Finite Group Databasebeta

← D11×#2415 #14922179

Subgroups — D11×#2415 #14922179

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C4×D4×D11C211yesmaximal, characteristic
4C2×D11×#117C211yesmaximal, characteristic, complemented
5#13072048C211yesmaximal, characteristic, complemented
6#13072047C211yesmaximal, characteristic, complemented
7#13072046C211yesmaximal, characteristic, complemented
8#13072045C211yesmaximal, characteristic, complemented
9#13072044C212yesmaximal, complemented
10#13072043C211yesmaximal, characteristic, complemented
11#13072042C212yesmaximal, complemented
12#13072041C211yesmaximal, characteristic, complemented
13#13072040C212yesmaximal, complemented
14#13072039C211yesmaximal, characteristic, complemented
15#13072038C212yesmaximal, complemented
16D11×#397C212yesmaximal, complemented
17D11×#394C212yesmaximal
18D11×#391C211yesmaximal, characteristic, complemented
19D11×#389C212yesmaximal, complemented
20D11×#389C211yesmaximal, characteristic, complemented
21D11×#388C212yesmaximal, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2415C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C11×C22⋊Q8C2211yescharacteristic, complemented
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic, complemented
32C2×#66999C2211yescharacteristic, complemented
33C2×#66999C2211yescharacteristic, complemented
34C2×D4×Dic11C2211yescharacteristic
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×#66979C2211yescharacteristic, complemented
38C2×#66977C2211yescharacteristic, complemented
39C2×#66977C2211yescharacteristic, complemented
40D11×C22⋊Q8—28no—
41D11×C22⋊Q8—28no—
42C4×D4×D11—28no—
43D11×#117—28no—
44C2×#66950C2211yescharacteristic, complemented
45C2×#66950C2211yescharacteristic, complemented
46C2×#66949C2212yescomplemented
47C2×#66949C2212yescomplemented
48C2×#66946C2211yescharacteristic
49C2×#66945C2211yescharacteristic, complemented
50C2×#66945C2211yescharacteristic, complemented
51C2×C4⋊C4×D11C2211yescharacteristic
52C2×C4⋊C4×D11C2211yescharacteristic
53C2×C4⋊C4×D11C2211yescharacteristic
54C2×C4⋊C4×D11C2212yes—
55C2×C4⋊C4×D11C2212yes—
56C2×C4⋊C4×D11C2212yes—
57C2×C4⋊C4×D11C2211yescharacteristic
58C2×(C22⋊D11)⋊C4C2211yescharacteristic
59C2×(C22⋊D11)⋊C4C2211yescharacteristic
60C2×C22⋊C4×D11C2212yes—
61C2×C22⋊C4×D11C2212yes—
62C2×C22⋊C4×D11C2211yescharacteristic
63C2×C22⋊C4×D11C2211yescharacteristic
64C2×C22⋊C4×D11C2212yes—
65C2×C22⋊C4×D11C2212yes—
66C2×#66931C2212yescomplemented
67C2×#66931C2212yescomplemented
68C2×#66930C2212yescomplemented
69C2×C4×D44C2211yescharacteristic
70C2×#66925C2212yescomplemented
71C2×C42×D11C2212yes—
72C2×C42×D11C2211yescharacteristic
73C11×#397C2212yescomplemented
74C11×#394C2212yes—
75C11×#391C2211yescharacteristic, complemented
76C11×#389C2211yescharacteristic, complemented
77C11×#389C2212yescomplemented
78C11×#388C2212yescomplemented
79C11×#380C2211yescharacteristic, complemented
80#10622843C2211yescharacteristic, complemented
81#10622835C2212yes—
82#10622825C2211yescharacteristic, complemented
83#10622606C2212yescomplemented
84#10622604C2212yes—
85#10622603C2212yescomplemented
86#10622600C2211yescharacteristic, complemented
87#10622600C2211yescharacteristic, complemented
88#10622598C2212yescomplemented
89#10622598C2211yescharacteristic, complemented
90#10622587C2211yescharacteristic, complemented
91#10622586C2212yescomplemented
92#10622586C2211yescharacteristic, complemented
93#10622585C2212yescomplemented
94#10622585C2212yescomplemented
