Finite Group Databasebeta

← D11×#2362 #14913308

Subgroups — D11×#2362 #14913308

Order 2816.

3310 conjugacy classes of subgroups.

The subgroup lattice has 1140 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
3C2×D11×#117C211yesmaximal, characteristic
4#13071648C211yesmaximal, characteristic, complemented
5#13071647C211yesmaximal, characteristic, complemented
6#13071646C212yesmaximal, complemented
7#13071645C211yesmaximal, characteristic, complemented
8#13071644C212yesmaximal, complemented
9#13071643C211yesmaximal, characteristic, complemented
10#13071642C211yesmaximal, characteristic, complemented
11#13071641C211yesmaximal, characteristic, complemented
12#13071640C212yesmaximal, complemented
13#13071639C211yesmaximal, characteristic, complemented
14#13071638C212yesmaximal, complemented
15D11×#391C211yesmaximal, characteristic, complemented
16D11×#389C211yesmaximal, characteristic, complemented
17D11×#388C212yesmaximal
18D11×#388C212yesmaximal
19D11×#387C212yesmaximal, complemented
20C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
21C4×C4⋊C4×D11C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic
23C11×#2362C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66979C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33D11×C22⋊Q8C4116yescomplemented
34C4×Q8×D11—28no—
35D11×#117—28no—
36C2×#66950C2211yescharacteristic
37C2×#66949C2212yes—
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×C4⋊C4×D11C2212yes—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2212yes—
43C2×C4⋊C4×D11C2212yes—
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66940C2212yescomplemented
47C2×#66940C2211yescharacteristic, complemented
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×#66931C2212yes—
53C2×#66930C2212yes—
54C2×#66925C2212yes—
55C2×C42×D11C2211yescharacteristic
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2212yes—
58C2×C42×D11C2212yes—
59C2×C42×D11C2212yes—
60C2×C4×Dic22C2211yescharacteristic, complemented
61C2×C4×Dic22C2212yescomplemented
62C11×#391C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#388C2212yes—
65C11×#388C2212yes—
66C11×#387C2212yescomplemented
67C4×C11×C4⋊C4C2212yescomplemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69C4×C11×C22⋊C4C2211yescharacteristic
70#10622843C2211yescharacteristic, complemented
71C4×C22⋊Dic11C2211yescharacteristic
72#10622603C2212yes—
73#10622603C2212yes—
74#10622598C2211yescharacteristic, complemented
75#10622594C2212yescomplemented
76#10622591C2212yescomplemented
77C4⋊C4×Dic11C2212yescomplemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2212yescomplemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81#10622587C2211yescharacteristic, complemented
82#10622586C2211yescharacteristic, complemented
83#10622585C2212yescomplemented
84#10622564C2212yes—
85#10622564C2212yes—
86#10622558C2212yes—
87#10622558C2212yes—
88#10622557C2212yes—
89#10622557C2212yes—
90C22⋊C4×Dic11C2211yescharacteristic
91C22⋊C4×Dic11C2211yescharacteristic
92#10622553C2212yes—
93#10622553C2212yes—
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×C4⋊Dic11C2212yescomplemented
97C4×C4⋊Dic11C2211yescharacteristic, complemented
