Finite Group Databasebeta

← D11×#2452 #14921676

Subgroups — D11×#2452 #14921676

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 1194 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⋊Q8C212yesmaximal, complemented
3C2×C4×D4×D11C211yesmaximal, characteristic
4#13072469C211yesmaximal, characteristic, complemented
5#13072468C211yesmaximal, characteristic, complemented
6#13072467C211yesmaximal, characteristic, complemented
7#13072466C211yesmaximal, characteristic, complemented
8#13072465C212yesmaximal, complemented
9#13072464C211yesmaximal, characteristic, complemented
10#13072463C212yesmaximal, complemented
11#13072462C211yesmaximal, characteristic, complemented
12#13072461C212yesmaximal, complemented
13#13072460C211yesmaximal, characteristic, complemented
14#13072459C212yesmaximal, complemented
15D11×#396C212yesmaximal, complemented
16D11×#393C212yesmaximal, complemented
17D11×#390C211yesmaximal, characteristic
18D11×#390C211yesmaximal, characteristic
19D11×#389C211yesmaximal, characteristic, complemented
20D11×#389C211yesmaximal, characteristic, complemented
21D11×#385C212yesmaximal, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2452C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2212yes—
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C11×C4⋊Q8C2211yescharacteristic, complemented
28C2×C11×C22⋊Q8C2212yescomplemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66999C2212yescomplemented
31C2×#66997C2212yescomplemented
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C2×#66977C2212yescomplemented
35D11×C4⋊Q8—28no—
36D11×C22⋊Q8—216no—
37C4×D4×D11—28no—
38C2×#66950C2212yescomplemented
39C2×#66949C2212yescomplemented
40C2×#66949C2212yescomplemented
41C2×#66946C2211yescharacteristic
42C2×C4⋊C4×D11C2212yes—
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2212yes—
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2212yes—
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66941C2212yescomplemented
51C2×#66941C2211yescharacteristic, complemented
52C2×#66941C2211yescharacteristic, complemented
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×C22⋊C4×D11C2212yes—
56C2×C22⋊C4×D11C2212yes—
57C2×C22⋊C4×D11C2212yes—
58C2×C22⋊C4×D11C2212yes—
59C2×#66931C2212yescomplemented
60C2×#66931C2212yescomplemented
61C2×C4×D44C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C2×C42×D11C2211yescharacteristic
64C2×C42×D11C2211yescharacteristic
65C2×#66922C2211yescharacteristic, complemented
66C11×#396C2212yescomplemented
67C11×#393C2212yescomplemented
68C11×#390C2211yescharacteristic
69C11×#390C2211yescharacteristic
70C11×#389C2211yescharacteristic, complemented
71C11×#389C2211yescharacteristic, complemented
72C11×#385C2212yescomplemented
73C4×C11×C4⋊C4C2211yescharacteristic, complemented
74#10622844C2212yescomplemented
75#10622834C2211yescharacteristic
76#10622834C2211yescharacteristic
77#10622823C2212yescomplemented
78#10622607C2212yescomplemented
79#10622607C2212yescomplemented
80#10622607C2212yescomplemented
81#10622602C2212yescomplemented
82#10622602C2212yescomplemented
83#10622601C2211yescharacteristic
84#10622601C2211yescharacteristic
85#10622598C2211yescharacteristic, complemented
86#10622598C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2211yescharacteristic, complemented
88C4⋊C4×Dic11C2211yescharacteristic, complemented
89#10622586C2211yescharacteristic, complemented
90#10622586C2211yescharacteristic, complemented
