Finite Group Databasebeta

← D11×#2454 #14921932

Subgroups — D11×#2454 #14921932

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic
3#13072491C211yesmaximal, characteristic, complemented
4#13072490C211yesmaximal, characteristic, complemented
5#13072489C211yesmaximal, characteristic, complemented
6#13072488C211yesmaximal, characteristic, complemented
7#13072487C212yesmaximal, complemented
8#13072486C211yesmaximal, characteristic, complemented
9#13072485C212yesmaximal, complemented
10#13072484C211yesmaximal, characteristic, complemented
11#13072483C212yesmaximal, complemented
12#13072482C211yesmaximal, characteristic, complemented
13#13072481C212yesmaximal, complemented
14D11×#399C212yesmaximal, complemented
15D11×#396C212yesmaximal, complemented
16D11×#390C211yesmaximal, characteristic
17D11×#390C211yesmaximal, characteristic
18D11×#389C211yesmaximal, characteristic, complemented
19D11×#389C211yesmaximal, characteristic, complemented
20D11×#385C212yesmaximal, complemented
21D11×#380C212yesmaximal, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2454C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C2×C11×#125C2211yescharacteristic, complemented
27C2×C4×D4×C11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11C2212yes—
30D11×#125—28no—
31C4×D4×D11—28no—
32C2×#66946C2211yescharacteristic
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2212yes—
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2212yes—
40C2×C4⋊C4×D11C2212yes—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66943C2211yescharacteristic, complemented
43C2×#66943C2211yescharacteristic, complemented
44C2×#66942C2212yescomplemented
45C2×#66942C2212yescomplemented
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×C4×D44C2211yescharacteristic
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C2×#66923C2211yescharacteristic, complemented
57C11×#399C2212yescomplemented
58C11×#396C2212yescomplemented
59C11×#390C2211yescharacteristic
60C11×#390C2211yescharacteristic
61C11×#389C2211yescharacteristic, complemented
62C11×#389C2211yescharacteristic, complemented
63C11×#385C2212yescomplemented
64C11×#380C2212yescomplemented
65C4×C11×C4⋊C4C2211yescharacteristic, complemented
66#10622834C2211yescharacteristic
67#10622834C2211yescharacteristic
68#10622825C2212yescomplemented
69#10622823C2212yescomplemented
70#10622607C2212yescomplemented
71#10622607C2212yescomplemented
72#10622607C2212yescomplemented
73#10622605C2212yescomplemented
74#10622605C2212yescomplemented
75#10622605C2212yescomplemented
76#10622602C2212yescomplemented
77#10622602C2212yescomplemented
78#10622601C2211yescharacteristic
79#10622601C2211yescharacteristic
80#10622600C2212yescomplemented
81#10622600C2212yescomplemented
82#10622598C2211yescharacteristic, complemented
83#10622598C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85C4⋊C4×Dic11C2211yescharacteristic, complemented
86#10622586C2211yescharacteristic, complemented
87#10622586C2211yescharacteristic, complemented
88#10622585C2212yescomplemented
89#10622585C2212yescomplemented
90#10622570C2212yes—
91#10622570C2212yes—
92#10622570C2212yes—
93#10622570C2212yes—
94#10622563C2212yescomplemented
95#10622562C2212yescomplemented
96#10622562C2212yescomplemented
97#10622562C2212yescomplemented
98#10622561C2212yescomplemented
99#10622561C2212yescomplemented
100#10622561C2212yescomplemented
101#10622559C2212yescomplemented
102#10622555C2212yescomplemented
103#10622555C2212yescomplemented
104#10622552C2211yescharacteristic
105#10622552C2211yescharacteristic
106C4×C4⋊Dic11C2211yescharacteristic, complemented
107C4×Dic11⋊C4C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2211yescharacteristic, complemented