98#10622546C2212yescomplemented
99C4×Dic11⋊C4C2212yescomplemented
100C4×Dic11⋊C4C2212yescomplemented
101C4×Dic11⋊C4C2212yescomplemented
102#10622542C2211yescharacteristic, complemented
103#10622541C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622283C2212yes—
106#10622282C2212yes—
107#10622282C2212yes—
108#10622279C2211yescharacteristic
109#10622279C2211yescharacteristic
110D11×#95C2211yescharacteristic
111D11×#95C2211yescharacteristic
112D11×#95C2212yes—
113D11×#95C2212yes—
114D11×#95C2212yes—
115D11×#95C2212yes—
116#10622268C2212yescomplemented
117#10622267C2212yescomplemented
118#10622266C2212yescomplemented
119#10622265C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622262C2212yescomplemented
123#10622260C2212yescomplemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C2×Q8×D11—24no—
131C2×Q8×D11—24no—
132C2×Q8×D11C2×C418yes—
133C22×C4×D11—24no—
134C22×C4×D11—24no—
135C22×C4×D11C2×C418yes—
136C22×C4×D11C2312yes—
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×Dic22C2312yes—
149C22×Dic22C2311yescharacteristic
150C11×C22⋊Q8C2×C418yescomplemented
151C4×Q8×C11—24no—
152C11×#117—24no—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172#66999C2×C418yescomplemented
173Q8×Dic11—24no—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182#66979—24no—
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189#66977C2×C418yescomplemented
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214#66950C2×C418yescomplemented
215#66949C2×C4116yescomplemented
216#66945—24no—
217#66945—24no—
218C4⋊C4×D11—24no—
219C4⋊C4×D11—28no—
220C4⋊C4×D11—28no—
221C4⋊C4×D11C2×C418yes—
222C4⋊C4×D11C2×C4116yes—
223C4⋊C4×D11D418yes—
224#66940—24no—
225#66940—28no—
226C22⋊C4×D11—28no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11—24no—
229C22⋊C4×D11C2×C4116yes—
230#66931C2×C4116yescomplemented
231#66930—28no—
232#66925—28no—
233C42×D11—28no—
234C42×D11—24no—
235C42×D11—28no—
236C42×D11—28no—
237C42×D11—24no—
238C4×Dic22—24no—
239C4×Dic22—28no—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264C2×#2362—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11C22×C414yes—
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×Q8×C11—22no—
276C2×Q8×C11—22no—
277C2×Q8×C11C22×C414yes—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11C22×C414yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11C22×C414yes—
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304Q8×D11—232no—
305C2×C4×D11—22no—
306C2×C4×D11—22no—
307C2×C4×D11—232no—
308C2×C4×D11—22no—
309C2×C4×D11—22no—
310C2×C4×D11—24no—
311C2×C4×D11—24no—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—24no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—22no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11C22×C418yes—
332C2×C4×D11C22×C418yes—
333C2×C4×D11C22×C414yes—
334C2×C4×D11C22×C414yes—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yes—
337C2×C4×D11C2×D418yes—
338C2×C4×D11C2×D414yes—
339C2×C4×D11#4114yes—
340C2×C4×D11#4114yes—
341C2×C4×D11#4114yes—
342C2×Dic22—24no—
343C2×Dic22—24no—
344C2×Dic22—22no—
345C2×Dic22—22no—
346C2×Dic22C22×C418yes—
347C2×Dic22C22×C414yes—
348C11×C4⋊C4—24no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—24no—
