Finite Group Databasebeta

← #29608149

Subgroups — #29608149

Order 15616.

2602 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519751C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal, complemented
3C2×#16839638C212yesmaximal, complemented
4#21444086C212yesmaximal, complemented
5#21444067C212yesmaximal, complemented
6#21444058C212yesmaximal, complemented
7#21444042C211yesmaximal, characteristic, complemented
8#21444040C212yesmaximal, complemented
9C61×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C23×C22⋊D61C2212yes—
12C23×C4×D61C2212yes—
13C2×#14519751—28no—
14C2×#14519751C418yescomplemented
15C22×C4⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21#16839640—28no—
22#16839638—28no—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C24×C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C24×D61C2312yes—
36C22×D244—41no—
37C22×D244—42no—
38C22×D244—41no—
39C22×D244C2×C414yes—
40C22×D244D418yes—
41C22×C22⋊D61—24no—
42C22×C22⋊D61—24no—
43C22×C22⋊D61—24no—
44C22×C22⋊D61—24no—
45C22×C22⋊D61—42no—
46C22×C22⋊D61—42no—
47C22×C22⋊D61C2×C418yescomplemented
48C23×Dic61C2312yes—
49C23×Dic61C2312yes—
50C23×Dic61C2312yes—
51C22×C4×D61—24no—
52C22×C4×D61—24no—
53C22×C4×D61—24no—
54C22×C4×D61—42no—
55C22×C4×D61—42no—
56C22×C4×D61—42no—
57C22×C4×D61—42no—
58#14519751—232no—
59C2×C4⋊Dic61—24no—
60C2×C4⋊Dic61C2×C414yescomplemented
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—42no—
64C2×#11758198—24no—
65C2×#11758198—24no—
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198C2×C418yescomplemented
76#14519684—24no—
77#14519684—24no—
78#14519684—24no—
79#14519684—41no—
80#14519684—42no—
81#14519684—42no—
82#14519684—41no—
83C25×C61C2311yescharacteristic
84C23×C4×C61—24no—
85C23×C4×C61—42no—
86C23×C4×C61—41no—
87C23×C4×C61—41no—
88C23×C4×C61C2×C414yescomplemented
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2312yes—
92C23×C4×C61C2311yescharacteristic
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—41no—
95C2×C22⋊C4×C61—41no—
96C2×C22⋊C4×C61—41no—
97C2×C22⋊C4×C61—41no—
98C2×C22⋊C4×C61D414yescomplemented
99#95×C61—24no—
100#95×C61—42no—
101C24×C61—22no—
102C24×C61—22no—
103C24×C61—22no—
104C24×C61—21no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—21no—
109C24×C61C22×C412yes—
110C24×C61C2×D412yes—
111C24×C61#4112yes—
112C24×C61C2411yescharacteristic
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61C22×C414yes—
126C23×D61C2×D414yes—
127C23×D61C2×D414yes—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—28no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—44no—
150C22×C4×C61—44no—
151C22×C4×C61—48no—
152C22×C4×C61—48no—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C2×D414yes—
156C22×C4×C61C2×D414yes—
157C2×C22⋊D61—216no—
158C2×C22⋊D61—216no—
159C2×C22⋊D61—48no—
160C2×C22⋊D61—48no—
161C2×C22⋊D61—48no—
162C2×C22⋊D61—48no—
163C2×C22⋊D61—48no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61C22×C414yes—
184C22×Dic61#4114yes—
185C2×D244—44no—
186C2×D244—44no—
187C2×D244—48no—
