Finite Group Databasebeta

← #14685008

Subgroups — #14685008

Order 2816.

2746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622283C212yesmaximal, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622571C211yesmaximal, characteristic
6C2×#10622563C211yesmaximal, characteristic, complemented
7#13066852C212yesmaximal, complemented
8#13066850C212yesmaximal, complemented
9#13066840C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2212yes—
24C22×C4×Dic11—24no—
25C22×C4×Dic11—28no—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30#10622826—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38#10622571—24no—
39#10622571C418yescomplemented
40#10622563—24no—
41#10622283—28no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11D414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11C2×C414yes—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—24no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—24no—
68C23×Dic11C2×C414yes—
69C23×Dic11D414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4C2×C414yes—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
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)⋊C4C2×C418yescomplemented
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11—24no—
97C2×C4×Dic11—232no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11D418yescomplemented
104C11×#95—24no—
105C11×#95—24no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95C2×C418yescomplemented
113#14696—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11C22×C412yes—
119C24×C11C2×D412yes—
120C24×C11C2×D412yes—
121C24×C11#4112yes—
122C24×C11#4112yes—
123C24×C11#4112yes—
124C24×C11#4112yes—
125C24×C11C2411yescharacteristic
126C23×D11—22no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11C22×C412yes—
137C22×C4×C11—216no—
138C22×C4×C11—216no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—28no—
147C22×C4×C11—28no—
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—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4114yes—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—44no—
170C2×C22⋊D11—44no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11—44no—
173C22×Dic11—28no—
174C22×Dic11—28no—
175C22×Dic11—28no—
176C22×Dic11—28no—
177C22×Dic11—216no—
178C22×Dic11—216no—
179C22×Dic11—216no—
180C22×Dic11—216no—
181C22×Dic11—28no—
182C22×Dic11—28no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C22×C412yes—
208C22×Dic11C22×C414yes—
209C22×Dic11C2×D414yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11#4114yes—
213C22×Dic11#4114yes—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—44no—
216C22⋊Dic11—44no—
217(C2×D11)⋊C4—216no—
218(C2×D11)⋊C4—48no—
219(C2×D11)⋊C4—44no—
220(C2×D11)⋊C4—44no—
221C4⋊Dic11—48no—
222C4×Dic11—216no—
223C4×Dic11—216no—
224C23×C42—111no—
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386—111no—
229C2×#385—111no—
230#1437—112no—
231#1436—112no—
232#1434—112no—
233C22⋊#95—111no—
234C22⋊#95D1111yescharacteristic, complemented
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11#11714yes—
252C23×C11C4×D414yes—
253C23×C11C4×D414yes—
254C23×C11#12114yes—
255C23×C11#12314yes—
256C23×C11#12414yes—
257C23×C11#12614yes—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D412yes—
261C23×C11C22×D411yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4112yes—
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4112yes—
268C23×C11C2×#4112yes—
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—24no—
274C22×D11—41no—
275C22×D11—42no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C2×C4×C11—232no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11#12014yes—
316C2×C4×C11#12314yes—
317C22⋊D11—416no—
318C2×Dic11—232no—
319C2×Dic11—232no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—42no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11C4×D418yes—
350C2×Dic11#12118yes—
351C23×D4—111no—
352C24×C4—111no—
353C24×C4—111no—
354C24×C4C2×D1111yescharacteristic
355C22×C4⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4C2×D1111yescharacteristic
362C22×C22⋊C4C2×D1111yescharacteristic
363C22×C42—112no—
364C22×C42—112no—
365C22×C42—228no—
366C22×C42—224no—
367#388—228no—
368#386—118no—
369#386—224no—
370#386—224no—
371#385—224no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—111no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95—111no—
379C2×#95C2×D1112yes—
380C2×#95C2×D1112yes—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—28no—
384C22×C11—28no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—28no—
388C22×C11—24no—
389C22×C11—28no—
390C22×C11—24no—
391C22×C11#38818yescomplemented
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C2×C4×D412yes—
396C22×C11C4×#4112yes—
397C22×C11C2×#12011yescharacteristic
398C22×C11C2×#12111yescharacteristic
399C22×C11C2×#12112yes—
400C22×C11C2×#12311yescharacteristic
401C22×C11C2×#12311yescharacteristic
402C22×C11#52511yescharacteristic
403C22×C11#52511yescharacteristic
404C22×C11#52512yes—
405C22×C11#52512yes—
406C22×C11#52512yes—
407C22×C11#52512yes—
408C22×C11C2×#12411yescharacteristic
409C22×C11C2×#12611yescharacteristic
410C22×C11#52912yes—
411C22×C11#52912yes—
412C22×C11#52912yes—
413C22×C11#52912yes—
414C22×C11#53212yes—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—42no—
418C2×D11—44no—
419C2×D11—42no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—82no—
423C2×D11—82no—
424C2×D11—81no—
425C2×D11—81no—
426C4×C11—24no—
427C4×C11—24no—
428C4×C11—44no—
429C4×C11—82no—
430Dic11—28no—
431Dic11—28no—
432Dic11—42no—
433Dic11—81no—
434Dic11—81no—
435C25—111no—
436C25C22×D1111yescharacteristic
