Finite Group Databasebeta

← #14685231

Subgroups — #14685231

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3C2×#10622269C211yesmaximal, characteristic, complemented
4C2×#10622286C211yesmaximal, characteristic, complemented
5C2×#10622281C212yesmaximal, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066861C212yesmaximal, complemented
9#13066855C212yesmaximal
10#13066851C212yesmaximal, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C2×C4×C22⋊D11—24no—
20C2×C4×C22⋊D11—24no—
21C2×C4×C22⋊D11—24no—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C2×#66977—24no—
28C2×#66977—28no—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C2×C11×#95C2212yes—
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622286—24no—
41#10622281—28no—
42#10622269—24no—
43C25×C11C2311yescharacteristic
44C24×D11C2311yescharacteristic
45C23×C4×C11—24no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—42no—
49C23×C4×C11D414yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11Q814yescomplemented
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—24no—
70C22×C4×D11—42no—
71C22×Dic22—22no—
72C22×Dic22—24no—
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—42no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—42no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C4×C22⋊D11—232no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4D414yes—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—42no—
100#66977—232no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4D414yes—
106C2×Dic11⋊C4D418yescomplemented
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C11×#95—22no—
111C11×#95—24no—
112C11×#95—22no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118#14723—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—22no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11C2×D412yes—
128C24×C11C2×Q812yes—
129C24×C11#4112yes—
130C24×C11C2411yescharacteristic
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—22no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11C2×D412yes—
140C23×D11C2×Q812yes—
141C23×D11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
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—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—28no—
154C22×C4×C11—28no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—44no—
163C22×C4×C11—48no—
164C22×C4×C11—48no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4114yes—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—28no—
173C2×C22⋊D11—28no—
174C2×C22⋊D11—28no—
175C2×C22⋊D11—28no—
176C2×C22⋊D11—28no—
177C2×C22⋊D11—28no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11C2×D412yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D412yes—
205C22×Dic11C2×D414yes—
206C22×Dic11C2×D412yes—
207C22×Dic11C2×Q812yes—
208C22×Dic11#4112yes—
209C2×C4×D11—28no—
210C2×C4×D11—48no—
211C2×C4×D11—48no—
212C2×C4×D11—44no—
213C2×C4×D11—44no—
214C2×Dic22—28no—
215C2×Dic22—48no—
216C2×Dic22—48no—
217C2×Dic22—44no—
218C2×Dic22—44no—
219C11×C22⋊C4—48no—
220C22⋊Dic11—216no—
221C22⋊Dic11—28no—
222(C2×D11)⋊C4—216no—
223(C2×D11)⋊C4—28no—
224(C2×D11)⋊C4—48no—
225C4⋊Dic11—28no—
226C4⋊Dic11—48no—
227Dic11⋊C4—28no—
228Dic11⋊C4—216no—
229C4×Dic11—28no—
230C22×C22⋊Q8—111no—
231C22×C4×D4—111no—
232C2×#395—111no—
233C2×#393—111no—
234C2×#385—112no—
235#1441—111no—
236#1439—111no—
237#1439—112no—
238#1438—112no—
239#1436—112no—
240C22⋊#95D1111yescharacteristic, complemented
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
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×C11C22⋊Q814yes—
264C23×C11C22×D411yescharacteristic
265C23×C11C22×D411yescharacteristic
266C23×C11C22×D411yescharacteristic
267C23×C11C22×D412yes—
268C23×C11C22×Q811yescharacteristic
269C23×C11C2×#4112yes—
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11H(5,𝔽2)12yes—
274C23×C112−1+412yes—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—24no—
283C22×D11—24no—
284C22×D11—24no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—42no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11C22⋊Q814yescomplemented