91#10622585C2212yescomplemented
92#10622585C2212yescomplemented
93#10622570C2212yes—
94#10622570C2212yes—
95#10622570C2212yes—
96#10622570C2212yes—
97#10622563C2212yescomplemented
98#10622561C2212yescomplemented
99#10622561C2212yescomplemented
100#10622561C2212yescomplemented
101#10622560C2212yescomplemented
102#10622560C2212yescomplemented
103#10622560C2212yescomplemented
104#10622559C2212yescomplemented
105#10622552C2211yescharacteristic
106#10622552C2211yescharacteristic
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2211yescharacteristic, complemented
109C4×Dic11⋊C4C2211yescharacteristic, complemented
110#10622541C2211yescharacteristic, complemented
111#10622541C2211yescharacteristic, complemented
112#10622289C2212yescomplemented
113#10622286C2212yescomplemented
114#10622286C2212yescomplemented
115#10622286C2212yescomplemented
116#10622281C2212yescomplemented
117#10622281C2212yescomplemented
118D11×#95C2211yescharacteristic
119D11×#95C2211yescharacteristic
120D11×#95C2212yes—
121D11×#95C2212yes—
122#10622262C2211yescharacteristic, complemented
123#10622262C2211yescharacteristic, complemented
124#10622260C2212yescomplemented
125#10622260C2212yescomplemented
126C24×D11C2312yes—
127C22×Q8×C11C2312yes—
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C23×Dic11C2312yes—
132C2×Q8×D11—28no—
133C2×Q8×D11—28no—
134C2×Q8×D11—44no—
135C2×D4×D11—24no—
136C2×D4×D11—24no—
137C2×D4×D11Q818yescomplemented
138C22×D44C2311yescharacteristic
139C22×C4×D11—28no—
140C22×C4×D11—28no—
141C22×C4×D11—44no—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
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×Dic22C2312yes—
155C22×Dic22C2312yes—
156C22×Dic22C2312yes—
157C11×C4⋊Q8—24no—
158C11×C22⋊Q8—28no—
159C4×D4×C11—24no—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181#66999—28no—
182#66997—28no—
183D4×Dic11—24no—
184C4×C22⋊D11—28no—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203#66977—28no—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226#66950—28no—
227#66949—28no—
228#66949—28no—
229#66946—24no—
230C4⋊C4×D11—24no—
231C4⋊C4×D11—28no—
232C4⋊C4×D11—28no—
233C4⋊C4×D11—28no—
234C4⋊C4×D11—24no—
235C4⋊C4×D11—24no—
236C4⋊C4×D11D418yes—
237C4⋊C4×D11D418yescomplemented
238#66941—24no—
239#66941—24no—
240#66941—28no—
241(C22⋊D11)⋊C4—28no—
242C22⋊C4×D11—28no—
243C22⋊C4×D11—28no—
244C22⋊C4×D11—28no—
245C22⋊C4×D11—28no—
246C22⋊C4×D11—44no—
247#66931—28no—
248#66931—28no—
249C4×D44—24no—
250C42×D11—24no—
251C42×D11—24no—
252C42×D11—24no—
253#66922—24no—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11×#95C2311yescharacteristic
257C11×#95C2311yescharacteristic
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2311yescharacteristic
266C11⋊#95C2311yescharacteristic
267C11⋊#95C2311yescharacteristic
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270C2×#2452—111nomaximal, Sylow
271C24×C11C2412yes—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—24no—
276C23×D11—24no—
277C23×D11—24no—
278C23×D11C2×Q818yes—
279C23×D11C2412yes—
280C23×D11C2411yescharacteristic
281C2×Q8×C11—24no—
282C2×Q8×C11—24no—
283C2×Q8×C11—42no—
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11C2×Q814yescomplemented
287C22×C4×C11—24no—
288C22×C4×C11—24no—
289C22×C4×C11—42no—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11C2×Q818yescomplemented
303C22×Dic11—24no—
304C22×Dic11—24no—
