Finite Group Databasebeta

← D11×#2661 #14920322

Subgroups — D11×#2661 #14920322

Order 2816.

3434 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#123C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13074751C211yesmaximal, characteristic, complemented
4#13074750C211yesmaximal, characteristic, complemented
5#13074749C211yesmaximal, characteristic, complemented
6#13074748C212yesmaximal, complemented
7#13074747C211yesmaximal, characteristic, complemented
8#13074746C212yesmaximal, complemented
9#13074745C211yesmaximal, characteristic, complemented
10#13074744C211yesmaximal, characteristic, complemented
11#13074743C212yesmaximal, complemented
12#13074742C211yesmaximal, characteristic, complemented
13#13074741C212yesmaximal, complemented
14D11×#398C211yesmaximal, characteristic, complemented
15D11×#397C211yesmaximal, characteristic, complemented
16D11×#394C212yesmaximal, complemented
17D11×#394C211yesmaximal, characteristic, complemented
18D11×#392C212yesmaximal, complemented
19D11×#392C211yesmaximal, characteristic, complemented
20D11×#390C212yesmaximal, complemented
21D11×#388C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2661C211yesmaximal, characteristic, complemented
24C22×D4×D11C2212yes—
25C22×D4×D11C2211yescharacteristic
26C22×D4×D11C2212yes—
27C22×D4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C2×C11×#123C2211yescharacteristic, complemented
30C2×C11×#121C2211yescharacteristic, complemented
31C2×#66992C2212yescomplemented
32C2×#66991C2211yescharacteristic, complemented
33C2×#66988C2211yescharacteristic, complemented
34C2×#66983C2211yescharacteristic, complemented
35C2×#66982C2211yescharacteristic, complemented
36D11×#123—28no—
37D11×#121—28no—
38C2×#66948C2211yescharacteristic, complemented
39C2×#66947C2211yescharacteristic, complemented
40C2×#66947C2211yescharacteristic, complemented
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2212yes—
45C2×#66939C2211yescharacteristic, complemented
46C2×#66937C2212yescomplemented
47C2×#66936C2211yescharacteristic, complemented
48C2×#66936C2211yescharacteristic, complemented
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2212yes—
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2212yes—
56C2×C22⋊C4×D11C2212yes—
57C2×C22⋊C4×D11C2212yes—
58C2×C42×D11C2212yes—
59C11×#398C2211yescharacteristic, complemented
60C11×#397C2211yescharacteristic, complemented
61C11×#394C2212yescomplemented
62C11×#394C2211yescharacteristic, complemented
63C11×#392C2212yescomplemented
64C11×#392C2211yescharacteristic, complemented
65C11×#390C2212yescomplemented
66C11×#388C2212yescomplemented
67C4×C11×C22⋊C4C2211yescharacteristic, complemented
68#10622836C2212yescomplemented
69#10622836C2212yescomplemented
70#10622836C2212yescomplemented
71#10622836C2211yescharacteristic, complemented
72#10622836C2212yescomplemented
73#10622835C2212yescomplemented
74#10622835C2211yescharacteristic, complemented
75#10622834C2212yescomplemented
76C4×C22⋊Dic11C2211yescharacteristic, complemented
77#10622606C2211yescharacteristic, complemented
78#10622604C2211yescharacteristic, complemented
79#10622604C2212yescomplemented
80#10622603C2212yescomplemented
81#10622601C2212yescomplemented
82#10622597C2212yescomplemented
83#10622596C2211yescharacteristic, complemented
84#10622593C2211yescharacteristic, complemented
