Finite Group Databasebeta

← D11×#2413 #14922467

Subgroups — D11×#2413 #14922467

Order 2816.

3570 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#123C211yesmaximal, characteristic
2C2×D11×#123C211yesmaximal, characteristic
3C2×D11×#117C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072026C211yesmaximal, characteristic, complemented
6#13072025C211yesmaximal, characteristic, complemented
7#13072024C211yesmaximal, characteristic, complemented
8#13072023C211yesmaximal, characteristic, complemented
9#13072022C212yesmaximal, complemented
10#13072021C211yesmaximal, characteristic, complemented
11#13072020C212yesmaximal, complemented
12#13072019C211yesmaximal, characteristic, complemented
13#13072018C212yesmaximal, complemented
14#13072017C211yesmaximal, characteristic, complemented
15#13072016C212yesmaximal, complemented
16D11×#398C212yesmaximal, complemented
17D11×#396C212yesmaximal, complemented
18D11×#389C212yesmaximal, complemented
19D11×#388C212yesmaximal, complemented
20D11×#386C211yesmaximal, characteristic
21D11×#385C211yesmaximal, characteristic, complemented
22D11×#381C211yesmaximal, characteristic, complemented
23C11×#2413C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#123C2211yescharacteristic
29C2×C11×#123C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic, complemented
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C2×#66988C2211yescharacteristic
33C2×#66988C2211yescharacteristic
34C2×#66982C2211yescharacteristic
35C2×#66982C2211yescharacteristic
36C2×#66979C2211yescharacteristic, complemented
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C22×Dic11⋊C4C2211yescharacteristic, complemented
39C22×Dic11⋊C4C2211yescharacteristic, complemented
40D11×#123—28no—
41D11×#123—28no—
42D11×#117—28no—
43C2×#66947C2211yescharacteristic
44C2×#66947C2212yes—
45C2×#66947C2211yescharacteristic
46C2×#66945C2212yescomplemented
47C2×C4⋊C4×D11—28no—
48C2×C4⋊C4×D11C2212yes—
49C2×C4⋊C4×D11C2212yes—
50C2×C4⋊C4×D11C2212yes—
51C2×C4⋊C4×D11C2212yes—
52C2×C4⋊C4×D11C2211yescharacteristic
53C2×C4⋊C4×D11C2212yes—
54C2×C4⋊C4×D11C2211yescharacteristic
55C2×C4⋊C4×D11C2212yescomplemented
56C2×C4⋊C4×D11C2212yescomplemented
57C2×#66939C2211yescharacteristic
58C2×#66939C2211yescharacteristic
59C2×#66936C2211yescharacteristic
60C2×#66936C2212yes—
61C2×#66936C2211yescharacteristic
62C2×C22⋊C4×D11C2211yescharacteristic
63C2×C22⋊C4×D11C2211yescharacteristic
64C2×C22⋊C4×D11C2212yes—
65C2×C22⋊C4×D11C2211yescharacteristic
66C2×C22⋊C4×D11C2212yes—
67C2×C22⋊C4×D11C2211yescharacteristic
68C2×C22⋊C4×D11C2211yescharacteristic
69C2×#66930C2211yescharacteristic, complemented
70C2×#66930C2211yescharacteristic, complemented
71C2×#66925C2212yescomplemented
72C2×C42×D11C2212yes—
73C11×#398C2212yescomplemented
74C11×#396C2212yescomplemented
75C11×#389C2212yescomplemented
76C11×#388C2212yescomplemented
77C11×#386C2211yescharacteristic
78C11×#385C2211yescharacteristic, complemented
79C11×#381C2211yescharacteristic, complemented
80#10622833C2211yescharacteristic
81#10622826C2211yescharacteristic
82#10622824C2211yescharacteristic, complemented
83#10622823C2211yescharacteristic, complemented
