Finite Group Databasebeta

← #14676838

Subgroups — #14676838

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C211yesmaximal, characteristic
2C2×#10622603C212yesmaximal, complemented
3C2×#10622568C211yesmaximal, characteristic
4C2×#10622568C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066852C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yescomplemented
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4—24no—
21C22×(C2×D11)⋊C4—28no—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic, complemented
29C22×C4×Dic11C2211yescharacteristic, complemented
30C11×#385—24no—
31C2×C11×#95C2212yescomplemented
32C2×C11⋊#95C2212yescomplemented
33C2×C11⋊#95C2212yescomplemented
34C2×C11⋊#95C2211yescharacteristic, complemented
35C2×C11⋊#95C2211yescharacteristic, complemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38#10622603—28no—
39#10622568—24no—
40#10622568C418yescomplemented
41C22⋊C4×Dic11—24no—
42C25×C11C2311yescharacteristic
43C24×D11—22no—
44C24×D11—22no—
45C24×D11—24no—
46C24×D11—24no—
47C24×D11—22no—
48C24×D11—22no—
49C24×D11—22no—
50C24×D11—22no—
51C24×D11—42no—
52C24×D11—42no—
53C24×D11C2×C414yes—
54C24×D11C2312yes—
55C23×C4×C11—22no—
56C23×C4×C11—24no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—42no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—24no—
67C23×Dic11—42no—
68C23×Dic11D414yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—42no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4C2×C414yes—
82C2×C11×C22⋊C4D414yes—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11C2×C414yes—
89C2×(C2×D11)⋊C4—232no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4—42no—
103C2×(C2×D11)⋊C4—42no—
104C2×(C2×D11)⋊C4—42no—
105C2×(C2×D11)⋊C4C2×C418yescomplemented
106C2×(C2×D11)⋊C4C2×C418yescomplemented
107C2×(C2×D11)⋊C4D418yes—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—42no—
112C11×#95—24no—
113C11⋊#95—24no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—24no—
117C11⋊#95—42no—
118C11⋊#95—42no—
119#13991—111nomaximal, Sylow
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11C22×C412yes—
125C24×C11C2×D412yes—
126C24×C11C2×D412yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11#4112yes—
130C24×C11#4112yes—
131C24×C11C2411yescharacteristic
132C23×D11—28no—
133C23×D11—216no—
134C23×D11—28no—
135C23×D11—28no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—216no—
149C23×D11—28no—
150C23×D11—28no—
151C23×D11—48no—
152C23×D11—48no—
153C23×D11—48no—
154C23×D11—48no—
155C23×D11—48no—
156C23×D11—48no—
157C23×D11—48no—
158C23×D11—48no—
159C23×D11—48no—
160C23×D11—44no—
161C23×D11—44no—
162C23×D11—48no—
163C23×D11—44no—
164C23×D11—44no—
165C23×D11—44no—
166C23×D11—44no—
167C23×D11C22×C414yes—
168C23×D11C2×D414yes—
169C23×D11#4114yes—
170C22×C4×C11—28no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—48no—
192C22×C4×C11—48no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11C22×C414yes—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—22no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—22no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—44no—
224C22×Dic11—48no—
225C22×Dic11—48no—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C412yes—
228C22×Dic11C2×D412yes—
229C22×Dic11C2×D414yes—
230C22×Dic11C2×D412yes—
231C11×C4⋊C4—48no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C22⋊Dic11—28no—
235C22⋊Dic11—44no—
236(C2×D11)⋊C4—216no—
237(C2×D11)⋊C4—216no—
238(C2×D11)⋊C4—216no—
239(C2×D11)⋊C4—48no—
240(C2×D11)⋊C4—48no—