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622574C2212yescomplemented
88#10622573C2212yescomplemented
89#10622573C2212yescomplemented
90#10622573C2211yescharacteristic, complemented
91#10622573C2212yescomplemented
92#10622573C2212yescomplemented
93#10622572C2212yescomplemented
94#10622572C2212yescomplemented
95#10622572C2212yescomplemented
96#10622570C2212yescomplemented
97#10622570C2212yescomplemented
98#10622570C2212yescomplemented
99#10622570C2212yescomplemented
100#10622566C2211yescharacteristic, complemented
101#10622565C2212yescomplemented
102#10622564C2212yescomplemented
103#10622558C2212yescomplemented
104#10622557C2212yescomplemented
105C22⋊C4×Dic11C2212yescomplemented
106#10622553C2212yescomplemented
107#10622552C2212yescomplemented
108C4×(C2×D11)⋊C4C2212yescomplemented
109#10622288C2212yescomplemented
110#10622287C2211yescharacteristic, complemented
111#10622285C2211yescharacteristic, complemented
112#10622285C2212yescomplemented
113#10622284C2211yescharacteristic, complemented
114#10622284C2212yescomplemented
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622279C2211yescharacteristic, complemented
118#10622279C2211yescharacteristic, complemented
119D11×#95C2211yescharacteristic
120D11×#95C2211yescharacteristic
121D11×#95C2212yes—
122D11×#95C2212yes—
123#10622274C2211yescharacteristic, complemented
124#10622270C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2312yes—
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C23×Dic11C2311yescharacteristic
141C2×D4×D11—28no—
142C2×D4×D11—24no—
143C2×D4×D11—24no—
144C2×D4×D11—28no—
145C2×D4×D11—44no—
146C2×D4×D11—44no—
147C2×D4×D11—44no—
148C2×D4×D11—44no—
149C2×D4×D11—44no—
150C2×D4×D11—44no—
151C22×D44C2312yes—
152C22×D44C2311yescharacteristic
153C22×D44C2311yescharacteristic
154C22×D44C2312yes—
155C22×C4×D11—44no—
156C22×C4×D11D418yescomplemented
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2312yes—
165C22×C4×D11C2311yescharacteristic
166C22×C4×D11C2311yescharacteristic
167C11×#123—24no—
168C11×#121—24no—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C42×C11C2312yes—
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192#66992—28no—
193#66991—24no—
194#66988—24no—
195#66983—24no—
196#66982—24no—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2311yescharacteristic
217C2×C4⋊Dic11C2311yescharacteristic
218C2×C4⋊Dic11C2312yes—
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229#66948—24no—
230#66947—24no—
231#66947—24no—
232C4⋊C4×D11—24no—
233C4⋊C4×D11—24no—
234C4⋊C4×D11—24no—
235C4⋊C4×D11—44no—
236#66939—24no—
237#66937—28no—
238#66936—24no—
239#66936—24no—
240C22⋊C4×D11—24no—
241C22⋊C4×D11—28no—
242C22⋊C4×D11—24no—
243C22⋊C4×D11—24no—
244C22⋊C4×D11—28no—
245C22⋊C4×D11—28no—
246C22⋊C4×D11—44no—
247C22⋊C4×D11—44no—
248C22⋊C4×D11—44no—
249C42×D11—44no—
250C11×#95C2312yes—
251C11×#95C2311yescharacteristic
252C11×#95C2311yescharacteristic
253C11×#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C2×#2661—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2412yes—
267C24×C11C2411yescharacteristic
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—24no—
276C23×D11—24no—
277C23×D11—22no—
278C23×D11—24no—
279C23×D11—24no—
280C23×D11—24no—
281C23×D11—24no—
282C23×D11—24no—
283C23×D11—22no—
284C23×D11C2×D414yes—
285C23×D11C2411yescharacteristic
286C23×D11C2412yes—
