Finite Group Databasebeta

← D11×#2325 #14912544

Subgroups — D11×#2325 #14912544

Order 2816.

4150 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C2×C4×D4×D11C212yesmaximal, complemented
3#13071321C211yesmaximal, characteristic, complemented
4#13071320C212yesmaximal, complemented
5#13071319C211yesmaximal, characteristic, complemented
6#13071318C212yesmaximal, complemented
7#13071317C212yesmaximal, complemented
8#13071316C211yesmaximal, characteristic, complemented
9#13071315C212yesmaximal, complemented
10#13071314C212yesmaximal, complemented
11#13071313C212yesmaximal, complemented
12D11×#388C212yesmaximal, complemented
13D11×#387C212yesmaximal, complemented
14D11×#386C212yesmaximal, complemented
15D11×#386C212yesmaximal, complemented
16D11×#385C212yesmaximal, complemented
17D11×#380C211yesmaximal, characteristic, complemented
18C2×D11×#95C211yesmaximal, characteristic, complemented
19C11×#2325C211yesmaximal, characteristic, complemented
20C22×D4×D11C2212yes—
21C22×D4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2212yes—
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2212yescomplemented
28C2×#66992C2212yes—
29C2×#66991C2211yescharacteristic
30C2×D4×Dic11C2212yescomplemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2212yescomplemented
33C2×C4×C22⋊D11C2212yescomplemented
34D11×#121C4116yescomplemented
35C4×D4×D11—216no—
36C2×#66948C2211yescharacteristic
37C2×#66946C2212yescomplemented
38C2×C4⋊C4×D11C2212yes—
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66937C2212yes—
43C2×(C22⋊D11)⋊C4C2212yescomplemented
44C2×(C22⋊D11)⋊C4C2212yescomplemented
45C2×C22⋊C4×D11C2212yes—
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C4×D44C2212yescomplemented
51C2×C42×D11C2212yes—
52C11×#388C2212yescomplemented
53C11×#387C2212yescomplemented
54C11×#386C2212yescomplemented
55C11×#386C2212yescomplemented
56C11×#385C2212yescomplemented
57C11×#380C2211yescharacteristic, complemented
58C2×C11×#95C2211yescharacteristic, complemented
59#10622833C2212yescomplemented
60#10622833C2212yescomplemented
61#10622826C2212yescomplemented
62#10622826C2212yescomplemented
63#10622825C2211yescharacteristic, complemented
64#10622823C2212yescomplemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67C2×C11⋊#95C2211yescharacteristic, complemented
68#10622603C2212yescomplemented
69#10622602C2212yescomplemented
70#10622602C2212yescomplemented
71#10622600C2211yescharacteristic, complemented
72#10622600C2211yescharacteristic, complemented
73#10622594C2212yescomplemented
74#10622591C2212yescomplemented
75#10622571C2212yescomplemented
76#10622571C2212yescomplemented
77#10622569C2212yescomplemented
78#10622569C2212yescomplemented
79#10622569C2212yescomplemented
80#10622569C2212yescomplemented
81#10622564C2212yescomplemented
82#10622563C2212yescomplemented
83#10622559C2212yescomplemented
84#10622558C2212yescomplemented
85#10622557C2212yescomplemented
86#10622555C2212yescomplemented
87#10622553C2212yescomplemented
88#10622546C2212yescomplemented
89#10622283C2212yescomplemented
90#10622282C2212yescomplemented
91#10622281C2212yescomplemented
92#10622281C2212yescomplemented
93#10622280C2212yescomplemented
94#10622278C2212yescomplemented
95#10622278C2212yescomplemented
96#10622278C2212yescomplemented
97#10622278C2212yescomplemented
98D11×#95C2212yes—
99D11×#95C2212yes—
100D11×#95C2212yes—
101D11×#95C2212yes—
102D11×#95C2212yes—
