Finite Group Databasebeta

← #14680779

Subgroups — #14680779

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×#10622573C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622570C212yesmaximal, complemented
4C2×#10622603C212yesmaximal, complemented
5#13066880C211yesmaximal, characteristic, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066860C212yesmaximal, complemented
8#13066856C211yesmaximal, characteristic, complemented
9#13066855C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, 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
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C11×#388—24no—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622603—28no—
37#10622573C418yescomplemented
38#10622570—28no—
39#10622552—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—24no—
49C22×C22⋊D11—24no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11—42no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11C2×C418yes—
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—42no—
61C22×D44—42no—
62C22×D44C2×C414yes—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4C2×C414yes—
72C2×C42×C11—42no—
73C2×C42×C11D414yescomplemented
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4C2×C418yes—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—42no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—42no—
96C2×Dic11⋊C4—42no—
97C2×C4×Dic11—42no—
98C2×C4×Dic11—42no—
99C2×C4×Dic11D418yescomplemented
100C11×#95—22no—
101C11×#95—22no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95C2×C414yes—
107#14321—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11C22×C412yes—
119C24×C11C2411yescharacteristic
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×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11C22×C414yes—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4112yes—
165C2×C22⋊D11—216no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—48no—
170C2×C22⋊D11—48no—
171C2×C22⋊D11—48no—
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×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11C22×C414yes—
190C22×Dic11C2×D414yes—
191C22×Dic11C2×D414yes—
192C22×Dic11#4114yes—
193C2×D44—28no—
194C2×D44—48no—
195C2×D44—44no—
196C2×D44—44no—
197C2×D44—48no—
198C11×C4⋊C4—44no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—44no—
201C11×C22⋊C4—44no—
202C42×C11—44no—
203C22⋊Dic11—48no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209C4⋊Dic11—44no—
210Dic11⋊C4—48no—
211C4×Dic11—48no—
212C2×#392—111no—
213C2×#390—111no—
214C2×#390—112no—
215C2×#388—112no—
216C2×#388D1111yescharacteristic, complemented
217#1444—111no—
218#1439—112no—
219#1439—111no—
220#1438—111no—
221#1438—112no—
222C4×#95—111no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—42no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—42no—
233C23×C11—42no—
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—41no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—41no—
246C23×C11C23×C411yescharacteristic
247C23×C11C22×D412yes—
248C23×C11C22×D411yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11C2×#4112yes—
251C23×C11H(5,𝔽2)12yes—
252C23×C11H(5,𝔽2)11yescharacteristic
253C23×C11H(5,𝔽2)12yes—
254C23×C11H(5,𝔽2)11yescharacteristic
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C112−1+411yescharacteristic
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
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—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—41no—
306C2×C4×C11—42no—
307C2×C4×C11—41no—
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×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—42no—
320C2×C4×C11C4×D414yes—
321C2×C4×C11#12714yes—
322C22⋊D11—432no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—42no—
333C2×Dic11—42no—
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—
344D44—416no—
345C23×D4—112no—
346C23×D4—111no—
347C22×C4⋊C4—112no—
348C22×C4⋊C4—111no—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4C2×D1111yescharacteristic
357C22×C22⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4C2×D1111yescharacteristic
359C22×C42—112no—
360C22×C42C2×D1111yescharacteristic
361#392—118no—
362#390—228no—
363#390—224no—
364#388—24no—
365#388—228no—
366C2×#95—111no—
367C2×#95—112no—
368C2×#95—111no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95C2×D1111yescharacteristic
372C2×#95C2×D1111yescharacteristic
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—42no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—82no—
382C22×C11—81no—
383C22×C11—82no—
384C22×C11C2×C4×D411yescharacteristic
385C22×C11C2×C4×D412yes—
386C22×C11#51811yescharacteristic
387C22×C11#51812yes—
388C22×C11#52011yescharacteristic
389C22×C11C2×#12711yescharacteristic
390C22×C11#53212yes—
391C22×C11#53211yescharacteristic
392C22×C11#53411yescharacteristic
393C22×C11#53412yes—
394C22×C11#53511yescharacteristic
395C22×C11#53511yescharacteristic
396C22×C11#53512yes—
397C22×C11#53512yes—
398C22×C11#53711yescharacteristic
399C22×C11#53712yes—
400C22×C11#53812yes—
401C22×C11#53812yes—
402C22×C11#53812yes—
403C22×C11#54011yescharacteristic
404C22×C11#54012yes—
405C22×C11#54212yes—
406C22×C11#54211yescharacteristic
407C2×D11—44no—