287C23×D11C2411yescharacteristic
288C23×D11C2411yescharacteristic
289C2×D4×C11—22no—
290C2×D4×C11—24no—
291C2×D4×C11—22no—
292C2×D4×C11—24no—
293C2×D4×C11—42no—
294C2×D4×C11—42no—
295C2×D4×C11—42no—
296C2×D4×C11—42no—
297C2×D4×C11—42no—
298C2×D4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11C2×D414yescomplemented
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11—42no—
325C2×C22⋊D11—42no—
326C2×C22⋊D11—42no—
327C2×C22⋊D11—42no—
328C22×Dic11—42no—
329C22×Dic11C2×D414yescomplemented
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2412yes—
338D4×D11—416no—
339D4×D11—432no—
340D4×D11—416no—
341D4×D11—432no—
342C2×D44—24no—
343C2×D44—22no—
344C2×D44—22no—
345C2×D44—24no—
346C2×D44—42no—
347C2×D44—42no—
348C2×D44—42no—
349C2×D44—42no—
350C2×D44—42no—
351C2×D44—42no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—24no—
355C2×C4×D11—22no—
356C2×C4×D11—24no—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—24no—
360C2×C4×D11—24no—
361C2×C4×D11—24no—
362C2×C4×D11—24no—
363C2×C4×D11—22no—
364C2×C4×D11—24no—
365C2×C4×D11—24no—
366C2×C4×D11—24no—
367C2×C4×D11—22no—
368C2×C4×D11—24no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—416no—
372C2×C4×D11C2×D414yes—
373C2×C4×D11C2×D414yes—
374C2×C4×D11C2×D414yescomplemented
375C2×C4×D11C2×D414yescomplemented
376C2×C4×D11#4118yes—
377C11×C4⋊C4—22no—
378C11×C4⋊C4—22no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—42no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—22no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—24no—
385C11×C22⋊C4—24no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—42no—
388C11×C22⋊C4—42no—
389C11×C22⋊C4—42no—
390C42×C11—42no—
391C22⋊Dic11—22no—
392C22⋊Dic11—22no—
393C22⋊Dic11—24no—
394C22⋊Dic11—24no—
395C22⋊Dic11—24no—
396C22⋊Dic11—22no—
397C22⋊Dic11—42no—
398C22⋊Dic11—42no—
399C22⋊Dic11—42no—
400(C2×D11)⋊C4—22no—
401(C2×D11)⋊C4—22no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—22no—
406(C2×D11)⋊C4—22no—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—22no—
409(C2×D11)⋊C4—22no—
410(C2×D11)⋊C4—24no—
411(C2×D11)⋊C4—24no—
412(C2×D11)⋊C4—42no—
413(C2×D11)⋊C4—42no—
414(C2×D11)⋊C4—42no—
415(C2×D11)⋊C4—42no—
416(C2×D11)⋊C4—42no—
417(C2×D11)⋊C4—42no—
418C4⋊Dic11—22no—
419C4⋊Dic11—22no—
420C4⋊Dic11—22no—
421C4⋊Dic11—42no—
422Dic11⋊C4—24no—
423Dic11⋊C4—22no—
424Dic11⋊C4—22no—
425Dic11⋊C4—22no—
426Dic11⋊C4—22no—
427Dic11⋊C4—42no—
428Dic11⋊C4—42no—
429C4×Dic11—42no—
430C4×Dic11—42no—
431C4×Dic11—42no—
432C22×#123—111no—
433C22×#121—111no—
434#2661—111no—
435#2661—111no—
436#2661—112no—
437#2661—111no—
438#2661—112no—
439#2661—111no—
440#2661—112no—
441#2661—112no—
442#2661—111no—
443#2661—111no—
444#2661—111no—
445#2661D1111yescharacteristic, direct product factor
446C2×#398—111no—
447C2×#397—111no—
448C2×#394—112no—
449C2×#394—111no—
450C2×#392—112no—
451C2×#392—111no—
452C2×#390—112no—
453C2×#388—112no—
454C2×C4×C22⋊C4—111no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—21no—
458C23×C11—21no—
459C23×C11—21no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11—22no—
464C23×C11—21no—
465C23×C11—22no—
466C23×C11—22no—
467C23×C11—22no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—21no—
471C23×C11C22×D412yes—
472C23×C11C2511yescharacteristic
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—28no—
478C22×D11—28no—
479C22×D11—28no—