103D11×#95C2212yescomplemented
104D11×#95C2212yescomplemented
105#10622268C2212yescomplemented
106#10622267C2212yescomplemented
107#10622266C2212yescomplemented
108#10622265C2212yescomplemented
109C24×D11C2312yes—
110C24×D11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C23×C4×C11C2312yes—
114C23×C4×C11C2311yescharacteristic
115C23×C4×C11C2311yescharacteristic
116C23×C4×C11C2311yescharacteristic
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2312yes—
120C23×Dic11C2312yes—
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C2×D4×D11—28no—
125C2×D4×D11—28no—
126C2×D4×D11—42no—
127C2×D4×D11—42no—
128C2×D4×D11C2×C4116yescomplemented
129C2×D4×D11C2×C418yescomplemented
130C22×D44C2312yes—
131C22×D44C2311yescharacteristic
132C22×C4×D11—24no—
133C22×C4×D11—28no—
134C22×C4×D11—42no—
135C22×C4×D11—42no—
136C22×C4×D11—42no—
137C22×C4×D11—42no—
138C22×C4×D11—44no—
139C22×C4×D11—44no—
140C22×C4×D11—42no—
141C22×C4×D11—42no—
142C22×C4×D11C2×C418yescomplemented
143C22×C4×D11D418yescomplemented
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C11×#121C2×C418yescomplemented
158C4×D4×C11—28no—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C42×C11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174#66992C2×C4116yescomplemented
175#66991C2×C418yescomplemented
176D4×Dic11—28no—
177#66983C2×C418yescomplemented
178C4×C22⋊D11—28no—
179C4×C22⋊D11—28no—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×C4⋊Dic11C2312yes—
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2311yescharacteristic
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202#66948C2×C418yescomplemented
203#66946—28no—
204C4⋊C4×D11—28no—
205C4⋊C4×D11—42no—
206C4⋊C4×D11—42no—
207C4⋊C4×D11C2×C418yescomplemented
208#66937C2×C4116yescomplemented
209(C22⋊D11)⋊C4—28no—
210(C22⋊D11)⋊C4—28no—
211C22⋊C4×D11—28no—
212C22⋊C4×D11—28no—
213C22⋊C4×D11—44no—
214C22⋊C4×D11—44no—
215C22⋊C4×D11C2×C4116yescomplemented
216C4×D44—28no—
217C42×D11—28no—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C2×#2325—111nomaximal, Sylow
239C24×C11C2412yes—
240C24×C11C2411yescharacteristic
241C23×D11—22no—
242C23×D11—22no—
243C23×D11—22no—
244C23×D11—22no—
245C23×D11—24no—
246C23×D11—24no—
247C23×D11—24no—
248C23×D11—24no—
249C23×D11—24no—
250C23×D11—24no—
251C23×D11C22×C418yes—
252C23×D11C22×C414yes—
253C23×D11C2×D414yes—
254C23×D11#4114yes—
255C23×D11C2412yes—
256C23×D11C2411yescharacteristic
257C23×D11C2411yescharacteristic
258C2×D4×C11—24no—
259C2×D4×C11—24no—
260C2×D4×C11—41no—
261C2×D4×C11—41no—
262C2×D4×C11C22×C418yescomplemented
263C2×D4×C11C22×C414yescomplemented
264C22×C4×C11—22no—
265C22×C4×C11—24no—
266C22×C4×C11—41no—
267C22×C4×C11—41no—
268C22×C4×C11—41no—
269C22×C4×C11—41no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—41no—
273C22×C4×C11—41no—
274C22×C4×C11C22×C414yescomplemented
275C22×C4×C11C2×D414yescomplemented
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C2×C22⋊D11—24no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11—24no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—42no—
289C2×C22⋊D11C22×C418yescomplemented
290C2×C22⋊D11C22×C418yescomplemented
291C2×C22⋊D11C22×C418yescomplemented
292C22×Dic11—24no—
293C22×Dic11—22no—
294C22×Dic11—41no—
295C22×Dic11—41no—
296C22×Dic11—41no—
297C22×Dic11—41no—
298C22×Dic11—41no—
299C22×Dic11—41no—
300C22×Dic11—42no—
301C22×Dic11—42no—
302C22×Dic11C22×C414yescomplemented
303C22×Dic11C2×D414yescomplemented