84#10622607C2212yescomplemented
85#10622607C2212yescomplemented
86#10622607C2212yescomplemented
87#10622603C2212yescomplemented
88#10622602C2212yescomplemented
89#10622598C2212yescomplemented
90#10622597C2212yescomplemented
91#10622597C2212yescomplemented
92#10622596C2212yescomplemented
93#10622593C2212yescomplemented
94#10622586C2212yescomplemented
95#10622585C2212yescomplemented
96#10622585C2212yescomplemented
97#10622571C2211yescharacteristic
98#10622569C2212yes—
99#10622564C2212yescomplemented
100#10622563C2211yescharacteristic, complemented
101#10622561C2212yescomplemented
102#10622561C2212yescomplemented
103#10622561C2212yescomplemented
104#10622559C2211yescharacteristic, complemented
105#10622558C2212yescomplemented
106#10622557C2212yescomplemented
107#10622556C2211yescharacteristic, complemented
108#10622556C2211yescharacteristic, complemented
109#10622553C2212yescomplemented
110#10622541C2212yescomplemented
111#10622289C2212yescomplemented
112#10622283C2212yescomplemented
113#10622282C2212yescomplemented
114#10622281C2212yescomplemented
115#10622278C2212yes—
116#10622277C2212yescomplemented
117#10622277C2212yescomplemented
118D11×#95C2212yes—
119D11×#95C2212yes—
120D11×#95C2212yes—
121D11×#95C2212yes—
122#10622274C2212yescomplemented
123#10622270C2212yescomplemented
124#10622270C2212yescomplemented
125#10622260C2212yescomplemented
126#10622260C2212yescomplemented
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C2×D4×D11—24no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C22×D44C2311yescharacteristic
142C22×C4×D11—24no—
143C22×C4×D11—24no—
144C22×C4×D11—24no—
145C22×C4×D11—28no—
146C22×C4×D11—24no—
147C22×C4×D11—24no—
148C22×C4×D11—24no—
149C22×C4×D11D418yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2312yes—
163C11×#123—24no—
164C11×#123—24no—
165C11×#117—24no—
166C2×C11×C4⋊C4—24no—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C42×C11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2311yescharacteristic
189#66988—24no—
190#66988—24no—
191#66982—24no—
192#66982—24no—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205#66979—24no—
206C2×C4⋊Dic11—24no—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2312yes—
214C2×Dic11⋊C4—24no—
215C2×Dic11⋊C4—24no—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2311yescharacteristic
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233#66947—24no—
234#66947—24no—
235#66947—28no—
236#66945—28no—
237C4⋊C4×D11—28no—
238C4⋊C4×D11—28no—
239C4⋊C4×D11—28no—
240C4⋊C4×D11—28no—
241C4⋊C4×D11—28no—
242C4⋊C4×D11—28no—
243C4⋊C4×D11—24no—
244C4⋊C4×D11—24no—
245C4⋊C4×D11—28no—
246#66939—24no—
247#66939—24no—
248#66936—24no—
249#66936—24no—
250#66936—28no—
251C22⋊C4×D11—24no—
252C22⋊C4×D11—24no—
253C22⋊C4×D11—24no—
254C22⋊C4×D11—24no—
255C22⋊C4×D11—28no—
256C22⋊C4×D11—28no—
257C22⋊C4×D11D418yes—
258#66930—24no—
259#66930—24no—
260#66925—28no—
261C42×D11—28no—
262C11×#95C2312yes—
263C11×#95C2312yes—
264C11×#95C2312yes—
265C11×#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2312yes—
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270C11⋊#95C2312yes—
271C11⋊#95C2312yes—
