Finite Group Databasebeta

← D11×#2635 #14920164

Subgroups — D11×#2635 #14920164

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074509C211yesmaximal, characteristic, complemented
4#13074508C211yesmaximal, characteristic, complemented
5#13074507C212yesmaximal, complemented
6#13074506C211yesmaximal, characteristic, complemented
7#13074505C211yesmaximal, characteristic, complemented
8#13074504C212yesmaximal, complemented
9#13074503C211yesmaximal, characteristic, complemented
10#13074502C212yesmaximal, complemented
11#13074501C211yesmaximal, characteristic, complemented
12#13074500C211yesmaximal, characteristic, complemented
13#13074499C212yesmaximal, complemented
14D11×#400C211yesmaximal, characteristic, complemented
15D11×#399C211yesmaximal, characteristic, complemented
16D11×#394C212yesmaximal, complemented
17D11×#394C211yesmaximal, characteristic, complemented
18D11×#392C211yesmaximal, characteristic, complemented
19D11×#392C212yesmaximal, complemented
20D11×#388C212yesmaximal, complemented
21D11×#386C212yesmaximal, complemented
22D11×#381C211yesmaximal, characteristic, complemented
23C11×#2635C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C22×D4×D11C2212yes—
27C22×D4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic, complemented
31C2×C4×D4×C11C2211yescharacteristic, complemented
32C2×#66992C2212yescomplemented
33C2×#66991C2211yescharacteristic, complemented
34C2×D4×Dic11C2211yescharacteristic, complemented
35C2×#66983C2211yescharacteristic, complemented
36C2×C4×C22⋊D11C2211yescharacteristic, complemented
37C2×C4×C22⋊D11C2211yescharacteristic, complemented
38D11×#121—28no—
39C4×D4×D11—28no—
40C2×#66948C2211yescharacteristic, complemented
41C2×#66946C2211yescharacteristic, complemented
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2212yes—
45C2×#66937C2212yescomplemented
46C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
47C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×C22⋊C4×D11C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×C22⋊C4×D11C2212yes—
56C2×C4×D44C2211yescharacteristic, complemented
57C2×C42×D11C2211yescharacteristic
58C11×#400C2211yescharacteristic, complemented
59C11×#399C2211yescharacteristic, complemented
60C11×#394C2212yescomplemented
61C11×#394C2211yescharacteristic, complemented
62C11×#392C2212yescomplemented
63C11×#392C2211yescharacteristic, complemented
64C11×#388C2212yescomplemented
65C11×#386C2212yescomplemented
66C11×#381C2211yescharacteristic, complemented
67#10622836C2212yescomplemented
68#10622836C2212yescomplemented
69#10622836C2212yescomplemented
70#10622836C2211yescharacteristic, complemented
71#10622836C2212yescomplemented
72#10622835C2212yescomplemented
73#10622835C2211yescharacteristic, complemented
74#10622833C2212yescomplemented
75#10622826C2212yescomplemented
76#10622824C2211yescharacteristic, complemented
77#10622605C2211yescharacteristic, complemented
78#10622605C2212yescomplemented
79#10622604C2211yescharacteristic, complemented
80#10622604C2212yescomplemented
81#10622603C2212yescomplemented
82#10622599C2211yescharacteristic, complemented
83#10622595C2211yescharacteristic, complemented
84#10622574C2212yescomplemented
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622573C2211yescharacteristic, complemented
88#10622573C2212yescomplemented
89#10622573C2212yescomplemented
90#10622573C2212yescomplemented
91#10622573C2212yescomplemented
92#10622572C2212yescomplemented