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311D4×D11—264no—
312D4×D11—416no—
313C2×D44—24no—
314C2×D44—24no—
315C2×D44—41no—
316C2×D44—41no—
317C2×D44C22×C418yescomplemented
318C2×D44C22×C414yescomplemented
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—24no—
325C2×C4×D11—24no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—41no—
340C2×C4×D11—41no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—416no—
352C2×C4×D11—416no—
353C2×C4×D11—416no—
354C2×C4×D11—432no—
355C2×C4×D11C22×C414yes—
356C2×C4×D11C22×C418yes—
357C2×C4×D11C22×C414yes—
358C2×C4×D11C22×C414yescomplemented
359C2×C4×D11C22×C414yescomplemented
360C2×C4×D11C2×D418yes—
361C2×C4×D11C2×D418yescomplemented
362C11×C4⋊C4—24no—
363C11×C4⋊C4—41no—
364C11×C4⋊C4—41no—
365C11×C4⋊C4C22×C414yescomplemented
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4C22×C418yescomplemented
371C42×C11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—42no—
375C22⋊Dic11—42no—
376C22⋊Dic11C22×C418yescomplemented
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4C22×C418yescomplemented
386(C2×D11)⋊C4C22×C418yescomplemented
387C4⋊Dic11—24no—
388C4⋊Dic11—41no—
389C4⋊Dic11—41no—
390C4⋊Dic11C22×C414yescomplemented
391Dic11⋊C4—24no—
392Dic11⋊C4—24no—
393Dic11⋊C4—42no—
394Dic11⋊C4—42no—
395Dic11⋊C4C22×C418yescomplemented
396C4×Dic11—24no—
397C4×Dic11—24no—
398C4×Dic11—24no—
399C22×#121—111no—
400C22×C4×D4—112no—
401#2325—112no—
402#2325—112no—
403#2325—112no—
404#2325—112no—
405#2325—112no—
406#2325—111no—
407#2325—111no—
408#2325—111no—
409#2325—112no—
410#2325D1111yescharacteristic, direct product factor
411C2×#388—112no—
412C2×#387—112no—
413C2×#386—112no—
414C2×#386—112no—
415C2×#385—112no—
416C2×#380—111no—
417C22×#95—111no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11C23×C414yes—
429C23×C11C23×C412yes—
430C23×C11C22×D412yes—
431C23×C11C2×#4112yes—
432C23×C11C2511yescharacteristic
433C22×D11—21no—
434C22×D11—21no—
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—28no—
438C22×D11—28no—
439C22×D11—28no—
440C22×D11—28no—
441C22×D11—28no—
442C22×D11—28no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—216no—
450C22×D11—216no—
451C22×D11—216no—
452C22×D11—48no—
453C22×D11—48no—
454C22×D11—48no—
455C22×D11—48no—
456C22×D11C4×D4116yes—
457C22×D11C23×C414yes—
458C22×D11C23×C412yes—
459C22×D11C23×C412yes—
460C22×D11C22×D412yes—
461C22×D11C22×D412yes—
462C22×D11C2×#4112yes—
463C22×D11C2×#4112yes—
464C22×D11H(5,𝔽2)12yes—
465C22×D11H(5,𝔽2)12yes—
466C22×D11H(5,𝔽2)12yes—
467C22×D112−1+412yes—
468D4×C11—216no—
469D4×C11—44no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—44no—
488C2×C4×C11—44no—
489C2×C4×C11—48no—
490C2×C4×C11—44no—
491C2×C4×C11C23×C414yes—
492C2×C4×C11C23×C412yes—
493C2×C4×C11C23×C412yes—
494C2×C4×C11C22×D414yes—
495C22⋊D11—216no—
496C22⋊D11—216no—
497C22⋊D11—48no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—44no—
516C2×Dic11—44no—
517C2×Dic11—48no—
518C2×Dic11—44no—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C414yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C22×D414yes—
523D44—216no—
524D44—44no—
525C4×D11—216no—
526C4×D11—28no—
527C4×D11—28no—
528C4×D11—216no—
529C4×D11—44no—
530C4×D11—44no—
531C4×D11—48no—
532C4×D11—48no—
533C4×D11—48no—
534C4×D11—48no—
535C4×D11—48no—
536C4×D11—48no—
537C4×D11—48no—
538C23×D4—112no—
539C23×D4—111no—
540C24×C4—111no—
541C24×C4—111no—
542C24×C4—112no—
