Finite Group Databasebeta

← D11×#2429 #14921785

Subgroups — D11×#2429 #14921785

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×D11×C22⋊Q8C211yesmaximal, characteristic
3C2×D11×C22⋊Q8C211yesmaximal, characteristic
4C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
5#13072218C211yesmaximal, characteristic, complemented
6#13072217C211yesmaximal, characteristic, complemented
7#13072216C211yesmaximal, characteristic, complemented
8#13072215C211yesmaximal, characteristic, complemented
9#13072214C212yesmaximal, complemented
10#13072213C211yesmaximal, characteristic, complemented
11#13072212C212yesmaximal, complemented
12#13072211C211yesmaximal, characteristic, complemented
13#13072210C212yesmaximal, complemented
14#13072209C211yesmaximal, characteristic, complemented
15#13072208C212yesmaximal, complemented
16D11×#398C212yesmaximal, complemented
17D11×#396C212yesmaximal
18D11×#391C211yesmaximal, characteristic, complemented
19D11×#389C211yesmaximal, characteristic, complemented
20D11×#389C212yesmaximal, complemented
21D11×#388C212yesmaximal
22C4×C22⋊C4×D11C211yesmaximal, characteristic
23C11×#2429C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×Q8×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×C4⋊Q8C2211yescharacteristic, complemented
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic, complemented
31C2×#66999C2211yescharacteristic
32C2×#66999C2211yescharacteristic
33C2×Q8×Dic11C2211yescharacteristic, complemented
34C2×#66997C2211yescharacteristic, complemented
35C2×#66997C2211yescharacteristic, complemented
36C2×#66977C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38D11×C4⋊Q8—28no—
39D11×C22⋊Q8—28no—
40D11×C22⋊Q8—28no—
41C4×Q8×D11—28no—
42C2×#66950C2211yescharacteristic
43C2×#66950C2211yescharacteristic
44C2×#66949C2212yes—
45C2×#66949C2212yes—
46C2×C4⋊C4×D11C2212yes—
47C2×C4⋊C4×D11C2212yes—
48C2×C4⋊C4×D11C2212yes—
49C2×C4⋊C4×D11C2212yes—
50C2×C4⋊C4×D11C2212yes—
51C2×C4⋊C4×D11C2212yes—
52C2×C4⋊C4×D11C2211yescharacteristic
53C2×C4⋊C4×D11C2211yescharacteristic
54C2×#66941C2212yescomplemented
55C2×#66941C2212yescomplemented
56C2×#66940C2212yescomplemented
57C2×#66940C2211yescharacteristic, complemented
58C2×C22⋊C4×D11C2211yescharacteristic
59C2×C22⋊C4×D11C2212yes—
60C2×C22⋊C4×D11C2212yes—
61C2×C22⋊C4×D11C2211yescharacteristic
62C2×#66931C2212yes—
63C2×#66931C2212yes—
64C2×C42×D11C2211yescharacteristic
65C2×C42×D11C2211yescharacteristic
66C2×C42×D11C2212yes—
67C2×#66922C2211yescharacteristic, complemented
68C2×C4×Dic22C2212yescomplemented
69C2×C4×Dic22C2211yescharacteristic, complemented
70C11×#398C2212yescomplemented
71C11×#396C2212yes—
72C11×#391C2211yescharacteristic, complemented
73C11×#389C2211yescharacteristic, complemented
74C11×#389C2212yescomplemented
75C11×#388C2212yes—
76C4×C11×C22⋊C4C2211yescharacteristic
77#10622843C2211yescharacteristic, complemented
78C4×C22⋊Dic11C2211yescharacteristic
79#10622607C2212yes—
80#10622607C2212yes—
81#10622607C2212yes—
82#10622603C2212yes—
83#10622598C2212yescomplemented
84#10622598C2211yescharacteristic, complemented
85#10622597C2212yescomplemented