272C11⋊#95C2312yes—
273C11⋊#95C2312yes—
274C11⋊#95C2312yes—
275C11⋊#95C2312yes—
276C11⋊#95C2312yes—
277C11⋊#95C2312yes—
278C2×#2413—111nomaximal, Sylow
279C24×C11C2411yescharacteristic
280C24×C11C2411yescharacteristic
281C23×D11—24no—
282C23×D11—24no—
283C23×D11—22no—
284C23×D11—22no—
285C23×D11—24no—
286C23×D11—22no—
287C23×D11—24no—
288C23×D11C2×D414yes—
289C23×D11C2×D414yes—
290C23×D11#4114yes—
291C23×D11C2411yescharacteristic
292C23×D11C2411yescharacteristic
293C23×D11C2411yescharacteristic
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—22no—
297C22×C4×C11—22no—
298C22×C4×C11—22no—
299C22×C4×C11—22no—
300C22×C4×C11—24no—
301C22×C4×C11—22no—
302C22×C4×C11—22no—
303C22×C4×C11—22no—
304C22×C4×C11C2×D414yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2412yes—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—22no—
320C22×Dic11—24no—
321C22×Dic11—22no—
322C22×Dic11—22no—
323C22×Dic11—22no—
324C22×Dic11—22no—
325C22×Dic11—22no—
326C22×Dic11—22no—
327C22×Dic11C2×D414yes—
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2412yes—
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2412yes—
337D4×D11—416no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44—22no—
341C2×C4×D11—232no—
342C2×C4×D11—24no—
343C2×C4×D11—232no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—22no—
349C2×C4×D11—22no—
350C2×C4×D11—24no—
351C2×C4×D11—22no—
352C2×C4×D11—22no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—24no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11—22no—
361C2×C4×D11—22no—
362C2×C4×D11—22no—
363C2×C4×D11—22no—
364C2×C4×D11—24no—
365C2×C4×D11—24no—
366C2×C4×D11—24no—
367C2×C4×D11—24no—
368C2×C4×D11—24no—
369C2×C4×D11—22no—
370C2×C4×D11—24no—
371C2×C4×D11—24no—
372C2×C4×D11—24no—
373C2×C4×D11—24no—
374C2×C4×D11—416no—
375C2×C4×D11C2×D418yes—
376C2×C4×D11C2×D414yes—
377C2×C4×D11C2×D414yes—
378C2×C4×D11C2×D414yes—
379C2×C4×D11C2×D414yes—
380C2×C4×D11#4118yes—
381C11×C4⋊C4—24no—
382C11×C4⋊C4—24no—
383C11×C4⋊C4—24no—
384C11×C4⋊C4—24no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—24no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—24no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—24no—
394C11×C22⋊C4C2×D414yes—
395C42×C11—24no—
396C22⋊Dic11—22no—
397C22⋊Dic11—22no—
398C22⋊Dic11—24no—
399C22⋊Dic11—24no—
400C22⋊Dic11—22no—
401C22⋊Dic11—22no—
402C22⋊Dic11C2×D414yes—
403(C2×D11)⋊C4—22no—
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—24no—
406(C2×D11)⋊C4—24no—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—22no—
409(C2×D11)⋊C4—22no—
410(C2×D11)⋊C4—24no—
411(C2×D11)⋊C4—22no—
412(C2×D11)⋊C4—22no—
413(C2×D11)⋊C4—24no—
414(C2×D11)⋊C4C2×D418yes—
415C4⋊Dic11—22no—
416C4⋊Dic11—22no—
417C4⋊Dic11—24no—
418C4⋊Dic11—24no—
419C4⋊Dic11—24no—
420C4⋊Dic11—24no—
421C4⋊Dic11—24no—
422Dic11⋊C4—24no—
423Dic11⋊C4—24no—
424Dic11⋊C4—24no—
425Dic11⋊C4—24no—
426Dic11⋊C4—22no—
427Dic11⋊C4—22no—
428Dic11⋊C4—24no—
429Dic11⋊C4—24no—
430Dic11⋊C4—24no—
431Dic11⋊C4—22no—
432Dic11⋊C4—22no—
433Dic11⋊C4—24no—
434Dic11⋊C4—24no—
435Dic11⋊C4—24no—
436C4×Dic11—24no—
437C4×Dic11—24no—
438C4×Dic11—24no—
439C22×#123—111no—
440C22×#123—111no—
441C22×#117—111no—
