Finite Group Databasebeta

← D11×#2367 #14913374

Subgroups — D11×#2367 #14913374

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#124C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3C2×C4×D4×D11C211yesmaximal, characteristic
4#13071692C211yesmaximal, characteristic, complemented
5#13071691C211yesmaximal, characteristic, complemented
6#13071690C212yesmaximal, complemented
7#13071689C211yesmaximal, characteristic, complemented
8#13071688C212yesmaximal, complemented
9#13071687C211yesmaximal, characteristic, complemented
10#13071686C211yesmaximal, characteristic, complemented
11#13071685C211yesmaximal, characteristic, complemented
12#13071684C212yesmaximal, complemented
13#13071683C211yesmaximal, characteristic, complemented
14#13071682C212yesmaximal, complemented
15D11×#391C211yesmaximal, characteristic, complemented
16D11×#390C211yesmaximal, characteristic
17D11×#388C212yesmaximal, complemented
18D11×#388C212yesmaximal, complemented
19D11×#385C212yesmaximal, complemented
20C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
21C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C212yesmaximal, complemented
23C11×#2367C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C11×#124C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×#67000C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C2×#66989C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×C4×C22⋊D11C2212yes—
35D11×#124C4116yescomplemented
36C4×Q8×D11—28no—
37C4×D4×D11—28no—
38C2×#66946C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2212yes—
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66940C2212yescomplemented
45C2×#66940C2211yescharacteristic, complemented
46C2×#66938C2212yes—
47C2×#66938C2212yes—
48C2×(C22⋊D11)⋊C4C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×#66928C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic
56C2×C42×D11C2212yes—
57C2×C42×D11C2211yescharacteristic
58C2×C42×D11C2211yescharacteristic
59C2×C42×D11C2212yes—
60C2×C42×D11C2211yescharacteristic
61C2×C4×Dic22C2211yescharacteristic, complemented
62C2×C4×Dic22C2212yescomplemented
63C11×#391C2211yescharacteristic, complemented
64C11×#390C2211yescharacteristic
65C11×#388C2212yescomplemented
66C11×#388C2212yescomplemented
67C11×#385C2212yescomplemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69C4×C11×C4⋊C4C2211yescharacteristic, complemented
70C4×C11×C22⋊C4C2212yescomplemented
71#10622843C2211yescharacteristic, complemented
72#10622834C2211yescharacteristic
73#10622823C2212yescomplemented
74C4×C22⋊Dic11C2212yescomplemented
75#10622603C2212yescomplemented
76#10622603C2212yescomplemented
77#10622602C2212yescomplemented
78#10622602C2212yescomplemented
79#10622601C2211yescharacteristic
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622587C2211yescharacteristic, complemented
85#10622570C2212yes—
86#10622570C2212yes—
87#10622564C2212yescomplemented
88#10622564C2212yescomplemented
89#10622563C2212yescomplemented
90#10622559C2212yescomplemented
91#10622558C2212yescomplemented
92#10622558C2212yescomplemented
93#10622557C2212yescomplemented
94#10622557C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96C22⋊C4×Dic11C2212yescomplemented
97#10622553C2212yescomplemented
98#10622553C2212yescomplemented
99#10622552C2211yescharacteristic
100C4×(C2×D11)⋊C4C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×C4⋊Dic11C2211yescharacteristic, complemented
