Finite Group Databasebeta

← D11×#2408 #14921566

Subgroups — D11×#2408 #14921566

Order 2816.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic, complemented
2C2×D11×#121C212yesmaximal, complemented
3C2×D11×#120C212yesmaximal, complemented
4C2×C4×D4×D11C211yesmaximal, characteristic, complemented
5#13071973C211yesmaximal, characteristic, complemented
6#13071972C211yesmaximal, characteristic, complemented
7#13071971C212yesmaximal, complemented
8#13071970C212yesmaximal, complemented
9#13071969C212yesmaximal, complemented
10#13071968C212yesmaximal, complemented
11#13071967C212yesmaximal, complemented
12#13071966C211yesmaximal, characteristic, complemented
13#13071965C212yesmaximal, complemented
14D11×#394C212yesmaximal, complemented
15D11×#392C212yesmaximal, complemented
16D11×#390C212yesmaximal, complemented
17D11×#380C211yesmaximal, characteristic, complemented
18D11×#379C212yesmaximal, complemented
19C11×#2408C211yesmaximal, characteristic, complemented
20C25×D11C2212yes—
21C23×D4×C11C2211yescharacteristic, complemented
22C23×C22⋊D11C2212yescomplemented
23C22×D4×D11—216no—
24C22×D4×D11—28no—
25C22×D4×D11C2212yes—
26C22×D4×D11C2212yes—
27C22×D4×D11C2211yescharacteristic
28C22×D4×D11C2212yescomplemented
29C22×D4×D11C2212yescomplemented
30C22×D4×D11C2214yescomplemented
31C23×D44C2211yescharacteristic, complemented
32C23×C4×D11C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic, complemented
34C2×C11×#121C2212yescomplemented
35C2×C11×#120C2212yescomplemented
36C2×C4×D4×C11C2211yescharacteristic, complemented
37C2×#67006C2212yescomplemented
38C2×#66992C2214yescomplemented
39C2×#66991C2212yescomplemented
40C2×#66990C2214yescomplemented
41C2×#66990C2212yescomplemented
42C2×D4×Dic11C2211yescharacteristic, complemented
43C2×#66983C2212yescomplemented
44C2×C4×C22⋊D11C2211yescharacteristic, complemented
45C2×C4×C22⋊D11C2211yescharacteristic, complemented
46D11×#121—216no—
47D11×#120—216no—
48C4×D4×D11—28no—
49C2×#66948C2212yescomplemented
50C2×#66946C2211yescharacteristic, complemented
51C2×C4⋊C4×D11C2212yescomplemented
52C2×C4⋊C4×D11C2211yescharacteristic, complemented
53C2×#66937C2214yescomplemented
54C2×#66935C2214yescomplemented
55C2×#66935C2212yescomplemented
56C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
57C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
58C2×C22⋊C4×D11C2211yescharacteristic
59C2×C22⋊C4×D11C2212yes—
60C2×C22⋊C4×D11C2214yescomplemented
61C2×C22⋊C4×D11C2211yescharacteristic, complemented
62C2×C22⋊C4×D11C2214yescomplemented
63C2×C22⋊C4×D11C2214yescomplemented
64C2×C4×D44C2211yescharacteristic, complemented
65C2×C42×D11C2211yescharacteristic, complemented
66C11×#394C2212yescomplemented
67C11×#392C2212yescomplemented
68C11×#390C2212yescomplemented
69C11×#380C2211yescharacteristic, complemented
70C11×#379C2212yescomplemented
71#10622860C2212yescomplemented
72#10622836C2214yescomplemented
73#10622836C2212yescomplemented
74#10622835C2212yescomplemented
75#10622834C2212yescomplemented
76#10622825C2211yescharacteristic, complemented
77#10622604C2212yescomplemented
78#10622601C2212yescomplemented
79#10622600C2212yescomplemented
80#10622574C2214yescomplemented
81#10622573C2212yescomplemented
82#10622573C2214yescomplemented
83#10622572C2214yescomplemented
84#10622570C2214yescomplemented
85#10622570C2214yescomplemented
86#10622568C2214yescomplemented
87#10622568C2214yescomplemented
88#10622568C2212yescomplemented
89#10622568C2212yescomplemented
90#10622555C2212yescomplemented
91#10622552C2212yescomplemented
92#10622285C2212yescomplemented
93#10622284C2212yescomplemented
94#10622280C2212yescomplemented
95D11×#95C2212yescomplemented
96C25×C11C2312yes—
97C24×D11—216no—
98C24×D11—28no—
99C24×D11—28no—
100C24×D11—28no—
101C24×D11—48no—
102C24×D11C2314yes—
103C24×D11C2311yescharacteristic
104C24×D11C2312yes—
105C24×D11C2314yes—
106C24×D11C2311yescharacteristic
