Finite Group Databasebeta

← #14675694

Subgroups — #14675694

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×#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×#380C211yesmaximal, 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—28no—
21C22×(C2×D11)⋊C4C418yescomplemented
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4×Dic11C2212yescomplemented
31C11×#380—24no—
32C2×C11×#95C2212yescomplemented
33C2×C11⋊#95C2212yescomplemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38#10622603—28no—
39#10622568—24no—
40#10622568—24no—
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×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×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—24no—
68C23×Dic11—42no—
69C23×Dic11C2×C414yes—
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
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⋊C4—22no—
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⋊Dic11D414yes—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—232no—
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×C414yes—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×(C2×D11)⋊C4C2×C414yes—
108C2×(C2×D11)⋊C4C2×C414yes—
109C2×(C2×D11)⋊C4D418yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—24no—
112C2×C4×Dic11—42no—
113C11×#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—42no—
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—22no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—21no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—28no—
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—44no—
200C22×C4×C11—48no—
201C22×C4×C11—48no—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C2×D414yes—
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—21no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—44no—
229C22×Dic11—48no—
230C22×Dic11—48no—
231C22×Dic11C22×C412yes—
232C22×Dic11C22×C412yes—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D414yes—
235C11×C4⋊C4—48no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—44no—
238C22⋊Dic11—28no—
239C22⋊Dic11—44no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—48no—
244(C2×D11)⋊C4—48no—
245(C2×D11)⋊C4—48no—
246(C2×D11)⋊C4—48no—
247(C2×D11)⋊C4C22⋊C4116yescomplemented
248C4×Dic11—48no—
249C23×C22⋊C4—111no—
250C2×#388—112no—
251C2×#380D1111yescharacteristic, complemented
252C2×#379—111no—
253C2×#379—111no—
254C2×C4×C22⋊C4—111no—
255#1440—112no—
256#1439—112no—
257#1437—112no—
258C22⋊#95—111no—
259C22⋊#95—111no—
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—24no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—416no—
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—416no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
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⋊C4C2×D1112yescomplemented
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—118no—
411C22×C22⋊C4—111no—
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—24no—
422#379—224no—
423#379—224no—
424C4×C22⋊C4—224no—
425C2×#95—112no—
426C2×#95—112no—
427C2×#95—112no—
428C2×#95—112no—
429C2×#95—112no—
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—44no—
491C4×C11—82no—
492Dic11—24no—
493Dic11—42no—
494Dic11—44no—
495Dic11—82no—
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—111no—
517C23×C4—114no—
518C23×C4—112no—
519C23×C4—224no—
520C23×C4—222no—
521C23×C4—222no—
522C23×C4—442no—
523C23×C4C4×D1114yes—
524C23×C4C22×D1112yes—
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1112yes—
527C23×C4C22×D1111yescharacteristic
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—42no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—118no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—2232no—
543C2×C22⋊C4—224no—
544C2×C22⋊C4—224no—
545C2×C22⋊C4—222no—
546C2×C22⋊C4—222no—
547C2×C22⋊C4—224no—
548C2×C22⋊C4—224no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C22⋊C4—224no—
552C2×C22⋊C4—224no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4—222no—
555C2×C22⋊C4—222no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4C22⋊D1114yes—
564C2×C42—224no—
565C2×C42—224no—
566C2×C42—442no—
567#95—24no—
568#95—224no—
569#95—224no—
570#95—224no—
571#95—442no—
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—222no—
603C24—221no—
604C24—221no—
605C24—221no—
606C24—221no—
607C24—222no—
608C24—222no—
609C24—221no—
610C24—221no—
611C24—221no—
612C24—221no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—221no—
617C24—221no—