480C22×D11—21no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—22no—
490C22×D11—21no—
491C22×D11—22no—
492C22×D11—48no—
493C22×D11—48no—
494C22×D11—44no—
495C22×D11—48no—
496C22×D11—44no—
497C22×D11—48no—
498C22×D11—48no—
499C22×D11—44no—
500C22×D11—48no—
501C22×D11—48no—
502C22×D11—48no—
503C22×D11—48no—
504C22×D11—48no—
505C22×D11—48no—
506C22×D11C22×D412yes—
507C22×D11C22×D412yes—
508C22×D11C2×#4114yes—
509C22×D11H(5,𝔽2)14yes—
510C22×D11H(5,𝔽2)12yes—
511C22×D11H(5,𝔽2)12yes—
512D4×C11—44no—
513D4×C11—48no—
514D4×C11—44no—
515D4×C11—48no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—21no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—44no—
534C2×C4×C11C22×D412yes—
535C2×C4×C11C22×D412yes—
536C2×C4×C11C2×#4114yes—
537C22⋊D11—48no—
538C22⋊D11—48no—
539C22⋊D11—48no—
540C22⋊D11—44no—
541C22⋊D11—48no—
542C22⋊D11—44no—
543C22⋊D11—48no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—21no—
549C2×Dic11—21no—
550C2×Dic11—21no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—21no—
556C2×Dic11—22no—
557C2×Dic11—21no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—44no—
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D412yes—
564C2×Dic11C2×#4114yes—
565D44—44no—
566D44—48no—
567D44—44no—
568D44—48no—
569C4×D11—28no—
570C4×D11—28no—
571C4×D11—216no—
572C4×D11—44no—
573C4×D11—44no—
574C4×D11—44no—
575C4×D11—44no—
576C4×D11—44no—
577C4×D11—48no—
578C4×D11—48no—
579C23×D4—111no—
580C23×D4—112no—
581C23×D4—111no—
582C23×D4—112no—
583C24×C4—111no—
584C2×#123—111no—
585C2×#123—111no—
586C2×#123—111no—
587C2×#123—111no—
588C2×#123—111no—
589C2×#123—111no—
590C2×#123—111no—
591C2×#123—228no—
592C2×#123C2×D1111yescharacteristic, complemented
593C2×#121—111no—
594C2×#121—112no—
595C2×#121—111no—
596C2×#121—111no—
597C2×#121—112no—
598C2×#121—228no—
599C2×#121C2×D1111yescharacteristic, complemented
600C22×C4⋊C4—111no—
601C22×C4⋊C4—111no—
602C22×C4⋊C4—111no—
603C22×C4⋊C4—112no—
604C22×C22⋊C4—112no—
605C22×C22⋊C4—112no—
606C22×C22⋊C4—111no—
607C22×C22⋊C4—111no—
608C22×C22⋊C4—112no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—112no—
611C22×C22⋊C4—112no—
612C22×C22⋊C4—112no—
613C22×C42—112no—
614#398—111no—
615#398—111no—
616#398—112no—
617#398—112no—
618#398—111no—
619#398C2×D1111yescharacteristic, complemented
620#397—111no—
621#397—112no—
622#397—111no—
623#397—111no—
624#397—112no—
625#397C2×D1111yescharacteristic, complemented
626#394—111no—
627#394—112no—
628#394—111no—
629#394—112no—
630#394—112no—
631#394—112no—
632#394—112no—
633#394—112no—
634#394—112no—
635#394—112no—
636#394—111no—
637#394—112no—
638#394C2×D1111yescharacteristic, complemented
639#394C2×D1112yescomplemented
640#392—112no—
641#392—111no—
642#392—112no—
643#392—112no—
644#392—112no—
645#392—112no—
646#392—111no—
647#392—112no—
648#392—112no—
649#392—112no—
650#392—111no—
651#392—112no—
652#392C2×D1111yescharacteristic, complemented
653#392C2×D1112yescomplemented
654#390—112no—
655#390—112no—
656#390—112no—
657#390—112no—
658#390—112no—
659#390—112no—
660#390—112no—
661#390C2×D1112yescomplemented
662#388—112no—
663#388—112no—
664#388—112no—
665#388—112no—
666#388—112no—
667#388—112no—
668#388—112no—
669#388C2×D1112yescomplemented
670C4×C22⋊C4—111no—
671C4×C22⋊C4—112no—
672C4×C22⋊C4—112no—
673C4×C22⋊C4—111no—
674C4×C22⋊C4—111no—
675C4×C22⋊C4C2×D1111yescharacteristic, complemented