109#10622541C2211yescharacteristic, complemented
110#10622541C2211yescharacteristic, complemented
111#10622290C2212yescomplemented
112#10622289C2212yescomplemented
113#10622281C2212yescomplemented
114#10622281C2212yescomplemented
115#10622280C2212yescomplemented
116#10622280C2212yescomplemented
117D11×#95C2211yescharacteristic
118D11×#95C2211yescharacteristic
119D11×#95C2212yes—
120D11×#95C2212yes—
121#10622262C2211yescharacteristic, complemented
122#10622262C2211yescharacteristic, complemented
123#10622260C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C22×C22⋊D11C2312yes—
129C23×Dic11C2312yes—
130C2×D4×D11—24no—
131C2×D4×D11—24no—
132C2×D4×D11Q818yes—
133C22×D44C2311yescharacteristic
134C22×C4×D11—28no—
135C22×C4×D11—28no—
136C22×C4×D11—44no—
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C11×#125—24no—
150C4×D4×C11—24no—
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173D4×Dic11—24no—
174C4×C22⋊D11—28no—
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×(C2×D11)⋊C4C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2312yes—
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2312yes—
192C2×C4⋊Dic11C2312yes—
193C2×C4⋊Dic11C2311yescharacteristic
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218#66946—24no—
219C4⋊C4×D11—28no—
220C4⋊C4×D11—28no—
221C4⋊C4×D11—24no—
222C4⋊C4×D11—24no—
223C4⋊C4×D11—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—44no—
226C4⋊C4×D11—44no—
227C4⋊C4×D11D418yes—
228#66943—24no—
229#66943—24no—
230#66942—28no—
231#66942—28no—
232(C22⋊D11)⋊C4—28no—
233C22⋊C4×D11—28no—
234C22⋊C4×D11—28no—
235C22⋊C4×D11—44no—
236C22⋊C4×D11—44no—
237C22⋊C4×D11—44no—
238C4×D44—24no—
239C42×D11—24no—
240C42×D11—24no—
241C42×D11—24no—
242#66923—24no—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C2×#2454—111nomaximal, Sylow
260C24×C11C2412yes—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—24no—
267C23×D11C2×Q818yes—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C2×D4×C11—22no—
271C2×D4×C11—22no—
272C2×D4×C11C2×Q814yes—
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—42no—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11C2×Q818yes—
289C22×Dic11—24no—
290C22×Dic11—24no—
291C22×Dic11—42no—
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2412yes—
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302D4×D11—232no—
303C2×D44—22no—
304C2×D44—22no—
305C2×D44C2×Q814yes—
306C2×C4×D11—24no—
307C2×C4×D11—24no—
308C2×C4×D11—22no—
309C2×C4×D11—22no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—24no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—24no—
316C2×C4×D11—22no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—24no—
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—22no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—432no—
337C2×C4×D11C2×D418yes—
338C2×C4×D11C2×D414yes—
339C2×C4×D11C2×Q814yes—
340C2×C4×D11#4114yes—
341C2×C4×D11#4114yes—
342C2×C4×D11#4114yes—
343C11×C4⋊C4—24no—
344C11×C4⋊C4—24no—
345C11×C4⋊C4—22no—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—42no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4C2×D414yes—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—22no—
360C22⋊Dic11—24no—
361C22⋊Dic11—24no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11—42no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375C4⋊Dic11—24no—
376C4⋊Dic11—22no—
377C4⋊Dic11—22no—
378C4⋊Dic11—24no—
379C4⋊Dic11—22no—
380C4⋊Dic11—22no—
381C4⋊Dic11—42no—
382C4⋊Dic11—42no—
383C4⋊Dic11C2×D414yes—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386Dic11⋊C4—24no—
387Dic11⋊C4—24no—
388Dic11⋊C4—22no—
389Dic11⋊C4—22no—
390Dic11⋊C4—22no—
