Finite Group Databasebeta

← #14675959

Subgroups — #14675959

Order 2816.

2690 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×C4×D44C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622281C212yesmaximal, complemented
4C2×#10622280C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066868C212yesmaximal, complemented
7#13066862C212yesmaximal, complemented
8#13066846C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C2×C4×D44—28no—
26C2×C4×D44C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622281—28no—
38#10622280—24no—
39#10622278—28no—
40D11×#95—24no—
41C24×D11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C22×D44—24no—
53C22×D44—24no—
54C22×D44C2×C414yes—
55C22×D44D414yes—
56C22×D44Q814yes—
57C22×C4×D11—24no—
58C22×C4×D11—24no—
59C22×C4×D11—24no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—24no—
68C22×C4×D11—42no—
69C22×C4×D11—42no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11C2×C414yes—
73C22×C4×D11C2×C414yescomplemented
74C2×C42×C11—24no—
75C2×C42×C11C2×C414yescomplemented
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
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—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×(C2×D11)⋊C4C2×C414yescomplemented
88C2×(C2×D11)⋊C4D418yes—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11—42no—
93C2×C4⋊Dic11C2×C414yescomplemented
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—42no—
97C4×D44—232no—
98C11×#95—24no—
99C11×#95—24no—
100C11×#95—22no—
101C11×#95D414yescomplemented
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—22no—
106C11⋊#95—24no—
107C11⋊#95—42no—
108#13899—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—21no—
120C23×D11—22no—
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11C22×C412yes—
125C23×D11C22×C412yes—
126C23×D11C2×D412yes—
127C23×D11C2×D414yes—
128C23×D11C2×D412yes—
129C23×D11C2×Q812yes—
130C23×D11C2×Q812yes—
131C23×D11#4114yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
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×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×Q812yes—
160C22×C4×C11#4112yes—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
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×Dic11C22×C412yes—
182C22×Dic11C22×C412yes—
183C22×Dic11C2×D414yes—
184C22×Dic11#4114yes—
185C2×D44—28no—
186C2×D44—28no—
187C2×D44—216no—
188C2×D44—216no—
189C2×D44C4⋊C4116yescomplemented
190C2×C4×D11—216no—
191C2×C4×D11—28no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—28no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—48no—
198C2×C4×D11—48no—
199C2×C4×D11—48no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11—48no—
203C2×C4×D11—48no—
204C2×C4×D11—48no—
205C2×C4×D11—48no—
206C2×C4×D11—48no—
207C42×C11—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4C22⋊C4116yescomplemented
213C4⋊Dic11—28no—
214C4⋊Dic11—48no—
215Dic11⋊C4—48no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×#385—112no—
219C2×#380—111no—
220C22×#95—111no—
221#1441—112no—
222#1439—112no—
223C4⋊#95—111no—
224#1434D1111yescharacteristic, complemented
225C22⋊#95—111no—
226C22⋊#95—111no—
227C23×C11C23×C411yescharacteristic
228C23×C11C22×D411yescharacteristic
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231C23×C11C22×Q811yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11H(5,𝔽2)12yes—
236C23×C11H(5,𝔽2)11yescharacteristic
237C23×C112−1+411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—22no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—22no—
252C22×D11—24no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—22no—
265C22×D11—24no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—24no—
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×D11C2×C22⋊C414yes—
279C22×D11C2×C4⋊C414yes—
280C22×D11C2×C4⋊C414yes—
281C22×D11#11714yes—
282C22×D11#12118yes—
283C22×D11C22⋊Q818yes—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