437C22×D4—114no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—222no—
441C22×D4—222no—
442C22×D4—222no—
443C22×D4—222no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—112no—
449C23×C4—112no—
450C23×C4—114no—
451C23×C4—114no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—224no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—222no—
460C23×C4—222no—
461C23×C4—222no—
462C23×C4—222no—
463C23×C4D4414yes—
464C23×C4C22×D1112yes—
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C2×C4⋊C4—224no—
469C2×C4⋊C4—224no—
470C2×C4⋊C4—224no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—118no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—222no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4C4×D1114yes—
490C2×C42—118no—
491C2×C42—224no—
492C2×C42—224no—
493C2×C42—2232no—
494C2×C42—224no—
495C2×C42—224no—
496C2×C42—224no—
497#95—24no—
498#95—24no—
499#95—118no—
500#95—224no—
501#95—224no—
502#95—224no—
503#95—224no—
504#95—222no—
505#95—222no—
506C2×C11—28no—
507C2×C11C2×#38811yescharacteristic
508C2×C11#229012yes—
509C2×C11C4×#12011yescharacteristic
510C2×C11C4×#12112yes—
511C2×C11C4×#12311yescharacteristic
512C2×C11#284711yescharacteristic
513C2×C11#284911yescharacteristic
514C2×C11#285012yes—
515C2×C11#285212yes—
516C2×C11#285311yescharacteristic
517C2×C11#285411yescharacteristic
518D11—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—112no—
524C24—221no—
525C24—221no—
526C24—222no—
527C24—221no—
528C24—222no—
529C24—221no—
530C24—221no—
531C24—221no—
532C24—222no—
533C24—222no—
534C24C2×C4×D1112yes—
535C24C2×D4412yes—
536C24#433912yes—
537C24D4×D1112yes—
538C24#434112yes—
539C24#434112yes—
540C24#434312yes—
541C24C23×D1111yescharacteristic
542C2×D4—228no—
543C2×D4—228no—
544C2×D4—228no—
545C2×D4—444no—
546C2×D4—444no—
547C2×D4—444no—
548C2×D4—444no—
549C22×C4—216no—
550C22×C4—216no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—114no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—114no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—112no—
580C22×C4—2216no—
581C22×C4—2216no—
582C22×C4—228no—
583C22×C4—228no—
584C22×C4—228no—
585C22×C4—228no—
586C22×C4—2216no—
587C22×C4—2216no—
588C22×C4—228no—
589C22×C4—228no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—221no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4C2×C4×D1114yes—
615C22×C4C2×D4412yes—
616C22×C4C2×D4412yes—
617C22×C4D4×D1114yes—
618C22×C4#434114yes—
619C4⋊C4—448no—
620C22⋊C4—28no—
621C22⋊C4—44no—
622C22⋊C4—2216no—
623C22⋊C4—448no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C42—2216no—
628C42—2216no—
629C11#1469611yescharacteristic, complemented, Sylow
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23—224no—
650C23—224no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23C4×D4414yes—
670C23(C22⋊D11)⋊C414yes—
671C23#6693814yes—
672C23#6693914yes—
673C23#6694514yes—
674C23#6694814yes—
675C23#6695114yes—
676C23C22×C4×D1111yescharacteristic
677C23C22×D4411yescharacteristic
678C23C2×#433911yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×D4×D1112yes—
681C23C2×#434111yescharacteristic
682C23C2×#434111yescharacteristic
683C23C2×#434112yes—
684C23C2×#434311yescharacteristic
685C23#41×D1112yes—
686C23#41×D1112yes—
687D4—4416no—
688C2×C4—232no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—118no—
712C2×C4—118no—
713C2×C4—2232no—
714C2×C4—2232no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4#6693514yes—
745C2×C4#6693914yes—
746C22—24no—
747C22—28no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—28no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—24no—
756C22—442no—
757C22—444no—
758C22—442no—
759C22—442no—
760C22—444no—
761C22—881no—
762C22—881no—
763C22—882no—
764C22—882no—
765C22—881no—
766C22—881no—
767C22#1062228318yescomplemented
768C22C2×C4×D4411yescharacteristic
769C22C2×(C22⋊D11)⋊C411yescharacteristic
770C22C2×#6693511yescharacteristic
771C22C2×#6693811yescharacteristic
772C22C2×#6693911yescharacteristic
773C22C2×#6693911yescharacteristic
774C22C2×#6694511yescharacteristic
775C22C2×#6694811yescharacteristic
776C22C2×#6695111yescharacteristic
777C22#1062305511yescharacteristic
778C22#1062305511yescharacteristic
779C22C4×#434112yes—
780C22#1062306912yes—
781C22C4×D4×D1112yes—
782C22#1062307812yes—
783C22#1062311712yes—
784C22#1062311712yes—
785C22#1062312712yes—
786C22D11×#12112yes—
787C22#1062315512yes—
788C22#1062315812yes—
789C22#1062318012yes—
790C22#1062318012yes—
791C4—24no—
792C4—24no—
793C4—44no—
794C4—82no—
795C4—228no—
796C4—228no—
797C4—442no—
798C4—881no—
799C4—881no—
800C2—28no—
801C2—882no—
802C2C2×#1062228311yescharacteristic
803C2#1307105212yes—
804C2C4×#6693511yescharacteristic
805C2#1307112612yes—
806C2C4×#6693911yescharacteristic
807C2#1307689911yescharacteristic
808C2#1307691011yescharacteristic
809C2#1307691312yes—
810C2#1307693312yes—
811C2#1307693911yescharacteristic
812C2#1307694811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14696
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C23×C4×Dic11C2semidirect
2. C2×#10622283C2semidirect
6. C2×#10622563C2semidirect
7. #13066852C2semidirect
8. #13066850C2semidirect
9. #13066840C2semidirect
10. #13066838C2semidirect
11. C11×C22⋊#95C2semidirect
39. #10622571C4semidirect
93. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×C4×Dic11D4semidirect
112. C11⋊#95C2×C4semidirect
234. C22⋊#95D11semidirect
391. C22×C11#388semidirect
629. C11#14696semidirect
767. C22#10622283semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
C2×#106222832
C2×#106228262
C2×#106225712
C2×#106225632
#130668522
#130668502
#130668402
#130668382
C11×C22⋊#952
#1469611