Finite Group Databasebeta

← D11×#2364 #14913349

Subgroups — D11×#2364 #14913349

Order 2816.

4262 conjugacy classes of subgroups.

The subgroup lattice has 1086 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#13071668C211yesmaximal, characteristic, complemented
4#13071667C212yesmaximal, complemented
5#13071666C211yesmaximal, characteristic, complemented
6#13071665C212yesmaximal, complemented
7#13071664C212yesmaximal, complemented
8#13071663C211yesmaximal, characteristic, complemented
9#13071662C212yesmaximal, complemented
10#13071661C212yesmaximal, complemented
11#13071660C212yesmaximal, complemented
12D11×#388C212yesmaximal, complemented
13D11×#387C212yesmaximal, complemented
14D11×#386C212yesmaximal, complemented
15D11×#386C212yesmaximal, complemented
16C4×C22⋊C4×D11C212yesmaximal, complemented
17C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
18C2×D11×#95C211yesmaximal, characteristic, complemented
19C11×#2364C211yesmaximal, characteristic, complemented
20C22×D4×D11C2212yes—
21C22×D4×D11C2211yescharacteristic
22C23×C4×D11C2212yes—
23C23×C4×D11C2212yes—
24C23×C4×D11C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2212yescomplemented
27C2×#66992C2212yes—
28C2×#66991C2211yescharacteristic
29C2×D4×Dic11C2212yescomplemented
30C2×#66983C2211yescharacteristic
31C2×C4×C22⋊D11C2212yescomplemented
32C2×C4×C22⋊D11C2212yescomplemented
33D11×#121C4116yescomplemented
34C4×D4×D11—216no—
35C2×#66948C2211yescharacteristic
36C2×#66946C2212yescomplemented
37C2×C4⋊C4×D11C2212yes—
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×#66937C2212yes—
40C2×(C22⋊D11)⋊C4C2212yescomplemented
41C2×(C22⋊D11)⋊C4C2212yescomplemented
42C2×C22⋊C4×D11C2211yescharacteristic
43C2×C22⋊C4×D11C2212yes—
44C2×C22⋊C4×D11C2212yes—
45C2×C22⋊C4×D11C2212yes—
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C4×D44C2212yescomplemented
49C2×C42×D11C2212yes—
50C2×C42×D11C2212yes—
51C11×#388C2212yescomplemented
52C11×#387C2212yescomplemented
53C11×#386C2212yescomplemented
54C11×#386C2212yescomplemented
55C4×C11×C22⋊C4C2211yescharacteristic, complemented
56C4×C11×C22⋊C4C2212yescomplemented
57C2×C11×#95C2211yescharacteristic, complemented
58#10622833C2212yescomplemented
59#10622833C2212yescomplemented
60#10622826C2212yescomplemented
61#10622826C2212yescomplemented
62C4×C22⋊Dic11C2212yescomplemented
63C4×C22⋊Dic11C2211yescharacteristic, complemented
64C2×C11⋊#95C2212yescomplemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66#10622603C2212yescomplemented
67#10622594C2212yescomplemented
68#10622591C2212yescomplemented
69#10622571C2212yescomplemented
70#10622571C2212yescomplemented
71#10622569C2212yescomplemented
72#10622569C2212yescomplemented
73#10622569C2212yescomplemented
74#10622569C2212yescomplemented
75#10622564C2212yescomplemented
76#10622558C2212yescomplemented
77#10622557C2212yescomplemented
78C22⋊C4×Dic11C2212yescomplemented
79C22⋊C4×Dic11C2211yescharacteristic, complemented
80C22⋊C4×Dic11C2211yescharacteristic, complemented
81C22⋊C4×Dic11C2212yescomplemented