103C4×C4⋊Dic11C2211yescharacteristic, complemented
104C4×Dic11⋊C4C2212yescomplemented
105C4×Dic11⋊C4C2211yescharacteristic, complemented
106C4×Dic11⋊C4C2211yescharacteristic, complemented
107#10622542C2211yescharacteristic, complemented
108#10622283C2212yescomplemented
109#10622283C2212yescomplemented
110#10622282C2212yescomplemented
111#10622282C2212yescomplemented
112#10622281C2212yescomplemented
113#10622281C2212yescomplemented
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116D11×#95C2211yescharacteristic
117D11×#95C2212yes—
118D11×#95C2212yes—
119D11×#95C2211yescharacteristic
120D11×#95C2212yes—
121#10622262C2211yescharacteristic, complemented
122#10622262C2212yescomplemented
123#10622262C2211yescharacteristic, complemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2312yes—
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C23×Dic11C2312yes—
132C2×Q8×D11—24no—
133C2×Q8×D11—24no—
134C2×Q8×D11C2×C418yescomplemented
135C2×D4×D11—24no—
136C2×D4×D11—24no—
137C2×D4×D11C2×C418yes—
138C22×D44C2311yescharacteristic
139C22×C4×D11—28no—
140C22×C4×D11—28no—
141C22×C4×D11—44no—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×Dic22C2311yescharacteristic
155C22×Dic22C2312yes—
156C11×#124C2×C418yescomplemented
157C4×Q8×C11—24no—
158C4×D4×C11—24no—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#67000C2×C418yescomplemented
180Q8×Dic11—24no—
181#66989C2×C418yescomplemented
182D4×Dic11—24no—
183C4×C22⋊D11—28no—
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×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222#66946—24no—
223C4⋊C4×D11—28no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—24no—
227C4⋊C4×D11D418yes—
228#66940—24no—
229#66940—28no—
230#66938C2×C4116yescomplemented
231#66938C2×C4116yescomplemented
232(C22⋊D11)⋊C4—28no—
233C22⋊C4×D11—28no—
234C22⋊C4×D11—28no—
235C22⋊C4×D11—44no—
236C22⋊C4×D11C2×C4116yescomplemented
237C22⋊C4×D11C2×C4116yescomplemented
238#66928C2×C418yescomplemented
239C4×D44—24no—
240C42×D11—24no—
241C42×D11—24no—
242C42×D11—28no—
243C42×D11—44no—
244C42×D11C2×C418yescomplemented
245C4×Dic22—24no—
246C4×Dic22—28no—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2311yescharacteristic
250C11×#95C2312yes—
251C11×#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2312yes—
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2312yes—
263C11⋊#95C2311yescharacteristic
264C11⋊#95C2311yescharacteristic
265C11⋊#95C2312yes—
266C11⋊#95C2311yescharacteristic
267C2×#2367—111nomaximal, Sylow
268C24×C11C2412yes—
269C23×D11—24no—
270C23×D11—24no—
271C23×D11—24no—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11C22×C418yes—
276C23×D11C2412yes—
277C23×D11C2411yescharacteristic
278C2×Q8×C11—22no—
279C2×Q8×C11—22no—
280C2×Q8×C11C22×C414yescomplemented
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11C22×C414yes—
284C22×C4×C11—24no—
285C22×C4×C11—24no—
286C22×C4×C11—42no—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11C22×C418yes—
300C22×Dic11—24no—
301C22×Dic11—24no—
302C22×Dic11—42no—
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2412yes—
305C22×Dic11C2411yescharacteristic
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313Q8×D11—232no—
314D4×D11—232no—
315C2×D44—22no—
316C2×D44—22no—
317C2×D44C22×C414yes—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—22no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—432no—