543C24×C4—111no—
544C2×#121—111no—
545C2×#121—112no—
546C2×#121—111no—
547C2×#121—1116no—
548C2×#121—111no—
549C2×#121—112no—
550C2×#121C2×D1111yescharacteristic
551C2×C4×D4—112no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—112no—
555C2×C4×D4—112no—
556C2×C4×D4—112no—
557C2×C4×D4—112no—
558C2×C4×D4—2216no—
559C2×C4×D4C2×D1112yescomplemented
560C22×C4⋊C4—111no—
561C22×C4⋊C4—112no—
562C22×C4⋊C4—111no—
563C22×C4⋊C4—111no—
564C22×C22⋊C4—112no—
565C22×C22⋊C4—112no—
566C22×C22⋊C4—112no—
567C22×C22⋊C4—112no—
568C22×C22⋊C4—112no—
569C22×C42—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388C2×D1112yescomplemented
578#387—112no—
579#387—112no—
580#387—112no—
581#387—112no—
582#387—112no—
583#387—112no—
584#387—112no—
585#387C2×D1112yescomplemented
586#386—112no—
587#386—112no—
588#386—112no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—112no—
597#386—112no—
598#386—112no—
599#386—112no—
600#386C2×D1112yescomplemented
601#386C2×D1112yescomplemented
602#385—112no—
603#385—112no—
604#385—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#385C2×D1112yescomplemented
610#380—111no—
611#380—111no—
612#380—111no—
613#380—112no—
614#380—112no—
615#380C2×D1111yescharacteristic, complemented
616C2×#95—111no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—112no—
620C2×#95—112no—
621C2×#95—112no—
622C2×#95—112no—
623C2×#95—112no—
624C2×#95—112no—
625C2×#95—112no—
626C2×#95C2×D1111yescharacteristic, complemented
627C22×C11—22no—
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—22no—
631C22×C11—22no—
632C22×C11—22no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11C2×C4×D414yes—
641C22×C11C24×C411yescharacteristic
642C22×C11C23×D411yescharacteristic
643C22×C11C22×#4111yescharacteristic
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C22×C11C2×H(5,𝔽2)11yescharacteristic
646C22×C11C2×H(5,𝔽2)11yescharacteristic
647C22×C11C2×2−1+411yescharacteristic
648C2×D11—22no—
649C2×D11—22no—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—232no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—432no—
663C2×D11C2×C4×D414yes—
664C2×D11C2×C4×D414yes—
665C2×D11#51814yes—
666C2×D11#52014yes—
667C2×D11#53414yes—
668C2×D11#53714yes—
669C2×D11#53814yes—
670C2×D11#53914yes—
671C4×C11—24no—
672C4×C11—22no—
673C4×C11—22no—
674C4×C11—24no—
675C4×C11—42no—
676C4×C11—42no—
677C4×C11—42no—
678Dic11—24no—
679Dic11—22no—
680Dic11—22no—
681Dic11—24no—
682Dic11—42no—
683Dic11—42no—
684Dic11—42no—
685C25—111no—
686C25—112no—
687C22×D4—112no—
688C22×D4—112no—
689C22×D4—112no—
690C22×D4—1116no—
691C22×D4—118no—
692C22×D4—112no—
693C22×D4—111no—
694C22×D4—228no—
695C22×D4—228no—
696C22×D4—442no—
697C22×D4—442no—
698C22×D4C22×D1112yes—
699C22×D4C22×D1111yescharacteristic
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—111no—
706C23×C4—118no—
707C23×C4—118no—
708C23×C4—112no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—112no—
712C23×C4—111no—
713C23×C4—112no—
714C23×C4—112no—
715C23×C4—112no—
716C23×C4—112no—
717C23×C4—112no—
718C23×C4—112no—
719C23×C4—228no—
720C23×C4—224no—
721C23×C4—442no—
722C23×C4—442no—
723C23×C4—442no—
724C23×C4—442no—
725C23×C4—444no—
726C23×C4—444no—
727C23×C4—442no—
728C23×C4—442no—
729C23×C4C22×D1112yes—
730C23×C4C22×D1111yescharacteristic
731C23×C4C22×D1111yescharacteristic
732C23×C4C22×D1111yescharacteristic
733#121—118no—
734#121—1116no—
735#121—118no—
736#121—118no—
737#121—1116no—