82#10622553C2212yescomplemented
83C4×(C2×D11)⋊C4C2212yescomplemented
84C4×(C2×D11)⋊C4C2212yescomplemented
85C4×(C2×D11)⋊C4C2212yescomplemented
86#10622546C2212yescomplemented
87#10622283C2212yescomplemented
88#10622282C2212yescomplemented
89#10622279C2212yescomplemented
90#10622279C2212yescomplemented
91#10622279C2212yescomplemented
92#10622278C2212yescomplemented
93#10622278C2212yescomplemented
94#10622278C2212yescomplemented
95#10622278C2212yescomplemented
96D11×#95C2211yescharacteristic
97D11×#95C2212yes—
98D11×#95C2211yescharacteristic
99D11×#95C2212yes—
100D11×#95C2212yes—
101D11×#95C2212yes—
102D11×#95C2211yescharacteristic, complemented
103D11×#95C2212yescomplemented
104D11×#95C2211yescharacteristic, complemented
105#10622268C2212yescomplemented
106#10622267C2212yescomplemented
107#10622266C2212yescomplemented
108#10622265C2212yescomplemented
109C24×D11C2312yes—
110C24×D11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C23×C4×C11C2312yes—
114C23×C4×C11C2312yes—
115C23×C4×C11C2311yescharacteristic
116C22×C22⋊D11C2312yes—
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C23×Dic11C2312yes—
120C23×Dic11C2312yes—
121C23×Dic11C2311yescharacteristic
122C2×D4×D11—28no—
123C2×D4×D11—28no—
124C2×D4×D11—44no—
125C2×D4×D11C2×C4116yescomplemented
126C2×D4×D11C2×C418yescomplemented
127C22×D44C2312yes—
128C22×D44C2311yescharacteristic
129C22×C4×D11—28no—
130C22×C4×D11—28no—
131C22×C4×D11—28no—
132C22×C4×D11—28no—
133C22×C4×D11—44no—
134C22×C4×D11—44no—
135C22×C4×D11—44no—
136C22×C4×D11C2×C418yescomplemented
137C22×C4×D11C2312yes—
138C22×C4×D11C2312yes—
139C22×C4×D11C2312yes—
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C11×#121C2×C418yescomplemented
151C4×D4×C11—28no—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C42×C11C2312yes—
161C2×C42×C11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168#66992C2×C4116yescomplemented
169#66991C2×C418yescomplemented
170D4×Dic11—28no—
171#66983C2×C418yescomplemented
172C4×C22⋊D11—28no—
173C4×C22⋊D11—28no—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195#66948C2×C418yescomplemented
196#66946—28no—
197C4⋊C4×D11—28no—
198C4⋊C4×D11C2×C418yescomplemented
199#66937C2×C4116yescomplemented
200(C22⋊D11)⋊C4—28no—
201(C22⋊D11)⋊C4—28no—
202C22⋊C4×D11—24no—
203C22⋊C4×D11—28no—
204C22⋊C4×D11—28no—
205C22⋊C4×D11—44no—
206C22⋊C4×D11C2×C4116yescomplemented
207C22⋊C4×D11D418yescomplemented
208C4×D44—28no—
209C42×D11—28no—
210C42×D11—44no—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2311yescharacteristic
216C11×#95C2311yescharacteristic
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C2×#2364—111nomaximal, Sylow
234C24×C11C2412yes—
235C24×C11C2411yescharacteristic
236C23×D11—24no—
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—24no—
240C23×D11—24no—
241C23×D11—24no—
242C23×D11—24no—
243C23×D11—24no—
244C23×D11C22×C418yes—
245C23×D11C22×C414yes—
246C23×D11C2×D414yes—
247C23×D11#4114yes—
248C23×D11C2412yes—
249C23×D11C2411yescharacteristic
250C23×D11C2411yescharacteristic
251C2×D4×C11—24no—
252C2×D4×C11—24no—
