Finite Group Databasebeta

← #14680298

Subgroups — #14680298

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal, complemented
3C2×#10622570C212yesmaximal
4C2×#10622589C211yesmaximal, characteristic, complemented
5C2×#10622261C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066860C212yesmaximal, complemented
9#13066859C212yesmaximal, complemented
10#13066858C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×#66938—24no—
29C2×#66938—24no—
30C2×#66938C418yescomplemented
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622589—24no—
39#10622570—28no—
40#10622261—24no—
41#10622259—28no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11C2×C414yes—
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—24no—
61C22×Dic22—24no—
62C22×Dic22C2×C414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—42no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4C2×C414yes—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2×C414yes—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C414yes—
88C2×(C2×D11)⋊C4C2×C414yes—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—42no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—42no—
96C2×Dic11⋊C4—42no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11C2×C414yes—
100C2×C4×Dic11D418yes—
101C2×C4×Dic11D414yes—
102C2×C4×Dic11D414yes—
103#66938—232no—
104C11×#95—24no—
105C11×#95—22no—
106C11⋊#95—24no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111#14273—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—21no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—22no—
122C24×C11C22×C412yes—
123C24×C11C2411yescharacteristic
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—21no—
129C23×D11—22no—
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—22no—
134C23×D11C22×C412yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
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×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—44no—
163C2×C22⋊D11—44no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C412yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C2×D414yes—
189C22×Dic11C2×D412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D414yes—
194C22×Dic11#4114yes—
195C2×Dic22—28no—
196C2×Dic22—216no—
197C2×Dic22—48no—
198C2×Dic22—44no—
199C2×Dic22—44no—
200C11×C4⋊C4—44no—
201C11×C22⋊C4—28no—
202C11×C22⋊C4—48no—
203C22⋊Dic11—28no—
204C22⋊Dic11—48no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209C4⋊Dic11—44no—
210Dic11⋊C4—48no—
211Dic11⋊C4—48no—
212C4×Dic11—216no—
213C4×Dic11C22⋊C4116yescomplemented
214C22×#124—111no—
215C2×#391—112no—
216C2×#390—112no—
217C2×#384—111no—
218C2×#376—111no—
219#1439—112no—
220#1439—111no—
221#1439—111no—
222#1439—112no—
223#1439—111no—
224#1439D1111yescharacteristic, complemented
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—42no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—41no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11C23×C411yescharacteristic
249C23×C11C22×D411yescharacteristic
250C23×C11C22×D411yescharacteristic
251C23×C11C22×D412yes—
252C23×C11C2×#4112yes—
253C23×C11H(5,𝔽2)11yescharacteristic
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C112−1+411yescharacteristic
257C23×C112−1+412yes—
258C23×C112−1+411yescharacteristic
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—42no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—41no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C2×C4×C11—24no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—42no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
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—42no—
305C2×C4×C11C2×C22⋊C414yes—
306C22⋊D11—416no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—42no—
319C2×Dic11—41no—
320C2×Dic11—41no—
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—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11C2×C22⋊C414yes—
333C2×Dic11C2×C22⋊C414yes—
334C2×Dic11C4×D418yes—
335C2×Dic11#12118yes—
336C2×Dic11#12414yes—
337C2×Dic11#12714yes—
338Dic22—416no—
339C23×Q8—111no—
340C23×D4—111no—
341C2×#124—118no—
342C2×#124—224no—
343C2×#124—224no—
344C22×C4⋊C4—112no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4C2×D1111yescharacteristic
355C22×C22⋊C4C2×D1112yes—
356C22×C42—111no—
357C22×C42—112no—
358#391—228no—
359#390—228no—
360#384—224no—
361#376—224no—
362C2×#95—112no—
363C2×#95—111no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95C2×D1111yescharacteristic
368C2×#95C2×D1112yes—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—42no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11C22×C22⋊C411yescharacteristic
381C22×C11C2×C4×D412yes—
382C22×C11#52011yescharacteristic
383C22×C11#52011yescharacteristic
384C22×C11#52012yes—
385C22×C11C2×#12112yes—
386C22×C11C2×#12411yescharacteristic
387C22×C11C2×#12711yescharacteristic
388C22×C11#53511yescharacteristic
389C22×C11#53512yes—
390C22×C11#53511yescharacteristic
391C22×C11#53512yes—
392C22×C11#53611yescharacteristic
393C22×C11#53612yes—
394C22×C11#53611yescharacteristic
395C22×C11#53612yes—
396C22×C11#53712yes—
397C22×C11#53711yescharacteristic
398C22×C11#53711yescharacteristic
399C22×C11#54212yes—
400C22×C11#54212yes—
401C22×C11#54212yes—
402C22×C11#54212yes—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—42no—
408C2×D11—82no—
409C2×D11—82no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C4×C11—24no—
415C4×C11—44no—
416C4×C11—42no—
417C4×C11—82no—
418Dic11—24no—
419Dic11—44no—
420Dic11—42no—