95#10622585C2212yescomplemented
96#10622574C2212yes—
97#10622574C2212yes—
98#10622572C2212yes—
99#10622572C2212yes—
100#10622566C2212yescomplemented
101#10622565C2212yescomplemented
102#10622565C2212yescomplemented
103#10622564C2212yescomplemented
104#10622558C2212yescomplemented
105#10622557C2212yescomplemented
106#10622555C2212yescomplemented
107#10622553C2212yescomplemented
108#10622542C2211yescharacteristic, complemented
109#10622541C2212yescomplemented
110#10622541C2211yescharacteristic, complemented
111#10622288C2212yescomplemented
112#10622288C2212yescomplemented
113#10622287C2212yescomplemented
114#10622285C2212yes—
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622280C2212yescomplemented
118D11×#95C2212yes—
119D11×#95C2212yes—
120D11×#95C2212yes—
121D11×#95C2212yes—
122#10622260C2212yescomplemented
123#10622260C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126#10622259C2212yescomplemented
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×Q8×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C2×Q8×D11—24no—
138C2×Q8×D11—24no—
139C2×Q8×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—24no—
142C2×D4×D11—24no—
143C22×D44C2311yescharacteristic
144C22×C4×D11—24no—
145C22×C4×D11—24no—
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×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×Dic22C2312yes—
164C22×Dic22C2311yescharacteristic
165C11×C22⋊Q8—24no—
166C11×C22⋊Q8—24no—
167C4×D4×C11—24no—
168C11×#117—24no—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2312yes—
182C2×C42×C11C2312yes—
183C2×C42×C11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2311yescharacteristic
189C2×C22⋊Dic11C2312yes—
190#66999—24no—
191#66999—24no—
192D4×Dic11—24no—
193C4×C22⋊D11—24no—
194C4×C22⋊D11—24no—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207#66979—24no—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215#66977—24no—
216#66977—24no—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234#66950—24no—
235#66950—24no—
236#66949—28no—
237#66949—28no—
238#66946—24no—
239#66945—24no—
240#66945—24no—
241C4⋊C4×D11—24no—
242C4⋊C4×D11—24no—
243C4⋊C4×D11—24no—
244C4⋊C4×D11—28no—
245C4⋊C4×D11—28no—
246C4⋊C4×D11—28no—
247C4⋊C4×D11D418yescomplemented
248(C22⋊D11)⋊C4—24no—
249(C22⋊D11)⋊C4—24no—
250C22⋊C4×D11—24no—
251C22⋊C4×D11—28no—
252C22⋊C4×D11—28no—
253C22⋊C4×D11—28no—
254C22⋊C4×D11—24no—
255C22⋊C4×D11—28no—
256#66931—28no—
257#66931—28no—
258#66930—28no—
259C4×D44—24no—
260#66925—28no—
261C42×D11—28no—
262C42×D11—24no—
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—
278C11⋊#95C2312yes—
279C2×#2415—111nomaximal, Sylow
280C24×C11C2411yescharacteristic
281C24×C11C2411yescharacteristic
282C23×D11—22no—
283C23×D11—22no—
284C23×D11—22no—
285C23×D11—22no—
286C23×D11—22no—
287C23×D11—22no—
288C23×D11—22no—
289C23×D11—22no—
290C23×D11—22no—
291C23×D11—22no—
292C23×D11—22no—
293C23×D11—22no—
294C23×D11C2×D414yes—
295C23×D11#4114yes—
296C23×D11C2411yescharacteristic
297C23×D11C2411yescharacteristic
298C23×D11C2411yescharacteristic
299C2×Q8×C11—22no—
300C2×Q8×C11—22no—
301C2×Q8×C11—22no—
302C2×D4×C11—22no—
303C2×D4×C11—22no—
304C2×D4×C11—22no—
305C22×C4×C11—22no—
306C22×C4×C11—22no—
307C22×C4×C11—22no—
308C22×C4×C11—22no—
309C22×C4×C11—22no—
310C22×C4×C11C2×D414yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2412yes—
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2412yes—
315C22×C4×C11C2412yes—
316C22×C4×C11C2412yes—
317C22×C4×C11C2411yescharacteristic
