Finite Group Databasebeta

← D11×#2422 #14921640

Subgroups — D11×#2422 #14921640

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#123C212yesmaximal, complemented
2C2×D11×#121C211yesmaximal, characteristic
3C2×C4×D4×D11C211yesmaximal, characteristic, complemented
4#13072133C211yesmaximal, characteristic, complemented
5#13072132C211yesmaximal, characteristic, complemented
6#13072131C211yesmaximal, characteristic, complemented
7#13072130C211yesmaximal, characteristic, complemented
8#13072129C212yesmaximal, complemented
9#13072128C211yesmaximal, characteristic, complemented
10#13072127C212yesmaximal, complemented
11#13072126C211yesmaximal, characteristic, complemented
12#13072125C212yesmaximal, complemented
13#13072124C211yesmaximal, characteristic, complemented
14#13072123C212yesmaximal, complemented
15D11×#397C212yesmaximal, complemented
16D11×#394C212yesmaximal, complemented
17D11×#390C211yesmaximal, characteristic, complemented
18D11×#389C211yesmaximal, characteristic, complemented
19D11×#385C212yesmaximal, complemented
20D11×#384C211yesmaximal, characteristic, complemented
21D11×#380C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2422C211yesmaximal, characteristic, complemented
24C22×D4×D11C2212yes—
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2212yes—
28C2×C11×#123C2212yescomplemented
29C2×C11×#121C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic, complemented
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic
33C2×#66988C2212yescomplemented
34C2×D4×Dic11C2211yescharacteristic, complemented
35C2×#66983C2211yescharacteristic
36C2×#66982C2212yescomplemented
37C2×C4×C22⋊D11C2212yescomplemented
38D11×#123—216no—
39D11×#121—28no—
40C4×D4×D11—28no—
41C2×#66948C2211yescharacteristic
42C2×#66947C2212yescomplemented
43C2×#66947C2212yescomplemented
44C2×#66946C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2212yes—
49C2×C4⋊C4×D11C2212yes—
50C2×C4⋊C4×D11C2212yes—
51C2×#66939C2212yescomplemented
52C2×#66937C2212yes—
53C2×#66936C2212yescomplemented
54C2×#66936C2212yescomplemented
55C2×(C22⋊D11)⋊C4C2212yescomplemented
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2212yes—
58C2×C22⋊C4×D11C2212yes—
59C2×C22⋊C4×D11C2212yes—
60C2×C22⋊C4×D11C2212yes—
61C2×C22⋊C4×D11C2212yes—
62C2×C22⋊C4×D11C2211yescharacteristic
63C2×C4×D44C2211yescharacteristic, complemented
64C2×C42×D11C2211yescharacteristic
65C2×C42×D11C2211yescharacteristic
66C11×#397C2212yescomplemented
67C11×#394C2212yescomplemented
68C11×#390C2211yescharacteristic, complemented
69C11×#389C2211yescharacteristic, complemented
70C11×#385C2212yescomplemented
71C11×#384C2211yescharacteristic, complemented
72C11×#380C2211yescharacteristic, complemented
73C4×C11×C22⋊C4C2211yescharacteristic, complemented
74#10622835C2212yescomplemented
75#10622834C2211yescharacteristic, complemented
76#10622825C2211yescharacteristic, complemented
77#10622823C2212yescomplemented
78C4×C22⋊Dic11C2211yescharacteristic, complemented
79#10622606C2212yescomplemented
80#10622604C2212yescomplemented
81#10622602C2212yescomplemented
82#10622602C2212yescomplemented
83#10622601C2211yescharacteristic, complemented
84#10622600C2211yescharacteristic, complemented
85#10622600C2211yescharacteristic, complemented
86#10622598C2211yescharacteristic, complemented
87#10622589C2212yescomplemented
88#10622589C2211yescharacteristic, complemented
89#10622589C2211yescharacteristic, complemented
90#10622589C2212yescomplemented
91#10622586C2211yescharacteristic, complemented
92#10622585C2212yescomplemented