421Dic11—82no—
422Dic11#39018yes—
423C25—111no—
424C25C22×D1111yescharacteristic
425C22×Q8—114no—
426C22×Q8—222no—
427C22×Q8—222no—
428C22×Q8—224no—
429C22×Q8—224no—
430C22×D4—114no—
431C22×D4—222no—
432C22×D4—222no—
433C22×D4—224no—
434C22×D4—224no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—112no—
440C23×C4C22×D1112yes—
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444#124—2232no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4—442no—
453C2×C4⋊C4—442no—
454C2×C4⋊C4—442no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C22⋊C4—442no—
476C2×C22⋊C4—442no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4C4×D1114yes—
479C2×C42—114no—
480C2×C42—114no—
481C2×C42—114no—
482C2×C42—118no—
483C2×C42—224no—
484C2×C42—224no—
485#95—22no—
486#95—24no—
487#95—224no—
488#95—224no—
489#95—224no—
490#95—222no—
491#95—224no—
492C2×C11—82no—
493C2×C11C2×#39011yescharacteristic
494C2×C11#231111yescharacteristic
495C2×C11#231111yescharacteristic
496C2×C11#232612yes—
497C2×C11#232612yes—
498C2×C11#262012yes—
499C2×C11#262012yes—
500C2×C11#264011yescharacteristic
501C2×C11#264011yescharacteristic
502C2×C11#265711yescharacteristic
503C2×C11#265811yescharacteristic
504D11—82no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—112no—
516C24—221no—
517C24—221no—
518C24—222no—
519C24—221no—
520C24—222no—
521C24—221no—
522C24—222no—
523C24—221no—
524C24—221no—
525C24—222no—
526C24C2×C4×D1112yes—
527C24C23×D1111yescharacteristic
528C2×Q8—228no—
529C2×Q8—2216no—
530C2×Q8—444no—
531C2×Q8—448no—
532C2×Q8—444no—
533C2×D4—228no—
534C2×D4—2216no—
535C2×D4—444no—
536C2×D4—448no—
537C2×D4—444no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
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—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—114no—
561C22×C4—114no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—114no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—222no—
576C22×C4—222no—
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×C4C2×C4×D1112yes—
589C22×C4C2×C4×D1112yes—
590C22×C4D4×D1114yes—
591C22×C4D4×D1112yes—
592C22×C4D4×D1112yes—
593C4⋊C4—44no—
594C4⋊C4—444no—
595C4⋊C4—448no—
596C4⋊C4—448no—
597C22⋊C4—28no—
598C22⋊C4—48no—
599C22⋊C4—228no—
600C22⋊C4—228no—
601C22⋊C4—228no—
602C22⋊C4—448no—
603C22⋊C4—448no—
604C22⋊C4—448no—
605C42—1116no—
606C42—2216no—
607C11#1427311yescharacteristic, complemented, Sylow
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—42no—
614C23—41no—
615C23—42no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—41no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—224no—
635C23—224no—
636C23—442no—
637C23—441no—
638C23—442no—
639C23—441no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—442no—
647C23—441no—
648C23—442no—
649C23—441no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—441no—
654C23C22×C4×D1111yescharacteristic
655C23C2×D4×D1111yescharacteristic
656C23C2×D4×D1112yes—
657C23C2×D4×D1111yescharacteristic
658C23#6703711yescharacteristic
659C23#6703712yes—
660C23#6704011yescharacteristic
661C23#41×D1112yes—
662C23#6704211yescharacteristic
663C23#6704312yes—
664C23#6704311yescharacteristic
665Q8—4416no—
666D4—4416no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—114no—
691C2×C4—114no—
692C2×C4—118no—
693C2×C4—118no—
694C2×C4—114no—
695C2×C4—114no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—442no—
708C2×C4—441no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—441no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4C22⋊C4×D1114yes—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—42no—
726C22—44no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—82no—
732C22—82no—
733C22—442no—
734C22—442no—
735C22—444no—
736C22—442no—
737C22—444no—
738C22—881no—
739C22—881no—
740C22—881no—
741C22—881no—
742C22—882no—
743C22—882no—
744C22C2×C22⋊C4×D1111yescharacteristic
745C22#1062303511yescharacteristic
746C22#1062305411yescharacteristic
747C22C4×D4×D1112yes—
748C22#1062307712yes—
749C22#1062312311yescharacteristic
750C22#1062312312yes—
751C22#1062312812yes—
752C22D11×#12112yes—
753C22#1062313811yescharacteristic
754C22#1062313812yes—
755C22#1062313911yescharacteristic
756C22#1062315911yescharacteristic
757C22#1062315912yes—
758C22#1062316011yescharacteristic
759C22#1062317112yes—
760C22#1062317911yescharacteristic
761C22#1062317912yes—
762C22#1062319312yes—
763C22#1062320012yes—
764C22D11×#12411yescharacteristic
765C22#1062324112yes—
766C22D11×#12711yescharacteristic
767C4—24no—
768C4—44no—
769C4—42no—
770C4—82no—
771C4—118no—
772C4—224no—
773C4—444no—
774C4—442no—
775C4—882no—
776C2—82no—
777C2—882no—
778C2D11×#39011yescharacteristic
779C2#1307120311yescharacteristic
780C2#1307120511yescharacteristic
781C2#1307132212yes—
782C2#1307132512yes—
783C2#1307437212yes—
784C2#1307437512yes—
785C2#1307455111yescharacteristic
786C2#1307455411yescharacteristic
787C2#1307472111yescharacteristic
788C2#1307472511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14273
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
4. C2×#10622589C2semidirect
5. C2×#10622261C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
10. #13066858C2semidirect
11. C11×#1439C2semidirect
30. C2×#66938C4semidirect
213. C4×Dic11C22⋊C4semidirect
224. #1439D11semidirect
607. C11#14273semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C2×#106222592
C2×#106225702
C2×#106225892
C2×#106222612
#130668622
#130668612
#130668602
#130668592
#130668582
C11×#14392
#1427311