107C22×D4×C11—28no—
108C22×D4×C11—24no—
109C22×D4×C11C2312yes—
110C22×D4×C11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2314yescomplemented
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic, complemented
115C22×C22⋊D11—216no—
116C22×C22⋊D11—28no—
117C22×C22⋊D11C2314yes—
118C22×C22⋊D11C2311yescharacteristic
119C22×C22⋊D11C2311yescharacteristic
120C22×C22⋊D11C2314yes—
121C22×C22⋊D11C2314yescomplemented
122C22×C22⋊D11C2314yescomplemented
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2311yescharacteristic, complemented
125C2×D4×D11—2128no—
126C2×D4×D11—24no—
127C2×D4×D11—216no—
128C2×D4×D11—24no—
129C2×D4×D11—28no—
130C2×D4×D11—216no—
131C2×D4×D11—216no—
132C2×D4×D11—216no—
133C2×D4×D11—28no—
134C2×D4×D11—28no—
135C2×D4×D11—28no—
136C2×D4×D11—28no—
137C2×D4×D11—28no—
138C2×D4×D11—28no—
139C2×D4×D11—48no—
140C2×D4×D11D4116yescomplemented
141C2×D4×D11D418yescomplemented
142C22×D44—24no—
143C22×D44—28no—
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×D44C2312yes—
147C22×D44C2314yescomplemented
148C22×C4×D11—28no—
149C22×C4×D11—24no—
150C22×C4×D11—28no—
151C22×C4×D11D418yescomplemented
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2314yes—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic, complemented
161C22×C4×D11C2311yescharacteristic, complemented
162C11×#121—28no—
163C11×#120—28no—
164C4×D4×C11—24no—
165C2×C11×C4⋊C4C2311yescharacteristic, complemented
166C2×C11×C4⋊C4C2312yescomplemented
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic, complemented
170C2×C11×C22⋊C4C2314yescomplemented
171C2×C11×C22⋊C4C2314yescomplemented
172C2×C11×C22⋊C4C2314yescomplemented
173C2×C42×C11C2311yescharacteristic, complemented
174#67006—28no—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic, complemented
178C2×C22⋊Dic11C2314yescomplemented
179C2×C22⋊Dic11C2314yescomplemented
180C2×C22⋊Dic11C2314yescomplemented
181#66992—216no—
182#66991—28no—
183#66990—28no—
184#66990—216no—
185D4×Dic11—24no—
186#66983—28no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—24no—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2314yes—
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic, complemented
193C2×(C2×D11)⋊C4C2314yescomplemented
194C2×(C2×D11)⋊C4C2314yescomplemented
195C2×(C2×D11)⋊C4C2314yescomplemented
196C2×(C2×D11)⋊C4C2311yescharacteristic, complemented
197C2×(C2×D11)⋊C4C2314yescomplemented
198C2×(C2×D11)⋊C4C2314yescomplemented
199C2×(C2×D11)⋊C4C2314yescomplemented
200C2×C4⋊Dic11C2311yescharacteristic, complemented
201C2×C4⋊Dic11C2312yescomplemented
202C2×Dic11⋊C4C2311yescharacteristic, complemented
203C2×Dic11⋊C4C2311yescharacteristic, complemented
204C2×Dic11⋊C4C2314yescomplemented
205C2×C4×Dic11C2311yescharacteristic, complemented
206C2×C4×Dic11C2311yescharacteristic, complemented
207C2×C4×Dic11C2311yescharacteristic, complemented
208#66948—28no—
209#66946—24no—
210C4⋊C4×D11—24no—
211C4⋊C4×D11—28no—
212#66937—216no—
213#66935—28no—
214#66935—216no—
215(C22⋊D11)⋊C4—24no—
216(C22⋊D11)⋊C4—24no—
217C22⋊C4×D11—24no—
218C22⋊C4×D11—28no—
219C22⋊C4×D11—216no—
220C22⋊C4×D11—24no—
221C22⋊C4×D11—216no—
222C22⋊C4×D11—48no—
223C4×D44—24no—
224C42×D11—24no—
225C11×#95C2312yescomplemented
226C11⋊#95C2312yescomplemented
227C11⋊#95C2314yescomplemented
228C2×#2408—111nomaximal, Sylow
229C24×C11—28no—
230C24×C11—24no—
231C24×C11—24no—
232C24×C11—24no—
233C24×C11—44no—
234C24×C11C2414yes—
235C24×C11C2411yescharacteristic
236C24×C11C2411yescharacteristic
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—264no—
240C23×D11—24no—
241C23×D11—28no—
242C23×D11—22no—
243C23×D11—28no—
244C23×D11—24no—
245C23×D11—28no—
246C23×D11—28no—
247C23×D11—28no—
248C23×D11—28no—
249C23×D11—28no—
250C23×D11—22no—
251C23×D11—28no—
252C23×D11—28no—
253C23×D11—24no—
254C23×D11—28no—
255C23×D11—24no—
256C23×D11—24no—
257C23×D11—28no—
258C23×D11—28no—
