Finite Group Databasebeta

← D11×#2636 #14920488

Subgroups — D11×#2636 #14920488

Order 2816.

3218 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#13074520C212yesmaximal, complemented
4#13074519C212yesmaximal, complemented
5#13074518C212yesmaximal, complemented
6#13074517C212yesmaximal, complemented
7#13074516C211yesmaximal, characteristic, complemented
8#13074515C211yesmaximal, characteristic, complemented
9#13074514C211yesmaximal, characteristic, complemented
10#13074513C211yesmaximal, characteristic, complemented
11#13074512C211yesmaximal, characteristic, complemented
12#13074511C211yesmaximal, characteristic, complemented
13#13074510C211yesmaximal, characteristic, complemented
14D11×#400C211yesmaximal, characteristic, complemented
15D11×#399C211yesmaximal, characteristic, complemented
16D11×#396C212yesmaximal, complemented
17D11×#394C212yesmaximal, complemented
18D11×#394C211yesmaximal, characteristic, complemented
19D11×#392C211yesmaximal, characteristic
20D11×#386C212yesmaximal, complemented
21D11×#385C212yesmaximal, complemented
22D11×#382C211yesmaximal, characteristic, complemented
23C11×#2636C211yesmaximal, 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×C4⋊C4×D11C2212yes—
43C2×(C22⋊D11)⋊C4C2212yescomplemented
44C2×C22⋊C4×D11C2211yescharacteristic
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×#66932C2211yescharacteristic, complemented
53C2×#66932C2211yescharacteristic, complemented
54C2×#66932C2211yescharacteristic, complemented
55C2×#66929C2211yescharacteristic, complemented
56C2×C4×D44C2211yescharacteristic, complemented
57C2×C42×D11C2211yescharacteristic
58C11×#400C2211yescharacteristic, complemented
59C11×#399C2211yescharacteristic, complemented
60C11×#396C2212yescomplemented
61C11×#394C2211yescharacteristic, complemented
62C11×#394C2212yescomplemented
63C11×#392C2211yescharacteristic
64C11×#386C2212yescomplemented
65C11×#385C2212yescomplemented
66C11×#382C2211yescharacteristic, complemented
67#10622836C2211yescharacteristic
68#10622836C2212yes—
69#10622835C2211yescharacteristic, complemented
70#10622835C2212yescomplemented
71#10622833C2212yescomplemented
72#10622826C2212yescomplemented
73#10622823C2212yescomplemented
74#10622607C2212yescomplemented
75#10622607C2212yescomplemented
76#10622607C2212yescomplemented
77#10622605C2211yescharacteristic, complemented
78#10622605C2212yescomplemented
79#10622604C2211yescharacteristic, complemented
80#10622604C2212yescomplemented
81#10622602C2212yescomplemented
82#10622602C2212yescomplemented
83#10622599C2211yescharacteristic, complemented
84#10622595C2211yescharacteristic, complemented
85#10622590C2212yescomplemented
86#10622574C2212yescomplemented
87#10622574C2212yescomplemented
88#10622574C2212yescomplemented
89#10622573C2211yescharacteristic
90#10622573C2212yes—
91#10622572C2212yescomplemented
92#10622572C2212yescomplemented
93#10622572C2212yescomplemented
94#10622571C2212yescomplemented
95#10622569C2212yescomplemented
96#10622569C2212yescomplemented
97#10622563C2212yescomplemented
98#10622562C2211yescharacteristic, complemented
99#10622562C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622561C2212yescomplemented
103#10622559C2212yescomplemented
104#10622549C2211yescharacteristic, complemented
105#10622290C2211yescharacteristic, complemented
106#10622289C2212yescomplemented
107#10622285C2211yescharacteristic, complemented
108#10622285C2212yescomplemented
109#10622284C2211yescharacteristic
110#10622281C2212yescomplemented
111#10622281C2212yescomplemented
112#10622278C2212yescomplemented
113#10622278C2212yescomplemented
114D11×#95C2212yes—
115D11×#95C2211yescharacteristic
116D11×#95C2211yescharacteristic
117D11×#95C2212yes—
118D11×#95C2212yes—
119#10622273C2212yescomplemented
120#10622272C2211yescharacteristic, complemented
121#10622271C2212yescomplemented
122#10622263C2211yescharacteristic, complemented
123#10622263C2211yescharacteristic, complemented
124#10622263C2212yescomplemented
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—44no—
138C2×D4×D11—44no—
139C22×D44C2311yescharacteristic
140C22×D44C2312yes—
141C22×C4×D11—28no—
142C22×C4×D11—44no—
143C22×C4×D11—44no—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
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×C4⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
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×C4⋊Dic11C2312yes—
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
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—
227C4⋊C4×D11—44no—
