Finite Group Databasebeta

← D11×#2360 #14913284

Subgroups — D11×#2360 #14913284

Order 2816.

3614 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D11C211yesmaximal, characteristic
4#13071626C211yesmaximal, characteristic, complemented
5#13071625C211yesmaximal, characteristic, complemented
6#13071624C212yesmaximal, complemented
7#13071623C211yesmaximal, characteristic, complemented
8#13071622C212yesmaximal, complemented
9#13071621C211yesmaximal, characteristic, complemented
10#13071620C211yesmaximal, characteristic, complemented
11#13071619C211yesmaximal, characteristic, complemented
12#13071618C212yesmaximal, complemented
13#13071617C211yesmaximal, characteristic, complemented
14#13071616C212yesmaximal, complemented
15D11×#391C211yesmaximal, characteristic, complemented
16D11×#389C211yesmaximal, characteristic, complemented
17D11×#389C212yesmaximal, complemented
18D11×#387C212yesmaximal, complemented
19D11×#385C212yesmaximal
20C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
21C4×C22⋊C4×D11C211yesmaximal, characteristic
22C4×C22⋊C4×D11C212yesmaximal
23C11×#2360C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C22×C4⋊Dic11C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35D11×C22⋊Q8C4116yescomplemented
36C4×Q8×D11—28no—
37C2×#66950C2211yescharacteristic
38C2×#66949C2212yes—
39C2×C4⋊C4×D11—28no—
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2212yes—
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×C4⋊C4×D11C2212yes—
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2212yes—
46C2×C4⋊C4×D11C2212yes—
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2212yes—
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66940C2212yescomplemented
51C2×#66940C2211yescharacteristic, complemented
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×#66931C2212yes—
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2212yes—
58C2×C42×D11C2211yescharacteristic
59C2×C42×D11C2212yes—
60C2×C4×Dic22C2211yescharacteristic, complemented
61C2×C4×Dic22C2212yescomplemented
62C11×#391C2211yescharacteristic, complemented
63C11×#389C2212yescomplemented
64C11×#389C2211yescharacteristic, complemented
65C11×#387C2212yescomplemented
66C11×#385C2212yes—
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yes—
70#10622843C2211yescharacteristic, complemented
71#10622823C2212yes—
72C4×C22⋊Dic11C2212yes—
73C4×C22⋊Dic11C2211yescharacteristic
74#10622602C2212yes—
75#10622602C2212yes—
76#10622598C2211yescharacteristic, complemented
77#10622598C2212yescomplemented
78#10622594C2212yescomplemented
79#10622591C2212yescomplemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82#10622587C2211yescharacteristic, complemented
83#10622586C2212yescomplemented
84#10622586C2211yescharacteristic, complemented
85#10622585C2212yescomplemented
86#10622585C2212yescomplemented
87#10622585C2212yescomplemented
88#10622563C2212yes—
89#10622559C2212yes—
90C22⋊C4×Dic11C2211yescharacteristic
91C22⋊C4×Dic11C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2211yescharacteristic
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2212yes—
96C4×(C2×D11)⋊C4C2212yes—
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×C4⋊Dic11C2211yescharacteristic, complemented
99#10622546C2212yescomplemented
100C4×Dic11⋊C4C2212yescomplemented
101#10622542C2211yescharacteristic, complemented
102#10622541C2211yescharacteristic, complemented
103#10622541C2212yescomplemented