351C11×C4⋊C4C22×C418yes—
352C11×C4⋊C4C22×C414yes—
353C11×C4⋊C4C2×D414yes—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4C22×C418yes—
358C42×C11—24no—
359C42×C11—22no—
360C42×C11—24no—
361C42×C11—24no—
362C42×C11—22no—
363C22⋊Dic11—24no—
364C22⋊Dic11—22no—
365C22⋊Dic11—22no—
366C22⋊Dic11C22×C418yes—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—22no—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4C22×C418yes—
374(C2×D11)⋊C4C22×C418yes—
375C4⋊Dic11—24no—
376C4⋊Dic11—24no—
377C4⋊Dic11—22no—
378C4⋊Dic11C22×C418yes—
379C4⋊Dic11C22×C414yes—
380C4⋊Dic11C2×D414yes—
381Dic11⋊C4—24no—
382Dic11⋊C4—24no—
383Dic11⋊C4—24no—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386Dic11⋊C4C22×C418yes—
387Dic11⋊C4C22×C418yes—
388Dic11⋊C4C22×C418yes—
389Dic11⋊C4C2×D418yes—
390C4×Dic11—24no—
391C4×Dic11—22no—
392C4×Dic11—24no—
393C4×Dic11—24no—
394C4×Dic11—22no—
395C4×Dic11—24no—
396C4×Dic11—24no—
397C4×Dic11—24no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—24no—
401C4×Dic11—24no—
402C4×Dic11—22no—
403C4×Dic11—24no—
404C4×Dic11—22no—
405C22×C22⋊Q8—111no—
406C22×C4×Q8—111no—
407C22×#117—111no—
408#2362—111no—
409#2362—111no—
410#2362—112no—
411#2362—112no—
412#2362—112no—
413#2362—112no—
414#2362—111no—
415#2362—111no—
416#2362—111no—
417#2362—111no—
418#2362—111no—
419#2362D1111yescharacteristic, direct product factor
420C2×#391—111no—
421C2×#389—111no—
422C2×#388—112no—
423C2×#388—112no—
424C2×#387—112no—
425C2×C4×C4⋊C4—111no—
426C2×C4×C4⋊C4—112no—
427C2×C4×C22⋊C4—111no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11C23×C412yes—
435C23×C11C2511yescharacteristic
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—21no—
441C22×D11—21no—
442C22×D11—28no—
443C22×D11—28no—
444C22×D11—28no—
445C22×D11—44no—
446C22×D11—44no—
447C22×D11—44no—
448C22×D11—44no—
449C22×D11C23×C412yes—
450C22×D11C23×C412yes—
451C22×D11C22×D412yes—
452C22×D11C2×#4112yes—
453C22×D11C2×#4112yes—
454C22×D11C2×#4112yes—
455C22×D112−1+412yes—
456C22×D112−1+412yes—
457Q8×C11—28no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—28no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C414yes—
482C2×C4×C11C23×C414yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C22×D414yes—
485C2×C4×C11C22×D412yes—
486C2×C4×C11C2×#4112yes—
487C2×C4×C11C2×#4112yes—
488C2×C4×C11C2×#4112yes—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—21no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—21no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—28no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11C23×C414yes—
512C2×Dic11C23×C412yes—
513C2×Dic11C23×C414yes—
514C2×Dic11C23×C412yes—
515C2×Dic11C22×D414yes—
516C2×Dic11C22×D412yes—
517C2×Dic11C2×#4112yes—
518C2×Dic11C2×#4112yes—
519C2×Dic11C2×#4112yes—
520C4×D11—28no—
521C4×D11—216no—
522C4×D11—216no—
523C4×D11—216no—
524C4×D11—28no—
525C4×D11—28no—
526C4×D11—28no—
527C4×D11—28no—
528C4×D11—44no—
529C4×D11—48no—
530C4×D11—44no—
531C4×D11C4×D4116yes—
532Dic22—28no—
533Dic22—216no—
534C23×Q8—111no—
535C24×C4—111no—
536C2×C22⋊Q8—111no—
537C2×C22⋊Q8—111no—
538C2×C22⋊Q8—1116no—
539C2×C22⋊Q8—112no—
540C2×C22⋊Q8—111no—
541C2×C22⋊Q8—112no—