93#10622572C2212yescomplemented
94#10622572C2212yescomplemented
95#10622571C2212yescomplemented
96#10622569C2212yescomplemented
97#10622569C2212yescomplemented
98#10622564C2212yescomplemented
99#10622562C2212yescomplemented
100#10622562C2211yescharacteristic, complemented
101#10622558C2212yescomplemented
102#10622557C2212yescomplemented
103#10622556C2212yescomplemented
104#10622553C2212yescomplemented
105#10622290C2211yescharacteristic, complemented
106#10622285C2211yescharacteristic, complemented
107#10622285C2212yescomplemented
108#10622284C2211yescharacteristic, complemented
109#10622284C2212yescomplemented
110#10622283C2212yescomplemented
111#10622282C2212yescomplemented
112#10622278C2212yescomplemented
113#10622278C2212yescomplemented
114#10622277C2212yescomplemented
115#10622277C2211yescharacteristic, complemented
116#10622277C2211yescharacteristic, complemented
117D11×#95C2212yes—
118D11×#95C2211yescharacteristic
119D11×#95C2211yescharacteristic
120D11×#95C2212yes—
121D11×#95C2212yes—
122#10622273C2212yescomplemented
123#10622272C2211yescharacteristic, complemented
124#10622271C2212yescomplemented
125C24×D11C2312yes—
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2311yescharacteristic
143C2×D4×D11—24no—
144C2×D4×D11—24no—
145C2×D4×D11—28no—
146C2×D4×D11—28no—
147C2×D4×D11—24no—
148C2×D4×D11—24no—
149C2×D4×D11—44no—
150C2×D4×D11—44no—
151C2×D4×D11—44no—
152C2×D4×D11—44no—
153C2×D4×D11—44no—
154C22×D44C2311yescharacteristic
155C22×D44C2312yes—
156C22×D44C2311yescharacteristic
157C22×D44C2312yes—
158C22×C4×D11—24no—
159C22×C4×D11—44no—
160C22×C4×D11—44no—
161C22×C4×D11D418yescomplemented
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2312yes—
164C22×C4×D11C2311yescharacteristic
165C22×C4×D11C2312yes—
166C22×C4×D11C2312yes—
167C22×C4×D11C2311yescharacteristic
168C22×C4×D11C2311yescharacteristic
169C22×C4×D11C2311yescharacteristic
170C22×C4×D11C2311yescharacteristic
171C22×C4×D11C2311yescharacteristic
172C22×C4×D11C2311yescharacteristic
173C22×C4×D11C2311yescharacteristic
174C11×#121—24no—
175C4×D4×C11—24no—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C42×C11C2311yescharacteristic
188C2×C22⋊Dic11C2311yescharacteristic
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2312yes—
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2312yes—
196#66992—28no—
197#66991—24no—
198D4×Dic11—24no—
199#66983—24no—
200C4×C22⋊D11—24no—
201C4×C22⋊D11—24no—
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2311yescharacteristic
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×(C2×D11)⋊C4C2312yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×(C2×D11)⋊C4C2312yes—
218C2×C4⋊Dic11C2311yescharacteristic
219C2×C4⋊Dic11C2311yescharacteristic
220C2×C4⋊Dic11C2312yes—
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229#66948—24no—
230#66946—24no—
231C4⋊C4×D11—24no—
232C4⋊C4×D11—24no—
233C4⋊C4×D11—44no—
234#66937—28no—
235(C22⋊D11)⋊C4—24no—
236(C22⋊D11)⋊C4—24no—
237C22⋊C4×D11—24no—
238C22⋊C4×D11—24no—
239C22⋊C4×D11—28no—
240C22⋊C4×D11—28no—
241C22⋊C4×D11—44no—
242C22⋊C4×D11—44no—
243C22⋊C4×D11—44no—
244C22⋊C4×D11—44no—
245C4×D44—24no—
246C42×D11—24no—
247C11×#95C2312yes—
248C11×#95C2311yescharacteristic
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2311yescharacteristic
264C11⋊#95C2311yescharacteristic
265C2×#2635—111nomaximal, Sylow
266C24×C11C2412yes—
267C24×C11C2411yescharacteristic
268C24×C11C2411yescharacteristic
