Finite Group Databasebeta

← #14684435

Subgroups — #14684435

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×#10622834C211yesmaximal, characteristic, complemented
2C2×#10622564C211yesmaximal, characteristic, complemented
3#13066873C211yesmaximal, characteristic, complemented
4#13066865C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066857C212yesmaximal, complemented
9#13066857C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C2×C11×#392C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#392C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28#10622834—24no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622564—24no—
38C25×C11C2311yescharacteristic
39C25×C11C2312yes—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11—42no—
45C22×D4×C11—42no—
46C22×D4×C11—42no—
47C22×D4×C11—42no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C22×D4×C11C2×C414yes—
51C22×D4×C11C2×C418yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—42no—
64C2×C11×C22⋊C4—42no—
65C2×C11×C22⋊C4C2×C414yes—
66C2×C11×C22⋊C4C2×C418yes—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—42no—
89C2×C4⋊Dic11—42no—
90C2×C4×Dic11—42no—
91C2×C4×Dic11D414yescomplemented
92C11×#95C2×C414yes—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101#14623—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11C22×C412yes—
127C24×C11C22×C414yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—28no—
130C2×D4×C11—48no—
131C2×D4×C11—48no—
132C2×D4×C11—48no—
133C2×D4×C11—48no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—48no—
140C2×D4×C11—48no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
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×C11—22no—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
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—21no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×D412yes—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—48no—
194C22⋊Dic11—44no—
195C22⋊Dic11—44no—
196C22⋊Dic11—48no—
197C22⋊Dic11—48no—
198C22⋊Dic11—48no—
199C22⋊Dic11—48no—
200C22⋊Dic11—48no—
201C4⋊Dic11—44no—
202C4⋊Dic11—44no—
203C4×Dic11—44no—
204C2×#392D1111yescharacteristic
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#1434—111no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—41no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—41no—
246C23×C11—42no—
247C23×C11—41no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11C23×C411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11H(5,𝔽2)12yes—
277C23×C11H(5,𝔽2)12yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C11H(5,𝔽2)12yes—
280C23×C11H(5,𝔽2)11yescharacteristic
281C23×C11H(5,𝔽2)11yescharacteristic
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C112−1+411yescharacteristic
284D4×C11—416no—
285D4×C11—432no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11C4×D414yes—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—41no—
318C2×Dic11—42no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
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×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C23×D4C2×D1111yescharacteristic
338C23×D4C2×D1112yes—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4C2×D1112yes—
350C22×C42—111no—
351#392Dic1118yescomplemented
352#390—224no—
353#388—224no—
354C2×#95—111no—
355C2×#95—111no—
356C2×#95—111no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95C2×D1111yescharacteristic
363C22×C11—44no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—44no—
367C22×C11—42no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—82no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—82no—
379C22×C11—82no—
380C22×C11—82no—
381C22×C11—82no—
382C22×C11—82no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—81no—
386C22×C11—82no—
387C22×C11—81no—
388C22×C11—82no—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11#51812yes—
391C22×C11#51811yescharacteristic
392C22×C11#51812yes—
393C22×C11#52011yescharacteristic
394C22×C11#53411yescharacteristic
395C22×C11#53511yescharacteristic
396C22×C11#53511yescharacteristic
397C22×C11#53511yescharacteristic
398C22×C11#53511yescharacteristic
399C22×C11#53711yescharacteristic
400C22×C11#53812yes—
401C22×C11#54012yes—
402C22×C11#54011yescharacteristic
403C22×C11#54211yescharacteristic
404C22×C11#56012yes—
405C22×C11#56012yes—
406C22×C11#56012yes—
407C22×C11#56012yes—
408C22×C11#56012yes—
409C22×C11H(3,𝔽4)12yes—
410C22×C11#56212yes—
411C22×C11#56212yes—
412C4×C11—24no—
413C4×C11—42no—
414C4×C11—44no—
415Dic11—42no—
416Dic11—42no—
417Dic11—82no—