542C2×C22⋊Q8C2×D1111yescharacteristic
543C2×C4×Q8—111no—
544C2×C4×Q8—112no—
545C2×C4×Q8—111no—
546C2×C4×Q8—112no—
547C2×C4×Q8—111no—
548C2×C4×Q8—228no—
549C2×C4×Q8C2×D1111yescharacteristic, complemented
550C2×#117—111no—
551C2×#117—111no—
552C2×#117—111no—
553C2×#117—112no—
554C2×#117—112no—
555C2×#117—228no—
556C2×#117C2×D1111yescharacteristic
557C22×C4⋊C4—111no—
558C22×C4⋊C4—112no—
559C22×C4⋊C4—111no—
560C22×C4⋊C4—111no—
561C22×C4⋊C4—112no—
562C22×C4⋊C4—112no—
563C22×C22⋊C4—112no—
564C22×C22⋊C4—112no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C42—112no—
568C22×C42—111no—
569C22×C42—112no—
570C22×C42—111no—
571C22×C42—112no—
572#391—111no—
573#391—111no—
574#391—111no—
575#391—112no—
576#391—112no—
577#391C2×D1111yescharacteristic, complemented
578#389—112no—
579#389—111no—
580#389—111no—
581#389—111no—
582#389—112no—
583#389C2×D1111yescharacteristic, complemented
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388—112no—
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388C2×D1112yes—
599#388C2×D1112yes—
600#387—112no—
601#387—112no—
602#387—112no—
603#387—112no—
604#387—112no—
605#387—112no—
606#387—112no—
607#387C2×D1112yescomplemented
608C4×C4⋊C4—112no—
609C4×C4⋊C4—112no—
610C4×C4⋊C4—111no—
611C4×C4⋊C4—111no—
612C4×C4⋊C4—112no—
613C4×C4⋊C4—112no—
614C4×C4⋊C4—112no—
615C4×C4⋊C4—112no—
616C4×C4⋊C4—111no—
617C4×C4⋊C4—112no—
618C4×C4⋊C4—112no—
619C4×C4⋊C4—112no—
620C4×C4⋊C4C2×D1112yescomplemented
621C4×C4⋊C4C2×D1111yescharacteristic, complemented
622C4×C22⋊C4—111no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—111no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—111no—
628C4×C22⋊C4—111no—
629C4×C22⋊C4C2×D1111yescharacteristic
630C2×#95—111no—
631C2×#95—111no—
632C2×#95—112no—
633C2×#95—112no—
634C2×#95—112no—
635C2×#95—112no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—41no—
640C22×C11—41no—
641C22×C11—41no—
642C22×C11—41no—
643C22×C11C24×C411yescharacteristic
644C22×C11C23×D411yescharacteristic
645C22×C11C22×#4111yescharacteristic
646C22×C11C22×#4111yescharacteristic
647C22×C11C22×#4111yescharacteristic
648C22×C11C2×2−1+411yescharacteristic
649C22×C11C2×2−1+411yescharacteristic
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—41no—
654C2×D11—41no—
655C2×D11—41no—
656C2×D11—41no—
657C2×D11—416no—
658C2×D11C2×C4×D414yes—
659C2×D11C4×#4114yes—
660C2×D11#51914yes—
661C2×D11#54714yes—
662C2×D11#54814yes—
663C2×D11#55214yes—
664C2×D11#55614yes—
665C4×C11—22no—
666C4×C11—24no—
667C4×C11—24no—
668C4×C11—24no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—41no—
672C4×C11—42no—
673C4×C11—41no—
674C4×C11C2×C4×D414yes—
675Dic11—24no—
676Dic11—22no—
677Dic11—24no—
678Dic11—24no—
679Dic11—22no—
680Dic11—22no—
681Dic11—41no—
682Dic11—42no—
683Dic11—41no—
684Dic11C2×C4×D414yes—
685C25—111no—
686C22×Q8—118no—
687C22×Q8—112no—
688C22×Q8—111no—
689C22×Q8—224no—
690C22×Q8—224no—
691C22×Q8C22×D1111yescharacteristic
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—118no—
695C23×C4—112no—
696C23×C4—112no—
697C23×C4—112no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—112no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—224no—
707C23×C4—224no—