241(C2×D11)⋊C4—48no—
242C4×Dic11—44no—
243C4×Dic11—44no—
244C23×C22⋊C4—111no—
245C2×#388—112no—
246C2×#385D1111yescharacteristic, complemented
247C2×#379—111no—
248C2×#379—111no—
249C2×C4×C22⋊C4—111no—
250#1440—112no—
251#1439—112no—
252#1437—112no—
253C22⋊#95—111no—
254C22⋊#95—111no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11#11714yes—
272C23×C11C4×D414yes—
273C23×C11C4×D414yes—
274C23×C11#12114yes—
275C23×C11#12314yes—
276C23×C11#12414yes—
277C23×C11#12614yes—
278C23×C11C23×C411yescharacteristic
279C23×C11C22×D411yescharacteristic
280C23×C11C22×D412yes—
281C23×C11C22×D411yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4112yes—
287C23×C11H(5,𝔽2)12yes—
288C23×C11H(5,𝔽2)12yes—
289C22×D11—232no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—432no—
309C22×D11—432no—
310C22×D11—416no—
311C22×D11—416no—
312C22×D11—416no—
313C22×D11—432no—
314C22×D11—432no—
315C22×D11—416no—
316C22×D11—416no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—416no—
334C22×D11C4×D418yes—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—24no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—416no—
346C2×C4×C11—41no—
347C2×C4×C11—42no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—416no—
372C2×Dic11—41no—
373C2×Dic11—42no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11#12014yes—
388C26—111no—
389C24×C4—111no—
390C24×C4C2×D1111yescharacteristic
391C22×C4⋊C4C2×D1112yescomplemented
392C22×C22⋊C4—111no—
393C22×C22⋊C4—112no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—112no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—112no—
398C22×C22⋊C4—112no—
399C22×C22⋊C4—112no—
400C22×C22⋊C4—228no—
401C22×C22⋊C4—224no—
402C22×C22⋊C4C2×D1111yescharacteristic
403C22×C22⋊C4C2×D1111yescharacteristic
404C22×C42—111no—
405C22×C42—111no—
406#388—228no—
407#385—24no—
408#379—118no—
409#379—224no—
410C4×C22⋊C4—224no—
411C2×#95—112no—
412C2×#95—112no—
413C2×#95—111no—
414C2×#95—111no—
415C2×#95—112no—
416C2×#95—112no—
417C2×#95C2×D1112yescomplemented
418C22×C11—24no—
419C22×C11—28no—
420C22×C11—28no—
421C22×C11—24no—
422C22×C11—24no—
423C22×C11—28no—
424C22×C11—28no—
425C22×C11—24no—
426C22×C11—24no—
427C22×C11—24no—
428C22×C11#38818yescomplemented
429C22×C11C2×#11711yescharacteristic
430C22×C11C2×C4×D411yescharacteristic
431C22×C11C2×C4×D411yescharacteristic
432C22×C11C2×C4×D412yes—
433C22×C11#51812yes—
434C22×C11C2×#12011yescharacteristic
435C22×C11C2×#12111yescharacteristic
436C22×C11C2×#12311yescharacteristic
437C22×C11#52512yes—
438C22×C11#52511yescharacteristic
439C22×C11C2×#12411yescharacteristic
440C22×C11C2×#12611yescharacteristic
441C22×C11#53411yescharacteristic
442C22×C11#53511yescharacteristic
443C22×C11#53812yes—
444C22×C11D4212yes—
445C22×C11#54612yes—
446C22×C11#54612yes—
447C22×C11#54612yes—
448C22×C11#54612yes—
449C22×C11#55112yes—
450C22×C11#55112yes—
451C22×C11#55112yes—
452C2×D11—28no—
453C2×D11—28no—
454C2×D11—28no—
455C2×D11—464no—
456C2×D11—44no—
457C2×D11—44no—
458C2×D11—44no—
459C2×D11—44no—
460C2×D11—44no—
461C2×D11—44no—
462C2×D11—44no—
463C2×D11—44no—
464C2×D11—44no—
465C2×D11—44no—
466C2×D11—44no—
467C2×D11—44no—
468C4×C11—44no—
469C4×C11—42no—
470C4×C11—44no—
471C4×C11—42no—
472Dic11—24no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—82no—
477C25—112no—
478C25—114no—
479C25—224no—
480C25—224no—
481C25—222no—
482C25—222no—
483C25—222no—
484C25—222no—
485C25—222no—
486C25—222no—
487C25—442no—
488C25—442no—
489C25C22×D1111yescharacteristic
490C23×C4—22no—