676C2×#95—111no—
677C2×#95—112no—
678C2×#95—111no—
679C2×#95—112no—
680C22×C11—22no—
681C22×C11—22no—
682C22×C11—22no—
683C22×C11—42no—
684C22×C11—42no—
685C22×C11—41no—
686C22×C11—42no—
687C22×C11—42no—
688C22×C11—41no—
689C22×C11—42no—
690C22×C11—41no—
691C22×C11—42no—
692C22×C11—42no—
693C22×C11—42no—
694C22×C11—42no—
695C22×C11—42no—
696C22×C11—42no—
697C22×C11C23×D411yescharacteristic
698C22×C11C22×#4112yes—
699C22×C11C2×H(5,𝔽2)12yes—
700C22×C11C2×H(5,𝔽2)11yescharacteristic
701C22×C11C2×H(5,𝔽2)11yescharacteristic
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—416no—
708C2×D11—41no—
709C2×D11—42no—
710C2×D11—41no—
711C2×D11—42no—
712C2×D11—41no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—816no—
721C2×D11—88no—
722C2×D11#53214yes—
723C2×D11#53414yes—
724C2×D11#53514yes—
725C2×D11#53818yes—
726C2×D11#54018yes—
727C4×C11—22no—
728C4×C11—22no—
729C4×C11—24no—
730C4×C11—41no—
731C4×C11—41no—
732C4×C11—42no—
733C4×C11—41no—
734C4×C11—42no—
735Dic11—22no—
736Dic11—22no—
737Dic11—24no—
738Dic11—41no—
739Dic11—41no—
740Dic11—41no—
741Dic11—42no—
742Dic11—42no—
743C25—111no—
744C25—111no—
745C25—112no—
746C22×D4—112no—
747C22×D4—112no—
748C22×D4—112no—
749C22×D4—111no—
750C22×D4—111no—
751C22×D4—112no—
752C22×D4—112no—
753C22×D4—112no—
754C22×D4—111no—
755C22×D4—111no—
756C22×D4—112no—
757C22×D4—224no—
758C22×D4—228no—
759C22×D4—228no—
760C22×D4—224no—
761C22×D4—444no—
762C22×D4—444no—
763C22×D4—444no—
764C22×D4—444no—
765C22×D4—444no—
766C22×D4—444no—
767C22×D4C22×D1112yes—
768C22×D4C22×D1111yescharacteristic
769C22×D4C22×D1111yescharacteristic
770C22×D4C22×D1112yes—
771C23×C4—111no—
772C23×C4—111no—
773C23×C4—112no—
774C23×C4—111no—
775C23×C4—118no—
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—111no—
779C23×C4—111no—
780C23×C4—112no—
781C23×C4—112no—
782C23×C4—111no—
783C23×C4—444no—
784C23×C4C22×D1111yescharacteristic
785#123—24no—
786#123—224no—
787#123—224no—
788#123—224no—
789#123—224no—
790#123—224no—
791#123—224no—
792#123—224no—
793#121—24no—
794#121—228no—
795#121—224no—
796#121—224no—
797#121—228no—
798#121—224no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—111no—
802C2×C4⋊C4—111no—
803C2×C4⋊C4—111no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—111no—
806C2×C4⋊C4—111no—
807C2×C4⋊C4—112no—
808C2×C4⋊C4—112no—
809C2×C4⋊C4—112no—
810C2×C4⋊C4—224no—
811C2×C4⋊C4—224no—
812C2×C4⋊C4—224no—
813C2×C4⋊C4—444no—
814C2×C4⋊C4C22×D1111yescharacteristic
815C2×C4⋊C4C22×D1111yescharacteristic
816C2×C4⋊C4C22×D1111yescharacteristic
817C2×C4⋊C4C22×D1112yes—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—111no—
820C2×C22⋊C4—111no—
821C2×C22⋊C4—111no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—111no—
827C2×C22⋊C4—111no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—111no—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—111no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—112no—
841C2×C22⋊C4—112no—
842C2×C22⋊C4—112no—
843C2×C22⋊C4—112no—
844C2×C22⋊C4—112no—
845C2×C22⋊C4—228no—
846C2×C22⋊C4—224no—
847C2×C22⋊C4—224no—
848C2×C22⋊C4—228no—
849C2×C22⋊C4—228no—
850C2×C22⋊C4—224no—
851C2×C22⋊C4—444no—
852C2×C22⋊C4—444no—
853C2×C22⋊C4—444no—
854C2×C22⋊C4C22×D1112yes—
855C2×C22⋊C4C22×D1111yescharacteristic
856C2×C22⋊C4C22×D1111yescharacteristic
857C2×C22⋊C4C22×D1111yescharacteristic
858C2×C22⋊C4C22×D1112yes—
