Finite Group Databasebeta

← #14675692

Subgroups — #14675692

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C211yesmaximal, characteristic
2C2×#10622282C212yesmaximal, complemented
3C2×#10622555C211yesmaximal, characteristic, complemented
4C2×#10622568C211yesmaximal, characteristic
5C2×#10622568C211yesmaximal, characteristic
6C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#13066864C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4—28no—
20C22×(C2×D11)⋊C4C418yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yescomplemented
30C22×C4×Dic11C2212yescomplemented
31C2×C11×#95C2212yescomplemented
32C2×C11×#95C2212yescomplemented
33C4×C22⋊Dic11—24no—
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38#10622568—24no—
39#10622568—24no—
40#10622555—24no—
41#10622282—28no—
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×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—24no—
59C23×C4×C11—42no—
60C23×C4×C11C2×C414yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—24no—
68C23×Dic11—42no—
69C23×Dic11C2×C414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11D414yes—
85C2×C22⋊Dic11D414yes—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
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—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4—42no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4D418yes—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—42no—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—24no—
112C2×C4×Dic11—42no—
113C11×#95—24no—
114C11×#95—42no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118C11⋊#95—42no—
119#13873—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—216no—
133C23×D11—216no—
134C23×D11—28no—
135C23×D11—22no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—22no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—28no—
154C23×D11—28no—
155C23×D11—28no—
156C23×D11—28no—
157C23×D11—44no—
158C23×D11—44no—
159C23×D11—48no—
160C23×D11—48no—
161C23×D11—48no—
162C23×D11—48no—
163C23×D11—48no—
164C23×D11—48no—
165C23×D11—48no—
166C23×D11—48no—
167C23×D11—48no—
168C23×D11—48no—
169C23×D11—44no—
170C23×D11—44no—
171C23×D11—44no—
172C23×D11—44no—
173C23×D11C22×C412yes—
174C23×D11C22×C412yes—
175C23×D11C2×D414yes—
176C23×D11#4114yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—28no—
181C22×C4×C11—21no—
182C22×C4×C11—22no—
183C22×C4×C11—21no—
184C22×C4×C11—22no—
185C22×C4×C11—28no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—44no—
201C22×C4×C11—48no—
202C22×C4×C11—48no—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C2×D414yes—
206C22×Dic11—28no—
207C22×Dic11—28no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—21no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—21no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—44no—
228C22×Dic11—48no—
229C22×Dic11—48no—
230C22×Dic11C22×C412yes—
231C22×Dic11C22×C412yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D414yes—
235C11×C22⋊C4—44no—
236C11×C22⋊C4—44no—
237C22⋊Dic11—28no—
238C22⋊Dic11—28no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—48no—
243(C2×D11)⋊C4—48no—
244(C2×D11)⋊C4—48no—
245(C2×D11)⋊C4—48no—
246(C2×D11)⋊C4C22⋊C4116yescomplemented
247Dic11⋊C4—48no—
248C4×Dic11—48no—
249C23×C22⋊C4—111no—
250C2×#388—112no—
251C2×#380—111no—
252C2×#379—111no—
253C2×#379—111no—
254C2×C4×C22⋊C4—111no—
255#1440—112no—
256#1439—112no—
257#1437—112no—
258C22⋊#95—111no—
259C22⋊#95D1111yescharacteristic, complemented
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—24no—
272C23×C11—24no—
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11#11714yes—