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—416no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11#12014yes—
322C2×C4×C11#12014yes—
323C22⋊D11—232no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—42no—
341C2×Dic11—41no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11C22⋊Q814yescomplemented
355C4×D11—416no—
356Dic22—416no—
357C23×Q8—111no—
358C23×D4—111no—
359C24×C4—111no—
360C24×C4C2×D1111yescharacteristic
361C2×C22⋊Q8—228no—
362C2×C22⋊Q8—224no—
363C2×C4×D4—224no—
364C2×C4×D4—224no—
365C2×C4×D4—224no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—112no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—112no—
370C22×C22⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—112no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4—112no—
375C22×C22⋊C4C2×D1112yes—
376C22×C42—111no—
377#395—224no—
378#393—224no—
379#385—228no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95C2×D1111yescharacteristic
386C2×#95C2×D1111yescharacteristic
387C2×#95C2×D1112yes—
388C22×C11—24no—
389C22×C11—24no—
390C22×C11—24no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—44no—
398C22×C11—44no—
399C22×C11C2×#12011yescharacteristic
400C22×C11C2×#12011yescharacteristic
401C22×C11C2×C22⋊Q811yescharacteristic
402C22×C11C2×C22⋊Q811yescharacteristic
403C22×C11C2×C22⋊Q811yescharacteristic
404C22×C11#52511yescharacteristic
405C22×C11#52512yes—
406C22×C11#52511yescharacteristic
407C22×C11#52511yescharacteristic
408C22×C11#53211yescharacteristic
409C22×C11#53212yes—
410C22×C11#53411yescharacteristic
411C22×C11#53611yescharacteristic
412C22×C11#53912yes—
413C22×C11#54212yes—
414C22×C11D4212yes—
415C22×C11D4212yes—
416C22×C11#54712yes—
417C22×C11#54812yes—
418C22×C11#54812yes—
419C22×C11D4×Q812yes—
420C22×C11#55112yes—
421C22×C11#55412yes—
422C2×D11—24no—
423C2×D11—28no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—44no—
431C2×D11—44no—
432C2×D11—44no—
433C4×C11—24no—
434C4×C11—24no—
435C4×C11—44no—
436C4×C11—82no—
437Dic11—24no—
438Dic11—44no—
439Dic11—44no—
440Dic11—42no—
441Dic11—42no—
442C25—111no—
443C25C22×D1111yescharacteristic
444C22×Q8—224no—
445C22×Q8—222no—
446C22×Q8—222no—
447C22×Q8—222no—
448C22×Q8—442no—
449C22×D4—114no—
450C22×D4—222no—
451C22×D4—222no—
452C22×D4—222no—
453C22×D4—222no—
454C22×D4—222no—
455C22×D4—222no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—24no—
459C23×C4—42no—
460C23×C4—111no—
461C23×C4—112no—
462C23×C4—112no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—222no—
466C23×C4—222no—
467C23×C4—222no—
468C23×C4—224no—
469C23×C4—442no—
470C23×C4D4414yes—
471C23×C4C22×D1112yes—
472C23×C4C22×D1112yes—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C22⋊Q8—2232no—
476C4×D4—2232no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—118no—
479C2×C4⋊C4—224no—
480C2×C4⋊C4—222no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—224no—
485C2×C4⋊C4—224no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—442no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—222no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—224no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—442no—
506C2×C42—222no—
507C2×C42—222no—
508C2×C42—222no—
509#95—24no—
510#95—22no—
511#95—22no—
512#95—224no—
513#95—224no—
514#95—224no—
515#95—224no—
516#95—224no—
517C2×C11—44no—
518C2×C11#238811yescharacteristic
519C2×C11#240311yescharacteristic
520C2×C11#240911yescharacteristic
521C2×C11#243211yescharacteristic
522C2×C11#244912yes—
523C2×C11#245212yes—
524C2×C11#246112yes—
525C2×C11#246312yes—
526C2×C11#256411yescharacteristic
527C2×C11#263811yescharacteristic
528C2×C11#284811yescharacteristic
529D11—44no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—112no—
539C24—112no—
540C24—112no—
541C24—221no—
542C24—222no—
543C24—222no—
544C24—221no—
545C24—221no—
546C24—222no—
547C24—221no—
548C24—222no—
549C24C2×D4412yes—
550C24#434112yes—
551C24Q8×D1112yes—
552C24C23×D1111yescharacteristic
553C2×Q8—228no—
554C2×Q8—448no—
555C2×Q8—448no—