86#10622597C2212yescomplemented
87#10622596C2212yescomplemented
88#10622593C2212yescomplemented
89#10622587C2211yescharacteristic, complemented
90#10622586C2212yescomplemented
91#10622586C2211yescharacteristic, complemented
92#10622585C2212yescomplemented
93#10622585C2212yescomplemented
94#10622585C2212yescomplemented
95#10622564C2212yes—
96#10622561C2212yes—
97#10622561C2212yes—
98#10622561C2212yes—
99#10622558C2212yes—
100#10622557C2212yes—
101C22⋊C4×Dic11C2211yescharacteristic
102C22⋊C4×Dic11C2211yescharacteristic
103#10622553C2212yes—
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106#10622542C2211yescharacteristic, complemented
107#10622541C2212yescomplemented
108#10622541C2211yescharacteristic, complemented
109#10622289C2212yes—
110#10622283C2212yes—
111#10622282C2212yes—
112#10622279C2211yescharacteristic
113#10622279C2211yescharacteristic
114D11×#95C2211yescharacteristic
115D11×#95C2211yescharacteristic
116D11×#95C2212yes—
117D11×#95C2212yes—
118D11×#95C2212yes—
119#10622274C2212yescomplemented
120#10622270C2212yescomplemented
121#10622270C2212yescomplemented
122#10622260C2212yescomplemented
123#10622260C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126#10622259C2212yescomplemented
127C24×D11C2311yescharacteristic
128C22×Q8×C11C2311yescharacteristic
129C22×Q8×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C2×Q8×D11—24no—
133C2×Q8×D11—24no—
134C2×Q8×D11—24no—
135C2×Q8×D11—24no—
136C2×Q8×D11—24no—
137C2×Q8×D11D418yes—
138C22×C4×D11—24no—
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×Dic22C2311yescharacteristic
154C22×Dic22C2312yes—
155C22×Dic22C2311yescharacteristic
156C22×Dic22C2312yes—
157C11×C4⋊Q8—24no—
158C11×C22⋊Q8—24no—
159C11×C22⋊Q8—24no—
160C4×Q8×C11—24no—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C42×C11C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180#66999—24no—
181#66999—24no—
182Q8×Dic11—24no—
183#66997—24no—
184#66997—24no—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×C4⋊Dic11C2312yes—
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201#66977—24no—
202#66977—24no—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226#66950—24no—
227#66950—24no—
228#66949—28no—
229#66949—28no—
230C4⋊C4×D11—28no—
231C4⋊C4×D11—28no—
232C4⋊C4×D11—28no—
233C4⋊C4×D11—24no—
234C4⋊C4×D11—28no—
235C4⋊C4×D11—28no—
236C4⋊C4×D11—28no—
237C4⋊C4×D11D418yes—
238#66941—28no—
239#66941—28no—
240#66940—24no—
241#66940—28no—
242C22⋊C4×D11—28no—
243C22⋊C4×D11—28no—
244C22⋊C4×D11—24no—
245C22⋊C4×D11Q818yescomplemented
246#66931—28no—
247#66931—28no—
248C42×D11—24no—
249C42×D11—24no—
250C42×D11—28no—
251#66922—24no—
252C4×Dic22—24no—
253C4×Dic22—28no—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11×#95C2311yescharacteristic
257C11×#95C2312yes—
258C11×#95C2311yescharacteristic
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2311yescharacteristic
266C11⋊#95C2312yes—
267C11⋊#95C2311yescharacteristic
268C11⋊#95C2312yes—
269C11⋊#95C2311yescharacteristic
270C11⋊#95C2311yescharacteristic
271C11⋊#95C2311yescharacteristic
272C11⋊#95C2311yescharacteristic
273C11⋊#95C2312yes—
274C2×#2429—111nomaximal, Sylow