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C2×C22⋊D11—22no—
321C2×C22⋊D11—22no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—22no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—22no—
326C22×Dic11—22no—
327C22×Dic11—22no—
328C22×Dic11—22no—
329C22×Dic11—22no—
330C22×Dic11—22no—
331C22×Dic11C2×D414yes—
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2412yes—
334C22×Dic11C2412yes—
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2412yes—
337C22×Dic11C2412yes—
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2411yescharacteristic
341Q8×D11—416no—
342D4×D11—232no—
343C2×D44—22no—
344C2×D44—22no—
345C2×D44—22no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—232no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—22no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—24no—
356C2×C4×D11—24no—
357C2×C4×D11—22no—
358C2×C4×D11—24no—
359C2×C4×D11—24no—
360C2×C4×D11—22no—
361C2×C4×D11—24no—
362C2×C4×D11—22no—
363C2×C4×D11—22no—
364C2×C4×D11—24no—
365C2×C4×D11—24no—
366C2×C4×D11—24no—
367C2×C4×D11—22no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—22no—
371C2×C4×D11—22no—
372C2×C4×D11—24no—
373C2×C4×D11—22no—
374C2×C4×D11—22no—
375C2×C4×D11—22no—
376C2×C4×D11—22no—
377C2×C4×D11—22no—
378C2×C4×D11—416no—
379C2×C4×D11C2×D418yes—
380C2×C4×D11C2×D414yes—
381C2×C4×D11C2×D414yes—
382C2×C4×D11C2×D414yes—
383C2×C4×D11C2×D414yes—
384C2×C4×D11C2×D414yes—
385C2×C4×D11#4114yes—
386C2×C4×D11#4114yes—
387C2×Dic22—24no—
388C2×Dic22—24no—
389C2×Dic22—24no—
390C2×Dic22—22no—
391C2×Dic22—22no—
392C2×Dic22—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—24no—
396C11×C4⋊C4—24no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—24no—
399C11×C4⋊C4C2×D414yescomplemented
400C11×C22⋊C4—24no—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—24no—
403C11×C22⋊C4—24no—
404C11×C22⋊C4—24no—
405C11×C22⋊C4—22no—
406C42×C11—24no—
407C42×C11—22no—
408C22⋊Dic11—24no—
409C22⋊Dic11—24no—
410C22⋊Dic11—22no—
411C22⋊Dic11—24no—
412C22⋊Dic11—22no—
413C22⋊Dic11—24no—
414(C2×D11)⋊C4—24no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—24no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—24no—
420(C2×D11)⋊C4—24no—
421(C2×D11)⋊C4—24no—
422(C2×D11)⋊C4—24no—
423(C2×D11)⋊C4—24no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—24no—
426C4⋊Dic11—22no—
427C4⋊Dic11—24no—
428C4⋊Dic11—24no—
429C4⋊Dic11—24no—
430C4⋊Dic11—22no—
431C4⋊Dic11—22no—
432C4⋊Dic11C2×D414yescomplemented
433Dic11⋊C4—24no—
434Dic11⋊C4—24no—
435Dic11⋊C4—24no—
436Dic11⋊C4—24no—
437Dic11⋊C4—22no—
438Dic11⋊C4—24no—
439Dic11⋊C4—24no—
440Dic11⋊C4—22no—
441Dic11⋊C4—24no—
442Dic11⋊C4—24no—
443Dic11⋊C4C2×D418yescomplemented
444C4×Dic11—24no—
445C4×Dic11—24no—
446C4×Dic11—22no—
447C4×Dic11—22no—
448C4×Dic11—24no—
449C4×Dic11—22no—
450C22×C22⋊Q8—111no—
451C22×C22⋊Q8—111no—
452C22×C4×D4—111no—
453C22×#117—111no—
454#2415—112no—
455#2415—112no—
456#2415—111no—
457#2415—111no—
458#2415—112no—
459#2415—112no—
460#2415—111no—
461#2415—111no—
462#2415—111no—
463#2415—111no—
464#2415—111no—
465#2415D1111yescharacteristic, direct product factor
466C2×#397—112no—
467C2×#394—112no—
468C2×#391—111no—
469C2×#389—111no—
470C2×#389—112no—
471C2×#388—112no—
472C2×#380—111no—
473C23×C11—21no—
474C23×C11—21no—
475C23×C11—21no—
476C23×C11—21no—
477C23×C11—21no—
478C23×C11—21no—
479C23×C11—21no—
480C23×C11—21no—
481C23×C11—21no—
482C23×C11—21no—
483C23×C11—21no—
484C23×C11—21no—
485C23×C11C22×D412yes—
486C23×C11C2×#4112yes—
487C23×C11C2511yescharacteristic
488C22×D11—21no—