188C2×D244—48no—
189C2×D244C22⋊C4116yescomplemented
190C2×C4×D61—48no—
191C2×C4×D61—48no—
192C2×C4×D61—48no—
193C2×C4×D61—48no—
194C2×C4×D61—48no—
195C2×C4×D61—48no—
196C2×C4×D61—48no—
197C22⋊C4×C61—44no—
198C22⋊C4×C61—44no—
199C22⋊Dic61—48no—
200#11758198—216no—
201#11758198—48no—
202#11758198—48no—
203#11758198—48no—
204C4⋊Dic61—28no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61C4×D414yes—
228C23×C61C23×C411yescharacteristic
229C23×C61C22×D412yes—
230C23×C61C22×D411yescharacteristic
231C23×C61C2×#4111yescharacteristic
232C23×C61C2×#4112yes—
233C23×C61H(5,𝔽2)11yescharacteristic
234C23×C61H(5,𝔽2)11yescharacteristic
235C23×C61H(5,𝔽2)12yes—
236C23×C61H(5,𝔽2)12yes—
237C23×C61H(5,𝔽2)11yescharacteristic
238C23×C612−1+411yescharacteristic
239C22×D61—24no—
240C22×D61—24no—
241C22×D61—24no—
242C22×D61—24no—
243C22×D61—24no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61C2×C22⋊C418yes—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—416no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61C2×C22⋊C414yes—
299C22⋊D61—432no—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321D244—416no—
322C4×D61—432no—
323#14417—611nomaximal, Sylow
324C22×C61—24no—
325C22×C61—24no—
326C22×C61—24no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61C22×C22⋊C411yescharacteristic
336C22×C61C2×C4×D411yescharacteristic
337C22×C61C4×#4111yescharacteristic
338C22×C61#51811yescharacteristic
339C22×C61#51811yescharacteristic
340C22×C61#51811yescharacteristic
341C22×C61#52011yescharacteristic
342C22×C61#53412yes—
343C22×C61#53412yes—
344C22×C61#53411yescharacteristic
345C22×C61#53711yescharacteristic
346C22×C61#53812yes—
347C22×C61#53811yescharacteristic
348C22×C61#53911yescharacteristic
349C22×C61#54012yes—
350C22×C61D4212yes—
351C22×C61#54612yes—
352C22×C61#54612yes—
353C22×C61#54612yes—
354C22×C61#54712yes—
355C22×C61#55312yes—
356C22×C61#56012yes—
357C22×C61#56212yes—
358C2×D61—28no—
359C2×D61—28no—
360C2×D61—28no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61—44no—
373C4×C61—24no—
374C4×C61—42no—
375C4×C61—44no—
376C4×C61—82no—
377Dic61—44no—
378Dic61—44no—
379Dic61—82no—
380C22×#121—611no—
381C2×#386—612no—
382C2×#386—612no—
383#1445—612no—
384#1440—612no—
385#1438—612no—
386C22⋊#95—612no—
387C22⋊#95—611no—
388C22⋊#95D6111yescharacteristic, complemented
389C2×C61—44no—
390C2×C61#230811yescharacteristic
391C2×C61#232511yescharacteristic
392C2×C61#233311yescharacteristic
393C2×C61D4×C22⋊C411yescharacteristic
394C2×C61#233911yescharacteristic
395C2×C61#236411yescharacteristic
396C2×C61#237711yescharacteristic
397C2×C61#266812yes—
398C2×C61#267112yes—
399C2×C61#268812yes—
400C2×C61#270812yes—
401D61—48no—
402C23×D4—612no—
403C23×D4—611no—
404C24×C4—612no—
405C24×C4C2×D6111yescharacteristic
406C2×#121—618no—
407C2×#121—1228no—
408C22×C4⋊C4—611no—
409C22×C22⋊C4—612no—
410C22×C22⋊C4—612no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4—612no—
413C22×C22⋊C4—612no—
414C22×C22⋊C4C2×D6111yescharacteristic