228(C22⋊D11)⋊C4—28no—
229C22⋊C4×D11—28no—
230C22⋊C4×D11—24no—
231C22⋊C4×D11—24no—
232C22⋊C4×D11—24no—
233C22⋊C4×D11—28no—
234C22⋊C4×D11—44no—
235C22⋊C4×D11—44no—
236C22⋊C4×D11—44no—
237#66932—24no—
238#66932—24no—
239#66932—24no—
240#66929—24no—
241C4×D44—24no—
242C42×D11D418yescomplemented
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C2×#2636—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—42no—
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×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
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×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317D4×D11—232no—
318D4×D11—432no—
319C2×D44—24no—
320C2×D44—24no—
321C2×D44—22no—
322C2×D44—42no—
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—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—24no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—432no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C11×C4⋊C4—22no—
355C11×C4⋊C4—22no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—42no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11C2×D414yescomplemented
369C22⋊Dic11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—42no—
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—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
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—
398C4⋊Dic11—42no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410C4×Dic11C2×D414yescomplemented
411C4×Dic11C2×D414yescomplemented
412C4×Dic11C2×D414yescomplemented
413C22×#126—111no—
414C22×C4×D4—111no—
415#2636—111no—
416#2636—111no—
417#2636—112no—
418#2636—111no—
419#2636—112no—
420#2636—111no—
421#2636—112no—
422#2636—112no—
423#2636—111no—
424#2636—111no—
425#2636—111no—
426#2636D1111yescharacteristic, direct product factor
427C2×#400—111no—
428C2×#399—111no—
429C2×#396—112no—
430C2×#394—112no—
431C2×#394—111no—
432C2×#392—111no—
433C2×#386—112no—
434C2×#385—112no—
435C2×#382—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×D11H(5,𝔽2)14yes—
476C22×D11H(5,𝔽2)12yes—
477C22×D112−1+412yes—
478D4×C11—28no—
479D4×C11—48no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—48no—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C22⋊D11—216no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—48no—
528C2×Dic11C22×D412yes—
529C2×Dic11C22×D412yes—
530C2×Dic11C22×D412yes—
531D44—28no—
532D44—48no—
533C4×D11—28no—
534C4×D11—28no—
535C4×D11—28no—
536C4×D11—48no—
537C4×D11—48no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—48no—
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×C4⋊C4—112no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—112no—
572C22×C22⋊C4—112no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—112no—
575C22×C22⋊C4—112no—
576C22×C22⋊C4—112no—
577C22×C42—111no—
578#400—111no—
579#400—111no—
580#400—112no—
581#400—111no—
582#400—112no—
583#400C2×D1111yescharacteristic, complemented
584#399—112no—
585#399—111no—
586#399—112no—
587#399—111no—
588#399—111no—
589#399C2×D1111yescharacteristic, complemented
590#396—112no—
591#396—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#396—112no—
597#396C2×D1112yescomplemented
598#394—111no—
599#394—112no—
600#394—111no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—112no—
608#394—111no—
609#394—112no—
610#394C2×D1111yescharacteristic, complemented
611#394C2×D1112yescomplemented
612#392—112no—
613#392—111no—
614#392—112no—
615#392—111no—
616#392—111no—
617#392C2×D1111yescharacteristic
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#382—112no—
635#382—111no—
636#382—111no—
637#382—111no—
638#382—112no—
639#382C2×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×C11C2×H(5,𝔽2)12yes—
660C22×C11C2×H(5,𝔽2)11yescharacteristic
661C22×C11C2×2−1+411yescharacteristic
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#53514yes—
678C2×D11#53714yes—
679C2×D11#53818yes—
680C2×D11#53918yes—
681C4×C11—22no—
682C4×C11—22no—
683C4×C11—22no—
684C4×C11—41no—
685C4×C11—42no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11—42no—
689C4×C11—42no—
690Dic11—22no—
691Dic11—22no—
692Dic11—22no—
693Dic11—41no—
694Dic11—42no—
695Dic11—41no—
696Dic11—41no—
697Dic11—42no—
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—444no—
710C22×D4—444no—
711C22×D4C22×D1111yescharacteristic
712C22×D4C22×D1112yes—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—112no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—112no—
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—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—224no—