346C2×C4×D11C22×C414yes—
347C2×C4×D11C22×C414yes—
348C2×C4×D11C22×C418yes—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C2×D418yes—
351C2×C4×D11C2×D414yes—
352C2×C4×D11#4114yes—
353C2×C4×D11#4114yes—
354C2×C4×D11#4114yes—
355C2×Dic22—24no—
356C2×Dic22—24no—
357C2×Dic22—22no—
358C2×Dic22—22no—
359C2×Dic22C22×C414yescomplemented
360C2×Dic22C22×C418yescomplemented
361C11×C4⋊C4—24no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4C2×D414yes—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4C22×C418yescomplemented
370C11×C22⋊C4C22×C418yescomplemented
371C42×C11—24no—
372C42×C11—22no—
373C42×C11—22no—
374C42×C11—42no—
375C42×C11C22×C414yescomplemented
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—42no—
379C22⋊Dic11C22×C418yescomplemented
380C22⋊Dic11C22×C418yescomplemented
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4C22×C418yescomplemented
388(C2×D11)⋊C4C22×C418yescomplemented
389(C2×D11)⋊C4C22×C418yescomplemented
390(C2×D11)⋊C4C22×C418yescomplemented
391C4⋊Dic11—24no—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11C2×D414yes—
396Dic11⋊C4—24no—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4C2×D418yes—
404C4×Dic11—24no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—42no—
414C4×Dic11—42no—
415C4×Dic11—42no—
416C4×Dic11C22×C414yescomplemented
417C4×Dic11C22×C414yescomplemented
418C4×Dic11C22×C414yescomplemented
419C22×#124—111no—
420C22×C4×Q8—111no—
421C22×C4×D4—111no—
422#2367—111no—
423#2367—111no—
424#2367—112no—
425#2367—112no—
426#2367—112no—
427#2367—111no—
428#2367—111no—
429#2367—112no—
430#2367—111no—
431#2367—111no—
432#2367—111no—
433#2367D1111yescharacteristic, direct product factor
434C2×#391—111no—
435C2×#390—111no—
436C2×#388—112no—
437C2×#388—112no—
438C2×#385—112no—
439C2×C4×C4⋊C4—111no—
440C2×C4×C4⋊C4—111no—
441C2×C4×C22⋊C4—112no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11C23×C414yes—
449C23×C11C2511yescharacteristic
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—216no—
457C22×D11—216no—
458C22×D11—216no—
459C22×D11—48no—
460C22×D11—48no—
461C22×D11—48no—
462C22×D11—48no—
463C22×D11C23×C414yes—
464C22×D11C23×C412yes—
465C22×D11C22×D412yes—
466C22×D11C2×#4112yes—
467C22×D11C2×#4112yes—
468C22×D11C2×#4112yes—
469C22×D11H(5,𝔽2)12yes—
470C22×D112−1+412yes—
471Q8×C11—28no—
472D4×C11—28no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—48no—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C414yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C22×D414yes—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C2×#4112yes—
502C2×C4×C11C2×#4112yes—
503C2×C4×C11C2×#4112yes—
504C22⋊D11—216no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—48no—
527C2×Dic11C23×C412yes—
528C2×Dic11C23×C412yes—
529C2×Dic11C23×C414yes—
530C2×Dic11C23×C412yes—
531C2×Dic11C22×D414yes—
532C2×Dic11C22×D412yes—
533C2×Dic11C2×#4112yes—
534C2×Dic11C2×#4112yes—
535C2×Dic11C2×#4112yes—
536D44—28no—
537C4×D11—216no—
538C4×D11—28no—
539C4×D11—28no—
540C4×D11—28no—
541C4×D11—216no—
542C4×D11—28no—
543C4×D11—48no—
544C4×D11—48no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—48no—
548C4×D11C4×D4116yes—
549Dic22—28no—
550Dic22—216no—
551C23×Q8—111no—
552C23×D4—111no—
553C24×C4—112no—
554C2×#124—111no—
555C2×#124—111no—
556C2×#124—1116no—
557C2×#124—112no—
558C2×#124—112no—
559C2×#124—111no—