442C23×C4⋊C4—111no—
443#2413—112no—
444#2413—112no—
445#2413—112no—
446#2413—112no—
447#2413—111no—
448#2413—111no—
449#2413—111no—
450#2413—111no—
451#2413—111no—
452#2413—111no—
453#2413—111no—
454#2413D1111yescharacteristic, direct product factor
455C2×#398—112no—
456C2×#396—112no—
457C2×#389—112no—
458C2×#388—112no—
459C2×#386—111no—
460C2×#385—111no—
461C2×#381—111no—
462C23×C11—22no—
463C23×C11—22no—
464C23×C11—21no—
465C23×C11—21no—
466C23×C11—22no—
467C23×C11—21no—
468C23×C11—22no—
469C23×C11C22×D412yes—
470C23×C11C22×D412yes—
471C23×C11C2×#4112yes—
472C23×C11C2511yescharacteristic
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—28no—
476C22×D11—28no—
477C22×D11—216no—
478C22×D11—216no—
479C22×D11—21no—
480C22×D11—21no—
481C22×D11—22no—
482C22×D11—21no—
483C22×D11—22no—
484C22×D11—44no—
485C22×D11—44no—
486C22×D11—44no—
487C22×D11—48no—
488C22×D11—48no—
489C22×D11#121116yes—
490C22×D11C22×D412yes—
491C22×D11C22×D412yes—
492C22×D11C22×D412yes—
493C22×D11C22×D412yes—
494C22×D11C2×#4112yes—
495C22×D11C2×#4112yes—
496C22×D11C2×#4114yes—
497C22×D112−1+414yes—
498D4×C11—44no—
499C2×C4×C11—28no—
500C2×C4×C11—28no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—22no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—44no—
523C2×C4×C11C22×D414yes—
524C2×C4×C11C22×D412yes—
525C2×C4×C11C22×D412yes—
526C2×C4×C11C2×#4114yes—
527C22⋊D11—44no—
528C22⋊D11—44no—
529C2×Dic11—28no—
530C2×Dic11—28no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—21no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—44no—
553C2×Dic11C22×D414yes—
554C2×Dic11C22×D412yes—
555C2×Dic11C22×D412yes—
556C2×Dic11C2×#4114yes—
557D44—44no—
558C4×D11—216no—
559C4×D11—28no—
560C4×D11—28no—
561C4×D11—28no—
562C4×D11—28no—
563C4×D11—216no—
564C4×D11—216no—
565C4×D11—48no—
566C4×D11—48no—
567C4×D11—44no—
568C4×D11—44no—
569C4×D11—44no—
570C4×D11—48no—
571C23×D4—111no—
572C24×C4—111no—
573C24×C4—111no—
574C24×C4—111no—
575C2×#123—111no—
576C2×#123—111no—
577C2×#123—111no—
578C2×#123—111no—
579C2×#123—112no—
580C2×#123—111no—
581C2×#123—111no—
582C2×#123—112no—
583C2×#123—111no—
584C2×#123—111no—
585C2×#123—111no—
586C2×#123—111no—
587C2×#123—228no—
588C2×#123—228no—
589C2×#123C2×D1111yescharacteristic
590C2×#123C2×D1111yescharacteristic
591C2×#117—111no—
592C2×#117—112no—
593C2×#117—111no—
594C2×#117—111no—
595C2×#117—112no—
596C2×#117—228no—
597C2×#117C2×D1111yescharacteristic, complemented
598C22×C4⋊C4—111no—
599C22×C4⋊C4—111no—
600C22×C4⋊C4—111no—
601C22×C4⋊C4—112no—
602C22×C4⋊C4—112no—
603C22×C4⋊C4—112no—
604C22×C4⋊C4—111no—
605C22×C4⋊C4—112no—
606C22×C4⋊C4—112no—
607C22×C4⋊C4—111no—
608C22×C4⋊C4—112no—
609C22×C4⋊C4—112no—
610C22×C4⋊C4—228no—
611C22×C4⋊C4C2×D1111yescharacteristic, complemented
612C22×C22⋊C4—111no—
613C22×C22⋊C4—111no—
614C22×C22⋊C4—112no—
615C22×C22⋊C4—112no—
616C22×C22⋊C4—111no—
617C22×C22⋊C4—111no—
618C22×C22⋊C4—111no—
619C22×C42—112no—
620#398—112no—
621#398—112no—
622#398—112no—
623#398—112no—
624#398—112no—
625#398—112no—
626#398—112no—
627#398C2×D1112yescomplemented
628#396—112no—
629#396—112no—
630#396—112no—
631#396—112no—
632#396—112no—
633#396—112no—