259C23×D11—44no—
260C23×D11—44no—
261C23×D11—44no—
262C23×D11—464no—
263C23×D11—464no—
264C23×D11—432no—
265C23×D11—432no—
266C23×D11C2×D4116yes—
267C23×D11C2×D414yes—
268C23×D11C2×D414yes—
269C23×D11C2×D414yescomplemented
270C23×D11#4114yes—
271C23×D11C2414yes—
272C23×D11C2411yescharacteristic
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×D4×C11—232no—
276C2×D4×C11—22no—
277C2×D4×C11—28no—
278C2×D4×C11—22no—
279C2×D4×C11—28no—
280C2×D4×C11—28no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—44no—
285C2×D4×C11C2×D418yescomplemented
286C2×D4×C11C2×D414yescomplemented
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11C2×D414yescomplemented
291C22×C4×C11C2414yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—264no—
298C2×C22⋊D11—28no—
299C2×C22⋊D11—28no—
300C2×C22⋊D11—28no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—28no—
303C2×C22⋊D11—28no—
304C2×C22⋊D11—28no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—28no—
308C2×C22⋊D11—28no—
309C2×C22⋊D11—28no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—44no—
312C2×C22⋊D11—44no—
313C2×C22⋊D11C2×D4116yescomplemented
314C2×C22⋊D11C2×D414yescomplemented
315C2×C22⋊D11C2×D414yescomplemented
316C22×Dic11—24no—
317C22×Dic11—22no—
318C22×Dic11—24no—
319C22×Dic11C2×D414yescomplemented
320C22×Dic11C2414yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326D4×D11—264no—
327D4×D11—264no—
328D4×D11—264no—
329D4×D11—264no—
330D4×D11—232no—
331D4×D11—464no—
332C2×D44—232no—
333C2×D44—22no—
334C2×D44—28no—
335C2×D44—28no—
336C2×D44—28no—
337C2×D44—22no—
338C2×D44—24no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—44no—
342C2×D44C2×D418yescomplemented
343C2×D44C2×D414yescomplemented
344C2×C4×D11—24no—
345C2×C4×D11—232no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—22no—
349C2×C4×D11—24no—
350C2×C4×D11—22no—
351C2×C4×D11—24no—
352C2×C4×D11—28no—
353C2×C4×D11—22no—
354C2×C4×D11—28no—
355C2×C4×D11—22no—
356C2×C4×D11—24no—
357C2×C4×D11—28no—
358C2×C4×D11—24no—
359C2×C4×D11—22no—
360C2×C4×D11—24no—
361C2×C4×D11—416no—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D418yes—
365C2×C4×D11C2×D414yescomplemented
366C2×C4×D11C2×D414yescomplemented
367C2×C4×D11C2×D414yescomplemented
368C11×C4⋊C4—22no—
369C11×C4⋊C4—24no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—28no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—28no—
375C11×C22⋊C4—44no—
376C42×C11—22no—
377C22⋊Dic11—22no—
378C22⋊Dic11—28no—
379C22⋊Dic11—22no—
380C22⋊Dic11—24no—
381C22⋊Dic11—28no—
382C22⋊Dic11—44no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—28no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—28no—
387(C2×D11)⋊C4—28no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—28no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—28no—
392(C2×D11)⋊C4—44no—
393(C2×D11)⋊C4—44no—
394C4⋊Dic11—22no—
395C4⋊Dic11—24no—
396Dic11⋊C4—22no—
397Dic11⋊C4—28no—
398Dic11⋊C4—22no—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C24×D4—111no—
403C22×#121—112no—
404C22×#120—112no—
405C22×C4×D4—111no—
406#2408—112no—
407#2408—112no—
408#2408—112no—
409#2408—111no—
410#2408—112no—
411#2408—111no—
412#2408—112no—
413#2408—112no—
414#2408—111no—
415#2408D1111yescharacteristic, direct product factor
416C2×#394—112no—
417C2×#392—112no—
418C2×#390—112no—
419C2×#380—111no—
420C2×#379—112no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—216no—
424C23×C11—21no—
425C23×C11—24no—
426C23×C11—22no—
427C23×C11—24no—
428C23×C11—24no—
429C23×C11—21no—
430C23×C11—24no—
431C23×C11—24no—
432C23×C11—22no—
433C23×C11—24no—
434C23×C11—416no—
435C23×C11—416no—
436C23×C11—48no—
437C23×C11—48no—
438C23×C11C22×D418yes—
439C23×C11C22×D412yes—
440C23×C11C22×D412yes—
441C23×C11C22×D412yescomplemented
442C23×C11C2×#4112yes—
443C23×C11C2511yescharacteristic
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—28no—
447C22×D11—28no—