277C23×C11C4×D414yes—
278C23×C11C4×D414yes—
279C23×C11#12114yes—
280C23×C11#12314yes—
281C23×C11#12414yes—
282C23×C11#12614yes—
283C23×C11C23×C411yescharacteristic
284C23×C11C22×D412yes—
285C23×C11C22×D411yescharacteristic
286C23×C11C22×D411yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4111yescharacteristic
291C23×C11C2×#4112yes—
292C23×C11H(5,𝔽2)12yes—
293C23×C11H(5,𝔽2)12yes—
294C22×D11—232no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—24no—
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—24no—
311C22×D11—24no—
312C22×D11—24no—
313C22×D11—24no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—24no—
317C22×D11—24no—
318C22×D11—24no—
319C22×D11—416no—
320C22×D11—416no—
321C22×D11—416no—
322C22×D11—416no—
323C22×D11—416no—
324C22×D11—432no—
325C22×D11—432no—
326C22×D11—432no—
327C22×D11—432no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—416no—
349C22×D11C2×C22⋊C414yes—
350C22×D11#11714yes—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—24no—
354C2×C4×C11—24no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—416no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11C2×C22⋊C414yes—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—24no—
379C2×Dic11—24no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—24no—
384C2×Dic11—24no—
385C2×Dic11—24no—
386C2×Dic11—24no—
387C2×Dic11—24no—
388C2×Dic11—24no—
389C2×Dic11—416no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11C2×C22⋊C414yes—
401C26—111no—
402C24×C4—111no—
403C24×C4C2×D1111yescharacteristic
404C22×C4⋊C4—112no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—118no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4—112no—
414C22×C22⋊C4—112no—
415C22×C22⋊C4—112no—
416C22×C22⋊C4—228no—
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C42—112no—
420#388—228no—
421#380—224no—
422#379—224no—
423#379—224no—
424C4×C22⋊C4—224no—
425C2×#95—112no—
426C2×#95—112no—
427C2×#95—112no—
428C2×#95—112no—
429C2×#95C2×D1112yescomplemented
430C2×#95C2×D1112yescomplemented
431C22×C11—24no—
432C22×C11—24no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—24no—
436C22×C11—28no—
437C22×C11—28no—
438C22×C11—28no—
439C22×C11—28no—
440C22×C11—24no—
441C22×C11#38818yescomplemented
442C22×C11C22×C22⋊C411yescharacteristic
443C22×C11C2×#11711yescharacteristic
444C22×C11C2×#11711yescharacteristic
445C22×C11C2×C4×D411yescharacteristic
446C22×C11C2×C4×D411yescharacteristic
447C22×C11#51811yescharacteristic
448C22×C11#51811yescharacteristic
449C22×C11C2×#12111yescharacteristic
450C22×C11C2×#12311yescharacteristic
451C22×C11#52512yes—
452C22×C11#52512yes—
453C22×C11C2×#12411yescharacteristic
454C22×C11C2×#12611yescharacteristic
455C22×C11#53812yes—
456C22×C11#53812yes—
457C22×C11D4212yes—
458C22×C11D4212yes—
459C22×C11#54612yes—
460C22×C11#54612yes—
461C22×C11#54612yes—
462C22×C11#54612yes—
463C22×C11#55112yes—
464C22×C11#55112yes—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—24no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—464no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—44no—
479C2×D11—44no—
480C2×D11—44no—
481C2×D11—44no—
482C2×D11—44no—
483C2×D11—44no—
484C2×D11—44no—
485C2×D11—44no—
486C2×D11—42no—
487C2×D11—42no—
488C4×C11—24no—
489C4×C11—42no—
490C4×C11—82no—
491C4×C11—82no—
492Dic11—24no—
493Dic11—42no—
494Dic11—44no—
495Dic11—44no—
496C25—111no—
497C25—111no—
498C25—114no—
499C25—224no—
500C25—224no—
501C25—222no—
502C25—222no—
503C25—222no—
504C25—222no—
505C25—222no—
506C25—222no—
507C25—442no—
508C25—442no—
509C25C22×D1111yescharacteristic