634#396—112no—
635#396C2×D1112yescomplemented
636#389—112no—
637#389—112no—
638#389—112no—
639#389—112no—
640#389—112no—
641#389—112no—
642#389—112no—
643#389C2×D1112yescomplemented
644#388—112no—
645#388—112no—
646#388—112no—
647#388—112no—
648#388—112no—
649#388—112no—
650#388—112no—
651#388C2×D1112yescomplemented
652#386—111no—
653#386—111no—
654#386—112no—
655#386—111no—
656#386—112no—
657#386C2×D1111yescharacteristic
658#385—111no—
659#385—112no—
660#385—111no—
661#385—111no—
662#385—112no—
663#385C2×D1111yescharacteristic, complemented
664#381—111no—
665#381—111no—
666#381—111no—
667#381—112no—
668#381—112no—
669#381C2×D1111yescharacteristic, complemented
670C2×#95—112no—
671C2×#95—112no—
672C2×#95—112no—
673C2×#95—112no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—24no—
677C22×C11—24no—
678C22×C11—41no—
679C22×C11—41no—
680C22×C11—41no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11C2×#12114yes—
684C22×C11C23×D411yescharacteristic
685C22×C11C23×D411yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C22×C11C22×#4112yes—
688C22×C11C2×2−1+412yes—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—232no—
694C2×D11—41no—
695C2×D11—41no—
696C2×D11—41no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—88no—
700C2×D11C2×#12114yes—
701C2×D11C2×#12114yes—
702C2×D11#52514yes—
703C2×D11#53614yes—
704C2×D11#54718yes—
705C2×D11#55218yes—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—24no—
709C4×C11—24no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11—41no—
713C4×C11—41no—
714C4×C11—42no—
715Dic11—22no—
716Dic11—22no—
717Dic11—24no—
718Dic11—24no—
719Dic11—42no—
720Dic11—41no—
721Dic11—41no—
722Dic11—41no—
723Dic11—42no—
724C25—111no—
725C25—111no—
726C22×D4—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—224no—
730C22×D4—224no—
731C22×D4—224no—
732C22×D4C22×D1111yescharacteristic
733C23×C4—111no—
734C23×C4—118no—
735C23×C4—112no—
736C23×C4—111no—
737C23×C4—112no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—112no—
746C23×C4—112no—
747C23×C4—111no—
748C23×C4—112no—
749C23×C4—112no—
750C23×C4—228no—
751C23×C4—224no—
752C23×C4—224no—
753C23×C4—224no—
754C23×C4—224no—
755C23×C4—224no—
756C23×C4—224no—
757C23×C4C22×D1111yescharacteristic
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760#123—24no—
761#123—24no—
762#123—228no—
763#123—224no—
764#123—224no—
765#123—224no—
766#123—228no—
767#123—224no—
768#123—224no—
769#123—224no—
770#123—224no—
771#123—224no—
772#123—224no—
773#123—224no—
774#117—24no—
775#117—228no—
776#117—224no—
777#117—228no—
778#117—224no—
779#117—224no—
780C2×C4⋊C4—24no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—111no—
791C2×C4⋊C4—111no—
792C2×C4⋊C4—111no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4—112no—
796C2×C4⋊C4—111no—
797C2×C4⋊C4—111no—
798C2×C4⋊C4—111no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—112no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—228no—
803C2×C4⋊C4—228no—
804C2×C4⋊C4—228no—
805C2×C4⋊C4—228no—
806C2×C4⋊C4—228no—
807C2×C4⋊C4—228no—
808C2×C4⋊C4—224no—
809C2×C4⋊C4—224no—
810C2×C4⋊C4—228no—
811C2×C4⋊C4—224no—
812C2×C4⋊C4—224no—
813C2×C4⋊C4—224no—
