Finite Group Databasebeta

← #14675812

Subgroups — #14675812

Order 2816.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622553C212yesmaximal, complemented
3C2×#10622277C211yesmaximal, characteristic, complemented
4#13066859C212yesmaximal, complemented
5#13066855C212yesmaximal
6#13066849C212yesmaximal, complemented
7Dic11⋊#95C211yesmaximal, characteristic, complemented
8#13066841C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C2×C4×C22⋊D11—28no—
20C2×C4×C22⋊D11C418yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C4×C11×C22⋊C4—24no—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622553—28no—
39#10622277—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—24no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—42no—
46C23×C4×C11C2×C414yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11C2×C414yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C22×C4×D11—24no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—42no—
65C22×C4×D11C2×C414yes—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C42×C11—24no—
70C2×C42×C11—24no—
71C2×C42×C11—42no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2×C414yes—
77C4×C22⋊D11—232no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4C2×C414yes—
85C2×(C2×D11)⋊C4D418yes—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—42no—
90C2×Dic11⋊C4C2×C414yes—
91C2×C4×Dic11—24no—
92C2×C4×Dic11C2×C414yes—
93C11×#95—22no—
94C11×#95D414yescomplemented
95C11⋊#95—24no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103#13886—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11C22×C412yes—
114C24×C11#4114yes—
115C24×C11C2411yescharacteristic
116C23×D11—21no—
117C23×D11—22no—
118C23×D11—21no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11C22×C412yes—
126C23×D11C2×D414yes—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
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—28no—
145C22×C4×C11—28no—
146C22×C4×C11—44no—
147C22×C4×C11—48no—
148C22×C4×C11—48no—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4114yes—
155C22×C4×C11#4112yes—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—28no—
161C22×Dic11—22no—
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—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C2×D414yes—
188C22×Dic11#4112yes—
189C22×Dic11#4112yes—
190C2×C4×D11—28no—
191C2×C4×D11—28no—
192C2×C4×D11—44no—
193C2×C4×D11—48no—
194C2×C4×D11—48no—
195C11×C22⋊C4—216no—
196C42×C11—48no—
197C22⋊Dic11—28no—
198C22⋊Dic11—48no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4C22⋊C4116yescomplemented
202Dic11⋊C4—28no—
203Dic11⋊C4—48no—
204C4×Dic11—28no—
205C22×C4×D4—111no—
206C2×#388—112no—
207C2×#381—111no—
208C2×C4×C22⋊C4D1111yescharacteristic, complemented
209#1439—112no—
210#1438—112no—
211#1436—112no—
212C4⋊#95—111no—
213#1434—111no—
214C22⋊#95—111no—
215C22⋊#95—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11#11714yes—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D412yes—
241C23×C11C22×D411yescharacteristic
242C23×C11C2×#4112yes—
243C23×C11C2×#4111yescharacteristic
244C23×C11C2×#4112yes—
245C23×C11C2×#4111yescharacteristic
246C23×C11C2×#4111yescharacteristic
247C23×C11H(5,𝔽2)12yes—
248C23×C11H(5,𝔽2)11yescharacteristic
249C23×C112−1+411yescharacteristic
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—42no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—42no—
272C22×D11C2×C22⋊C414yes—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—416no—
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×C11C2×C22⋊C414yes—
297C2×C4×C11C4×D414yes—
298C22⋊D11—232no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
327C2×Dic11#11714yes—
328C4×D11—416no—
329C23×D4—111no—
330C24×C4—111no—