275C24×C11C2411yescharacteristic
276C23×D11—22no—
277C23×D11—22no—
278C23×D11—22no—
279C23×D11—22no—
280C23×D11—22no—
281C23×D11—22no—
282C23×D11C2×Q814yes—
283C23×D11C2411yescharacteristic
284C23×D11C2411yescharacteristic
285C2×Q8×C11—22no—
286C2×Q8×C11—22no—
287C2×Q8×C11—22no—
288C2×Q8×C11—22no—
289C2×Q8×C11—22no—
290C2×Q8×C11C2×D414yes—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317Q8×D11—232no—
318Q8×D11—416no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—24no—
326C2×C4×D11—22no—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—24no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—416no—
348C2×C4×D11C2×D418yes—
349C2×C4×D11C2×D418yes—
350C2×C4×D11C2×D414yes—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×Q814yes—
353C2×C4×D11C2×Q814yes—
354C2×C4×D11#4114yes—
355C2×C4×D11#4114yes—
356C2×Dic22—24no—
357C2×Dic22—24no—
358C2×Dic22—24no—
359C2×Dic22—24no—
360C2×Dic22—24no—
361C2×Dic22—22no—
362C2×Dic22—22no—
363C2×Dic22—22no—
364C2×Dic22—22no—
365C2×Dic22—22no—
366C2×Dic22C2×D414yes—
367C2×Dic22C2×D418yes—
368C11×C4⋊C4—24no—
369C11×C4⋊C4—24no—
370C11×C4⋊C4—24no—
371C11×C4⋊C4—24no—
372C11×C4⋊C4—24no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—24no—
375C11×C4⋊C4C2×D414yes—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—24no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4C2×Q814yescomplemented
380C42×C11—24no—
381C42×C11—22no—
382C42×C11—22no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—22no—
386C22⋊Dic11C2×Q814yescomplemented
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4C2×Q814yescomplemented
394(C2×D11)⋊C4C2×Q814yescomplemented
395C4⋊Dic11—24no—
396C4⋊Dic11—24no—
397C4⋊Dic11—24no—
398C4⋊Dic11—24no—
399C4⋊Dic11—24no—
400C4⋊Dic11—24no—
401C4⋊Dic11—22no—
402C4⋊Dic11C2×D414yes—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—24no—
413Dic11⋊C4—24no—
414Dic11⋊C4—24no—
415Dic11⋊C4—24no—
416Dic11⋊C4C2×D418yes—
417C4×Dic11—24no—
418C4×Dic11—22no—
419C4×Dic11—22no—
420C4×Dic11—24no—
421C4×Dic11—22no—
422C4×Dic11—22no—
423C4×Dic11—24no—
424C4×Dic11—22no—
425C4×Dic11—22no—
426C22×C4⋊Q8—111no—
427C22×C22⋊Q8—111no—
428C22×C22⋊Q8—111no—
429C22×C4×Q8—111no—
430#2429—112no—
431#2429—112no—
432#2429—111no—
433#2429—111no—
434#2429—112no—
435#2429—112no—
436#2429—111no—
437#2429—111no—
438#2429—111no—
439#2429—111no—
440#2429—111no—
441#2429D1111yescharacteristic, direct product factor
442C2×#398—112no—
443C2×#396—112no—
444C2×#391—111no—
445C2×#389—111no—
446C2×#389—112no—
447C2×#388—112no—
448C2×C4×C22⋊C4—111no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—21no—
454C23×C11—21no—
455C23×C11C22×Q812yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—28no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11C22×D412yes—
471C22×D11C22×D412yes—
472C22×D11C22×Q812yes—
473C22×D11C22×Q812yes—
474C22×D11C2×#4112yes—
475C22×D11C2×#4112yes—
476C22×D112−1+412yes—
477C22×D112−1+412yes—
478Q8×C11—28no—
479Q8×C11—44no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—44no—
503C2×C4×C11C22×D414yes—
504C2×C4×C11C22×D414yes—
505C2×C4×C11C22×D412yes—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×Q812yes—