448C22×D11—216no—
449C22×D11—216no—
450C22×D11—216no—
451C22×D11—232no—
452C22×D11—21no—
453C22×D11—24no—
454C22×D11—22no—
455C22×D11—24no—
456C22×D11—24no—
457C22×D11—21no—
458C22×D11—24no—
459C22×D11—24no—
460C22×D11—22no—
461C22×D11—24no—
462C22×D11—232no—
463C22×D11—28no—
464C22×D11—216no—
465C22×D11—232no—
466C22×D11—232no—
467C22×D11—416no—
468C22×D11—416no—
469C22×D11—416no—
470C22×D11—416no—
471C22×D11—416no—
472C22×D11—416no—
473C22×D11—416no—
474C22×D11—4256no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—44no—
478C22×D11—416no—
479C22×D11—416no—
480C22×D11—44no—
481C22×D11—416no—
482C22×D11—416no—
483C22×D11—48no—
484C22×D11—416no—
485C22×D11#121116yescomplemented
486C22×D11C22×D418yes—
487C22×D11C22×D412yes—
488C22×D11C22×D412yes—
489C22×D11C22×D412yes—
490C22×D11C22×D414yes—
491C22×D11C22×D412yes—
492C22×D11C22×D412yescomplemented
493C22×D11C2×#4112yes—
494C22×D11C2×#4112yes—
495C22×D11H(5,𝔽2)14yes—
496D4×C11—216no—
497D4×C11—28no—
498D4×C11—216no—
499D4×C11—416no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—28no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—24no—
507C2×C4×C11—22no—
508C2×C4×C11—24no—
509C2×C4×C11—22no—
510C2×C4×C11—24no—
511C2×C4×C11—44no—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D414yes—
515C2×C4×C11C22×D412yescomplemented
516C22⋊D11—232no—
517C22⋊D11—28no—
518C22⋊D11—28no—
519C22⋊D11—232no—
520C22⋊D11—416no—
521C22⋊D11—416no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—28no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—24no—
529C2×Dic11—22no—
530C2×Dic11—24no—
531C2×Dic11—22no—
532C2×Dic11—24no—
533C2×Dic11—44no—
534C2×Dic11C22×D412yes—
535C2×Dic11C22×D412yes—
536C2×Dic11C22×D414yes—
537C2×Dic11C22×D412yescomplemented
538D44—216no—
539D44—28no—
540D44—216no—
541D44—416no—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—416no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11#120116yescomplemented
552C26—112no—
553C23×D4—112no—
554C23×D4—111no—
555C23×D4—112no—
556C23×D4—112no—
557C23×D4—112no—
558C23×D4—112no—
559C23×D4—114no—
560C23×D4—111no—
561C23×D4—228no—
562C23×D4—2216no—
563C23×D4C2×D1111yescharacteristic, complemented
564C24×C4—111no—
565C24×C4—111no—
566C2×#121—112no—
567C2×#121—114no—
568C2×#121—112no—
569C2×#121—112no—
570C2×#121—114no—
571C2×#121—2216no—
572C2×#121C2×D1112yescomplemented
573C2×#120—112no—
574C2×#120—112no—
575C2×#120—114no—
576C2×#120—112no—
577C2×#120—114no—
578C2×#120—2216no—
579C2×#120C2×D1112yescomplemented
580C2×C4×D4—111no—
581C2×C4×D4—111no—
582C2×C4×D4—111no—
583C2×C4×D4—111no—
584C2×C4×D4—111no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—228no—
588C2×C4×D4C2×D1111yescharacteristic, complemented
589C22×C4⋊C4—111no—
590C22×C4⋊C4—112no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—112no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—114no—
595C22×C22⋊C4—114no—
596C22×C22⋊C4—114no—
597C22×C42—111no—
598#394—112no—
599#394—112no—
600#394—114no—
601#394—114no—
602#394—112no—
603#394C2×D1112yescomplemented
604#392—112no—
605#392—114no—
606#392—114no—
607#392—112no—
608#392—112no—
609#392C2×D1112yescomplemented
610#390—112no—
611#390—112no—
612#390—114no—
613#390—114no—
614#390—112no—
615#390C2×D1112yescomplemented
616#380—111no—
617#380—112no—
618#380—112no—
619#380—112no—
620#380C2×D1111yescharacteristic, complemented
621#379—112no—
622#379—112no—
623#379—112no—
624#379—114no—
625#379—114no—
626#379C2×D1112yescomplemented
627C2×#95—112no—
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—24no—
631C22×C11—24no—
632C22×C11—28no—
633C22×C11—22no—
634C22×C11—24no—
635C22×C11—28no—
636C22×C11—28no—
637C22×C11—432no—
638C22×C11—41no—
639C22×C11—44no—
640C22×C11—44no—
641C22×C11—41no—
642C22×C11—44no—
643C22×C11—44no—
644C22×C11—42no—
645C22×C11C2×#12114yescomplemented
646C22×C11C23×D411yescharacteristic
647C22×C11C23×D412yes—