738#121C4×D1118yescomplemented
739C4×D4—28no—
740C4×D4—228no—
741C4×D4—228no—
742C4×D4—228no—
743C4×D4—228no—
744C4×D4—228no—
745C4×D4—228no—
746C4×D4—228no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—118no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—228no—
758C2×C4⋊C4—442no—
759C2×C4⋊C4—442no—
760C2×C4⋊C4C22×D1112yes—
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—1116no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—228no—
781C2×C22⋊C4—228no—
782C2×C22⋊C4—444no—
783C2×C22⋊C4—444no—
784C2×C22⋊C4C22×D1112yes—
785C2×C22⋊C4C22×D1112yes—
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1112yes—
788C2×C22⋊C4C22×D1112yes—
789C2×C42—112no—
790C2×C42—112no—
791C2×C42—112no—
792C2×C42—228no—
793C2×C42C22×D1112yes—
794#95—112no—
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95C22×D1112yes—
810#95C22×D1112yes—
811#95C22×D1112yes—
812#95C22×D1112yes—
813#95C22×D1112yes—
814C2×C11—24no—
815C2×C11—44no—
816C2×C11C22×C4×D411yescharacteristic
817C2×C11C2×#51811yescharacteristic
818C2×C11C2×#52011yescharacteristic
819C2×C11C2×#53411yescharacteristic
820C2×C11C2×#53711yescharacteristic
821C2×C11C2×#53811yescharacteristic
822C2×C11C2×#53911yescharacteristic
823D11—24no—
824D11—44no—
825D11#232518yesdirect product factor
826C24—111no—
827C24—114no—
828C24—114no—
829C24—114no—
830C24—111no—
831C24—118no—
832C24—112no—
833C24—222no—
834C24—222no—
835C24—222no—
836C24—222no—
837C24—224no—
838C24—224no—
839C24—224no—
840C24—224no—
841C24—224no—
842C24—224no—
843C24C23×D1112yes—
844C24C23×D1111yescharacteristic
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—118no—
850C2×D4—118no—
851C2×D4—118no—
852C2×D4—118no—
853C2×D4—114no—
854C2×D4—224no—
855C2×D4—224no—
856C2×D4—2264no—
857C2×D4—224no—
858C2×D4—224no—
859C2×D4—224no—
860C2×D4—224no—
861C2×D4—441no—
862C2×D4—441no—
863C2×D4—4416no—
864C2×D4—442no—
865C2×D4—442no—
866C2×D4C2×C4×D1118yescomplemented
867C2×D4C2×C4×D1114yescomplemented
868C22×C4—22no—
869C22×C4—24no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—111no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—111no—
882C22×C4—114no—
883C22×C4—114no—
884C22×C4—114no—
885C22×C4—118no—
886C22×C4—114no—
887C22×C4—118no—
888C22×C4—114no—
889C22×C4—114no—
890C22×C4—118no—
891C22×C4—112no—
892C22×C4—112no—
893C22×C4—112no—
894C22×C4—224no—
895C22×C4—224no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—222no—
901C22×C4—222no—
902C22×C4—224no—
903C22×C4—224no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—224no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—222no—
915C22×C4—224no—
916C22×C4—441no—
917C22×C4—441no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—441no—
923C22×C4—441no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—4416no—
929C22×C4—4416no—
930C22×C4—4432no—
931C22×C4—4416no—
932C22×C4—441no—
933C22×C4—441no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—441no—
939C22×C4—441no—
940C22×C4C2×C4×D1114yescomplemented
941C22×C4D4×D1114yescomplemented
942C22×C4C23×D1112yes—
943C22×C4C23×D1112yes—
944C22×C4C23×D1112yes—
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1112yes—
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1112yes—
949C4⋊C4—24no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—118no—
953C4⋊C4—114no—
954C4⋊C4—224no—
955C4⋊C4—224no—
956C4⋊C4—224no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—441no—
960C4⋊C4—441no—