104#10622281C2212yes—
105#10622281C2212yes—
106#10622279C2211yescharacteristic
107#10622279C2212yes—
108#10622279C2212yes—
109#10622279C2211yescharacteristic
110D11×#95C2211yescharacteristic
111D11×#95C2212yes—
112D11×#95C2211yescharacteristic
113D11×#95C2212yes—
114D11×#95C2212yes—
115D11×#95C2212yes—
116#10622268C2212yescomplemented
117#10622267C2212yescomplemented
118#10622266C2212yescomplemented
119#10622265C2212yescomplemented
120#10622262C2212yescomplemented
121#10622260C2212yescomplemented
122#10622260C2212yescomplemented
123#10622260C2212yescomplemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×Dic11C2312yes—
131C23×Dic11C2311yescharacteristic
132C2×Q8×D11—24no—
133C2×Q8×D11—24no—
134C2×Q8×D11C2×C418yescomplemented
135C22×C4×D11—24no—
136C22×C4×D11—24no—
137C22×C4×D11—28no—
138C22×C4×D11—28no—
139C22×C4×D11—44no—
140C22×C4×D11C2×C418yes—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×Dic22C2312yes—
156C22×Dic22C2311yescharacteristic
157C11×C22⋊Q8C2×C418yescomplemented
158C4×Q8×C11—24no—
159C2×C11×C4⋊C4—24no—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177#66999C2×C418yescomplemented
178Q8×Dic11—24no—
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×C4⋊Dic11—24no—
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2312yes—
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2312yes—
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193#66977C2×C418yescomplemented
194C2×Dic11⋊C4—28no—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218#66950C2×C418yescomplemented
219#66949C2×C4116yescomplemented
220C4⋊C4×D11—24no—
221C4⋊C4×D11—28no—
222C4⋊C4×D11—28no—
223C4⋊C4×D11—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—28no—
226C4⋊C4×D11—44no—
227C4⋊C4×D11C2×C418yescomplemented
228C4⋊C4×D11C2×C4116yescomplemented
229C4⋊C4×D11D418yes—
230#66940—24no—
231#66940—28no—
232C22⋊C4×D11—24no—
233C22⋊C4×D11C2×C4116yes—
234C22⋊C4×D11Q818yescomplemented
235#66931C2×C4116yescomplemented
236C42×D11—24no—
237C42×D11—28no—
238C42×D11—24no—
239C42×D11—44no—
240C4×Dic22—24no—
241C4×Dic22—28no—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2311yescharacteristic
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2312yes—
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2311yescharacteristic
264C11⋊#95C2312yes—
265C11⋊#95C2311yescharacteristic
266C2×#2360—111nomaximal, Sylow
267C24×C11C2411yescharacteristic
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11C22×C414yes—
273C23×D11C2×Q814yes—
274C23×D11#4114yes—
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C2×Q8×C11—22no—
278C2×Q8×C11—22no—
279C2×Q8×C11C22×C414yescomplemented
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—24no—
284C22×C4×C11—42no—
285C22×C4×C11C22×C414yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—24no—
299C22×Dic11—24no—
300C22×Dic11—42no—
301C22×Dic11C22×C414yes—
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2412yes—
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312Q8×D11—232no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—232no—
316C2×C4×D11—24no—
317C2×C4×D11—22no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—24no—
325C2×C4×D11—24no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—22no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—432no—
346C2×C4×D11C22×C418yes—
347C2×C4×D11C22×C418yes—