418Dic11—81no—
419Dic11—82no—
420Dic11—81no—
421C25C22×D1111yescharacteristic
422C25C22×D1112yes—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—42no—
426C22×D4—42no—
427C22×D4—42no—
428C22×D4—42no—
429C22×D4—42no—
430C22×D4—42no—
431C22×D4—42no—
432C22×D4—42no—
433C22×D4C2×Dic1114yes—
434C22×D4C2×Dic1118yes—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—111no—
440C23×C4—112no—
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—222no—
445C2×C4⋊C4—222no—
446C2×C4⋊C4—442no—
447C2×C4⋊C4—442no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
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⋊C4C2×Dic1114yes—
472C2×C22⋊C4C2×Dic1118yes—
473C2×C42—114no—
474C2×C42—442no—
475#95—222no—
476#95—222no—
477#95—222no—
478#95—442no—
479#95—442no—
480#95—442no—
481#95—442no—
482#95—442no—
483#95C2×Dic1114yes—
484C2×C11—84no—
485C2×C11—82no—
486C2×C11#232111yescharacteristic
487C2×C11#232411yescharacteristic
488C2×C11#232811yescharacteristic
489C2×C11#237512yes—
490C2×C11#237712yes—
491C2×C11#281311yescharacteristic
492C2×C11#281511yescharacteristic
493C2×C11#281811yescharacteristic
494C2×C11#281911yescharacteristic
495C2×C11#282812yes—
496C2×C11#282912yes—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24C22×Dic1112yes—
522C24C22×Dic1114yes—
523C24C23×D1111yescharacteristic
524C2×D4—28no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
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—112no—
549C22×C4—112no—
550C22×C4—221no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—221no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4D4×D1112yes—
583C22×C4#434112yes—
584C22×C4C22×Dic1114yes—
585C22×C4C22×Dic1112yes—
586C22×C4C22×Dic1112yes—
587C4⋊C4—444no—
588C4⋊C4—444no—
589C22⋊C4—28no—
590C22⋊C4—48no—
591C22⋊C4—448no—
592C22⋊C4—444no—
593C22⋊C4—444no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C22⋊C4—448no—
597C22⋊C4—448no—
598C42—444no—
599C11#1462311yescharacteristic, complemented, Sylow
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C2×D4×D1111yescharacteristic
659C23C2×#434111yescharacteristic
660C23#6703712yes—
661C23#6703712yes—
662C23#6703712yes—
663C23#6703712yes—
664C23#6703711yescharacteristic
665C23#6703711yescharacteristic
666C23#6704211yescharacteristic
667C23#6704311yescharacteristic
668C23C23×Dic1111yescharacteristic
669D4—416no—
670D4—432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—442no—
701C2×C4—441no—
702C2×C4—442no—
703C2×C4—441no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—441no—
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×C4D4×Dic1114yes—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—42no—
733C22—44no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—81no—
742C22—81no—
743C22—82no—
744C22—82no—
745C22—81no—
746C22—81no—
747C22—82no—
748C22#1062312011yescharacteristic
749C22#1062312311yescharacteristic
750C22#1062312412yes—
751C22#1062312512yes—
752C22#1062312612yes—
753C22#1062312612yes—
754C22#1062312612yes—
755C22#1062313411yescharacteristic
756C22#1062313811yescharacteristic
757C22#1062313911yescharacteristic
758C22#1062315011yescharacteristic
759C22#1062315112yes—
760C22#1062315112yes—
761C22#1062315212yes—
762C22#1062315212yes—
763C22#1062324611yescharacteristic
764C22#1062324611yescharacteristic
765C22#1062325012yes—
766C22C2×D4×Dic1111yescharacteristic
767C22#1062332911yescharacteristic
768C22#1062332912yes—
769C22#1062332912yes—
770C22#1062335811yescharacteristic
771C4—24no—
772C4—44no—
773C4—42no—
774C4—442no—
775C4—442no—
776C4—882no—
777C4—881no—
778C4—882no—
779C4—881no—
780C2—82no—
781C2—84no—
782C2#1307127711yescharacteristic
783C2#1307131111yescharacteristic
784C2#1307134211yescharacteristic
785C2#1307175712yes—
786C2#1307177312yes—
787C2#1307661511yescharacteristic
788C2#1307663711yescharacteristic
789C2#1307665511yescharacteristic
790C2#1307666311yescharacteristic
791C2#1307673812yes—
792C2#1307674812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC2×C11×#392C2
socle, cosocleC24×C11C24
hypercenterC2×#392D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#10622834C2semidirect
2. C2×#10622564C2semidirect
3. #13066873C2semidirect
4. #13066865C2semidirect
5. #13066861C2semidirect
6. #13066861C2semidirect
7. #13066857C2semidirect
8. #13066857C2semidirect
9. #13066857C2semidirect
10. #13066841C2semidirect
26. C11×#392C4semidirect
91. C2×C4×Dic11D4semidirect
351. #392Dic11semidirect
599. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225642
#130668732
#130668652
#130668612
#130668572
#130668412
C2×C11×#3922
#1462311