708C23×C4C22×D1111yescharacteristic
709C22⋊Q8—118no—
710C22⋊Q8—118no—
711C22⋊Q8—1116no—
712C22⋊Q8—118no—
713C22⋊Q8—1116no—
714C22⋊Q8C4×D1118yescomplemented
715C4×Q8—24no—
716C4×Q8—228no—
717C4×Q8—224no—
718C4×Q8—228no—
719C4×Q8—224no—
720C4×Q8—224no—
721#117—24no—
722#117—228no—
723#117—228no—
724#117—224no—
725#117—224no—
726#117—224no—
727C2×C4⋊C4—112no—
728C2×C4⋊C4—111no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—118no—
735C2×C4⋊C4—1116no—
736C2×C4⋊C4—118no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—224no—
746C2×C4⋊C4—228no—
747C2×C4⋊C4—228no—
748C2×C4⋊C4C22×D1111yescharacteristic
749C2×C4⋊C4C22×D1112yes—
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1112yes—
752C2×C4⋊C4C22×D1111yescharacteristic
753C2×C4⋊C4C22×D1111yescharacteristic
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—1116no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—111no—
760C2×C22⋊C4—111no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—228no—
768C2×C22⋊C4—224no—
769C2×C22⋊C4—224no—
770C2×C22⋊C4C22×D1112yes—
771C2×C22⋊C4C22×D1111yescharacteristic
772C2×C22⋊C4C22×D1111yescharacteristic
773C2×C22⋊C4C22×D1112yes—
774C2×C42—112no—
775C2×C42—112no—
776C2×C42—112no—
777C2×C42—111no—
778C2×C42—111no—
779C2×C42—111no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42—112no—
783C2×C42—111no—
784C2×C42—111no—
785C2×C42—111no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—112no—
789C2×C42—228no—
790C2×C42—224no—
791C2×C42—228no—
792C2×C42—224no—
793C2×C42—228no—
794C2×C42C22×D1112yes—
795C2×C42C22×D1111yescharacteristic
796C2×C42C22×D1112yes—
797C2×C42C22×D1111yescharacteristic
798C2×C42C22×D1112yes—
799#95—111no—
800#95—111no—
801#95—111no—
802#95—111no—
803#95—111no—
804#95—111no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95C22×D1111yescharacteristic
818#95C22×D1111yescharacteristic
819#95C22×D1112yes—
820#95C22×D1112yes—
821#95C22×D1112yes—
822#95C22×D1112yes—
823C2×C11—42no—
824C2×C11C22×C4×D411yescharacteristic
825C2×C11C2×C4×#4111yescharacteristic
826C2×C11C2×#51911yescharacteristic
827C2×C11C2×#54711yescharacteristic
828C2×C11C2×#54811yescharacteristic
829C2×C11C2×#55211yescharacteristic
830C2×C11C2×#55611yescharacteristic
831D11—42no—
832D11#236218yesdirect product factor
833C24—111no—
834C24—114no—
835C24—111no—
836C24—222no—
837C24—222no—
838C24—222no—
839C24—222no—
840C24—222no—
841C24—222no—
842C24C23×D1111yescharacteristic
843C2×Q8—22no—
844C2×Q8—22no—
845C2×Q8—118no—
846C2×Q8—114no—
847C2×Q8—224no—
848C2×Q8—224no—
849C2×Q8—2232no—
850C2×Q8—222no—
851C2×Q8—222no—
852C2×Q8C2×C4×D1114yes—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—111no—
856C22×C4—114no—
857C22×C4—114no—
858C22×C4—114no—
859C22×C4—114no—
860C22×C4—111no—
861C22×C4—111no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—111no—
866C22×C4—118no—
867C22×C4—118no—
868C22×C4—114no—
869C22×C4—114no—
870C22×C4—114no—
871C22×C4—118no—
872C22×C4—114no—
873C22×C4—114no—
874C22×C4—111no—
875C22×C4—112no—
876C22×C4—111no—
877C22×C4—222no—
878C22×C4—222no—
879C22×C4—2232no—
880C22×C4—222no—
881C22×C4—222no—
882C22×C4—224no—
883C22×C4—224no—
884C22×C4—224no—
885C22×C4—222no—
886C22×C4—224no—
887C22×C4—222no—