348C2×C4×D11C22×C414yes—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C22×C414yes—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C2×D418yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×Q814yes—
355C2×C4×D11C2×Q814yes—
356C2×C4×D11#4114yes—
357C2×Dic22—24no—
358C2×Dic22—24no—
359C2×Dic22—22no—
360C2×Dic22—22no—
361C2×Dic22C22×C418yescomplemented
362C2×Dic22C22×C414yescomplemented
363C11×C4⋊C4—24no—
364C11×C4⋊C4—24no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—42no—
367C11×C4⋊C4C22×C418yescomplemented
368C11×C4⋊C4C22×C414yescomplemented
369C11×C4⋊C4C2×D414yes—
370C11×C22⋊C4—22no—
371C11×C22⋊C4C22×C418yes—
372C11×C22⋊C4C2×Q814yescomplemented
373C42×C11—24no—
374C42×C11—22no—
375C42×C11—22no—
376C42×C11—42no—
377C22⋊Dic11—22no—
378C22⋊Dic11C22×C418yes—
379C22⋊Dic11C2×Q814yescomplemented
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4C22×C418yes—
383(C2×D11)⋊C4C22×C418yes—
384(C2×D11)⋊C4C2×Q814yescomplemented
385(C2×D11)⋊C4C2×Q814yescomplemented
386C4⋊Dic11—24no—
387C4⋊Dic11—24no—
388C4⋊Dic11—22no—
389C4⋊Dic11—42no—
390C4⋊Dic11C22×C418yescomplemented
391C4⋊Dic11C22×C414yescomplemented
392C4⋊Dic11C2×D414yes—
393Dic11⋊C4—24no—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—24no—
397Dic11⋊C4—24no—
398Dic11⋊C4—42no—
399Dic11⋊C4—42no—
400Dic11⋊C4C22×C418yescomplemented
401Dic11⋊C4C22×C418yescomplemented
402Dic11⋊C4C22×C418yescomplemented
403Dic11⋊C4C2×D418yes—
404C4×Dic11—24no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—24no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—42no—
414C4×Dic11—42no—
415C4×Dic11—42no—
416C22×C22⋊Q8—111no—
417C22×C4×Q8—111no—
418C23×C4⋊C4—111no—
419#2360—111no—
420#2360—112no—
421#2360—111no—
422#2360—112no—
423#2360—112no—
424#2360—111no—
425#2360—111no—
426#2360—112no—
427#2360—111no—
428#2360—111no—
429#2360—111no—
430#2360D1111yescharacteristic, direct product factor
431C2×#391—111no—
432C2×#389—111no—
433C2×#389—112no—
434C2×#387—112no—
435C2×#385—112no—
436C2×C4×C4⋊C4—111no—
437C2×C4×C22⋊C4—112no—
438C2×C4×C22⋊C4—111no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11C23×C412yes—
444C23×C11C22×Q812yes—
445C23×C11C2×#4112yes—
446C23×C11C2511yescharacteristic
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—28no—
452C22×D11—28no—
453C22×D11—28no—
454C22×D11—28no—
455C22×D11—28no—
456C22×D11—28no—
457C22×D11C4×Q8116yescomplemented
458C22×D11C23×C412yes—
459C22×D11C23×C412yes—
460C22×D11C22×D412yes—
461C22×D11C22×Q812yes—
462C22×D11C22×Q812yes—
463C22×D11C2×#4112yes—
464C22×D11C2×#4112yes—
465C22×D11C2×#4112yes—
466C22×D11H(5,𝔽2)12yes—
467C22×D112−1+412yes—
468Q8×C11—28no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—28no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—48no—
492C2×C4×C11C23×C412yes—
493C2×C4×C11C23×C414yes—
494C2×C4×C11C23×C414yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C22×D414yes—
497C2×C4×C11C22×D412yes—
498C2×C4×C11C22×Q812yes—
499C2×C4×C11C22×Q812yes—
500C2×C4×C11C2×#4112yes—
501C2×Dic11—21no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—21no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—28no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—48no—
524C2×Dic11C23×C414yes—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C414yes—
527C2×Dic11C23×C412yes—
528C2×Dic11C22×D414yes—
529C2×Dic11C22×D412yes—
530C2×Dic11C22×Q812yes—
531C2×Dic11C22×Q812yes—
532C2×Dic11C2×#4112yes—
533C4×D11—28no—
534C4×D11—216no—
535C4×D11—216no—
536C4×D11—216no—
537C4×D11—28no—
538C4×D11—28no—
539C4×D11—28no—
