Finite Group Databasebeta

← D11×#2603 #14924409

Subgroups — D11×#2603 #14924409

Order 2816.

3330 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#126C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074246C211yesmaximal, characteristic, complemented
4#13074245C211yesmaximal, characteristic, complemented
5#13074244C211yesmaximal, characteristic, complemented
6#13074243C211yesmaximal, characteristic, complemented
7#13074242C212yesmaximal, complemented
8#13074241C212yesmaximal, complemented
9#13074240C212yesmaximal, complemented
10#13074239C212yesmaximal, complemented
11#13074238C211yesmaximal, characteristic, complemented
12#13074237C211yesmaximal, characteristic, complemented
13#13074236C211yesmaximal, characteristic, complemented
14D11×#398C211yesmaximal, characteristic, complemented
15D11×#397C211yesmaximal, characteristic, complemented
16D11×#394C211yesmaximal, characteristic, complemented
17D11×#392C211yesmaximal, characteristic
18D11×#390C212yesmaximal, complemented
19D11×#388C212yesmaximal, complemented
20D11×#386C212yesmaximal, complemented
21D11×#385C212yesmaximal, complemented
22D11×#376C211yesmaximal, characteristic, complemented
23C11×#2603C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C23×C4×D11C2212yes—
27C2×C11×#126C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×D4×Dic11C2211yescharacteristic, complemented
30C2×C4×C22⋊D11C2212yescomplemented
31D11×#126—28no—
32C4×D4×D11—28no—
33C2×#66951C2211yescharacteristic, complemented
34C2×#66951C2211yescharacteristic, complemented
35C2×#66951C2211yescharacteristic, complemented
36C2×#66946C2211yescharacteristic, complemented
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2212yes—
42C2×(C22⋊D11)⋊C4C2212yescomplemented
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×C22⋊C4×D11C2211yescharacteristic
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×#66932C2211yescharacteristic, complemented
52C2×#66932C2211yescharacteristic, complemented
53C2×#66932C2211yescharacteristic, complemented
54C2×#66929C2211yescharacteristic, complemented
55C2×C4×D44C2211yescharacteristic, complemented
56C2×C42×D11C2212yes—
57C2×C42×D11C2211yescharacteristic
58C11×#398C2211yescharacteristic, complemented
59C11×#397C2211yescharacteristic, complemented
60C11×#394C2211yescharacteristic, complemented
61C11×#392C2211yescharacteristic
62C11×#390C2212yescomplemented
63C11×#388C2212yescomplemented
64C11×#386C2212yescomplemented
65C11×#385C2212yescomplemented
66C11×#376C2211yescharacteristic, complemented
67#10622836C2211yescharacteristic
68#10622836C2212yes—
69#10622835C2211yescharacteristic, complemented
70#10622834C2212yescomplemented
71#10622833C2212yescomplemented
72#10622826C2212yescomplemented
73#10622823C2212yescomplemented
74#10622606C2211yescharacteristic, complemented
75#10622604C2211yescharacteristic, complemented
76#10622603C2212yescomplemented
77#10622602C2212yescomplemented
78#10622602C2212yescomplemented
79#10622601C2212yescomplemented
80#10622597C2212yescomplemented
81#10622596C2211yescharacteristic, complemented
82#10622593C2211yescharacteristic, complemented
83#10622574C2212yescomplemented
84#10622573C2212yes—
85#10622573C2211yescharacteristic
86#10622572C2212yescomplemented
87#10622571C2212yescomplemented
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622569C2212yescomplemented
93#10622569C2212yescomplemented
94#10622566C2211yescharacteristic, complemented
95#10622565C2212yescomplemented
96#10622564C2212yescomplemented
97#10622563C2212yescomplemented
98#10622559C2212yescomplemented
99#10622558C2212yescomplemented