391Dic11⋊C4—24no—
392Dic11⋊C4—24no—
393Dic11⋊C4—22no—
394Dic11⋊C4—42no—
395Dic11⋊C4—42no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4C2×D418yes—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—22no—
403C4×Dic11—22no—
404C4×Dic11—22no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—22no—
408C22×#125—111no—
409C22×C4×D4—111no—
410#2454—112no—
411#2454—112no—
412#2454—111no—
413#2454—111no—
414#2454—111no—
415#2454—111no—
416#2454—112no—
417#2454—112no—
418#2454—111no—
419#2454—111no—
420#2454—111no—
421#2454D1111yescharacteristic, direct product factor
422C2×#399—112no—
423C2×#396—112no—
424C2×#390—111no—
425C2×#390—111no—
426C2×#389—111no—
427C2×#389—111no—
428C2×#385—112no—
429C2×#380—112no—
430C2×C4×C4⋊C4—111no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11C22×Q814yes—
438C23×C11C2511yescharacteristic
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—216no—
446C22×D11—216no—
447C22×D11—216no—
448C22×D11—48no—
449C22×D11—48no—
450C22×D11—48no—
451C22×D11—48no—
452C22×D11C22×D412yes—
453C22×D11C22×Q814yes—
454C22×D11C22×Q812yes—
455C22×D11C2×#4112yes—
456C22×D11C2×#4112yes—
457C22×D11C2×#4112yes—
458C22×D11H(5,𝔽2)12yes—
459C22×D11H(5,𝔽2)12yes—
460D4×C11—28no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—48no—
486C2×C4×C11C22×D414yes—
487C2×C4×C11C22×D412yes—
488C2×C4×C11C22×Q812yes—
489C2×C4×C11C2×#4112yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11C2×#4112yes—
492C22⋊D11—216no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—22no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—48no—
518C2×Dic11C22×D414yes—
519C2×Dic11C22×D412yes—
520C2×Dic11C22×Q812yes—
521C2×Dic11C2×#4112yes—
522C2×Dic11C2×#4112yes—
523C2×Dic11C2×#4112yes—
524D44—28no—
525C4×D11—28no—
526C4×D11—28no—
527C4×D11—216no—
528C4×D11—48no—
529C4×D11—48no—
530C4×D11—44no—
531C4×D11—48no—
532C4×D11—44no—
533C4×D11—44no—
534C4×D11—44no—
535C4×D11—48no—
536C4×D11C22⋊Q8116yes—
537C23×D4—111no—
538C24×C4—112no—
539C2×#125—112no—
540C2×#125—112no—
541C2×#125—111no—
542C2×#125—111no—
543C2×#125—111no—
544C2×#125—228no—
545C2×#125C2×D1111yescharacteristic, complemented
546C2×C4×D4—111no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4—112no—
550C2×C4×D4—111no—
551C2×C4×D4—228no—
552C2×C4×D4C2×D1111yescharacteristic
553C22×C4⋊C4—111no—
554C22×C4⋊C4—112no—
555C22×C4⋊C4—111no—
556C22×C4⋊C4—112no—
557C22×C4⋊C4—111no—
558C22×C4⋊C4—111no—
559C22×C4⋊C4—111no—
560C22×C4⋊C4—112no—
561C22×C4⋊C4—112no—
562C22×C22⋊C4—112no—
563C22×C22⋊C4—112no—
564C22×C22⋊C4—112no—
565C22×C22⋊C4—112no—
566C22×C22⋊C4—112no—
567C22×C42—111no—
568C22×C42—111no—
569C22×C42—111no—
570#399—112no—
571#399—112no—
572#399—112no—
573#399—112no—
574#399—112no—
575#399—112no—
576#399—112no—
577#399C2×D1112yescomplemented
578#396—112no—
579#396—112no—
580#396—112no—
581#396—112no—
582#396—112no—
583#396—112no—
584#396—112no—
585#396C2×D1112yescomplemented
586#390—111no—
587#390—111no—
588#390—111no—
589#390—111no—
590#390—112no—
591#390—112no—
592#390—112no—
593#390—112no—
594#390—111no—
595#390—111no—
596#390C2×D1111yescharacteristic
597#390C2×D1111yescharacteristic
598#389—112no—
599#389—112no—
600#389—111no—
601#389—111no—
602#389—111no—
603#389—111no—
604#389—111no—
605#389—111no—
606#389—112no—
607#389—112no—
608#389C2×D1111yescharacteristic, complemented
609#389C2×D1111yescharacteristic, complemented
610#385—112no—
611#385—112no—
612#385—112no—
613#385—112no—
614#385—112no—
615#385—112no—
616#385—112no—
617#385C2×D1112yescomplemented
618#380—112no—
619#380—112no—
620#380—112no—
621#380—112no—
622#380—112no—
623#380—112no—
624#380—112no—
625#380C2×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—111no—