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—24no—
276C23×D11—24no—
277C23×D11—24no—
278C23×D11—24no—
279C23×D11—24no—
280C23×D11—24no—
281C23×D11—24no—
282C23×D11—24no—
283C23×D11—24no—
284C23×D11C2×D414yes—
285C23×D11#4114yes—
286C23×D11C2412yes—
287C23×D11C2411yescharacteristic
288C23×D11C2411yescharacteristic
289C23×D11C2411yescharacteristic
290C2×D4×C11—22no—
291C2×D4×C11—22no—
292C2×D4×C11—24no—
293C2×D4×C11—24no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—42no—
297C2×D4×C11—42no—
298C2×D4×C11—42no—
299C2×D4×C11—42no—
300C2×D4×C11—42no—
301C22×C4×C11—22no—
302C22×C4×C11—42no—
303C22×C4×C11—42no—
304C22×C4×C11C2×D414yescomplemented
305C22×C4×C11C2412yes—
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C2×C22⋊D11—24no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—24no—
324C2×C22⋊D11—42no—
325C2×C22⋊D11—42no—
326C2×C22⋊D11—42no—
327C2×C22⋊D11—42no—
328C2×C22⋊D11—42no—
329C2×C22⋊D11—42no—
330C2×C22⋊D11—42no—
331C2×C22⋊D11—42no—
332C2×C22⋊D11—42no—
333C2×C22⋊D11—42no—
334C22×Dic11—22no—
335C22×Dic11—42no—
336C22×Dic11—42no—
337C22×Dic11C2×D414yescomplemented
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340C22×Dic11C2412yes—
341C22×Dic11C2411yescharacteristic
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2411yescharacteristic
346D4×D11—232no—
347D4×D11—432no—
348D4×D11—432no—
349D4×D11—416no—
350C2×D44—22no—
351C2×D44—24no—
352C2×D44—22no—
353C2×D44—24no—
354C2×D44—22no—
355C2×D44—22no—
356C2×D44—42no—
357C2×D44—42no—
358C2×D44—42no—
359C2×D44—42no—
360C2×D44—42no—
361C2×C4×D11—22no—
362C2×C4×D11—22no—
363C2×C4×D11—22no—
364C2×C4×D11—22no—
365C2×C4×D11—24no—
366C2×C4×D11—22no—
367C2×C4×D11—24no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—24no—
371C2×C4×D11—24no—
372C2×C4×D11—24no—
373C2×C4×D11—24no—
374C2×C4×D11—24no—
375C2×C4×D11—24no—
376C2×C4×D11—24no—
377C2×C4×D11—24no—
378C2×C4×D11—24no—
379C2×C4×D11—22no—
380C2×C4×D11—42no—
381C2×C4×D11—42no—
382C2×C4×D11—42no—
383C2×C4×D11—42no—
384C2×C4×D11—416no—
385C2×C4×D11—416no—
386C2×C4×D11C2×D414yes—
387C2×C4×D11C2×D414yes—
388C2×C4×D11C2×D414yescomplemented
389C2×C4×D11C2×D414yescomplemented
390C2×C4×D11#4114yes—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—42no—
394C11×C22⋊C4—22no—
395C11×C22⋊C4—22no—
396C11×C22⋊C4—24no—
397C11×C22⋊C4—24no—
398C11×C22⋊C4—42no—
399C11×C22⋊C4—42no—
400C11×C22⋊C4—42no—
401C11×C22⋊C4—42no—
402C42×C11—22no—
403C22⋊Dic11—22no—
404C22⋊Dic11—24no—
405C22⋊Dic11—24no—
406C22⋊Dic11—22no—
407C22⋊Dic11—42no—
408C22⋊Dic11—42no—
409C22⋊Dic11—42no—
410C22⋊Dic11—42no—
411(C2×D11)⋊C4—22no—
412(C2×D11)⋊C4—24no—
413(C2×D11)⋊C4—24no—
414(C2×D11)⋊C4—22no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—24no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—24no—
419(C2×D11)⋊C4—42no—
420(C2×D11)⋊C4—42no—
421(C2×D11)⋊C4—42no—
422(C2×D11)⋊C4—42no—
423(C2×D11)⋊C4—42no—
424(C2×D11)⋊C4—42no—
425(C2×D11)⋊C4—42no—
426(C2×D11)⋊C4—42no—
427C4⋊Dic11—22no—
428C4⋊Dic11—22no—
429C4⋊Dic11—42no—
430Dic11⋊C4—22no—
431Dic11⋊C4—24no—
432Dic11⋊C4—22no—
433Dic11⋊C4—42no—
434Dic11⋊C4—42no—
435C4×Dic11—22no—
436C4×Dic11—22no—
437C4×Dic11—22no—
438C22×#121—111no—
439C22×C4×D4—111no—
440#2635—111no—
441#2635—111no—
442#2635—112no—
443#2635—111no—
444#2635—112no—
445#2635—111no—
446#2635—112no—
447#2635—112no—
448#2635—111no—
449#2635—111no—
450#2635—111no—
451#2635D1111yescharacteristic, direct product factor
452C2×#400—111no—