100#10622557C2212yescomplemented
101#10622553C2212yescomplemented
102#10622552C2212yescomplemented
103#10622545C2211yescharacteristic, complemented
104#10622545C2212yescomplemented
105#10622288C2212yescomplemented
106#10622287C2211yescharacteristic, complemented
107#10622285C2211yescharacteristic, complemented
108#10622284C2211yescharacteristic
109#10622283C2212yescomplemented
110#10622282C2212yescomplemented
111#10622281C2212yescomplemented
112#10622281C2212yescomplemented
113#10622278C2212yescomplemented
114#10622278C2212yescomplemented
115D11×#95C2212yes—
116D11×#95C2211yescharacteristic
117D11×#95C2211yescharacteristic
118D11×#95C2212yes—
119D11×#95C2212yes—
120#10622274C2211yescharacteristic, complemented
121#10622270C2212yescomplemented
122#10622261C2211yescharacteristic, complemented
123#10622261C2211yescharacteristic, complemented
124#10622261C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C2×D4×D11—28no—
135C2×D4×D11—28no—
136C2×D4×D11—24no—
137C2×D4×D11—28no—
138C2×D4×D11—44no—
139C22×D44C2311yescharacteristic
140C22×D44C2312yes—
141C22×C4×D11—28no—
142C22×C4×D11—44no—
143C22×C4×D11—44no—
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C11×#126—24no—
156C4×D4×C11—24no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C42×C11C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180D4×Dic11—24no—
181C4×C22⋊D11—28no—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218#66951—24no—
219#66951—24no—
220#66951—24no—
221#66946—24no—
222C4⋊C4×D11—24no—
223C4⋊C4×D11—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—44no—
227(C22⋊D11)⋊C4—28no—
228C22⋊C4×D11—28no—
229C22⋊C4×D11—24no—
230C22⋊C4×D11—24no—
231C22⋊C4×D11—24no—
232C22⋊C4×D11—28no—
233C22⋊C4×D11—28no—
234C22⋊C4×D11—44no—
235C22⋊C4×D11—44no—
236#66932—24no—
237#66932—24no—
238#66932—24no—
239#66929—24no—
240C4×D44—24no—
241C42×D11—28no—
242C42×D11D418yescomplemented
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C2×#2603—111nomaximal, Sylow
262C24×C11C2411yescharacteristic
263C24×C11C2412yes—
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—24no—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—22no—
271C23×D11—24no—
272C23×D11—24no—
273C23×D11—22no—
274C23×D11—22no—
275C23×D11#4118yes—
276C23×D11C2411yescharacteristic
277C23×D11C2412yes—
278C23×D11C2411yescharacteristic
279C2×D4×C11—24no—
280C2×D4×C11—24no—
281C2×D4×C11—22no—
282C2×D4×C11—24no—
283C2×D4×C11—42no—
284C22×C4×C11—24no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C22×Dic11—24no—
306C22×Dic11—42no—
307C22×Dic11—42no—
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317D4×D11—232no—
318D4×D11—432no—
319C2×D44—24no—
320C2×D44—24no—
321C2×D44—22no—
322C2×D44—24no—
323C2×D44—42no—
324C2×C4×D11—24no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—432no—
350C2×C4×D11C2×D414yes—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11#4118yes—
354C11×C4⋊C4—22no—
355C11×C4⋊C4—22no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—42no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C42×C11—24no—
368C42×C11C2×D414yescomplemented
369C22⋊Dic11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—42no—
376C22⋊Dic11—42no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—42no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407C4×Dic11—24no—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11C2×D414yescomplemented
411C4×Dic11C2×D414yescomplemented
412C4×Dic11C2×D414yescomplemented
413C22×#126—111no—
414C22×C4×D4—111no—
415#2603—111no—
416#2603—111no—
417#2603—111no—
418#2603—111no—
419#2603—112no—
420#2603—112no—
421#2603—112no—
422#2603—112no—