888C22×C4—224no—
889C22×C4—224no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—224no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—224no—
898C22×C4—222no—
899C22×C4—224no—
900C22×C4—222no—
901C22×C4—222no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4C2×C4×D1114yes—
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1112yes—
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1112yes—
911C22×C4C23×D1112yes—
912C22×C4C23×D1112yes—
913C22×C4C23×D1111yescharacteristic
914C22×C4C23×D1111yescharacteristic
915C22×C4C23×D1111yescharacteristic
916C4⋊C4—22no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—118no—
920C4⋊C4—118no—
921C4⋊C4—118no—
922C4⋊C4—114no—
923C4⋊C4—118no—
924C4⋊C4—118no—
925C4⋊C4—114no—
926C4⋊C4—224no—
927C4⋊C4—224no—
928C4⋊C4—224no—
929C4⋊C4—224no—
930C4⋊C4—224no—
931C4⋊C4—222no—
932C4⋊C4—224no—
933C4⋊C4—224no—
934C4⋊C4C2×C4×D1114yes—
935C4⋊C4C2×C4×D1118yes—
936C4⋊C4D4×D1114yes—
937C22⋊C4—24no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—118no—
941C22⋊C4—118no—
942C22⋊C4—118no—
943C22⋊C4—224no—
944C22⋊C4—222no—
945C22⋊C4—222no—
946C22⋊C4—224no—
947C22⋊C4—222no—
948C22⋊C4—222no—
949C22⋊C4—224no—
950C22⋊C4—222no—
951C22⋊C4—222no—
952C22⋊C4C2×C4×D1118yes—
953C42—24no—
954C42—24no—
955C42—22no—
956C42—24no—
957C42—22no—
958C42—224no—
959C42—224no—
960C42—222no—
961C42—224no—
962C42—224no—
963C42—222no—
964C42—222no—
965C42—224no—
966C42—224no—
967C42—222no—
968C42—224no—
969C42—224no—
970C42—222no—
971C42—224no—
972C42—222no—
973C11C2×#236211yescharacteristic, complemented, Sylow
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—112no—
981C23—112no—
982C23—112no—
983C23—112no—
984C23—112no—
985C23—112no—
986C23—112no—
987C23—112no—
988C23—228no—
989C23—228no—
990C23—228no—
991C23—221no—
992C23—221no—
993C23—221no—
994C23—221no—
995C23—221no—
996C23—221no—
997C23—444no—
998C23—444no—
999C23—444no—
1000C23—444no—
1001C23C22×C4×D1112yes—
1002C23C24×D1111yescharacteristic
1003Q8—28no—
1004Q8—2216no—
1005Q8—228no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—28no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—112no—
1029C2×C4—112no—
1030C2×C4—112no—
1031C2×C4—1116no—
1032C2×C4—114no—
1033C2×C4—114no—
1034C2×C4—112no—
1035C2×C4—114no—
1036C2×C4—112no—
1037C2×C4—112no—
1038C2×C4—228no—
1039C2×C4—228no—
1040C2×C4—2216no—
1041C2×C4—228no—
1042C2×C4—2216no—
1043C2×C4—2216no—
1044C2×C4—228no—
1045C2×C4—228no—
1046C2×C4—221no—
1047C2×C4—221no—
1048C2×C4—222no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—221no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—222no—
1057C2×C4—221no—
1058C2×C4—228no—
1059C2×C4—222no—
1060C2×C4—221no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—222no—
1068C2×C4—444no—
1069C2×C4—444no—
1070C2×C4—448no—
1071C2×C4C22×C4×D1114yes—
1072C2×C4C22×C4×D1114yes—
1073C2×C4C22×C4×D1112yes—
1074C2×C4C22×C4×D1112yes—
1075C2×C4C2×D4×D1114yes—
1076C2×C4C2×D4×D1112yes—
1077C2×C4#41×D1112yes—
1078C2×C4#41×D1112yes—
1079C2×C4#41×D1112yes—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—114no—
1088C22—114no—
1089C22—114no—
1090C22—114no—
1091C22—114no—
1092C22—114no—
1093C22—114no—
1094C22—222no—
1095C22—222no—
