Finite Group Databasebeta

← #14681176

Subgroups — #14681176

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622603C212yesmaximal, complemented
2C2×#10622568C212yesmaximal
3C2×#10622568C211yesmaximal, characteristic
4#13066864C212yesmaximal, complemented
5#13066862C212yesmaximal, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066853C212yesmaximal, complemented
8#13066852C212yesmaximal, complemented
9C11×#1439C211yesmaximal, characteristic, complemented
10C25×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic, complemented
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic, complemented
23C22×C4×Dic11C2212yescomplemented
24C2×C11×#95C2212yescomplemented
25C2×C11×#95C2211yescharacteristic, complemented
26C2×C11⋊#95C2212yescomplemented
27C2×C11⋊#95C2212yescomplemented
28C2×C11⋊#95C2211yescharacteristic, complemented
29C2×C11⋊#95C2212yescomplemented
30C2×C11⋊#95C2212yescomplemented
31#10622603—28no—
32#10622568—28no—
33#10622568C418yescomplemented
34C25×C11C2311yescharacteristic
35C24×D11—22no—
36C24×D11—22no—
37C24×D11—24no—
38C24×D11—24no—
39C24×D11—41no—
40C24×D11—41no—
41C24×D11—42no—
42C24×D11—42no—
43C24×D11—41no—
44C24×D11—41no—
45C24×D11C2×C414yes—
46C24×D11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—41no—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—41no—
59C2×C11×C22⋊C4—41no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4C2×C414yes—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—41no—
65C2×C22⋊Dic11—41no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11C2×C414yes—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4—42no—
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)⋊C4C2×C418yes—
84C2×(C2×D11)⋊C4C2×C418yes—
85C2×(C2×D11)⋊C4D418yes—
86C2×C4⋊Dic11—41no—
87C2×C4⋊Dic11—42no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—42no—
90C2×C4×Dic11—42no—
91C11×#95—42no—
92C11×#95—41no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—41no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98#14366—111nomaximal, Sylow
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—21no—
102C24×C11—21no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11C22×C412yes—
108C24×C11#4112yes—
109C24×C11#4112yes—
110C24×C11C2411yescharacteristic
111C23×D11—22no—
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—28no—
124C23×D11—216no—
125C23×D11—48no—
126C23×D11—44no—
127C23×D11—44no—
128C23×D11—44no—
129C23×D11—48no—
130C23×D11—44no—
131C23×D11—48no—
132C23×D11—48no—
133C23×D11—48no—
134C23×D11—48no—
135C23×D11—48no—
136C23×D11—48no—
137C23×D11—48no—
138C23×D11—48no—
139C23×D11—44no—
140C23×D11—44no—
141C23×D11—44no—
142C23×D11—44no—
143C23×D11—44no—
144C23×D11—48no—
145C23×D11—44no—
146C23×D11C22×C414yes—
147C23×D11C2×D414yes—
148C23×D11#4114yes—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C22×C412yes—
172C22×C4×C11C2×D414yes—
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×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11C22×C414yes—
193C22×Dic11C2×D414yes—
194C11×C4⋊C4—44no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4—48no—
197C22⋊Dic11—44no—
198C22⋊Dic11—48no—
199(C2×D11)⋊C4—216no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202(C2×D11)⋊C4—48no—
203(C2×D11)⋊C4—48no—
204(C2×D11)⋊C4—48no—
205C4⋊Dic11—44no—
206C4×Dic11—48no—
207C2×#388—112no—
208C2×#379—111no—
209C2×#379—112no—
210#1440—112no—
211#1439—112no—
212#1439—111no—
213#1439D1111yescharacteristic, complemented
214#1437—112no—
215#1437—112no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11#11714yes—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D412yes—
241C23×C11C2×#4111yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11C2×#4112yes—
244C23×C11H(5,𝔽2)12yes—
245C23×C11H(5,𝔽2)11yescharacteristic
246C23×C11H(5,𝔽2)11yescharacteristic
247C23×C11H(5,𝔽2)11yescharacteristic
