Finite Group Databasebeta

← #14684431

Subgroups — #14684431

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×#10622573C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3#13066872C211yesmaximal, characteristic, complemented
4#13066864C212yesmaximal, complemented
5#13066861C211yesmaximal, characteristic, complemented
6#13066858C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066843C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C11×#388—24no—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622573C418yescomplemented
37#10622552—24no—
38C25×C11C2311yescharacteristic
39C24×D11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—42no—
47C22×C22⋊D11—42no—
48C22×C22⋊D11—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11C2×C418yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—42no—
59C22×D44—42no—
60C22×D44C2×C414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C11×C22⋊C4C2×C414yes—
70C2×C42×C11—42no—
71C2×C42×C11D414yescomplemented
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4C2×C418yes—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—42no—
92C11×#95—22no—
93C11×#95—22no—
94C11⋊#95—22no—
95C11⋊#95—42no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95C2×C414yes—
101#14623—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11C22×C412yes—
113C24×C11C2411yescharacteristic
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—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11C22×C414yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C22×Dic11—22no—
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×Dic11C22×C414yes—
187C2×D44—28no—
188C2×D44—48no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44—48no—
192C11×C4⋊C4—44no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—44no—
195C11×C22⋊C4—44no—
196C42×C11—44no—
197C22⋊Dic11—48no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202(C2×D11)⋊C4—48no—
203C4⋊Dic11—44no—
204C2×#392—111no—
205C2×#390—111no—
206C2×#388D1111yescharacteristic, complemented
207#1442—111no—
208#1440—112no—
209#1439—112no—
210#1439—111no—
211#1438—111no—
212#1438—112no—
213#1438—112no—
214#1434—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11—41no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11C23×C411yescharacteristic
239C23×C11C22×D411yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11H(5,𝔽2)12yes—
242C23×C11H(5,𝔽2)12yes—
243C23×C11H(5,𝔽2)12yes—
244C23×C11H(5,𝔽2)12yes—
245C23×C11H(5,𝔽2)11yescharacteristic
246C23×C11H(5,𝔽2)11yescharacteristic
247C23×C11H(5,𝔽2)11yescharacteristic
248C23×C112−1+411yescharacteristic
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
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—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11C4×D414yes—
314C22⋊D11—432no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
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—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336D44—416no—
337C23×D4—112no—
338C23×D4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—112no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4C2×D1111yescharacteristic
350C22×C42C2×D1111yescharacteristic
351#392—118no—
352#390—224no—
353#388—24no—
354C2×#95—111no—
355C2×#95—111no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95C2×D1111yescharacteristic
362C2×#95C2×D1111yescharacteristic
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—82no—
371C22×C11—82no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11C2×C4×D411yescharacteristic
375C22×C11#51811yescharacteristic
376C22×C11#51812yes—
377C22×C11#51812yes—
378C22×C11#52011yescharacteristic
379C22×C11#53411yescharacteristic
380C22×C11#53511yescharacteristic
381C22×C11#53511yescharacteristic
382C22×C11#53511yescharacteristic
383C22×C11#53511yescharacteristic
384C22×C11#53711yescharacteristic
385C22×C11#53812yes—
386C22×C11#54011yescharacteristic
387C22×C11#54012yes—
388C22×C11#54211yescharacteristic
389C22×C11#56012yes—
390C22×C11#56012yes—
391C22×C11#56012yes—
392C22×C11#56012yes—
393C22×C11#56012yes—
394C22×C11H(3,𝔽4)12yes—
395C22×C11#56212yes—
396C22×C11#56212yes—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—82no—
405C2×D11—82no—
406C2×D11—82no—
407C2×D11—82no—
408C2×D11—82no—
409C2×D11—82no—
410C2×D11—82no—
411C2×D11—82no—
412C4×C11—24no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—81no—
417C4×C11—81no—
418Dic11—44no—
419Dic11—82no—
420Dic11—82no—
421C25—112no—
422C25C22×D1111yescharacteristic
423C22×D4—118no—
424C22×D4—114no—
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—112no—
436C23×C4—112no—
437C23×C4—112no—
438C23×C4C22×D1111yescharacteristic