253C2×D4×C11—42no—
254C2×D4×C11C22×C418yescomplemented
255C2×D4×C11C22×C414yescomplemented
256C22×C4×C11—24no—
257C22×C4×C11—24no—
258C22×C4×C11—24no—
259C22×C4×C11—24no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11—42no—
263C22×C4×C11C22×C414yescomplemented
264C22×C4×C11C2412yes—
265C22×C4×C11C2412yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C2×C22⋊D11—24no—
272C2×C22⋊D11—24no—
273C2×C22⋊D11—24no—
274C2×C22⋊D11—24no—
275C2×C22⋊D11—42no—
276C2×C22⋊D11—42no—
277C2×C22⋊D11C22×C418yescomplemented
278C2×C22⋊D11C22×C418yescomplemented
279C2×C22⋊D11C22×C418yescomplemented
280C22×Dic11—24no—
281C22×Dic11—24no—
282C22×Dic11—24no—
283C22×Dic11—24no—
284C22×Dic11—42no—
285C22×Dic11—42no—
286C22×Dic11—42no—
287C22×Dic11C22×C414yescomplemented
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295D4×D11—264no—
296D4×D11—416no—
297C2×D44—24no—
298C2×D44—24no—
299C2×D44—42no—
300C2×D44C22×C418yescomplemented
301C2×D44C22×C414yescomplemented
302C2×C4×D11—24no—
303C2×C4×D11—24no—
304C2×C4×D11—24no—
305C2×C4×D11—24no—
306C2×C4×D11—24no—
307C2×C4×D11—24no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—24no—
311C2×C4×D11—24no—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—416no—
331C2×C4×D11—432no—
332C2×C4×D11—432no—
333C2×C4×D11C22×C414yes—
334C2×C4×D11C22×C418yes—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yescomplemented
337C2×C4×D11C22×C414yescomplemented
338C2×C4×D11C2×D418yes—
339C2×C4×D11#4118yes—
340C11×C4⋊C4—24no—
341C11×C4⋊C4C22×C414yescomplemented
342C11×C22⋊C4—22no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4C22×C418yescomplemented
347C11×C22⋊C4C2×D414yescomplemented
348C42×C11—24no—
349C42×C11—42no—
350C22⋊Dic11—24no—
351C22⋊Dic11—24no—
352C22⋊Dic11—22no—
353C22⋊Dic11—42no—
354C22⋊Dic11C22×C418yescomplemented
355C22⋊Dic11C2×D414yescomplemented
356(C2×D11)⋊C4—24no—
357(C2×D11)⋊C4—24no—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4C22×C418yescomplemented
364(C2×D11)⋊C4C22×C418yescomplemented
365(C2×D11)⋊C4C2×D418yescomplemented
366C4⋊Dic11—24no—
367C4⋊Dic11C22×C414yescomplemented
368Dic11⋊C4—24no—
369Dic11⋊C4—24no—
370Dic11⋊C4C22×C418yescomplemented
371C4×Dic11—24no—
372C4×Dic11—24no—
373C4×Dic11—24no—
374C4×Dic11—42no—
375C4×Dic11—42no—
376C4×Dic11—42no—
377C22×#121—111no—
378C22×C4×D4—112no—
379#2364—112no—
380#2364—112no—
381#2364—112no—
382#2364—112no—
383#2364—111no—
384#2364—112no—
385#2364—111no—
386#2364—111no—
387#2364—112no—
388#2364D1111yescharacteristic, direct product factor
389C2×#388—112no—
390C2×#387—112no—
391C2×#386—112no—
392C2×#386—112no—
393C2×C4×C22⋊C4—111no—
394C2×C4×C22⋊C4—112no—
395C22×#95—111no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11C23×C414yes—
405C23×C11C23×C412yes—
406C23×C11C22×D412yes—
407C23×C11C2×#4112yes—
408C23×C11C2511yescharacteristic
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—28no—
412C22×D11—28no—
413C22×D11—216no—
414C22×D11—216no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—216no—
422C22×D11—216no—
423C22×D11—216no—
424C22×D11—48no—