453C2×#399—111no—
454C2×#394—111no—
455C2×#394—112no—
456C2×#392—112no—
457C2×#392—111no—
458C2×#388—112no—
459C2×#386—112no—
460C2×#381—111no—
461C23×C11—21no—
462C23×C11—21no—
463C23×C11—21no—
464C23×C11—21no—
465C23×C11—22no—
466C23×C11—22no—
467C23×C11—22no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—22no—
472C23×C11—22no—
473C23×C11—22no—
474C23×C11—22no—
475C23×C11—22no—
476C23×C11C22×D412yes—
477C23×C11C2×#4112yes—
478C23×C11C2511yescharacteristic
479C22×D11—21no—
480C22×D11—21no—
481C22×D11—21no—
482C22×D11—21no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—28no—
488C22×D11—28no—
489C22×D11—28no—
490C22×D11—28no—
491C22×D11—216no—
492C22×D11—22no—
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—22no—
497C22×D11—22no—
498C22×D11—22no—
499C22×D11—44no—
500C22×D11—44no—
501C22×D11—48no—
502C22×D11—48no—
503C22×D11—48no—
504C22×D11—48no—
505C22×D11—48no—
506C22×D11—48no—
507C22×D11—48no—
508C22×D11—48no—
509C22×D11—48no—
510C22×D11—48no—
511C22×D11C22×D412yes—
512C22×D11C22×D412yes—
513C22×D11C2×#4112yes—
514C22×D11C2×#4112yes—
515C22×D11C2×#4112yes—
516C22×D11H(5,𝔽2)14yes—
517C22×D11H(5,𝔽2)14yes—
518D4×C11—28no—
519D4×C11—44no—
520D4×C11—48no—
521D4×C11—48no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—44no—
540C2×C4×C11—44no—
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D412yes—
543C2×C4×C11C2×#4112yes—
544C22⋊D11—28no—
545C22⋊D11—28no—
546C22⋊D11—48no—
547C22⋊D11—48no—
548C22⋊D11—48no—
549C22⋊D11—48no—
550C22⋊D11—48no—
551C2×Dic11—21no—
552C2×Dic11—21no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—21no—
556C2×Dic11—21no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—22no—
567C2×Dic11—22no—
568C2×Dic11—44no—
569C2×Dic11—44no—
570C2×Dic11C22×D412yes—
571C2×Dic11C22×D412yes—
572C2×Dic11C2×#4112yes—
573D44—28no—
574D44—44no—
575D44—48no—
576D44—48no—
577C4×D11—28no—
578C4×D11—28no—
579C4×D11—28no—
580C4×D11—44no—
581C4×D11—44no—
582C4×D11—44no—
583C4×D11—44no—
584C4×D11—44no—
585C4×D11—44no—
586C4×D11—48no—
587C4×D11—48no—
588C4×D11—48no—
589C23×D4—111no—
590C23×D4—112no—
591C23×D4—111no—
592C23×D4—112no—
593C24×C4—111no—
594C24×C4—111no—
595C2×#121—111no—
596C2×#121—112no—
597C2×#121—111no—
598C2×#121—111no—
599C2×#121—112no—
600C2×#121—228no—
601C2×#121C2×D1111yescharacteristic, complemented
602C2×C4×D4—111no—
603C2×C4×D4—111no—
604C2×C4×D4—111no—
605C2×C4×D4—111no—
606C2×C4×D4—111no—
607C2×C4×D4—111no—
608C2×C4×D4—111no—
609C2×C4×D4—228no—
610C2×C4×D4C2×D1111yescharacteristic, complemented
611C22×C4⋊C4—111no—
612C22×C4⋊C4—111no—
613C22×C4⋊C4—112no—
614C22×C22⋊C4—112no—
615C22×C22⋊C4—111no—
616C22×C22⋊C4—111no—
617C22×C22⋊C4—112no—
618C22×C22⋊C4—112no—
619C22×C22⋊C4—112no—
620C22×C22⋊C4—112no—
621C22×C22⋊C4—112no—
622C22×C42—111no—
623#400—111no—
624#400—111no—
625#400—112no—
626#400—111no—
627#400—112no—
628#400C2×D1111yescharacteristic, complemented
629#399—112no—
630#399—111no—
631#399—112no—
632#399—111no—
633#399—111no—
634#399C2×D1111yescharacteristic, complemented
635#394—111no—
636#394—112no—
637#394—111no—
638#394—112no—
639#394—112no—
640#394—112no—
641#394—112no—
642#394—112no—
643#394—112no—
644#394—112no—
645#394—111no—
646#394—112no—
647#394C2×D1111yescharacteristic, complemented
648#394C2×D1112yescomplemented
649#392—112no—
650#392—111no—
651#392—112no—
652#392—112no—
653#392—112no—
654#392—112no—
655#392—111no—
656#392—112no—
657#392—112no—
658#392—112no—
659#392—111no—
