Finite Group Databasebeta

← #14680662

Subgroups — #14680662

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622278C212yesmaximal, complemented
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066856C212yesmaximal, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066852C212yesmaximal, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2212yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622552—24no—
36C4×(C2×D11)⋊C4—24no—
37#10622284C418yescomplemented
38#10622278—28no—
39C24×D11C2312yes—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×D44—24no—
51C22×D44—24no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—42no—
55C22×D44—42no—
56C22×D44—42no—
57C22×D44—42no—
58C22×D44—42no—
59C22×D44—42no—
60C22×D44C2×C418yes—
61C22×D44C2×C414yescomplemented
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—42no—
65C22×C4×D11—42no—
66C22×C4×D11D414yescomplemented
67C2×C42×C11—42no—
68C2×C42×C11D414yescomplemented
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4C2×C414yes—
92C2×(C2×D11)⋊C4C2×C418yescomplemented
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—42no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—42no—
97C11×#95—24no—
98C11×#95—22no—
99C11×#95—42no—
100C11×#95C2×C414yescomplemented
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106#14311—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—22no—
113C23×D11—22no—
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×D11—22no—
129C23×D11—22no—
130C23×D11C22×C414yes—
131C23×D11C22×C412yes—
132C23×D11C2×D412yes—
133C23×D11#4112yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
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—22no—
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×C11C22×C414yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
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×Dic11C22×C412yes—
183C22×Dic11C2×D412yes—
184C22×Dic11#4112yes—
185C2×D44—216no—
186C2×D44—28no—
187C2×D44—48no—
188C2×D44—48no—
189C2×D44—48no—
190C2×D44—44no—
191C2×D44—44no—
192C2×D44—48no—
193C2×D44—48no—
194C2×D44—48no—
195C2×D44—48no—
196C2×D44—48no—
197C2×C4×D11—28no—
198C2×C4×D11—48no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—48no—
202C42×C11—44no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—48no—
211C4⋊Dic11—44no—
212C4×Dic11—44no—
213C2×#392—111no—
214C2×#390—111no—
215C2×#386—112no—
216C2×C4×C22⋊C4—111no—
217#1442—111no—
218#1440—112no—
219#1439—111no—
220#1438—112no—
221#1438—111no—
222#1437—112no—
223#1434D1111yescharacteristic, complemented
224C23×C11C23×C411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11H(5,𝔽2)12yes—
234C23×C11H(5,𝔽2)12yes—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
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—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11C4×D414yes—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
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×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11C4×D414yes—
321C2×C4×C11#12114yes—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
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×Dic11—42no—
344D44—416no—
345D44—432no—
346C4×D11—416no—
347C23×D4—112no—
348C23×D4—111no—
349C24×C4—111no—
350C22×C4⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4—112no—
358C22×C22⋊C4—112no—
359C22×C42—111no—
360C22×C42C2×D1111yescharacteristic
361#392—118no—
362#390—224no—
363#386—228no—
364C4×C22⋊C4—224no—
365C2×#95—111no—
366C2×#95—111no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95C2×D1112yes—
371C2×#95C2×D1111yescharacteristic
372C2×#95C2×D1112yes—
373C2×#95C2×D1111yescharacteristic
374C22×C11C2×C4×D411yescharacteristic
375C22×C11C2×C4×D411yescharacteristic
376C22×C11C4×#4111yescharacteristic
377C22×C11#51812yes—
378C22×C11#51812yes—
379C22×C11C2×#12111yescharacteristic
380C22×C11#52511yescharacteristic
381C22×C11#52911yescharacteristic
382C22×C11#53211yescharacteristic
383C22×C11#53411yescharacteristic
384C22×C11#53412yes—
385C22×C11#53511yescharacteristic
386C22×C11#53511yescharacteristic
387C22×C11#53511yescharacteristic
388C22×C11#53512yes—
389C22×C11#53812yes—
390C22×C11#53812yes—
391C22×C11#53812yes—
392C22×C11#53812yes—
393C22×C11#53812yes—
394C22×C11#54012yes—
395C22×C11#54012yes—
396C22×C11#54012yes—
397C2×D11—28no—
398C2×D11—24no—
399C2×D11—42no—
400C2×D11—42no—
401C2×D11—44no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—44no—
407C2×D11—44no—
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—82no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—82no—
420C2×D11—82no—
421C2×D11—82no—
422C2×D11—82no—
423C4×C11—24no—
424C4×C11—24no—
425C4×C11—44no—
426C4×C11—42no—
427C4×C11—82no—
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—82no—
432C25—111no—
433C25—112no—
434C22×D4—118no—
435C22×D4—114no—
436C22×D4—224no—
437C22×D4—224no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—442no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4—442no—
445C22×D4—442no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—114no—
450C23×C4—112no—
451C23×C4—222no—
452C23×C4—222no—
453C23×C4—442no—
454C23×C4—442no—
