Finite Group Databasebeta

← #14681914

Subgroups — #14681914

Order 2816.

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×#66983C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal, complemented
3C2×#10622569C212yesmaximal, complemented
4#13066885C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066855C212yesmaximal, complemented
7#13066839C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×C22⋊#95C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2212yes—
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C2×#66983—28no—
18C2×#66983C418yescomplemented
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33#10622569—28no—
34#10622278—28no—
35C25×C11C2311yescharacteristic
36C24×D11C2312yes—
37C23×C4×C11—24no—
38C23×C4×C11—42no—
39C23×C4×C11—41no—
40C23×C4×C11—41no—
41C23×C4×C11C2×C414yescomplemented
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—24no—
47C22×C22⋊D11—24no—
48C22×C22⋊D11—24no—
49C22×C22⋊D11—24no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11C2×C418yescomplemented
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C22×D44—41no—
57C22×D44—42no—
58C22×D44—41no—
59C22×D44C2×C414yes—
60C22×D44D418yes—
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—42no—
65C22×C4×D11—42no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—42no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—41no—
73C2×C22⋊Dic11—41no—
74C2×C22⋊Dic11—41no—
75C2×C22⋊Dic11—41no—
76C2×C22⋊Dic11D414yescomplemented
77#66983—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—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4C2×C418yescomplemented
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11C2×C414yescomplemented
92C11×#95—24no—
93C11×#95—41no—
94C11×#95—41no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101#14417—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—21no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11C22×C412yes—
111C24×C11C2×D412yes—
112C24×C11#4112yes—
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11C22×C414yes—
127C23×D11C2×D414yes—
128C23×D11C2×D414yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
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—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—28no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11#4114yes—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C22×Dic11—22no—
166C22×Dic11—22no—
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—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11C22×C414yes—
185C22×Dic11C2×D414yes—
186C2×D44—44no—
187C2×D44—44no—
188C2×D44—48no—
189C2×D44—48no—
190C2×D44C22⋊C4116yescomplemented
191C2×C4×D11—48no—
192C2×C4×D11—48no—
193C2×C4×D11—48no—
194C2×C4×D11—48no—
195C2×C4×D11—48no—
196C2×C4×D11—48no—
197C2×C4×D11—48no—
198C11×C22⋊C4—48no—
199C22⋊Dic11—44no—
200C22⋊Dic11—44no—
201(C2×D11)⋊C4—216no—
202(C2×D11)⋊C4—48no—
203(C2×D11)⋊C4—48no—
204(C2×D11)⋊C4—48no—
205C4⋊Dic11—28no—
206C22×#121—111no—
207C2×#386—112no—
208C2×#386—112no—
209#1445—112no—
210#1440—112no—
211#1438—112no—
212C22⋊#95—112no—
213C22⋊#95—111no—
214C22⋊#95D1111yescharacteristic, complemented
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C4×D414yes—
238C23×C11C23×C411yescharacteristic
239C23×C11C22×D412yes—
240C23×C11C22×D411yescharacteristic
241C23×C11C2×#4112yes—
242C23×C11C2×#4111yescharacteristic
243C23×C11H(5,𝔽2)11yescharacteristic
244C23×C11H(5,𝔽2)11yescharacteristic
245C23×C11H(5,𝔽2)12yes—
246C23×C11H(5,𝔽2)12yes—
247C23×C11H(5,𝔽2)11yescharacteristic
248C23×C112−1+411yescharacteristic
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—24no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11C2×C22⋊C418yes—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—416no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11C2×C22⋊C414yes—
309C22⋊D11—432no—
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×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331D44—416no—
332C4×D11—432no—
333C23×D4—112no—
334C23×D4—111no—
335C24×C4—112no—
336C24×C4C2×D1111yescharacteristic
337C2×#121—118no—
338C2×#121—228no—
339C22×C4⋊C4—111no—
340C22×C22⋊C4—112no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4C2×D1112yes—
347#386—228no—
348#386—228no—
349C2×#95—112no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95C2×D1112yes—
356C2×#95C2×D1111yescharacteristic
357C2×#95C2×D1111yescharacteristic
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11C22×C22⋊C411yescharacteristic
370C22×C11C2×C4×D411yescharacteristic
371C22×C11C4×#4111yescharacteristic
372C22×C11#51811yescharacteristic
373C22×C11#51811yescharacteristic
374C22×C11#51811yescharacteristic
375C22×C11#52011yescharacteristic
376C22×C11#53412yes—
377C22×C11#53412yes—
378C22×C11#53411yescharacteristic
379C22×C11#53711yescharacteristic
380C22×C11#53812yes—
381C22×C11#53811yescharacteristic
382C22×C11#53911yescharacteristic
383C22×C11#54012yes—
384C22×C11D4212yes—
385C22×C11#54612yes—
386C22×C11#54612yes—
387C22×C11#54612yes—
388C22×C11#54712yes—
389C22×C11#55312yes—
390C22×C11#56012yes—
391C22×C11#56212yes—
392C2×D11—28no—
393C2×D11—28no—
394C2×D11—28no—
395C2×D11—44no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C4×C11—24no—
408C4×C11—42no—
409C4×C11—44no—
410C4×C11—82no—
411Dic11—44no—
412Dic11—44no—
413Dic11—82no—
414C25—112no—
415C25C22×D1111yescharacteristic
416C22×D4—118no—
417C22×D4—114no—
418C22×D4—118no—
419C22×D4—224no—
420C22×D4—224no—
421C22×D4—224no—
422C22×D4—224no—