859C2×C22⋊C4C22×D1112yes—
860C2×C22⋊C4C22×D1112yes—
861C2×C22⋊C4C22×D1112yes—
862C2×C22⋊C4C22×D1112yes—
863C2×C42—112no—
864C2×C42—112no—
865C2×C42—112no—
866C2×C42—444no—
867C2×C42C22×D1112yes—
868#95—111no—
869#95—112no—
870#95—112no—
871#95—111no—
872#95—112no—
873#95—112no—
874#95—112no—
875#95—112no—
876#95—112no—
877#95—112no—
878#95C22×D1111yescharacteristic
879#95C22×D1111yescharacteristic
880#95C22×D1112yes—
881#95C22×D1112yes—
882C2×C11—42no—
883C2×C11—82no—
884C2×C11—81no—
885C2×C11C2×#53211yescharacteristic
886C2×C11C2×#53411yescharacteristic
887C2×C11C2×#53511yescharacteristic
888C2×C11C2×#53812yes—
889C2×C11C2×#54012yes—
890D11—42no—
891D11—81no—
892D11—82no—
893D11#266118yesdirect product factor
894C24—111no—
895C24—114no—
896C24—111no—
897C24—111no—
898C24—112no—
899C24—224no—
900C24—224no—
901C24—222no—
902C24—222no—
903C24—222no—
904C24—224no—
905C24—224no—
906C24—222no—
907C24—224no—
908C24—224no—
909C24—224no—
910C24—224no—
911C24—224no—
912C24—224no—
913C24—224no—
914C24—222no—
915C24C23×D1111yescharacteristic
916C24C23×D1112yes—
917C24C23×D1111yescharacteristic
918C2×D4—24no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—24no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—224no—
929C2×D4—222no—
930C2×D4—224no—
931C2×D4—224no—
932C2×D4—224no—
933C2×D4—224no—
934C2×D4—222no—
935C2×D4—224no—
936C2×D4—222no—
937C2×D4—222no—
938C2×D4—224no—
939C2×D4—442no—
940C2×D4—442no—
941C2×D4—442no—
942C2×D4—442no—
943C2×D4—442no—
944C2×D4—442no—
945C2×D4—4416no—
946C2×D4—4432no—
947C2×D4—442no—
948C2×D4—442no—
949C2×D4—442no—
950C2×D4—442no—
951C2×D4—442no—
952C2×D4—442no—
953C2×D4—442no—
954C2×D4—442no—
955C2×D4—442no—
956C2×D4—442no—
957C2×D4—442no—
958C2×D4—442no—
959C2×D4—4416no—
960C2×D4—4432no—
961C22×C4—42no—
962C22×C4—112no—
963C22×C4—111no—
964C22×C4—111no—
965C22×C4—114no—
966C22×C4—114no—
967C22×C4—114no—
968C22×C4—118no—
969C22×C4—114no—
970C22×C4—114no—
971C22×C4—112no—
972C22×C4—111no—
973C22×C4—112no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—224no—
977C22×C4—224no—
978C22×C4—224no—
979C22×C4—224no—
980C22×C4—224no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—224no—
984C22×C4—224no—
985C22×C4—224no—
986C22×C4—222no—
987C22×C4—224no—
988C22×C4—224no—
989C22×C4—224no—
990C22×C4—222no—
991C22×C4—222no—
992C22×C4—224no—
993C22×C4—442no—
994C22×C4—442no—
995C22×C4—4416no—
996C22×C4—442no—
997C22×C4D4×D1114yescomplemented
998C22×C4C23×D1112yes—
999C22×C4C23×D1111yescharacteristic
1000C22×C4C23×D1112yes—
1001C22×C4C23×D1111yescharacteristic
1002C22×C4C23×D1111yescharacteristic
1003C22×C4C23×D1111yescharacteristic
1004C22×C4C23×D1111yescharacteristic
1005C22×C4C23×D1112yes—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—42no—
1010C4⋊C4—224no—
1011C4⋊C4—222no—
1012C4⋊C4—222no—
1013C4⋊C4—222no—
1014C4⋊C4—222no—
1015C4⋊C4—222no—
1016C4⋊C4—222no—
1017C4⋊C4—222no—
1018C4⋊C4—442no—
1019C4⋊C4—442no—
1020C4⋊C4—442no—
1021C22⋊C4—22no—
1022C22⋊C4—24no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—224no—
1031C22⋊C4—222no—
1032C22⋊C4—222no—
1033C22⋊C4—224no—
1034C22⋊C4—224no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—224no—
1038C22⋊C4—222no—
1039C22⋊C4—222no—
1040C22⋊C4—224no—
1041C22⋊C4—224no—
1042C22⋊C4—222no—
1043C22⋊C4—224no—
1044C22⋊C4—222no—
1045C22⋊C4—222no—
1046C22⋊C4—224no—
1047C22⋊C4—224no—
