Finite Group Databasebeta

← #14680423

Subgroups — #14680423

Order 2816.

1934 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×#66938C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066886C212yesmaximal, complemented
5#13066862C211yesmaximal, characteristic, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal
9#13066853C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C2×#66938—24no—
27C2×#66938—24no—
28C2×#66938C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4⋊C4×Dic11—24no—
39#10622264—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×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—42no—
59C22×Dic22—42no—
60C22×Dic22C2×C414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—24no—
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—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—24no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11—42no—
91C2×C4×Dic11—42no—
92C2×C4×Dic11C2×C414yes—
93C2×C4×Dic11D414yes—
94C2×C4×Dic11D414yes—
95#66938—232no—
96C11×#95—22no—
97C11×#95—42no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14288—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—21no—
119C23×D11—21no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11C22×C412yes—
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—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11C22×C412yes—
182C22×Dic11C22×C412yes—
183C22×Dic11C22×C412yes—
184C22×Dic11C2×D412yes—
185C22×Dic11C2×D412yes—
186C22×Dic11C2×D412yes—
187C22×Dic11C2×D412yes—
188C22×Dic11#4114yes—
189C2×Dic22—28no—
190C2×Dic22—48no—
191C2×Dic22—44no—
192C2×Dic22—48no—
193C2×Dic22—44no—
194C11×C4⋊C4—28no—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—48no—
197C22⋊Dic11—28no—
198C22⋊Dic11—48no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—48no—
202(C2×D11)⋊C4—48no—
203C4⋊Dic11—28no—
204C4×Dic11—48no—
205C4×Dic11C22⋊C4116yescomplemented
206C22×#124—111no—
207C2×#383—111no—
208C2×C4×C4⋊C4—111no—
209#1446—112no—
210#1439—111no—
211#1439—111no—
212#1439—111no—
213#1439D1111yescharacteristic, complemented
214#1438—112no—
215#1437—112no—
216#1437—112no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—42no—
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—22no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—42no—
259C22×D11—41no—
260C22×D11—42no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
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—42no—
286C2×C4×C11—41no—
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—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—42no—
315C2×Dic11—41no—
316C2×Dic11—42no—
317C2×Dic11—41no—
318C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
329C2×Dic11C2×C22⋊C414yes—
330Dic22—416no—
331C23×Q8—111no—
332C23×D4—111no—
333C2×#124—118no—
334C2×#124—224no—
335C2×#124—224no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4C2×D1111yescharacteristic
338C22×C22⋊C4—111no—
339C22×C22⋊C4—111no—
340C22×C22⋊C4—111no—
341C22×C22⋊C4—112no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4C2×D1111yescharacteristic
345C22×C22⋊C4C2×D1112yes—
346C22×C42—111no—
347C22×C42—112no—
348#383—224no—
349C4×C4⋊C4—224no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—111no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95C2×D1111yescharacteristic
358C2×#95C2×D1112yes—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—44no—
362C22×C11—44no—
363C22×C11—42no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—82no—
369C22×C11—82no—
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11C4×#4112yes—
372C22×C11#51812yes—
373C22×C11#52011yescharacteristic
374C22×C11#52011yescharacteristic
375C22×C11#52511yescharacteristic
376C22×C11#52511yescharacteristic
377C22×C11#53212yes—
378C22×C11#53511yescharacteristic
379C22×C11#53512yes—
380C22×C11#53511yescharacteristic
381C22×C11#53511yescharacteristic
382C22×C11#53611yescharacteristic
383C22×C11#53711yescharacteristic
384C22×C11#53711yescharacteristic
385C22×C11#53812yes—
386C22×C11#53812yes—
387C22×C11#53812yes—
388C22×C11#53812yes—
389C22×C11#54212yes—
390C22×C11#54212yes—
391C22×C11#54212yes—
392C22×C11#54212yes—
393C2×D11—42no—
394C2×D11—42no—
395C2×D11—44no—
396C2×D11—44no—
397C2×D11—42no—
398C2×D11—81no—
399C2×D11—81no—
400C2×D11—81no—
401C2×D11—81no—
402C2×D11—82no—
403C2×D11—82no—
404C4×C11—24no—
405C4×C11—42no—
406C4×C11—44no—
407C4×C11—82no—
408Dic11—24no—
409Dic11—24no—
410Dic11—42no—
411Dic11—44no—
412Dic11—82no—
413C25—111no—
414C25C22×D1111yescharacteristic
415C22×Q8—114no—
416C22×Q8—222no—
417C22×Q8—222no—
418C22×Q8—442no—
419C22×Q8—442no—
420C22×D4—114no—
421C22×D4—222no—
422C22×D4—222no—
423C22×D4—442no—
424C22×D4—442no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4—112no—
428C23×C4—111no—
429C23×C4—112no—
430C23×C4C22×D1112yes—
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1112yes—
433C23×C4C22×D1111yescharacteristic
434#124—2232no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4—222no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—114no—
445C2×C22⋊C4—114no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—224no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—442no—