93#10622574C2212yescomplemented
94#10622574C2212yescomplemented
95#10622572C2212yescomplemented
96#10622572C2212yescomplemented
97#10622570C2212yescomplemented
98#10622570C2212yescomplemented
99#10622566C2212yescomplemented
100#10622565C2212yescomplemented
101#10622565C2212yescomplemented
102#10622563C2212yescomplemented
103#10622559C2212yescomplemented
104#10622555C2212yescomplemented
105C22⋊C4×Dic11C2211yescharacteristic, complemented
106C22⋊C4×Dic11C2211yescharacteristic, complemented
107#10622552C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
110#10622548C2211yescharacteristic, complemented
111#10622541C2211yescharacteristic, complemented
112#10622288C2212yescomplemented
113#10622288C2212yescomplemented
114#10622287C2212yescomplemented
115#10622285C2212yescomplemented
116#10622281C2212yescomplemented
117#10622281C2212yescomplemented
118#10622280C2212yescomplemented
119#10622279C2211yescharacteristic, complemented
120#10622279C2211yescharacteristic, complemented
121D11×#95C2211yescharacteristic
122D11×#95C2211yescharacteristic
123D11×#95C2212yes—
124D11×#95C2212yes—
125#10622260C2212yescomplemented
126C24×D11C2312yes—
127C24×D11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C22×D4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2312yes—
137C2×D4×D11—28no—
138C2×D4×D11—28no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—44no—
142C2×D4×D11D418yes—
143C22×D44C2312yes—
144C22×D44C2311yescharacteristic
145C22×C4×D11—28no—
146C22×C4×D11—24no—
147C22×C4×D11—28no—
148C22×C4×D11—24no—
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C11×#123—28no—
165C11×#121—24no—
166C4×D4×C11—24no—
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C42×C11C2311yescharacteristic
181C2×C42×C11C2311yescharacteristic
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2311yescharacteristic
189#66992—28no—
190#66991—24no—
191#66988—28no—
192D4×Dic11—24no—
193#66983—24no—
194#66982—28no—
195C4×C22⋊D11—28no—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×(C2×D11)⋊C4C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231#66948—24no—
232#66947—28no—
233#66947—28no—
234#66946—24no—
235C4⋊C4×D11—24no—
236C4⋊C4×D11—24no—
237C4⋊C4×D11—28no—
238C4⋊C4×D11—28no—
239C4⋊C4×D11—24no—
240C4⋊C4×D11—44no—
241#66939—28no—
242#66937—28no—
243#66936—28no—
244#66936—28no—
245(C22⋊D11)⋊C4—28no—
246C22⋊C4×D11—28no—
247C22⋊C4×D11—28no—
248C22⋊C4×D11—28no—
249C22⋊C4×D11—28no—
250C22⋊C4×D11—24no—
251C22⋊C4×D11—28no—
252C22⋊C4×D11D418yescomplemented
253C4×D44—24no—
254C42×D11—24no—
255C42×D11—24no—
256C11×#95C2312yes—
257C11×#95C2311yescharacteristic
258C11×#95C2311yescharacteristic
259C11×#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264C11⋊#95C2311yescharacteristic
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2311yescharacteristic
268C11⋊#95C2311yescharacteristic
269C11⋊#95C2311yescharacteristic
270C11⋊#95C2312yes—
271C11⋊#95C2312yes—
272C2×#2422—111nomaximal, Sylow
273C24×C11C2412yes—
274C24×C11C2411yescharacteristic
275C23×D11—24no—
276C23×D11—22no—
277C23×D11—22no—
278C23×D11—24no—
279C23×D11—22no—
280C23×D11—22no—
281C23×D11—24no—
282C23×D11—24no—
283C23×D11—24no—
284C23×D11—22no—
285C23×D11—24no—
286C23×D11—22no—
287C23×D11C2×D414yes—
288C23×D11C2×D418yes—
289C23×D11C2412yes—
290C23×D11C2411yescharacteristic
291C23×D11C2411yescharacteristic
292C2×D4×C11—24no—
293C2×D4×C11—24no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—42no—
297C2×D4×C11C2×D414yes—
298C22×C4×C11—24no—
299C22×C4×C11—24no—
300C22×C4×C11—22no—