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—24no—
513C23×C4—42no—
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—112no—
517C23×C4—111no—
518C23×C4—114no—
519C23×C4—224no—
520C23×C4—222no—
521C23×C4—222no—
522C23×C4—442no—
523C23×C4C4×D1114yes—
524C23×C4C22×D1112yes—
525C23×C4C22×D1112yes—
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C2×C4⋊C4—224no—
529C2×C4⋊C4—224no—
530C2×C4⋊C4—442no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—118no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—2232no—
545C2×C22⋊C4—224no—
546C2×C22⋊C4—224no—
547C2×C22⋊C4—222no—
548C2×C22⋊C4—222no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—222no—
551C2×C22⋊C4—224no—
552C2×C22⋊C4—224no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C42—224no—
565C2×C42—224no—
566C2×C42—442no—
567#95—24no—
568#95—42no—
569#95—224no—
570#95—224no—
571#95—224no—
572#95—442no—
573C2×C11—28no—
574C2×C11#228011yescharacteristic
575C2×C11C2×#38811yescharacteristic
576C2×C11#231211yescharacteristic
577C2×C11D4×C22⋊C411yescharacteristic
578C2×C11D4×C22⋊C411yescharacteristic
579C2×C11#234211yescharacteristic
580C2×C11#234211yescharacteristic
581C2×C11#241812yes—
582C2×C11#242412yes—
583C2×C11#247212yes—
584C2×C11#248012yes—
585D11—44no—
586D11—44no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—112no—
592C24—112no—
593C24—114no—
594C24—114no—
595C24—228no—
596C24—228no—
597C24—2216no—
598C24—2216no—
599C24—228no—
600C24—221no—
601C24—221no—
602C24—221no—
603C24—221no—
604C24—222no—
605C24—221no—
606C24—221no—
607C24—221no—
608C24—221no—
609C24—221no—
610C24—221no—
611C24—222no—
612C24—222no—
613C24—221no—
614C24—221no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—228no—
619C24—228no—
620C24—444no—
621C24—444no—
622C24—448no—
623C24—448no—
624C24—448no—
625C24—448no—
626C24—448no—
627C24—448no—
628C24—448no—
629C24—448no—
630C24—448no—
631C24—448no—
632C24—444no—
633C24—444no—
634C24—444no—
635C24—444no—
636C24C2×C4×D1112yes—
637C24#433912yes—
638C24#433912yes—
639C24D4×D1112yes—
640C24D4×D1112yes—
641C24#434112yes—
642C24#434312yes—
643C24C23×D1111yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—44no—
668C22×C4—48no—
669C22×C4—48no—
670C22×C4—112no—
671C22×C4—114no—
672C22×C4—112no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—228no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—222no—
679C22×C4—228no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—221no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—221no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—444no—
697C22×C4—448no—
698C22×C4—448no—
699C22×C4C2×C4×D1112yes—
700C22×C4C2×C4×D1112yes—
701C22×C4D4×D1114yes—
702C4⋊C4—448no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—1116no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—228no—
711C22⋊C4—448no—
712C22⋊C4—448no—
713C22⋊C4—448no—
714C22⋊C4—448no—
715C42—448no—
716C11#1387311yescharacteristic, complemented, Sylow
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—114no—
734C23—114no—
735C23—2232no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—224no—
749C23—224no—
750C23—224no—
751C23—224no—
752C23—224no—
753C23—224no—
754C23—224no—
755C23—224no—
756C23—224no—
757C23—224no—
758C23—224no—
759C23—224no—
760C23—4416no—
761C23—4416no—
762C23—4416no—
763C23—4416no—
764C23—4432no—
765C23—4432no—
766C23—4416no—
767C23—4432no—
768C23—4432no—
769C23—441no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—4416no—
778C23—442no—
779C23—442no—
780C23—442no—
781C23—442no—
782C23—442no—
783C23—442no—
784C23—442no—
