Finite Group Databasebeta

← #14690488

Subgroups — #14690488

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic, complemented
2C2×#10622286C211yesmaximal, characteristic, complemented
3C2×#10622560C211yesmaximal, characteristic, complemented
4C2×#10622844C211yesmaximal, characteristic, complemented
5C2×#10622570C212yesmaximal
6C2×#10622570C211yesmaximal, characteristic
7#13066860C212yesmaximal, complemented
8#13066859C212yesmaximal, complemented
9Dic11⋊#95C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#393C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C2×#66997—28no—
20C2×#66997—24no—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C11×#393—24no—
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33#10622844—24no—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39#10622570—28no—
40#10622570—24no—
41#10622560—24no—
42#10622286—24no—
43C25×C11C2311yescharacteristic
44C24×D11C2311yescharacteristic
45C22×Q8×C11—24no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—42no—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—24no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11Q814yescomplemented
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C22×Dic22—22no—
65C22×Dic22—24no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—42no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—42no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—42no—
80#66997—232no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4D418yes—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—24no—
104C2×C4×Dic11D414yes—
105C11×#95—24no—
106C11×#95D414yescomplemented
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95D414yescomplemented
112#15144—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—22no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—22no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11C2×Q812yes—
124C24×C11C2411yescharacteristic
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—21no—
132C23×D11—22no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11C2×Q812yes—
136C2×Q8×C11—28no—
137C2×Q8×C11—48no—
138C2×Q8×C11—48no—
139C2×Q8×C11—44no—
140C2×Q8×C11—44no—
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—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—216no—
167C2×C22⋊D11—44no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—44no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
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—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11C2×D414yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D414yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×Q812yes—
196C22×Dic11#4114yes—
197C22×Dic11#4112yes—
198C22×Dic11#4114yes—
199C2×Dic22—28no—
200C2×Dic22—48no—
201C2×Dic22—48no—
202C2×Dic22—44no—
203C2×Dic22—44no—
204C11×C22⋊C4—48no—
205C11×C22⋊C4—44no—
206C22⋊Dic11—48no—
207C22⋊Dic11—44no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—44no—
211(C2×D11)⋊C4—44no—
212Dic11⋊C4—216no—
213Dic11⋊C4—216no—
214Dic11⋊C4—44no—
215C4×Dic11—28no—
216C4×Dic11—48no—
217C22×C4⋊Q8—111no—
218C2×#393—111no—
219C2×#393—111no—
220C2×#393—111no—
221C2×#393D1111yescharacteristic, complemented
222C2×#390—111no—
223C2×#390—112no—
224#1439—112no—
225#1439—112no—
226C4⋊#95—112no—
227C4×#95—111no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11C22×D411yescharacteristic
252C23×C11C22×D412yes—
253C23×C11C22×D411yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C22×Q811yescharacteristic
256C23×C11C2×#4112yes—
257C23×C11C2×#4111yescharacteristic
258C23×C11C2×#4112yes—
259C23×C11H(5,𝔽2)12yes—
260C23×C112−1+411yescharacteristic
261C23×C112−1+411yescharacteristic
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—24no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—42no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285Q8×C11—416no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
