Finite Group Databasebeta

← #14680778

Subgroups — #14680778

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×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622570C212yesmaximal, complemented
4C2×#10622564C211yesmaximal, characteristic, complemented
5C2×#10622283C212yesmaximal, complemented
6#13066879C211yesmaximal, characteristic, complemented
7#13066860C212yesmaximal, complemented
8#13066856C211yesmaximal, characteristic, complemented
9#13066855C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35#10622601—24no—
36#10622573C418yescomplemented
37#10622570—28no—
38#10622564—24no—
39#10622283—28no—
40C25×C11C2311yescharacteristic
41C24×D11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—24no—
47C22×C22⋊D11—24no—
48C22×C22⋊D11—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11C2×C418yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—42no—
61C22×D44—42no—
62C22×D44C2×C414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—42no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4C2×C414yes—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—42no—
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—24no—
82C2×(C2×D11)⋊C4—24no—
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—24no—
91C2×C4⋊Dic11—22no—
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×Dic11D418yescomplemented
99C2×C4×Dic11D414yescomplemented
100C11×#95—24no—
101C11×#95—22no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—22no—
105C11⋊#95—24no—
106C11⋊#95C2×C414yes—
107#14321—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—21no—
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—22no—
136C22×C4×C11—22no—
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—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×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C2×C22⋊D11—216no—
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—21no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11C22×C414yes—
188C22×Dic11C2×D412yes—
189C22×Dic11C2×D414yes—
190C22×Dic11C2×D414yes—
191C22×Dic11C2×D412yes—
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—48no—
201C22⋊Dic11—44no—
202C22⋊Dic11—44no—
203(C2×D11)⋊C4—216no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208C4⋊Dic11—44no—
209Dic11⋊C4—48no—
210C4×Dic11—44no—
211C4×Dic11—48no—
212C2×#392—111no—
213C2×#390—111no—
214C2×#390—112no—
215C2×#388—112no—
216C2×#388—111no—
217#1444—111no—
218#1439—112no—
219#1439D1111yescharacteristic, complemented
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×D411yescharacteristic
248C23×C11C22×D412yes—
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—22no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—41no—
302C2×C4×C11—42no—
303C2×C4×C11—41no—
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×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11C4×D414yes—
316C22⋊D11—432no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—41no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—42no—
341C2×Dic11—41no—
342C2×Dic11C4×D418yes—
343C2×Dic11#12714yes—
344D44—416no—
345C23×D4—112no—
346C23×D4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—112no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—111no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4C2×D1112yes—
359C22×C42—112no—
360C22×C42—111no—
361#392—118no—
362#390—228no—
363#390—224no—
364#388—228no—
365#388—224no—
366C2×#95—111no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—111no—
370C2×#95—111no—
371C2×#95C2×D1111yescharacteristic
372C2×#95C2×D1112yes—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—44no—
376C22×C11—42no—
377C22×C11—44no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—82no—
381C22×C11—81no—
382C22×C11—82no—
383C22×C11—81no—
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#53412yes—
393C22×C11#53411yescharacteristic
394C22×C11#53511yescharacteristic
395C22×C11#53512yes—
396C22×C11#53512yes—
397C22×C11#53511yescharacteristic
398C22×C11#53712yes—
399C22×C11#53711yescharacteristic
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—42no—
424C4×C11—44no—
425C4×C11—82no—
426Dic11—28no—
427Dic11—24no—
428Dic11—42no—
429Dic11—81no—
430Dic11—81no—
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—111no—
446C23×C4—112no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4C22×D1112yes—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1112yes—
