Finite Group Databasebeta

← #14681921

Subgroups — #14681921

Order 2816.

2386 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C212yesmaximal, complemented
2C2×#10622594C212yesmaximal, complemented
3#13066861C212yesmaximal, complemented
4#13066857C212yesmaximal, complemented
5#13066857C212yesmaximal, complemented
6#13066853C212yesmaximal, complemented
7#13066839C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic, complemented
9C22×C11×#121C211yesmaximal, characteristic
10C23×D4×C11C2212yes—
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C2×C11×#121—28no—
14C2×C11×#121C418yescomplemented
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4×Dic11C2212yes—
26#10622834—28no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34#10622594—28no—
35C25×C11C2312yes—
36C25×C11C2311yescharacteristic
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—24no—
41C22×D4×C11—24no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11—41no—
45C22×D4×C11—41no—
46C22×D4×C11—42no—
47C22×D4×C11C2×C418yes—
48C22×D4×C11C2×C414yes—
49C23×C4×C11—24no—
50C23×C4×C11—41no—
51C23×C4×C11—41no—
52C23×C4×C11—42no—
53C23×C4×C11C2×C414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C11×#121—232no—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C11×C4⋊C4D418yes—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4C2×C418yes—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—41no—
75C2×C22⋊Dic11—41no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11—41no—
78C2×C22⋊Dic11—41no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11D414yescomplemented
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—42no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—42no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—41no—
99C11⋊#95—42no—
100C11⋊#95—41no—
101#14418—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×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11C22×C414yes—
125C24×C11C22×C412yes—
126C24×C11C2×D412yes—
127C24×C11#4112yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—216no—
130C2×D4×C11—216no—
131C2×D4×C11—28no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—48no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—48no—
140C2×D4×C11—48no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—28no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C414yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D414yes—
163C22×Dic11—22no—
164C22×Dic11—22no—
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×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11C2×D414yes—
190C22×Dic11#4114yes—
191C11×C4⋊C4C22⋊C4116yescomplemented
192C11×C22⋊C4—216no—
193C22⋊Dic11—44no—
194C22⋊Dic11—48no—
195C22⋊Dic11—44no—
196C22⋊Dic11—48no—
197C22⋊Dic11—48no—
198C22⋊Dic11—48no—
199C22⋊Dic11—48no—
200C4⋊Dic11—48no—
201C4×Dic11—48no—
202C22×#121D1111yescharacteristic
203C2×#390—112no—
204C2×#387—112no—
205#1439—112no—
206#1438—112no—
207#1438—112no—
208#1437—112no—
209C22⋊#95—111no—
210C22⋊#95—111no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
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×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11C4×D414yes—
269C23×C11C23×C411yescharacteristic
270C23×C11C22×D411yescharacteristic
271C23×C11C22×D412yes—
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4112yes—
274C23×C11H(5,𝔽2)11yescharacteristic
275C23×C11H(5,𝔽2)11yescharacteristic
276C23×C11H(5,𝔽2)12yes—
277C23×C11H(5,𝔽2)12yes—
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C112−1+411yescharacteristic