814C2×C4⋊C4C22×D1112yes—
815C2×C4⋊C4C22×D1112yes—
816C2×C4⋊C4C22×D1112yes—
817C2×C4⋊C4C22×D1111yescharacteristic
818C2×C4⋊C4C22×D1112yes—
819C2×C4⋊C4C22×D1111yescharacteristic
820C2×C4⋊C4C22×D1112yes—
821C2×C22⋊C4—111no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—118no—
824C2×C22⋊C4—111no—
825C2×C22⋊C4—111no—
826C2×C22⋊C4—111no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—112no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—111no—
832C2×C22⋊C4—111no—
833C2×C22⋊C4—111no—
834C2×C22⋊C4—111no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—111no—
838C2×C22⋊C4—111no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—112no—
841C2×C22⋊C4—228no—
842C2×C22⋊C4—224no—
843C2×C22⋊C4—224no—
844C2×C22⋊C4—228no—
845C2×C22⋊C4—224no—
846C2×C22⋊C4—224no—
847C2×C22⋊C4C22×D1111yescharacteristic
848C2×C22⋊C4C22×D1111yescharacteristic
849C2×C22⋊C4C22×D1111yescharacteristic
850C2×C22⋊C4C22×D1112yes—
851C2×C22⋊C4C22×D1111yescharacteristic
852C2×C22⋊C4C22×D1112yes—
853C2×C22⋊C4C22×D1111yescharacteristic
854C2×C42—112no—
855C2×C42—112no—
856C2×C42—112no—
857C2×C42—228no—
858C2×C42C22×D1112yes—
859#95—112no—
860#95—112no—
861#95—112no—
862#95—112no—
863#95—112no—
864#95—112no—
865#95—112no—
866#95—112no—
867#95—112no—
868#95—112no—
869#95—112no—
870#95—112no—
871#95C22×D1112yes—
872#95C22×D1112yes—
873#95C22×D1112yes—
874#95C22×D1112yes—
875C2×C11—24no—
876C2×C11—81no—
877C2×C11C22×#12111yescharacteristic
878C2×C11C2×#52511yescharacteristic
879C2×C11C2×#53611yescharacteristic
880C2×C11C2×#54712yes—
881C2×C11C2×#55212yes—
882D11—24no—
883D11—81no—
884D11#241318yesdirect product factor
885C24—111no—
886C24—114no—
887C24—114no—
888C24—114no—
889C24—111no—
890C24—111no—
891C24—224no—
892C24—224no—
893C24—222no—
894C24—222no—
895C24—224no—
896C24—222no—
897C24—224no—
898C24C23×D1111yescharacteristic
899C24C23×D1111yescharacteristic
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—222no—
910C2×D4—222no—
911C2×D4—222no—
912C2×D4—4416no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—24no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—114no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—118no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—118no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—111no—
934C22×C4—112no—
935C22×C4—111no—
936C22×C4—224no—
937C22×C4—222no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—2232no—
945C22×C4—224no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—2232no—
952C22×C4—224no—
953C22×C4—222no—
954C22×C4—222no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—224no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—224no—
962C22×C4—224no—
963C22×C4—224no—
964C22×C4—224no—
965C22×C4—222no—
966C22×C4—224no—
967C22×C4—224no—
968C22×C4—224no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—224no—
973C22×C4—222no—
974C22×C4—222no—
975C22×C4—222no—
976C22×C4—4416no—
977C22×C4D4×D1114yes—
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1112yes—
980C22×C4C23×D1111yescharacteristic
981C22×C4C23×D1112yes—
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1112yes—
984C22×C4C23×D1111yescharacteristic