301C22×C4×C11—22no—
302C22×C4×C11—22no—
303C22×C4×C11—42no—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11C2×D418yes—
322C22×Dic11—24no—
323C22×Dic11—22no—
324C22×Dic11—22no—
325C22×Dic11—22no—
326C22×Dic11—24no—
327C22×Dic11—42no—
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2412yes—
331C22×Dic11C2412yes—
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337D4×D11—232no—
338D4×D11—432no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—22no—
342C2×D44—22no—
343C2×D44—42no—
344C2×D44C2×D414yes—
345C2×C4×D11—24no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—24no—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—24no—
362C2×C4×D11—22no—
363C2×C4×D11—24no—
364C2×C4×D11—22no—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—22no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—22no—
371C2×C4×D11—22no—
372C2×C4×D11—24no—
373C2×C4×D11—22no—
374C2×C4×D11—22no—
375C2×C4×D11—22no—
376C2×C4×D11—42no—
377C2×C4×D11—42no—
378C2×C4×D11—432no—
379C2×C4×D11—416no—
380C2×C4×D11C2×D414yes—
381C2×C4×D11C2×D414yes—
382C2×C4×D11C2×D414yes—
383C2×C4×D11#4114yes—
384C2×C4×D11#4114yes—
385C2×C4×D11#4114yes—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—24no—
388C11×C4⋊C4—24no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—42no—
392C11×C22⋊C4—24no—
393C11×C22⋊C4—24no—
394C11×C22⋊C4—24no—
395C11×C22⋊C4—24no—
396C11×C22⋊C4—22no—
397C11×C22⋊C4—24no—
398C11×C22⋊C4C2×D414yescomplemented
399C42×C11—22no—
400C42×C11—22no—
401C22⋊Dic11—24no—
402C22⋊Dic11—22no—
403C22⋊Dic11—24no—
404C22⋊Dic11—24no—
405C22⋊Dic11—24no—
406C22⋊Dic11—24no—
407C22⋊Dic11C2×D414yescomplemented
408(C2×D11)⋊C4—24no—
409(C2×D11)⋊C4—22no—
410(C2×D11)⋊C4—24no—
411(C2×D11)⋊C4—24no—
412(C2×D11)⋊C4—24no—
413(C2×D11)⋊C4—24no—
414(C2×D11)⋊C4—24no—
415(C2×D11)⋊C4—24no—
416(C2×D11)⋊C4—24no—
417(C2×D11)⋊C4—24no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—24no—
420(C2×D11)⋊C4C2×D414yescomplemented
421(C2×D11)⋊C4C2×D414yescomplemented
422C4⋊Dic11—24no—
423C4⋊Dic11—22no—
424C4⋊Dic11—24no—
425C4⋊Dic11—22no—
426C4⋊Dic11—22no—
427C4⋊Dic11—42no—
428Dic11⋊C4—24no—
429Dic11⋊C4—24no—
430Dic11⋊C4—24no—
431Dic11⋊C4—24no—
432Dic11⋊C4—24no—
433Dic11⋊C4—24no—
434Dic11⋊C4—24no—
435Dic11⋊C4—42no—
436Dic11⋊C4—42no—
437C4×Dic11—22no—
438C4×Dic11—22no—
439C4×Dic11—22no—
440C4×Dic11—22no—
441C4×Dic11—22no—
442C4×Dic11—22no—
443C22×#123—112no—
444C22×#121—111no—
445C22×C4×D4—111no—
446#2422—112no—
447#2422—112no—
448#2422—111no—
449#2422—111no—
450#2422—112no—
451#2422—111no—
452#2422—111no—
453#2422—111no—
454#2422—112no—
455#2422—111no—
456#2422—111no—
457#2422D1111yescharacteristic, direct product factor
458C2×#397—112no—
459C2×#394—112no—
460C2×#390—111no—
461C2×#389—111no—
462C2×#385—112no—
463C2×#384—111no—
464C2×#380—111no—
465C2×C4×C22⋊C4—111no—
466C23×C11—22no—
467C23×C11—21no—
468C23×C11—21no—
469C23×C11—22no—
470C23×C11—21no—
471C23×C11—21no—
472C23×C11—22no—
473C23×C11—22no—
474C23×C11—22no—
475C23×C11—21no—
476C23×C11—21no—
477C23×C11—22no—
478C23×C11C22×D412yes—
479C23×C11C22×D414yes—
480C23×C11C2511yescharacteristic
481C22×D11—22no—
482C22×D11—21no—
483C22×D11—21no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—21no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—22no—
490C22×D11—21no—
491C22×D11—21no—
492C22×D11—22no—
493C22×D11—216no—
494C22×D11—28no—
495C22×D11—216no—
496C22×D11—28no—
497C22×D11—216no—
498C22×D11—28no—
499C22×D11—44no—
500C22×D11—48no—
501C22×D11—44no—
502C22×D11—48no—
503C22×D11—44no—
504C22×D11—48no—
505C22×D11—44no—