660#392—112no—
661#392C2×D1111yescharacteristic, complemented
662#392C2×D1112yescomplemented
663#388—112no—
664#388—112no—
665#388—112no—
666#388—112no—
667#388—112no—
668#388—112no—
669#388—112no—
670#388C2×D1112yescomplemented
671#386—112no—
672#386—112no—
673#386—112no—
674#386—112no—
675#386—112no—
676#386—112no—
677#386—112no—
678#386C2×D1112yescomplemented
679#381—111no—
680#381—112no—
681#381—111no—
682#381—111no—
683#381—112no—
684#381C2×D1111yescharacteristic, complemented
685C2×#95—111no—
686C2×#95—112no—
687C2×#95—111no—
688C2×#95—112no—
689C2×#95—112no—
690C22×C11—22no—
691C22×C11—22no—
692C22×C11—22no—
693C22×C11—22no—
694C22×C11—24no—
695C22×C11—41no—
696C22×C11—41no—
697C22×C11—42no—
698C22×C11—42no—
699C22×C11—42no—
700C22×C11—42no—
701C22×C11—42no—
702C22×C11—42no—
703C22×C11—42no—
704C22×C11—42no—
705C22×C11—42no—
706C22×C11—42no—
707C22×C11C23×D411yescharacteristic
708C22×C11C22×#4111yescharacteristic
709C22×C11C22×#4111yescharacteristic
710C22×C11C2×H(5,𝔽2)12yes—
711C22×C11C2×H(5,𝔽2)12yes—
712C2×D11—22no—
713C2×D11—22no—
714C2×D11—22no—
715C2×D11—22no—
716C2×D11—24no—
717C2×D11—41no—
718C2×D11—41no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—416no—
723C2×D11—416no—
724C2×D11—42no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—42no—
731C2×D11—816no—
732C2×D11#52514yes—
733C2×D11#53414yes—
734C2×D11#53514yes—
735C2×D11#53818yes—
736C2×D11#54018yes—
737C4×C11—22no—
738C4×C11—22no—
739C4×C11—22no—
740C4×C11—41no—
741C4×C11—42no—
742C4×C11—41no—
743C4×C11—42no—
744C4×C11—42no—
745Dic11—22no—
746Dic11—22no—
747Dic11—22no—
748Dic11—41no—
749Dic11—41no—
750Dic11—42no—
751Dic11—42no—
752Dic11—42no—
753C25—111no—
754C25—111no—
755C25—112no—
756C22×D4—111no—
757C22×D4—111no—
758C22×D4—112no—
759C22×D4—112no—
760C22×D4—112no—
761C22×D4—112no—
762C22×D4—112no—
763C22×D4—111no—
764C22×D4—112no—
765C22×D4—111no—
766C22×D4—112no—
767C22×D4—224no—
768C22×D4—224no—
769C22×D4—224no—
770C22×D4—224no—
771C22×D4—228no—
772C22×D4—228no—
773C22×D4—444no—
774C22×D4—444no—
775C22×D4—444no—
776C22×D4—444no—
777C22×D4—444no—
778C22×D4C22×D1111yescharacteristic
779C22×D4C22×D1112yes—
780C22×D4C22×D1111yescharacteristic
781C22×D4C22×D1112yes—
782C23×C4—111no—
783C23×C4—111no—
784C23×C4—111no—
785C23×C4—111no—
786C23×C4—118no—
787C23×C4—111no—
788C23×C4—111no—
789C23×C4—111no—
790C23×C4—111no—
791C23×C4—112no—
792C23×C4—111no—
793C23×C4—112no—
794C23×C4—112no—
795C23×C4—111no—
796C23×C4—111no—
797C23×C4—224no—
798C23×C4—444no—
799C23×C4—444no—
800C23×C4C22×D1111yescharacteristic
801C23×C4C22×D1111yescharacteristic
802#121—24no—
803#121—228no—
804#121—224no—
805#121—224no—
806#121—228no—
807#121—224no—
808C4×D4—24no—
809C4×D4—224no—
810C4×D4—224no—
811C4×D4—224no—
812C4×D4—224no—
813C4×D4—224no—
814C4×D4—224no—
815C4×D4—224no—
816C2×C4⋊C4—111no—
817C2×C4⋊C4—111no—
818C2×C4⋊C4—111no—
819C2×C4⋊C4—112no—
820C2×C4⋊C4—111no—
821C2×C4⋊C4—112no—
822C2×C4⋊C4—112no—
823C2×C4⋊C4—112no—
824C2×C4⋊C4—224no—
825C2×C4⋊C4—224no—
826C2×C4⋊C4—444no—
827C2×C4⋊C4C22×D1111yescharacteristic
828C2×C4⋊C4C22×D1111yescharacteristic
829C2×C4⋊C4C22×D1112yes—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—111no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—111no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—111no—
837C2×C22⋊C4—111no—
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—112no—
846C2×C22⋊C4—112no—
847C2×C22⋊C4—112no—
848C2×C22⋊C4—112no—