489C22×D11—21no—
490C22×D11—21no—
491C22×D11—21no—
492C22×D11—21no—
493C22×D11—21no—
494C22×D11—21no—
495C22×D11—21no—
496C22×D11—21no—
497C22×D11—21no—
498C22×D11—21no—
499C22×D11—21no—
500C22×D11—28no—
501C22×D11—28no—
502C22×D11—28no—
503C22×D11—28no—
504C22×D11—28no—
505C22×D11—28no—
506C22×D11—44no—
507C22×D11—44no—
508C22×D11—44no—
509C22×D11—44no—
510C22×D11—44no—
511C22×D11—44no—
512C22×D11—44no—
513C22×D11—44no—
514C22×D11C22×D412yes—
515C22×D11C22×D412yes—
516C22×D11C22×D412yes—
517C22×D11C2×#4112yes—
518C22×D11C2×#4112yes—
519C22×D11C2×#4112yes—
520C22×D11C2×#4112yes—
521C22×D112−1+412yes—
522C22×D112−1+412yes—
523Q8×C11—44no—
524D4×C11—28no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—28no—
532C2×C4×C11—22no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—22no—
547C2×C4×C11—44no—
548C2×C4×C11C22×D414yes—
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D412yes—
552C2×C4×C11C2×#4112yes—
553C2×C4×C11C2×#4112yes—
554C22⋊D11—28no—
555C22⋊D11—28no—
556C2×Dic11—21no—
557C2×Dic11—21no—
558C2×Dic11—22no—
559C2×Dic11—21no—
560C2×Dic11—21no—
561C2×Dic11—22no—
562C2×Dic11—28no—
563C2×Dic11—22no—
564C2×Dic11—21no—
565C2×Dic11—22no—
566C2×Dic11—21no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—21no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—21no—
577C2×Dic11—22no—
578C2×Dic11—44no—
579C2×Dic11C22×D414yes—
580C2×Dic11C22×D412yes—
581C2×Dic11C22×D412yes—
582C2×Dic11C22×D412yes—
583C2×Dic11C2×#4112yes—
584C2×Dic11C2×#4112yes—
585D44—28no—
586C4×D11—28no—
587C4×D11—28no—
588C4×D11—216no—
589C4×D11—28no—
590C4×D11—28no—
591C4×D11—44no—
592C4×D11—48no—
593C4×D11—48no—
594C4×D11—44no—
595C4×D11—48no—
596C4×D11—44no—
597C4×D11—44no—
598C4×D11#121116yes—
599Dic22—44no—
600Dic22—48no—
601C23×Q8—111no—
602C23×D4—111no—
603C24×C4—111no—
604C24×C4—111no—
605C2×C22⋊Q8—111no—
606C2×C22⋊Q8—111no—
607C2×C22⋊Q8—111no—
608C2×C22⋊Q8—111no—
609C2×C22⋊Q8—112no—
610C2×C22⋊Q8—112no—
611C2×C22⋊Q8—111no—
612C2×C22⋊Q8—111no—
613C2×C22⋊Q8—112no—
614C2×C22⋊Q8—112no—
615C2×C22⋊Q8—228no—
616C2×C22⋊Q8—228no—
617C2×C22⋊Q8C2×D1111yescharacteristic, complemented
618C2×C22⋊Q8C2×D1111yescharacteristic, complemented
619C2×C4×D4—111no—
620C2×C4×D4—111no—
621C2×C4×D4—111no—
622C2×C4×D4—111no—
623C2×C4×D4—111no—
624C2×C4×D4—111no—
625C2×C4×D4—111no—
626C2×C4×D4—228no—
627C2×C4×D4C2×D1111yescharacteristic
628C2×#117—111no—
629C2×#117—111no—
630C2×#117—111no—
631C2×#117—112no—
632C2×#117—112no—
633C2×#117—228no—
634C2×#117C2×D1111yescharacteristic, complemented
635C22×C4⋊C4—111no—
636C22×C4⋊C4—112no—
637C22×C4⋊C4—112no—
638C22×C4⋊C4—111no—
639C22×C4⋊C4—111no—
640C22×C4⋊C4—111no—
641C22×C4⋊C4—112no—
642C22×C22⋊C4—112no—
643C22×C22⋊C4—112no—
644C22×C22⋊C4—112no—
645C22×C22⋊C4—112no—
646C22×C22⋊C4—111no—
647C22×C22⋊C4—111no—
648C22×C42—112no—
649C22×C42—111no—
650#397—112no—
651#397—112no—
652#397—112no—
653#397—112no—
654#397—112no—
655#397—112no—
656#397—112no—
657#397C2×D1112yescomplemented
658#394—112no—
659#394—112no—
660#394—112no—
661#394—112no—
662#394—112no—
663#394—112no—
664#394—112no—
665#394C2×D1112yes—
666#391—111no—
667#391—111no—
668#391—111no—
669#391—112no—
670#391—112no—
671#391C2×D1111yescharacteristic, complemented
672#389—112no—
673#389—112no—
674#389—112no—
675#389—112no—
676#389—111no—
677#389—112no—
678#389—111no—
679#389—112no—
680#389—111no—
681#389—112no—
682#389—112no—
683#389—112no—
684#389C2×D1112yescomplemented
685#389C2×D1111yescharacteristic, complemented
686#388—112no—
687#388—112no—