423#2603—111no—
424#2603—111no—
425#2603—111no—
426#2603D1111yescharacteristic, direct product factor
427C2×#398—111no—
428C2×#397—111no—
429C2×#394—111no—
430C2×#392—111no—
431C2×#390—112no—
432C2×#388—112no—
433C2×#386—112no—
434C2×#385—112no—
435C2×#376—111no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11C2×#4114yes—
448C23×C11C2511yescharacteristic
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—216no—
456C22×D11—216no—
457C22×D11—216no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—48no—
464C22×D11—48no—
465C22×D11—48no—
466C22×D11—48no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11C22×D412yes—
473C22×D11C2×#4114yes—
474C22×D11C2×#4114yes—
475C22×D11C2×#4114yes—
476C22×D11H(5,𝔽2)12yes—
477C22×D11H(5,𝔽2)12yes—
478D4×C11—28no—
479D4×C11—48no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
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—22no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—48no—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C2×#4114yes—
504C22⋊D11—216no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—48no—
527C2×Dic11C22×D412yes—
528C2×Dic11C22×D412yes—
529C2×Dic11C22×D412yes—
530C2×Dic11C2×#4114yes—
531D44—28no—
532D44—48no—
533C4×D11—28no—
534C4×D11—28no—
535C4×D11—28no—
536C4×D11—216no—
537C4×D11—48no—
538C4×D11—48no—
539C4×D11—44no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—48no—
543C4×D11—48no—
544C23×D4—111no—
545C23×D4—112no—
546C24×C4—112no—
547C2×#126—111no—
548C2×#126—111no—
549C2×#126—111no—
550C2×#126—111no—
551C2×#126—111no—
552C2×#126—111no—
553C2×#126—111no—
554C2×#126—228no—
555C2×#126C2×D1111yescharacteristic, complemented
556C2×C4×D4—111no—
557C2×C4×D4—112no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—111no—
561C2×C4×D4—228no—
562C2×C4×D4C2×D1111yescharacteristic, complemented
563C22×C4⋊C4—111no—
564C22×C4⋊C4—111no—
565C22×C4⋊C4—111no—
566C22×C4⋊C4—111no—
567C22×C4⋊C4—112no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C22⋊C4—112no—
571C22×C22⋊C4—112no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—112no—
575C22×C22⋊C4—112no—
576C22×C42—111no—
577C22×C42—112no—
578#398—111no—
579#398—111no—
580#398—112no—
581#398—112no—
582#398—111no—
583#398C2×D1111yescharacteristic, complemented
584#397—111no—
585#397—112no—
586#397—111no—
587#397—111no—
588#397—112no—
589#397C2×D1111yescharacteristic, complemented
590#394—111no—
591#394—111no—
592#394—112no—
593#394—112no—
594#394—111no—
595#394C2×D1111yescharacteristic, complemented
596#392—112no—
597#392—111no—
598#392—112no—
599#392—111no—
600#392—111no—
601#392C2×D1111yescharacteristic
602#390—112no—
603#390—112no—
604#390—112no—
605#390—112no—
606#390—112no—
607#390—112no—
608#390—112no—
609#390C2×D1112yescomplemented
610#388—112no—
611#388—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#388C2×D1112yescomplemented
618#386—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386C2×D1112yescomplemented
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#385—112no—
631#385—112no—
632#385—112no—
633#385C2×D1112yescomplemented
634#376—112no—
635#376—111no—
636#376—111no—
637#376—111no—
638#376—112no—
639#376C2×D1111yescharacteristic, complemented
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—112no—
643C2×#95—112no—
644C2×#95—112no—
645C22×C11—24no—
646C22×C11—24no—
647C22×C11—24no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11C23×D411yescharacteristic
658C22×C11C22×#4112yes—
659C22×C11C22×#4112yes—
660C22×C11C2×H(5,𝔽2)11yescharacteristic
661C22×C11C2×H(5,𝔽2)11yescharacteristic
662C2×D11—24no—
663C2×D11—24no—