560C2×#124C2×D1111yescharacteristic
561C2×C4×Q8—111no—
562C2×C4×Q8—112no—
563C2×C4×Q8—111no—
564C2×C4×Q8—111no—
565C2×C4×Q8—112no—
566C2×C4×Q8—228no—
567C2×C4×Q8C2×D1111yescharacteristic, complemented
568C2×C4×D4—111no—
569C2×C4×D4—112no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—228no—
574C2×C4×D4C2×D1111yescharacteristic
575C22×C4⋊C4—111no—
576C22×C4⋊C4—112no—
577C22×C4⋊C4—111no—
578C22×C4⋊C4—111no—
579C22×C4⋊C4—111no—
580C22×C22⋊C4—112no—
581C22×C22⋊C4—112no—
582C22×C22⋊C4—112no—
583C22×C22⋊C4—112no—
584C22×C22⋊C4—112no—
585C22×C42—111no—
586C22×C42—111no—
587C22×C42—112no—
588C22×C42—111no—
589C22×C42—112no—
590#391—111no—
591#391—111no—
592#391—111no—
593#391—112no—
594#391—112no—
595#391C2×D1111yescharacteristic, complemented
596#390—111no—
597#390—111no—
598#390—112no—
599#390—112no—
600#390—111no—
601#390C2×D1111yescharacteristic
602#388—112no—
603#388—112no—
604#388—112no—
605#388—112no—
606#388—112no—
607#388—112no—
608#388—112no—
609#388—112no—
610#388—112no—
611#388—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388C2×D1112yescomplemented
617#388C2×D1112yescomplemented
618#385—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#385—112no—
625#385C2×D1112yescomplemented
626C4×C4⋊C4—111no—
627C4×C4⋊C4—111no—
628C4×C4⋊C4—111no—
629C4×C4⋊C4—111no—
630C4×C4⋊C4—111no—
631C4×C4⋊C4—111no—
632C4×C4⋊C4—112no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—111no—
636C4×C4⋊C4—112no—
637C4×C4⋊C4—111no—
638C4×C4⋊C4C2×D1111yescharacteristic, complemented
639C4×C4⋊C4C2×D1111yescharacteristic, complemented
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4C2×D1112yescomplemented
648C2×#95—111no—
649C2×#95—112no—
650C2×#95—112no—
651C2×#95—111no—
652C2×#95—112no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11C24×C411yescharacteristic
661C22×C11C23×D411yescharacteristic
662C22×C11C22×#4111yescharacteristic
663C22×C11C22×#4111yescharacteristic
664C22×C11C22×#4111yescharacteristic
665C22×C11C2×H(5,𝔽2)11yescharacteristic
666C22×C11C2×2−1+411yescharacteristic
667C2×D11—24no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—432no—
675C2×D11C2×C4×D414yes—
676C2×D11C4×#4114yes—
677C2×D11#52014yes—
678C2×D11#54614yes—
679C2×D11#54814yes—
680C2×D11#55614yes—
681C2×D11#55914yes—
682C4×C11—24no—
683C4×C11—22no—
684C4×C11—22no—
685C4×C11—22no—
686C4×C11—24no—
687C4×C11—22no—
688C4×C11—41no—
689C4×C11—41no—
690C4×C11—42no—
691C4×C11C2×C4×D414yes—
692Dic11—24no—
693Dic11—22no—
694Dic11—22no—
695Dic11—22no—
696Dic11—24no—
697Dic11—22no—
698Dic11—41no—
699Dic11—41no—
700Dic11—42no—
701Dic11C2×C4×D414yes—
702C25—112no—
703C22×Q8—118no—
704C22×Q8—112no—
705C22×Q8—111no—
706C22×Q8—224no—
707C22×Q8—224no—
708C22×Q8C22×D1111yescharacteristic
709C22×D4—112no—
710C22×D4—118no—
711C22×D4—111no—
712C22×D4—224no—
713C22×D4—224no—
714C22×D4C22×D1111yescharacteristic
715C23×C4—111no—
716C23×C4—111no—
717C23×C4—112no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—112no—
721C23×C4—111no—
722C23×C4—112no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—112no—
726C23×C4—112no—
727C23×C4—112no—
728C23×C4—228no—
729C23×C4—228no—
730C23×C4—444no—
731C23×C4C22×D1112yes—
732#124—118no—
733#124—118no—
734#124—1116no—
735#124—1116no—
736#124—118no—
737#124C4×D1118yescomplemented
738C4×Q8—24no—
739C4×Q8—228no—
740C4×Q8—224no—
741C4×Q8—228no—
742C4×Q8—224no—
743C4×Q8—224no—
744C4×D4—24no—