688#388—112no—
689#388—112no—
690#388—112no—
691#388—112no—
692#388—112no—
693#388C2×D1112yescomplemented
694#380—111no—
695#380—111no—
696#380—111no—
697#380—112no—
698#380—112no—
699#380C2×D1111yescharacteristic, complemented
700C2×#95—112no—
701C2×#95—112no—
702C2×#95—112no—
703C2×#95—112no—
704C22×C11—22no—
705C22×C11—22no—
706C22×C11—22no—
707C22×C11—22no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—41no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—41no—
714C22×C11—41no—
715C22×C11—41no—
716C22×C11—41no—
717C22×C11—41no—
718C22×C11C23×D411yescharacteristic
719C22×C11C23×D411yescharacteristic
720C22×C11C22×#4111yescharacteristic
721C22×C11C22×#4111yescharacteristic
722C22×C11C22×#4111yescharacteristic
723C22×C11C2×2−1+411yescharacteristic
724C22×C11C2×2−1+411yescharacteristic
725C2×D11—22no—
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—22no—
730C2×D11—22no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—41no—
734C2×D11—41no—
735C2×D11—41no—
736C2×D11—41no—
737C2×D11—41no—
738C2×D11—41no—
739C2×D11—416no—
740C2×D11—416no—
741C2×D11C2×#12114yes—
742C2×D11#52514yes—
743C2×D11#53614yes—
744C2×D11#54714yes—
745C2×D11#54814yes—
746C2×D11#55214yes—
747C2×D11#55614yes—
748C4×C11—22no—
749C4×C11—22no—
750C4×C11—24no—
751C4×C11—41no—
752C4×C11—42no—
753C4×C11—42no—
754C4×C11—41no—
755C4×C11—42no—
756C4×C11C2×#12114yes—
757Dic11—22no—
758Dic11—22no—
759Dic11—24no—
760Dic11—42no—
761Dic11—41no—
762Dic11—42no—
763Dic11—41no—
764Dic11—42no—
765Dic11C2×#12114yes—
766C25—111no—
767C25—111no—
768C22×Q8—112no—
769C22×Q8—111no—
770C22×Q8—224no—
771C22×Q8—224no—
772C22×Q8—224no—
773C22×Q8C22×D1111yescharacteristic
774C22×D4—111no—
775C22×D4—111no—
776C22×D4—111no—
777C22×D4—224no—
778C22×D4—224no—
779C22×D4—224no—
780C22×D4C22×D1111yescharacteristic
781C23×C4—111no—
782C23×C4—111no—
783C23×C4—118no—
784C23×C4—112no—
785C23×C4—111no—
786C23×C4—111no—
787C23×C4—111no—
788C23×C4—111no—
789C23×C4—111no—
790C23×C4—112no—
791C23×C4—112no—
792C23×C4—112no—
793C23×C4—111no—
794C23×C4—111no—
795C23×C4—111no—
796C23×C4—111no—
797C23×C4—224no—
798C23×C4—224no—
799C23×C4—224no—
800C23×C4—224no—
801C23×C4—224no—
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C22⋊Q8—24no—
805C22⋊Q8—24no—
806C22⋊Q8—228no—
807C22⋊Q8—228no—
808C22⋊Q8—228no—
809C22⋊Q8—228no—
810C22⋊Q8—224no—
811C22⋊Q8—224no—
812C22⋊Q8—224no—
813C22⋊Q8—224no—
814C22⋊Q8—224no—
815C22⋊Q8—224no—
816C4×D4—24no—
817C4×D4—224no—
818C4×D4—224no—
819C4×D4—224no—
820C4×D4—224no—
821C4×D4—224no—
822C4×D4—224no—
823C4×D4—224no—
824#117—24no—
825#117—228no—
826#117—228no—
827#117—224no—
828#117—224no—
829#117—224no—
830C2×C4⋊C4—112no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—118no—
833C2×C4⋊C4—112no—
834C2×C4⋊C4—111no—
835C2×C4⋊C4—111no—
836C2×C4⋊C4—111no—
837C2×C4⋊C4—111no—
838C2×C4⋊C4—112no—
839C2×C4⋊C4—111no—
840C2×C4⋊C4—112no—
841C2×C4⋊C4—112no—
842C2×C4⋊C4—112no—
843C2×C4⋊C4—112no—
844C2×C4⋊C4—112no—
845C2×C4⋊C4—112no—
846C2×C4⋊C4—112no—
847C2×C4⋊C4—112no—
848C2×C4⋊C4—112no—
849C2×C4⋊C4—224no—
850C2×C4⋊C4—224no—
851C2×C4⋊C4—224no—
852C2×C4⋊C4—228no—
853C2×C4⋊C4—228no—
854C2×C4⋊C4—228no—
855C2×C4⋊C4C22×D1111yescharacteristic
856C2×C4⋊C4C22×D1111yescharacteristic
857C2×C4⋊C4C22×D1111yescharacteristic
858C2×C4⋊C4C22×D1112yes—
859C2×C4⋊C4C22×D1112yes—
860C2×C4⋊C4C22×D1112yes—
861C2×C4⋊C4C22×D1111yescharacteristic
862C2×C22⋊C4—112no—
863C2×C22⋊C4—111no—
864C2×C22⋊C4—111no—
865C2×C22⋊C4—112no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—111no—