664C2×D11—24no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—432no—
670C2×D11—41no—
671C2×D11—41no—
672C2×D11—41no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—88no—
676C2×D11#52514yes—
677C2×D11#53214yes—
678C2×D11#53514yes—
679C2×D11#55118yes—
680C2×D11#55318yes—
681C4×C11—22no—
682C4×C11—22no—
683C4×C11—22no—
684C4×C11—24no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—42no—
688C4×C11—41no—
689C4×C11—42no—
690Dic11—22no—
691Dic11—22no—
692Dic11—22no—
693Dic11—24no—
694Dic11—41no—
695Dic11—41no—
696Dic11—42no—
697Dic11—41no—
698Dic11—42no—
699C25—112no—
700C25—111no—
701C22×D4—112no—
702C22×D4—112no—
703C22×D4—112no—
704C22×D4—111no—
705C22×D4—112no—
706C22×D4—224no—
707C22×D4—228no—
708C22×D4—228no—
709C22×D4—228no—
710C22×D4—444no—
711C22×D4C22×D1111yescharacteristic
712C22×D4C22×D1112yes—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—112no—
717C23×C4—112no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—112no—
722C23×C4—112no—
723C23×C4—112no—
724C23×C4—112no—
725C23×C4—228no—
726C23×C4—444no—
727C23×C4—444no—
728C23×C4C22×D1112yes—
729#126—24no—
730#126—224no—
731#126—224no—
732#126—224no—
733#126—224no—
734#126—224no—
735#126—224no—
736#126—224no—
737C4×D4—24no—
738C4×D4—228no—
739C4×D4—224no—
740C4×D4—228no—
741C4×D4—224no—
742C4×D4—224no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—111no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—224no—
758C2×C4⋊C4—224no—
759C2×C4⋊C4—224no—
760C2×C4⋊C4—224no—
761C2×C4⋊C4—444no—
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C4⋊C4C22×D1111yescharacteristic
766C2×C4⋊C4C22×D1112yes—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—111no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
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—112no—
791C2×C22⋊C4—228no—
792C2×C22⋊C4—224no—
793C2×C22⋊C4—224no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—228no—
796C2×C22⋊C4—228no—
797C2×C22⋊C4—444no—
798C2×C22⋊C4—444no—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1111yescharacteristic
801C2×C22⋊C4C22×D1111yescharacteristic
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C22⋊C4C22×D1112yes—
804C2×C22⋊C4C22×D1112yes—
805C2×C22⋊C4C22×D1112yes—
806C2×C22⋊C4C22×D1112yes—
807C2×C42—111no—
808C2×C42—111no—
809C2×C42—111no—
810C2×C42—118no—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—112no—
814C2×C42—228no—
815C2×C42C22×D1112yes—
816C2×C42C22×D1111yescharacteristic
817#95—112no—
818#95—112no—
819#95—112no—
820#95—111no—
821#95—112no—
822#95—112no—
823#95—111no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95C22×D1112yes—
831#95C22×D1111yescharacteristic
832#95C22×D1111yescharacteristic
833#95C22×D1112yes—
834#95C22×D1112yes—
835C2×C11—44no—
836C2×C11—81no—
837C2×C11C2×#52511yescharacteristic
838C2×C11C2×#53211yescharacteristic
839C2×C11C2×#53511yescharacteristic
840C2×C11C2×#55112yes—
841C2×C11C2×#55312yes—
842D11—44no—
843D11—81no—
844D11#260318yesdirect product factor
845C24—111no—
846C24—118no—
847C24—112no—
848C24—111no—
849C24—224no—
850C24—224no—
851C24—224no—
852C24—224no—
853C24—224no—
854C24—224no—
855C24—222no—
856C24—222no—
857C24—224no—
858C24—224no—
859C24—222no—
860C24C23×D1111yescharacteristic
861C24C23×D1112yes—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—24no—
866C2×D4—42no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—224no—
870C2×D4—224no—
871C2×D4—224no—
872C2×D4—2232no—
873C2×D4—224no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—222no—
878C2×D4—224no—
879C2×D4—442no—
880C2×D4—4432no—
881C2×D4—442no—
882C2×D4—442no—
