Finite Group Databasebeta

← #14675863

Subgroups — #14675863

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×#10622265C212yesmaximal, complemented
3C2×#10622280C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13066859C212yesmaximal, complemented
6#13066855C212yesmaximal
7#13066852C212yesmaximal, complemented
8#13066842C211yesmaximal, characteristic, complemented
9#13066841C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C2×C4×C22⋊D11—28no—
19C2×C4×C22⋊D11C418yescomplemented
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C4×C22⋊Dic11—24no—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622280—24no—
39#10622265—28no—
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—22no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—24no—
55C22×C22⋊D11C2×C414yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—24no—
64C22×C4×D11—42no—
65C22×C4×D11C2×C414yes—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11C2×C414yes—
74C4×C22⋊D11—232no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4C2×C414yes—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—42no—
86C2×Dic11⋊C4C2×C414yes—
87C2×Dic11⋊C4D418yes—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—42no—
92C2×C4×Dic11C2×C414yes—
93C11×#95—24no—
94C11×#95—22no—
95C11×#95—22no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95D414yescomplemented
103#13890—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—22no—
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—22no—
119C23×D11—21no—
120C23×D11—22no—
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11C22×C412yes—
125C23×D11#4112yes—
126C23×D11#4112yes—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
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×C11—44no—
149C22×C4×C11—48no—
150C22×C4×C11—48no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D412yes—
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—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—21no—
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—21no—
182C22×Dic11—22no—
183C22×Dic11C22×C412yes—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C2×D414yes—
187C22×Dic11C2×D414yes—
188C22×Dic11C2×D414yes—
189C22×Dic11#4114yes—
190C2×C4×D11—28no—
191C2×C4×D11—28no—
192C2×C4×D11—44no—
193C2×C4×D11—48no—
194C2×C4×D11—48no—
195C11×C22⋊C4—48no—
196C22⋊Dic11—216no—
197C22⋊Dic11—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201Dic11⋊C4—48no—
202Dic11⋊C4C22⋊C4116yescomplemented
203C4×Dic11—28no—
204C4×Dic11—48no—
205C22×C4×D4—111no—
206C2×#387—112no—
207C2×#380—111no—
208C2×C4×C22⋊C4—111no—
209#1439—112no—
210#1438—112no—
211#1437—112no—
212#1434—111no—
213#1434—111no—
214C22⋊#95—111no—
215C22⋊#95D1111yescharacteristic, complemented
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—41no—
231C23×C11—42no—
232C23×C11—41no—
233C23×C11—42no—
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×#4111yescharacteristic
245C23×C11C2×#4111yescharacteristic
246C23×C11C2×#4112yes—
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—22no—
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11#11714yes—
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—416no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
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×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—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
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×Dic11C2×C22⋊C414yes—
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×C42—112no—
344#387—228no—
345#380—224no—
346C4×C22⋊C4—224no—
347C2×#95—111no—
348C2×#95—111no—
349C2×#95—112no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95C2×D1111yescharacteristic
355C2×#95C2×D1111yescharacteristic
356C2×#95C2×D1112yes—
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#54611yescharacteristic
384C22×C11#54812yes—
385C22×C11#54811yescharacteristic
386C22×C11#55012yes—
387C22×C11#55112yes—
388C22×C11#55211yescharacteristic
389C22×C11#55311yescharacteristic
390C22×C11#55312yes—
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—82no—
405C4×C11—82no—
406Dic11—24no—
407Dic11—24no—
408Dic11—42no—
409Dic11—44no—
410Dic11—44no—
411C25—111no—
412C25C22×D1111yescharacteristic
413C22×D4—114no—
414C22×D4—224no—
415C22×D4—222no—
416C22×D4—222no—
417C22×D4—224no—
418C23×C4—24no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—42no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—112no—
425C23×C4—111no—
426C23×C4—112no—
427C23×C4—114no—
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—118no—
440C2×C4⋊C4—224no—
441C2×C4⋊C4—224no—
442C2×C4⋊C4—442no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—114no—
448C2×C22⋊C4—224no—
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—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—442no—