648C22×C11C23×D411yescharacteristic
649C22×C11C22×#4111yescharacteristic
650C22×C11C2×H(5,𝔽2)12yes—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—232no—
656C2×D11—28no—
657C2×D11—22no—
658C2×D11—28no—
659C2×D11—24no—
660C2×D11—28no—
661C2×D11—464no—
662C2×D11—432no—
663C2×D11—41no—
664C2×D11—44no—
665C2×D11—41no—
666C2×D11—44no—
667C2×D11—44no—
668C2×D11—42no—
669C2×D11—44no—
670C2×D11—416no—
671C2×D11—464no—
672C2×D11C2×#12014yes—
673C2×D11C2×#12114yes—
674C2×D11C2×#12114yescomplemented
675C2×D11#53514yes—
676C2×D11D4218yes—
677C2×D11#54618yes—
678C4×C11—22no—
679C4×C11—22no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11—44no—
683C4×C11C2×#12014yescomplemented
684Dic11—22no—
685Dic11—22no—
686Dic11—41no—
687Dic11—41no—
688Dic11—44no—
689Dic11C2×#12014yescomplemented
690C25—111no—
691C25—114no—
692C25—111no—
693C25—114no—
694C25—112no—
695C25—228no—
696C25—2216no—
697C25—228no—
698C25—228no—
699C25—448no—
700C25C22×D1112yes—
701C22×D4—28no—
702C22×D4—24no—
703C22×D4—111no—
704C22×D4—111no—
705C22×D4—114no—
706C22×D4—118no—
707C22×D4—1116no—
708C22×D4—114no—
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—111no—
712C22×D4—112no—
713C22×D4—112no—
714C22×D4—114no—
715C22×D4—228no—
716C22×D4—228no—
717C22×D4—228no—
718C22×D4—228no—
719C22×D4—228no—
720C22×D4—228no—
721C22×D4—228no—
722C22×D4—2216no—
723C22×D4—228no—
724C22×D4—224no—
725C22×D4—2216no—
726C22×D4—224no—
727C22×D4—22128no—
728C22×D4—2216no—
729C22×D4—2216no—
730C22×D4—2216no—
731C22×D4—228no—
732C22×D4—224no—
733C22×D4—448no—
734C22×D4C22×D1112yes—
735C22×D4C22×D1111yescharacteristic
736C22×D4C22×D1112yes—
737C22×D4C22×D1114yescomplemented
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—118no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—114no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—228no—
752C23×C4—224no—
753C23×C4—228no—
754C23×C4C22×D1111yescharacteristic
755C23×C4C22×D1111yescharacteristic, complemented
756#121—28no—
757#121—2216no—
758#121—228no—
759#121—228no—
760#121—2216no—
761#121—228no—
762#120—28no—
763#120—228no—
764#120—2216no—
765#120—2216no—
766#120—228no—
767#120—228no—
768C4×D4—24no—
769C4×D4—224no—
770C4×D4—224no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—224no—
775C4×D4—224no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—114no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—224no—
782C2×C4⋊C4—228no—
783C2×C4⋊C4C22×D1111yescharacteristic, complemented
784C2×C4⋊C4C22×D1112yescomplemented
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—114no—
789C2×C22⋊C4—114no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—114no—
795C2×C22⋊C4—114no—
796C2×C22⋊C4—114no—
797C2×C22⋊C4—114no—
798C2×C22⋊C4—114no—
799C2×C22⋊C4—114no—
800C2×C22⋊C4—114no—
801C2×C22⋊C4—114no—
802C2×C22⋊C4—224no—
803C2×C22⋊C4—2216no—
804C2×C22⋊C4—224no—
805C2×C22⋊C4—228no—
806C2×C22⋊C4—2216no—
807C2×C22⋊C4—448no—
808C2×C22⋊C4C22×D1111yescharacteristic
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1111yescharacteristic, complemented
811C2×C22⋊C4C22×D1114yescomplemented
812C2×C22⋊C4C22×D1114yescomplemented
813C2×C22⋊C4C22×D1114yescomplemented
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—224no—
818C2×C42C22×D1111yescharacteristic, complemented
819#95—114no—
820#95—112no—
821#95C22×D1112yescomplemented
822C2×C11—24no—
823C2×C11—48no—
824C2×C11—42no—
825C2×C11C22×#12011yescharacteristic
826C2×C11C22×#12111yescharacteristic
827C2×C11C2×#53511yescharacteristic
828C2×C11C2×D4212yes—
829C2×C11C2×#54612yes—
830D11—24no—
831D11—42no—
832D11—48no—
833D11#240818yesdirect product factor
834C24—28no—
835C24—24no—
836C24—24no—
837C24—24no—
838C24—44no—
839C24—111no—
840C24—114no—
841C24—114no—
842C24—114no—
843C24—111no—
844C24—1116no—
845C24—114no—
846C24—114no—
847C24—111no—
848C24—224no—
849C24—224no—
850C24—222no—
851C24—228no—
852C24—228no—
853C24—224no—