633C4×C4⋊C4C2×D1111yescharacteristic, complemented
634C2×#95—111no—
635C2×#95—112no—
636C2×#95—111no—
637C2×#95—112no—
638C22×C11—24no—
639C22×C11—24no—
640C22×C11—24no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11C23×D411yescharacteristic
646C22×C11C23×Q811yescharacteristic
647C22×C11C22×#4111yescharacteristic
648C22×C11C22×#4111yescharacteristic
649C22×C11C22×#4111yescharacteristic
650C22×C11C2×H(5,𝔽2)11yescharacteristic
651C22×C11C2×H(5,𝔽2)11yescharacteristic
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—432no—
660C2×D11C2×C22⋊Q814yes—
661C2×D11#52914yes—
662C2×D11#54014yes—
663C2×D11#54614yes—
664C2×D11#55014yes—
665C2×D11#55414yes—
666C2×D11#55414yes—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—24no—
670C4×C11—41no—
671C4×C11—42no—
672C4×C11—41no—
673C4×C11—41no—
674C4×C11—41no—
675C4×C11—42no—
676C4×C11C2×C22⋊Q814yes—
677Dic11—22no—
678Dic11—22no—
679Dic11—24no—
680Dic11—41no—
681Dic11—42no—
682Dic11—41no—
683Dic11—41no—
684Dic11—41no—
685Dic11—42no—
686Dic11C2×C22⋊Q814yes—
687C25—112no—
688C22×D4—112no—
689C22×D4—118no—
690C22×D4—111no—
691C22×D4—224no—
692C22×D4—224no—
693C22×D4C22×D1111yescharacteristic
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—112no—
697C23×C4—111no—
698C23×C4—112no—
699C23×C4—112no—
700C23×C4—112no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—111no—
704C23×C4—111no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—228no—
708C23×C4—228no—
709C23×C4—444no—
710C23×C4C22×D1112yes—
711#125—24no—
712#125—224no—
713#125—228no—
714#125—228no—
715#125—224no—
716#125—224no—
717C4×D4—24no—
718C4×D4—224no—
719C4×D4—228no—
720C4×D4—228no—
721C4×D4—224no—
722C4×D4—224no—
723C2×C4⋊C4—112no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—118no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—112no—
728C2×C4⋊C4—112no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—111no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—224no—
749C2×C4⋊C4—228no—
750C2×C4⋊C4—228no—
751C2×C4⋊C4—224no—
752C2×C4⋊C4—224no—
753C2×C4⋊C4—224no—
754C2×C4⋊C4—444no—
755C2×C4⋊C4—444no—
756C2×C4⋊C4C22×D1112yes—
757C2×C4⋊C4C22×D1112yes—
758C2×C4⋊C4C22×D1111yescharacteristic
759C2×C4⋊C4C22×D1111yescharacteristic
760C2×C4⋊C4C22×D1111yescharacteristic
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1112yes—
763C2×C4⋊C4C22×D1112yes—
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
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⋊C4—444no—
785C2×C22⋊C4C22×D1112yes—
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1112yes—
788C2×C22⋊C4C22×D1112yes—
789C2×C22⋊C4C22×D1112yes—
790C2×C42—111no—
791C2×C42—111no—
792C2×C42—111no—
793C2×C42—111no—
794C2×C42—111no—
795C2×C42—111no—
796C2×C42—111no—
797C2×C42—111no—
798C2×C42—111no—
799C2×C42—224no—
800C2×C42—224no—
801C2×C42—224no—
802C2×C42C22×D1111yescharacteristic
803C2×C42C22×D1111yescharacteristic
804C2×C42C22×D1111yescharacteristic
805#95—111no—
806#95—111no—
807#95—111no—
808#95—111no—
809#95—111no—
810#95—111no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95C22×D1111yescharacteristic
818#95C22×D1111yescharacteristic
819#95C22×D1112yes—
820#95C22×D1112yes—
821C2×C11—44no—
822C2×C11C22×C22⋊Q811yescharacteristic
823C2×C11C2×#52911yescharacteristic
824C2×C11C2×#54011yescharacteristic
825C2×C11C2×#54611yescharacteristic
826C2×C11C2×#55011yescharacteristic
827C2×C11C2×#55411yescharacteristic
828C2×C11C2×#55411yescharacteristic
829D11—44no—
830D11#245418yesdirect product factor
831C24—111no—
832C24—118no—
833C24—112no—
834C24—224no—
835C24—224no—
836C24—224no—
837C24—224no—
838C24—224no—
839C24—224no—