508C2×C4×C11C22×Q812yes—
509C2×C4×C11C2×#4112yes—
510C2×C4×C11C2×#4112yes—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—44no—
534C2×Dic11C22×D414yes—
535C2×Dic11C22×D414yes—
536C2×Dic11C22×D412yes—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×Q812yes—
539C2×Dic11C22×Q812yes—
540C2×Dic11C2×#4112yes—
541C2×Dic11C2×#4112yes—
542C4×D11—216no—
543C4×D11—216no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—44no—
548C4×D11—48no—
549C4×D11—44no—
550C4×D11—48no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11#121116yes—
554Dic22—28no—
555Dic22—216no—
556Dic22—44no—
557Dic22—48no—
558C23×Q8—111no—
559C23×Q8—111no—
560C24×C4—111no—
561C2×C4⋊Q8—111no—
562C2×C4⋊Q8—111no—
563C2×C4⋊Q8—112no—
564C2×C4⋊Q8—112no—
565C2×C4⋊Q8—111no—
566C2×C4⋊Q8—228no—
567C2×C4⋊Q8C2×D1111yescharacteristic, complemented
568C2×C22⋊Q8—111no—
569C2×C22⋊Q8—111no—
570C2×C22⋊Q8—111no—
571C2×C22⋊Q8—111no—
572C2×C22⋊Q8—112no—
573C2×C22⋊Q8—112no—
574C2×C22⋊Q8—111no—
575C2×C22⋊Q8—111no—
576C2×C22⋊Q8—112no—
577C2×C22⋊Q8—112no—
578C2×C22⋊Q8—228no—
579C2×C22⋊Q8—228no—
580C2×C22⋊Q8C2×D1111yescharacteristic
581C2×C22⋊Q8C2×D1111yescharacteristic
582C2×C4×Q8—111no—
583C2×C4×Q8—112no—
584C2×C4×Q8—111no—
585C2×C4×Q8—112no—
586C2×C4×Q8—111no—
587C2×C4×Q8—228no—
588C2×C4×Q8C2×D1111yescharacteristic, complemented
589C22×C4⋊C4—111no—
590C22×C4⋊C4—112no—
591C22×C4⋊C4—112no—
592C22×C4⋊C4—112no—
593C22×C4⋊C4—112no—
594C22×C4⋊C4—112no—
595C22×C4⋊C4—112no—
596C22×C4⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—112no—
600C22×C22⋊C4—112no—
601C22×C42—111no—
602C22×C42—112no—
603C22×C42—111no—
604#398—112no—
605#398—112no—
606#398—112no—
607#398—112no—
608#398—112no—
609#398—112no—
610#398—112no—
611#398C2×D1112yescomplemented
612#396—112no—
613#396—112no—
614#396—112no—
615#396—112no—
616#396—112no—
617#396—112no—
618#396—112no—
619#396C2×D1112yes—
620#391—111no—
621#391—111no—
622#391—111no—
623#391—112no—
624#391—112no—
625#391C2×D1111yescharacteristic, complemented
626#389—112no—
627#389—112no—
628#389—112no—
629#389—112no—
630#389—111no—
631#389—112no—
632#389—111no—
633#389—112no—
634#389—111no—
635#389—112no—
636#389—112no—
637#389—112no—
638#389C2×D1112yescomplemented
639#389C2×D1111yescharacteristic, complemented
640#388—112no—
641#388—112no—
642#388—112no—
643#388—112no—
644#388—112no—
645#388—112no—
646#388—112no—
647#388C2×D1112yes—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4C2×D1111yescharacteristic
656C2×#95—112no—
657C2×#95—111no—
658C2×#95—112no—
659C2×#95—111no—
660C2×#95—112no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11C23×D411yescharacteristic
669C22×C11C23×D411yescharacteristic
670C22×C11C23×Q811yescharacteristic
671C22×C11C22×#4111yescharacteristic
672C22×C11C22×#4111yescharacteristic
673C22×C11C2×2−1+411yescharacteristic
674C22×C11C2×2−1+411yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—416no—
683C2×D11C2×#12114yes—
684C2×D11#53314yes—
685C2×D11#54114yes—
686C2×D11#54714yes—
687C2×D11#54814yes—
688C2×D11D4×Q814yes—
689C2×D11D4×Q814yes—
690C4×C11—24no—
691C4×C11—24no—
