Finite Group Databasebeta

← #14680418

Subgroups — #14680418

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2C2×#10622600C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic, complemented
4#13066870C211yesmaximal, characteristic, complemented
5#13066866C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal
9#13066853C212yesmaximal, complemented
10#13066850C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C2×#66936—24no—
27C2×#66936—24no—
28C2×#66936C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622279—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11C2×C414yes—
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D414yes—
60C22×C4×D11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4C2×C414yes—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C414yes—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4C2×C414yes—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—42no—
88C2×C4⋊Dic11C2×C414yes—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4C2×C414yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—42no—
94C2×C4×Dic11—42no—
95#66936—232no—
96C11×#95—22no—
97C11×#95—24no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14287—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11C22×C412yes—
117C24×C11C2411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11C22×C412yes—
127C23×D11C2×D412yes—
128C23×D11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4114yes—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—44no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—44no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11C22×C412yes—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C2×D412yes—
187C22×Dic11C2×D412yes—
188C22×Dic11#4114yes—
189C2×C4×D11—48no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—48no—
193C2×C4×D11C22⋊C4116yescomplemented
194C11×C4⋊C4—44no—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—48no—
197C22⋊Dic11—28no—
198C22⋊Dic11—48no—
199(C2×D11)⋊C4—216no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—48no—
202C4⋊Dic11—28no—
203C4⋊Dic11—44no—
204Dic11⋊C4—28no—
205C4×Dic11—48no—
206C22×#123—111no—
207C2×#380—111no—
208C2×C4×C22⋊C4—111no—
209#1441—111no—
210#1441—111no—
211#1440—112no—
212#1439—111no—
213#1439D1111yescharacteristic, complemented
214#1438—112no—
215#1437—112no—
216#1436—112no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C23×C411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C22×D411yescharacteristic
243C23×C11C2×#4112yes—
244C23×C11C2×#4112yes—
245C23×C11H(5,𝔽2)12yes—
246C23×C11H(5,𝔽2)11yescharacteristic
247C23×C11H(5,𝔽2)12yes—
248C23×C11H(5,𝔽2)11yescharacteristic
249C23×C112−1+411yescharacteristic
250C23×C112−1+411yescharacteristic
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—24no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11C2×C22⋊C414yes—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—42no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11C2×C22⋊C414yes—
298C22⋊D11—416no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—42no—
312C2×Dic11—41no—
313C2×Dic11—42no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11C2×C22⋊C414yes—
330C4×D11—416no—
331C23×D4—111no—
332C24×C4—111no—
333C2×#123—118no—
334C2×#123—224no—
335C2×#123—224no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4C2×D1111yescharacteristic
340C22×C22⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4C2×D1111yescharacteristic
346C22×C22⋊C4C2×D1112yes—
347C22×C42—112no—
348#380—224no—
349C4×C22⋊C4—224no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—111no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95C2×D1112yes—
358C2×#95C2×D1111yescharacteristic
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—44no—
362C22×C11—44no—
363C22×C11—42no—
364C22×C11—82no—
365C22×C11—82no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11C4×#4112yes—
372C22×C11#51812yes—
373C22×C11#52011yescharacteristic
374C22×C11#52011yescharacteristic
375C22×C11#52512yes—
376C22×C11#53211yescharacteristic
377C22×C11#53211yescharacteristic
378C22×C11#53411yescharacteristic
379C22×C11#53412yes—
380C22×C11#53411yescharacteristic
381C22×C11#53511yescharacteristic
382C22×C11#53611yescharacteristic
383C22×C11#53711yescharacteristic
384C22×C11#53711yescharacteristic
385C22×C11#53812yes—
386C22×C11#53812yes—
387C22×C11#53912yes—
388C22×C11#53912yes—
389C22×C11#54012yes—
390C22×C11#54012yes—
391C22×C11#54212yes—
392C22×C11#54212yes—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C4×C11—24no—
405C4×C11—44no—
406C4×C11—42no—
407C4×C11—82no—
408Dic11—24no—
409Dic11—42no—
410Dic11—42no—
411Dic11—44no—
412Dic11—82no—
413C25—111no—
414C25C22×D1111yescharacteristic
415C22×D4—114no—
416C22×D4—222no—
417C22×D4—222no—
418C22×D4—442no—
419C22×D4—442no—
420C23×C4—111no—
421C23×C4—114no—
422C23×C4—114no—
423C23×C4—114no—
424C23×C4—111no—
425C23×C4—112no—
426C23×C4—111no—
427C23×C4—112no—
428C23×C4—442no—
429C23×C4—442no—
430C23×C4C22×D1112yes—
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1112yes—
433C23×C4C22×D1111yescharacteristic