425C22×D11—48no—
426C22×D11—48no—
427C22×D11—48no—
428C22×D11C4×D4116yes—
429C22×D11C23×C414yes—
430C22×D11C23×C412yes—
431C22×D11C23×C412yes—
432C22×D11C22×D412yes—
433C22×D11C22×D412yes—
434C22×D11C2×#4112yes—
435C22×D11C2×#4112yes—
436C22×D11C2×#4114yes—
437C22×D11H(5,𝔽2)14yes—
438D4×C11—216no—
439D4×C11—44no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—44no—
455C2×C4×C11—48no—
456C2×C4×C11—48no—
457C2×C4×C11C23×C414yes—
458C2×C4×C11C23×C412yes—
459C2×C4×C11C23×C412yes—
460C2×C4×C11C22×D414yes—
461C2×C4×C11C2×#4114yes—
462C22⋊D11—216no—
463C22⋊D11—216no—
464C22⋊D11—48no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—44no—
480C2×Dic11—48no—
481C2×Dic11—48no—
482C2×Dic11C23×C412yes—
483C2×Dic11C23×C414yes—
484C2×Dic11C23×C412yes—
485C2×Dic11C22×D414yes—
486C2×Dic11C2×#4114yes—
487D44—216no—
488D44—44no—
489C4×D11—216no—
490C4×D11—28no—
491C4×D11—28no—
492C4×D11—216no—
493C4×D11—216no—
494C4×D11—44no—
495C4×D11—44no—
496C4×D11—48no—
497C4×D11—48no—
498C4×D11—48no—
499C4×D11—48no—
500C4×D11—48no—
501C4×D11—48no—
502C23×D4—112no—
503C23×D4—111no—
504C24×C4—111no—
505C24×C4—112no—
506C24×C4—112no—
507C2×#121—111no—
508C2×#121—112no—
509C2×#121—111no—
510C2×#121—1116no—
511C2×#121—111no—
512C2×#121—112no—
513C2×#121C2×D1111yescharacteristic
514C2×C4×D4—112no—
515C2×C4×D4—112no—
516C2×C4×D4—112no—
517C2×C4×D4—112no—
518C2×C4×D4—112no—
519C2×C4×D4—112no—
520C2×C4×D4—112no—
521C2×C4×D4—2216no—
522C2×C4×D4C2×D1112yescomplemented
523C22×C4⋊C4—111no—
524C22×C4⋊C4—112no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—112no—
527C22×C22⋊C4—112no—
528C22×C22⋊C4—112no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—112no—
531C22×C42—112no—
532C22×C42—112no—
533#388—112no—
534#388—112no—
535#388—112no—
536#388—112no—
537#388—112no—
538#388—112no—
539#388—112no—
540#388C2×D1112yescomplemented
541#387—112no—
542#387—112no—
543#387—112no—
544#387—112no—
545#387—112no—
546#387—112no—
547#387—112no—
548#387C2×D1112yescomplemented
549#386—112no—
550#386—112no—
551#386—112no—
552#386—112no—
553#386—112no—
554#386—112no—
555#386—112no—
556#386—112no—
557#386—112no—
558#386—112no—
559#386—112no—
560#386—112no—
561#386—112no—
562#386—112no—
563#386C2×D1112yescomplemented
564#386C2×D1112yescomplemented
565C4×C22⋊C4—112no—
566C4×C22⋊C4—111no—
567C4×C22⋊C4—112no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—111no—
570C4×C22⋊C4—111no—
571C4×C22⋊C4—112no—
572C4×C22⋊C4—112no—
573C4×C22⋊C4—112no—
574C4×C22⋊C4—112no—
575C4×C22⋊C4—112no—
576C4×C22⋊C4—112no—
577C4×C22⋊C4C2×D1112yescomplemented
578C4×C22⋊C4C2×D1111yescharacteristic, complemented
579C2×#95—112no—
580C2×#95—111no—
581C2×#95—111no—
582C2×#95—112no—
583C2×#95—111no—
584C2×#95—111no—
585C2×#95—112no—
586C2×#95—111no—
587C2×#95—112no—
588C2×#95—112no—
589C2×#95—112no—
590C2×#95C2×D1111yescharacteristic, complemented
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—24no—
597C22×C11—24no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11C2×C4×D414yes—
603C22×C11C24×C411yescharacteristic