745C4×D4—224no—
746C4×D4—228no—
747C4×D4—228no—
748C4×D4—224no—
749C4×D4—224no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—118no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—228no—
765C2×C4⋊C4—224no—
766C2×C4⋊C4—224no—
767C2×C4⋊C4—224no—
768C2×C4⋊C4C22×D1112yes—
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1111yescharacteristic
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1111yescharacteristic
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—1116no—
780C2×C22⋊C4—1116no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—228no—
791C2×C22⋊C4—228no—
792C2×C22⋊C4—444no—
793C2×C22⋊C4C22×D1112yes—
794C2×C22⋊C4C22×D1112yes—
795C2×C22⋊C4C22×D1112yes—
796C2×C22⋊C4C22×D1112yes—
797C2×C22⋊C4C22×D1112yes—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—118no—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—111no—
809C2×C42—111no—
810C2×C42—111no—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—112no—
814C2×C42—224no—
815C2×C42—224no—
816C2×C42—228no—
817C2×C42—444no—
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1112yes—
820C2×C42C22×D1111yescharacteristic
821C2×C42C22×D1112yes—
822C2×C42C22×D1111yescharacteristic
823#95—111no—
824#95—111no—
825#95—111no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—111no—
833#95—111no—
834#95—111no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95C22×D1111yescharacteristic
839#95C22×D1112yes—
840#95C22×D1112yes—
841#95C22×D1111yescharacteristic
842#95C22×D1112yes—
843C2×C11—44no—
844C2×C11C22×C4×D411yescharacteristic
845C2×C11C2×C4×#4111yescharacteristic
846C2×C11C2×#52011yescharacteristic
847C2×C11C2×#54611yescharacteristic
848C2×C11C2×#54811yescharacteristic
849C2×C11C2×#55611yescharacteristic
850C2×C11C2×#55911yescharacteristic
851D11—44no—
852D11#236718yesdirect product factor
853C24—111no—
854C24—118no—
855C24—112no—
856C24—224no—
857C24—224no—
858C24—224no—
859C24—224no—
860C24—224no—
861C24—224no—
862C24C23×D1112yes—
863C2×Q8—22no—
864C2×Q8—22no—
865C2×Q8—118no—
866C2×Q8—114no—
867C2×Q8—224no—
868C2×Q8—224no—
869C2×Q8—2232no—
870C2×Q8—222no—
871C2×Q8—222no—
872C2×Q8C2×C4×D1114yescomplemented
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—118no—
876C2×D4—114no—
877C2×D4—2232no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4C2×C4×D1114yes—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—111no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—114no—
890C22×C4—111no—
891C22×C4—111no—
892C22×C4—111no—
893C22×C4—112no—
894C22×C4—111no—
895C22×C4—112no—
896C22×C4—114no—
897C22×C4—114no—
898C22×C4—118no—
899C22×C4—118no—
900C22×C4—114no—
901C22×C4—114no—
902C22×C4—111no—
903C22×C4—112no—
904C22×C4—111no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—222no—
908C22×C4—224no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—224no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—224no—
915C22×C4—222no—
916C22×C4—224no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—224no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—224no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—4432no—
935C22×C4—442no—
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1112yes—
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—118no—
951C4⋊C4—114no—
952C4⋊C4—224no—
953C4⋊C4—224no—
954C4⋊C4—224no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—222no—
