Finite Group Databasebeta

← #14684434

Subgroups — #14684434

Order 2816.

1910 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
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622553C211yesmaximal, characteristic, complemented
4#13066873C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066860C212yesmaximal, complemented
8#13066856C212yesmaximal, complemented
9#13066856C212yesmaximal, complemented
10#13066856C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×D44C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622553—24no—
36#10622552—24no—
37#10622284C418yescomplemented
38C24×D11C2311yescharacteristic
39C24×D11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44—42no—
54C22×D44—42no—
55C22×D44—42no—
56C22×D44—42no—
57C22×D44—42no—
58C22×D44—42no—
59C22×D44C2×C414yes—
60C22×D44C2×C418yes—
61C2×C42×C11—42no—
62C2×C42×C11D414yescomplemented
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×(C2×D11)⋊C4C2×C418yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—42no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—42no—
92C11×#95—22no—
93C11×#95—42no—
94C11×#95—42no—
95C11×#95C2×C414yes—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101#14623—111nomaximal, Sylow
102C24×C11C2411yescharacteristic
103C23×D11—21no—
104C23×D11—22no—
105C23×D11—21no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—21no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—22no—
127C23×D11C22×C412yes—
128C23×D11C22×C414yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
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×C414yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11C22×C412yes—
180C2×D44—28no—
181C2×D44—48no—
182C2×D44—48no—
183C2×D44—48no—
184C2×D44—48no—
185C2×D44—44no—
186C2×D44—44no—
187C2×D44—48no—
188C2×D44—48no—
189C2×D44—48no—
190C2×D44—48no—
191C2×D44—48no—
192C42×C11—44no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—48no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—48no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202C4⋊Dic11—44no—
203Dic11⋊C4—44no—
204C2×#392—111no—
205C2×#390—111no—
206C2×#388—111no—
207#1442—111no—
208#1440—112no—
209#1439—112no—
210#1439—111no—
211#1438—112no—
212#1438—112no—
213#1438—111no—
214#1434D1111yescharacteristic, complemented
215C23×C11C23×C411yescharacteristic
216C23×C11C22×D411yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11H(5,𝔽2)12yes—
219C23×C11H(5,𝔽2)11yescharacteristic
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C11H(5,𝔽2)12yes—
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C11H(5,𝔽2)11yescharacteristic
225C23×C112−1+411yescharacteristic
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—41no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—41no—
243C22×D11—42no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—42no—
248C22×D11—41no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—41no—
257C22×D11—42no—
258C22×D11—41no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
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×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
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×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×C11C4×D414yes—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—42no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335D44—416no—
336D44—432no—
337C23×D4—111no—
338C23×D4—112no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C42C2×D1111yescharacteristic
351#392—118no—
352#390—224no—
353#388—224no—
354C2×#95—111no—
355C2×#95—111no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95C2×D1111yescharacteristic
360C2×#95C2×D1112yes—
361C2×#95C2×D1112yes—
362C2×#95C2×D1111yescharacteristic
363C22×C11C2×C4×D411yescharacteristic
364C22×C11#51812yes—
365C22×C11#51812yes—
366C22×C11#51811yescharacteristic
367C22×C11#52011yescharacteristic
368C22×C11#53411yescharacteristic
369C22×C11#53511yescharacteristic
370C22×C11#53511yescharacteristic
371C22×C11#53511yescharacteristic
372C22×C11#53511yescharacteristic
373C22×C11#53711yescharacteristic
374C22×C11#53812yes—
375C22×C11#54012yes—
376C22×C11#54011yescharacteristic
377C22×C11#54211yescharacteristic
378C22×C11#56012yes—
379C22×C11#56012yes—
380C22×C11#56012yes—
381C22×C11#56012yes—
382C22×C11#56012yes—
383C22×C11H(3,𝔽4)12yes—
384C22×C11#56212yes—
385C22×C11#56212yes—
386C2×D11—42no—
387C2×D11—44no—
388C2×D11—42no—
389C2×D11—44no—
390C2×D11—42no—
391C2×D11—44no—
392C2×D11—44no—
393C2×D11—44no—
394C2×D11—44no—
395C2×D11—44no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—82no—
399C2×D11—81no—
400C2×D11—81no—
401C2×D11—82no—
402C2×D11—82no—
403C2×D11—82no—
404C2×D11—82no—
405C2×D11—82no—
406C2×D11—82no—
407C2×D11—82no—
408C2×D11—81no—
409C2×D11—82no—
410C2×D11—81no—
411C2×D11—82no—
412C4×C11—24no—
413C4×C11—44no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—82no—
417Dic11—42no—
418Dic11—82no—
419Dic11—81no—
420Dic11—81no—
421C25—111no—
422C25—112no—
423C22×D4—114no—
424C22×D4—118no—
425C22×D4—222no—
426C22×D4—222no—
427C22×D4—442no—
428C22×D4—442no—
429C22×D4—442no—
430C22×D4—442no—
431C22×D4—442no—
432C22×D4—442no—
433C22×D4—442no—
434C22×D4—442no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—112no—
438C23×C4—111no—
439C23×C4C22×D1112yes—