506C22×D11—48no—
507C22×D11C22×D412yes—
508C22×D11C22×D414yes—
509C22×D11C22×D412yes—
510C22×D11C22×D412yes—
511C22×D11C2×#4112yes—
512C22×D11C2×#4112yes—
513C22×D11C2×#4112yes—
514C22×D11H(5,𝔽2)12yes—
515C22×D112−1+412yes—
516D4×C11—28no—
517D4×C11—48no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—48no—
540C2×C4×C11—44no—
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D412yes—
543C2×C4×C11C22×D412yes—
544C2×C4×C11C2×#4112yes—
545C2×C4×C11C2×#4112yes—
546C2×C4×C11C2×#4112yes—
547C22⋊D11—216no—
548C22⋊D11—48no—
549C22⋊D11—48no—
550C2×Dic11—21no—
551C2×Dic11—21no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—21no—
556C2×Dic11—21no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—21no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—21no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—21no—
571C2×Dic11—48no—
572C2×Dic11—44no—
573C2×Dic11C22×D412yes—
574C2×Dic11C22×D412yes—
575C2×Dic11C22×D412yes—
576C2×Dic11C2×#4112yes—
577C2×Dic11C2×#4112yes—
578C2×Dic11C2×#4112yes—
579D44—28no—
580D44—48no—
581C4×D11—28no—
582C4×D11—28no—
583C4×D11—28no—
584C4×D11—48no—
585C4×D11—48no—
586C4×D11—44no—
587C4×D11—48no—
588C4×D11—48no—
589C4×D11—48no—
590C4×D11—44no—
591C4×D11—44no—
592C4×D11—44no—
593C4×D11#123116yescomplemented
594C23×D4—111no—
595C23×D4—112no—
596C24×C4—111no—
597C24×C4—112no—
598C2×#123—112no—
599C2×#123—112no—
600C2×#123—112no—
601C2×#123—112no—
602C2×#123—112no—
603C2×#123—112no—
604C2×#123—112no—
605C2×#123—2216no—
606C2×#123C2×D1112yescomplemented
607C2×#121—111no—
608C2×#121—112no—
609C2×#121—111no—
610C2×#121—111no—
611C2×#121—112no—
612C2×#121—228no—
613C2×#121C2×D1111yescharacteristic
614C2×C4×D4—111no—
615C2×C4×D4—112no—
616C2×C4×D4—111no—
617C2×C4×D4—112no—
618C2×C4×D4—111no—
619C2×C4×D4—228no—
620C2×C4×D4C2×D1111yescharacteristic, complemented
621C22×C4⋊C4—112no—
622C22×C4⋊C4—111no—
623C22×C4⋊C4—111no—
624C22×C4⋊C4—112no—
625C22×C4⋊C4—111no—
626C22×C4⋊C4—112no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4—111no—
629C22×C22⋊C4—112no—
630C22×C22⋊C4—112no—
631C22×C22⋊C4—112no—
632C22×C22⋊C4—112no—
633C22×C22⋊C4—112no—
634C22×C42—111no—
635C22×C42—111no—
636#397—112no—
637#397—112no—
638#397—112no—
639#397—112no—
640#397—112no—
641#397—112no—
642#397—112no—
643#397C2×D1112yescomplemented
644#394—112no—
645#394—112no—
646#394—112no—
647#394—112no—
648#394—112no—
649#394—112no—
650#394—112no—
651#394C2×D1112yescomplemented
652#390—111no—
653#390—111no—
654#390—112no—
655#390—112no—
656#390—111no—
657#390C2×D1111yescharacteristic, complemented
658#389—112no—
659#389—111no—
660#389—111no—
661#389—111no—
662#389—112no—
663#389C2×D1111yescharacteristic, complemented
664#385—112no—
665#385—112no—
666#385—112no—
667#385—112no—
668#385—112no—
669#385—112no—
670#385—112no—
671#385C2×D1112yescomplemented
672#384—112no—
673#384—112no—
674#384—111no—
675#384—111no—
676#384—111no—
677#384C2×D1111yescharacteristic, complemented
678#380—111no—
679#380—111no—
680#380—111no—
681#380—112no—
682#380—112no—
683#380C2×D1111yescharacteristic, complemented
684C4×C22⋊C4—111no—
685C4×C22⋊C4—111no—
686C4×C22⋊C4—111no—
687C4×C22⋊C4—111no—
688C4×C22⋊C4—111no—
689C4×C22⋊C4—111no—
690C4×C22⋊C4—111no—
691C4×C22⋊C4C2×D1111yescharacteristic, complemented
692C2×#95—112no—
693C2×#95—111no—
694C2×#95—112no—
695C2×#95—111no—
696C22×C11—24no—
697C22×C11—22no—
698C22×C11—24no—
699C22×C11—22no—
700C22×C11—22no—
701C22×C11—24no—
702C22×C11—41no—
703C22×C11—42no—
704C22×C11—41no—
705C22×C11—42no—
706C22×C11—42no—
707C22×C11—41no—