455C23×C4C22×D1112yes—
456C23×C4C22×D1112yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C2×C4⋊C4—222no—
461C2×C4⋊C4—442no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—118no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
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—442no—
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⋊C4—442no—
486C2×C42—42no—
487C2×C42—222no—
488C2×C42—442no—
489C2×C42D4414yescomplemented
490#95—22no—
491#95—24no—
492#95—42no—
493#95—224no—
494#95—222no—
495#95—222no—
496#95—442no—
497#95—442no—
498#95C4×D1114yescomplemented
499C2×C11C4×#12111yescharacteristic
500C2×C11#232112yes—
501C2×C11#232111yescharacteristic
502C2×C11#232811yescharacteristic
503C2×C11#233312yes—
504C2×C11#261711yescharacteristic
505C2×C11#261911yescharacteristic
506C2×C11#263111yescharacteristic
507C2×C11#263511yescharacteristic
508C2×C11#264812yes—
509C2×C11#266112yes—
510D11—44no—
511D11—84no—
512C24—112no—
513C24—112no—
514C24—112no—
515C24—114no—
516C24—221no—
517C24—221no—
518C24—222no—
519C24—221no—
520C24—221no—
521C24—222no—
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—
536C24—222no—
537C24—222no—
538C24C23×D1111yescharacteristic
539C2×D4—2216no—
540C2×D4—228no—
541C2×D4—448no—
542C2×D4—448no—
543C2×D4—448no—
544C2×D4—444no—
545C2×D4—444no—
546C2×D4—448no—
547C2×D4—448no—
548C2×D4—448no—
549C2×D4—448no—
550C2×D4—448no—
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—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—228no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—448no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4—448no—
599C22×C4C2×C4×D1114yes—
600C22×C4C2×C4×D1112yes—
601C22×C4C2×D4412yes—
602C22×C4C2×D4412yes—
603C22×C4C2×D4412yes—
604C22×C4#433912yes—
605C22×C4D4×D1112yes—
606C22×C4#434312yes—
607C4⋊C4—444no—
608C22⋊C4—228no—
609C22⋊C4—228no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—44no—
617C42—444no—
618C11#1431111yescharacteristic, complemented, Sylow
619C23—114no—
620C23—224no—
621C23—222no—
622C23—222no—
623C23—224no—
624C23—222no—
625C23—224no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—224no—
639C23—442no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
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—
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—
674C23—442no—
675C23—442no—
676C23—442no—
677C23C22×C4×D1111yescharacteristic
678C23C22×D4411yescharacteristic
679C23C2×#433911yescharacteristic
680C23C2×D4×D1111yescharacteristic
681C23#6703712yes—
682C23C2×#434311yescharacteristic
683C23#41×D1111yescharacteristic
684C23#41×D1111yescharacteristic
685C23#6704212yes—
686C23#6704212yes—
687C23#6704212yes—
688D4—4416no—
689D4—4432no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—224no—
723C2×C4—4416no—
724C2×C4—442no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4C4×D4414yes—
741C2×C4#6694814yes—
742C22—224no—
743C22—228no—
744C22—444no—
745C22—442no—
746C22—444no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—444no—
751C22—442no—
752C22—442no—
753C22—444no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22—444no—
759C22—444no—
760C22—882no—
761C22—882no—
762C22—882no—
763C22—882no—
764C22—882no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22C2×C4×D4411yescharacteristic
769C22#1062302411yescharacteristic
770C22C2×#6694811yescharacteristic
771C22#1062305212yes—
772C22#1062305511yescharacteristic
773C22#1062305611yescharacteristic
774C22#1062305611yescharacteristic
775C22#1062305611yescharacteristic
776C22#1062306612yes—
777C22C4×D4×D1111yescharacteristic
778C22#1062307612yes—
779C22#1062307911yescharacteristic
780C22#1062309112yes—
781C22C4×#434311yescharacteristic
782C22#1062311111yescharacteristic
783C22#1062313612yes—
784C22#1062317512yes—
785C22#1062318812yes—
786C22#1062319412yes—
787C22#1062320512yes—
788C22#1062322912yes—
789C22#1062323512yes—
790C22#1062323512yes—
791C4—24no—
792C4—24no—
793C4—42no—
794C4—44no—
795C4—82no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4—882no—
800C2—444no—
801C2—884no—
802C2C4×#6694811yescharacteristic
803C2#1307126912yes—
804C2#1307127611yescharacteristic
805C2#1307134111yescharacteristic
806C2#1307138012yes—
807C2#1307435311yescharacteristic
808C2#1307436911yescharacteristic
809C2#1307447111yescharacteristic
810C2#1307450311yescharacteristic
811C2#1307461012yes—
812C2#1307474812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1434D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622278C2semidirect
4. C2×C4×(C2×D11)⋊C4C2semidirect
5. #13066873C2semidirect
6. #13066864C2semidirect
7. #13066862C2semidirect
8. #13066856C2semidirect
9. #13066856C2semidirect
10. #13066852C2semidirect
11. C11×#1434C2semidirect
37. #10622284C4semidirect
61. C22×D44C2×C4semidirect
66. C22×C4×D11D4semidirect
68. C2×C42×C11D4semidirect
92. C2×(C2×D11)⋊C4C2×C4semidirect
100. C11×#95C2×C4semidirect
223. #1434D11semidirect
489. C2×C42D44semidirect
498. #95C4×D11semidirect
618. C11#14311semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106225522
C2×#106222782
C2×C4×(C2×D11)⋊C42
#130668732
#130668642
#130668622
#130668562
#130668522
C11×#14342
#1431111