331C24×C4C2×D1111yescharacteristic
332C2×C4×D4—118no—
333C2×C4×D4—228no—
334C22×C4⋊C4—111no—
335C22×C4⋊C4—112no—
336C22×C22⋊C4—111no—
337C22×C22⋊C4—111no—
338C22×C22⋊C4—112no—
339C22×C22⋊C4—112no—
340C22×C22⋊C4—112no—
341C22×C22⋊C4C2×D1112yes—
342C22×C42—111no—
343C22×C42C2×D1112yes—
344#388—228no—
345#381—224no—
346C4×C22⋊C4—24no—
347C2×#95—111no—
348C2×#95—111no—
349C2×#95—112no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95C2×D1111yescharacteristic
356C2×#95C2×D1111yescharacteristic
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11C22×C22⋊C411yescharacteristic
369C22×C11C2×#11711yescharacteristic
370C22×C11C2×#11711yescharacteristic
371C22×C11C2×C4×D411yescharacteristic
372C22×C11C4×#4111yescharacteristic
373C22×C11#51811yescharacteristic
374C22×C11#52011yescharacteristic
375C22×C11#52512yes—
376C22×C11#52512yes—
377C22×C11#52512yes—
378C22×C11#52912yes—
379C22×C11#53812yes—
380C22×C11#53912yes—
381C22×C11D4212yes—
382C22×C11#54612yes—
383C22×C11#54612yes—
384C22×C11#54712yes—
385C22×C11#54711yescharacteristic
386C22×C11#55011yescharacteristic
387C22×C11#55312yes—
388C22×C11#55511yescharacteristic
389C22×C11#55611yescharacteristic
390C22×C11#55912yes—
391C2×D11—24no—
392C2×D11—24no—
393C2×D11—24no—
394C2×D11—42no—
395C2×D11—42no—
396C2×D11—42no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—42no—
402C4×C11—24no—
403C4×C11—24no—
404C4×C11—44no—
405C4×C11—44no—
406Dic11—24no—
407Dic11—24no—
408Dic11—42no—
409Dic11—82no—
410Dic11—82no—
411C25—111no—
412C25C22×D1111yescharacteristic
413C22×D4—114no—
414C22×D4—222no—
415C22×D4—222no—
416C22×D4—224no—
417C22×D4—224no—
418C23×C4—22no—
419C23×C4—24no—
420C23×C4—22no—
421C23×C4—42no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—114no—
426C23×C4—112no—
427C23×C4—112no—
428C23×C4—224no—
429C23×C4—222no—
430C23×C4—222no—
431C23×C4—442no—
432C23×C4C4×D1114yes—
433C23×C4C22×D1112yes—
434C23×C4C22×D1112yes—
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C4×D4—2232no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—224no—
440C2×C4⋊C4—224no—
441C2×C4⋊C4—224no—
442C2×C4⋊C4—442no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—118no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—224no—
450C2×C22⋊C4—224no—
451C2×C22⋊C4—224no—
452C2×C22⋊C4—224no—
453C2×C22⋊C4—224no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—442no—
456C2×C22⋊C4—442no—
457C2×C22⋊C4—442no—
458C2×C22⋊C4—442no—
459C2×C42—24no—
460C2×C42—24no—
461C2×C42—42no—
462C2×C42—114no—
463C2×C42—224no—
464#95—22no—
465#95—224no—
466#95—224no—
467#95—224no—
468#95—222no—
469#95—224no—
470#95—224no—
471#95—222no—
472#95—442no—
473#95C22⋊D1114yescomplemented
474C2×C11—44no—
475C2×C11#228011yescharacteristic
476C2×C11#229011yescharacteristic
477C2×C11#231811yescharacteristic
478C2×C11D4×C22⋊C411yescharacteristic
479C2×C11#233911yescharacteristic
480C2×C11#235411yescharacteristic
481C2×C11#235711yescharacteristic
482C2×C11#245512yes—
483C2×C11#245612yes—
484C2×C11#245912yes—
485C2×C11#246612yes—
486D11—44no—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—112no—
497C24—114no—
498C24—222no—
499C24—221no—
500C24—222no—
501C24—222no—
502C24—221no—
503C24—221no—
504C24—221no—
505C24—221no—
506C24—221no—
507C24C2×C4×D1112yes—
508C24#433914yes—
509C24C23×D1111yescharacteristic
510C2×D4—228no—
511C2×D4—228no—
512C2×D4—2216no—
513C2×D4—2216no—
514C2×D4—228no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
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—28no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—114no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—112no—
543C22×C4—228no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—221no—
553C22×C4—228no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