280D4×C11—432no—
281D4×C11—416no—
282C2×C4×C11—24no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—416no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11C2×C22⋊C418yes—
299C2×C4×C11C2×C22⋊C414yes—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
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×Dic11—42no—
327C2×Dic11—42no—
328C23×D4C2×D1112yes—
329C23×D4C2×D1111yescharacteristic
330C24×C4C2×D1111yescharacteristic
331C2×#121—28no—
332C2×#121Dic1118yescomplemented
333C22×C4⋊C4—112no—
334C22×C4⋊C4C2×D1111yescharacteristic
335C22×C22⋊C4—111no—
336C22×C22⋊C4—112no—
337C22×C22⋊C4—112no—
338C22×C22⋊C4—111no—
339C22×C22⋊C4—112no—
340C22×C22⋊C4—112no—
341C22×C22⋊C4—112no—
342C22×C22⋊C4C2×D1112yes—
343C22×C42—112no—
344#390—228no—
345#387—228no—
346C2×#95—112no—
347C2×#95—112no—
348C2×#95—112no—
349C2×#95—112no—
350C2×#95—111no—
351C2×#95—112no—
352C2×#95—111no—
353C22×C11—24no—
354C22×C11—24no—
355C22×C11—24no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—44no—
361C22×C11—44no—
362C22×C11—44no—
363C22×C11—44no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11—82no—
379C22×C11C22×C22⋊C411yescharacteristic
380C22×C11C2×C4×D411yescharacteristic
381C22×C11C4×#4111yescharacteristic
382C22×C11#51811yescharacteristic
383C22×C11#51811yescharacteristic
384C22×C11#51811yescharacteristic
385C22×C11#52011yescharacteristic
386C22×C11#53411yescharacteristic
387C22×C11#53512yes—
388C22×C11#53512yes—
389C22×C11#53711yescharacteristic
390C22×C11#53812yes—
391C22×C11#53811yescharacteristic
392C22×C11#53911yescharacteristic
393C22×C11#54012yes—
394C22×C11D4212yes—
395C22×C11#54612yes—
396C22×C11#54612yes—
397C22×C11#54812yes—
398C22×C11#55012yes—
399C22×C11#55312yes—
400C22×C11#56012yes—
401C22×C11#56212yes—
402C4×C11—24no—
403C4×C11—28no—
404C4×C11—42no—
405Dic11—44no—
406Dic11—44no—
407Dic11—82no—
408Dic11—82no—
409C25C22×D1112yes—
410C25C22×D1111yescharacteristic
411C22×D4—24no—
412C22×D4—24no—
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—42no—
417C22×D4—42no—
418C22×D4—41no—
419C22×D4—42no—
420C22×D4—41no—
421C22×D4C2×Dic1118yes—
422C22×D4C2×Dic1114yes—
423C23×C4—24no—
424C23×C4—41no—
425C23×C4—42no—
426C23×C4—41no—
427C23×C4—112no—
428C23×C4—112no—
429C23×C4—112no—
430C23×C4—112no—
431C23×C4C2×Dic1114yes—
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1112yes—
434C23×C4C22×D1111yescharacteristic
435#121—232no—
436C2×C4⋊C4—224no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4—442no—
439C2×C4⋊C4C2×Dic1114yes—
440C2×C4⋊C4C22⋊D1118yes—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—114no—
444C2×C22⋊C4—224no—
445C2×C22⋊C4—224no—
446C2×C22⋊C4—224no—
447C2×C22⋊C4—224no—
448C2×C22⋊C4—224no—
449C2×C22⋊C4—224no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—441no—
452C2×C22⋊C4—441no—
453C2×C22⋊C4—442no—
454C2×C22⋊C4—442no—
455C2×C22⋊C4—442no—
456C2×C22⋊C4—442no—
457C2×C22⋊C4—442no—
458C2×C22⋊C4—442no—
459C2×C22⋊C4—441no—
460C2×C22⋊C4—441no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4C2×Dic1118yes—
465C2×C42—224no—
466C2×C42—224no—
467C2×C42—442no—
468#95—224no—
469#95—224no—
470#95—224no—
471#95—224no—
472#95—441no—
473#95—442no—
474#95—441no—
475C2×C11—44no—
476C2×C11—84no—
477C2×C11#230911yescharacteristic
478C2×C11#232511yescharacteristic
479C2×C11#233311yescharacteristic
480C2×C11D4×C22⋊C411yescharacteristic
481C2×C11#234111yescharacteristic
482C2×C11#236411yescharacteristic
483C2×C11#237711yescharacteristic
484C2×C11#267312yes—
485C2×C11#267612yes—