540C4×D11—28no—
541C4×D11—48no—
542C4×D11—48no—
543C4×D11—44no—
544C4×D11—48no—
545C4×D11—44no—
546C4×D11C4×D4116yes—
547Dic22—28no—
548Dic22—216no—
549C23×Q8—111no—
550C24×C4—111no—
551C24×C4—112no—
552C2×C22⋊Q8—111no—
553C2×C22⋊Q8—111no—
554C2×C22⋊Q8—1116no—
555C2×C22⋊Q8—112no—
556C2×C22⋊Q8—111no—
557C2×C22⋊Q8—112no—
558C2×C22⋊Q8C2×D1111yescharacteristic
559C2×C4×Q8—111no—
560C2×C4×Q8—112no—
561C2×C4×Q8—111no—
562C2×C4×Q8—111no—
563C2×C4×Q8—112no—
564C2×C4×Q8—228no—
565C2×C4×Q8C2×D1111yescharacteristic, complemented
566C22×C4⋊C4—111no—
567C22×C4⋊C4—111no—
568C22×C4⋊C4—112no—
569C22×C4⋊C4—112no—
570C22×C4⋊C4—111no—
571C22×C4⋊C4—112no—
572C22×C4⋊C4—111no—
573C22×C4⋊C4—111no—
574C22×C4⋊C4—112no—
575C22×C4⋊C4—111no—
576C22×C4⋊C4—112no—
577C22×C4⋊C4—112no—
578C22×C4⋊C4—228no—
579C22×C4⋊C4C2×D1111yescharacteristic
580C22×C22⋊C4—112no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C42—112no—
584C22×C42—111no—
585C22×C42—111no—
586C22×C42—112no—
587#391—111no—
588#391—111no—
589#391—111no—
590#391—112no—
591#391—112no—
592#391C2×D1111yescharacteristic, complemented
593#389—112no—
594#389—112no—
595#389—112no—
596#389—111no—
597#389—112no—
598#389—111no—
599#389—112no—
600#389—111no—
601#389—112no—
602#389—112no—
603#389—112no—
604#389—112no—
605#389C2×D1111yescharacteristic, complemented
606#389C2×D1112yescomplemented
607#387—112no—
608#387—112no—
609#387—112no—
610#387—112no—
611#387—112no—
612#387—112no—
613#387—112no—
614#387C2×D1112yescomplemented
615#385—112no—
616#385—112no—
617#385—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385C2×D1112yes—
623C4×C4⋊C4—111no—
624C4×C4⋊C4—111no—
625C4×C4⋊C4—112no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—112no—
628C4×C4⋊C4C2×D1111yescharacteristic, complemented
629C4×C22⋊C4—111no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—111no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—111no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—111no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4C2×D1111yescharacteristic
644C4×C22⋊C4C2×D1112yes—
645C2×#95—111no—
646C2×#95—112no—
647C2×#95—111no—
648C2×#95—112no—
649C2×#95—112no—
650C2×#95—112no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11C2×C4×Q814yescomplemented
658C22×C11C24×C411yescharacteristic
659C22×C11C23×D411yescharacteristic
660C22×C11C23×Q811yescharacteristic
661C22×C11C22×#4111yescharacteristic
662C22×C11C22×#4111yescharacteristic
663C22×C11C2×H(5,𝔽2)11yescharacteristic
664C22×C11C2×2−1+411yescharacteristic
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—232no—
672C2×D11C2×C4×D414yes—
673C2×D11C2×C4×Q814yes—
674C2×D11C2×C4×Q814yescomplemented
675C2×D11#52014yes—
676C2×D11#54614yes—
677C2×D11D4×Q814yes—
678C2×D11#55214yes—
679C2×D11#55414yes—
680C4×C11—22no—
681C4×C11—24no—
682C4×C11—24no—
683C4×C11—24no—
684C4×C11—22no—
685C4×C11—22no—
686C4×C11—42no—
687C4×C11—41no—
688C4×C11—41no—
689C4×C11C2×C4×D414yes—
690Dic11—24no—
691Dic11—22no—
692Dic11—24no—
693Dic11—24no—
694Dic11—22no—
695Dic11—22no—
696Dic11—42no—
697Dic11—41no—
698Dic11—41no—
699Dic11C2×C4×D414yes—
700C25—111no—
701C22×Q8—118no—
702C22×Q8—112no—
703C22×Q8—111no—
704C22×Q8—224no—
705C22×Q8—224no—
706C22×Q8C22×D1111yescharacteristic
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—118no—
710C23×C4—112no—
711C23×C4—112no—
712C23×C4—111no—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—112no—
716C23×C4—111no—
717C23×C4—111no—