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—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
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×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11C2×C22⋊C414yes—
311C2×C4×C11C2×C4⋊C414yes—
312C2×C4×C11C4×D414yes—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11C2×C22⋊C414yes—
337D44—232no—
338C4×D11—416no—
339C4×D11—416no—
340C4×D11—432no—
341C23×D4—111no—
342C24×C4—111no—
343C24×C4—111no—
344C24×C4—112no—
345C2×C4×D4—118no—
346C2×C4×D4—228no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C42C2×D1111yescharacteristic
356#386—228no—
357#385—228no—
358#380—224no—
359C2×#95—111no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—224no—
366C2×#95C2×D1111yescharacteristic
367C2×#95C2×D1112yes—
368C2×#95C2×D1112yes—
369C2×#95C2×D1111yescharacteristic
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11C22×C4⋊C411yescharacteristic
372C22×C11C2×#11711yescharacteristic
373C22×C11C2×C4×D411yescharacteristic
374C22×C11C4×#4111yescharacteristic
375C22×C11#51811yescharacteristic
376C22×C11#52011yescharacteristic
377C22×C11C2×#12112yes—
378C22×C11C2×C22⋊Q812yes—
379C22×C11#52512yes—
380C22×C11#52912yes—
381C22×C11#53812yes—
382C22×C11#53912yes—
383C22×C11D4212yes—
384C22×C11D4211yescharacteristic
385C22×C11#54612yes—
386C22×C11#54612yes—
387C22×C11#54612yes—
388C22×C11#54711yescharacteristic
389C22×C11#54712yes—
390C22×C11D4×Q811yescharacteristic
391C22×C11#55411yescharacteristic
392C22×C11#55412yes—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—28no—
399C2×D11—28no—
400C2×D11—28no—
401C2×D11—28no—
402C2×D11—24no—
403C2×D11—24no—
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—42no—
414C2×D11#38018yescomplemented
415C4×C11—24no—
416C4×C11—24no—
417C4×C11—24no—
418C4×C11—44no—
419C4×C11—82no—
420Dic11—24no—
421Dic11—42no—
422Dic11—44no—
423Dic11—82no—
424C25—111no—
425C25—111no—
426C22×D4—114no—
427C22×D4—114no—
428C22×D4—114no—
429C22×D4—224no—
430C22×D4—224no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—112no—
434C23×C4—114no—
435C23×C4—114no—
436C23×C4—112no—
437C23×C4—224no—
438C23×C4—224no—
439C23×C4—224no—
440C23×C4—224no—
441C23×C4—224no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—442no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4C22×D1112yes—
453C23×C4C22×D1112yes—
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C4×D4—2232no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—442no—
465C2×C4⋊C4—442no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C42—24no—
480C2×C42C4×D1114yescomplemented
481#95—22no—
482#95—24no—
483#95—24no—
484#95—224no—
485#95—224no—
486#95—222no—
487#95—222no—
488#95—224no—
489#95—442no—
490#95D4414yescomplemented
491C2×C11C2×#38011yescharacteristic
492C2×C11#229011yescharacteristic
493C2×C11#231811yescharacteristic
494C2×C11D4×C22⋊C411yescharacteristic
495C2×C11#233911yescharacteristic
496C2×C11D4×C4⋊C411yescharacteristic
497C2×C11#234911yescharacteristic
498C2×C11#242412yes—
499C2×C11#242512yes—
500C2×C11#244912yes—
501C2×C11#245012yes—
502D11—28no—
503D11—44no—
504C24—112no—
505C24—114no—
506C24—112no—
507C24—112no—
508C24—114no—
509C24—112no—
510C24—112no—
511C24—112no—
512C24—221no—
513C24—221no—
514C24—222no—
515C24—221no—
516C24—222no—
517C24—221no—
518C24—221no—
519C24—221no—
520C24—222no—
521C24—222no—
522C24—222no—
523C24—221no—
524C24—222no—
525C24—221no—
526C24C23×D1111yescharacteristic
527C2×D4—1116no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—2216no—
531C2×D4—2216no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—112no—
553C22×C4—114no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—228no—
557C22×C4—228no—
558C22×C4—2216no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—222no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—228no—
573C22×C4—228no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—444no—
582C22×C4—444no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4—448no—