985C22×C4C23×D1111yescharacteristic
986C22×C4C23×D1112yes—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—224no—
995C4⋊C4—224no—
996C4⋊C4—224no—
997C4⋊C4—224no—
998C4⋊C4—224no—
999C4⋊C4—224no—
1000C4⋊C4—224no—
1001C4⋊C4—224no—
1002C4⋊C4—222no—
1003C4⋊C4—222no—
1004C4⋊C4—222no—
1005C4⋊C4—222no—
1006C4⋊C4—224no—
1007C4⋊C4—224no—
1008C4⋊C4—224no—
1009C4⋊C4—224no—
1010C4⋊C4—224no—
1011C4⋊C4—222no—
1012C4⋊C4—222no—
1013C4⋊C4—224no—
1014C4⋊C4—224no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—114no—
1022C22⋊C4—118no—
1023C22⋊C4—222no—
1024C22⋊C4—222no—
1025C22⋊C4—224no—
1026C22⋊C4—224no—
1027C22⋊C4—224no—
1028C22⋊C4—222no—
1029C22⋊C4—222no—
1030C22⋊C4—224no—
1031C22⋊C4—222no—
1032C22⋊C4—222no—
1033C22⋊C4—224no—
1034C22⋊C4—222no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—222no—
1038C22⋊C4—224no—
1039C22⋊C4—224no—
1040C22⋊C4D4×D1114yes—
1041C42—24no—
1042C42—224no—
1043C42—224no—
1044C42—224no—
1045C11C2×#241311yescharacteristic, complemented, Sylow
1046C23—22no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—21no—
1052C23—22no—
1053C23—112no—
1054C23—112no—
1055C23—114no—
1056C23—112no—
1057C23—114no—
1058C23—1116no—
1059C23—112no—
1060C23—112no—
1061C23—112no—
1062C23—228no—
1063C23—2216no—
1064C23—228no—
1065C23—2216no—
1066C23—222no—
1067C23—222no—
1068C23—221no—
1069C23—221no—
1070C23—222no—
1071C23—221no—
1072C23—222no—
1073C23—444no—
1074C23—448no—
1075C23—444no—
1076C23—448no—
1077C23—444no—
1078C23C2×D4×D1112yes—
1079C23C2×D4×D1112yes—
1080C23#41×D1112yes—
1081C23C24×D1111yescharacteristic
1082D4—44no—
1083D4—444no—
1084D4—444no—
1085D4—444no—
1086C2×C4—28no—
1087C2×C4—28no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—44no—
1110C2×C4—114no—
1111C2×C4—112no—
1112C2×C4—112no—
1113C2×C4—114no—
1114C2×C4—228no—
1115C2×C4—228no—
1116C2×C4—228no—
1117C2×C4—228no—
1118C2×C4—2216no—
1119C2×C4—2216no—
1120C2×C4—2216no—
1121C2×C4—228no—
1122C2×C4—228no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—221no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—221no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—448no—
1145C2×C4—448no—
1146C2×C4—444no—
1147C2×C4—444no—
1148C2×C4—448no—
1149C2×C4—444no—
1150C2×C4—444no—
1151C2×C4C2×D4×D1114yes—
1152C2×C4C2×D4×D1112yes—
1153C2×C4C2×D4×D1112yes—
1154C2×C4#41×D1114yes—
1155C22—24no—
1156C22—22no—
1157C22—24no—
1158C22—22no—
1159C22—42no—
1160C22—41no—
1161C22—42no—
1162C22—41no—
1163C22—41no—
1164C22—118no—
1165C22—114no—
1166C22—118no—
1167C22—114no—
1168C22—114no—
1169C22—114no—
1170C22—2232no—
1171C22—224no—
1172C22—222no—
1173C22—224no—
1174C22—222no—
1175C22—442no—
1176C22—441no—
1177C22—442no—
1178C22—441no—
1179C22—441no—
1180C22—888no—
1181C22D11×#12114yes—
1182C22C22×D4×D1111yescharacteristic
1183C22C22×D4×D1111yescharacteristic
1184C22C2×#41×D1111yescharacteristic
1185C22C2×#41×D1112yes—
1186C22D11×2−1+412yes—
1187C4—24no—
1188C4—22no—
1189C4—22no—
1190C4—24no—
1191C4—41no—
1192C4—42no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—224no—
1197C4—222no—
1198C4—222no—
1199C4—224no—
1200C4—441no—
1201C4—442no—
1202C4—442no—
1203C4—441no—
1204C4—441no—
1205C2—24no—