883C22×C4—24no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—112no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—111no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—114no—
893C22×C4—118no—
894C22×C4—112no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—112no—
898C22×C4—111no—
899C22×C4—224no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—224no—
911C22×C4—224no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—222no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—222no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—4432no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4C23×D1112yes—
929C22×C4C23×D1111yescharacteristic
930C22×C4C23×D1111yescharacteristic
931C22×C4C23×D1112yes—
932C22×C4C23×D1111yescharacteristic
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1112yes—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—42no—
942C4⋊C4—224no—
943C4⋊C4—222no—
944C4⋊C4—222no—
945C4⋊C4—222no—
946C4⋊C4—222no—
947C4⋊C4—222no—
948C4⋊C4—222no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—24no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—224no—
965C22⋊C4—222no—
966C22⋊C4—222no—
967C22⋊C4—222no—
968C22⋊C4—224no—
969C22⋊C4—224no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—222no—
973C22⋊C4—222no—
974C22⋊C4—222no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—224no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C42—24no—
989C42—114no—
990C42—114no—
991C42—114no—
992C42—224no—
993C42—224no—
994C42—224no—
995C42D4×D1114yescomplemented
996C11C2×#260311yescharacteristic, complemented, Sylow
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—21no—
1008C23—112no—
1009C23—114no—
1010C23—114no—
1011C23—112no—
1012C23—112no—
1013C23—114no—
1014C23—2216no—
1015C23—2216no—
1016C23—2216no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—222no—
1023C23—221no—
1024C23—222no—
1025C23—222no—
1026C23—221no—
1027C23—221no—
1028C23—448no—
1029C23—448no—
1030C23—448no—
1031C23—448no—
1032C23—448no—
1033C23—448no—
1034C23—444no—
1035C23—444no—
1036C23—444no—
1037C23#41×D1114yes—
1038C23C24×D1111yescharacteristic
1039D4—28no—
1040D4—48no—
1041D4—228no—
1042D4—2216no—
1043D4—448no—
1044D4—448no—
1045D4—448no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—48no—
1066C2×C4—112no—
1067C2×C4—112no—
1068C2×C4—112no—
1069C2×C4—114no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—2216no—
1073C2×C4—228no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—221no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—221no—
1090C2×C4—222no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—448no—
1094C2×C4—448no—
1095C2×C4—448no—
1096C2×C4—448no—
1097C2×C4—444no—
1098C2×C4—444no—
1099C2×C4—444no—
1100C2×C4—448no—
1101C2×C4C2×D4×D1112yes—
1102C2×C4C2×D4×D1112yes—
1103C2×C4C2×D4×D1112yes—
1104C2×C4#41×D1114yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—42no—
1117C22—118no—
1118C22—114no—
1119C22—114no—
1120C22—114no—
1121C22—118no—
1122C22—224no—
1123C22—224no—
1124C22—224no—
1125C22—4432no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—441no—
1132C22—441no—
1133C22—441no—
1134C22—442no—
1135C22—888no—
1136C22C22×D4×D1111yescharacteristic
1137C22C2×#41×D1112yes—
1138C22C2×#41×D1112yes—
1139C22D11×H(5,𝔽2)11yescharacteristic
1140C22D11×H(5,𝔽2)11yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—24no—
1145C4—42no—
1146C4—41no—
1147C4—42no—
1148C4—41no—
1149C4—41no—
1150C4—222no—
1151C4—222no—
1152C4—222no—
1153C4—224no—
1154C4—442no—
1155C4—441no—
1156C4—442no—
1157C4—441no—
1158C4—441no—
1159C2—44no—
1160C2—81no—
1161C2—118no—
1162C2—444no—
1163C2—881no—
1164C2D11×#52511yescharacteristic
