Finite Group Databasebeta

← #14680780

Subgroups — #14680780

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×#10622570C212yesmaximal, complemented
3C2×#10622558C212yesmaximal, complemented
4C2×#10622553C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066859C212yesmaximal, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066857C211yesmaximal, characteristic, complemented
9#13066855C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C11×#390—24no—
29#10622836C418yescomplemented
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37#10622570—28no—
38#10622558—28no—
39#10622553—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×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
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×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C42×C11—42no—
72C2×C42×C11D414yescomplemented
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11C2×C418yes—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4C2×C414yes—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—24no—
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—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—21no—
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—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
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—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
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—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11C22×C412yes—
194C22×Dic11C22×C414yes—
195C22×Dic11C2×D414yes—
196C22×Dic11C2×D414yes—
197C22×Dic11#4114yes—
198C11×C4⋊C4—44no—
199C11×C22⋊C4—48no—
200C11×C22⋊C4—48no—
201C42×C11—44no—
202C22⋊Dic11—216no—
203C22⋊Dic11—48no—
204C22⋊Dic11—48no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—44no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—44no—
209Dic11⋊C4—48no—
210Dic11⋊C4—44no—
211C4×Dic11—48no—
212C2×#392—111no—
213C2×#390—112no—
214C2×#390D1111yescharacteristic, complemented
215C2×#388—111no—
216C2×#388—112no—
217#1444—111no—
218#1439—111no—
219#1439—112no—
220#1438—111no—
221#1438—112no—
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×D412yes—
260C23×C11C22×D411yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4112yes—
263C23×C11H(5,𝔽2)12yes—
264C23×C11H(5,𝔽2)12yes—
265C23×C11H(5,𝔽2)11yescharacteristic
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—41no—
291C22×D11—42no—
292D4×C11—416no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
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×C11—42no—
313C2×C4×C11C4×D414yes—
314C2×C4×C11#12714yes—
315C22⋊D11—432no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—41no—
328C2×Dic11—42no—
329C2×Dic11—41no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—42no—
344C2×Dic11C4×D418yes—
345C23×D4—112no—
346C23×D4C2×D1111yescharacteristic
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—112no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—111no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—111no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1112yes—
358C22×C22⋊C4C2×D1112yes—
359C22×C42—112no—
360C22×C42C2×D1111yescharacteristic
361#392—118no—
362#390—24no—
363#390—228no—
364#388—228no—
365#388—224no—
366C2×#95—111no—
367C2×#95—112no—
368C2×#95—111no—
369C2×#95—112no—
370C2×#95—111no—
371C2×#95—112no—
372C2×#95—111no—
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#53411yescharacteristic
397C22×C11#53412yes—
398C22×C11#53512yes—
399C22×C11#53512yes—
400C22×C11#53511yescharacteristic
401C22×C11#53511yescharacteristic
402C22×C11#53711yescharacteristic
403C22×C11#53712yes—
404C22×C11#53812yes—
405C22×C11#53812yes—
406C22×C11#53812yes—
407C22×C11#54011yescharacteristic
408C22×C11#54012yes—
409C22×C11#54211yescharacteristic
410C22×C11#54212yes—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—42no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—82no—
420C2×D11—81no—
421C2×D11—82no—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—42no—
425C4×C11—82no—
426Dic11—28no—
427Dic11—42no—
428Dic11—44no—
429Dic11—81no—
430Dic11—81no—
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—112no—
446C23×C4—111no—
447C23×C4—112no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4C22×D1112yes—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
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—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—222no—
478C2×C22⋊C4—222no—
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⋊C4—442no—
486C2×C42—42no—
487C2×C42—118no—
488C2×C42—442no—
489C2×C42—442no—
490C2×C42C22⋊D1114yescomplemented
491#95—114no—
492#95—224no—
493#95—224no—
494#95—224no—
495#95—222no—
496#95—222no—
497#95—222no—
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#266111yescharacteristic
507C2×C11#266112yes—
508C2×C11#266211yescharacteristic
509C2×C11#266212yes—
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—222no—
530C24—222no—
531C24—221no—
532C24—222no—
533C24—221no—
534C24—221no—
535C24—221no—
536C24C2×C4×D1114yes—
537C24C23×D1111yescharacteristic
538C2×D4—28no—
539C2×D4—48no—
540C2×D4—48no—
541C2×D4—44no—
542C2×D4—44no—
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—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—114no—
567C22×C4—114no—
568C22×C4—114no—
569C22×C4—112no—
570C22×C4—114no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
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—448no—
603C4⋊C4—444no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—2216no—
607C22⋊C4—228no—
608C22⋊C4—444no—
609C22⋊C4—448no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C22⋊C4—444no—
613C42—44no—
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—224no—
652C23—222no—
653C23—224no—
654C23—222no—
655C23—222no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—441no—
660C23—442no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—441no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23C22×C4×D1111yescharacteristic
675C23C2×#433911yescharacteristic
676C23C2×D4×D1112yes—
677C23#6703712yes—
678C23#6703711yescharacteristic
679C23#6703711yescharacteristic
680C23#6703712yes—
681C23#41×D1112yes—
682C23#6704211yescharacteristic
683C23#6704311yescharacteristic
684C23C22×C22⋊D1111yescharacteristic
685D4—416no—
686D4—4432no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—118no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—442no—
720C2×C4—441no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—441no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4C4×C22⋊D1114yes—
737C2×C4#6699314yes—
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—881no—
761C22—882no—
762C22—881no—
763C22—882no—
764C22#1062301712yes—
765C22#1062302512yes—
766C22C4×D4×D1112yes—
767C22#1062307611yescharacteristic
768C22#1062307711yescharacteristic
769C22#1062307912yes—
770C22#1062309211yescharacteristic
771C22#1062309311yescharacteristic
772C22#1062312812yes—
773C22#1062313612yes—
774C22#1062314412yes—
775C22#1062314612yes—
776C22#1062320012yes—
777C22#1062320912yes—
778C22#1062324612yes—
779C22#1062324612yes—
780C22C2×C4×C22⋊D1111yescharacteristic
781C22C2×#6699311yescharacteristic
782C22#1062333511yescharacteristic
783C22#1062333611yescharacteristic
784C22#1062333611yescharacteristic
785C22#1062336311yescharacteristic
786C22#1062336411yescharacteristic
787C4—24no—
788C4—24no—
789C4—42no—
790C4—82no—
791C4—228no—
792C4—444no—
793C4—442no—
794C4—881no—
795C4—881no—
796C2—84no—
797C2—882no—
798C2C4×#6699311yescharacteristic
799C2#1307127411yescharacteristic
800C2#1307127512yes—
801C2#1307130212yes—
802C2#1307130311yescharacteristic
803C2#1307472011yescharacteristic
804C2#1307472311yescharacteristic
805C2#1307474511yescharacteristic
806C2#1307474612yes—
807C2#1307475511yescharacteristic
808C2#1307475712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#390D11
hypocenterC11#14321
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622558C2semidirect
4. C2×#10622553C2semidirect
5. #13066879C2semidirect
6. #13066859C2semidirect
7. #13066858C2semidirect
8. #13066857C2semidirect
9. #13066855C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#390C2semidirect
29. #10622836C4semidirect
72. C2×C42×C11D4semidirect
99. C2×C4×Dic11D4semidirect
214. C2×#390D11semidirect
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×#106228362
C2×#106225702
C2×#106225582
C2×#106225532
#130668792
#130668592
#130668582
#130668572
#130668552
C4×C11⋊#952
C2×C11×#3902
#1432111