761C2×C4⋊C4—224no—
762C2×C4⋊C4—224no—
763C2×C4⋊C4—224no—
764C2×C4⋊C4—444no—
765C2×C4⋊C4—444no—
766C2×C4⋊C4C22×D1111yescharacteristic
767C2×C4⋊C4C22×D1111yescharacteristic
768C2×C4⋊C4C22×D1111yescharacteristic
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1112yes—
771C2×C4⋊C4C22×D1112yes—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
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—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—228no—
797C2×C22⋊C4—224no—
798C2×C22⋊C4—224no—
799C2×C22⋊C4—224no—
800C2×C22⋊C4—228no—
801C2×C22⋊C4—444no—
802C2×C22⋊C4—444no—
803C2×C22⋊C4—444no—
804C2×C22⋊C4C22×D1112yes—
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1111yescharacteristic
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—118no—
816C2×C42C22×D1111yescharacteristic
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—111no—
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×#53511yescharacteristic
839C2×C11C2×#53711yescharacteristic
840C2×C11C2×#53812yes—
841C2×C11C2×#53912yes—
842D11—44no—
843D11—81no—
844D11#263618yesdirect 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—224no—
857C24—224no—
858C24—222no—
859C24—222no—
860C24C23×D1111yescharacteristic
861C24C23×D1112yes—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—224no—
870C2×D4—2232no—
871C2×D4—224no—
872C2×D4—224no—
873C2×D4—224no—
874C2×D4—224no—
875C2×D4—222no—
876C2×D4—442no—
877C2×D4—442no—
878C2×D4—442no—
879C2×D4—442no—
880C2×D4—442no—
881C2×D4—442no—
882C2×D4—4432no—
883C22×C4—24no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—111no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—114no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—112no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—112no—
896C22×C4—112no—
897C22×C4—111no—
898C22×C4—224no—
899C22×C4—222no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—222no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—222no—
910C22×C4—224no—
911C22×C4—224no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—224no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—222no—
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×D1112yes—
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1111yescharacteristic
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—224no—
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—222no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—224no—
969C22⋊C4—222no—
970C22⋊C4—222no—
971C22⋊C4—222no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4—222no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C42—114no—
993C42—114no—
994C42—114no—
995C42D4×D1114yescomplemented
996C11C2×#263611yescharacteristic, 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—444no—
1034C23—444no—
1035C23—448no—
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—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—48no—
1067C2×C4—112no—
1068C2×C4—112no—
1069C2×C4—112no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—228no—
1073C2×C4—222no—
1074C2×C4—221no—
1075C2×C4—222no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—221no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—221no—
1093C2×C4—448no—
1094C2×C4—448no—
1095C2×C4—448no—
1096C2×C4—448no—
1097C2×C4—444no—
1098C2×C4—444no—
1099C2×C4—448no—
1100C2×C4—444no—
1101C2×C4—448no—
1102C2×C4C2×D4×D1112yes—
1103C2×C4C2×D4×D1112yes—
1104C2×C4C2×D4×D1112yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—41no—
1114C22—42no—
1115C22—42no—
1116C22—41no—
1117C22—114no—
1118C22—114no—
1119C22—118no—
1120C22—118no—
1121C22—114no—
1122C22—224no—
1123C22—224no—
1124C22—224no—
1125C22—4432no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—441no—
1131C22—441no—
1132C22—442no—
1133C22—442no—
1134C22—441no—
1135C22—888no—
1136C22C22×D4×D1111yescharacteristic
1137C22C2×#41×D1112yes—
1138C22D11×H(5,𝔽2)12yes—
1139C22D11×H(5,𝔽2)11yescharacteristic
1140C22D11×2−1+411yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—42no—
1149C4—41no—
1150C4—222no—
1151C4—222no—
1152C4—222no—
1153C4—442no—
1154C4—441no—
1155C4—441no—
1156C4—442no—
1157C4—442no—
1158C4—441no—
1159C2—44no—
1160C2—81no—
1161C2—118no—
1162C2—444no—
1163C2—881no—
1164C2D11×#52511yescharacteristic
1165C2D11×#53511yescharacteristic
1166C2D11×#53711yescharacteristic
1167C2D11×#53812yes—
1168C2D11×#53912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2636C2
prime radicalD11×#392C2
hypercenter#2636D11
hypocenterC11C2×#2636
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2636