961C4⋊C4C2×C4×D1114yescomplemented
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—118no—
967C22⋊C4—118no—
968C22⋊C4—118no—
969C22⋊C4—224no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4C2×C4×D1118yescomplemented
982C42—24no—
983C42—224no—
984C42—224no—
985C42—224no—
986C11C2×#232511yescharacteristic, complemented, Sylow
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—112no—
998C23—112no—
999C23—112no—
1000C23—112no—
1001C23—112no—
1002C23—112no—
1003C23—112no—
1004C23—1116no—
1005C23—112no—
1006C23—112no—
1007C23—112no—
1008C23—114no—
1009C23—228no—
1010C23—228no—
1011C23—228no—
1012C23—228no—
1013C23—228no—
1014C23—228no—
1015C23—2216no—
1016C23—2216no—
1017C23—2216no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—448no—
1029C23—448no—
1030C23—448no—
1031C23—448no—
1032C23C22×C4×D1114yes—
1033C23C22×C4×D1112yes—
1034C23C2×D4×D1112yes—
1035C23#41×D1112yes—
1036C23C24×D1111yescharacteristic
1037D4—216no—
1038D4—44no—
1039D4—2216no—
1040D4—2216no—
1041D4—2216no—
1042D4—444no—
1043D4—448no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—48no—
1064C2×C4—44no—
1065C2×C4—112no—
1066C2×C4—114no—
1067C2×C4—112no—
1068C2×C4—114no—
1069C2×C4—2216no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—2216no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—448no—
1091C2×C4—444no—
1092C2×C4—444no—
1093C2×C4—448no—
1094C2×C4—448no—
1095C2×C4—448no—
1096C2×C4—448no—
1097C2×C4—448no—
1098C2×C4—448no—
1099C2×C4—444no—
1100C2×C4—444no—
1101C2×C4—448no—
1102C2×C4—444no—
1103C2×C4C22×C4×D1112yes—
1104C2×C4C22×C4×D1114yes—
1105C2×C4C22×C4×D1112yes—
1106C2×C4C2×D4×D1114yes—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—114no—
1121C22—114no—
1122C22—114no—
1123C22—114no—
1124C22—114no—
1125C22—114no—
1126C22—114no—
1127C22—114no—
1128C22—2232no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—222no—
1133C22—222no—
1134C22—222no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—4432no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22C4×D4×D1114yes—
1144C22C23×C4×D1111yescharacteristic
1145C22C22×D4×D1111yescharacteristic
1146C22C2×#41×D1111yescharacteristic
1147C22D11×H(5,𝔽2)11yescharacteristic
1148C22D11×H(5,𝔽2)11yescharacteristic
1149C22D11×H(5,𝔽2)11yescharacteristic
1150C22D11×2−1+411yescharacteristic
1151C4—24no—
1152C4—24no—
1153C4—22no—
1154C4—22no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—224no—
1159C4—224no—
1160C4—222no—
1161C4—222no—
1162C4—442no—
1163C4—442no—
1164C4—442no—
1165C2—24no—
1166C2—44no—
1167C2—118no—
1168C2—224no—
1169C2—444no—
1170C2C2×C4×D4×D1111yescharacteristic
1171C2D11×#51811yescharacteristic
1172C2D11×#52011yescharacteristic
1173C2D11×#53411yescharacteristic
1174C2D11×#53711yescharacteristic
1175C2D11×#53811yescharacteristic
1176C2D11×#53911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2325C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2325D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D11C2semidirect
3. #13071321C2semidirect
4. #13071320C2semidirect
5. #13071319C2semidirect
6. #13071318C2semidirect
7. #13071317C2semidirect
8. #13071316C2semidirect
9. #13071315C2semidirect
10. #13071314C2semidirect
11. #13071313C2semidirect
12. D11×#388C2semidirect
13. D11×#387C2semidirect
14. D11×#386C2semidirect
15. D11×#386C2semidirect
16. D11×#385C2semidirect
17. D11×#380C2semidirect
18. C2×D11×#95C2semidirect
19. C11×#2325C2semidirect