708C22×C11—41no—
709C22×C11—42no—
710C22×C11C23×D411yescharacteristic
711C22×C11C23×D411yescharacteristic
712C22×C11C22×#4111yescharacteristic
713C22×C11C22×#4111yescharacteristic
714C22×C11C22×#4111yescharacteristic
715C22×C11C2×H(5,𝔽2)11yescharacteristic
716C22×C11C2×2−1+411yescharacteristic
717C2×D11—24no—
718C2×D11—22no—
719C2×D11—24no—
720C2×D11—22no—
721C2×D11—22no—
722C2×D11—24no—
723C2×D11—41no—
724C2×D11—42no—
725C2×D11—41no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—41no—
729C2×D11—41no—
730C2×D11—42no—
731C2×D11—432no—
732C2×D11—416no—
733C2×D11C2×#12314yes—
734C2×D11#53214yes—
735C2×D11#54214yes—
736C2×D11D4214yes—
737C2×D11#54714yes—
738C2×D11#54714yes—
739C2×D11#55314yes—
740C4×C11—22no—
741C4×C11—22no—
742C4×C11—22no—
743C4×C11—41no—
744C4×C11—42no—
745C4×C11—42no—
746C4×C11—42no—
747C4×C11—41no—
748C4×C11C2×#12314yescomplemented
749Dic11—22no—
750Dic11—22no—
751Dic11—22no—
752Dic11—41no—
753Dic11—42no—
754Dic11—42no—
755Dic11—42no—
756Dic11—41no—
757Dic11C2×#12314yescomplemented
758C25—111no—
759C25—112no—
760C22×D4—112no—
761C22×D4—118no—
762C22×D4—112no—
763C22×D4—112no—
764C22×D4—111no—
765C22×D4—112no—
766C22×D4—224no—
767C22×D4—224no—
768C22×D4—228no—
769C22×D4—228no—
770C22×D4—444no—
771C22×D4C22×D1112yes—
772C22×D4C22×D1111yescharacteristic
773C23×C4—111no—
774C23×C4—111no—
775C23×C4—111no—
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—112no—
779C23×C4—112no—
780C23×C4—111no—
781C23×C4—112no—
782C23×C4—111no—
783C23×C4—112no—
784C23×C4—111no—
785C23×C4—111no—
786C23×C4—112no—
787C23×C4—112no—
788C23×C4—224no—
789C23×C4—228no—
790C23×C4—224no—
791C23×C4—224no—
792C23×C4—228no—
793C23×C4—444no—
794C23×C4C22×D1111yescharacteristic
795C23×C4C22×D1112yes—
796#123—28no—
797#123—228no—
798#123—228no—
799#123—228no—
800#123—228no—
801#123—228no—
802#123—228no—
803#123—228no—
804#121—24no—
805#121—228no—
806#121—224no—
807#121—224no—
808#121—228no—
809#121—224no—
810C4×D4—24no—
811C4×D4—224no—
812C4×D4—228no—
813C4×D4—224no—
814C4×D4—228no—
815C4×D4—224no—
816C2×C4⋊C4—112no—
817C2×C4⋊C4—111no—
818C2×C4⋊C4—112no—
819C2×C4⋊C4—111no—
820C2×C4⋊C4—112no—
821C2×C4⋊C4—112no—
822C2×C4⋊C4—112no—
823C2×C4⋊C4—112no—
824C2×C4⋊C4—112no—
825C2×C4⋊C4—112no—
826C2×C4⋊C4—112no—
827C2×C4⋊C4—111no—
828C2×C4⋊C4—112no—
829C2×C4⋊C4—112no—
830C2×C4⋊C4—112no—
831C2×C4⋊C4—224no—
832C2×C4⋊C4—224no—
833C2×C4⋊C4—228no—
834C2×C4⋊C4—228no—
835C2×C4⋊C4—224no—
836C2×C4⋊C4—444no—
837C2×C4⋊C4C22×D1111yescharacteristic
838C2×C4⋊C4C22×D1111yescharacteristic
839C2×C4⋊C4C22×D1112yes—
840C2×C4⋊C4C22×D1112yes—
841C2×C4⋊C4C22×D1111yescharacteristic
842C2×C4⋊C4C22×D1112yes—
843C2×C22⋊C4—111no—
844C2×C22⋊C4—111no—
845C2×C22⋊C4—111no—
846C2×C22⋊C4—118no—
847C2×C22⋊C4—112no—
848C2×C22⋊C4—112no—
849C2×C22⋊C4—112no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—111no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—112no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—111no—
862C2×C22⋊C4—111no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—228no—
866C2×C22⋊C4—224no—
867C2×C22⋊C4—228no—
868C2×C22⋊C4—228no—
869C2×C22⋊C4—228no—
870C2×C22⋊C4—228no—
871C2×C22⋊C4C22×D1112yes—
872C2×C22⋊C4C22×D1112yes—
873C2×C22⋊C4C22×D1112yes—
874C2×C22⋊C4C22×D1112yes—
875C2×C22⋊C4C22×D1111yescharacteristic
876C2×C22⋊C4C22×D1112yes—
877C2×C22⋊C4C22×D1111yescharacteristic
878C2×C42—111no—
879C2×C42—111no—
880C2×C42—111no—
881C2×C42—111no—
882C2×C42—111no—
883C2×C42—111no—
884C2×C42—224no—
885C2×C42—224no—
886C2×C42C22×D1111yescharacteristic
