Finite Group Databasebeta

← #14680420

Subgroups — #14680420

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622600C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066856C212yesmaximal
9#13066852C212yesmaximal, complemented
10#13066847C212yesmaximal, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C2×#66947—24no—
27C2×#66947—24no—
28C2×#66947C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622279—24no—
40C24×D11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—42no—
54C22×D44—42no—
55C22×D44C2×C414yes—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D414yes—
60C22×C4×D11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—24no—
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—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4C2×C414yes—
85C2×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—42no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4C2×C414yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—42no—
94C2×C4×Dic11—42no—
95#66947—232no—
96C11×#95—22no—
97C11×#95—42no—
98C11×#95—42no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14287—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11C22×C412yes—
126C23×D11C22×C412yes—
127C23×D11C2×D412yes—
128C23×D11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
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×C11C22×C412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4114yes—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
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×Dic11C22×C412yes—
180C22×Dic11C22×C412yes—
181C22×Dic11C2×D412yes—
182C22×Dic11C2×D412yes—
183C22×Dic11#4114yes—
184C2×D44—28no—
185C2×D44—48no—
186C2×D44—44no—
187C2×D44—48no—
188C2×D44—44no—
189C2×C4×D11—48no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—48no—
193C2×C4×D11C22⋊C4116yescomplemented
194C11×C4⋊C4—28no—
195C11×C4⋊C4—44no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202(C2×D11)⋊C4—48no—
203C4⋊Dic11—44no—
204Dic11⋊C4—28no—
205C4×Dic11—48no—
206C22×#123—111no—
207C2×#380—111no—
208C2×C4×C22⋊C4—111no—
209#1441—111no—
210#1441D1111yescharacteristic, complemented
211#1440—112no—
212#1439—111no—
213#1439—111no—
214#1438—112no—
215#1437—112no—
216#1436—112no—
217C23×C11C23×C411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11H(5,𝔽2)12yes—
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)11yescharacteristic
226C23×C112−1+411yescharacteristic
227C23×C112−1+411yescharacteristic
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—24no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—42no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
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×D11C2×C22⋊C414yes—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—24no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—42no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11C2×C22⋊C414yes—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—42no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11C2×C22⋊C414yes—
329D44—416no—
330C4×D11—416no—
331C23×D4—111no—
332C24×C4—111no—
333C2×#123—118no—
334C2×#123—224no—
335C2×#123—224no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4C2×D1111yescharacteristic
339C22×C4⋊C4C2×D1111yescharacteristic
340C22×C22⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C42—112no—
348#380—224no—
349C4×C22⋊C4—224no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—111no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95C2×D1111yescharacteristic
357C2×#95C2×D1112yes—
358C2×#95C2×D1112yes—
359C22×C11C22×C22⋊C411yescharacteristic
360C22×C11C4×#4112yes—
361C22×C11#51812yes—
362C22×C11#52011yescharacteristic
363C22×C11#52011yescharacteristic
364C22×C11#52512yes—
365C22×C11#53211yescharacteristic
366C22×C11#53211yescharacteristic
367C22×C11#53411yescharacteristic
368C22×C11#53412yes—
369C22×C11#53411yescharacteristic
370C22×C11#53511yescharacteristic
371C22×C11#53611yescharacteristic
372C22×C11#53711yescharacteristic
373C22×C11#53711yescharacteristic
374C22×C11#53812yes—
375C22×C11#53812yes—
376C22×C11#53912yes—
377C22×C11#53912yes—
378C22×C11#54012yes—
379C22×C11#54012yes—
380C22×C11#54212yes—
381C22×C11#54212yes—
382C2×D11—24no—
383C2×D11—24no—
384C2×D11—24no—
385C2×D11—44no—
386C2×D11—44no—
387C2×D11—44no—
388C2×D11—44no—
389C2×D11—42no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—42no—
394C2×D11—42no—
395C2×D11—44no—
396C2×D11—44no—
397C2×D11—42no—
398C2×D11—82no—
399C2×D11—82no—
400C2×D11—81no—
401C2×D11—81no—
402C2×D11—81no—
403C2×D11—81no—
404C4×C11—24no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—44no—
408C4×C11—82no—
409Dic11—24no—
410Dic11—44no—
411Dic11—42no—
412Dic11—82no—
413C25—111no—
414C25—111no—
415C22×D4—114no—
416C22×D4—222no—
417C22×D4—222no—
418C22×D4—442no—
419C22×D4—442no—
420C23×C4—111no—
421C23×C4—114no—
422C23×C4—114no—
423C23×C4—114no—
424C23×C4—111no—
425C23×C4—112no—
426C23×C4—112no—
427C23×C4—442no—
428C23×C4—442no—
429C23×C4C22×D1112yes—
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1112yes—
433C23×C4C22×D1111yescharacteristic
434#123—2232no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—442no—
444C2×C4⋊C4C4×D1114yes—