434#123—2232no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—442no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—114no—
451C2×C22⋊C4—114no—
452C2×C22⋊C4—224no—
453C2×C22⋊C4—222no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4C4×D1114yes—
466C2×C42—224no—
467C2×C42—442no—
468C2×C42—442no—
469#95—22no—
470#95—24no—
471#95—224no—
472#95—224no—
473#95—222no—
474#95—442no—
475#95—442no—
476#95—442no—
477#95—442no—
478C2×C11—82no—
479C2×C11#229711yescharacteristic
480C2×C11#230811yescharacteristic
481C2×C11#231111yescharacteristic
482C2×C11#233512yes—
483C2×C11#233512yes—
484C2×C11#263012yes—
485C2×C11#263012yes—
486C2×C11#266111yescharacteristic
487C2×C11#266111yescharacteristic
488C2×C11#266311yescharacteristic
489C2×C11#266311yescharacteristic
490D11—44no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—21no—
495C24—22no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—22no—
500C24—21no—
501C24—112no—
502C24—112no—
503C24—112no—
504C24—222no—
505C24—221no—
506C24—222no—
507C24—221no—
508C24—222no—
509C24—221no—
510C24—222no—
511C24—221no—
512C24C2×C4×D1112yes—
513C24C23×D1111yescharacteristic
514C2×D4—228no—
515C2×D4—448no—
516C2×D4—444no—
517C2×D4—448no—
518C2×D4—444no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—1116no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—114no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—222no—
553C22×C4—221no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—222no—
558C22×C4—221no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—448no—
571C22×C4—444no—
572C22×C4—448no—
573C22×C4—444no—
574C22×C4C2×C4×D1112yes—
575C22×C4C2×C4×D1112yes—
576C22×C4D4×D1112yes—
577C22×C4D4×D1112yes—
578C22×C4#434114yes—
579C4⋊C4—44no—
580C4⋊C4—228no—
581C4⋊C4—228no—
582C4⋊C4—444no—
583C22⋊C4—28no—
584C22⋊C4—48no—
585C22⋊C4—228no—
586C22⋊C4—2216no—
587C22⋊C4—228no—
588C22⋊C4—448no—
589C22⋊C4—448no—
590C42—448no—
591C11#1428711yescharacteristic, complemented, Sylow
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—42no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—42no—
615C23—114no—
616C23—222no—
617C23—222no—
618C23—222no—
619C23—224no—
620C23—224no—
621C23—222no—
622C23—224no—
623C23—224no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23C22×C4×D1111yescharacteristic
639C23C2×D4×D1111yescharacteristic
640C23C2×D4×D1111yescharacteristic
641C23C2×#434112yes—
642C23#6703711yescharacteristic
643C23#6703712yes—
644C23#6704011yescharacteristic
645C23#41×D1112yes—
646C23#6704211yescharacteristic
647C23#6704212yes—
648C23#6704311yescharacteristic
649D4—4416no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—114no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—224no—
677C2×C4—222no—
678C2×C4—224no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—4416no—
687C2×C4—441no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—442no—
693C2×C4—441no—
694C2×C4—442no—
695C2×C4—441no—
696C2×C4—442no—
697C2×C4—441no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4C22⋊C4×D1114yes—
706C22—44no—
707C22—44no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—82no—
712C22—82no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—224no—
718C22—224no—
719C22—224no—
720C22—444no—
721C22—444no—
722C22—444no—
723C22—444no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22C2×C22⋊C4×D1111yescharacteristic
729C22#1062303511yescharacteristic
730C22#1062305411yescharacteristic
731C22C4×#434112yes—
732C22#1062307612yes—
733C22#1062312011yescharacteristic
734C22#1062312412yes—
735C22#1062313612yes—
736C22#1062313712yes—
737C22#1062313811yescharacteristic
738C22#1062313911yescharacteristic
739C22#1062315012yes—
740C22#1062315911yescharacteristic
741C22#1062316011yescharacteristic
742C22#1062316912yes—
743C22#1062317412yes—
744C22#1062318411yescharacteristic
745C22#1062319412yes—
746C22#1062319612yes—
747C22#1062319911yescharacteristic
748C22#1062320012yes—
749C22#1062323512yes—
750C22#1062324711yescharacteristic
751C4—24no—
752C4—44no—
753C4—42no—
754C4—82no—
755C4—224no—
756C4—444no—
757C4—442no—
758C4—442no—
759C4—882no—
760C2—82no—
761C2—444no—
762C2#1307110311yescharacteristic
763C2#1307119011yescharacteristic
764C2#1307120511yescharacteristic
765C2#1307140112yes—
766C2#1307141312yes—
767C2#1307446012yes—
768C2#1307446412yes—
769C2#1307474711yescharacteristic
770C2#1307475011yescharacteristic
771C2#1307476911yescharacteristic
772C2#1307477211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14287
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622600C2semidirect
3. C2×#10622279C2semidirect
4. #13066870C2semidirect
5. #13066866C2semidirect
6. #13066864C2semidirect
7. #13066861C2semidirect
9. #13066853C2semidirect
10. #13066850C2semidirect
11. C11×#1439C2semidirect
28. C2×#66936C4semidirect
193. C2×C4×D11C22⋊C4semidirect
213. #1439D11semidirect
591. C11#14287semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
C2×#106226002
C2×#106222792
#130668702
#130668662
#130668642
#130668612
#130668552
#130668532
#130668502
C11×#14392
#1428711