305C22×Dic11—42no—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316Q8×D11—432no—
317D4×D11—232no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44C2×Q814yescomplemented
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—24no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—432no—
350C2×C4×D11C2×D414yes—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×D418yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×Q814yes—
356C2×C4×D11#4114yes—
357C2×C4×D11#4114yes—
358C2×Dic22—24no—
359C2×Dic22—24no—
360C2×Dic22—24no—
361C2×Dic22—24no—
362C2×Dic22—24no—
363C2×Dic22—24no—
364C2×Dic22—42no—
365C2×Dic22—42no—
366C2×Dic22—42no—
367C11×C4⋊C4—24no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—24no—
370C11×C4⋊C4—24no—
371C11×C4⋊C4—22no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4C2×D414yes—
374C11×C4⋊C4C2×D414yescomplemented
375C11×C22⋊C4—24no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—24no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—42no—
380C42×C11—22no—
381C42×C11—22no—
382C42×C11—22no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—24no—
386C22⋊Dic11—24no—
387C22⋊Dic11—42no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—42no—
398C4⋊Dic11—24no—
399C4⋊Dic11—24no—
400C4⋊Dic11—24no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11C2×D414yes—
405C4⋊Dic11C2×D414yescomplemented
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—22no—
411Dic11⋊C4—24no—
412Dic11⋊C4—24no—
413Dic11⋊C4—24no—
414Dic11⋊C4—24no—
415Dic11⋊C4—22no—
416Dic11⋊C4C2×D418yes—
417Dic11⋊C4C2×D414yescomplemented
418Dic11⋊C4C2×D414yescomplemented
419C4×Dic11—22no—
420C4×Dic11—22no—
421C4×Dic11—22no—
422C4×Dic11—22no—
423C4×Dic11—22no—
424C4×Dic11—22no—
425C4×Dic11—22no—
426C4×Dic11—22no—
427C4×Dic11—22no—
428C22×C4⋊Q8—111no—
429C22×C22⋊Q8—112no—
430C22×C4×D4—111no—
431#2452—112no—
432#2452—112no—
433#2452—111no—
434#2452—111no—
435#2452—111no—
436#2452—111no—
437#2452—112no—
438#2452—111no—
439#2452—111no—
440#2452—112no—
441#2452—111no—
442#2452D1111yescharacteristic, direct product factor
443C2×#396—112no—
444C2×#393—112no—
445C2×#390—111no—
446C2×#390—111no—
447C2×#389—111no—
448C2×#389—111no—
449C2×#385—112no—
450C2×C4×C4⋊C4—111no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11C22×Q814yes—
458C23×C11C2511yescharacteristic
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—216no—
466C22×D11—216no—
467C22×D11—216no—
468C22×D11—48no—
469C22×D11—48no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11C22×D412yes—
473C22×D11C22×D412yes—
474C22×D11C22×Q814yes—
475C22×D11C22×Q812yes—
476C22×D11C2×#4112yes—
477C22×D11C2×#4112yes—
478C22×D11H(5,𝔽2)12yes—
479C22×D112−1+412yes—
480Q8×C11—48no—
481D4×C11—28no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—48no—
505C2×C4×C11C22×D412yes—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D414yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C22×Q812yes—
511C2×C4×C11C2×#4112yes—
512C2×C4×C11C2×#4112yes—
513C22⋊D11—216no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—48no—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C22×D414yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C22×D412yes—
542C2×Dic11C22×Q812yes—
543C2×Dic11C2×#4112yes—
544C2×Dic11C2×#4112yes—
545D44—28no—
546C4×D11—28no—
547C4×D11—28no—
548C4×D11—216no—
549C4×D11—28no—
550C4×D11—28no—
551C4×D11—48no—
552C4×D11—48no—
553C4×D11—48no—
554C4×D11—44no—
555C4×D11—48no—
556C4×D11—44no—
557C4×D11C22⋊Q8116yescomplemented