849C2×C22⋊C4—112no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—112no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—112no—
854C2×C22⋊C4—224no—
855C2×C22⋊C4—228no—
856C2×C22⋊C4—228no—
857C2×C22⋊C4—224no—
858C2×C22⋊C4—444no—
859C2×C22⋊C4—444no—
860C2×C22⋊C4—444no—
861C2×C22⋊C4—444no—
862C2×C22⋊C4C22×D1111yescharacteristic
863C2×C22⋊C4C22×D1111yescharacteristic
864C2×C22⋊C4C22×D1112yes—
865C2×C22⋊C4C22×D1112yes—
866C2×C22⋊C4C22×D1112yes—
867C2×C22⋊C4C22×D1112yes—
868C2×C22⋊C4C22×D1112yes—
869C2×C22⋊C4C22×D1112yes—
870C2×C42—111no—
871C2×C42—111no—
872C2×C42—111no—
873C2×C42—224no—
874C2×C42C22×D1111yescharacteristic
875#95—112no—
876#95—112no—
877#95—112no—
878#95—112no—
879#95—111no—
880#95—112no—
881#95—111no—
882#95—112no—
883#95—112no—
884#95—112no—
885#95—112no—
886#95—112no—
887#95—112no—
888#95C22×D1112yes—
889#95C22×D1111yescharacteristic
890#95C22×D1111yescharacteristic
891#95C22×D1112yes—
892#95C22×D1112yes—
893C2×C11—42no—
894C2×C11—42no—
895C2×C11—82no—
896C2×C11C2×#52511yescharacteristic
897C2×C11C2×#53411yescharacteristic
898C2×C11C2×#53511yescharacteristic
899C2×C11C2×#53812yes—
900C2×C11C2×#54012yes—
901D11—42no—
902D11—42no—
903D11—82no—
904D11#263518yesdirect product factor
905C24—111no—
906C24—114no—
907C24—114no—
908C24—111no—
909C24—111no—
910C24—112no—
911C24—222no—
912C24—224no—
913C24—224no—
914C24—224no—
915C24—222no—
916C24—222no—
917C24—222no—
918C24—224no—
919C24—224no—
920C24—224no—
921C24—224no—
922C24—224no—
923C24—224no—
924C24—224no—
925C24—224no—
926C24C23×D1112yes—
927C24C23×D1111yescharacteristic
928C24C23×D1111yescharacteristic
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—222no—
941C2×D4—222no—
942C2×D4—224no—
943C2×D4—224no—
944C2×D4—222no—
945C2×D4—222no—
946C2×D4—224no—
947C2×D4—2232no—
948C2×D4—222no—
949C2×D4—222no—
950C2×D4—222no—
951C2×D4—222no—
952C2×D4—224no—
953C2×D4—224no—
954C2×D4—224no—
955C2×D4—224no—
956C2×D4—222no—
957C2×D4—222no—
958C2×D4—442no—
959C2×D4—442no—
960C2×D4—442no—
961C2×D4—442no—
962C2×D4—442no—
963C2×D4—4416no—
964C2×D4—442no—
965C2×D4—442no—
966C2×D4—442no—
967C2×D4—442no—
968C2×D4—442no—
969C2×D4—442no—
970C2×D4—442no—
971C2×D4—442no—
972C2×D4—442no—
973C2×D4—442no—
974C2×D4—4432no—
975C2×D4—4432no—
976C22×C4—22no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—111no—
980C22×C4—111no—
981C22×C4—111no—
982C22×C4—114no—
983C22×C4—114no—
984C22×C4—114no—
985C22×C4—114no—
986C22×C4—114no—
987C22×C4—114no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—111no—
991C22×C4—112no—
992C22×C4—111no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—224no—
996C22×C4—224no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—224no—
1001C22×C4—224no—
1002C22×C4—224no—
1003C22×C4—224no—
1004C22×C4—224no—
1005C22×C4—224no—
1006C22×C4—224no—
1007C22×C4—224no—
1008C22×C4—224no—
1009C22×C4—224no—
1010C22×C4—224no—
1011C22×C4—222no—
1012C22×C4—222no—
1013C22×C4—442no—
1014C22×C4—442no—
1015C22×C4—442no—
1016C22×C4—442no—
1017C22×C4—4416no—
1018C22×C4—4416no—
1019C22×C4—442no—
1020C22×C4—442no—
1021C22×C4D4×D1114yescomplemented
1022C22×C4C23×D1112yes—
1023C22×C4C23×D1112yes—
1024C22×C4C23×D1111yescharacteristic
1025C22×C4C23×D1112yes—
1026C22×C4C23×D1111yescharacteristic
1027C22×C4C23×D1111yescharacteristic
1028C22×C4C23×D1111yescharacteristic
1029C22×C4C23×D1111yescharacteristic
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—42no—
1033C4⋊C4—222no—