Complements

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

NH ≅ G/Ntype
1. C2×D11×#126C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074520C2semidirect
4. #13074519C2semidirect
5. #13074518C2semidirect
6. #13074517C2semidirect
7. #13074516C2semidirect
8. #13074515C2semidirect
9. #13074514C2semidirect
10. #13074513C2semidirect
11. #13074512C2semidirect
12. #13074511C2semidirect
13. #13074510C2semidirect
14. D11×#400C2semidirect
15. D11×#399C2semidirect
16. D11×#396C2semidirect
17. D11×#394C2semidirect
18. D11×#394C2semidirect
20. D11×#386C2semidirect
21. D11×#385C2semidirect
22. D11×#382C2semidirect
23. C11×#2636C2semidirect
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
43. C2×(C22⋊D11)⋊C4C22semidirect
52. C2×#66932C22semidirect
53. C2×#66932C22semidirect
54. C2×#66932C22semidirect
55. C2×#66929C22semidirect
56. C2×C4×D44C22semidirect
58. C11×#400C22semidirect
59. C11×#399C22semidirect
60. C11×#396C22semidirect
61. C11×#394C22semidirect
62. C11×#394C22semidirect
64. C11×#386C22semidirect
65. C11×#385C22semidirect
66. C11×#382C22semidirect
69. #10622835C22semidirect
70. #10622835C22semidirect
71. #10622833C22semidirect
72. #10622826C22semidirect
73. #10622823C22semidirect
74. #10622607C22semidirect
75. #10622607C22semidirect
76. #10622607C22semidirect
77. #10622605C22semidirect
78. #10622605C22semidirect
79. #10622604C22semidirect
80. #10622604C22semidirect
81. #10622602C22semidirect
82. #10622602C22semidirect
83. #10622599C22semidirect
84. #10622595C22semidirect
85. #10622590C22semidirect
86. #10622574C22semidirect
87. #10622574C22semidirect
88. #10622574C22semidirect
91. #10622572C22semidirect
92. #10622572C22semidirect
93. #10622572C22semidirect
94. #10622571C22semidirect
95. #10622569C22semidirect
96. #10622569C22semidirect
97. #10622563C22semidirect
98. #10622562C22semidirect
99. #10622562C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622561C22semidirect
103. #10622559C22semidirect
104. #10622549C22semidirect
105. #10622290C22semidirect
106. #10622289C22semidirect
107. #10622285C22semidirect
108. #10622285C22semidirect
110. #10622281C22semidirect
111. #10622281C22semidirect
112. #10622278C22semidirect
113. #10622278C22semidirect
119. #10622273C22semidirect
120. #10622272C22semidirect
121. #10622271C22semidirect
122. #10622263C22semidirect
123. #10622263C22semidirect
124. #10622263C22semidirect
242. C42×D11D4semidirect
368. C42×C11C2×D4semidirect
410. C4×Dic11C2×D4semidirect
411. C4×Dic11C2×D4semidirect
412. C4×Dic11C2×D4semidirect
426. #2636D11direct (N × H)
555. C2×#126C2×D11semidirect
562. C2×C4×D4C2×D11semidirect
583. #400C2×D11semidirect
589. #399C2×D11semidirect
597. #396C2×D11semidirect
610. #394C2×D11semidirect
611. #394C2×D11semidirect
625. #386C2×D11semidirect
633. #385C2×D11semidirect
639. #382C2×D11semidirect
844. D11#2636direct (N × H)
995. C42D4×D11semidirect
996. C11C2×#2636semidirect

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
#130745202
#130745192
#130745182
#130745172
#130745162
#130745152
#130745142
#130745132
#130745122
#130745112
#130745102
D11×#4002
D11×#3992
D11×#3962
D11×#3942
D11×#3922
D11×#3862
D11×#3852
D11×#3822
C11×#26362
C2×#263611