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—82no—
415C2×D11—82no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—82no—
420C2×D11—82no—
421C2×D11—82no—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—81no—
427C4×C11—81no—
428Dic11—28no—
429Dic11—44no—
430Dic11—82no—
431C25—112no—
432C25C22×D1111yescharacteristic
433C22×D4—118no—
434C22×D4—114no—
435C22×D4—224no—
436C22×D4—224no—
437C22×D4—222no—
438C22×D4—222no—
439C22×D4—442no—
440C22×D4—442no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4—442no—
445C23×C4—112no—
446C23×C4—112no—
447C23×C4—112no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—442no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4—442no—
480C2×C22⋊C4—442no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C22⋊C4—442no—
484C2×C22⋊C4—442no—
485C2×C22⋊C4C4×D1114yes—
486C2×C42—42no—
487C2×C42—118no—
488C2×C42—442no—
489C2×C42—442no—
490C2×C42C22⋊D1114yescomplemented
491#95—22no—
492#95—22no—
493#95—114no—
494#95—224no—
495#95—224no—
496#95—224no—
497#95—222no—
498C2×C11—82no—
499C2×C11C4×#12711yescharacteristic
500C2×C11#232112yes—
501C2×C11#232111yescharacteristic
502C2×C11#232412yes—
503C2×C11#232411yescharacteristic
504C2×C11#265611yescharacteristic
505C2×C11#265711yescharacteristic
506C2×C11#266111yescharacteristic
507C2×C11#266112yes—
508C2×C11#266211yescharacteristic
509C2×C11#266212yes—
510D11—84no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—21no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—114no—
522C24—222no—
523C24—222no—
524C24—222no—
525C24—222no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24C2×C4×D1112yes—
537C24C23×D1111yescharacteristic
538C2×D4—2216no—
539C2×D4—228no—
540C2×D4—448no—
541C2×D4—444no—
542C2×D4—448no—
543C2×D4—444no—
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—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—114no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—114no—
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×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4C2×C4×D1112yes—
595C22×C4C2×C4×D1112yes—
596C22×C4#433912yes—
597C22×C4D4×D1114yes—
598C22×C4C2×C22⋊D1112yes—
599C22×C4C2×C22⋊D1112yes—
600C22×C4C2×C22⋊D1112yes—
601C4⋊C4—44no—
602C4⋊C4—444no—
603C4⋊C4—448no—
604C22⋊C4—28no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—2216no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C22⋊C4—448no—
613C42—44no—
614C42—448no—
615C11#1432111yescharacteristic, complemented, Sylow
616C23—22no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—224no—
640C23—224no—
641C23—224no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23C22×C4×D1111yescharacteristic
675C23C2×#433911yescharacteristic
676C23C2×D4×D1112yes—
677C23#6703712yes—
678C23#41×D1112yes—
679C23#6704211yescharacteristic
680C23#6704212yes—
681C23#6704211yescharacteristic
682C23#6704211yescharacteristic
683C23#6704311yescharacteristic
684C23C22×C22⋊D1111yescharacteristic
685D4—4416no—
686D4—4432no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—118no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4C4×C22⋊D1114yes—
737C2×C4#6699314yes—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—82no—
747C22—81no—
748C22—82no—
749C22—444no—
750C22—444no—
751C22—444no—
752C22—444no—
753C22—444no—
754C22—444no—
755C22—444no—
756C22—882no—
757C22—882no—
758C22—882no—
759C22—882no—
760C22—882no—
761C22—882no—
762C22—882no—
763C22—882no—
764C22#1062305211yescharacteristic
765C22#1062305411yescharacteristic
766C22#1062306511yescharacteristic
767C22#1062306611yescharacteristic
768C22C4×D4×D1112yes—
769C22#1062307612yes—
770C22#1062307912yes—
771C22#1062309112yes—
772C22#1062312812yes—
773C22#1062313612yes—
774C22#1062318812yes—
775C22#1062319412yes—
776C22#1062320512yes—
777C22#1062320512yes—
778C22#1062323512yes—
779C22#1062324112yes—
780C22C2×C4×C22⋊D1111yescharacteristic
781C22C2×#6699311yescharacteristic
782C22#1062333511yescharacteristic
783C22#1062336111yescharacteristic
784C22#1062336111yescharacteristic
785C22#1062336311yescharacteristic
786C22#1062336411yescharacteristic
787C4—24no—
788C4—24no—
789C4—42no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—228no—
794C4—444no—
795C4—882no—
796C2—82no—
797C2—884no—
798C2C4×#6699311yescharacteristic
799C2#1307126912yes—
800C2#1307127011yescharacteristic
801C2#1307130412yes—
802C2#1307130911yescharacteristic
803C2#1307472011yescharacteristic
804C2#1307472411yescharacteristic
805C2#1307474411yescharacteristic
806C2#1307474812yes—
807C2#1307475611yescharacteristic
808C2#1307475912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11#14321
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. C2×#10622570C2semidirect
4. C2×#10622603C2semidirect
5. #13066880C2semidirect
6. #13066861C2semidirect
7. #13066860C2semidirect
8. #13066856C2semidirect
9. #13066855C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#388C2semidirect
37. #10622573C4semidirect
73. C2×C42×C11D4semidirect
99. C2×C4×Dic11D4semidirect
216. C2×#388D11semidirect
490. C2×C42C22⋊D11semidirect
615. C11#14321semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106225522
C2×#106225702
C2×#106226032
#130668802
#130668612
#130668602
#130668562
#130668552
C4×C11⋊#952
C2×C11×#3882
#1432111