887C2×C42C22×D1111yescharacteristic
888#95—111no—
889#95—111no—
890#95—111no—
891#95—111no—
892#95—111no—
893#95—111no—
894#95—112no—
895#95—112no—
896#95—112no—
897#95—112no—
898#95—112no—
899#95—112no—
900#95C22×D1111yescharacteristic
901#95C22×D1111yescharacteristic
902#95C22×D1112yes—
903#95C22×D1112yes—
904C2×C11—44no—
905C2×C11—42no—
906C2×C11C22×#12311yescharacteristic
907C2×C11C2×#53211yescharacteristic
908C2×C11C2×#54211yescharacteristic
909C2×C11C2×D4211yescharacteristic
910C2×C11C2×#54711yescharacteristic
911C2×C11C2×#54711yescharacteristic
912C2×C11C2×#55311yescharacteristic
913D11—44no—
914D11—42no—
915D11#242218yesdirect product factor
916C24—111no—
917C24—114no—
918C24—118no—
919C24—111no—
920C24—112no—
921C24—224no—
922C24—222no—
923C24—224no—
924C24—222no—
925C24—222no—
926C24—222no—
927C24—224no—
928C24—224no—
929C24—224no—
930C24—222no—
931C24—222no—
932C24—224no—
933C24C23×D1112yes—
934C24C23×D1111yescharacteristic
935C2×D4—24no—
936C2×D4—24no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—42no—
940C2×D4—118no—
941C2×D4—114no—
942C2×D4—224no—
943C2×D4—224no—
944C2×D4—2232no—
945C2×D4—224no—
946C2×D4—224no—
947C2×D4—224no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—224no—
951C2×D4—222no—
952C2×D4—222no—
953C2×D4—442no—
954C2×D4—442no—
955C2×D4—442no—
956C2×D4—4432no—
957C2×D4D4×D1114yes—
958C22×C4—24no—
959C22×C4—22no—
960C22×C4—24no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—42no—
964C22×C4—111no—
965C22×C4—114no—
966C22×C4—114no—
967C22×C4—114no—
968C22×C4—111no—
969C22×C4—111no—
970C22×C4—111no—
971C22×C4—114no—
972C22×C4—114no—
973C22×C4—114no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—112no—
977C22×C4—112no—
978C22×C4—112no—
979C22×C4—222no—
980C22×C4—224no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—222no—
984C22×C4—222no—
985C22×C4—222no—
986C22×C4—222no—
987C22×C4—222no—
988C22×C4—222no—
989C22×C4—222no—
990C22×C4—224no—
991C22×C4—222no—
992C22×C4—224no—
993C22×C4—224no—
994C22×C4—224no—
995C22×C4—224no—
996C22×C4—222no—
997C22×C4—224no—
998C22×C4—224no—
999C22×C4—224no—
1000C22×C4—224no—
1001C22×C4—224no—
1002C22×C4—224no—
1003C22×C4—222no—
1004C22×C4—222no—
1005C22×C4—222no—
1006C22×C4—222no—
1007C22×C4—224no—
1008C22×C4—222no—
1009C22×C4—222no—
1010C22×C4—224no—
1011C22×C4—222no—
1012C22×C4—224no—
1013C22×C4—222no—
1014C22×C4—222no—
1015C22×C4—442no—
1016C22×C4—442no—
1017C22×C4—4416no—
1018C22×C4—4432no—
1019C22×C4—442no—
1020C22×C4C23×D1111yescharacteristic
1021C22×C4C23×D1111yescharacteristic
1022C22×C4C23×D1112yes—
1023C22×C4C23×D1112yes—
1024C22×C4C23×D1112yes—
1025C22×C4C23×D1111yescharacteristic
1026C22×C4C23×D1111yescharacteristic
1027C22×C4C23×D1111yescharacteristic
1028C22×C4C23×D1111yescharacteristic
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—22no—
1034C4⋊C4—42no—
1035C4⋊C4—224no—
1036C4⋊C4—224no—
1037C4⋊C4—224no—
1038C4⋊C4—224no—
1039C4⋊C4—224no—
1040C4⋊C4—224no—
1041C4⋊C4—224no—
1042C4⋊C4—222no—
1043C4⋊C4—222no—
1044C4⋊C4—224no—
1045C4⋊C4—224no—
1046C4⋊C4—222no—
1047C4⋊C4—442no—
1048C4⋊C4—442no—
1049C4⋊C4—442no—
1050C22⋊C4—24no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—22no—
1055C22⋊C4—24no—
1056C22⋊C4—114no—
1057C22⋊C4—114no—
1058C22⋊C4—114no—
1059C22⋊C4—224no—
1060C22⋊C4—222no—
1061C22⋊C4—224no—
1062C22⋊C4—224no—
1063C22⋊C4—224no—
1064C22⋊C4—224no—
1065C22⋊C4—224no—
1066C22⋊C4—224no—
1067C22⋊C4—224no—
1068C22⋊C4—224no—
1069C22⋊C4—222no—
1070C22⋊C4—224no—
1071C22⋊C4—224no—
1072C22⋊C4—224no—
1073C22⋊C4—224no—
1074C22⋊C4—224no—
