⋊C4—1224no—
491C2×C4⋊C4—1224no—
492C2×C4⋊C4—1224no—
493C2×C4⋊C4—1224no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4—2442no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—614no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1224no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—2442no—
513C2×C22⋊C4—2442no—
514C2×C22⋊C4—2442no—
515C2×C22⋊C4C4×D6114yes—
516C2×C42—614no—
517C2×C42—614no—
518C2×C42—614no—
519C2×C42—1224no—
520C2×C42—1224no—
521C2×C42—1224no—
522#95—22no—
523#95—24no—
524#95—1224no—
525#95—1224no—
526#95—1222no—
527#95—1224no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—612no—
537C24—612no—
538C24—612no—
539C24—1222no—
540C24—1221no—
541C24—1221no—
542C24—1222no—
543C24—1221no—
544C24—1221no—
545C24—1222no—
546C24—1222no—
547C24C2×C4×D6112yes—
548C24D4×D6112yes—
549C24Q8×D6112yes—
550C24C23×D6111yescharacteristic
551C2×D4—6116no—
552C2×D4—1228no—
553C2×D4—1228no—
554C2×D4—1228no—
555C2×D4—1228no—
556C2×D4—1228no—
557C2×D4—1228no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—614no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—614no—
589C22×C4—612no—
590C22×C4—614no—
591C22×C4—1228no—
592C22×C4—12216no—
593C22×C4—1228no—
594C22×C4—12216no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1221no—
599C22×C4—1221no—
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—2448no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4—2448no—
616C22×C4—2444no—
617C22×C4—2444no—
618C22×C4C2×C4×D6112yes—
619C22×C4C2×C4×D6112yes—
620C22×C4D4×D6114yes—
621C22×C4D4×D6112yes—
622C22×C4D4×D6112yes—
623C4⋊C4—44no—
624C4⋊C4—12216no—
625C4⋊C4—1228no—
626C4⋊C4—2444no—
627C4⋊C4—2448no—
628C4⋊C4—2448no—
629C22⋊C4—28no—
630C22⋊C4—48no—
631C22⋊C4—1228no—
632C22⋊C4—2448no—
633C22⋊C4—2448no—
634C22⋊C4—2448no—
635C42—6116no—
636C42—2448no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—614no—
660C23—1222no—
661C23—1224no—
662C23—1222no—
663C23—1224no—
664C23—1224no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1224no—
670C23—1224no—
671C23—1224no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23C4⋊C4×D6114yes—
683C23C22×C4×D6111yescharacteristic
684C23C2×D4×D6111yescharacteristic
685C23C2×D4×D6111yescharacteristic
686C23C2×D4×D6111yescharacteristic
687C23C2×D4×D6112yes—
688C23C2×Q8×D6111yescharacteristic
689C23#41×D6112yes—
690C23#41×D6111yescharacteristic
691C23#41×D6111yescharacteristic
692C23#1451982212yes—
693C23#1451982412yes—
694D4—12232no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—614no—
719C2×C4—614no—
720C2×C4—614no—
721C2×C4—614no—
722C2×C4—618no—
723C2×C4—614no—
724C2×C4—618no—
725C2×C4—614no—
726C2×C4—614no—
727C2×C4—614no—
728C2×C4—614no—
729C2×C4—614no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—24416no—
736C2×C4—24416no—
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—2441no—
748C2×C4—2441no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4C22⋊C4×D6114yes—
752C22—28no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—1228no—
764C22—1224no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2444no—
769C22—2442no—
770C22—2442no—
771C22—2444no—
772C22—2442no—
773C22—2444no—
774C22C2×C22⋊C4×D6111yescharacteristic
775C22C2×C4⋊C4×D6111yescharacteristic
776C22#117×D6111yescharacteristic
777C22C4×D4×D6112yes—
778C22#1684024112yes—
779C22#121×D6111yescharacteristic
780C22#121×D6112yes—
781C22#121×D6111yescharacteristic
782C22C22⋊Q8×D6111yescharacteristic
783C22C22⋊Q8×D6111yescharacteristic
784C22#124×D6111yescharacteristic
785C22#127×D6111yescharacteristic
786C22#1684032711yescharacteristic
787C22#1684033411yescharacteristic
788C22#1684033912yes—
789C22#1684039412yes—
790C22#1684041012yes—
791C22#1684041012yes—
792C22#1684042512yes—
793C22#1684043012yes—
794C22#1684046612yes—
795C22#1684047412yes—
796C22#1684047912yes—
797C4—24no—
798C4—42no—
799C4—44no—
800C4—82no—
801C4—618no—
802C4—618no—
803C4—4882no—
804C4—2442no—
805C4—2444no—
806C2—44no—
807C2—2444no—
808C2#380×D6111yescharacteristic
809C2#390×D6111yescharacteristic
810C2#2144840611yescharacteristic
811C2#2144871712yes—
812C2#2144876512yes—
813C2#2145073112yes—
814C2#2145073612yes—
815C2#2145076011yescharacteristic
816C2#2145076711yescharacteristic
817C2#2145081011yescharacteristic
818C2#2145098711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#13906
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#16839631C2semidirect
4. C2×#16839621C2semidirect
5. C2×#16839620C2semidirect
6. C2×#16839613C2semidirect
7. #21444065C2semidirect
8. #21444064C2semidirect
9. #21444061C2semidirect
10. #21444047C2semidirect
11. C61×#1439C2semidirect
17. C2×#14519737C4semidirect
80. C2×#11758196D4semidirect
171. C2×C22⋊D61C4⋊C4semidirect
226. C4×Dic61C22⋊C4semidirect
395. Dic61#380semidirect
396. Dic61#390semidirect
406. #1439D61semidirect
452. C61#13906semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396622
C2×#168396312
C2×#168396212
C2×#168396202
C2×#168396132
#214440652
#214440642
#214440612
#214440472
C61×#14392
#1390661