457C2×C22⋊C4—442no—
458C2×C22⋊C4—442no—
459C2×C22⋊C4—442no—
460C2×C22⋊C4—442no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4C4×D1114yes—
463C2×C42—114no—
464C2×C42—114no—
465C2×C42—114no—
466C2×C42—224no—
467C2×C42—442no—
468C2×C42—442no—
469#95—22no—
470#95—42no—
471#95—224no—
472#95—224no—
473#95—224no—
474#95—222no—
475#95—442no—
476#95—442no—
477#95—442no—
478C2×C11—82no—
479C2×C11#229711yescharacteristic
480C2×C11#230911yescharacteristic
481C2×C11#231111yescharacteristic
482C2×C11#233712yes—
483C2×C11#233712yes—
484C2×C11#263111yescharacteristic
485C2×C11#263111yescharacteristic
486C2×C11#263211yescharacteristic
487C2×C11#263211yescharacteristic
488C2×C11#266212yes—
489C2×C11#266212yes—
490D11—82no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—21no—
495C24—22no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—22no—
500C24—21no—
501C24—112no—
502C24—221no—
503C24—221no—
504C24—222no—
505C24—221no—
506C24—222no—
507C24—221no—
508C24—222no—
509C24—221no—
510C24—222no—
511C24—221no—
512C24C2×C4×D1112yes—
513C24C23×D1111yescharacteristic
514C2×Q8—228no—
515C2×Q8—448no—
516C2×Q8—444no—
517C2×Q8—448no—
518C2×Q8—444no—
519C2×D4—228no—
520C2×D4—448no—
521C2×D4—444no—
522C2×D4—448no—
523C2×D4—444no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
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—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—112no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—114no—
551C22×C4—221no—
552C22×C4—222no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—222no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4C2×C4×D1112yes—
575C22×C4C2×C4×D1112yes—
576C22×C4D4×D1112yes—
577C22×C4D4×D1112yes—
578C22×C4#434114yes—
579C4⋊C4—28no—
580C4⋊C4—228no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—228no—
584C22⋊C4—228no—
585C22⋊C4—228no—
586C22⋊C4—448no—
587C22⋊C4—448no—
588C22⋊C4—448no—
589C42—1116no—
590C42—448no—
591C11#1428811yescharacteristic, 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—222no—
616C23—222no—
617C23—222no—
618C23—224no—
619C23—224no—
620C23—442no—
621C23—441no—
622C23—441no—
623C23—442no—
624C23—442no—
625C23—442no—
626C23—441no—
627C23—441no—
628C23—442no—
629C23—441no—
630C23—441no—
631C23—442no—
632C23—442no—
633C23—441no—
634C23—442no—
635C23—442no—
636C23—441no—
637C23—442no—
638C23C22×C4×D1111yescharacteristic
639C23C2×D4×D1111yescharacteristic
640C23C2×D4×D1111yescharacteristic
641C23C2×#434112yes—
642C23#6703712yes—
643C23#6703711yescharacteristic
644C23#6704011yescharacteristic
645C23#41×D1112yes—
646C23#6704211yescharacteristic
647C23#6704212yes—
648C23#6704311yescharacteristic
649Q8—4416no—
650D4—4416no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—114no—
675C2×C4—114no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—224no—
680C2×C4—222no—
681C2×C4—224no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—224no—
687C2×C4—222no—
688C2×C4—224no—
689C2×C4—224no—
690C2×C4—224no—
691C2×C4—442no—
692C2×C4—441no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—441no—
697C2×C4—442no—
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—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—82no—
716C22—82no—
717C22—444no—
718C22—444no—
719C22—442no—
720C22—442no—
721C22—442no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22—882no—
727C22—882no—
728C22C2×C22⋊C4×D1111yescharacteristic
729C22#1062303511yescharacteristic
730C22#1062305411yescharacteristic
731C22C4×#434112yes—
732C22#1062307612yes—
733C22#1062311711yescharacteristic
734C22#1062312412yes—
735C22#1062312712yes—
736C22#1062313811yescharacteristic
737C22#1062313812yes—
738C22#1062313911yescharacteristic
739C22#1062314812yes—
740C22#1062315911yescharacteristic
741C22#1062316011yescharacteristic
742C22#1062317112yes—
743C22#1062317412yes—
744C22#1062318711yescharacteristic
745C22#1062318812yes—
746C22#1062319312yes—
747C22#1062320511yescharacteristic
748C22#1062321312yes—
749C22#1062323512yes—
750C22#1062324611yescharacteristic
751C4—24no—
752C4—44no—
753C4—42no—
754C4—82no—
755C4—224no—
756C4—224no—
757C4—444no—
758C4—442no—
759C4—882no—
760C2—82no—
761C2—882no—
762C2#1307110111yescharacteristic
763C2#1307119511yescharacteristic
764C2#1307120511yescharacteristic
765C2#1307142312yes—
766C2#1307143012yes—
767C2#1307446711yescharacteristic
768C2#1307447011yescharacteristic
769C2#1307447511yescharacteristic
770C2#1307447811yescharacteristic
771C2#1307475212yes—
772C2#1307475412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14288
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622264C2semidirect
3. C2×C4⋊C4×Dic11C2semidirect
4. #13066886C2semidirect
5. #13066862C2semidirect
6. #13066861C2semidirect
7. #13066858C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. C11×#1439C2semidirect
28. C2×#66938C4semidirect
205. C4×Dic11C22⋊C4semidirect
213. #1439D11semidirect
591. C11#14288semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C2×#106222642
C2×C4⋊C4×Dic112
#130668862
#130668622
#130668612
#130668582
#130668552
#130668532
#130668522
C11×#14392
#1428811