871C2×C22⋊C4—111no—
872C2×C22⋊C4—111no—
873C2×C22⋊C4—111no—
874C2×C22⋊C4—112no—
875C2×C22⋊C4—112no—
876C2×C22⋊C4—112no—
877C2×C22⋊C4—112no—
878C2×C22⋊C4—112no—
879C2×C22⋊C4—112no—
880C2×C22⋊C4—228no—
881C2×C22⋊C4—224no—
882C2×C22⋊C4—228no—
883C2×C22⋊C4—224no—
884C2×C22⋊C4—228no—
885C2×C22⋊C4—228no—
886C2×C22⋊C4C22×D1112yes—
887C2×C22⋊C4C22×D1111yescharacteristic
888C2×C22⋊C4C22×D1111yescharacteristic
889C2×C22⋊C4C22×D1112yes—
890C2×C22⋊C4C22×D1112yes—
891C2×C22⋊C4C22×D1112yes—
892C2×C42—112no—
893C2×C42—112no—
894C2×C42—112no—
895C2×C42—111no—
896C2×C42—111no—
897C2×C42—111no—
898C2×C42—228no—
899C2×C42—224no—
900C2×C42C22×D1112yes—
901C2×C42C22×D1111yescharacteristic
902#95—112no—
903#95—112no—
904#95—112no—
905#95—112no—
906#95—112no—
907#95—112no—
908#95—112no—
909#95—112no—
910#95—112no—
911#95—112no—
912#95—112no—
913#95—112no—
914#95C22×D1112yes—
915#95C22×D1112yes—
916#95C22×D1112yes—
917#95C22×D1112yes—
918C2×C11—42no—
919C2×C11—42no—
920C2×C11C22×#12111yescharacteristic
921C2×C11C2×#52511yescharacteristic
922C2×C11C2×#53611yescharacteristic
923C2×C11C2×#54711yescharacteristic
924C2×C11C2×#54811yescharacteristic
925C2×C11C2×#55211yescharacteristic
926C2×C11C2×#55611yescharacteristic
927D11—42no—
928D11—42no—
929D11#241518yesdirect product factor
930C24—111no—
931C24—114no—
932C24—114no—
933C24—111no—
934C24—111no—
935C24—222no—
936C24—222no—
937C24—222no—
938C24—222no—
939C24—222no—
940C24—222no—
941C24—222no—
942C24—222no—
943C24—222no—
944C24—222no—
945C24—222no—
946C24—222no—
947C24C23×D1111yescharacteristic
948C24C23×D1111yescharacteristic
949C2×Q8—22no—
950C2×Q8—22no—
951C2×Q8—22no—
952C2×Q8—224no—
953C2×Q8—224no—
954C2×Q8—224no—
955C2×Q8—222no—
956C2×Q8—222no—
957C2×Q8—222no—
958C2×Q8—4416no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—222no—
963C2×D4—222no—
964C2×D4—222no—
965C2×D4—222no—
966C2×D4—2232no—
967C2×D4—222no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—222no—
971C2×D4—222no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—111no—
978C22×C4—114no—
979C22×C4—114no—
980C22×C4—114no—
981C22×C4—114no—
982C22×C4—111no—
983C22×C4—112no—
984C22×C4—111no—
985C22×C4—118no—
986C22×C4—114no—
987C22×C4—114no—
988C22×C4—114no—
989C22×C4—114no—
990C22×C4—111no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—111no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—2232no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—222no—
1001C22×C4—222no—
1002C22×C4—222no—
1003C22×C4—224no—
1004C22×C4—222no—
1005C22×C4—222no—
1006C22×C4—224no—
1007C22×C4—222no—
1008C22×C4—224no—
1009C22×C4—224no—
1010C22×C4—222no—
1011C22×C4—224no—
1012C22×C4—224no—
1013C22×C4—224no—
1014C22×C4—224no—
1015C22×C4—222no—
1016C22×C4—224no—
1017C22×C4—222no—
1018C22×C4—224no—
1019C22×C4—224no—
1020C22×C4—222no—
1021C22×C4—222no—
1022C22×C4—222no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—222no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4—222no—
1030C22×C4—222no—
1031C22×C4—222no—
1032C22×C4—4416no—
1033C22×C4D4×D1114yes—
1034C22×C4C23×D1111yescharacteristic
1035C22×C4C23×D1112yes—
1036C22×C4C23×D1112yes—
1037C22×C4C23×D1112yes—
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1112yes—
1040C22×C4C23×D1111yescharacteristic
1041C22×C4C23×D1111yescharacteristic
1042C22×C4C23×D1111yescharacteristic
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—118no—
1050C4⋊C4—114no—
1051C4⋊C4—224no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—224no—