854C24—228no—
855C24—228no—
856C24—228no—
857C24—228no—
858C24—228no—
859C24—222no—
860C24—224no—
861C24—228no—
862C24—228no—
863C24—228no—
864C24—228no—
865C24—2264no—
866C24—228no—
867C24—224no—
868C24—224no—
869C24—224no—
870C24—444no—
871C24—444no—
872C24—444no—
873C24—4432no—
874C24—4464no—
875C24—4464no—
876C24—4432no—
877C24C23×D1114yes—
878C24C23×D1111yescharacteristic
879C24C23×D1111yescharacteristic
880C2×D4—232no—
881C2×D4—22no—
882C2×D4—28no—
883C2×D4—22no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—44no—
890C2×D4—114no—
891C2×D4—1116no—
892C2×D4—114no—
893C2×D4—118no—
894C2×D4—114no—
895C2×D4—222no—
896C2×D4—228no—
897C2×D4—222no—
898C2×D4—2232no—
899C2×D4—228no—
900C2×D4—228no—
901C2×D4—2264no—
902C2×D4—228no—
903C2×D4—228no—
904C2×D4—228no—
905C2×D4—2232no—
906C2×D4—2264no—
907C2×D4—2264no—
908C2×D4—2264no—
909C2×D4—222no—
910C2×D4—228no—
911C2×D4—222no—
912C2×D4—2264no—
913C2×D4—222no—
914C2×D4—228no—
915C2×D4—222no—
916C2×D4—228no—
917C2×D4—228no—
918C2×D4—228no—
919C2×D4—228no—
920C2×D4—224no—
921C2×D4—224no—
922C2×D4—224no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—444no—
926C2×D4—4464no—
927C2×D4D4×D1118yescomplemented
928C2×D4D4×D1114yescomplemented
929C22×C4—24no—
930C22×C4—22no—
931C22×C4—24no—
932C22×C4—111no—
933C22×C4—114no—
934C22×C4—118no—
935C22×C4—114no—
936C22×C4—111no—
937C22×C4—111no—
938C22×C4—114no—
939C22×C4—114no—
940C22×C4—114no—
941C22×C4—114no—
942C22×C4—114no—
943C22×C4—111no—
944C22×C4—111no—
945C22×C4—224no—
946C22×C4—2232no—
947C22×C4—222no—
948C22×C4—224no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—222no—
952C22×C4—222no—
953C22×C4—224no—
954C22×C4—228no—
955C22×C4—222no—
956C22×C4—228no—
957C22×C4—224no—
958C22×C4—228no—
959C22×C4—224no—
960C22×C4—222no—
961C22×C4—224no—
962C22×C4—224no—
963C22×C4—222no—
964C22×C4—224no—
965C22×C4—4416no—
966C22×C4D4×D1114yescomplemented
967C22×C4C23×D1114yes—
968C22×C4C23×D1111yescharacteristic
969C22×C4C23×D1111yescharacteristic
970C22×C4C23×D1111yescharacteristic
971C22×C4C23×D1111yescharacteristic
972C22×C4C23×D1111yescharacteristic
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—228no—
978C4⋊C4—222no—
979C4⋊C4—224no—
980C22⋊C4—22no—
981C22⋊C4—24no—
982C22⋊C4—28no—
983C22⋊C4—22no—
984C22⋊C4—28no—
985C22⋊C4—44no—
986C22⋊C4—222no—
987C22⋊C4—228no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—228no—
991C22⋊C4—228no—
992C22⋊C4—228no—
993C22⋊C4—222no—
994C22⋊C4—228no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—228no—
998C22⋊C4—222no—
999C22⋊C4—228no—
1000C22⋊C4—444no—
1001C22⋊C4—444no—
1002C22⋊C4—444no—
1003C42—22no—
1004C42—222no—
1005C42—222no—
1006C42—222no—
1007C11C2×#240811yescharacteristic, complemented, Sylow
1008C23—22no—
1009C23—22no—
1010C23—216no—
1011C23—21no—
1012C23—24no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—21no—
1017C23—24no—
1018C23—24no—
1019C23—22no—
1020C23—24no—
1021C23—416no—
1022C23—416no—
1023C23—48no—
1024C23—48no—
1025C23—112no—
1026C23—112no—
1027C23—114no—
1028C23—112no—
1029C23—114no—
1030C23—1116no—
1031C23—112no—
1032C23—112no—
1033C23—112no—
1034C23—118no—
1035C23—112no—
1036C23—228no—
1037C23—228no—
1038C23—2216no—
1039C23—2216no—
1040C23—2232no—
1041C23—228no—
1042C23—2216no—
1043C23—2232no—
1044C23—2232no—
1045C23—2216no—
1046C23—2232no—
1047C23—222no—
1048C23—222no—
1049C23—221no—
1050C23—224no—
1051C23—222no—
1052C23—224no—
1053C23—224no—
1054C23—221no—
1055C23—224no—
1056C23—224no—
1057C23—222no—
1058C23—224no—
1059C23—4416no—
1060C23—4416no—
1061C23—4416no—
1062C23—4416no—
1063C23—448no—
1064C23—444no—
1065C23—444no—
1066C23—448no—
1067C23—4416no—
1068C23—4416no—
1069C23—4416no—
1070C23—4416no—
1071C23—4416no—
1072C23—4416no—
1073C23—4416no—
1074C23—44256no—
1075C23—4416no—
1076C23—448no—
1077C23C2×D4×D1118yes—
1078C23C2×D4×D1112yes—
1079C23C2×D4×D1112yes—
1080C23C2×D4×D1112yescomplemented