458C2×C22⋊C4—442no—
459C2×C42—114no—
460C2×C42—224no—
461C2×C42—224no—
462C2×C42—224no—
463C2×C42—442no—
464#95—22no—
465#95—24no—
466#95—22no—
467#95—114no—
468#95—224no—
469#95—224no—
470#95—224no—
471#95—224no—
472#95—222no—
473#95—442no—
474C2×C11—44no—
475C2×C11#228011yescharacteristic
476C2×C11#229011yescharacteristic
477C2×C11#231811yescharacteristic
478C2×C11D4×C22⋊C411yescharacteristic
479C2×C11#234111yescharacteristic
480C2×C11#235211yescharacteristic
481C2×C11#235311yescharacteristic
482C2×C11#245612yes—
483C2×C11#246012yes—
484C2×C11#246312yes—
485C2×C11#246712yes—
486D11—44no—
487C24—21no—
488C24—22no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—21no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—112no—
497C24—112no—
498C24—112no—
499C24—222no—
500C24—221no—
501C24—222no—
502C24—221no—
503C24—221no—
504C24—222no—
505C24—221no—
506C24—222no—
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—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—28no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—114no—
542C22×C4—114no—
543C22×C4—112no—
544C22×C4—114no—
545C22×C4—114no—
546C22×C4—228no—
547C22×C4—222no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—222no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—228no—
570C22×C4—444no—
571C22×C4—448no—
572C22×C4—448no—
573C22×C4C2×C4×D1112yes—
574C22×C4C2×C4×D1112yes—
575C22×C4D4×D1114yes—
576C22×C4D4×D1112yes—
577C22×C4#434112yes—
578C4⋊C4—1116no—
579C4⋊C4—448no—
580C22⋊C4—48no—
581C22⋊C4—228no—
582C22⋊C4—2216no—
583C22⋊C4—228no—
584C22⋊C4—448no—
585C22⋊C4—448no—
586C42—228no—
587C42—448no—
588C11#1389011yescharacteristic, complemented, Sylow
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—42no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—114no—
612C23—222no—
613C23—222no—
614C23—222no—
615C23—222no—
616C23—222no—
617C23—222no—
618C23—224no—
619C23—224no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—224no—
625C23—224no—
626C23—442no—
627C23—442no—
628C23—442no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23#6692514yes—
635C23C22×C4×D1111yescharacteristic
636C23C2×#433912yes—
637C23C2×D4×D1112yes—
638C23C2×D4×D1111yescharacteristic
639C23C2×#434111yescharacteristic
640C23#6703712yes—
641C23#6703711yescharacteristic
642C23#6704011yescharacteristic
643C23#41×D1111yescharacteristic
644C23#41×D1111yescharacteristic
645C23#41×D1112yes—
646D4—2232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—416no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
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—224no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—4416no—
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×C4(C22⋊D11)⋊C414yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—42no—
710C22—44no—
711C22—42no—
712C22—44no—
713C22—224no—
714C22—224no—
715C22—224no—
716C22—444no—
717C22—442no—
718C22—442no—
719C22—444no—
720C22—442no—
721C22—444no—
722C22—442no—
723C22—444no—
724C22C2×#6692511yescharacteristic
725C22C2×C22⋊C4×D1111yescharacteristic
726C22C2×(C22⋊D11)⋊C411yescharacteristic
727C22#1062301711yescharacteristic
728C22#1062302512yes—
729C22#1062303511yescharacteristic
730C22#1062304612yes—
731C22D11×#11711yescharacteristic
732C22#1062305311yescharacteristic
733C22#1062306912yes—
734C22#1062307812yes—
735C22#1062307812yes—
736C22#1062307812yes—
737C22#1062312112yes—
738C22#1062312212yes—
739C22#1062313012yes—
740C22#1062314311yescharacteristic
741C22#1062314511yescharacteristic
742C22#1062316412yes—
743C22#1062316411yescharacteristic
744C22#1062317011yescharacteristic
745C22#1062319012yes—
746C22#1062319212yes—
747C4—24no—
748C4—24no—
749C4—82no—
750C4—82no—
751C4—224no—
752C4—224no—
753C4—442no—
754C4—444no—
755C4—444no—
756C2—44no—
757C2—444no—
758C2#1307099711yescharacteristic
759C2#1307105511yescharacteristic
760C2#1307125011yescharacteristic
761C2#1307143211yescharacteristic
762C2#1307145311yescharacteristic
763C2#1307153811yescharacteristic
764C2#1307155311yescharacteristic
765C2#1307251012yes—
766C2#1307257012yes—
767C2#1307261212yes—
768C2#1307266912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13890
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622265C2semidirect
3. C2×#10622280C2semidirect
4. C2×C4×C22⋊Dic11C2semidirect
5. #13066859C2semidirect
7. #13066852C2semidirect
8. #13066842C2semidirect
9. #13066841C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C22⋊#95C2semidirect
19. C2×C4×C22⋊D11C4semidirect
102. C11⋊#95D4semidirect
202. Dic11⋊C4C22⋊C4semidirect
215. C22⋊#95D11semidirect
588. C11#13890semidirect

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×#106222652
C2×#106222802
C2×C4×C22⋊Dic112
#130668592
#130668552
#130668522
#130668422
#130668412
(C2×D11)⋊#952
C11×C22⋊#952
#1389011