248C23×C11H(5,𝔽2)11yescharacteristic
249C23×C11H(5,𝔽2)12yes—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—416no—
269C22×D11—432no—
270C22×D11—432no—
271C22×D11—416no—
272C22×D11—416no—
273C22×D11—416no—
274C22×D11—416no—
275C22×D11—432no—
276C22×D11—432no—
277C22×D11—416no—
278C22×D11—416no—
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×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11C4×D418yes—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—41no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
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×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
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—
341C26—111no—
342C22×C4⋊C4—111no—
343C22×C4⋊C4C2×D1111yescharacteristic, complemented
344C22×C22⋊C4—112no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4C2×D1112yes—
353C22×C22⋊C4C2×D1111yescharacteristic
354C22×C42—112no—
355#388—228no—
356#379—118no—
357#379—228no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95C2×D1112yescomplemented
364C2×#95C2×D1111yescharacteristic, complemented
365C22×C11—24no—
366C22×C11—28no—
367C22×C11—44no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11C2×#11711yescharacteristic
377C22×C11C2×C4×D412yes—
378C22×C11#51811yescharacteristic
379C22×C11#51811yescharacteristic
380C22×C11#51812yes—
381C22×C11#53412yes—
382C22×C11#53512yes—
383C22×C11#53812yes—
384C22×C11#53811yescharacteristic
385C22×C11#53811yescharacteristic
386C22×C11#53811yescharacteristic
387C22×C11#53811yescharacteristic
388C22×C11#53812yes—
389C22×C11D4211yescharacteristic
390C22×C11#54612yes—
391C22×C11#54612yes—
392C22×C11#54612yes—
393C22×C11#55112yes—
394C22×C11#55112yes—
395C22×C11#55111yescharacteristic
396C22×C11#56011yescharacteristic
397C22×C11#56012yes—
398C22×C11H(3,𝔽4)11yescharacteristic
399C2×D11—28no—
400C2×D11—28no—
401C2×D11—28no—
402C2×D11—464no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
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—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—44no—
418C4×C11—82no—
419Dic11—44no—
420Dic11—44no—
421Dic11—82no—
422C25—112no—
423C25—114no—
424C25—224no—
425C25—224no—
426C25—222no—
427C25—222no—
428C25—442no—
429C25—441no—
430C25—441no—
431C25—442no—
432C25—441no—
433C25—441no—
434C25C22×D1111yescharacteristic
435C23×C4—112no—
436C23×C4—112no—
437C23×C4—112no—
438C23×C4C22×D1112yes—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1112yes—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—441no—
445C2×C4⋊C4—442no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—118no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—118no—
454C2×C22⋊C4—118no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—441no—
473C2×C22⋊C4—441no—
474C2×C22⋊C4—442no—
475C2×C22⋊C4C4×D1114yes—
476C2×C42—224no—
477C2×C42—442no—
478C2×C42—442no—
479#95—41no—
480#95—42no—
481#95—224no—
482#95—224no—
483#95—441no—
484#95—442no—
485#95—442no—
486C2×C11—44no—
487C2×C11#231211yescharacteristic
488C2×C11#232112yes—
489C2×C11#234212yes—
490C2×C11#235811yescharacteristic
491C2×C11#237511yescharacteristic
492C2×C11#266811yescharacteristic
493C2×C11#267011yescharacteristic
494C2×C11#268512yes—
495C2×C11#269712yes—
496C2×C11#273511yescharacteristic
497C2×C11#273611yescharacteristic
498D11—48no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—114no—
508C24—114no—
509C24—114no—
510C24—2216no—
511C24—222no—
512C24—222no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—222no—
522C24—222no—
523C24—228no—
524C24—444no—
525C24—444no—
526C24—448no—
527C24—448no—
528C24—448no—
529C24—448no—
530C24—448no—
531C24—444no—
532C24—444no—
533C24—444no—
534C24—444no—
535C24—444no—
536C24—448no—
537C24—444no—
538C24—448no—
539C24—448no—
540C24—448no—
541C24—448no—
542C24—444no—
543C24—448no—
544C24—444no—