415C22×C22⋊C4C2×D6111yescharacteristic
416#386—1228no—
417#386—1228no—
418C2×#95—612no—
419C2×#95—612no—
420C2×#95—612no—
421C2×#95—611no—
422C2×#95—612no—
423C2×#95—611no—
424C2×#95—612no—
425C2×#95C2×D6112yes—
426C2×#95C2×D6112yes—
427C61#1441711yescharacteristic, complemented, Sylow
428C25—612no—
429C25C22×D6111yescharacteristic
430C22×D4—618no—
431C22×D4—614no—
432C22×D4—618no—
433C22×D4—1224no—
434C22×D4—1224no—
435C22×D4—1224no—
436C22×D4—1224no—
437C22×D4—2441no—
438C22×D4—2442no—
439C22×D4—2441no—
440C22×D4—2442no—
441C22×D4—2442no—
442C23×C4—24no—
443C23×C4—42no—
444C23×C4—41no—
445C23×C4—41no—
446C23×C4—612no—
447C23×C4—612no—
448C23×C4—612no—
449C23×C4—1224no—
450C23×C4—1224no—
451C23×C4—1224no—
452C23×C4—2442no—
453C23×C4—2442no—
454C23×C4—2442no—
455C23×C4—2442no—
456C23×C4C4×D6114yescomplemented
457C23×C4C22×D6112yes—
458C23×C4C22×D6111yescharacteristic
459C23×C4C22×D6112yes—
460C23×C4C22×D6111yescharacteristic
461#121—12232no—
462C2×C4⋊C4—614no—
463C2×C4⋊C4—1224no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—41no—
466C2×C22⋊C4—41no—
467C2×C22⋊C4—41no—
468C2×C22⋊C4—41no—
469C2×C22⋊C4—618no—
470C2×C22⋊C4—1224no—
471C2×C22⋊C4—1224no—
472C2×C22⋊C4—1224no—
473C2×C22⋊C4—1224no—
474C2×C22⋊C4—1224no—
475C2×C22⋊C4—1224no—
476C2×C22⋊C4—1224no—
477C2×C22⋊C4—1224no—
478C2×C22⋊C4—1224no—
479C2×C22⋊C4—2442no—
480C2×C22⋊C4—2442no—
481C2×C22⋊C4—2442no—
482C2×C22⋊C4—2442no—
483C2×C22⋊C4—2442no—
484C2×C22⋊C4D24414yescomplemented
485#95—24no—
486#95—42no—
487#95—1224no—
488#95—1224no—
489#95—1224no—
490#95—2441no—
491#95—2441no—
492#95—2442no—
493#95—2442no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—614no—
503C24—614no—
504C24—614no—
505C24—1222no—
506C24—1222no—
507C24—1222no—
508C24—1222no—
509C24—1222no—
510C24—1222no—
511C24—1222no—
512C24—1222no—
513C24—1222no—
514C24—1222no—
515C24—1222no—
516C24—1222no—
517C24C2×C4×D6112yes—
518C24C2×D24412yes—
519C24#1175822212yes—
520C24C23×D6111yescharacteristic
521C2×D4—6116no—
522C2×D4—12216no—
523C2×D4—12216no—
524C2×D4—2444no—
525C2×D4—2444no—
526C2×D4—2448no—
527C2×D4—2448no—
528C2×D4—2448no—
529C2×D4—2448no—
530C2×D4—2448no—
531C2×D4—2448no—
532C2×D4—2448no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—614no—
559C22×C4—614no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—2448no—
580C22×C4—2448no—
581C22×C4—2448no—
582C22×C4—2448no—
583C22×C4—2448no—
584C22×C4—2448no—
585C22×C4—2448no—
586C22×C4C2×C4×D6112yes—
587C22×C4C2×C4×D6112yes—
588C22×C4C2×D24414yes—
589C22×C4D4×D6114yes—
590C4⋊C4—1228no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—12216no—
594C22⋊C4—2448no—
595C22⋊C4—2448no—
596C22⋊C4—2448no—
597C22⋊C4—2448no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—618no—
621C23—1224no—
622C23—1224no—
623C23—1224no—
624C23—1224no—
625C23—1224no—
626C23—1224no—
627C23—1224no—
628C23—1224no—
629C23—1224no—
630C23—1224no—
631C23—1224no—
632C23—1224no—
633C23—1224no—
634C23—1224no—
635C23—1224no—
636C23—1224no—
637C23—1224no—
638C23—1224no—
639C23—2442no—