558Dic22—48no—
559Dic22—48no—
560Dic22—48no—
561C23×Q8—112no—
562C23×D4—111no—
563C24×C4—112no—
564C2×C4⋊Q8—112no—
565C2×C4⋊Q8—112no—
566C2×C4⋊Q8—111no—
567C2×C4⋊Q8—111no—
568C2×C4⋊Q8—111no—
569C2×C4⋊Q8—228no—
570C2×C4⋊Q8C2×D1111yescharacteristic, complemented
571C2×C22⋊Q8—112no—
572C2×C22⋊Q8—112no—
573C2×C22⋊Q8—112no—
574C2×C22⋊Q8—112no—
575C2×C22⋊Q8—112no—
576C2×C22⋊Q8—112no—
577C2×C22⋊Q8—112no—
578C2×C22⋊Q8—2216no—
579C2×C22⋊Q8C2×D1112yescomplemented
580C2×C4×D4—111no—
581C2×C4×D4—112no—
582C2×C4×D4—111no—
583C2×C4×D4—112no—
584C2×C4×D4—111no—
585C2×C4×D4—228no—
586C2×C4×D4C2×D1111yescharacteristic
587C22×C4⋊C4—111no—
588C22×C4⋊C4—111no—
589C22×C4⋊C4—111no—
590C22×C4⋊C4—112no—
591C22×C4⋊C4—112no—
592C22×C4⋊C4—112no—
593C22×C4⋊C4—111no—
594C22×C4⋊C4—111no—
595C22×C22⋊C4—112no—
596C22×C22⋊C4—112no—
597C22×C22⋊C4—112no—
598C22×C22⋊C4—112no—
599C22×C22⋊C4—112no—
600C22×C42—111no—
601C22×C42—111no—
602C22×C42—111no—
603#396—112no—
604#396—112no—
605#396—112no—
606#396—112no—
607#396—112no—
608#396—112no—
609#396—112no—
610#396C2×D1112yescomplemented
611#393—112no—
612#393—112no—
613#393—112no—
614#393—112no—
615#393—112no—
616#393—112no—
617#393—112no—
618#393C2×D1112yescomplemented
619#390—111no—
620#390—111no—
621#390—111no—
622#390—111no—
623#390—112no—
624#390—112no—
625#390—112no—
626#390—112no—
627#390—111no—
628#390—111no—
629#390C2×D1111yescharacteristic
630#390C2×D1111yescharacteristic
631#389—112no—
632#389—112no—
633#389—111no—
634#389—111no—
635#389—111no—
636#389—111no—
637#389—111no—
638#389—111no—
639#389—112no—
640#389—112no—
641#389C2×D1111yescharacteristic, complemented
642#389C2×D1111yescharacteristic, complemented
643#385—112no—
644#385—112no—
645#385—112no—
646#385—112no—
647#385—112no—
648#385—112no—
649#385—112no—
650#385C2×D1112yescomplemented
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C4⋊C4—111no—
654C4×C4⋊C4—111no—
655C4×C4⋊C4—111no—
656C4×C4⋊C4—111no—
657C4×C4⋊C4—111no—
658C4×C4⋊C4C2×D1111yescharacteristic, complemented
659C2×#95—111no—
660C2×#95—112no—
661C2×#95—112no—
662C2×#95—111no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11C23×D411yescharacteristic
671C22×C11C23×D411yescharacteristic
672C22×C11C23×Q811yescharacteristic
673C22×C11C22×#4111yescharacteristic
674C22×C11C22×#4111yescharacteristic
675C22×C11C2×H(5,𝔽2)11yescharacteristic
676C22×C11C2×2−1+411yescharacteristic
677C2×D11—24no—
678C2×D11—24no—
679C2×D11—24no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—432no—
685C2×D11C2×C22⋊Q814yes—
686C2×D11#53214yes—
687C2×D11#54214yes—
688C2×D11D4214yes—
689C2×D11#54814yes—
690C2×D11D4×Q814yes—
691C2×D11#55414yes—
692C4×C11—22no—
693C4×C11—22no—
694C4×C11—24no—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—42no—
698C4×C11—41no—
699C4×C11—42no—
700C4×C11—41no—
701C4×C11C2×C22⋊Q814yescomplemented
702Dic11—22no—
703Dic11—22no—
704Dic11—24no—
705Dic11—22no—
706Dic11—22no—
707Dic11—42no—
708Dic11—41no—
709Dic11—42no—
710Dic11—41no—
711Dic11C2×C22⋊Q814yescomplemented
712C25—112no—
713C22×Q8—112no—
714C22×Q8—112no—
715C22×Q8—112no—
716C22×Q8—228no—
717C22×Q8—228no—
718C22×Q8—444no—
719C22×Q8C22×D1112yes—
720C22×D4—112no—
721C22×D4—118no—
722C22×D4—111no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4C22×D1111yescharacteristic
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—111no—
732C23×C4—112no—
733C23×C4—112no—
734C23×C4—112no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—112no—