545C24C2×C4×D1112yes—
546C24#434112yes—
547C24#434312yes—
548C24C23×D1111yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
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—22no—
570C22×C4—114no—
571C22×C4—114no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
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×C4C2×C4×D1112yes—
592C22×C4C2×C4×D1112yes—
593C22×C4D4×D1114yes—
594C4⋊C4—44no—
595C4⋊C4—444no—
596C22⋊C4—44no—
597C22⋊C4—48no—
598C22⋊C4—2216no—
599C22⋊C4—448no—
600C22⋊C4—448no—
601C22⋊C4—448no—
602C22⋊C4—448no—
603C22⋊C4—448no—
604C22⋊C4—444no—
605C22⋊C4—448no—
606C42—448no—
607C11#1436611yescharacteristic, complemented, Sylow
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—41no—
630C23—118no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—224no—
639C23—224no—
640C23—224no—
641C23—224no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—4432no—
650C23—4416no—
651C23—4416no—
652C23—4432no—
653C23—4432no—
654C23—4416no—
655C23—4416no—
656C23—4416no—
657C23—4416no—
658C23—4416no—
659C23—4432no—
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#6694514yes—
677C23C22×C4×D1111yescharacteristic
678C23C2×D4×D1112yes—
679C23C2×#434111yescharacteristic
680C23#6703711yescharacteristic
681C23#6703712yes—
682C23#6703711yescharacteristic
683C23C2×#434311yescharacteristic
684C23#41×D1112yes—
685C23#6704211yescharacteristic
686C23#6704212yes—
687C23#6704211yescharacteristic
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C22—28no—
734C22—24no—
735C22—44no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—42no—
744C22—228no—
745C22—228no—
746C22—228no—
747C22—4464no—
748C22—444no—
749C22—444no—
750C22—444no—
751C22—444no—
752C22—444no—
753C22—444no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22—444no—
759C22—444no—
760C22#1062301711yescharacteristic
761C22C2×#6694511yescharacteristic
762C22#1062305211yescharacteristic
763C22C4×D4×D1112yes—
764C22#1062307612yes—
765C22#1062312111yescharacteristic
766C22#1062312212yes—
767C22#1062313612yes—
768C22#1062314312yes—
769C22#1062314811yescharacteristic
770C22#1062314811yescharacteristic
771C22#1062315112yes—
772C22#1062316112yes—
773C22#1062316812yes—
774C22#1062317511yescharacteristic
775C22#1062317511yescharacteristic
776C22#1062318812yes—
777C22#1062318912yes—
778C22#1062319011yescharacteristic
779C22#1062320512yes—
780C22#1062321411yescharacteristic
781C22#1062323512yes—
782C22#1062325111yescharacteristic
783C4—44no—
784C4—42no—
785C4—42no—
786C4—82no—
787C4—444no—
788C4—444no—
789C4—882no—
790C2—44no—
791C2—448no—
792C2#1307121311yescharacteristic
793C2#1307126912yes—
794C2#1307146312yes—
795C2#1307159911yescharacteristic
796C2#1307175311yescharacteristic
797C2#1307481811yescharacteristic
798C2#1307483611yescharacteristic
799C2#1307500612yes—
800C2#1307517412yes—
801C2#1307565811yescharacteristic
802C2#1307566311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1439D11
hypocenterC11#14366
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#10622603C2semidirect
4. #13066864C2semidirect
5. #13066862C2semidirect
6. #13066861C2semidirect
7. #13066853C2semidirect
8. #13066852C2semidirect
9. C11×#1439C2semidirect
11. C22×C11×C4⋊C4C22semidirect
22. C22×C4⋊Dic11C22semidirect
23. C22×C4×Dic11C22semidirect
24. C2×C11×#95C22semidirect
25. C2×C11×#95C22semidirect
26. C2×C11⋊#95C22semidirect
27. C2×C11⋊#95C22semidirect
28. C2×C11⋊#95C22semidirect
29. C2×C11⋊#95C22semidirect
30. C2×C11⋊#95C22semidirect
33. #10622568C4semidirect
213. #1439D11semidirect
343. C22×C4⋊C4C2×D11semidirect
363. C2×#95C2×D11semidirect
364. C2×#95C2×D11semidirect
607. C11#14366semidirect

Maximal subgroups

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

subgroupindex
C2×#106226032
C2×#106225682
#130668642
#130668622
#130668612
#130668532
#130668522
C11×#14392
#1436611