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—
638C24D4×D1112yes—
639C24#434112yes—
640C24#434312yes—
641C24#434312yes—
642C24C2×C22⋊D1112yes—
643C24C23×D1111yescharacteristic
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—21no—
647C22×C4—28no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—28no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—44no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—112no—
670C22×C4—114no—
671C22×C4—112no—
672C22×C4—114no—
673C22×C4—228no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—222no—
677C22×C4—228no—
678C22×C4—222no—
679C22×C4—221no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—221no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—444no—
696C22×C4—448no—
697C22×C4—448no—
698C22×C4C2×C4×D1112yes—
699C22×C4C2×C4×D1112yes—
700C22×C4D4×D1114yes—
701C22×C4C2×C22⋊D1114yes—
702C4⋊C4—48no—
703C22⋊C4—28no—
704C22⋊C4—44no—
705C22⋊C4—1116no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—448no—
711C22⋊C4—448no—
712C22⋊C4—448no—
713C22⋊C4—448no—
714C22⋊C4—444no—
715C42—448no—
716C11#1387311yescharacteristic, complemented, Sylow
717C23—22no—
718C23—22no—
719C23—24no—
720C23—22no—
721C23—22no—
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—224no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—224no—
748C23—222no—
749C23—222no—
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—4416no—
766C23—4432no—
767C23—4432no—
768C23—4432no—
769C23—442no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—442no—
775C23—442no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—442no—
781C23—4416no—
782C23—442no—
783C23—442no—
784C23—442no—
785C23—442no—
786C23—442no—
787C23—442no—
788C23—442no—
789C23—442no—
790C23#6694514yes—
791C23#6694614yes—
792C23#6694714yes—
793C23#6695114yes—
794C23C4×C22⋊D1114yes—
795C23#6699214yes—
796C23#6700014yes—
797C23C22×C4×D1111yescharacteristic
798C23C2×#433911yescharacteristic
799C23C2×D4×D1112yes—
800C23C2×D4×D1111yescharacteristic
801C23C2×#434111yescharacteristic
802C23#6703712yes—
803C23C2×#434311yescharacteristic
804C23C2×#434311yescharacteristic
805C23#41×D1112yes—
806C23#6704212yes—
807C23C22×C22⋊D1111yescharacteristic
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—416no—
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—222no—
839C2×C4—224no—
840C2×C4—222no—
841C2×C4—224no—
842C2×C4—224no—
843C2×C4—4416no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
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—24no—
864C22—28no—
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—442no—
882C22—442no—
883C22—444no—
884C22—444no—
885C22—442no—
886C22—442no—
887C22—444no—
888C22—444no—
889C22—444no—
890C22—444no—
891C22#1062260318yescomplemented
892C22C2×C22⋊C4×D1111yescharacteristic
893C22#1062301711yescharacteristic
894C22#1062302112yes—
895C22C2×#6694511yescharacteristic
896C22C2×#6694611yescharacteristic
897C22C2×#6694711yescharacteristic
898C22C2×#6695111yescharacteristic
899C22D11×#11711yescharacteristic
900C22#1062305211yescharacteristic
901C22#1062305812yes—
902C22#1062313712yes—
903C22#1062314012yes—
904C22#1062314112yes—
905C22#1062314812yes—
906C22#1062315812yes—
907C22#1062316112yes—
908C22#1062316812yes—
909C22#1062317512yes—
910C22C2×C4×C22⋊D1111yescharacteristic
911C22D4×C22⋊D1112yes—
912C22C2×#6699211yescharacteristic
913C22C2×#6700011yescharacteristic
914C22#1062336012yes—
915C4—24no—
916C4—44no—
917C4—42no—
918C4—82no—
919C4—224no—
920C4—442no—
921C4—444no—
922C4—882no—
923C2—28no—
924C2—444no—
925C2—444no—
926C2#1307099811yescharacteristic
927C2C2×#1062260311yescharacteristic
928C2#1307121311yescharacteristic
929C2C22⋊C4×C22⋊D1111yescharacteristic
930C2#1307143611yescharacteristic
931C2#1307146211yescharacteristic
932C2#1307146611yescharacteristic
933C2#1307208412yes—
934C2#1307215812yes—
935C2#1307274912yes—
936C2#1307286712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#380D11
hypocenterC11#13873
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

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×#380C2semidirect
15. C22×C11×C4⋊C4C22semidirect
21. C22×(C2×D11)⋊C4C4semidirect
30. C22×C4×Dic11C22semidirect
32. C2×C11×#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
247. (C2×D11)⋊C4C22⋊C4semidirect
251. C2×#380D11semidirect
404. C22×C4⋊C4C2×D11semidirect
430. C2×#95C2×D11semidirect
441. C22×C11#388semidirect
716. C11#13873semidirect
891. 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×#3802
#1387311