556C2×Q8—444no—
557C2×Q8—444no—
558C2×D4—228no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—228no—
562C2×D4—228no—
563C2×D4—228no—
564C2×D4—228no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—112no—
595C22×C4—228no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—222no—
602C22×C4—221no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—222no—
612C22×C4—221no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—448no—
621C22×C4—448no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4C2×D4412yes—
625C22×C4C2×D4412yes—
626C22×C4#433914yes—
627C22×C4D4×D1112yes—
628C22×C4D4×D1112yes—
629C22×C4D4×D1114yes—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—2216no—
633C4⋊C4—448no—
634C22⋊C4—48no—
635C22⋊C4—2216no—
636C22⋊C4—228no—
637C22⋊C4—2216no—
638C22⋊C4—228no—
639C22⋊C4—448no—
640C42—228no—
641C11#1472311yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—114no—
665C23—222no—
666C23—222no—
667C23—224no—
668C23—222no—
669C23—224no—
670C23—224no—
671C23—224no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—224no—
676C23—224no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—442no—
681C23—441no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23#6695014yes—
688C23C22×D4411yescharacteristic
689C23C2×#433912yes—
690C23C2×D4×D1112yes—
691C23C2×D4×D1111yescharacteristic
692C23C2×D4×D1111yescharacteristic
693C23C2×#434111yescharacteristic
694C23#6703712yes—
695C23C2×Q8×D1111yescharacteristic
696C23#41×D1111yescharacteristic
697C23#41×D1111yescharacteristic
698C23#6704312yes—
699Q8—4416no—
700D4—2232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—416no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—114no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—224no—
733C2×C4—222no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—4416no—
742C2×C4—441no—
743C2×C4—442no—
744C2×C4—441no—
745C2×C4—442no—
746C2×C4—441no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—441no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4#6693514yes—
757C2×C4#6693514yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—228no—
770C22—224no—
771C22—442no—
772C22—444no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—444no—
778C22—442no—
779C22—444no—
780C22#1062300811yescharacteristic
781C22C2×#6693511yescharacteristic
782C22C2×#6693511yescharacteristic
783C22#1062302411yescharacteristic
784C22#1062302612yes—
785C22C2×#6695011yescharacteristic
786C22#1062304212yes—
787C22#1062305511yescharacteristic
788C22#1062305711yescharacteristic
789C22#1062307812yes—
790C22#1062307912yes—
791C22#1062308212yes—
792C22#1062308312yes—
793C22#1062312112yes—
794C22#1062312112yes—
795C22#1062312912yes—
796C22#1062313711yescharacteristic
797C22#1062313711yescharacteristic
798C22D11×C22⋊Q811yescharacteristic
799C22D11×C22⋊Q811yescharacteristic
800C22#1062316312yes—
801C22#1062319112yes—
802C22#1062319312yes—
803C4—24no—
804C4—24no—
805C4—44no—
806C4—82no—
807C4—224no—
808C4—442no—
809C4—444no—
810C4—442no—
811C4—444no—
812C2—44no—
813C2—444no—
814C2#1307183211yescharacteristic
815C2#1307192911yescharacteristic
816C2#1307198211yescharacteristic
817C2#1307224411yescharacteristic
818C2#1307242412yes—
819C2#1307246312yes—
820C2#1307258812yes—
821C2#1307261412yes—
822C2#1307379611yescharacteristic
823C2#1307453611yescharacteristic
824C2#1307690411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×C22⋊#95C2
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
3. C2×#10622269C2semidirect
4. C2×#10622286C2semidirect
5. C2×#10622281C2semidirect
6. #13066870C2semidirect
7. #13066862C2semidirect
8. #13066861C2semidirect
10. #13066851C2semidirect
11. C11×C22⋊#95C2semidirect
60. C22×C22⋊D11Q8semidirect
106. C2×Dic11⋊C4D4semidirect
240. C22⋊#95D11semidirect
297. C22×D11C22⋊Q8semidirect
354. C2×Dic11C22⋊Q8semidirect
641. C11#14723semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C4×C22⋊D112
C2×#106222692
C2×#106222862
C2×#106222812
#130668702
#130668622
#130668612
#130668552
#130668512
C11×C22⋊#952
#1472311