1048C22⋊C4—442no—
1049C22⋊C4—442no—
1050C22⋊C4—442no—
1051C22⋊C4—442no—
1052C22⋊C4—442no—
1053C22⋊C4—442no—
1054C22⋊C4—442no—
1055C22⋊C4—442no—
1056C22⋊C4—442no—
1057C42—42no—
1058C42—442no—
1059C42—442no—
1060C42—442no—
1061C11C2×#266111yescharacteristic, complemented, Sylow
1062C23—22no—
1063C23—22no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—21no—
1078C23—112no—
1079C23—114no—
1080C23—114no—
1081C23—112no—
1082C23—112no—
1083C23—112no—
1084C23—228no—
1085C23—228no—
1086C23—228no—
1087C23—222no—
1088C23—222no—
1089C23—221no—
1090C23—221no—
1091C23—221no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—221no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
1100C23—222no—
1101C23—222no—
1102C23—221no—
1103C23—448no—
1104C23—448no—
1105C23—448no—
1106C23—444no—
1107C23—448no—
1108C23—448no—
1109C23—448no—
1110C23—444no—
1111C23—448no—
1112C23—444no—
1113C23—448no—
1114C23—448no—
1115C23—448no—
1116C23—448no—
1117C23C2×D4×D1112yes—
1118C23C24×D1111yescharacteristic
1119D4—44no—
1120D4—48no—
1121D4—44no—
1122D4—48no—
1123D4—444no—
1124D4—448no—
1125D4—444no—
1126D4—448no—
1127D4—448no—
1128D4—448no—
1129D4—448no—
1130D4—444no—
1131D4—448no—
1132D4—444no—
1133D4—448no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—44no—
1152C2×C4—112no—
1153C2×C4—112no—
1154C2×C4—114no—
1155C2×C4—228no—
1156C2×C4—228no—
1157C2×C4—2216no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—222no—
1165C2×C4—221no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—222no—
1169C2×C4—221no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—221no—
1174C2×C4—222no—
1175C2×C4—444no—
1176C2×C4—444no—
1177C2×C4—444no—
1178C2×C4—448no—
1179C2×C4—444no—
1180C2×C4—444no—
1181C2×C4—448no—
1182C2×C4—444no—
1183C2×C4C2×D4×D1112yes—
1184C2×C4C2×D4×D1112yes—
1185C2×C4#41×D1114yes—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—42no—
1190C22—42no—
1191C22—41no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—42no—
1196C22—41no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—114no—
1204C22—114no—
1205C22—114no—
1206C22—118no—
1207C22—118no—
1208C22—222no—
1209C22—222no—
1210C22—222no—
1211C22—4416no—
1212C22—442no—
1213C22—442no—
1214C22—441no—
1215C22—442no—
1216C22—442no—
1217C22—441no—
1218C22—442no—
1219C22—441no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—442no—
1226C22—8816no—
1227C22—888no—
1228C22C22×D4×D1111yescharacteristic
1229C22C2×#41×D1112yes—
1230C22D11×H(5,𝔽2)12yes—
1231C22D11×H(5,𝔽2)11yescharacteristic
1232C22D11×H(5,𝔽2)11yescharacteristic
1233C4—22no—
1234C4—22no—
1235C4—24no—
1236C4—41no—
1237C4—41no—
1238C4—42no—
1239C4—41no—
1240C4—42no—
1241C4—222no—
1242C4—222no—
1243C4—224no—
1244C4—441no—
1245C4—441no—
1246C4—442no—
1247C4—441no—
1248C4—442no—
1249C2—42no—
1250C2—82no—
1251C2—81no—
1252C2—118no—
1253C2—442no—
1254C2—882no—
1255C2—881no—
1256C2D11×#53211yescharacteristic
1257C2D11×#53411yescharacteristic
1258C2D11×#53511yescharacteristic
1259C2D11×#53812yes—
1260C2D11×#54012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2661C2
hypercenter#2661D11
hypocenterC11C2×#2661
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2661

Complements

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

NH ≅ G/Ntype
1. C2×D11×#123C2semidirect
2. C2×D11×#121C2semidirect
3. #13074751C2semidirect
4. #13074750C2semidirect