1075C22⋊C4—222no—
1076C22⋊C4—224no—
1077C22⋊C4D4×D1114yescomplemented
1078C42—22no—
1079C42—22no—
1080C42—222no—
1081C42—222no—
1082C42—222no—
1083C42—222no—
1084C42—222no—
1085C42—222no—
1086C11C2×#242211yescharacteristic, complemented, Sylow
1087C23—22no—
1088C23—21no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—112no—
1100C23—112no—
1101C23—112no—
1102C23—112no—
1103C23—112no—
1104C23—112no—
1105C23—112no—
1106C23—112no—
1107C23—114no—
1108C23—2216no—
1109C23—2216no—
1110C23—228no—
1111C23—228no—
1112C23—228no—
1113C23—2216no—
1114C23—222no—
1115C23—221no—
1116C23—221no—
1117C23—222no—
1118C23—221no—
1119C23—221no—
1120C23—222no—
1121C23—222no—
1122C23—222no—
1123C23—221no—
1124C23—221no—
1125C23—222no—
1126C23—444no—
1127C23—444no—
1128C23—448no—
1129C23—448no—
1130C23—444no—
1131C23—448no—
1132C23—448no—
1133C23—444no—
1134C23C2×D4×D1112yes—
1135C23C2×D4×D1114yes—
1136C23C24×D1111yescharacteristic
1137D4—28no—
1138D4—48no—
1139D4—2216no—
1140D4—228no—
1141D4—448no—
1142D4—448no—
1143D4—448no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—48no—
1166C2×C4—44no—
1167C2×C4—112no—
1168C2×C4—112no—
1169C2×C4—112no—
1170C2×C4—1116no—
1171C2×C4—112no—
1172C2×C4—112no—
1173C2×C4—112no—
1174C2×C4—228no—
1175C2×C4—228no—
1176C2×C4—228no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—221no—
1180C2×C4—221no—
1181C2×C4—221no—
1182C2×C4—221no—
1183C2×C4—221no—
1184C2×C4—222no—
1185C2×C4—221no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—221no—
1192C2×C4—222no—
1193C2×C4—221no—
1194C2×C4—221no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—221no—
1198C2×C4—448no—
1199C2×C4—444no—
1200C2×C4—448no—
1201C2×C4—448no—
1202C2×C4—444no—
1203C2×C4—448no—
1204C2×C4—448no—
1205C2×C4—444no—
1206C2×C4—444no—
1207C2×C4—448no—
1208C2×C4—444no—
1209C2×C4C2×D4×D1112yes—
1210C2×C4C2×D4×D1112yes—
1211C2×C4C2×D4×D1112yes—
1212C2×C4#41×D1112yes—
1213C2×C4#41×D1112yes—
1214C2×C4#41×D1112yes—
1215C22—22no—
1216C22—24no—
1217C22—22no—
1218C22—22no—
1219C22—24no—
1220C22—24no—
1221C22—41no—
1222C22—42no—
1223C22—42no—
1224C22—41no—
1225C22—42no—
1226C22—42no—
1227C22—41no—
1228C22—41no—
1229C22—114no—
1230C22—114no—
1231C22—114no—
1232C22—114no—
1233C22—114no—
1234C22—114no—
1235C22—114no—
1236C22—222no—
1237C22—224no—
1238C22—222no—
1239C22—222no—
1240C22—224no—
1241C22—224no—
1242C22—4432no—
1243C22—4416no—
1244C22—441no—
1245C22—442no—
1246C22—442no—
1247C22—441no—
1248C22—442no—
1249C22—442no—
1250C22—441no—
1251C22—441no—
1252C22C22×D4×D1111yescharacteristic
1253C22C22×D4×D1111yescharacteristic
1254C22C2×#41×D1111yescharacteristic
1255C22C2×#41×D1111yescharacteristic
1256C22C2×#41×D1111yescharacteristic
1257C22D11×H(5,𝔽2)11yescharacteristic
1258C22D11×2−1+411yescharacteristic
1259C4—22no—
1260C4—22no—
1261C4—22no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—41no—
1266C4—41no—
1267C4—114no—
1268C4—222no—
1269C4—222no—
1270C4—222no—
1271C4—442no—
1272C4—442no—
1273C4—442no—
1274C4—441no—
1275C4—441no—
1276C4D11×#12314yescomplemented
1277C2—42no—
1278C2—44no—
1279C2—118no—
1280C2—442no—
1281C2—444no—
1282C2C2×D11×#12311yescharacteristic
1283C2D11×#53211yescharacteristic
1284C2D11×#54211yescharacteristic
1285C2D42×D1111yescharacteristic
1286C2D11×#54711yescharacteristic
1287C2D11×#54711yescharacteristic
1288C2D11×#55311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2422C2
prime radicalC2×D11×#121C2
hypercenter#2422D11
hypocenterC11C2×#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2422

Complements