491C23×C4—24no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—42no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—114no—
500C23×C4—112no—
501C23×C4—224no—
502C23×C4—222no—
503C23×C4—222no—
504C23×C4—442no—
505C23×C4C22×D1112yes—
506C23×C4C22×D1112yes—
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—118no—
518C2×C22⋊C4—118no—
519C2×C22⋊C4—118no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—224no—
525C2×C22⋊C4—224no—
526C2×C22⋊C4—2232no—
527C2×C22⋊C4—222no—
528C2×C22⋊C4—222no—
529C2×C22⋊C4—224no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4—222no—
534C2×C22⋊C4—222no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—224no—
537C2×C22⋊C4—442no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4—442no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4C4×D1114yes—
542C2×C22⋊C4C22⋊D1114yes—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—224no—
546C2×C42—442no—
547#95—24no—
548#95—222no—
549#95—222no—
550#95—224no—
551#95—224no—
552#95—442no—
553#95—442no—
554C2×C11—28no—
555C2×C11C2×#38811yescharacteristic
556C2×C11C4×#12011yescharacteristic
557C2×C11#232111yescharacteristic
558C2×C11#234212yes—
559C2×C11#235812yes—
560C2×C11#240511yescharacteristic
561C2×C11#240811yescharacteristic
562C2×C11#247212yes—
563C2×C11#248012yes—
564C2×C11#248211yescharacteristic
565C2×C11#253411yescharacteristic
566D11—48no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—114no—
572C24—114no—
573C24—114no—
574C24—2216no—
575C24—228no—
576C24—2216no—
577C24—228no—
578C24—228no—
579C24—222no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24—222no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—222no—
588C24—222no—
589C24—222no—
590C24—222no—
591C24—228no—
592C24—228no—
593C24—448no—
594C24—448no—
595C24—448no—
596C24—448no—
597C24—448no—
598C24—448no—
599C24—448no—
600C24—448no—
601C24—448no—
602C24—444no—
603C24—448no—
604C24—444no—
605C24—444no—
606C24—444no—
607C24—444no—
608C24—444no—
609C24C2×C4×D1112yes—
610C24#433912yes—
611C24D4×D1112yes—
612C24#434112yes—
613C24#434312yes—
614C24#434312yes—
615C24C2×C22⋊D1112yes—
616C24C23×D1111yescharacteristic
617C22×C4—28no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—48no—
639C22×C4—48no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—114no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—228no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—222no—
651C22×C4—228no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—444no—
672C22×C4—448no—
673C22×C4—448no—
674C22×C4C2×C4×D1114yes—
675C22×C4D4×D1114yes—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C2×C22⋊D1112yes—
678C4⋊C4—48no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—2216no—
682C22⋊C4—2216no—
683C22⋊C4—2216no—
684C22⋊C4—228no—
685C22⋊C4—448no—
686C22⋊C4—448no—
687C22⋊C4—448no—
688C22⋊C4—444no—
689C42—444no—
690C42—444no—
691C11#1399111yescharacteristic, complemented, Sylow
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—118no—
709C23—2232no—
710C23—224no—
711C23—224no—
712C23—224no—
713C23—224no—
714C23—224no—
715C23—224no—
716C23—224no—
717C23—224no—
718C23—224no—
719C23—224no—
720C23—224no—
721C23—224no—
722C23—224no—
723C23—224no—
724C23—224no—
725C23—224no—
726C23—224no—
727C23—224no—
728C23—4432no—
729C23—4432no—
730C23—4416no—
731C23—4416no—
732C23—4416no—
733C23—4432no—
734C23—4416no—
735C23—4432no—
736C23—4416no—
737C23—442no—
738C23—442no—
739C23—442no—
740C23—442no—
741C23—442no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—4416no—