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—444no—
569C22×C4—448no—
570C22×C4—448no—
571C22×C4C2×C4×D1112yes—
572C22×C4C2×C4×D1112yes—
573C22×C4#433914yes—
574C22×C4#433912yes—
575C22×C4D4×D1114yes—
576C22×C4C2×C22⋊D1114yes—
577C22×C4C2×C22⋊D1112yes—
578C4⋊C4—228no—
579C4⋊C4—448no—
580C22⋊C4—216no—
581C22⋊C4—1116no—
582C22⋊C4—228no—
583C22⋊C4—448no—
584C22⋊C4—448no—
585C22⋊C4—448no—
586C42—48no—
587C42—228no—
588C11#1388611yescharacteristic, complemented, Sylow
589C23—22no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—114no—
612C23—222no—
613C23—222no—
614C23—222no—
615C23—224no—
616C23—222no—
617C23—222no—
618C23—222no—
619C23—224no—
620C23—224no—
621C23—224no—
622C23—224no—
623C23—224no—
624C23—442no—
625C23—441no—
626C23—441no—
627C23—442no—
628C23—442no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—441no—
633C23—441no—
634C23#6692514yes—
635C23C22×C4×D1111yescharacteristic
636C23C2×#433912yes—
637C23C2×#433912yes—
638C23C2×#433911yescharacteristic
639C23C2×D4×D1112yes—
640C23#6703712yes—
641C23#41×D1111yescharacteristic
642C23#41×D1111yescharacteristic
643C23#6704211yescharacteristic
644C23#6704311yescharacteristic
645C23C22×C22⋊D1111yescharacteristic
646D4—2232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—416no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—114no—
671C2×C4—114no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—224no—
677C2×C4—224no—
678C2×C4—224no—
679C2×C4—224no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—4416no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—442no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4C22⋊C4×D1114yes—
701C2×C4C4×C22⋊D1114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—42no—
712C22—42no—
713C22—224no—
714C22—224no—
715C22—224no—
716C22—444no—
717C22—444no—
718C22—444no—
719C22—442no—
720C22—444no—
721C22—442no—
722C22—442no—
723C22—442no—
724C22C2×#6692511yescharacteristic
725C22C4×#433911yescharacteristic
726C22#1062301012yes—
727C22C2×C22⋊C4×D1111yescharacteristic
728C22#1062301711yescharacteristic
729C22#1062302112yes—
730C22D11×#11711yescharacteristic
731C22#1062305411yescharacteristic
732C22#1062306311yescharacteristic
733C22#1062306411yescharacteristic
734C22#1062307112yes—
735C22#1062307812yes—
736C22#1062307812yes—
737C22#1062308112yes—
738C22#1062308212yes—
739C22#1062309012yes—
740C22#1062309112yes—
741C22#1062309512yes—
742C22C2×C4×C22⋊D1111yescharacteristic
743C22#1062332212yes—
744C22D4×C22⋊D1112yes—
745C22#1062335511yescharacteristic
746C22#1062336511yescharacteristic
747C4—24no—
748C4—24no—
749C4—44no—
750C4—44no—
751C4—224no—
752C4—224no—
753C4—442no—
754C4—882no—
755C4—882no—
756C2—44no—
757C2—444no—
758C2#1307099711yescharacteristic
759C2#1307105911yescharacteristic
760C2#1307124311yescharacteristic
761C2C22⋊C4×C22⋊D1111yescharacteristic
762C2#1307144711yescharacteristic
763C2#1307156611yescharacteristic
764C2#1307159011yescharacteristic
765C2#1307249312yes—
766C2#1307250212yes—
767C2#1307255312yes—
768C2#1307265212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13886
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622277C2semidirect
4. #13066859C2semidirect
6. #13066849C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066841C2semidirect
9. #13066839C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
20. C2×C4×C22⋊D11C4semidirect
94. C11×#95D4semidirect
201. (C2×D11)⋊C4C22⋊C4semidirect
208. C2×C4×C22⋊C4D11semidirect
473. #95C22⋊D11semidirect
588. C11#13886semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225532
C2×#106222772
#130668592
#130668552
#130668492
Dic11⋊#952
#130668412
#130668392
(C2×D11)⋊#952
C2×C4×C11×C22⋊C42
#1388611