Finite Group Databasebeta

← #14680776

Subgroups — #14680776

Order 2816.

2174 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622570C212yesmaximal, complemented
4C2×#10622282C211yesmaximal, characteristic, complemented
5C2×#10622557C212yesmaximal, complemented
6#13066880C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066859C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30#10622836C418yescomplemented
31#10622834—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622570—28no—
38#10622557—28no—
39#10622282—24no—
40C25×C11C2312yes—
41C24×D11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—42no—
45C22×D4×C11—42no—
46C22×D4×C11C2×C414yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11—42no—
57C22×C22⋊D11C2×C418yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11C2×C418yes—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C414yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—42no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—42no—
94C2×Dic11⋊C4—42no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11—42no—
97C2×C4×Dic11—42no—
98C2×C4×Dic11D414yescomplemented
99C2×C4×Dic11D418yescomplemented
100C11×#95—22no—
101C11×#95—22no—
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95C2×C414yes—
107#14321—111nomaximal, Sylow
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×C11C22×C414yes—
123C24×C11C2411yescharacteristic
124C23×D11—21no—
125C23×D11—22no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—21no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11C22×C412yes—
135C2×D4×C11—28no—
136C2×D4×C11—48no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C2×D4×C11—48no—
140C22×C4×C11—22no—
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—21no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11—48no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C414yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D414yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D414yes—
197C22×Dic11#4114yes—
198C11×C22⋊C4—48no—
199C11×C22⋊C4—48no—
200C22⋊Dic11—216no—
201C22⋊Dic11—48no—
202C22⋊Dic11—48no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—44no—
206(C2×D11)⋊C4—44no—
207C4⋊Dic11—44no—
208Dic11⋊C4—48no—
209Dic11⋊C4—44no—
210C4×Dic11—44no—
211C4×Dic11—48no—
212C2×#392—111no—
213C2×#390—111no—
214C2×#390—112no—
215C2×#388—111no—
216C2×#388—112no—
217#1444—111no—
218#1439—111no—
219#1439—112no—
220#1438—112no—
221#1438D1111yescharacteristic, complemented
222C4×#95—111no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
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×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
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—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D412yes—
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4112yes—
263C23×C11H(5,𝔽2)11yescharacteristic
264C23×C11H(5,𝔽2)12yes—
265C23×C11H(5,𝔽2)12yes—
266C23×C11H(5,𝔽2)11yescharacteristic
267C23×C11H(5,𝔽2)11yescharacteristic
268C23×C112−1+411yescharacteristic
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—22no—
272C22×D11—24no—
273C22×D11—22no—
274C22×D11—41no—
275C22×D11—42no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—41no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—41no—
292D4×C11—416no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—42no—
313C2×C4×C11—41no—
314C2×C4×C11C4×D414yes—
315C22⋊D11—432no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11C4×D418yes—
344C2×Dic11#12714yes—
345C23×D4—112no—
346C23×D4C2×D1111yescharacteristic
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4—111no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—111no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—111no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1112yes—
358C22×C22⋊C4C2×D1112yes—
359C22×C42—112no—
360C22×C42—111no—
361#392—118no—
362#390—228no—
363#390—224no—
364#388—224no—
365#388—228no—
366C2×#95—111no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95C2×D1111yescharacteristic
372C2×#95C2×D1111yescharacteristic
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—82no—
381C22×C11—82no—
382C22×C11—82no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—82no—
386C22×C11—82no—
387C22×C11—82no—
388C22×C11C2×C4×D411yescharacteristic
389C22×C11C2×C4×D412yes—
390C22×C11#51812yes—
391C22×C11#51811yescharacteristic
392C22×C11#52011yescharacteristic
393C22×C11C2×#12711yescharacteristic
394C22×C11#53212yes—
395C22×C11#53211yescharacteristic
396C22×C11#53412yes—
397C22×C11#53411yescharacteristic
398C22×C11#53511yescharacteristic
399C22×C11#53512yes—
400C22×C11#53512yes—
401C22×C11#53511yescharacteristic
402C22×C11#53712yes—
403C22×C11#53711yescharacteristic
404C22×C11#53812yes—
405C22×C11#53812yes—
406C22×C11#53812yes—
407C22×C11#54011yescharacteristic
408C22×C11#54012yes—
409C22×C11#54212yes—
410C22×C11#54211yescharacteristic
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—42no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—82no—
419C2×D11—81no—
420C2×D11—82no—
421C2×D11—81no—
422C4×C11—24no—
423C4×C11—44no—
424C4×C11—81no—
425C4×C11—81no—
426Dic11—28no—
427Dic11—24no—
428Dic11—42no—
429Dic11—42no—
430Dic11—82no—
431C25—111no—
432C25C22×D1112yes—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—42no—
436C22×D4—42no—