440C23×C4C22×D1112yes—
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—222no—
445C2×C4⋊C4—222no—
446C2×C4⋊C4—442no—
447C2×C4⋊C4—442no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—118no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—222no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—442no—
457C2×C22⋊C4—442no—
458C2×C22⋊C4—442no—
459C2×C22⋊C4—442no—
460C2×C22⋊C4—442no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C42—42no—
474C2×C42D4414yescomplemented
475#95—22no—
476#95—42no—
477#95—42no—
478#95—222no—
479#95—222no—
480#95—442no—
481#95—442no—
482#95—442no—
483#95C4×D1114yes—
484C2×C11#232111yescharacteristic
485C2×C11#232411yescharacteristic
486C2×C11#232811yescharacteristic
487C2×C11#237512yes—
488C2×C11#237712yes—
489C2×C11#281311yescharacteristic
490C2×C11#281511yescharacteristic
491C2×C11#281811yescharacteristic
492C2×C11#281911yescharacteristic
493C2×C11#282812yes—
494C2×C11#282912yes—
495D11—82no—
496D11—84no—
497C24—112no—
498C24—114no—
499C24—221no—
500C24—222no—
501C24—221no—
502C24—222no—
503C24—222no—
504C24—222no—
505C24—222no—
506C24—222no—
507C24—221no—
508C24—221no—
509C24—222no—
510C24—222no—
511C24—222no—
512C24—221no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—221no—
522C24—222no—
523C24C23×D1111yescharacteristic
524C2×D4—228no—
525C2×D4—448no—
526C2×D4—448no—
527C2×D4—448no—
528C2×D4—448no—
529C2×D4—444no—
530C2×D4—444no—
531C2×D4—448no—
532C2×D4—448no—
533C2×D4—448no—
534C2×D4—448no—
535C2×D4—448no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
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—112no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4C2×C4×D1114yes—
582C22×C4C2×C4×D1112yes—
583C22×C4C2×D4412yes—
584C22×C4C2×D4412yes—
585C22×C4C2×D4412yes—
586C22×C4#433912yes—
587C4⋊C4—444no—
588C4⋊C4—444no—
589C22⋊C4—228no—
590C22⋊C4—448no—
591C22⋊C4—444no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—444no—
595C22⋊C4—448no—
596C22⋊C4—448no—
597C22⋊C4—448no—
598C42—44no—
599C11#1462311yescharacteristic, complemented, Sylow
600C23—222no—
601C23—224no—
602C23—224no—
603C23—224no—
604C23—224no—
605C23—222no—
606C23—224no—
607C23—224no—
608C23—224no—
609C23—224no—
610C23—224no—
611C23—222no—
612C23—442no—
613C23—442no—
614C23—442no—
615C23—442no—
616C23—442no—
617C23—442no—
618C23—441no—
619C23—442no—
620C23—441no—
621C23—442no—
622C23—442no—
623C23—442no—
624C23—441no—
625C23—442no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—441no—
637C23—442no—
638C23—441no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C22×C4×D1111yescharacteristic
659C23C22×D4411yescharacteristic
660C23C2×#433911yescharacteristic
661C23#6703712yes—
662C23#6703711yescharacteristic
663C23#6704011yescharacteristic
664C23#6704212yes—
665C23#6704212yes—
666C23#6704211yescharacteristic
667C23#6704211yescharacteristic
668C23#6704212yes—
669D4—4416no—
670D4—4432no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—42no—
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—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—222no—
700C2×C4—224no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—442no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4C4×D4414yes—
722C22—444no—
723C22—444no—
724C22—444no—
725C22—444no—
726C22—444no—
727C22—444no—
728C22—444no—
729C22—442no—
730C22—442no—
731C22—444no—
732C22—442no—
733C22—444no—
734C22—882no—
735C22—882no—
736C22—882no—
737C22—881no—
738C22—882no—
739C22—881no—
740C22—882no—
741C22—881no—
742C22—882no—
743C22—881no—
744C22—882no—
745C22—882no—
746C22—882no—
747C22—882no—
748C22C2×C4×D4411yescharacteristic
749C22#1062302411yescharacteristic
750C22#1062304111yescharacteristic
751C22#1062305212yes—
752C22#1062305611yescharacteristic
753C22#1062305611yescharacteristic
754C22#1062305611yescharacteristic
755C22#1062305611yescharacteristic
756C22#1062306612yes—
757C22#1062307611yescharacteristic
758C22#1062307612yes—
759C22#1062309112yes—
760C22#1062309311yescharacteristic
761C22#1062310511yescharacteristic
762C22#1062311311yescharacteristic
763C22#1062315112yes—
764C22#1062317812yes—
765C22#1062319712yes—
766C22#1062319712yes—
767C22#1062321412yes—
768C22#1062323112yes—
769C22#1062324212yes—
770C22#1062324212yes—
771C4—24no—
772C4—44no—
773C4—42no—
774C4—42no—
775C4—82no—
776C4—442no—
777C4—881no—
778C4—882no—
779C4—881no—
780C2—882no—
781C2—884no—
782C2#1307127611yescharacteristic
783C2#1307131011yescharacteristic
784C2#1307134111yescharacteristic
785C2#1307175612yes—
786C2#1307177112yes—
787C2#1307662011yescharacteristic
788C2#1307664011yescharacteristic
789C2#1307665911yescharacteristic
790C2#1307666211yescharacteristic
791C2#1307673312yes—
792C2#1307674612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1434D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622553C2semidirect
4. #13066873C2semidirect
5. #13066864C2semidirect
6. #13066862C2semidirect
7. #13066860C2semidirect
8. #13066856C2semidirect
9. #13066856C2semidirect
10. #13066856C2semidirect
11. C11×#1434C2semidirect
37. #10622284C4semidirect
62. C2×C42×C11D4semidirect
214. #1434D11semidirect
474. C2×C42D44semidirect
599. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106225522
C2×#106225532
#130668732
#130668642
#130668622
#130668602
#130668562
C11×#14342
#1462311