Finite Group Databasebeta

← #14676066

Subgroups — #14676066

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal, complemented
2C2×#10622824C211yesmaximal, characteristic, complemented
3C2×#10622825C211yesmaximal, characteristic, complemented
4#13066869C212yesmaximal, complemented
5#13066857C212yesmaximal
6#13066853C212yesmaximal, complemented
7#13066843C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C2×C4×D4×C11—28no—
16C2×C4×D4×C11C418yescomplemented
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×C4×Dic11C2212yes—
27#10622825—24no—
28#10622824—24no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39#10622564—28no—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—24no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11C2×C414yes—
47C23×C4×C11—24no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—24no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11C2×C414yes—
56C23×C4×C11C2×C414yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C4×D4×C11—232no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4C2×C414yes—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4C2×C414yes—
71C2×C11×C22⋊C4C2×C414yes—
72C2×C11×C22⋊C4D418yes—
73C2×C42×C11—24no—
74C2×C42×C11C2×C414yes—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11—42no—
87C2×C4⋊Dic11—24no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—42no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—42no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95D414yescomplemented
103#13912—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11C22×C412yes—
122C24×C11C22×C412yes—
123C24×C11C2×D414yes—
124C24×C11#4112yes—
125C24×C11#4112yes—
126C24×C11C2411yescharacteristic
127C2×D4×C11—216no—
128C2×D4×C11—216no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—28no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11—28no—
150C22×C4×C11—28no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4114yes—
166C22×C4×C11#4112yes—
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×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11C2×D414yes—
194C22×Dic11#4114yes—
195C11×C4⋊C4—28no—
196C11×C22⋊C4—28no—
197C11×C22⋊C4C22⋊C4116yescomplemented
198C42×C11—28no—
199C22⋊Dic11—48no—
200C22⋊Dic11—48no—
201C22⋊Dic11—48no—
202C22⋊Dic11—48no—
203C4⋊Dic11—48no—
204C4×Dic11—48no—
205C22×C4×D4D1111yescharacteristic
206C2×#388—112no—
207C2×#381—111no—
208C2×#380—111no—
209#1441—112no—
210#1438—112no—
211#1437—112no—
212#1434—111no—
213C22⋊#95—111no—
214C22⋊#95—111no—
215C4×#95—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—22no—
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—41no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—41no—
258C23×C11—42no—
259C23×C11—41no—
260C23×C11C2×C22⋊C414yes—
261C23×C11#11714yes—
262C23×C11C23×C411yescharacteristic
263C23×C11C22×D411yescharacteristic
264C23×C11C22×D412yes—
265C23×C11C2×#4112yes—
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4112yes—
270C23×C11H(5,𝔽2)12yes—
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C112−1+411yescharacteristic
273D4×C11—232no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—416no—
294C2×C4×C11—416no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11C2×C22⋊C414yes—
298C2×C4×C11C2×C22⋊C414yes—
299C2×C4×C11#11714yes—
300C2×C4×C11C4×D414yes—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
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—
328C2×Dic11—42no—
329C23×D4C2×D1111yescharacteristic
330C24×C4C2×D1111yescharacteristic
331C24×C4C2×D1111yescharacteristic
332C2×C4×D4—28no—
333C2×C4×D4Dic1118yescomplemented
334C22×C4⋊C4—112no—
335C22×C4⋊C4C2×D1111yescharacteristic
336C22×C22⋊C4—112no—
337C22×C22⋊C4—112no—
338C22×C22⋊C4—112no—
339C22×C22⋊C4—112no—
340C22×C22⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4C2×D1111yescharacteristic
342C22×C42—112no—
343C22×C42C2×D1111yescharacteristic
344#388—228no—
345#381—224no—
346#380—224no—
347C2×#95—111no—
348C2×#95—111no—
349C2×#95—112no—
350C2×#95—111no—
351C2×#95—111no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11C22×C22⋊C411yescharacteristic
380C22×C11C2×#11711yescharacteristic
381C22×C11C2×#11711yescharacteristic
382C22×C11C2×C4×D411yescharacteristic
383C22×C11C4×#4111yescharacteristic
384C22×C11#51811yescharacteristic
385C22×C11#52011yescharacteristic
386C22×C11#52512yes—
387C22×C11#52512yes—
388C22×C11#52912yes—
389C22×C11#53212yes—
390C22×C11#54012yes—
391C22×C11#54212yes—
392C22×C11D4212yes—
393C22×C11#54611yescharacteristic
394C22×C11#54612yes—
395C22×C11#54612yes—
396C22×C11#54712yes—
397C22×C11#54811yescharacteristic
398C22×C11#55112yes—
399C22×C11#55211yescharacteristic
400C22×C11#55312yes—
401C22×C11#55311yescharacteristic
402C4×C11—24no—
403C4×C11—24no—
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—42no—
407Dic11—44no—
408Dic11—44no—
409Dic11—82no—
410Dic11—82no—
411C25C22×D1111yescharacteristic
412C25C22×D1111yescharacteristic
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4C2×Dic1114yes—