5. #13074749C2semidirect
6. #13074748C2semidirect
7. #13074747C2semidirect
8. #13074746C2semidirect
9. #13074745C2semidirect
10. #13074744C2semidirect
11. #13074743C2semidirect
12. #13074742C2semidirect
13. #13074741C2semidirect
14. D11×#398C2semidirect
15. D11×#397C2semidirect
16. D11×#394C2semidirect
17. D11×#394C2semidirect
18. D11×#392C2semidirect
19. D11×#392C2semidirect
20. D11×#390C2semidirect
21. D11×#388C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2661C2semidirect
29. C2×C11×#123C22semidirect
30. C2×C11×#121C22semidirect
31. C2×#66992C22semidirect
32. C2×#66991C22semidirect
33. C2×#66988C22semidirect
34. C2×#66983C22semidirect
35. C2×#66982C22semidirect
38. C2×#66948C22semidirect
39. C2×#66947C22semidirect
40. C2×#66947C22semidirect
45. C2×#66939C22semidirect
46. C2×#66937C22semidirect
47. C2×#66936C22semidirect
48. C2×#66936C22semidirect
59. C11×#398C22semidirect
60. C11×#397C22semidirect
61. C11×#394C22semidirect
62. C11×#394C22semidirect
63. C11×#392C22semidirect
64. C11×#392C22semidirect
65. C11×#390C22semidirect
66. C11×#388C22semidirect
67. C4×C11×C22⋊C4C22semidirect
68. #10622836C22semidirect
69. #10622836C22semidirect
70. #10622836C22semidirect
71. #10622836C22semidirect
72. #10622836C22semidirect
73. #10622835C22semidirect
74. #10622835C22semidirect
75. #10622834C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. #10622606C22semidirect
78. #10622604C22semidirect
79. #10622604C22semidirect
80. #10622603C22semidirect
81. #10622601C22semidirect
82. #10622597C22semidirect
83. #10622596C22semidirect
84. #10622593C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
87. #10622574C22semidirect
88. #10622573C22semidirect
89. #10622573C22semidirect
90. #10622573C22semidirect
91. #10622573C22semidirect
92. #10622573C22semidirect
93. #10622572C22semidirect
94. #10622572C22semidirect
95. #10622572C22semidirect
96. #10622570C22semidirect
97. #10622570C22semidirect
98. #10622570C22semidirect
99. #10622570C22semidirect
100. #10622566C22semidirect
101. #10622565C22semidirect
102. #10622564C22semidirect
103. #10622558C22semidirect
104. #10622557C22semidirect
105. C22⋊C4×Dic11C22semidirect
106. #10622553C22semidirect
107. #10622552C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. #10622288C22semidirect
110. #10622287C22semidirect
111. #10622285C22semidirect
112. #10622285C22semidirect
113. #10622284C22semidirect
114. #10622284C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
123. #10622274C22semidirect
124. #10622270C22semidirect
156. C22×C4×D11D4semidirect
300. C22×C4×C11C2×D4semidirect
329. C22×Dic11C2×D4semidirect
374. C2×C4×D11C2×D4semidirect
375. C2×C4×D11C2×D4semidirect
445. #2661D11direct (N × H)
592. C2×#123C2×D11semidirect
599. C2×#121C2×D11semidirect
619. #398C2×D11semidirect
625. #397C2×D11semidirect
638. #394C2×D11semidirect
639. #394C2×D11semidirect
652. #392C2×D11semidirect
653. #392C2×D11semidirect
661. #390C2×D11semidirect
669. #388C2×D11semidirect
675. C4×C22⋊C4C2×D11semidirect
893. D11#2661direct (N × H)
997. C22×C4D4×D11semidirect
1061. C11C2×#2661semidirect

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
#130747512
#130747502
#130747492
#130747482
#130747472
#130747462
#130747452
#130747442
#130747432
#130747422
#130747412
D11×#3982
D11×#3972
D11×#3942
D11×#3922
D11×#3902
D11×#3882
C4×C22⋊C4×D112
C11×#26612
C2×#266111