692C4×C11—22no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11—42no—
699C4×C11C2×#12114yes—
700Dic11—24no—
701Dic11—24no—
702Dic11—22no—
703Dic11—22no—
704Dic11—22no—
705Dic11—42no—
706Dic11—41no—
707Dic11—41no—
708Dic11—42no—
709Dic11C2×#12114yes—
710C25—111no—
711C22×Q8—118no—
712C22×Q8—112no—
713C22×Q8—111no—
714C22×Q8—112no—
715C22×Q8—111no—
716C22×Q8—224no—
717C22×Q8—224no—
718C22×Q8—224no—
719C22×Q8—224no—
720C22×Q8—224no—
721C22×Q8C22×D1111yescharacteristic
722C22×Q8C22×D1111yescharacteristic
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—224no—
737C23×C4—224no—
738C23×C4—224no—
739C23×C4C22×D1111yescharacteristic
740C4⋊Q8—24no—
741C4⋊Q8—224no—
742C4⋊Q8—228no—
743C4⋊Q8—228no—
744C4⋊Q8—224no—
745C4⋊Q8—224no—
746C22⋊Q8—24no—
747C22⋊Q8—24no—
748C22⋊Q8—228no—
749C22⋊Q8—228no—
750C22⋊Q8—228no—
751C22⋊Q8—228no—
752C22⋊Q8—224no—
753C22⋊Q8—224no—
754C22⋊Q8—224no—
755C22⋊Q8—224no—
756C22⋊Q8—224no—
757C22⋊Q8—224no—
758C4×Q8—24no—
759C4×Q8—228no—
760C4×Q8—224no—
761C4×Q8—228no—
762C4×Q8—224no—
763C4×Q8—224no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—118no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
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—228no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4—228no—
790C2×C4⋊C4—228no—
791C2×C4⋊C4—228no—
792C2×C4⋊C4—228no—
793C2×C4⋊C4—228no—
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1112yes—
797C2×C4⋊C4C22×D1112yes—
798C2×C4⋊C4C22×D1112yes—
799C2×C4⋊C4C22×D1112yes—
800C2×C4⋊C4C22×D1112yes—
801C2×C4⋊C4C22×D1111yescharacteristic
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—118no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—111no—
814C2×C22⋊C4—111no—
815C2×C22⋊C4—228no—
816C2×C22⋊C4—228no—
817C2×C22⋊C4—224no—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—111no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—111no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—224no—
832C2×C42—228no—
833C2×C42—224no—
834C2×C42C22×D1111yescharacteristic
835C2×C42C22×D1112yes—
836C2×C42C22×D1111yescharacteristic
837#95—111no—
838#95—111no—
839#95—111no—
840#95—111no—
841#95—111no—
842#95—111no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95C22×D1111yescharacteristic
853#95C22×D1111yescharacteristic
854#95C22×D1112yes—
855#95C22×D1112yes—
856#95C22×D1112yes—
857C2×C11—42no—
858C2×C11C22×#12111yescharacteristic
859C2×C11C2×#53311yescharacteristic
860C2×C11C2×#54111yescharacteristic
861C2×C11C2×#54711yescharacteristic
862C2×C11C2×#54811yescharacteristic
863C2×C11C2×D4×Q811yescharacteristic
864C2×C11C2×D4×Q811yescharacteristic
865D11—42no—
866D11#242918yesdirect product factor
867C24—111no—
868C24—114no—
869C24—111no—
870C24—222no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—222no—
875C24—222no—
876C24C23×D1111yescharacteristic
877C2×Q8—22no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8—118no—
883C2×Q8—114no—
884C2×Q8—224no—
885C2×Q8—224no—
886C2×Q8—224no—
887C2×Q8—224no—
888C2×Q8—224no—
889C2×Q8—2232no—
890C2×Q8—222no—
891C2×Q8—222no—
892C2×Q8—222no—
893C2×Q8—222no—
894C2×Q8—222no—
895C2×Q8—4416no—