1096C22—222no—
1097C22—4416no—
1098C22—441no—
1099C22—441no—
1100C22—441no—
1101C22—441no—
1102C22C23×C4×D1111yescharacteristic
1103C22C22×D4×D1111yescharacteristic
1104C22C2×#41×D1111yescharacteristic
1105C22C2×#41×D1111yescharacteristic
1106C22C2×#41×D1111yescharacteristic
1107C22D11×2−1+411yescharacteristic
1108C22D11×2−1+411yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—24no—
1112C4—24no—
1113C4—24no—
1114C4—22no—
1115C4—41no—
1116C4—41no—
1117C4—42no—
1118C4—114no—
1119C4—222no—
1120C4—222no—
1121C4—224no—
1122C4—224no—
1123C4—224no—
1124C4—222no—
1125C4—441no—
1126C4—441no—
1127C4—442no—
1128C4C4×D4×D1114yes—
1129C2—42no—
1130C2—118no—
1131C2—442no—
1132C2C2×C4×D4×D1111yescharacteristic
1133C2C4×#41×D1111yescharacteristic
1134C2D11×#51911yescharacteristic
1135C2D11×#54711yescharacteristic
1136C2D11×#54811yescharacteristic
1137C2D11×#55211yescharacteristic
1138C2D11×#55611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2362C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2362D11
hypocenterC11C2×#2362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
4. #13071648C2semidirect
5. #13071647C2semidirect
6. #13071646C2semidirect
7. #13071645C2semidirect
8. #13071644C2semidirect
9. #13071643C2semidirect
10. #13071642C2semidirect
11. #13071641C2semidirect
12. #13071640C2semidirect
13. #13071639C2semidirect
14. #13071638C2semidirect
15. D11×#391C2semidirect
16. D11×#389C2semidirect
19. D11×#387C2semidirect
20. C4×C4⋊C4×D11C2semidirect
21. C4×C4⋊C4×D11C2semidirect
23. C11×#2362C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
33. D11×C22⋊Q8C4semidirect
46. C2×#66940C22semidirect
47. C2×#66940C22semidirect
60. C2×C4×Dic22C22semidirect
61. C2×C4×Dic22C22semidirect
62. C11×#391C22semidirect
63. C11×#389C22semidirect
66. C11×#387C22semidirect
67. C4×C11×C4⋊C4C22semidirect
68. C4×C11×C4⋊C4C22semidirect
70. #10622843C22semidirect
74. #10622598C22semidirect
75. #10622594C22semidirect
76. #10622591C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622587C22semidirect
82. #10622586C22semidirect
83. #10622585C22semidirect
96. C4×C4⋊Dic11C22semidirect
97. C4×C4⋊Dic11C22semidirect
98. #10622546C22semidirect
99. C4×Dic11⋊C4C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. #10622542C22semidirect
103. #10622541C22semidirect
116. #10622268C22semidirect
117. #10622267C22semidirect
118. #10622266C22semidirect
119. #10622265C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
150. C11×C22⋊Q8C2×C4semidirect
172. #66999C2×C4semidirect
189. #66977C2×C4semidirect
214. #66950C2×C4semidirect
215. #66949C2×C4semidirect
230. #66931C2×C4semidirect
419. #2362D11direct (N × H)
549. C2×C4×Q8C2×D11semidirect
577. #391C2×D11semidirect
583. #389C2×D11semidirect
607. #387C2×D11semidirect
620. C4×C4⋊C4C2×D11semidirect
621. C4×C4⋊C4C2×D11semidirect
714. C22⋊Q8C4×D11semidirect
832. D11#2362direct (N × H)
973. C11C2×#2362semidirect

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
C2×D11×#1172
#130716482
#130716472
#130716462
#130716452
#130716442
#130716432
#130716422
#130716412
#130716402
#130716392
#130716382
D11×#3912
D11×#3892
D11×#3882
D11×#3872
C4×C4⋊C4×D112
C4×C22⋊C4×D112
C11×#23622
C2×#236211