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—22no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—222no—
447C2×C4⋊C4—442no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—118no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
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⋊C4C4×D1114yes—
473C2×C42—42no—
474C2×C42C22⋊D1114yescomplemented
475#95—22no—
476#95—22no—
477#95—114no—
478#95—222no—
479#95—442no—
480#95—442no—
481#95—442no—
482#95—442no—
483#95—442no—
484C2×C11—82no—
485C2×C11#232111yescharacteristic
486C2×C11#232411yescharacteristic
487C2×C11#232811yescharacteristic
488C2×C11#237512yes—
489C2×C11#237712yes—
490C2×C11#281311yescharacteristic
491C2×C11#281511yescharacteristic
492C2×C11#281811yescharacteristic
493C2×C11#281911yescharacteristic
494C2×C11#282812yes—
495C2×C11#282912yes—
496D11—84no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—114no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24—222no—
512C24—222no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—222no—
522C24C2×C4×D1112yes—
523C24C23×D1111yescharacteristic
524C2×D4—228no—
525C2×D4—448no—
526C2×D4—444no—
527C2×D4—448no—
528C2×D4—444no—
529C2×D4—448no—
530C2×D4—448no—
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—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—114no—
561C22×C4—222no—
562C22×C4—222no—
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—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4C2×C4×D1112yes—
582C22×C4C2×C4×D1112yes—
583C22×C4#433912yes—
584C22×C4C2×C22⋊D1112yes—
585C22×C4C2×C22⋊D1112yes—
586C22×C4C2×C22⋊D1112yes—
587C4⋊C4—44no—
588C4⋊C4—444no—
589C22⋊C4—28no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C22⋊C4—448no—
597C22⋊C4—448no—
598C42—44no—
599C11#1462311yescharacteristic, complemented, Sylow
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—42no—
606C23—42no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—224no—
624C23—224no—
625C23—224no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—224no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
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
659C23C2×#433911yescharacteristic
660C23#6703712yes—
661C23#6703712yes—
662C23#6704211yescharacteristic
663C23#6704211yescharacteristic
664C23#6704212yes—
665C23#6704212yes—
666C23#6704211yescharacteristic
667C23#6704311yescharacteristic
668C23C22×C22⋊D1111yescharacteristic
669D4—4416no—
670D4—4432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—442no—
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—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×C4C4×C22⋊D1114yes—
722C22—44no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—82no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—82no—
733C22—444no—
734C22—444no—
735C22—444no—
736C22—444no—
737C22—444no—
738C22—444no—
739C22—444no—
740C22—882no—
741C22—882no—
742C22—882no—
743C22—882no—
744C22—882no—
745C22—882no—
746C22—882no—
747C22—882no—
748C22#1062305211yescharacteristic
749C22#1062305411yescharacteristic
750C22#1062306511yescharacteristic
751C22#1062306611yescharacteristic
752C22#1062307612yes—
753C22#1062307612yes—
754C22#1062309112yes—
755C22#1062309312yes—
756C22#1062315112yes—
757C22#1062315112yes—
758C22#1062319712yes—
759C22#1062319812yes—
760C22#1062321412yes—
761C22#1062321512yes—
762C22#1062324212yes—
763C22#1062324212yes—
764C22C2×C4×C22⋊D1111yescharacteristic
765C22#1062333511yescharacteristic
766C22#1062333611yescharacteristic
767C22#1062336111yescharacteristic
768C22#1062336111yescharacteristic
769C22#1062336111yescharacteristic
770C22#1062336411yescharacteristic
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—81no—
776C4—81no—
777C4—444no—
778C4—882no—
779C4—882no—
780C2—82no—
781C2—884no—
782C2#1307127011yescharacteristic
783C2#1307130911yescharacteristic
784C2#1307133811yescharacteristic
785C2#1307175612yes—
786C2#1307176912yes—
787C2#1307661811yescharacteristic
788C2#1307663811yescharacteristic
789C2#1307665611yescharacteristic
790C2#1307666111yescharacteristic
791C2#1307673312yes—
792C2#1307674212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. #13066872C2semidirect
4. #13066864C2semidirect
5. #13066861C2semidirect
6. #13066858C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066843C2semidirect
11. C2×C11×#388C2semidirect
36. #10622573C4semidirect
71. C2×C42×C11D4semidirect
206. C2×#388D11semidirect
474. C2×C42C22⋊D11semidirect
599. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106225522
#130668722
#130668642
#130668612
#130668582
#130668562
#130668552
#130668432
C2×C11×#3882
#1462311