896C2×Q8D4×D1114yes—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—111no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—114no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—112no—
907C22×C4—111no—
908C22×C4—112no—
909C22×C4—118no—
910C22×C4—118no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—111no—
915C22×C4—112no—
916C22×C4—112no—
917C22×C4—111no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—4416no—
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1112yes—
952C22×C4C23×D1112yes—
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1112yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1111yescharacteristic
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—118no—
968C4⋊C4—114no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—224no—
978C4⋊C4—224no—
979C4⋊C4—224no—
980C4⋊C4—224no—
981C4⋊C4—224no—
982C4⋊C4—224no—
983C4⋊C4—224no—
984C4⋊C4—222no—
985C4⋊C4—224no—
986C4⋊C4—224no—
987C4⋊C4—224no—
988C4⋊C4—224no—
989C4⋊C4D4×D1114yes—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—22no—
993C22⋊C4—114no—
994C22⋊C4—114no—
995C22⋊C4—114no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—222no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—222no—
1005C22⋊C4Q8×D1114yescomplemented
1006C42—24no—
1007C42—22no—
1008C42—22no—
1009C42—222no—
1010C42—224no—
1011C42—224no—
1012C42—222no—
1013C42—222no—
1014C42—222no—
1015C42—224no—
1016C42—222no—
1017C42—222no—
1018C11C2×#242911yescharacteristic, complemented, Sylow
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—112no—
1026C23—112no—
1027C23—112no—
1028C23—112no—
1029C23—112no—
1030C23—112no—
1031C23—112no—
1032C23—112no—
1033C23—228no—
1034C23—228no—
1035C23—228no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—221no—
1041C23—221no—
1042C23—444no—
1043C23—444no—
1044C23—444no—
1045C23—444no—
1046C23C2×Q8×D1112yes—
1047C23C24×D1111yescharacteristic
1048Q8—28no—
1049Q8—44no—
1050Q8—2216no—
1051Q8—228no—
1052Q8—448no—
1053Q8—444no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—44no—
1077C2×C4—112no—
1078C2×C4—112no—
1079C2×C4—112no—
1080C2×C4—1116no—
1081C2×C4—114no—
1082C2×C4—114no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—2216no—
1087C2×C4—2216no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—228no—
1091C2×C4—221no—
1092C2×C4—221no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—221no—
1110C2×C4—222no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—444no—
1114C2×C4—444no—
1115C2×C4—448no—
1116C2×C4—444no—
1117C2×C4—448no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4C2×D4×D1114yes—
1121C2×C4C2×D4×D1114yes—
1122C2×C4C2×D4×D1112yes—
1123C2×C4C2×D4×D1112yes—
1124C2×C4C2×Q8×D1112yes—
1125C2×C4C2×Q8×D1112yes—
1126C2×C4#41×D1112yes—
1127C2×C4#41×D1112yes—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—114no—
1136C22—114no—
1137C22—114no—
1138C22—114no—
1139C22—114no—
1140C22—114no—
1141C22—114no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—4416no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22C22×D4×D1111yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C22×Q8×D1111yescharacteristic