604C22×C11C23×D411yescharacteristic
605C22×C11C22×#4111yescharacteristic
606C22×C11C22×#4112yes—
607C22×C11C2×H(5,𝔽2)12yes—
608C2×D11—22no—
609C2×D11—22no—
610C2×D11—24no—
611C2×D11—24no—
612C2×D11—232no—
613C2×D11—24no—
614C2×D11—24no—
615C2×D11—24no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—432no—
621C2×D11C2×C4×D414yes—
622C2×D11C2×C4×D414yes—
623C2×D11C4×#4114yes—
624C2×D11#51814yes—
625C2×D11#54618yes—
626C2×D11#55318yes—
627C4×C11—24no—
628C4×C11—22no—
629C4×C11—22no—
630C4×C11—24no—
631C4×C11—24no—
632C4×C11—42no—
633C4×C11—42no—
634Dic11—24no—
635Dic11—22no—
636Dic11—22no—
637Dic11—24no—
638Dic11—24no—
639Dic11—42no—
640Dic11—42no—
641C25—111no—
642C25—112no—
643C22×D4—112no—
644C22×D4—112no—
645C22×D4—112no—
646C22×D4—1116no—
647C22×D4—118no—
648C22×D4—112no—
649C22×D4—111no—
650C22×D4—228no—
651C22×D4—228no—
652C22×D4—444no—
653C22×D4C22×D1112yes—
654C22×D4C22×D1111yescharacteristic
655C23×C4—111no—
656C23×C4—112no—
657C23×C4—111no—
658C23×C4—112no—
659C23×C4—112no—
660C23×C4—111no—
661C23×C4—118no—
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—112no—
665C23×C4—112no—
666C23×C4—112no—
667C23×C4—112no—
668C23×C4—112no—
669C23×C4—112no—
670C23×C4—112no—
671C23×C4—112no—
672C23×C4—228no—
673C23×C4—228no—
674C23×C4—228no—
675C23×C4—228no—
676C23×C4—444no—
677C23×C4—444no—
678C23×C4—444no—
679C23×C4C22×D1112yes—
680C23×C4C22×D1112yes—
681C23×C4C22×D1111yescharacteristic
682#121—118no—
683#121—1116no—
684#121—118no—
685#121—118no—
686#121—1116no—
687#121C4×D1118yescomplemented
688C4×D4—28no—
689C4×D4—228no—
690C4×D4—228no—
691C4×D4—228no—
692C4×D4—228no—
693C4×D4—228no—
694C4×D4—228no—
695C4×D4—228no—
696C2×C4⋊C4—112no—
697C2×C4⋊C4—111no—
698C2×C4⋊C4—118no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—228no—
703C2×C4⋊C4C22×D1112yes—
704C2×C4⋊C4C22×D1111yescharacteristic
705C2×C22⋊C4—111no—
706C2×C22⋊C4—112no—
707C2×C22⋊C4—112no—
708C2×C22⋊C4—112no—
709C2×C22⋊C4—112no—
710C2×C22⋊C4—1116no—
711C2×C22⋊C4—118no—
712C2×C22⋊C4—112no—
713C2×C22⋊C4—112no—
714C2×C22⋊C4—111no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4—112no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4—112no—
723C2×C22⋊C4—228no—
724C2×C22⋊C4—228no—
725C2×C22⋊C4—224no—
726C2×C22⋊C4—444no—
727C2×C22⋊C4C22×D1112yes—
728C2×C22⋊C4C22×D1111yescharacteristic
729C2×C22⋊C4C22×D1112yes—
730C2×C22⋊C4C22×D1112yes—
731C2×C22⋊C4C22×D1112yes—
732C2×C22⋊C4C22×D1111yescharacteristic
733C2×C42—112no—
734C2×C42—112no—
735C2×C42—112no—
736C2×C42—112no—
737C2×C42—112no—
738C2×C42—112no—
739C2×C42—228no—
740C2×C42—444no—
741C2×C42C22×D1112yes—
742C2×C42C22×D1112yes—
743#95—111no—
744#95—112no—
745#95—112no—
746#95—112no—
747#95—112no—
748#95—112no—
749#95—111no—
750#95—112no—
751#95—112no—
752#95—112no—
753#95—112no—
754#95—112no—
755#95—112no—
756#95—112no—
757#95—112no—
758#95—112no—
759#95C22×D1111yescharacteristic
760#95C22×D1112yes—
761#95C22×D1111yescharacteristic
762#95C22×D1112yes—
763#95C22×D1112yes—
764#95C22×D1112yes—
765C2×C11—24no—
766C2×C11—44no—
767C2×C11C22×C4×D411yescharacteristic