418C23×C4—24no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—112no—
427C23×C4—112no—
428C23×C4—112no—
429C23×C4—112no—
430C23×C4C2×Dic1114yes—
431C23×C4C2×Dic1114yes—
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C4×D4—232no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—224no—
440C2×C4⋊C4—224no—
441C2×C4⋊C4—442no—
442C2×C4⋊C4C2×Dic1114yes—
443C2×C22⋊C4—24no—
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—224no—
451C2×C22⋊C4—224no—
452C2×C22⋊C4—442no—
453C2×C22⋊C4—442no—
454C2×C22⋊C4—442no—
455C2×C22⋊C4—442no—
456C2×C22⋊C4C2×Dic1114yes—
457C2×C22⋊C4C2×Dic1114yes—
458C2×C22⋊C4C22⋊D1118yes—
459C2×C42—24no—
460C2×C42—224no—
461C2×C42—224no—
462C2×C42—442no—
463C2×C42C2×Dic1114yes—
464#95—114no—
465#95—224no—
466#95—224no—
467#95—224no—
468#95—222no—
469#95—222no—
470#95—222no—
471#95—224no—
472#95—224no—
473#95—442no—
474C2×C11—44no—
475C2×C11—44no—
476C2×C11#228011yescharacteristic
477C2×C11#229311yescharacteristic
478C2×C11#231911yescharacteristic
479C2×C11D4×C22⋊C411yescharacteristic
480C2×C11#233911yescharacteristic
481C2×C11#235211yescharacteristic
482C2×C11#235311yescharacteristic
483C2×C11#245712yes—
484C2×C11#246112yes—
485C2×C11#246412yes—
486C2×C11#246812yes—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24#433912yes—
505C24#433912yes—
506C24C22×Dic1112yes—
507C24C22×Dic1112yes—
508C24C2×C22⋊D1114yes—
509C24C23×D1111yescharacteristic
510C2×D4—216no—
511C2×D4—216no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—28no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—28no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—114no—
541C22×C4—114no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
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#433914yes—
569C22×C4D4×D1112yes—
570C22×C4#434112yes—
571C22×C4C22×Dic1112yes—
572C22×C4C22×Dic1112yes—
573C22×C4C22×Dic1112yes—
574C22×C4C22×Dic1112yes—
575C22×C4C22×Dic1112yes—
576C22×C4C2×C22⋊D1114yes—
577C22×C4C2×C22⋊D1114yes—
578C4⋊C4—28no—
579C4⋊C4—448no—
580C22⋊C4—28no—
581C22⋊C4—448no—
582C22⋊C4—448no—
583C22⋊C4—448no—
584C22⋊C4—448no—
585C22⋊C4C22⋊Dic11116yescomplemented
586C42—28no—
587C42—448no—
588C11#1391211yescharacteristic, complemented, Sylow
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—42no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23#6697914yes—
634C23C2×C22⋊Dic1114yes—
635C23C2×#433911yescharacteristic
636C23C2×#433912yes—
637C23C2×#433911yescharacteristic
638C23C2×D4×D1111yescharacteristic
639C23C2×#434111yescharacteristic
640C23#6703712yes—
641C23#41×D1112yes—
642C23#6704211yescharacteristic
643C23#6704311yescharacteristic
644C23C23×Dic1111yescharacteristic
645C23C22×C22⋊D1112yes—
646D4—232no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—224no—
671C2×C4—224no—
672C2×C4—224no—
673C2×C4—224no—
674C2×C4—224no—
675C2×C4—224no—
676C2×C4—442no—
677C2×C4—442no—
678C2×C4—442no—
679C2×C4—442no—
680C2×C4—442no—
681C2×C4—442no—
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#6697914yes—
699C2×C4D4×Dic1114yes—
700C2×C4C2×C22⋊Dic1114yes—
701C2×C4C2×C22⋊Dic1114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—44no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—44no—
718C22—44no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22#1062307112yes—
725C22#1062307211yescharacteristic
726C22#1062307912yes—
727C22#1062308111yescharacteristic
728C22#1062308311yescharacteristic
729C22#1062308712yes—
730C22#1062308812yes—
731C22#1062309212yes—
732C22#1062309312yes—
733C22#1062309611yescharacteristic
734C22C2×#6697911yescharacteristic
735C22C2×#6697911yescharacteristic
736C22#1062332212yes—
737C22#1062332212yes—
738C22C2×D4×Dic1111yescharacteristic
739C22#1062332911yescharacteristic
740C22D4×C22⋊D1112yes—
741C22#1062333712yes—
742C22#1062335512yes—
743C22#41×Dic1111yescharacteristic
744C22#1062335811yescharacteristic
745C22#1062336012yes—
746C22C22×C22⋊Dic1111yescharacteristic
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—444no—
753C4—444no—
754C4—882no—
755C4—882no—
756C2—44no—
757C2—44no—
758C2#1307099911yescharacteristic
759C2#1307108111yescharacteristic
760C2#1307125911yescharacteristic
761C2D4×C22⋊Dic1111yescharacteristic
762C2#1307144611yescharacteristic
763C2#1307154511yescharacteristic
764C2#1307155611yescharacteristic
765C2#1307251712yes—
766C2#1307257712yes—
767C2#1307261612yes—
768C2#1307267612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13912
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
2. C2×#10622824C2semidirect
3. C2×#10622825C2semidirect
4. #13066869C2semidirect
6. #13066853C2semidirect
7. #13066843C2semidirect
8. #13066839C2semidirect
9. #13066839C2semidirect
10. C4×C11⋊#95C2semidirect
16. C2×C4×D4×C11C4semidirect
102. C11⋊#95D4semidirect
197. C11×C22⋊C4C22⋊C4semidirect
333. C2×C4×D4Dic11semidirect
585. C22⋊C4C22⋊Dic11semidirect
588. C11#13912semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228242
C2×#106228252
#130668692
#130668572
#130668532
#130668432
#130668392
C4×C11⋊#952
C22×C4×D4×C112
#1391211