453C23×C4C22×D1111yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—118no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—222no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
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—118no—
487C2×C42—114no—
488C2×C42—442no—
489C2×C42—442no—
490C2×C42—442no—
491#95—24no—
492#95—22no—
493#95—114no—
494#95—224no—
495#95—222no—
496#95—224no—
497#95—222no—
498C2×C11—82no—
499C2×C11C4×#12711yescharacteristic
500C2×C11#232112yes—
501C2×C11#232111yescharacteristic
502C2×C11#232411yescharacteristic
503C2×C11#232412yes—
504C2×C11#265611yescharacteristic
505C2×C11#265711yescharacteristic
506C2×C11#266112yes—
507C2×C11#266111yescharacteristic
508C2×C11#266212yes—
509C2×C11#266211yescharacteristic
510D11—84no—
511C24—21no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—22no—
518C24—22no—
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—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—114no—
570C22×C4—114no—
571C22×C4—112no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—112no—
575C22×C4—222no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—221no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—221no—
593C22×C4—222no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4C2×C4×D1112yes—
597C22×C4C2×C4×D1112yes—
598C22×C4D4×D1114yes—
599C22×C4D4×D1112yes—
600C22×C4#434112yes—
601C4⋊C4—44no—
602C4⋊C4—444no—
603C4⋊C4—448no—
604C22⋊C4—28no—
605C22⋊C4—48no—
606C22⋊C4—2216no—
607C22⋊C4—448no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C22⋊C4—448no—
611C22⋊C4—444no—
612C22⋊C4—444no—
613C42—444no—
614C42—448no—
615C11#1432111yescharacteristic, complemented, Sylow
616C23—22no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—41no—
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×D4×D1111yescharacteristic
676C23C2×D4×D1112yes—
677C23C2×#434111yescharacteristic
678C23#6703711yescharacteristic
679C23#6703712yes—
680C23#6704011yescharacteristic
681C23#41×D1112yes—
682C23#6704211yescharacteristic
683C23#6704212yes—
684C23#6704211yescharacteristic
685D4—4416no—
686D4—4432no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—114no—
711C2×C4—118no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—224no—
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—442no—
726C2×C4—442no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—442no—
730C2×C4—441no—
731C2×C4—442no—
732C2×C4—441no—
733C2×C4—442no—
734C2×C4—441no—
735C2×C4—442no—
736C2×C4—441no—
737C2×C4(C22⋊D11)⋊C414yes—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—81no—
744C22—81no—
745C22—82no—
746C22—81no—
747C22—82no—
748C22—81no—
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—
764C22C2×(C22⋊D11)⋊C411yescharacteristic
765C22#1062303511yescharacteristic
766C22#1062305211yescharacteristic
767C22C4×D4×D1112yes—
768C22#1062307612yes—
769C22#1062312312yes—
770C22#1062312311yescharacteristic
771C22#1062312712yes—
772C22#1062313811yescharacteristic
773C22#1062313812yes—
774C22#1062314812yes—
775C22#1062315011yescharacteristic
776C22#1062316012yes—
777C22#1062316011yescharacteristic
778C22#1062317112yes—
779C22#1062317411yescharacteristic
780C22#1062318412yes—
781C22#1062318411yescharacteristic
782C22#1062319412yes—
783C22#1062319911yescharacteristic
784C22#1062320912yes—
785C22#1062323512yes—
786C22D11×#12711yescharacteristic
787C4—24no—
788C4—44no—
789C4—42no—
790C4—82no—
791C4—224no—
792C4—228no—
793C4—442no—
794C4—881no—
795C4—881no—
796C2—82no—
797C2—884no—
798C2#1307118011yescharacteristic
799C2#1307127812yes—
800C2#1307127911yescharacteristic
801C2#1307130511yescharacteristic
802C2#1307130812yes—
803C2#1307471911yescharacteristic
804C2#1307472111yescharacteristic
805C2#1307474312yes—
806C2#1307475011yescharacteristic
807C2#1307475412yes—
808C2#1307476211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14321
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622564C2semidirect
5. C2×#10622283C2semidirect
6. #13066879C2semidirect
7. #13066860C2semidirect
8. #13066856C2semidirect
9. #13066855C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1439C2semidirect
36. #10622573C4semidirect
98. C2×C4×Dic11D4semidirect
99. C2×C4×Dic11D4semidirect
219. #1439D11semidirect
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×#106226012
C2×#106225702
C2×#106225642
C2×#106222832
#130668792
#130668602
#130668562
#130668552
#95×Dic112
C11×#14392
#1432111