768C2×C11C2×C4×#4111yescharacteristic
769C2×C11C2×#51811yescharacteristic
770C2×C11C2×#54612yes—
771C2×C11C2×#55312yes—
772D11—24no—
773D11—44no—
774D11#236418yesdirect product factor
775C24—111no—
776C24—114no—
777C24—114no—
778C24—114no—
779C24—111no—
780C24—118no—
781C24—112no—
782C24—224no—
783C24—224no—
784C24—224no—
785C24—224no—
786C24—224no—
787C24—224no—
788C24—224no—
789C24—224no—
790C24C23×D1112yes—
791C24C23×D1111yescharacteristic
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—42no—
795C2×D4—118no—
796C2×D4—118no—
797C2×D4—118no—
798C2×D4—118no—
799C2×D4—114no—
800C2×D4—224no—
801C2×D4—224no—
802C2×D4—2264no—
803C2×D4—224no—
804C2×D4—224no—
805C2×D4—224no—
806C2×D4—224no—
807C2×D4—442no—
808C2×D4—4416no—
809C2×D4—442no—
810C2×D4—442no—
811C2×D4C2×C4×D1118yescomplemented
812C2×D4C2×C4×D1114yescomplemented
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—111no—
821C22×C4—112no—
822C22×C4—111no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—114no—
826C22×C4—114no—
827C22×C4—118no—
828C22×C4—114no—
829C22×C4—118no—
830C22×C4—118no—
831C22×C4—114no—
832C22×C4—114no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—224no—
836C22×C4—224no—
837C22×C4—224no—
838C22×C4—224no—
839C22×C4—224no—
840C22×C4—224no—
841C22×C4—224no—
842C22×C4—224no—
843C22×C4—224no—
844C22×C4—224no—
845C22×C4—224no—
846C22×C4—224no—
847C22×C4—224no—
848C22×C4—224no—
849C22×C4—224no—
850C22×C4—224no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—224no—
854C22×C4—224no—
855C22×C4—224no—
856C22×C4—224no—
857C22×C4—224no—
858C22×C4—224no—
859C22×C4—224no—
860C22×C4—224no—
861C22×C4—442no—
862C22×C4—442no—
863C22×C4—442no—
864C22×C4—442no—
865C22×C4—442no—
866C22×C4—442no—
867C22×C4—4416no—
868C22×C4—4432no—
869C22×C4—4432no—
870C22×C4—442no—
871C22×C4—442no—
872C22×C4—442no—
873C22×C4C2×C4×D1114yescomplemented
874C22×C4C23×D1112yes—
875C22×C4C23×D1112yes—
876C22×C4C23×D1111yescharacteristic
877C22×C4C23×D1111yescharacteristic
878C22×C4C23×D1112yes—
879C22×C4C23×D1112yes—
880C22×C4C23×D1112yes—
881C4⋊C4—24no—
882C4⋊C4—118no—
883C4⋊C4—114no—
884C4⋊C4—224no—
885C4⋊C4—224no—
886C4⋊C4—224no—
887C4⋊C4C2×C4×D1114yescomplemented
888C22⋊C4—22no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—42no—
892C22⋊C4—118no—
893C22⋊C4—114no—
894C22⋊C4—118no—
895C22⋊C4—118no—
896C22⋊C4—118no—
897C22⋊C4—224no—
898C22⋊C4—224no—
899C22⋊C4—224no—
900C22⋊C4—224no—
901C22⋊C4—224no—
902C22⋊C4—222no—
903C22⋊C4—224no—
904C22⋊C4—224no—
905C22⋊C4—442no—
906C22⋊C4—442no—
907C22⋊C4—442no—
908C22⋊C4C2×C4×D1118yescomplemented
909C22⋊C4D4×D1114yescomplemented
910C42—24no—
911C42—42no—
912C42—224no—
913C42—224no—
914C42—224no—
915C42—442no—
916C42—442no—
917C42—442no—
918C11C2×#236411yescharacteristic, complemented, Sylow
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—112no—
928C23—112no—
929C23—114no—
930C23—112no—
931C23—114no—
932C23—1116no—
933C23—112no—
934C23—112no—
935C23—112no—
936C23—114no—
937C23—228no—
938C23—2216no—
939C23—2216no—
940C23—228no—
941C23—2216no—
942C23—2216no—