437C22×D4—118no—
438C22×D4—224no—
439C22×D4—224no—
440C22×D4—442no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4C4×D1114yes—
445C23×C4—111no—
446C23×C4—112no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—112no—
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1112yes—
453C23×C4C22×D1111yescharacteristic
454C2×C4⋊C4—222no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—442no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—222no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C22⋊C4—442no—
484C2×C22⋊C4—442no—
485C2×C22⋊C4—442no—
486C2×C42—118no—
487C2×C42—114no—
488C2×C42—442no—
489C2×C42—442no—
490C2×C42—442no—
491#95—22no—
492#95—22no—
493#95—114no—
494#95—224no—
495#95—222no—
496#95—224no—
497#95—224no—
498C2×C11—84no—
499C2×C11C4×#12711yescharacteristic
500C2×C11#232111yescharacteristic
501C2×C11#232112yes—
502C2×C11#232412yes—
503C2×C11#232411yescharacteristic
504C2×C11#265611yescharacteristic
505C2×C11#265711yescharacteristic
506C2×C11#266112yes—
507C2×C11#266111yescharacteristic
508C2×C11#266212yes—
509C2×C11#266211yescharacteristic
510D11—82no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—112no—
526C24—221no—
527C24—222no—
528C24—221no—
529C24—221no—
530C24—222no—
531C24—222no—
532C24—221no—
533C24—222no—
534C24—221no—
535C24—221no—
536C24C2×C4×D1114yes—
537C24C23×D1111yescharacteristic
538C2×D4—28no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—48no—
543C2×D4—2216no—
544C2×D4—448no—
545C2×D4—448no—
546C2×D4—448no—
547C2×D4—448no—
548C2×D4—448no—
549C2×D4—448no—
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—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—114no—
569C22×C4—114no—
570C22×C4—112no—
571C22×C4—114no—
572C22×C4—114no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—221no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4C2×C4×D1112yes—
598C22×C4D4×D1114yes—
599C22×C4D4×D1112yes—
600C22×C4#434112yes—
601C4⋊C4—444no—
602C4⋊C4—444no—
603C4⋊C4—448no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—2216no—
607C22⋊C4—228no—
608C22⋊C4—448no—
609C22⋊C4—444no—
610C22⋊C4—444no—
611C22⋊C4—448no—
612C22⋊C4—448no—
613C42—444no—
614C42—448no—
615C11#1432111yescharacteristic, complemented, Sylow
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
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—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—222no—
652C23—224no—
653C23—224no—
654C23—222no—
655C23—222no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—442no—
660C23—442no—
661C23—441no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—441no—
666C23—442no—
667C23—441no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—441no—
673C23—441no—
674C23C22×C4×D1111yescharacteristic
675C23C2×D4×D1111yescharacteristic
676C23C2×D4×D1112yes—
677C23C2×#434111yescharacteristic
678C23#6703711yescharacteristic
679C23#6703711yescharacteristic
680C23#6703712yes—
681C23#6703712yes—
682C23#41×D1112yes—
683C23#6704211yescharacteristic
684C23#6704311yescharacteristic
685D4—416no—
686D4—4432no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—114no—
709C2×C4—118no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—222no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—441no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—441no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4(C22⋊D11)⋊C414yes—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—442no—
754C22—442no—
755C22—444no—
756C22—444no—
757C22—442no—
758C22—881no—
759C22—881no—
760C22—882no—
761C22—881no—
762C22—882no—
763C22—881no—
764C22C2×(C22⋊D11)⋊C411yescharacteristic
765C22#1062301712yes—
766C22C4×D4×D1112yes—
767C22#1062307611yescharacteristic
768C22#1062307711yescharacteristic
769C22#1062312012yes—
770C22#1062312011yescharacteristic
771C22#1062312312yes—
772C22#1062312311yescharacteristic
773C22#1062312412yes—
774C22#1062312712yes—
775C22#1062313811yescharacteristic
776C22#1062313812yes—
777C22#1062313912yes—
778C22#1062313911yescharacteristic
779C22#1062314412yes—
780C22#1062314612yes—
781C22#1062318812yes—
782C22#1062319312yes—
783C22#1062319911yescharacteristic
784C22#1062321311yescharacteristic
785C22D11×#12711yescharacteristic
786C22#1062325011yescharacteristic
787C4—24no—
788C4—44no—
789C4—81no—
790C4—81no—
791C4—224no—
792C4—228no—
793C4—442no—
794C4—442no—
795C4—882no—
796C2—84no—
797C2—882no—
798C2#1307118011yescharacteristic
799C2#1307127111yescharacteristic
800C2#1307127212yes—
801C2#1307130612yes—
802C2#1307131211yescharacteristic
803C2#1307471711yescharacteristic
804C2#1307472111yescharacteristic
805C2#1307474112yes—
806C2#1307475111yescharacteristic
807C2#1307475212yes—
808C2#1307476111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14321
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622282C2semidirect
5. C2×#10622557C2semidirect
6. #13066880C2semidirect
7. #13066862C2semidirect
8. #13066859C2semidirect
9. #13066855C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1438C2semidirect
30. #10622836C4semidirect
98. C2×C4×Dic11D4semidirect
99. C2×C4×Dic11D4semidirect
221. #1438D11semidirect
615. C11#14321semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106228342
C2×#106225702
C2×#106222822
C2×#106225572
#130668802
#130668622
#130668592
#130668552
#95×Dic112
C11×#14382
#1432111