840C24C23×D1112yes—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—118no—
844C2×D4—114no—
845C2×D4—2232no—
846C2×D4—224no—
847C2×D4—224no—
848C2×D4—222no—
849C2×D4—222no—
850C2×D4Q8×D1114yes—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—42no—
854C22×C4—111no—
855C22×C4—114no—
856C22×C4—114no—
857C22×C4—114no—
858C22×C4—111no—
859C22×C4—111no—
860C22×C4—112no—
861C22×C4—118no—
862C22×C4—114no—
863C22×C4—114no—
864C22×C4—111no—
865C22×C4—112no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—111no—
869C22×C4—112no—
870C22×C4—224no—
871C22×C4—224no—
872C22×C4—222no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—224no—
876C22×C4—224no—
877C22×C4—222no—
878C22×C4—222no—
879C22×C4—222no—
880C22×C4—222no—
881C22×C4—222no—
882C22×C4—224no—
883C22×C4—222no—
884C22×C4—222no—
885C22×C4—222no—
886C22×C4—224no—
887C22×C4—224no—
888C22×C4—224no—
889C22×C4—224no—
890C22×C4—224no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—224no—
897C22×C4—224no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—442no—
901C22×C4—442no—
902C22×C4—4432no—
903C22×C4—442no—
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1112yes—
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1112yes—
910C22×C4C23×D1112yes—
911C22×C4C23×D1111yescharacteristic
912C22×C4C23×D1111yescharacteristic
913C22×C4C23×D1111yescharacteristic
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—118no—
923C4⋊C4—114no—
924C4⋊C4—224no—
925C4⋊C4—224no—
926C4⋊C4—224no—
927C4⋊C4—224no—
928C4⋊C4—224no—
929C4⋊C4—224no—
930C4⋊C4—222no—
931C4⋊C4—222no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—224no—
935C4⋊C4—224no—
936C4⋊C4—222no—
937C4⋊C4—222no—
938C4⋊C4—222no—
939C4⋊C4—222no—
940C4⋊C4—442no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4—442no—
944C4⋊C4—442no—
945C4⋊C4—442no—
946C4⋊C4D4×D1114yes—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—224no—
953C22⋊C4—224no—
954C22⋊C4—224no—
955C22⋊C4—224no—
956C22⋊C4—224no—
957C22⋊C4—224no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4—442no—
961C22⋊C4—442no—
962C22⋊C4—442no—
963C22⋊C4—442no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4—442no—
967C42—22no—
968C42—22no—
969C42—22no—
970C42—222no—
971C42—222no—
972C42—222no—
973C42—222no—
974C42—222no—
975C42—222no—
976C42—222no—
977C42—222no—
978C42—222no—
979C11C2×#245411yescharacteristic, complemented, Sylow
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—112no—
987C23—112no—
988C23—112no—
989C23—112no—
990C23—112no—
991C23—112no—
992C23—112no—
993C23—114no—
994C23—2216no—
995C23—2216no—
996C23—2216no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—448no—
1004C23—448no—
1005C23—448no—
1006C23—448no—
1007C23C2×Q8×D1114yes—
1008C23C24×D1111yescharacteristic
1009D4—28no—
1010D4—2216no—
1011D4—228no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—48no—
1037C2×C4—112no—
1038C2×C4—112no—
1039C2×C4—112no—
1040C2×C4—1116no—
1041C2×C4—114no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—228no—
1045C2×C4—2216no—
1046C2×C4—228no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—222no—
1057C2×C4—221no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—221no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—448no—
1072C2×C4—448no—
1073C2×C4—444no—
1074C2×C4—448no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—448no—
1079C2×C4—448no—
1080C2×C4C2×D4×D1114yes—
1081C2×C4C2×D4×D1112yes—
1082C2×C4C2×Q8×D1112yes—
1083C2×C4#41×D1112yes—
1084C2×C4#41×D1112yes—
1085C2×C4#41×D1112yes—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—114no—
1094C22—114no—
1095C22—114no—
1096C22—114no—
1097C22—114no—
1098C22—114no—
1099C22—114no—
1100C22—224no—
1101C22—224no—
1102C22—224no—