1153C22C2×#41×D1111yescharacteristic
1154C22C2×#41×D1111yescharacteristic
1155C22D11×2−1+411yescharacteristic
1156C22D11×2−1+411yescharacteristic
1157C4—24no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—24no—
1162C4—41no—
1163C4—42no—
1164C4—41no—
1165C4—42no—
1166C4—114no—
1167C4—224no—
1168C4—222no—
1169C4—222no—
1170C4—222no—
1171C4—224no—
1172C4—441no—
1173C4—442no—
1174C4—441no—
1175C4—442no—
1176C4D11×#12114yes—
1177C2—42no—
1178C2—118no—
1179C2—442no—
1180C2C2×D11×#12111yescharacteristic
1181C2D11×#53311yescharacteristic
1182C2D11×#54111yescharacteristic
1183C2D11×#54711yescharacteristic
1184C2D11×#54811yescharacteristic
1185C2D4×Q8×D1111yescharacteristic
1186C2D4×Q8×D1111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2429C2
prime radicalC24×D11C23
hypercenter#2429D11
hypocenterC11C2×#2429
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
4. C2×C4×Q8×D11C2semidirect
5. #13072218C2semidirect
6. #13072217C2semidirect
7. #13072216C2semidirect
8. #13072215C2semidirect
9. #13072214C2semidirect
10. #13072213C2semidirect
11. #13072212C2semidirect
12. #13072211C2semidirect
13. #13072210C2semidirect
14. #13072209C2semidirect
15. #13072208C2semidirect
16. D11×#398C2semidirect
18. D11×#391C2semidirect
19. D11×#389C2semidirect
20. D11×#389C2semidirect
23. C11×#2429C2semidirect
27. C2×C11×C4⋊Q8C22semidirect
30. C2×C4×Q8×C11C22semidirect
33. C2×Q8×Dic11C22semidirect
34. C2×#66997C22semidirect
35. C2×#66997C22semidirect
54. C2×#66941C22semidirect
55. C2×#66941C22semidirect
56. C2×#66940C22semidirect
57. C2×#66940C22semidirect
67. C2×#66922C22semidirect
68. C2×C4×Dic22C22semidirect
69. C2×C4×Dic22C22semidirect
70. C11×#398C22semidirect
72. C11×#391C22semidirect
73. C11×#389C22semidirect
74. C11×#389C22semidirect
77. #10622843C22semidirect
83. #10622598C22semidirect
84. #10622598C22semidirect
85. #10622597C22semidirect
86. #10622597C22semidirect
87. #10622596C22semidirect
88. #10622593C22semidirect
89. #10622587C22semidirect
90. #10622586C22semidirect
91. #10622586C22semidirect
92. #10622585C22semidirect
93. #10622585C22semidirect
94. #10622585C22semidirect
106. #10622542C22semidirect
107. #10622541C22semidirect
108. #10622541C22semidirect
119. #10622274C22semidirect
120. #10622270C22semidirect
121. #10622270C22semidirect
122. #10622260C22semidirect
123. #10622260C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
126. #10622259C22semidirect
245. C22⋊C4×D11Q8semidirect
379. C11×C22⋊C4C2×Q8semidirect
386. C22⋊Dic11C2×Q8semidirect
393. (C2×D11)⋊C4C2×Q8semidirect
394. (C2×D11)⋊C4C2×Q8semidirect
441. #2429D11direct (N × H)
567. C2×C4⋊Q8C2×D11semidirect
588. C2×C4×Q8C2×D11semidirect
611. #398C2×D11semidirect
625. #391C2×D11semidirect
638. #389C2×D11semidirect
639. #389C2×D11semidirect
866. D11#2429direct (N × H)
1005. C22⋊C4Q8×D11semidirect
1018. C11C2×#2429semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×D11×C22⋊Q82
C2×C4×Q8×D112
#130722182
#130722172
#130722162
#130722152
#130722142
#130722132
#130722122
#130722112
#130722102
#130722092
#130722082
D11×#3982
D11×#3962
D11×#3912
D11×#3892
D11×#3882
C4×C22⋊C4×D112
C11×#24292
C2×#242911