1081C23#41×D1112yes—
1082C23C24×D1111yescharacteristic
1083D4—216no—
1084D4—28no—
1085D4—216no—
1086D4—416no—
1087D4—228no—
1088D4—2216no—
1089D4—2232no—
1090D4—228no—
1091D4—2232no—
1092D4—228no—
1093D4—2216no—
1094D4—4416no—
1095D4—4416no—
1096D4—4416no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—28no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—21no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—44no—
1109C2×C4—112no—
1110C2×C4—114no—
1111C2×C4—1116no—
1112C2×C4—112no—
1113C2×C4—112no—
1114C2×C4—228no—
1115C2×C4—228no—
1116C2×C4—228no—
1117C2×C4—228no—
1118C2×C4—221no—
1119C2×C4—222no—
1120C2×C4—221no—
1121C2×C4—228no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—224no—
1125C2×C4—221no—
1126C2×C4—224no—
1127C2×C4—222no—
1128C2×C4—224no—
1129C2×C4—444no—
1130C2×C4—444no—
1131C2×C4—4416no—
1132C2×C4—444no—
1133C2×C4—444no—
1134C2×C4—444no—
1135C2×C4C2×D4×D1112yes—
1136C2×C4C2×D4×D1112yes—
1137C2×C4C2×D4×D1114yes—
1138C2×C4C2×D4×D1112yescomplemented
1139C22—22no—
1140C22—24no—
1141C22—24no—
1142C22—22no—
1143C22—24no—
1144C22—28no—
1145C22—28no—
1146C22—28no—
1147C22—22no—
1148C22—432no—
1149C22—44no—
1150C22—41no—
1151C22—44no—
1152C22—44no—
1153C22—42no—
1154C22—41no—
1155C22—44no—
1156C22—114no—
1157C22—118no—
1158C22—118no—
1159C22—114no—
1160C22—114no—
1161C22—114no—
1162C22—2232no—
1163C22—222no—
1164C22—224no—
1165C22—224no—
1166C22—222no—
1167C22—224no—
1168C22—228no—
1169C22—228no—
1170C22—228no—
1171C22—222no—
1172C22—4432no—
1173C22—4464no—
1174C22—4416no—
1175C22—4464no—
1176C22—444no—
1177C22—441no—
1178C22—444no—
1179C22—444no—
1180C22—442no—
1181C22—441no—
1182C22—444no—
1183C22D11×#12114yescomplemented
1184C22C22×D4×D1111yescharacteristic
1185C22C22×D4×D1111yescharacteristic
1186C22C22×D4×D1112yes—
1187C22C2×#41×D1111yescharacteristic
1188C22D11×H(5,𝔽2)12yes—
1189C4—22no—
1190C4—22no—
1191C4—41no—
1192C4—44no—
1193C4—41no—
1194C4—114no—
1195C4—222no—
1196C4—222no—
1197C4—441no—
1198C4—444no—
1199C4—441no—
1200C4D11×#12014yescomplemented
1201C2—24no—
1202C2—48no—
1203C2—42no—
1204C2—118no—
1205C2—224no—
1206C2—448no—
1207C2—442no—
1208C2C2×D11×#12011yescharacteristic
1209C2C2×D11×#12111yescharacteristic
1210C2D11×#53511yescharacteristic
1211C2D42×D1112yes—
1212C2D11×#54612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2408C2
hypercenter#2408D11
hypocenterC11C2×#2408
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C2×D11×#121C2semidirect
3. C2×D11×#120C2semidirect
4. C2×C4×D4×D11C2semidirect
5. #13071973C2semidirect
6. #13071972C2semidirect
7. #13071971C2semidirect
8. #13071970C2semidirect
9. #13071969C2semidirect
10. #13071968C2semidirect
11. #13071967C2semidirect
12. #13071966C2semidirect
13. #13071965C2semidirect
14. D11×#394C2semidirect
15. D11×#392C2semidirect
16. D11×#390C2semidirect
17. D11×#380C2semidirect
18. D11×#379C2semidirect
19. C11×#2408C2semidirect
21. C23×D4×C11C22semidirect
22. C23×C22⋊D11C22semidirect
28. C22×D4×D11C22semidirect
29. C22×D4×D11C22semidirect
30. C22×D4×D11C22semidirect
31. C23×D44C22semidirect
33. C23×C4×D11C22semidirect
34. C2×C11×#121C22semidirect
35. C2×C11×#120C22semidirect
36. C2×C4×D4×C11C22semidirect
37. C2×#67006C22semidirect
38. C2×#66992C22semidirect
39. C2×#66991C22semidirect
40. C2×#66990C22semidirect
41. C2×#66990C22semidirect
42. C2×D4×Dic11C22semidirect
43. C2×#66983C22semidirect
44. C2×C4×C22⋊D11C22semidirect
45. C2×C4×C22⋊D11C22semidirect
49. C2×#66948C22semidirect
50. C2×#66946C22semidirect
51. C2×C4⋊C4×D11C22semidirect
52. C2×C4⋊C4×D11C22semidirect
53. C2×#66937C22semidirect
54. C2×#66935C22semidirect
55. C2×#66935C22semidirect
56. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×(C22⋊D11)⋊C4C22semidirect
60. C2×C22⋊C4×D11C22semidirect
61. C2×C22⋊C4×D11C22semidirect
62. C2×C22⋊C4×D11C22semidirect
63. C2×C22⋊C4×D11C22semidirect
64. C2×C4×D44C22semidirect