958C4⋊C4—222no—
959C4⋊C4—224no—
960C4⋊C4—222no—
961C4⋊C4—222no—
962C4⋊C4—222no—
963C4⋊C4D4×D1114yes—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—42no—
967C22⋊C4—118no—
968C22⋊C4—118no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—118no—
972C22⋊C4—118no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4C2×C4×D1118yescomplemented
983C22⋊C4C2×C4×D1118yescomplemented
984C42—22no—
985C42—24no—
986C42—22no—
987C42—42no—
988C42—114no—
989C42—114no—
990C42—114no—
991C42—222no—
992C42—222no—
993C42—222no—
994C42—224no—
995C42—224no—
996C42—222no—
997C42—222no—
998C42—224no—
999C42—222no—
1000C42—442no—
1001C42—442no—
1002C42—442no—
1003C42C2×C4×D1114yescomplemented
1004C11C2×#236711yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—112no—
1012C23—112no—
1013C23—112no—
1014C23—112no—
1015C23—112no—
1016C23—112no—
1017C23—112no—
1018C23—114no—
1019C23—2216no—
1020C23—2216no—
1021C23—2216no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—448no—
1029C23—448no—
1030C23—448no—
1031C23—448no—
1032C23C22×C4×D1114yes—
1033C23C24×D1111yescharacteristic
1034Q8—28no—
1035Q8—2216no—
1036Q8—228no—
1037D4—28no—
1038D4—2216no—
1039D4—228no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—48no—
1062C2×C4—112no—
1063C2×C4—112no—
1064C2×C4—112no—
1065C2×C4—1116no—
1066C2×C4—112no—
1067C2×C4—112no—
1068C2×C4—114no—
1069C2×C4—114no—
1070C2×C4—112no—
1071C2×C4—112no—
1072C2×C4—228no—
1073C2×C4—2216no—
1074C2×C4—2216no—
1075C2×C4—228no—
1076C2×C4—228no—
1077C2×C4—228no—
1078C2×C4—221no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—221no—
1086C2×C4—222no—
1087C2×C4—221no—
1088C2×C4—221no—
1089C2×C4—221no—
1090C2×C4—221no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—448no—
1100C2×C4—448no—
1101C2×C4—448no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—448no—
1105C2×C4C22×C4×D1112yes—
1106C2×C4C22×C4×D1112yes—
1107C2×C4C22×C4×D1114yes—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C2×D4×D1114yes—
1110C2×C4C2×D4×D1112yes—
1111C2×C4#41×D1112yes—
1112C2×C4#41×D1112yes—
1113C2×C4#41×D1112yes—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—114no—
1122C22—114no—
1123C22—114no—
1124C22—114no—
1125C22—114no—
1126C22—114no—
1127C22—114no—
1128C22—224no—
1129C22—224no—
1130C22—224no—
1131C22—4432no—
1132C22—442no—
1133C22—442no—
1134C22—442no—
1135C22—442no—
1136C22C23×C4×D1111yescharacteristic
1137C22C22×D4×D1111yescharacteristic
1138C22C2×#41×D1111yescharacteristic
1139C22C2×#41×D1111yescharacteristic
1140C22C2×#41×D1111yescharacteristic
1141C22D11×H(5,𝔽2)11yescharacteristic
1142C22D11×2−1+411yescharacteristic
1143C4—24no—
1144C4—22no—
1145C4—22no—
1146C4—24no—
1147C4—22no—
1148C4—22no—
1149C4—42no—
1150C4—41no—
1151C4—41no—
1152C4—114no—
1153C4—224no—
1154C4—222no—
1155C4—222no—
1156C4—224no—
1157C4—222no—
1158C4—222no—
1159C4—442no—
1160C4—441no—
1161C4—441no—
1162C4C4×D4×D1114yes—
1163C2—44no—
1164C2—118no—
1165C2—444no—
1166C2C2×C4×D4×D1111yescharacteristic
1167C2C4×#41×D1111yescharacteristic
1168C2D11×#52011yescharacteristic
1169C2D11×#54611yescharacteristic
1170C2D11×#54811yescharacteristic
1171C2D11×#55611yescharacteristic
1172C2D11×#55911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2367D11
hypocenterC11C2×#2367
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
4. #13071692C2semidirect
5. #13071691C2semidirect
6. #13071690C2semidirect
7. #13071689C2semidirect