718C23×C4—112no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—112no—
722C23×C4—112no—
723C23×C4—112no—
724C23×C4—224no—
725C23×C4—224no—
726C23×C4—228no—
727C23×C4—228no—
728C23×C4—444no—
729C23×C4C22×D1112yes—
730C23×C4C22×D1111yescharacteristic
731C22⋊Q8—118no—
732C22⋊Q8—118no—
733C22⋊Q8—1116no—
734C22⋊Q8—118no—
735C22⋊Q8—1116no—
736C22⋊Q8C4×D1118yescomplemented
737C4×Q8—24no—
738C4×Q8—228no—
739C4×Q8—224no—
740C4×Q8—228no—
741C4×Q8—224no—
742C4×Q8—224no—
743C2×C4⋊C4—24no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—118no—
752C2×C4⋊C4—1116no—
753C2×C4⋊C4—118no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—228no—
766C2×C4⋊C4—224no—
767C2×C4⋊C4—224no—
768C2×C4⋊C4—228no—
769C2×C4⋊C4—228no—
770C2×C4⋊C4—228no—
771C2×C4⋊C4—224no—
772C2×C4⋊C4—224no—
773C2×C4⋊C4—444no—
774C2×C4⋊C4C22×D1112yes—
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1112yes—
777C2×C4⋊C4C22×D1112yes—
778C2×C4⋊C4C22×D1111yescharacteristic
779C2×C4⋊C4C22×D1112yes—
780C2×C4⋊C4C22×D1111yescharacteristic
781C2×C22⋊C4—112no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—1116no—
788C2×C22⋊C4—118no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—224no—
793C2×C22⋊C4C22×D1111yescharacteristic
794C2×C22⋊C4C22×D1112yes—
795C2×C22⋊C4C22×D1111yescharacteristic
796C2×C42—112no—
797C2×C42—112no—
798C2×C42—112no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—111no—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—224no—
809C2×C42—228no—
810C2×C42—224no—
811C2×C42—444no—
812C2×C42C22×D1112yes—
813C2×C42C22×D1111yescharacteristic
814C2×C42C22×D1111yescharacteristic
815C2×C42C22×D1112yes—
816#95—111no—
817#95—111no—
818#95—111no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—111no—
823#95—111no—
824#95—111no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95C22×D1111yescharacteristic
835#95C22×D1112yes—
836#95C22×D1111yescharacteristic
837#95C22×D1112yes—
838#95C22×D1112yes—
839#95C22×D1112yes—
840C2×C11—24no—
841C2×C11C22×C4×D411yescharacteristic
842C2×C11C22×C4×Q811yescharacteristic
843C2×C11C2×#52011yescharacteristic
844C2×C11C2×#54611yescharacteristic
845C2×C11C2×D4×Q811yescharacteristic
846C2×C11C2×#55211yescharacteristic
847C2×C11C2×#55411yescharacteristic
848D11—24no—
849D11#236018yesdirect product factor
850C24—111no—
851C24—114no—
852C24—114no—
853C24—114no—
854C24—111no—
855C24—222no—
856C24—222no—
857C24—222no—
858C24—222no—
859C24C23×D1111yescharacteristic
860C2×Q8—22no—
861C2×Q8—22no—
862C2×Q8—118no—
863C2×Q8—114no—
864C2×Q8—224no—
865C2×Q8—224no—
866C2×Q8—2232no—
867C2×Q8—222no—
868C2×Q8—222no—
869C2×Q8C2×C4×D1114yescomplemented
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—42no—
875C22×C4—111no—
876C22×C4—114no—
877C22×C4—114no—
878C22×C4—114no—
879C22×C4—114no—
880C22×C4—111no—
881C22×C4—111no—
882C22×C4—112no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—112no—
886C22×C4—118no—
887C22×C4—118no—
888C22×C4—114no—
889C22×C4—114no—
890C22×C4—114no—
891C22×C4—118no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—111no—
895C22×C4—112no—
896C22×C4—111no—
897C22×C4—222no—
898C22×C4—222no—
899C22×C4—2232no—
900C22×C4—224no—
901C22×C4—222no—
902C22×C4—224no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—224no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—224no—
918C22×C4—222no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—4432no—
934C22×C4—442no—
935C22×C4C2×C4×D1114yes—