746C23—442no—
747C23—442no—
748C23—442no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23#6694514yes—
755C23#6694614yes—
756C23#6694714yes—
757C23#6695114yes—
758C23C4×C22⋊D1114yes—
759C23#6699214yes—
760C23#6700014yes—
761C23C22×C4×D1111yescharacteristic
762C23C2×#433911yescharacteristic
763C23C2×D4×D1111yescharacteristic
764C23C2×D4×D1112yes—
765C23C2×#434111yescharacteristic
766C23#6703712yes—
767C23C2×#434311yescharacteristic
768C23C2×#434311yescharacteristic
769C23#41×D1112yes—
770C23#6704212yes—
771C23C22×C22⋊D1111yescharacteristic
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—416no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—114no—
798C2×C4—222no—
799C2×C4—224no—
800C2×C4—224no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—224no—
806C2×C4—224no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—4416no—
810C2×C4—442no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—442no—
819C2×C4—442no—
820C2×C4—442no—
821C2×C4—442no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—442no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—28no—
830C22—28no—
831C22—24no—
832C22—28no—
833C22—28no—
834C22—24no—
835C22—228no—
836C22—228no—
837C22—228no—
838C22—4464no—
839C22—444no—
840C22—444no—
841C22—444no—
842C22—444no—
843C22—444no—
844C22—444no—
845C22—444no—
846C22—444no—
847C22—444no—
848C22—444no—
849C22—444no—
850C22—444no—
851C22#1062260318yescomplemented
852C22C2×#6694511yescharacteristic
853C22C2×#6694611yescharacteristic
854C22C2×#6694711yescharacteristic
855C22C2×#6695111yescharacteristic
856C22C4×D4×D1112yes—
857C22#1062307612yes—
858C22#1062308112yes—
859C22#1062308712yes—
860C22D11×#12011yescharacteristic
861C22#1062312212yes—
862C22#1062312311yescharacteristic
863C22#1062315812yes—
864C22#1062316112yes—
865C22#1062316812yes—
866C22#1062317512yes—
867C22#1062318411yescharacteristic
868C22#1062318711yescharacteristic
869C22#1062318912yes—
870C22C2×C4×C22⋊D1111yescharacteristic
871C22D4×C22⋊D1112yes—
872C22C2×#6699211yescharacteristic
873C22C2×#6700011yescharacteristic
874C22#1062336012yes—
875C4—44no—
876C4—42no—
877C4—42no—
878C4—44no—
879C4—224no—
880C4—442no—
881C4—442no—
882C4—442no—
883C4—882no—
884C2—28no—
885C2—448no—
886C2C2×#1062260311yescharacteristic
887C2#1307111711yescharacteristic
888C2#1307127311yescharacteristic
889C2#1307146312yes—
890C2#1307159312yes—
891C2#1307194511yescharacteristic
892C2#1307196911yescharacteristic
893C2#1307274912yes—
894C2#1307286912yes—
895C2#1307288911yescharacteristic
896C2#1307350511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#385D11
hypocenterC11#13991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#10622603C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. #13066864C2semidirect
7. #13066858C2semidirect
8. #13066852C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
11. C2×C11×#385C2semidirect
15. C22×C11×C4⋊C4C22semidirect
28. C22×C4×Dic11C22semidirect
29. C22×C4×Dic11C22semidirect
31. C2×C11×#95C22semidirect
32. C2×C11⋊#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
40. #10622568C4semidirect
105. C2×(C2×D11)⋊C4C2×C4semidirect
106. C2×(C2×D11)⋊C4C2×C4semidirect
246. C2×#385D11semidirect
391. C22×C4⋊C4C2×D11semidirect
417. C2×#95C2×D11semidirect
428. C22×C11#388semidirect
691. C11#13991semidirect
851. C22#10622603semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C2×#106226032
C2×#106225682
C2×C22⋊C4×Dic112
#130668642
#130668582
#130668522
#130668392
#130668382
C2×C11×#3852
#1399111