1034C4⋊C4—222no—
1035C4⋊C4—224no—
1036C4⋊C4—222no—
1037C4⋊C4—222no—
1038C4⋊C4—442no—
1039C4⋊C4—442no—
1040C4⋊C4—442no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—222no—
1050C22⋊C4—224no—
1051C22⋊C4—224no—
1052C22⋊C4—222no—
1053C22⋊C4—222no—
1054C22⋊C4—222no—
1055C22⋊C4—224no—
1056C22⋊C4—224no—
1057C22⋊C4—222no—
1058C22⋊C4—222no—
1059C22⋊C4—224no—
1060C22⋊C4—224no—
1061C22⋊C4—442no—
1062C22⋊C4—442no—
1063C22⋊C4—442no—
1064C22⋊C4—442no—
1065C22⋊C4—442no—
1066C22⋊C4—442no—
1067C22⋊C4—442no—
1068C22⋊C4—442no—
1069C22⋊C4—442no—
1070C22⋊C4—442no—
1071C22⋊C4—442no—
1072C22⋊C4—442no—
1073C42—22no—
1074C42—222no—
1075C42—222no—
1076C42—222no—
1077C11C2×#263511yescharacteristic, complemented, Sylow
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—112no—
1094C23—112no—
1095C23—112no—
1096C23—114no—
1097C23—114no—
1098C23—112no—
1099C23—112no—
1100C23—228no—
1101C23—228no—
1102C23—228no—
1103C23—228no—
1104C23—2216no—
1105C23—221no—
1106C23—221no—
1107C23—221no—
1108C23—221no—
1109C23—222no—
1110C23—222no—
1111C23—222no—
1112C23—222no—
1113C23—222no—
1114C23—222no—
1115C23—222no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23—444no—
1121C23—444no—
1122C23—448no—
1123C23—448no—
1124C23—448no—
1125C23—448no—
1126C23—448no—
1127C23—448no—
1128C23—448no—
1129C23—448no—
1130C23—448no—
1131C23—448no—
1132C23C2×D4×D1112yes—
1133C23#41×D1112yes—
1134C23C24×D1111yescharacteristic
1135D4—28no—
1136D4—44no—
1137D4—48no—
1138D4—48no—
1139D4—228no—
1140D4—228no—
1141D4—228no—
1142D4—444no—
1143D4—448no—
1144D4—448no—
1145D4—448no—
1146D4—448no—
1147D4—448no—
1148D4—448no—
1149D4—448no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—112no—
1170C2×C4—112no—
1171C2×C4—112no—
1172C2×C4—228no—
1173C2×C4—228no—
1174C2×C4—228no—
1175C2×C4—221no—
1176C2×C4—221no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—221no—
1180C2×C4—221no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—444no—
1193C2×C4—444no—
1194C2×C4—444no—
1195C2×C4—444no—
1196C2×C4—444no—
1197C2×C4—448no—
1198C2×C4—448no—
1199C2×C4—444no—
1200C2×C4—448no—
1201C2×C4—444no—
1202C2×C4—444no—
1203C2×C4C2×D4×D1112yes—
1204C2×C4C2×D4×D1112yes—
1205C2×C4#41×D1112yes—
1206C22—22no—
1207C22—22no—
1208C22—24no—
1209C22—22no—
1210C22—22no—
1211C22—41no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—114no—
1224C22—114no—
1225C22—118no—
1226C22—118no—
1227C22—114no—
1228C22—222no—
1229C22—222no—
1230C22—224no—
1231C22—222no—
1232C22—222no—
1233C22—4416no—
1234C22—4416no—
1235C22—441no—
1236C22—441no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—8816no—
1248C22C22×D4×D1111yescharacteristic
1249C22C2×#41×D1111yescharacteristic
1250C22C2×#41×D1111yescharacteristic
1251C22D11×H(5,𝔽2)12yes—
1252C22D11×H(5,𝔽2)12yes—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—41no—
1257C4—42no—
1258C4—41no—
1259C4—42no—
1260C4—42no—
1261C4—222no—
1262C4—222no—
1263C4—222no—
1264C4—441no—
1265C4—442no—
1266C4—441no—
1267C4—442no—
1268C4—442no—
1269C2—42no—
1270C2—42no—
1271C2—82no—
1272C2—118no—
1273C2—442no—
1274C2—442no—
1275C2—882no—
1276C2D11×#52511yescharacteristic
1277C2D11×#53411yescharacteristic
1278C2D11×#53511yescharacteristic
1279C2D11×#53812yes—
1280C2D11×#54012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2635C2
hypercenter#2635D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C2×D11×#121C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074509C2semidirect
4. #13074508C2semidirect