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—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11#12714yes—
310C22⋊D11—416no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
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—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11#12014yes—
335C2×Dic11C22⋊Q814yes—
336C2×Dic11C22⋊Q818yes—
337C2×Dic11#12414yes—
338C2×Dic11#12418yes—
339C2×Dic11#12414yes—
340Dic22—416no—
341C23×Q8—111no—
342C23×Q8C2×D1111yescharacteristic
343C23×D4—111no—
344C2×C4⋊Q8—224no—
345C2×C4⋊Q8—228no—
346C22×C4⋊C4—112no—
347C22×C4⋊C4—112no—
348C22×C4⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4C2×D1111yescharacteristic
356C22×C22⋊C4C2×D1112yes—
357C22×C42—111no—
358C22×C42—112no—
359#393—24no—
360#393—224no—
361#393—224no—
362#393—224no—
363#390—224no—
364#390—228no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95C2×D1112yes—
371C2×#95C2×D1111yescharacteristic
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—42no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—82no—
382C22×C11—82no—
383C22×C11C2×#12011yescharacteristic
384C22×C11C2×C22⋊Q811yescharacteristic
385C22×C11C2×C22⋊Q812yes—
386C22×C11C2×#12411yescharacteristic
387C22×C11C2×#12411yescharacteristic
388C22×C11C2×#12412yes—
389C22×C11C2×#12711yescharacteristic
390C22×C11#53212yes—
391C22×C11#53212yes—
392C22×C11#53511yescharacteristic
393C22×C11#53611yescharacteristic
394C22×C11#54212yes—
395C22×C11#54212yes—
396C22×C11D4212yes—
397C22×C11D4212yes—
398C22×C11#54711yescharacteristic
399C22×C11#54711yescharacteristic
400C22×C11#54812yes—
401C22×C11#54812yes—
402C22×C11D4×Q811yescharacteristic
403C22×C11D4×Q811yescharacteristic
404C22×C11#55412yes—
405C22×C11#55512yes—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—42no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—82no—
416C2×D11—82no—
417C4×C11—24no—
418C4×C11—44no—
419C4×C11—44no—
420C4×C11—81no—
421Dic11—24no—
422Dic11—44no—
423Dic11—44no—
424Dic11—81no—
425Dic11#39318yescomplemented
426C25—111no—
427C25C22×D1111yescharacteristic
428C22×Q8—24no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—42no—
433C22×Q8—224no—
434C22×Q8—222no—
435C22×Q8—222no—
436C22×Q8—222no—
437C22×Q8—442no—
438C22×D4—114no—
439C22×D4—222no—
440C22×D4—224no—
441C22×D4—222no—
442C22×D4—224no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—112no—
446C23×C4—112no—
447C23×C4—111no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1112yes—
450C23×C4C22×D1112yes—
451C23×C4C22×D1111yescharacteristic
452C4⋊Q8—2232no—
453C2×C4⋊C4—118no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—224no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—222no—
477C2×C22⋊C4—222no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—222no—
480C2×C22⋊C4—442no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C42—114no—
484C2×C42—224no—
485C2×C42—224no—
486C2×C42—224no—
487C2×C42—224no—
488#95—24no—
489#95—114no—
490#95—224no—
491#95—224no—
492#95—224no—
493#95—224no—
494#95C22⋊D1114yescomplemented
495C2×C11—82no—
496C2×C11C2×#39311yescharacteristic
497C2×C11#243311yescharacteristic
498C2×C11#243611yescharacteristic
499C2×C11#245212yes—
500C2×C11#245212yes—
501C2×C11#249112yes—
502C2×C11#249112yes—
503C2×C11#254211yescharacteristic
504C2×C11#256311yescharacteristic
505C2×C11#264011yescharacteristic
506C2×C11#285811yescharacteristic
507D11—82no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—21no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24—112no—
519C24—221no—
520C24—222no—
521C24—221no—
522C24—222no—
523C24—221no—
524C24—222no—
525C24—221no—
526C24—222no—
527C24—221no—
528C24—221no—
529C24Q8×D1112yes—
530C24C23×D1111yescharacteristic
531C2×Q8—28no—
532C2×Q8—48no—
533C2×Q8—48no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—228no—
537C2×Q8—448no—
538C2×Q8—448no—
539C2×Q8—444no—
540C2×Q8—444no—
541C2×D4—2216no—