27. C2×C4×D4×C11C22semidirect
30. C2×D4×Dic11C22semidirect
32. C2×C4×C22⋊D11C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. D11×#121C4semidirect
37. C2×#66946C22semidirect
43. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×C4×D44C22semidirect
52. C11×#388C22semidirect
53. C11×#387C22semidirect
54. C11×#386C22semidirect
55. C11×#386C22semidirect
56. C11×#385C22semidirect
57. C11×#380C22semidirect
58. C2×C11×#95C22semidirect
59. #10622833C22semidirect
60. #10622833C22semidirect
61. #10622826C22semidirect
62. #10622826C22semidirect
63. #10622825C22semidirect
64. #10622823C22semidirect
65. C2×C11⋊#95C22semidirect
66. C2×C11⋊#95C22semidirect
67. C2×C11⋊#95C22semidirect
68. #10622603C22semidirect
69. #10622602C22semidirect
70. #10622602C22semidirect
71. #10622600C22semidirect
72. #10622600C22semidirect
73. #10622594C22semidirect
74. #10622591C22semidirect
75. #10622571C22semidirect
76. #10622571C22semidirect
77. #10622569C22semidirect
78. #10622569C22semidirect
79. #10622569C22semidirect
80. #10622569C22semidirect
81. #10622564C22semidirect
82. #10622563C22semidirect
83. #10622559C22semidirect
84. #10622558C22semidirect
85. #10622557C22semidirect
86. #10622555C22semidirect
87. #10622553C22semidirect
88. #10622546C22semidirect
89. #10622283C22semidirect
90. #10622282C22semidirect
91. #10622281C22semidirect
92. #10622281C22semidirect
93. #10622280C22semidirect
94. #10622278C22semidirect
95. #10622278C22semidirect
96. #10622278C22semidirect
97. #10622278C22semidirect
103. D11×#95C22semidirect
104. D11×#95C22semidirect
105. #10622268C22semidirect
106. #10622267C22semidirect
107. #10622266C22semidirect
108. #10622265C22semidirect
128. C2×D4×D11C2×C4semidirect
129. C2×D4×D11C2×C4semidirect
142. C22×C4×D11C2×C4semidirect
143. C22×C4×D11D4semidirect
157. C11×#121C2×C4semidirect
174. #66992C2×C4semidirect
175. #66991C2×C4semidirect
177. #66983C2×C4semidirect
202. #66948C2×C4semidirect
207. C4⋊C4×D11C2×C4semidirect
208. #66937C2×C4semidirect
215. C22⋊C4×D11C2×C4semidirect
262. C2×D4×C11C22×C4semidirect
263. C2×D4×C11C22×C4semidirect
274. C22×C4×C11C22×C4semidirect
275. C22×C4×C11C2×D4semidirect
289. C2×C22⋊D11C22×C4semidirect
290. C2×C22⋊D11C22×C4semidirect
291. C2×C22⋊D11C22×C4semidirect
302. C22×Dic11C22×C4semidirect
303. C22×Dic11C2×D4semidirect
317. C2×D44C22×C4semidirect
318. C2×D44C22×C4semidirect
358. C2×C4×D11C22×C4semidirect
359. C2×C4×D11C22×C4semidirect
361. C2×C4×D11C2×D4semidirect
365. C11×C4⋊C4C22×C4semidirect
370. C11×C22⋊C4C22×C4semidirect
376. C22⋊Dic11C22×C4semidirect
385. (C2×D11)⋊C4C22×C4semidirect
386. (C2×D11)⋊C4C22×C4semidirect
390. C4⋊Dic11C22×C4semidirect
395. Dic11⋊C4C22×C4semidirect
410. #2325D11direct (N × H)
559. C2×C4×D4C2×D11semidirect
577. #388C2×D11semidirect
585. #387C2×D11semidirect
600. #386C2×D11semidirect
601. #386C2×D11semidirect
609. #385C2×D11semidirect
615. #380C2×D11semidirect
626. C2×#95C2×D11semidirect
738. #121C4×D11semidirect
825. D11#2325direct (N × H)
866. C2×D4C2×C4×D11semidirect
867. C2×D4C2×C4×D11semidirect
940. C22×C4C2×C4×D11semidirect
941. C22×C4D4×D11semidirect
961. C4⋊C4C2×C4×D11semidirect
981. C22⋊C4C2×C4×D11semidirect
986. C11C2×#2325semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×C4×D4×D112
#130713212
#130713202
#130713192
#130713182
#130713172
#130713162
#130713152
#130713142
#130713132
D11×#3882
D11×#3872
D11×#3862
D11×#3852
D11×#3802
C2×D11×#952
C11×#23252
C2×#232511