640C23—2442no—
641C23—2442no—
642C23—2442no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23C4×D24414yes—
656C23C22×C4×D6111yescharacteristic
657C23C2×D4×D6112yes—
658C23C22×D24411yescharacteristic
659C23#41×D6112yes—
660C23C2×#1175822211yescharacteristic
661C23#1451982212yes—
662C23#1451982211yescharacteristic
663C23#1451982211yescharacteristic
664C23#1451982211yescharacteristic
665C23#1451982312yes—
666C23#1451982511yescharacteristic
667D4—24416no—
668D4—24432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—416no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—1224no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1224no—
699C2×C4—24432no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4C22⋊C4×D6114yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—1228no—
728C22—1228no—
729C22—1228no—
730C22—2444no—
731C22—2444no—
732C22—2444no—
733C22—2444no—
734C22—2444no—
735C22—2444no—
736C22—2444no—
737C22—2444no—
738C22—2444no—
739C22—2444no—
740C22—2444no—
741C22—2444no—
742C22C2×C22⋊C4×D6111yescharacteristic
743C22C2×C4×D24411yescharacteristic
744C22#1684023011yescharacteristic
745C22#1684023511yescharacteristic
746C22#1684023511yescharacteristic
747C22#1684023611yescharacteristic
748C22#1684024311yescharacteristic
749C22#1684032212yes—
750C22#1684032212yes—
751C22#1684032411yescharacteristic
752C22#1684034311yescharacteristic
753C22#1684034812yes—
754C22#1684035011yescharacteristic
755C22#1684035911yescharacteristic
756C22#1684036412yes—
757C22D4×D24412yes—
758C22#1684040712yes—
759C22#1684040812yes—
760C22#1684040912yes—
761C22#1684041412yes—
762C22#1684046112yes—
763C22#1684050012yes—
764C22#1684050812yes—
765C4—24no—
766C4—42no—
767C4—44no—
768C4—82no—
769C4—4882no—
770C4—2444no—
771C4—2444no—
772C2—44no—
773C2—2448no—
774C2#2144839511yescharacteristic
775C2#2144852211yescharacteristic
776C2#2144858111yescharacteristic
777C2C22⋊C4×D24411yescharacteristic
778C2#2144864711yescharacteristic
779C2#2144886911yescharacteristic
780C2#2144897311yescharacteristic
781C2#2145202512yes—
782C2#2145205812yes—
783C2#2145225612yes—
784C2#2145254012yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC22×#14519751C2
hypercenterC22⋊#95D61
hypocenterC61#14417
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16839640C2semidirect
3. C2×#16839638C2semidirect
4. #21444086C2semidirect
5. #21444067C2semidirect
6. #21444058C2semidirect
7. #21444042C2semidirect
8. #21444040C2semidirect
9. C61×C22⋊#95C2semidirect
14. C2×#14519751C4semidirect
47. C22×C22⋊D61C2×C4semidirect
60. C2×C4⋊Dic61C2×C4semidirect
75. C2×#11758198C2×C4semidirect
88. C23×C4×C61C2×C4semidirect
98. C2×C22⋊C4×C61D4semidirect
189. C2×D244C22⋊C4semidirect
388. C22⋊#95D61semidirect
427. C61#14417semidirect
456. C23×C4C4×D61semidirect
484. C2×C22⋊C4D244semidirect

Maximal subgroups

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

subgroupindex
C22×#145197512
C2×#168396402
C2×#168396382
#214440862
#214440672
#214440582
#214440422
#214440402
C61×C22⋊#952
#1441761