8. #13071688C2semidirect
9. #13071687C2semidirect
10. #13071686C2semidirect
11. #13071685C2semidirect
12. #13071684C2semidirect
13. #13071683C2semidirect
14. #13071682C2semidirect
15. D11×#391C2semidirect
17. D11×#388C2semidirect
18. D11×#388C2semidirect
19. D11×#385C2semidirect
20. C4×C4⋊C4×D11C2semidirect
21. C4×C4⋊C4×D11C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2367C2semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×Q8×Dic11C22semidirect
35. D11×#124C4semidirect
44. C2×#66940C22semidirect
45. C2×#66940C22semidirect
61. C2×C4×Dic22C22semidirect
62. C2×C4×Dic22C22semidirect
63. C11×#391C22semidirect
65. C11×#388C22semidirect
66. C11×#388C22semidirect
67. C11×#385C22semidirect
68. C4×C11×C4⋊C4C22semidirect
69. C4×C11×C4⋊C4C22semidirect
70. C4×C11×C22⋊C4C22semidirect
71. #10622843C22semidirect
73. #10622823C22semidirect
74. C4×C22⋊Dic11C22semidirect
75. #10622603C22semidirect
76. #10622603C22semidirect
77. #10622602C22semidirect
78. #10622602C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622587C22semidirect
87. #10622564C22semidirect
88. #10622564C22semidirect
89. #10622563C22semidirect
90. #10622559C22semidirect
91. #10622558C22semidirect
92. #10622558C22semidirect
93. #10622557C22semidirect
94. #10622557C22semidirect
95. C22⋊C4×Dic11C22semidirect
96. C22⋊C4×Dic11C22semidirect
97. #10622553C22semidirect
98. #10622553C22semidirect
100. C4×(C2×D11)⋊C4C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. C4×C4⋊Dic11C22semidirect
103. C4×C4⋊Dic11C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. C4×Dic11⋊C4C22semidirect
106. C4×Dic11⋊C4C22semidirect
107. #10622542C22semidirect
108. #10622283C22semidirect
109. #10622283C22semidirect
110. #10622282C22semidirect
111. #10622282C22semidirect
112. #10622281C22semidirect
113. #10622281C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
134. C2×Q8×D11C2×C4semidirect
156. C11×#124C2×C4semidirect
179. #67000C2×C4semidirect
181. #66989C2×C4semidirect
230. #66938C2×C4semidirect
231. #66938C2×C4semidirect
236. C22⋊C4×D11C2×C4semidirect
237. C22⋊C4×D11C2×C4semidirect
238. #66928C2×C4semidirect
244. C42×D11C2×C4semidirect
280. C2×Q8×C11C22×C4semidirect
359. C2×Dic22C22×C4semidirect
360. C2×Dic22C22×C4semidirect
369. C11×C22⋊C4C22×C4semidirect
370. C11×C22⋊C4C22×C4semidirect
375. C42×C11C22×C4semidirect
379. C22⋊Dic11C22×C4semidirect
380. C22⋊Dic11C22×C4semidirect
387. (C2×D11)⋊C4C22×C4semidirect
388. (C2×D11)⋊C4C22×C4semidirect
389. (C2×D11)⋊C4C22×C4semidirect
390. (C2×D11)⋊C4C22×C4semidirect
416. C4×Dic11C22×C4semidirect
417. C4×Dic11C22×C4semidirect
418. C4×Dic11C22×C4semidirect
433. #2367D11direct (N × H)
567. C2×C4×Q8C2×D11semidirect
595. #391C2×D11semidirect
616. #388C2×D11semidirect
617. #388C2×D11semidirect
625. #385C2×D11semidirect
638. C4×C4⋊C4C2×D11semidirect
639. C4×C4⋊C4C2×D11semidirect
647. C4×C22⋊C4C2×D11semidirect
737. #124C4×D11semidirect
852. D11#2367direct (N × H)
872. C2×Q8C2×C4×D11semidirect
982. C22⋊C4C2×C4×D11semidirect
983. C22⋊C4C2×C4×D11semidirect
1003. C42C2×C4×D11semidirect
1004. C11C2×#2367semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1242
C2×C4×Q8×D112
C2×C4×D4×D112
#130716922
#130716912
#130716902
#130716892
#130716882
#130716872
#130716862
#130716852
#130716842
#130716832
#130716822
D11×#3912
D11×#3902
D11×#3882
D11×#3852
C4×C4⋊C4×D112
C4×C22⋊C4×D112
C11×#23672
C2×#236711