943C23—2216no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—448no—
953C23—448no—
954C23—448no—
955C23—448no—
956C23C22×C4×D1114yes—
957C23C22×C4×D1112yes—
958C23C2×D4×D1112yes—
959C23#41×D1112yes—
960C23C24×D1111yescharacteristic
961D4—216no—
962D4—44no—
963D4—2216no—
964D4—2216no—
965D4—2216no—
966D4—444no—
967D4—448no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—44no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—112no—
986C2×C4—114no—
987C2×C4—112no—
988C2×C4—114no—
989C2×C4—114no—
990C2×C4—2216no—
991C2×C4—228no—
992C2×C4—228no—
993C2×C4—2216no—
994C2×C4—2216no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—444no—
1010C2×C4—444no—
1011C2×C4—448no—
1012C2×C4—448no—
1013C2×C4—448no—
1014C2×C4—448no—
1015C2×C4—448no—
1016C2×C4—448no—
1017C2×C4—444no—
1018C2×C4—448no—
1019C2×C4—448no—
1020C2×C4C22×C4×D1112yes—
1021C2×C4C22×C4×D1114yes—
1022C2×C4C22×C4×D1112yes—
1023C2×C4C2×D4×D1114yes—
1024C2×C4#41×D1114yes—
1025C22—24no—
1026C22—22no—
1027C22—22no—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—118no—
1037C22—114no—
1038C22—114no—
1039C22—114no—
1040C22—118no—
1041C22—114no—
1042C22—2232no—
1043C22—224no—
1044C22—222no—
1045C22—222no—
1046C22—224no—
1047C22—224no—
1048C22—224no—
1049C22—224no—
1050C22—4432no—
1051C22—442no—
1052C22—442no—
1053C22—442no—
1054C22—442no—
1055C22C4×D4×D1114yes—
1056C22C23×C4×D1111yescharacteristic
1057C22C22×D4×D1111yescharacteristic
1058C22C2×#41×D1111yescharacteristic
1059C22C2×#41×D1112yes—
1060C22D11×H(5,𝔽2)12yes—
1061C4—24no—
1062C4—22no—
1063C4—22no—
1064C4—24no—
1065C4—24no—
1066C4—42no—
1067C4—42no—
1068C4—224no—
1069C4—222no—
1070C4—222no—
1071C4—224no—
1072C4—224no—
1073C4—442no—
1074C4—442no—
1075C2—24no—
1076C2—44no—
1077C2—118no—
1078C2—224no—
1079C2—444no—
1080C2C2×C4×D4×D1111yescharacteristic
1081C2C4×#41×D1111yescharacteristic
1082C2D11×#51811yescharacteristic
1083C2D11×#54612yes—
1084C2D11×#55312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2364C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2364D11
hypocenterC11C2×#2364
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D11C2semidirect
3. #13071668C2semidirect
4. #13071667C2semidirect
5. #13071666C2semidirect
6. #13071665C2semidirect
7. #13071664C2semidirect
8. #13071663C2semidirect
9. #13071662C2semidirect
10. #13071661C2semidirect
11. #13071660C2semidirect
12. D11×#388C2semidirect
13. D11×#387C2semidirect
14. D11×#386C2semidirect
15. D11×#386C2semidirect
16. C4×C22⋊C4×D11C2semidirect
17. C4×C22⋊C4×D11C2semidirect
18. C2×D11×#95C2semidirect
19. C11×#2364C2semidirect
26. C2×C4×D4×C11C22semidirect
29. C2×D4×Dic11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
32. C2×C4×C22⋊D11C22semidirect
33. D11×#121C4semidirect
36. C2×#66946C22semidirect
40. C2×(C22⋊D11)⋊C4C22semidirect
41. C2×(C22⋊D11)⋊C4C22semidirect
48. C2×C4×D44C22semidirect
51. C11×#388C22semidirect
52. C11×#387C22semidirect
53. C11×#386C22semidirect
54. C11×#386C22semidirect
55. C4×C11×C22⋊C4C22semidirect
56. C4×C11×C22⋊C4C22semidirect