1055C4⋊C4—224no—
1056C4⋊C4—224no—
1057C4⋊C4—224no—
1058C4⋊C4—224no—
1059C4⋊C4—224no—
1060C4⋊C4—224no—
1061C4⋊C4—222no—
1062C4⋊C4—222no—
1063C4⋊C4—224no—
1064C4⋊C4—222no—
1065C4⋊C4—224no—
1066C4⋊C4—224no—
1067C4⋊C4D4×D1114yescomplemented
1068C22⋊C4—22no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—22no—
1073C22⋊C4—24no—
1074C22⋊C4—224no—
1075C22⋊C4—222no—
1076C22⋊C4—224no—
1077C22⋊C4—222no—
1078C22⋊C4—222no—
1079C22⋊C4—224no—
1080C22⋊C4—224no—
1081C22⋊C4—224no—
1082C22⋊C4—224no—
1083C22⋊C4—224no—
1084C22⋊C4—222no—
1085C22⋊C4—224no—
1086C22⋊C4—222no—
1087C22⋊C4—224no—
1088C22⋊C4—224no—
1089C22⋊C4—224no—
1090C22⋊C4—222no—
1091C22⋊C4—224no—
1092C42—24no—
1093C42—22no—
1094C42—224no—
1095C42—224no—
1096C42—222no—
1097C42—222no—
1098C42—224no—
1099C42—222no—
1100C11C2×#241511yescharacteristic, complemented, Sylow
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—112no—
1114C23—112no—
1115C23—112no—
1116C23—112no—
1117C23—112no—
1118C23—112no—
1119C23—112no—
1120C23—112no—
1121C23—112no—
1122C23—228no—
1123C23—228no—
1124C23—228no—
1125C23—228no—
1126C23—228no—
1127C23—228no—
1128C23—221no—
1129C23—221no—
1130C23—221no—
1131C23—221no—
1132C23—221no—
1133C23—221no—
1134C23—221no—
1135C23—221no—
1136C23—221no—
1137C23—221no—
1138C23—221no—
1139C23—221no—
1140C23—444no—
1141C23—444no—
1142C23—444no—
1143C23—444no—
1144C23—444no—
1145C23—444no—
1146C23—444no—
1147C23—444no—
1148C23C2×D4×D1112yes—
1149C23#41×D1112yes—
1150C23C24×D1111yescharacteristic
1151Q8—44no—
1152Q8—448no—
1153Q8—444no—
1154D4—28no—
1155D4—228no—
1156D4—228no—
1157D4—228no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—28no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—44no—
1181C2×C4—112no—
1182C2×C4—112no—
1183C2×C4—112no—
1184C2×C4—1116no—
1185C2×C4—114no—
1186C2×C4—112no—
1187C2×C4—112no—
1188C2×C4—228no—
1189C2×C4—228no—
1190C2×C4—228no—
1191C2×C4—2216no—
1192C2×C4—228no—
1193C2×C4—221no—
1194C2×C4—221no—
1195C2×C4—222no—
1196C2×C4—221no—
1197C2×C4—221no—
1198C2×C4—222no—
1199C2×C4—228no—
1200C2×C4—221no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—221no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—221no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—221no—
1211C2×C4—222no—
1212C2×C4—221no—
1213C2×C4—221no—
1214C2×C4—222no—
1215C2×C4—444no—
1216C2×C4—444no—
1217C2×C4—448no—
1218C2×C4—444no—
1219C2×C4—448no—
1220C2×C4—448no—
1221C2×C4—444no—
1222C2×C4—444no—
1223C2×C4C2×D4×D1114yes—
1224C2×C4C2×D4×D1112yes—
1225C2×C4C2×D4×D1112yes—
1226C2×C4C2×D4×D1112yes—
1227C2×C4#41×D1112yes—
1228C2×C4#41×D1112yes—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—114no—
1244C22—114no—
1245C22—114no—
1246C22—114no—
1247C22—114no—
1248C22—114no—
1249C22—114no—
1250C22—222no—
1251C22—222no—
1252C22—222no—
1253C22—222no—
1254C22—222no—
1255C22—222no—
1256C22—4416no—
1257C22—4416no—
1258C22—441no—
1259C22—441no—
1260C22—441no—
1261C22—441no—
1262C22—441no—
1263C22—441no—
1264C22—441no—
1265C22—441no—
1266C22C22×D4×D1111yescharacteristic
1267C22C22×D4×D1111yescharacteristic
1268C22C2×#41×D1111yescharacteristic
1269C22C2×#41×D1111yescharacteristic
1270C22C2×#41×D1111yescharacteristic
1271C22D11×2−1+411yescharacteristic
1272C22D11×2−1+411yescharacteristic
1273C4—24no—
1274C4—22no—
1275C4—22no—
1276C4—41no—
1277C4—42no—
1278C4—41no—
1279C4—42no—
1280C4—42no—
1281C4—114no—
1282C4—224no—
1283C4—222no—
1284C4—222no—
1285C4—441no—
1286C4—442no—
1287C4—441no—
1288C4—442no—
1289C4—442no—
1290C4D11×#12114yes—
1291C2—42no—