1206C2—81no—
1207C2—118no—
1208C2—224no—
1209C2—881no—
1210C2C2×D11×#12111yescharacteristic
1211C2D11×#52511yescharacteristic
1212C2D11×#53611yescharacteristic
1213C2D11×#54712yes—
1214C2D11×#55212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2413C2
prime radicalC22×D4×D11C22
hypercenter#2413D11
hypocenterC11C2×#2413
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2413

Complements

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

NH ≅ G/Ntype
3. C2×D11×#117C2semidirect
4. C22×C4⋊C4×D11C2semidirect
5. #13072026C2semidirect
6. #13072025C2semidirect
7. #13072024C2semidirect
8. #13072023C2semidirect
9. #13072022C2semidirect
10. #13072021C2semidirect
11. #13072020C2semidirect
12. #13072019C2semidirect
13. #13072018C2semidirect
14. #13072017C2semidirect
15. #13072016C2semidirect
16. D11×#398C2semidirect
17. D11×#396C2semidirect
18. D11×#389C2semidirect
19. D11×#388C2semidirect
21. D11×#385C2semidirect
22. D11×#381C2semidirect
23. C11×#2413C2semidirect
30. C2×C11×#117C22semidirect
31. C22×C11×C4⋊C4C22semidirect
36. C2×#66979C22semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×Dic11⋊C4C22semidirect
39. C22×Dic11⋊C4C22semidirect
46. C2×#66945C22semidirect
55. C2×C4⋊C4×D11C22semidirect
56. C2×C4⋊C4×D11C22semidirect
69. C2×#66930C22semidirect
70. C2×#66930C22semidirect
71. C2×#66925C22semidirect
73. C11×#398C22semidirect
74. C11×#396C22semidirect
75. C11×#389C22semidirect
76. C11×#388C22semidirect
78. C11×#385C22semidirect
79. C11×#381C22semidirect
82. #10622824C22semidirect
83. #10622823C22semidirect
84. #10622607C22semidirect
85. #10622607C22semidirect
86. #10622607C22semidirect
87. #10622603C22semidirect
88. #10622602C22semidirect
89. #10622598C22semidirect
90. #10622597C22semidirect
91. #10622597C22semidirect
92. #10622596C22semidirect
93. #10622593C22semidirect
94. #10622586C22semidirect
95. #10622585C22semidirect
96. #10622585C22semidirect
99. #10622564C22semidirect
100. #10622563C22semidirect
101. #10622561C22semidirect
102. #10622561C22semidirect
103. #10622561C22semidirect
104. #10622559C22semidirect
105. #10622558C22semidirect
106. #10622557C22semidirect
107. #10622556C22semidirect
108. #10622556C22semidirect
109. #10622553C22semidirect
110. #10622541C22semidirect
111. #10622289C22semidirect
112. #10622283C22semidirect
113. #10622282C22semidirect
114. #10622281C22semidirect
116. #10622277C22semidirect
117. #10622277C22semidirect
122. #10622274C22semidirect
123. #10622270C22semidirect
124. #10622270C22semidirect
125. #10622260C22semidirect
126. #10622260C22semidirect
454. #2413D11direct (N × H)
597. C2×#117C2×D11semidirect
611. C22×C4⋊C4C2×D11semidirect
627. #398C2×D11semidirect
635. #396C2×D11semidirect
643. #389C2×D11semidirect
651. #388C2×D11semidirect
663. #385C2×D11semidirect
669. #381C2×D11semidirect
884. D11#2413direct (N × H)
1045. C11C2×#2413semidirect

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×#1172
C22×C4⋊C4×D112
#130720262
#130720252
#130720242
#130720232
#130720222
#130720212
#130720202
#130720192
#130720182
#130720172
#130720162
D11×#3982
D11×#3962
D11×#3892
D11×#3882
D11×#3862
D11×#3852
D11×#3812
C11×#24132
C2×#241311