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1112yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—42no—
950C4⋊C4—118no—
951C4⋊C4—118no—
952C4⋊C4—118no—
953C4⋊C4—114no—
954C4⋊C4—118no—
955C4⋊C4—118no—
956C4⋊C4—114no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—224no—
960C4⋊C4—224no—
961C4⋊C4—224no—
962C4⋊C4—224no—
963C4⋊C4—222no—
964C4⋊C4—224no—
965C4⋊C4—442no—
966C4⋊C4—442no—
967C4⋊C4—442no—
968C4⋊C4C2×C4×D1114yescomplemented
969C4⋊C4C2×C4×D1118yescomplemented
970C4⋊C4D4×D1114yes—
971C22⋊C4—22no—
972C22⋊C4—118no—
973C22⋊C4—114no—
974C22⋊C4—118no—
975C22⋊C4—118no—
976C22⋊C4—114no—
977C22⋊C4—114no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4C2×C4×D1118yes—
982C22⋊C4Q8×D1114yescomplemented
983C42—24no—
984C42—22no—
985C42—22no—
986C42—42no—
987C42—222no—
988C42—224no—
989C42—224no—
990C42—222no—
991C42—222no—
992C42—222no—
993C42—224no—
994C42—222no—
995C42—222no—
996C42—442no—
997C42—442no—
998C42—442no—
999C11C2×#236011yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—112no—
1005C23—112no—
1006C23—112no—
1007C23—112no—
1008C23—112no—
1009C23—112no—
1010C23—112no—
1011C23—1116no—
1012C23—112no—
1013C23—112no—
1014C23—112no—
1015C23—228no—
1016C23—228no—
1017C23—228no—
1018C23—228no—
1019C23—228no—
1020C23—228no—
1021C23—221no—
1022C23—221no—
1023C23—221no—
1024C23—221no—
1025C23C22×C4×D1112yes—
1026C23C2×Q8×D1112yes—
1027C23#41×D1112yes—
1028C23C24×D1111yescharacteristic
1029Q8—28no—
1030Q8—2216no—
1031Q8—228no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—28no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—48no—
1055C2×C4—112no—
1056C2×C4—112no—
1057C2×C4—112no—
1058C2×C4—1116no—
1059C2×C4—114no—
1060C2×C4—114no—
1061C2×C4—112no—
1062C2×C4—114no—
1063C2×C4—112no—
1064C2×C4—112no—
1065C2×C4—228no—
1066C2×C4—228no—
1067C2×C4—2216no—
1068C2×C4—2216no—
1069C2×C4—228no—
1070C2×C4—2216no—
1071C2×C4—228no—
1072C2×C4—228no—
1073C2×C4—221no—
1074C2×C4—222no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—221no—
1085C2×C4—228no—
1086C2×C4—221no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—221no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—448no—
1096C2×C4—448no—
1097C2×C4—448no—
1098C2×C4—444no—
1099C2×C4—444no—
1100C2×C4—448no—
1101C2×C4C22×C4×D1114yes—
1102C2×C4C22×C4×D1114yes—
1103C2×C4C22×C4×D1112yes—
1104C2×C4C22×C4×D1112yes—
1105C2×C4C2×D4×D1114yes—
1106C2×C4C2×D4×D1112yes—
1107C2×C4C2×Q8×D1112yes—
1108C2×C4C2×Q8×D1112yes—
1109C2×C4#41×D1112yes—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—114no—
1117C22—114no—
1118C22—114no—
1119C22—114no—
1120C22—114no—
1121C22—114no—
1122C22—114no—
1123C22—114no—
1124C22—2232no—
1125C22—222no—
1126C22—222no—
1127C22—222no—
1128C22—222no—
1129C22—222no—
1130C22—222no—
1131C22C4×Q8×D1114yescomplemented
1132C22C23×C4×D1111yescharacteristic
1133C22C22×D4×D1111yescharacteristic
1134C22C22×Q8×D1111yescharacteristic
1135C22C2×#41×D1111yescharacteristic
1136C22C2×#41×D1111yescharacteristic
1137C22D11×H(5,𝔽2)11yescharacteristic
1138C22D11×2−1+411yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—24no—
1142C4—24no—
1143C4—24no—
1144C4—22no—
1145C4—41no—
1146C4—42no—
1147C4—41no—
1148C4—114no—
1149C4—222no—
1150C4—222no—
1151C4—224no—
1152C4—224no—
1153C4—224no—
1154C4—222no—
1155C4—441no—
1156C4—442no—
1157C4—441no—
1158C4C4×D4×D1114yes—
1159C2—24no—
1160C2—118no—
1161C2—224no—
1162C2C2×C4×D4×D1111yescharacteristic
1163C2C2×C4×Q8×D1111yescharacteristic