785C23—442no—
786C23—442no—
787C23—442no—
788C23—442no—
789C23—442no—
790C23#6692514yes—
791C23(C22⋊D11)⋊C414yes—
792C23#6693714yes—
793C23#6693814yes—
794C23#6694614yes—
795C23#6694714yes—
796C23#6695114yes—
797C23C22×C4×D1111yescharacteristic
798C23C2×#433911yescharacteristic
799C23C2×#433911yescharacteristic
800C23C2×D4×D1112yes—
801C23C2×D4×D1111yescharacteristic
802C23C2×D4×D1111yescharacteristic
803C23C2×#434111yescharacteristic
804C23#6703712yes—
805C23C2×#434311yescharacteristic
806C23#41×D1112yes—
807C23#6704212yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—416no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—114no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—224no—
836C2×C4—224no—
837C2×C4—222no—
838C2×C4—224no—
839C2×C4—222no—
840C2×C4—224no—
841C2×C4—222no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—224no—
845C2×C4—224no—
846C2×C4—4416no—
847C2×C4—442no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—442no—
853C2×C4—442no—
854C2×C4—442no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4C22⋊C4×D1114yes—
858C22—28no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—28no—
864C22—24no—
865C22—24no—
866C22—28no—
867C22—28no—
868C22—224no—
869C22—224no—
870C22—224no—
871C22—224no—
872C22—224no—
873C22—224no—
874C22—4464no—
875C22—444no—
876C22—444no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22—444no—
882C22—444no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—444no—
888C22—444no—
889C22—444no—
890C22—444no—
891C22#1062228218yescomplemented
892C22C2×#6692511yescharacteristic
893C22C2×C22⋊C4×D1111yescharacteristic
894C22C2×(C22⋊D11)⋊C411yescharacteristic
895C22#1062301711yescharacteristic
896C22C2×#6693711yescharacteristic
897C22C2×#6693811yescharacteristic
898C22C2×#6694611yescharacteristic
899C22C2×#6694711yescharacteristic
900C22C2×#6695111yescharacteristic
901C22D11×#11711yescharacteristic
902C22#1062305211yescharacteristic
903C22#1062307812yes—
904C22#1062307812yes—
905C22#1062309112yes—
906C22#1062309112yes—
907C22#1062312112yes—
908C22#1062312212yes—
909C22#1062314012yes—
910C22#1062314112yes—
911C22#1062316112yes—
912C22#1062316812yes—
913C22#1062318512yes—
914C22#1062318912yes—
915C4—24no—
916C4—42no—
917C4—82no—
918C4—82no—
919C4—224no—
920C4—444no—
921C4—442no—
922C4—444no—
923C2—28no—
924C2—444no—
925C2—444no—
926C2#1307099711yescharacteristic
927C2C2×#1062228211yescharacteristic
928C2#1307121111yescharacteristic
929C2#1307143211yescharacteristic
930C2#1307143611yescharacteristic
931C2#1307145811yescharacteristic
932C2#1307146211yescharacteristic
933C2#1307208012yes—
934C2#1307215412yes—
935C2#1307274412yes—
936C2#1307286412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC22⋊#95D11
hypocenterC11#13873
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622282C2semidirect
3. C2×#10622555C2semidirect
6. C2×C4×C22⋊Dic11C2semidirect
7. #13066864C2semidirect
8. #13066860C2semidirect
9. #13066852C2semidirect
10. #13066838C2semidirect
11. C11×C22⋊#95C2semidirect
20. C22×(C2×D11)⋊C4C4semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×C4×Dic11C22semidirect
31. C2×C11×#95C22semidirect
32. C2×C11×#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
246. (C2×D11)⋊C4C22⋊C4semidirect
259. C22⋊#95D11semidirect
429. C2×#95C2×D11semidirect
430. C2×#95C2×D11semidirect
441. C22×C11#388semidirect
716. C11#13873semidirect
891. C22#10622282semidirect

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×#106222822
C2×#106225552
C2×#106225682
C2×C4×C22⋊Dic112
#130668642
#130668602
#130668522
#130668382
C11×C22⋊#952
#1387311