65. C2×C42×D11C22semidirect
66. C11×#394C22semidirect
67. C11×#392C22semidirect
68. C11×#390C22semidirect
69. C11×#380C22semidirect
70. C11×#379C22semidirect
71. #10622860C22semidirect
72. #10622836C22semidirect
73. #10622836C22semidirect
74. #10622835C22semidirect
75. #10622834C22semidirect
76. #10622825C22semidirect
77. #10622604C22semidirect
78. #10622601C22semidirect
79. #10622600C22semidirect
80. #10622574C22semidirect
81. #10622573C22semidirect
82. #10622573C22semidirect
83. #10622572C22semidirect
84. #10622570C22semidirect
85. #10622570C22semidirect
86. #10622568C22semidirect
87. #10622568C22semidirect
88. #10622568C22semidirect
89. #10622568C22semidirect
90. #10622555C22semidirect
91. #10622552C22semidirect
92. #10622285C22semidirect
93. #10622284C22semidirect
94. #10622280C22semidirect
95. D11×#95C22semidirect
112. C22×D4×C11C23semidirect
114. C23×C4×C11C23semidirect
121. C22×C22⋊D11C23semidirect
122. C22×C22⋊D11C23semidirect
124. C23×Dic11C23semidirect
140. C2×D4×D11D4semidirect
141. C2×D4×D11D4semidirect
147. C22×D44C23semidirect
151. C22×C4×D11D4semidirect
160. C22×C4×D11C23semidirect
161. C22×C4×D11C23semidirect
165. C2×C11×C4⋊C4C23semidirect
166. C2×C11×C4⋊C4C23semidirect
169. C2×C11×C22⋊C4C23semidirect
170. C2×C11×C22⋊C4C23semidirect
171. C2×C11×C22⋊C4C23semidirect
172. C2×C11×C22⋊C4C23semidirect
173. C2×C42×C11C23semidirect
177. C2×C22⋊Dic11C23semidirect
178. C2×C22⋊Dic11C23semidirect
179. C2×C22⋊Dic11C23semidirect
180. C2×C22⋊Dic11C23semidirect
192. C2×(C2×D11)⋊C4C23semidirect
193. C2×(C2×D11)⋊C4C23semidirect
194. C2×(C2×D11)⋊C4C23semidirect
195. C2×(C2×D11)⋊C4C23semidirect
196. C2×(C2×D11)⋊C4C23semidirect
197. C2×(C2×D11)⋊C4C23semidirect
198. C2×(C2×D11)⋊C4C23semidirect
199. C2×(C2×D11)⋊C4C23semidirect
200. C2×C4⋊Dic11C23semidirect
201. C2×C4⋊Dic11C23semidirect
202. C2×Dic11⋊C4C23semidirect
203. C2×Dic11⋊C4C23semidirect
204. C2×Dic11⋊C4C23semidirect
205. C2×C4×Dic11C23semidirect
206. C2×C4×Dic11C23semidirect
207. C2×C4×Dic11C23semidirect
225. C11×#95C23semidirect
226. C11⋊#95C23semidirect
227. C11⋊#95C23semidirect
269. C23×D11C2×D4semidirect
285. C2×D4×C11C2×D4semidirect
286. C2×D4×C11C2×D4semidirect
290. C22×C4×C11C2×D4semidirect
313. C2×C22⋊D11C2×D4semidirect
314. C2×C22⋊D11C2×D4semidirect
315. C2×C22⋊D11C2×D4semidirect
319. C22×Dic11C2×D4semidirect
342. C2×D44C2×D4semidirect
343. C2×D44C2×D4semidirect
365. C2×C4×D11C2×D4semidirect
366. C2×C4×D11C2×D4semidirect
367. C2×C4×D11C2×D4semidirect
415. #2408D11direct (N × H)
441. C23×C11C22×D4semidirect
485. C22×D11#121semidirect
492. C22×D11C22×D4semidirect
515. C2×C4×C11C22×D4semidirect
537. C2×Dic11C22×D4semidirect
551. C4×D11#120semidirect
563. C23×D4C2×D11semidirect
572. C2×#121C2×D11semidirect
579. C2×#120C2×D11semidirect
588. C2×C4×D4C2×D11semidirect
603. #394C2×D11semidirect
609. #392C2×D11semidirect
615. #390C2×D11semidirect
620. #380C2×D11semidirect
626. #379C2×D11semidirect
645. C22×C11C2×#121semidirect
674. C2×D11C2×#121semidirect
683. C4×C11C2×#120semidirect
689. Dic11C2×#120semidirect
737. C22×D4C22×D11semidirect
755. C23×C4C22×D11semidirect
783. C2×C4⋊C4C22×D11semidirect
784. C2×C4⋊C4C22×D11semidirect
810. C2×C22⋊C4C22×D11semidirect
811. C2×C22⋊C4C22×D11semidirect
812. C2×C22⋊C4C22×D11semidirect
813. C2×C22⋊C4C22×D11semidirect
818. C2×C42C22×D11semidirect
821. #95C22×D11semidirect
833. D11#2408direct (N × H)
927. C2×D4D4×D11semidirect
928. C2×D4D4×D11semidirect
966. C22×C4D4×D11semidirect
1007. C11C2×#2408semidirect
1080. C23C2×D4×D11semidirect
1138. C2×C4C2×D4×D11semidirect
1183. C22D11×#121semidirect
1200. C4D11×#120semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D112
C2×D11×#1212
C2×D11×#1202
C2×C4×D4×D112
#130719732
#130719722
#130719712
#130719702
#130719692
#130719682
#130719672
#130719662
#130719652
D11×#3942
D11×#3922
D11×#3902
D11×#3802
D11×#3792
C11×#24082
C2×#240811