1164C2D11×#52011yescharacteristic
1165C2D11×#54611yescharacteristic
1166C2D4×Q8×D1111yescharacteristic
1167C2D11×#55211yescharacteristic
1168C2D11×#55411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2360C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2360D11
hypocenterC11C2×#2360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
4. #13071626C2semidirect
5. #13071625C2semidirect
6. #13071624C2semidirect
7. #13071623C2semidirect
8. #13071622C2semidirect
9. #13071621C2semidirect
10. #13071620C2semidirect
11. #13071619C2semidirect
12. #13071618C2semidirect
13. #13071617C2semidirect
14. #13071616C2semidirect
15. D11×#391C2semidirect
16. D11×#389C2semidirect
17. D11×#389C2semidirect
18. D11×#387C2semidirect
20. C4×C4⋊C4×D11C2semidirect
23. C11×#2360C2semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×Q8×Dic11C22semidirect
35. D11×C22⋊Q8C4semidirect
50. C2×#66940C22semidirect
51. C2×#66940C22semidirect
60. C2×C4×Dic22C22semidirect
61. C2×C4×Dic22C22semidirect
62. C11×#391C22semidirect
63. C11×#389C22semidirect
64. C11×#389C22semidirect
65. C11×#387C22semidirect
67. C4×C11×C4⋊C4C22semidirect
70. #10622843C22semidirect
76. #10622598C22semidirect
77. #10622598C22semidirect
78. #10622594C22semidirect
79. #10622591C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. #10622587C22semidirect
83. #10622586C22semidirect
84. #10622586C22semidirect
85. #10622585C22semidirect
86. #10622585C22semidirect
87. #10622585C22semidirect
98. C4×C4⋊Dic11C22semidirect
99. #10622546C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. #10622542C22semidirect
102. #10622541C22semidirect
103. #10622541C22semidirect
116. #10622268C22semidirect
117. #10622267C22semidirect
118. #10622266C22semidirect
119. #10622265C22semidirect
120. #10622262C22semidirect
121. #10622260C22semidirect
122. #10622260C22semidirect
123. #10622260C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
134. C2×Q8×D11C2×C4semidirect
157. C11×C22⋊Q8C2×C4semidirect
177. #66999C2×C4semidirect
193. #66977C2×C4semidirect
218. #66950C2×C4semidirect
219. #66949C2×C4semidirect
227. C4⋊C4×D11C2×C4semidirect
228. C4⋊C4×D11C2×C4semidirect
234. C22⋊C4×D11Q8semidirect
235. #66931C2×C4semidirect
279. C2×Q8×C11C22×C4semidirect
361. C2×Dic22C22×C4semidirect
362. C2×Dic22C22×C4semidirect
367. C11×C4⋊C4C22×C4semidirect
368. C11×C4⋊C4C22×C4semidirect
372. C11×C22⋊C4C2×Q8semidirect
379. C22⋊Dic11C2×Q8semidirect
384. (C2×D11)⋊C4C2×Q8semidirect
385. (C2×D11)⋊C4C2×Q8semidirect
390. C4⋊Dic11C22×C4semidirect
391. C4⋊Dic11C22×C4semidirect
400. Dic11⋊C4C22×C4semidirect
401. Dic11⋊C4C22×C4semidirect
402. Dic11⋊C4C22×C4semidirect
430. #2360D11direct (N × H)
457. C22×D11C4×Q8semidirect
565. C2×C4×Q8C2×D11semidirect
592. #391C2×D11semidirect
605. #389C2×D11semidirect
606. #389C2×D11semidirect
614. #387C2×D11semidirect
628. C4×C4⋊C4C2×D11semidirect
657. C22×C11C2×C4×Q8semidirect
674. C2×D11C2×C4×Q8semidirect
736. C22⋊Q8C4×D11semidirect
849. D11#2360direct (N × H)
869. C2×Q8C2×C4×D11semidirect
968. C4⋊C4C2×C4×D11semidirect
969. C4⋊C4C2×C4×D11semidirect
982. C22⋊C4Q8×D11semidirect
999. C11C2×#2360semidirect
1131. C22C4×Q8×D11semidirect

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×Q8×D112
C22×C4⋊C4×D112
#130716262
#130716252
#130716242
#130716232
#130716222
#130716212
#130716202
#130716192
#130716182
#130716172
#130716162
D11×#3912
D11×#3892
D11×#3872
D11×#3852
C4×C4⋊C4×D112
C4×C22⋊C4×D112
C11×#23602
C2×#236011