57. C2×C11×#95C22semidirect
58. #10622833C22semidirect
59. #10622833C22semidirect
60. #10622826C22semidirect
61. #10622826C22semidirect
62. C4×C22⋊Dic11C22semidirect
63. C4×C22⋊Dic11C22semidirect
64. C2×C11⋊#95C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622603C22semidirect
67. #10622594C22semidirect
68. #10622591C22semidirect
69. #10622571C22semidirect
70. #10622571C22semidirect
71. #10622569C22semidirect
72. #10622569C22semidirect
73. #10622569C22semidirect
74. #10622569C22semidirect
75. #10622564C22semidirect
76. #10622558C22semidirect
77. #10622557C22semidirect
78. C22⋊C4×Dic11C22semidirect
79. C22⋊C4×Dic11C22semidirect
80. C22⋊C4×Dic11C22semidirect
81. C22⋊C4×Dic11C22semidirect
82. #10622553C22semidirect
83. C4×(C2×D11)⋊C4C22semidirect
84. C4×(C2×D11)⋊C4C22semidirect
85. C4×(C2×D11)⋊C4C22semidirect
86. #10622546C22semidirect
87. #10622283C22semidirect
88. #10622282C22semidirect
89. #10622279C22semidirect
90. #10622279C22semidirect
91. #10622279C22semidirect
92. #10622278C22semidirect
93. #10622278C22semidirect
94. #10622278C22semidirect
95. #10622278C22semidirect
102. D11×#95C22semidirect
103. D11×#95C22semidirect
104. D11×#95C22semidirect
105. #10622268C22semidirect
106. #10622267C22semidirect
107. #10622266C22semidirect
108. #10622265C22semidirect
125. C2×D4×D11C2×C4semidirect
126. C2×D4×D11C2×C4semidirect
136. C22×C4×D11C2×C4semidirect
150. C11×#121C2×C4semidirect
168. #66992C2×C4semidirect
169. #66991C2×C4semidirect
171. #66983C2×C4semidirect
195. #66948C2×C4semidirect
198. C4⋊C4×D11C2×C4semidirect
199. #66937C2×C4semidirect
206. C22⋊C4×D11C2×C4semidirect
207. C22⋊C4×D11D4semidirect
254. C2×D4×C11C22×C4semidirect
255. C2×D4×C11C22×C4semidirect
263. C22×C4×C11C22×C4semidirect
277. C2×C22⋊D11C22×C4semidirect
278. C2×C22⋊D11C22×C4semidirect
279. C2×C22⋊D11C22×C4semidirect
287. C22×Dic11C22×C4semidirect
300. C2×D44C22×C4semidirect
301. C2×D44C22×C4semidirect
336. C2×C4×D11C22×C4semidirect
337. C2×C4×D11C22×C4semidirect
341. C11×C4⋊C4C22×C4semidirect
346. C11×C22⋊C4C22×C4semidirect
347. C11×C22⋊C4C2×D4semidirect
354. C22⋊Dic11C22×C4semidirect
355. C22⋊Dic11C2×D4semidirect
363. (C2×D11)⋊C4C22×C4semidirect
364. (C2×D11)⋊C4C22×C4semidirect
365. (C2×D11)⋊C4C2×D4semidirect
367. C4⋊Dic11C22×C4semidirect
370. Dic11⋊C4C22×C4semidirect
388. #2364D11direct (N × H)
522. C2×C4×D4C2×D11semidirect
540. #388C2×D11semidirect
548. #387C2×D11semidirect
563. #386C2×D11semidirect
564. #386C2×D11semidirect
577. C4×C22⋊C4C2×D11semidirect
578. C4×C22⋊C4C2×D11semidirect
590. C2×#95C2×D11semidirect
687. #121C4×D11semidirect
774. D11#2364direct (N × H)
811. C2×D4C2×C4×D11semidirect
812. C2×D4C2×C4×D11semidirect
873. C22×C4C2×C4×D11semidirect
887. C4⋊C4C2×C4×D11semidirect
908. C22⋊C4C2×C4×D11semidirect
909. C22⋊C4D4×D11semidirect
918. C11C2×#2364semidirect

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
#130716682
#130716672
#130716662
#130716652
#130716642
#130716632
#130716622
#130716612
#130716602
D11×#3882
D11×#3872
D11×#3862
C4×C22⋊C4×D112
C2×D11×#952
C11×#23642
C2×#236411