486C2×C11#271112yes—
487C2×C11#271412yes—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24D4×D1112yes—
511C24#434112yes—
512C24C22×Dic1114yes—
513C24C22×Dic1112yes—
514C24C23×D1111yescharacteristic
515C2×D4—216no—
516C2×D4—216no—
517C2×D4—28no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—48no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—114no—
544C22×C4—114no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
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—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4C22×Dic1112yes—
572C22×C4C22×Dic1114yes—
573C22×C4C22×Dic1112yes—
574C22×C4C2×C22⋊D1114yes—
575C22×C4C2×C22⋊D1114yes—
576C22×C4C2×C22⋊D1114yes—
577C4⋊C4—448no—
578C4⋊C4C22⋊Dic11116yescomplemented
579C22⋊C4—216no—
580C22⋊C4—444no—
581C22⋊C4—448no—
582C22⋊C4—448no—
583C22⋊C4—448no—
584C22⋊C4—448no—
585C22⋊C4—444no—
586C22⋊C4—448no—
587C42—448no—
588C11#1441811yescharacteristic, complemented, Sylow
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23D4×Dic1114yes—
647C23C2×D4×D1111yescharacteristic
648C23C2×#434111yescharacteristic
649C23#6703712yes—
650C23#6703711yescharacteristic
651C23#6703712yes—
652C23#6703711yescharacteristic
653C23#41×D1112yes—
654C23#6704211yescharacteristic
655C23#6704311yescharacteristic
656C23C23×Dic1111yescharacteristic
657C23C22×C22⋊D1112yes—
658D4—432no—
659D4—416no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—224no—
677C2×C4—224no—
678C2×C4—224no—
679C2×C4—224no—
680C2×C4—224no—
681C2×C4—224no—
682C2×C4—442no—
683C2×C4—442no—
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×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4C2×C22⋊Dic1118yes—
705C2×C4C2×C22⋊Dic1114yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22#1062312811yescharacteristic
733C22#1062313212yes—
734C22#1062313311yescharacteristic
735C22#1062313611yescharacteristic
736C22#1062314112yes—
737C22#1062314412yes—
738C22#1062314612yes—
739C22#1062314811yescharacteristic
740C22#1062315112yes—
741C22#1062315212yes—
742C22C2×D4×Dic1111yescharacteristic
743C22#1062332911yescharacteristic
744C22#1062332911yescharacteristic
745C22#1062332911yescharacteristic
746C22D4×C22⋊D1112yes—
747C22#1062333612yes—
748C22#1062333612yes—
749C22#1062333712yes—
750C22#41×Dic1111yescharacteristic
751C22#1062335811yescharacteristic
752C22#1062336212yes—
753C22#1062336512yes—
754C22C22×C22⋊Dic1111yescharacteristic
755C4—28no—
756C4—24no—
757C4—42no—
758C4—444no—
759C4—444no—
760C4—882no—
761C4—882no—
762C2—44no—
763C2—84no—
764C2#1307119811yescharacteristic
765C2#1307132111yescharacteristic
766C2#1307138311yescharacteristic
767C2D4×C22⋊Dic1111yescharacteristic
768C2#1307145711yescharacteristic
769C2#1307166811yescharacteristic
770C2#1307177311yescharacteristic
771C2#1307487712yes—
772C2#1307491112yes—
773C2#1307536712yes—
774C2#1307540612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#121C2
socle, cosocleC24×C11C24
hypercenterC22×#121D11
hypocenterC11#14418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622834C2semidirect
2. C2×#10622594C2semidirect
3. #13066861C2semidirect
4. #13066857C2semidirect
5. #13066857C2semidirect
6. #13066853C2semidirect
7. #13066839C2semidirect
8. #13066839C2semidirect
14. C2×C11×#121C4semidirect
87. C2×C22⋊Dic11D4semidirect
191. C11×C4⋊C4C22⋊C4semidirect
332. C2×#121Dic11semidirect
578. C4⋊C4C22⋊Dic11semidirect
588. C11#14418semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225942
#130668612
#130668572
#130668532
#130668392
C22×C11×#1212
#1441811