586C22×C4—448no—
587C22×C4—448no—
588C22×C4—448no—
589C22×C4—448no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4C2×C4×D1112yes—
594C22×C4C2×C4×D1112yes—
595C22×C4C2×C4×D1112yes—
596C22×C4C2×D4414yes—
597C22×C4C2×D4412yes—
598C22×C4#433912yes—
599C22×C4D4×D1114yes—
600C22×C4D4×D1112yes—
601C22×C4Q8×D1112yes—
602C4⋊C4—228no—
603C4⋊C4—448no—
604C4⋊C4—448no—
605C22⋊C4—1116no—
606C22⋊C4—228no—
607C22⋊C4—448no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—28no—
611C11#1389911yescharacteristic, complemented, Sylow
612C23—114no—
613C23—114no—
614C23—114no—
615C23—118no—
616C23—118no—
617C23—114no—
618C23—224no—
619C23—224no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—224no—
625C23—224no—
626C23—222no—
627C23—224no—
628C23—224no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—224no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C22×C4×D1111yescharacteristic
659C23C22×D4411yescharacteristic
660C23C2×#433911yescharacteristic
661C23C2×D4×D1112yes—
662C23C2×D4×D1111yescharacteristic
663C23C2×Q8×D1111yescharacteristic
664C23#41×D1112yes—
665C23#41×D1112yes—
666C23#6704211yescharacteristic
667C23#6704212yes—
668C23#6704311yescharacteristic
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
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—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—114no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—4416no—
708C2×C4—4416no—
709C2×C4—4432no—
710C2×C4—442no—
711C2×C4—442no—
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—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4C4×D4414yes—
724C2×C4C22⋊C4×D1114yes—
725C2×C4C4⋊C4×D1114yes—
726C22—118no—
727C22—228no—
728C22—228no—
729C22—228no—
730C22—228no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—224no—
736C22—224no—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—444no—
741C22—444no—
742C22—444no—
743C22—444no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22C2×C4×D4411yescharacteristic
749C22C2×C22⋊C4×D1111yescharacteristic
750C22C2×C4⋊C4×D1111yescharacteristic
751C22D11×#11711yescharacteristic
752C22#1062305211yescharacteristic
753C22#1062305311yescharacteristic
754C22#1062305411yescharacteristic
755C22#1062305512yes—
756C22#1062305912yes—
757C22D4×D4411yescharacteristic
758C22D4×D4412yes—
759C22#1062308112yes—
760C22#1062308211yescharacteristic
761C22Q8×D4411yescharacteristic
762C22#1062311011yescharacteristic
763C22D11×#12112yes—
764C22D11×C22⋊Q812yes—
765C22#1062318512yes—
766C22#1062318612yes—
767C22#1062320712yes—
768C22#1062322112yes—
769C22#1062323512yes—
770C22#1062323812yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—44no—
775C4—82no—
776C4—224no—
777C4—444no—
778C4—442no—
779C4—882no—
780C2—228no—
781C2—444no—
782C2D11×#38011yescharacteristic
783C2#1307106011yescharacteristic
784C2#1307124711yescharacteristic
785C2C22⋊C4×D4411yescharacteristic
786C2#1307144011yescharacteristic
787C2C4⋊C4×D4411yescharacteristic
788C2#1307152411yescharacteristic
789C2#1307215712yes—
790C2#1307217212yes—
791C2#1307243012yes—
792C2#1307243912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#13899
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622281C2semidirect
4. C2×#10622280C2semidirect
5. C2×D11×#95C2semidirect
6. #13066868C2semidirect
7. #13066862C2semidirect
8. #13066846C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1434C2semidirect
26. C2×C4×D44C4semidirect
73. C22×C4×D11C2×C4semidirect
75. C2×C42×C11C2×C4semidirect
87. C2×(C2×D11)⋊C4C2×C4semidirect
93. C2×C4⋊Dic11C2×C4semidirect
101. C11×#95D4semidirect
189. C2×D44C4⋊C4semidirect
212. (C2×D11)⋊C4C22⋊C4semidirect
224. #1434D11semidirect
414. C2×D11#380semidirect
480. C2×C42C4×D11semidirect
490. #95D44semidirect
611. C11#13899semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106222782
C2×#106222812
C2×#106222802
C2×D11×#952
#130668682
#130668622
#130668462
(C2×D11)⋊#952
C11×#14342
#1389911