1292C2—42no—
1293C2—118no—
1294C2—442no—
1295C2—442no—
1296C2C2×D11×#12111yescharacteristic
1297C2D11×#52511yescharacteristic
1298C2D11×#53611yescharacteristic
1299C2D11×#54711yescharacteristic
1300C2D11×#54811yescharacteristic
1301C2D11×#55211yescharacteristic
1302C2D11×#55611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2415C2
prime radicalC22×D4×D11C22
hypercenter#2415D11
hypocenterC11C2×#2415
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2415

Complements

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

NH ≅ G/Ntype
1. C2×D11×C22⋊Q8C2semidirect
2. C2×D11×C22⋊Q8C2semidirect
4. C2×D11×#117C2semidirect
5. #13072048C2semidirect
6. #13072047C2semidirect
7. #13072046C2semidirect
8. #13072045C2semidirect
9. #13072044C2semidirect
10. #13072043C2semidirect
11. #13072042C2semidirect
12. #13072041C2semidirect
13. #13072040C2semidirect
14. #13072039C2semidirect
15. #13072038C2semidirect
16. D11×#397C2semidirect
18. D11×#391C2semidirect
19. D11×#389C2semidirect
20. D11×#389C2semidirect
21. D11×#388C2semidirect
22. D11×#380C2semidirect
23. C11×#2415C2semidirect
28. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×C22⋊Q8C22semidirect
31. C2×C11×#117C22semidirect
32. C2×#66999C22semidirect
33. C2×#66999C22semidirect
37. C2×#66979C22semidirect
38. C2×#66977C22semidirect
39. C2×#66977C22semidirect
44. C2×#66950C22semidirect
45. C2×#66950C22semidirect
46. C2×#66949C22semidirect
47. C2×#66949C22semidirect
49. C2×#66945C22semidirect
50. C2×#66945C22semidirect
66. C2×#66931C22semidirect
67. C2×#66931C22semidirect
68. C2×#66930C22semidirect
70. C2×#66925C22semidirect
73. C11×#397C22semidirect
75. C11×#391C22semidirect
76. C11×#389C22semidirect
77. C11×#389C22semidirect
78. C11×#388C22semidirect
79. C11×#380C22semidirect
80. #10622843C22semidirect
82. #10622825C22semidirect
83. #10622606C22semidirect
85. #10622603C22semidirect
86. #10622600C22semidirect
87. #10622600C22semidirect
88. #10622598C22semidirect
89. #10622598C22semidirect
90. #10622587C22semidirect
91. #10622586C22semidirect
92. #10622586C22semidirect
93. #10622585C22semidirect
94. #10622585C22semidirect
95. #10622585C22semidirect
100. #10622566C22semidirect
101. #10622565C22semidirect
102. #10622565C22semidirect
103. #10622564C22semidirect
104. #10622558C22semidirect
105. #10622557C22semidirect
106. #10622555C22semidirect
107. #10622553C22semidirect
108. #10622542C22semidirect
109. #10622541C22semidirect
110. #10622541C22semidirect
111. #10622288C22semidirect
112. #10622288C22semidirect
113. #10622287C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
117. #10622280C22semidirect
122. #10622260C22semidirect
123. #10622260C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
126. #10622259C22semidirect
247. C4⋊C4×D11D4semidirect
399. C11×C4⋊C4C2×D4semidirect
432. C4⋊Dic11C2×D4semidirect
443. Dic11⋊C4C2×D4semidirect
465. #2415D11direct (N × H)
617. C2×C22⋊Q8C2×D11semidirect
618. C2×C22⋊Q8C2×D11semidirect
634. C2×#117C2×D11semidirect
657. #397C2×D11semidirect
671. #391C2×D11semidirect
684. #389C2×D11semidirect
685. #389C2×D11semidirect
693. #388C2×D11semidirect
699. #380C2×D11semidirect
929. D11#2415direct (N × H)
1067. C4⋊C4D4×D11semidirect
1100. C11C2×#2415semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×C4×D4×D112
C2×D11×#1172
#130720482
#130720472
#130720462
#130720452
#130720442
#130720432
#130720422
#130720412
#130720402
#130720392
#130720382
D11×#3972
D11×#3942
D11×#3912
D11×#3892
D11×#3882
D11×#3802
C11×#24152
C2×#241511