542C2×D4—228no—
543C2×D4—444no—
544C2×D4—448no—
545C2×D4—444no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—112no—
566C22×C4—114no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—114no—
570C22×C4—112no—
571C22×C4—114no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4D4×D1114yes—
595C22×C4D4×D1112yes—
596C22×C4D4×D1112yes—
597C22×C4C2×C22⋊D1114yes—
598C22×C4C2×C22⋊D1112yes—
599C4⋊C4—2216no—
600C4⋊C4—2216no—
601C4⋊C4—444no—
602C22⋊C4—48no—
603C22⋊C4—44no—
604C22⋊C4—448no—
605C22⋊C4—448no—
606C22⋊C4—444no—
607C22⋊C4—444no—
608C22⋊C4—448no—
609C22⋊C4—444no—
610C42—228no—
611C42—448no—
612C11#1514411yescharacteristic, complemented, Sylow
613C23—22no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—222no—
637C23—224no—
638C23—222no—
639C23—222no—
640C23—224no—
641C23—442no—
642C23—441no—
643C23—441no—
644C23—442no—
645C23—441no—
646C23—442no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—441no—
656C23—442no—
657C23—441no—
658C23—442no—
659C23C2×D4×D1112yes—
660C23C2×D4×D1111yescharacteristic
661C23C2×D4×D1111yescharacteristic
662C23#6703712yes—
663C23C2×Q8×D1111yescharacteristic
664C23#6704011yescharacteristic
665C23#41×D1111yescharacteristic
666C23#41×D1112yes—
667C23#41×D1112yes—
668C23#6704311yescharacteristic
669C23C22×C22⋊D1111yescharacteristic
670Q8—416no—
671Q8—4416no—
672D4—4416no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
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—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—114no—
697C2×C4—118no—
698C2×C4—114no—
699C2×C4—118no—
700C2×C4—114no—
701C2×C4—114no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—441no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4#6699314yes—
726C22—44no—
727C22—44no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—82no—
732C22—82no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—444no—
738C22—444no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—882no—
743C22—882no—
744C22—881no—
745C22—881no—
746C22—881no—
747C22—881no—
748C22D11×#12011yescharacteristic
749C22#1062312112yes—
750C22#1062312311yescharacteristic
751C22D11×C22⋊Q812yes—
752C22D11×C22⋊Q811yescharacteristic
753C22#1062315911yescharacteristic
754C22#1062316211yescharacteristic
755C22#1062316311yescharacteristic
756C22#1062316412yes—
757C22#1062316712yes—
758C22#1062317112yes—
759C22#1062319912yes—
760C22#1062320012yes—
761C22#1062320112yes—
762C22D11×#12412yes—
763C22D11×#12411yescharacteristic
764C22D11×#12411yescharacteristic
765C22#1062320812yes—
766C22D4×C22⋊D1112yes—
767C22C2×#6699311yescharacteristic
768C22Q8×C22⋊D1111yescharacteristic
769C22#1062335511yescharacteristic
770C22#1062336312yes—
771C4—24no—
772C4—44no—
773C4—44no—
774C4—81no—
775C4—118no—
776C4—224no—
777C4—444no—
778C4—444no—
779C4—881no—
780C2—82no—
781C2—882no—
782C2D11×#39311yescharacteristic
783C2#1307225111yescharacteristic
784C2#1307226911yescharacteristic
785C2#1307246112yes—
786C2#1307246512yes—
787C2#1307297412yes—
788C2#1307297612yes—
789C2#1307356611yescharacteristic
790C2#1307378411yescharacteristic
791C2#1307455411yescharacteristic
792C2#1307697111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#393C2
prime radicalC23×C22⋊D11C22
hypercenterC2×#393D11
hypocenterC11#15144
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66997C2semidirect
2. C2×#10622286C2semidirect
3. C2×#10622560C2semidirect
4. C2×#10622844C2semidirect
7. #13066860C2semidirect
8. #13066859C2semidirect
9. Dic11⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C2×C11×#393C2semidirect
58. C22×C22⋊D11Q8semidirect
106. C11×#95D4semidirect
111. C11⋊#95D4semidirect
221. C2×#393D11semidirect
425. Dic11#393semidirect
494. #95C22⋊D11semidirect
612. C11#15144semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106222862
C2×#106225602
C2×#106228442
C2×#106225702
#130668602
#130668592
Dic11⋊#952
#95×Dic112
C2×C11×#3932
#1514411