1165C2D11×#53211yescharacteristic
1166C2D11×#53511yescharacteristic
1167C2D11×#55112yes—
1168C2D11×#55312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2603C2
prime radicalD11×#392C2
hypercenter#2603D11
hypocenterC11C2×#2603
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2603

Complements

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

NH ≅ G/Ntype
1. C2×D11×#126C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074246C2semidirect
4. #13074245C2semidirect
5. #13074244C2semidirect
6. #13074243C2semidirect
7. #13074242C2semidirect
8. #13074241C2semidirect
9. #13074240C2semidirect
10. #13074239C2semidirect
11. #13074238C2semidirect
12. #13074237C2semidirect
13. #13074236C2semidirect
14. D11×#398C2semidirect
15. D11×#397C2semidirect
16. D11×#394C2semidirect
18. D11×#390C2semidirect
19. D11×#388C2semidirect
20. D11×#386C2semidirect
21. D11×#385C2semidirect
22. D11×#376C2semidirect
23. C11×#2603C2semidirect
27. C2×C11×#126C22semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×D4×Dic11C22semidirect
30. C2×C4×C22⋊D11C22semidirect
33. C2×#66951C22semidirect
34. C2×#66951C22semidirect
35. C2×#66951C22semidirect
36. C2×#66946C22semidirect
42. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66932C22semidirect
52. C2×#66932C22semidirect
53. C2×#66932C22semidirect
54. C2×#66929C22semidirect
55. C2×C4×D44C22semidirect
58. C11×#398C22semidirect
59. C11×#397C22semidirect
60. C11×#394C22semidirect
62. C11×#390C22semidirect
63. C11×#388C22semidirect
64. C11×#386C22semidirect
65. C11×#385C22semidirect
66. C11×#376C22semidirect
69. #10622835C22semidirect
70. #10622834C22semidirect
71. #10622833C22semidirect
72. #10622826C22semidirect
73. #10622823C22semidirect
74. #10622606C22semidirect
75. #10622604C22semidirect
76. #10622603C22semidirect
77. #10622602C22semidirect
78. #10622602C22semidirect
79. #10622601C22semidirect
80. #10622597C22semidirect
81. #10622596C22semidirect
82. #10622593C22semidirect
83. #10622574C22semidirect
86. #10622572C22semidirect
87. #10622571C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
94. #10622566C22semidirect
95. #10622565C22semidirect
96. #10622564C22semidirect
97. #10622563C22semidirect
98. #10622559C22semidirect
99. #10622558C22semidirect
100. #10622557C22semidirect
101. #10622553C22semidirect
102. #10622552C22semidirect
103. #10622545C22semidirect
104. #10622545C22semidirect
105. #10622288C22semidirect
106. #10622287C22semidirect
107. #10622285C22semidirect
109. #10622283C22semidirect
110. #10622282C22semidirect
111. #10622281C22semidirect
112. #10622281C22semidirect
113. #10622278C22semidirect
114. #10622278C22semidirect
120. #10622274C22semidirect
121. #10622270C22semidirect
122. #10622261C22semidirect
123. #10622261C22semidirect
124. #10622261C22semidirect
242. C42×D11D4semidirect
368. C42×C11C2×D4semidirect
410. C4×Dic11C2×D4semidirect
411. C4×Dic11C2×D4semidirect
412. C4×Dic11C2×D4semidirect
426. #2603D11direct (N × H)
555. C2×#126C2×D11semidirect
562. C2×C4×D4C2×D11semidirect
583. #398C2×D11semidirect
589. #397C2×D11semidirect
595. #394C2×D11semidirect
609. #390C2×D11semidirect
617. #388C2×D11semidirect
625. #386C2×D11semidirect
633. #385C2×D11semidirect
639. #376C2×D11semidirect
844. D11#2603direct (N × H)
995. C42D4×D11semidirect
996. C11C2×#2603semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1262
C2×C4×D4×D112
#130742462
#130742452
#130742442
#130742432
#130742422
#130742412
#130742402
#130742392
#130742382
#130742372
#130742362
D11×#3982
D11×#3972
D11×#3942
D11×#3922
D11×#3902
D11×#3882
D11×#3862
D11×#3852
D11×#3762
C11×#26032
C2×#260311