1103C22—4432no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22C22×D4×D1111yescharacteristic
1109C22C22×Q8×D1111yescharacteristic
1110C22C2×#41×D1111yescharacteristic
1111C22C2×#41×D1111yescharacteristic
1112C22C2×#41×D1111yescharacteristic
1113C22D11×H(5,𝔽2)11yescharacteristic
1114C22D11×H(5,𝔽2)11yescharacteristic
1115C4—22no—
1116C4—22no—
1117C4—24no—
1118C4—41no—
1119C4—42no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—42no—
1124C4—114no—
1125C4—222no—
1126C4—222no—
1127C4—224no—
1128C4—441no—
1129C4—442no—
1130C4—441no—
1131C4—441no—
1132C4—441no—
1133C4—442no—
1134C4D11×C22⋊Q814yes—
1135C2—44no—
1136C2—118no—
1137C2—444no—
1138C2C2×D11×C22⋊Q811yescharacteristic
1139C2D11×#52911yescharacteristic
1140C2D11×#54011yescharacteristic
1141C2D11×#54611yescharacteristic
1142C2D11×#55011yescharacteristic
1143C2D11×#55411yescharacteristic
1144C2D11×#55411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2454C2
prime radicalC22×D4×D11C22
hypercenter#2454D11
hypocenterC11C2×#2454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
3. #13072491C2semidirect
4. #13072490C2semidirect
5. #13072489C2semidirect
6. #13072488C2semidirect
7. #13072487C2semidirect
8. #13072486C2semidirect
9. #13072485C2semidirect
10. #13072484C2semidirect
11. #13072483C2semidirect
12. #13072482C2semidirect
13. #13072481C2semidirect
14. D11×#399C2semidirect
15. D11×#396C2semidirect
18. D11×#389C2semidirect
19. D11×#389C2semidirect
20. D11×#385C2semidirect
21. D11×#380C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2454C2semidirect
26. C2×C11×#125C22semidirect
42. C2×#66943C22semidirect
43. C2×#66943C22semidirect
44. C2×#66942C22semidirect
45. C2×#66942C22semidirect
56. C2×#66923C22semidirect
57. C11×#399C22semidirect
58. C11×#396C22semidirect
61. C11×#389C22semidirect
62. C11×#389C22semidirect
63. C11×#385C22semidirect
64. C11×#380C22semidirect
65. C4×C11×C4⋊C4C22semidirect
68. #10622825C22semidirect
69. #10622823C22semidirect
70. #10622607C22semidirect
71. #10622607C22semidirect
72. #10622607C22semidirect
73. #10622605C22semidirect
74. #10622605C22semidirect
75. #10622605C22semidirect
76. #10622602C22semidirect
77. #10622602C22semidirect
80. #10622600C22semidirect
81. #10622600C22semidirect
82. #10622598C22semidirect
83. #10622598C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. C4⋊C4×Dic11C22semidirect
86. #10622586C22semidirect
87. #10622586C22semidirect
88. #10622585C22semidirect
89. #10622585C22semidirect
94. #10622563C22semidirect
95. #10622562C22semidirect
96. #10622562C22semidirect
97. #10622562C22semidirect
98. #10622561C22semidirect
99. #10622561C22semidirect
100. #10622561C22semidirect
101. #10622559C22semidirect
102. #10622555C22semidirect
103. #10622555C22semidirect
106. C4×C4⋊Dic11C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622541C22semidirect
110. #10622541C22semidirect
111. #10622290C22semidirect
112. #10622289C22semidirect
113. #10622281C22semidirect
114. #10622281C22semidirect
115. #10622280C22semidirect
116. #10622280C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
124. #10622260C22semidirect
421. #2454D11direct (N × H)
545. C2×#125C2×D11semidirect
577. #399C2×D11semidirect
585. #396C2×D11semidirect
608. #389C2×D11semidirect
609. #389C2×D11semidirect
617. #385C2×D11semidirect
625. #380C2×D11semidirect
633. C4×C4⋊C4C2×D11semidirect
830. D11#2454direct (N × H)
979. C11C2×#2454semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×C4×D4×D112
#130724912
#130724902
#130724892
#130724882
#130724872
#130724862
#130724852
#130724842
#130724832
#130724822
#130724812
D11×#3992
D11×#3962
D11×#3902
D11×#3892
D11×#3852
D11×#3802
C4×C4⋊C4×D112
C11×#24542
C2×#245411