5. #13074507C2semidirect
6. #13074506C2semidirect
7. #13074505C2semidirect
8. #13074504C2semidirect
9. #13074503C2semidirect
10. #13074502C2semidirect
11. #13074501C2semidirect
12. #13074500C2semidirect
13. #13074499C2semidirect
14. D11×#400C2semidirect
15. D11×#399C2semidirect
16. D11×#394C2semidirect
17. D11×#394C2semidirect
18. D11×#392C2semidirect
19. D11×#392C2semidirect
20. D11×#388C2semidirect
21. D11×#386C2semidirect
22. D11×#381C2semidirect
23. C11×#2635C2semidirect
30. C2×C11×#121C22semidirect
31. C2×C4×D4×C11C22semidirect
32. C2×#66992C22semidirect
33. C2×#66991C22semidirect
34. C2×D4×Dic11C22semidirect
35. C2×#66983C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C2×C4×C22⋊D11C22semidirect
40. C2×#66948C22semidirect
41. C2×#66946C22semidirect
45. C2×#66937C22semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×(C22⋊D11)⋊C4C22semidirect
56. C2×C4×D44C22semidirect
58. C11×#400C22semidirect
59. C11×#399C22semidirect
60. C11×#394C22semidirect
61. C11×#394C22semidirect
62. C11×#392C22semidirect
63. C11×#392C22semidirect
64. C11×#388C22semidirect
65. C11×#386C22semidirect
66. C11×#381C22semidirect
67. #10622836C22semidirect
68. #10622836C22semidirect
69. #10622836C22semidirect
70. #10622836C22semidirect
71. #10622836C22semidirect
72. #10622835C22semidirect
73. #10622835C22semidirect
74. #10622833C22semidirect
75. #10622826C22semidirect
76. #10622824C22semidirect
77. #10622605C22semidirect
78. #10622605C22semidirect
79. #10622604C22semidirect
80. #10622604C22semidirect
81. #10622603C22semidirect
82. #10622599C22semidirect
83. #10622595C22semidirect
84. #10622574C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
87. #10622573C22semidirect
88. #10622573C22semidirect
89. #10622573C22semidirect
90. #10622573C22semidirect
91. #10622573C22semidirect
92. #10622572C22semidirect
93. #10622572C22semidirect
94. #10622572C22semidirect
95. #10622571C22semidirect
96. #10622569C22semidirect
97. #10622569C22semidirect
98. #10622564C22semidirect
99. #10622562C22semidirect
100. #10622562C22semidirect
101. #10622558C22semidirect
102. #10622557C22semidirect
103. #10622556C22semidirect
104. #10622553C22semidirect
105. #10622290C22semidirect
106. #10622285C22semidirect
107. #10622285C22semidirect
108. #10622284C22semidirect
109. #10622284C22semidirect
110. #10622283C22semidirect
111. #10622282C22semidirect
112. #10622278C22semidirect
113. #10622278C22semidirect
114. #10622277C22semidirect
115. #10622277C22semidirect
116. #10622277C22semidirect
122. #10622273C22semidirect
123. #10622272C22semidirect
124. #10622271C22semidirect
161. C22×C4×D11D4semidirect
304. C22×C4×C11C2×D4semidirect
337. C22×Dic11C2×D4semidirect
388. C2×C4×D11C2×D4semidirect
389. C2×C4×D11C2×D4semidirect
451. #2635D11direct (N × H)
601. C2×#121C2×D11semidirect
610. C2×C4×D4C2×D11semidirect
628. #400C2×D11semidirect
634. #399C2×D11semidirect
647. #394C2×D11semidirect
648. #394C2×D11semidirect
661. #392C2×D11semidirect
662. #392C2×D11semidirect
670. #388C2×D11semidirect
678. #386C2×D11semidirect
684. #381C2×D11semidirect
904. D11#2635direct (N × H)
1021. C22×C4D4×D11semidirect
1077. C11C2×#2635semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×C4×D4×D112
#130745092
#130745082
#130745072
#130745062
#130745052
#130745042
#130745032
#130745022
#130745012
#130745002
#130744992
D11×#4002
D11×#3992
D11×#3942
D11×#3922
D11×#3882
D11×#3862
D11×#3812
C11×#26352
C2×#263511