445C2×C22⋊C4—114no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—114no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—224no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—224no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—222no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—442no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C42—224no—
467C2×C42—442no—
468C2×C42—442no—
469#95—22no—
470#95—42no—
471#95—42no—
472#95—224no—
473#95—224no—
474#95—222no—
475#95—224no—
476#95—442no—
477#95—442no—
478C2×C11#229711yescharacteristic
479C2×C11#230811yescharacteristic
480C2×C11#231111yescharacteristic
481C2×C11#233512yes—
482C2×C11#233512yes—
483C2×C11#263012yes—
484C2×C11#263012yes—
485C2×C11#266111yescharacteristic
486C2×C11#266111yescharacteristic
487C2×C11#266311yescharacteristic
488C2×C11#266311yescharacteristic
489D11—44no—
490D11—82no—
491C24—112no—
492C24—112no—
493C24—112no—
494C24—112no—
495C24—221no—
496C24—222no—
497C24—222no—
498C24—221no—
499C24—222no—
500C24—221no—
501C24—222no—
502C24—221no—
503C24—221no—
504C24—221no—
505C24—221no—
506C24—222no—
507C24—222no—
508C24—221no—
509C24—222no—
510C24—221no—
511C24—222no—
512C24—221no—
513C24C23×D1111yescharacteristic
514C2×D4—228no—
515C2×D4—448no—
516C2×D4—444no—
517C2×D4—448no—
518C2×D4—444no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—112no—
547C22×C4—1116no—
548C22×C4—112no—
549C22×C4—114no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—448no—
570C22×C4—444no—
571C22×C4—448no—
572C22×C4—444no—
573C22×C4C2×C4×D1112yes—
574C22×C4C2×C4×D1112yes—
575C22×C4C2×C4×D1112yes—
576C22×C4D4×D1112yes—
577C22×C4D4×D1112yes—
578C22×C4#434314yes—
579C4⋊C4—28no—
580C4⋊C4—44no—
581C4⋊C4—228no—
582C4⋊C4—444no—
583C22⋊C4—228no—
584C22⋊C4—228no—
585C22⋊C4—2216no—
586C22⋊C4—228no—
587C22⋊C4—448no—
588C22⋊C4—448no—
589C22⋊C4—448no—
590C42—448no—
591C11#1428711yescharacteristic, complemented, Sylow
592C23—114no—
593C23—222no—
594C23—222no—
595C23—222no—
596C23—224no—
597C23—224no—
598C23—222no—
599C23—224no—
600C23—222no—
601C23—222no—
602C23—224no—
603C23—222no—
604C23—222no—
605C23—222no—
606C23—222no—
607C23—222no—
608C23—222no—
609C23—222no—
610C23—224no—
611C23—224no—
612C23—442no—
613C23—442no—
614C23—442no—
615C23—442no—
616C23—442no—
617C23—442no—
618C23—442no—
619C23—442no—
620C23—442no—
621C23—441no—
622C23—442no—
623C23—441no—
624C23—442no—
625C23—441no—
626C23—441no—
627C23—442no—
628C23—442no—
629C23—441no—
630C23—441no—
631C23—442no—
632C23—442no—
633C23—441no—
634C23—442no—
635C23—441no—
636C23—442no—
637C23—442no—
638C23C22×C4×D1111yescharacteristic
639C23C2×D4×D1111yescharacteristic
640C23C2×D4×D1111yescharacteristic
641C23#6703712yes—
642C23#6703711yescharacteristic
643C23C2×#434312yes—
644C23#6704011yescharacteristic
645C23#41×D1112yes—
646C23#6704212yes—
647C23#6704211yescharacteristic
648C23#6704311yescharacteristic
649D4—4416no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—114no—
681C2×C4—224no—
682C2×C4—222no—
683C2×C4—224no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—224no—
690C2×C4—4416no—
691C2×C4—441no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—441no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4C22⋊C4×D1114yes—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—444no—
710C22—444no—
711C22—444no—
712C22—444no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—442no—
718C22—444no—
719C22—444no—
720C22—442no—
721C22—442no—
722C22—882no—
723C22—882no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22C2×C22⋊C4×D1111yescharacteristic
729C22#1062303511yescharacteristic
730C22#1062305411yescharacteristic
731C22#1062307612yes—
732C22C4×#434312yes—
733C22#1062312011yescharacteristic
734C22#1062313612yes—
735C22#1062313811yescharacteristic
736C22#1062313911yescharacteristic
737C22#1062314612yes—
738C22#1062315812yes—
739C22#1062315911yescharacteristic
740C22#1062316011yescharacteristic
741C22#1062317512yes—
742C22#1062317612yes—
743C22#1062318411yescharacteristic
744C22#1062318812yes—
745C22#1062319911yescharacteristic
746C22#1062322312yes—
747C22#1062322912yes—
748C22#1062324112yes—
749C22#1062325611yescharacteristic
750C22#1062326412yes—
751C4—24no—
752C4—44no—
753C4—42no—
754C4—42no—
755C4—82no—
756C4—224no—
757C4—442no—
758C4—444no—
759C4—882no—
760C2—444no—
761C2—882no—
762C2#1307110511yescharacteristic
763C2#1307119011yescharacteristic
764C2#1307120511yescharacteristic
765C2#1307140512yes—
766C2#1307140912yes—
767C2#1307446212yes—
768C2#1307446612yes—
769C2#1307474911yescharacteristic
770C2#1307475111yescharacteristic
771C2#1307477111yescharacteristic
772C2#1307477311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14287
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#10622600C2semidirect
3. C2×#10622279C2semidirect
4. #13066869C2semidirect
5. #13066864C2semidirect
6. #13066862C2semidirect
7. #13066858C2semidirect
9. #13066852C2semidirect
10. #13066847C2semidirect
11. C11×#1441C2semidirect
28. C2×#66947C4semidirect
193. C2×C4×D11C22⋊C4semidirect
210. #1441D11semidirect
591. C11#14287semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106226002
C2×#106222792
#130668692
#130668642
#130668622
#130668582
#130668562
#130668522
#130668472
C11×#14412
#1428711