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

NH ≅ G/Ntype
1. C2×D11×#123C2semidirect
3. C2×C4×D4×D11C2semidirect
4. #13072133C2semidirect
5. #13072132C2semidirect
6. #13072131C2semidirect
7. #13072130C2semidirect
8. #13072129C2semidirect
9. #13072128C2semidirect
10. #13072127C2semidirect
11. #13072126C2semidirect
12. #13072125C2semidirect
13. #13072124C2semidirect
14. #13072123C2semidirect
15. D11×#397C2semidirect
16. D11×#394C2semidirect
17. D11×#390C2semidirect
18. D11×#389C2semidirect
19. D11×#385C2semidirect
20. D11×#384C2semidirect
21. D11×#380C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2422C2semidirect
28. C2×C11×#123C22semidirect
30. C2×C4×D4×C11C22semidirect
33. C2×#66988C22semidirect
34. C2×D4×Dic11C22semidirect
36. C2×#66982C22semidirect
37. C2×C4×C22⋊D11C22semidirect
42. C2×#66947C22semidirect
43. C2×#66947C22semidirect
44. C2×#66946C22semidirect
51. C2×#66939C22semidirect
53. C2×#66936C22semidirect
54. C2×#66936C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
63. C2×C4×D44C22semidirect
66. C11×#397C22semidirect
67. C11×#394C22semidirect
68. C11×#390C22semidirect
69. C11×#389C22semidirect
70. C11×#385C22semidirect
71. C11×#384C22semidirect
72. C11×#380C22semidirect
73. C4×C11×C22⋊C4C22semidirect
74. #10622835C22semidirect
75. #10622834C22semidirect
76. #10622825C22semidirect
77. #10622823C22semidirect
78. C4×C22⋊Dic11C22semidirect
79. #10622606C22semidirect
80. #10622604C22semidirect
81. #10622602C22semidirect
82. #10622602C22semidirect
83. #10622601C22semidirect
84. #10622600C22semidirect
85. #10622600C22semidirect
86. #10622598C22semidirect
87. #10622589C22semidirect
88. #10622589C22semidirect
89. #10622589C22semidirect
90. #10622589C22semidirect
91. #10622586C22semidirect
92. #10622585C22semidirect
93. #10622574C22semidirect
94. #10622574C22semidirect
95. #10622572C22semidirect
96. #10622572C22semidirect
97. #10622570C22semidirect
98. #10622570C22semidirect
99. #10622566C22semidirect
100. #10622565C22semidirect
101. #10622565C22semidirect
102. #10622563C22semidirect
103. #10622559C22semidirect
104. #10622555C22semidirect
105. C22⋊C4×Dic11C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. #10622552C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. #10622548C22semidirect
111. #10622541C22semidirect
112. #10622288C22semidirect
113. #10622288C22semidirect
114. #10622287C22semidirect
115. #10622285C22semidirect
116. #10622281C22semidirect
117. #10622281C22semidirect
118. #10622280C22semidirect
119. #10622279C22semidirect
120. #10622279C22semidirect
125. #10622260C22semidirect
252. C22⋊C4×D11D4semidirect
398. C11×C22⋊C4C2×D4semidirect
407. C22⋊Dic11C2×D4semidirect
420. (C2×D11)⋊C4C2×D4semidirect
421. (C2×D11)⋊C4C2×D4semidirect
457. #2422D11direct (N × H)
593. C4×D11#123semidirect
606. C2×#123C2×D11semidirect
620. C2×C4×D4C2×D11semidirect
643. #397C2×D11semidirect
651. #394C2×D11semidirect
657. #390C2×D11semidirect
663. #389C2×D11semidirect
671. #385C2×D11semidirect
677. #384C2×D11semidirect
683. #380C2×D11semidirect
691. C4×C22⋊C4C2×D11semidirect
748. C4×C11C2×#123semidirect
757. Dic11C2×#123semidirect
915. D11#2422direct (N × H)
1077. C22⋊C4D4×D11semidirect
1086. C11C2×#2422semidirect
1276. C4D11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1232
C2×D11×#1212
C2×C4×D4×D112
#130721332
#130721322
#130721312
#130721302
#130721292
#130721282
#130721272
#130721262
#130721252
#130721242
#130721232
D11×#3972
D11×#3942
D11×#3902
D11×#3892
D11×#3852
D11×#3842
D11×#3802
C4×C22⋊C4×D112
C11×#24222
C2×#242211