423C22×D4—441no—
424C22×D4—442no—
425C22×D4—441no—
426C22×D4—442no—
427C22×D4—442no—
428C23×C4—24no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4—42no—
432C23×C4—112no—
433C23×C4—112no—
434C23×C4—112no—
435C23×C4—224no—
436C23×C4—224no—
437C23×C4—224no—
438C23×C4—442no—
439C23×C4—442no—
440C23×C4—442no—
441C23×C4—442no—
442C23×C4C4×D1114yescomplemented
443C23×C4C22×D1112yes—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1112yes—
446C23×C4C22×D1111yescharacteristic
447#121—2232no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—224no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—118no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—222no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—441no—
468C2×C22⋊C4—441no—
469C2×C22⋊C4—441no—
470C2×C22⋊C4—441no—
471#95—24no—
472#95—41no—
473#95—41no—
474#95—224no—
475#95—224no—
476#95—224no—
477#95—442no—
478#95—442no—
479#95—442no—
480C2×C11—44no—
481C2×C11#230811yescharacteristic
482C2×C11#232511yescharacteristic
483C2×C11#233311yescharacteristic
484C2×C11D4×C22⋊C411yescharacteristic
485C2×C11#233911yescharacteristic
486C2×C11#236411yescharacteristic
487C2×C11#237711yescharacteristic
488C2×C11#266812yes—
489C2×C11#267112yes—
490C2×C11#268812yes—
491C2×C11#270812yes—
492D11—48no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—22no—
500C24—21no—
501C24—114no—
502C24—114no—
503C24—114no—
504C24—222no—
505C24—222no—
506C24—222no—
507C24—222no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24—222no—
512C24—222no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24C2×C4×D1112yes—
517C24D4×D1112yes—
518C24#434312yes—
519C24C23×D1111yescharacteristic
520C2×D4—1116no—
521C2×D4—2216no—
522C2×D4—2216no—
523C2×D4—444no—
524C2×D4—444no—
525C2×D4—448no—
526C2×D4—448no—
527C2×D4—448no—
528C2×D4—448no—
529C2×D4—448no—
530C2×D4—448no—
531C2×D4—448no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—114no—
558C22×C4—114no—
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—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—448no—
579C22×C4—448no—
580C22×C4—448no—
581C22×C4—448no—
582C22×C4—448no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4C2×C4×D1112yes—
586C22×C4C2×C4×D1112yes—
587C22×C4#433914yes—
588C22×C4D4×D1114yes—
589C4⋊C4—228no—
590C22⋊C4—48no—
591C22⋊C4—2216no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C22⋊C4—444no—
596C22⋊C4—444no—
597C11#1441711yescharacteristic, complemented, Sylow
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—22no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—118no—
621C23—224no—
622C23—224no—
623C23—224no—
624C23—224no—
625C23—224no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—224no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23#6694614yes—
656C23C22×C4×D1111yescharacteristic
657C23C2×#433912yes—
658C23C2×D4×D1112yes—
659C23C2×D4×D1111yescharacteristic
660C23#6703712yes—
661C23#6703711yescharacteristic
662C23#6703711yescharacteristic
663C23C2×#434311yescharacteristic
664C23#6704212yes—
665C23#6704211yescharacteristic
666C23#6704311yescharacteristic
667D4—4416no—
668D4—4432no—
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—224no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—4432no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4C22⋊C4×D1114yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—42no—
726C22—44no—
727C22—228no—
728C22—228no—
729C22—228no—
730C22—444no—
731C22—444no—
732C22—444no—
733C22—444no—
734C22—444no—
735C22—444no—
736C22—444no—
737C22—444no—
738C22—444no—
739C22—444no—
740C22—444no—
741C22—444no—
742C22C4×#433911yescharacteristic
743C22C2×C22⋊C4×D1111yescharacteristic
744C22#1062301711yescharacteristic
745C22#1062301711yescharacteristic
746C22#1062302112yes—
747C22C2×#6694611yescharacteristic
748C22#1062304512yes—
749C22#1062305211yescharacteristic
750C22#1062305411yescharacteristic
751C22#1062308112yes—
752C22#1062308212yes—
753C22#1062309112yes—
754C22#1062309312yes—
755C22#1062312012yes—
756C22#1062312012yes—
757C22#1062312811yescharacteristic
758C22#1062313611yescharacteristic
759C22#1062314012yes—
760C22#1062316112yes—
761C22#1062317511yescharacteristic
762C22#1062317611yescharacteristic
763C22#1062319712yes—
764C22#1062319812yes—
765C4—24no—
766C4—42no—
767C4—44no—
768C4—82no—
769C4—444no—
770C4—444no—
771C4—882no—
772C2—44no—
773C2—448no—
774C2#1307119211yescharacteristic
775C2#1307131611yescharacteristic
776C2#1307138111yescharacteristic
777C2#1307143611yescharacteristic
778C2#1307144711yescharacteristic
779C2#1307166311yescharacteristic
780C2#1307177511yescharacteristic
781C2#1307482112yes—
782C2#1307485312yes—
783C2#1307505512yes—
784C2#1307533512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC22×#66983C2
hypercenterC22⋊#95D11
hypocenterC11#14417
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622569C2semidirect
4. #13066885C2semidirect
5. #13066864C2semidirect
6. #13066855C2semidirect
7. #13066839C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×C22⋊#95C2semidirect
18. C2×#66983C4semidirect
41. C23×C4×C11C2×C4semidirect
52. C22×C22⋊D11C2×C4semidirect
76. C2×C22⋊Dic11D4semidirect
89. C2×(C2×D11)⋊C4C2×C4semidirect
91. C2×C4⋊Dic11C2×C4semidirect
190. C2×D44C22⋊C4semidirect
214. C22⋊#95D11semidirect
442. C23×C4C4×D11semidirect
597. C11#14417semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106222782
C2×#106225692
#130668852
#130668642
#130668552
#130668392
(C2×D11)⋊#952
C11×C22⋊#952
#1441711