738C23×C4—112no—
739C23×C4—228no—
740C23×C4—228no—
741C23×C4—444no—
742C23×C4C22×D1112yes—
743C4⋊Q8—24no—
744C4⋊Q8—224no—
745C4⋊Q8—228no—
746C4⋊Q8—224no—
747C4⋊Q8—228no—
748C4⋊Q8—224no—
749C22⋊Q8—28no—
750C22⋊Q8—228no—
751C22⋊Q8—228no—
752C22⋊Q8—228no—
753C22⋊Q8—228no—
754C22⋊Q8—228no—
755C22⋊Q8—228no—
756C22⋊Q8—228no—
757C4×D4—24no—
758C4×D4—224no—
759C4×D4—228no—
760C4×D4—228no—
761C4×D4—224no—
762C4×D4—224no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—118no—
769C2×C4⋊C4—118no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
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—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—228no—
787C2×C4⋊C4—228no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4—228no—
790C2×C4⋊C4—224no—
791C2×C4⋊C4—224no—
792C2×C4⋊C4C22×D1112yes—
793C2×C4⋊C4C22×D1112yes—
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C4⋊C4C22×D1111yescharacteristic
799C2×C4⋊C4C22×D1111yescharacteristic
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—228no—
816C2×C22⋊C4—228no—
817C2×C22⋊C4—228no—
818C2×C22⋊C4—228no—
819C2×C22⋊C4—444no—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C42—111no—
826C2×C42—111no—
827C2×C42—111no—
828C2×C42—111no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—224no—
835C2×C42—224no—
836C2×C42—224no—
837C2×C42C22×D1111yescharacteristic
838C2×C42C22×D1111yescharacteristic
839C2×C42C22×D1111yescharacteristic
840#95—111no—
841#95—111no—
842#95—111no—
843#95—111no—
844#95—111no—
845#95—111no—
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—
856C2×C11—44no—
857C2×C11C22×C22⋊Q811yescharacteristic
858C2×C11C2×#53211yescharacteristic
859C2×C11C2×#54211yescharacteristic
860C2×C11C2×D4211yescharacteristic
861C2×C11C2×#54811yescharacteristic
862C2×C11C2×D4×Q811yescharacteristic
863C2×C11C2×#55411yescharacteristic
864D11—44no—
865D11#245218yesdirect product factor
866C24—111no—
867C24—118no—
868C24—112no—
869C24—224no—
870C24—224no—
871C24—224no—
872C24—224no—
873C24—224no—
874C24—224no—
875C24C23×D1112yes—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—42no—
879C2×Q8—224no—
880C2×Q8—224no—
881C2×Q8—224no—
882C2×Q8—224no—
883C2×Q8—224no—
884C2×Q8—224no—
885C2×Q8—442no—
886C2×Q8—442no—
887C2×Q8—442no—
888C2×Q8—4432no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—118no—
892C2×D4—114no—
893C2×D4—2232no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4Q8×D1114yescomplemented
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—42no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—118no—
914C22×C4—114no—
915C22×C4—114no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—112no—
919C22×C4—112no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—222no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—224no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—4432no—
951C22×C4—442no—
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1112yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—118no—
969C4⋊C4—114no—
970C4⋊C4—114no—
971C4⋊C4—114no—
972C4⋊C4—114no—
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—222no—
982C4⋊C4—222no—
983C4⋊C4—224no—
984C4⋊C4—224no—
985C4⋊C4—224no—
986C4⋊C4—222no—
987C4⋊C4—222no—
988C4⋊C4—222no—
989C4⋊C4D4×D1114yes—
990C4⋊C4D4×D1114yescomplemented
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—42no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C42—22no—
1012C42—22no—
1013C42—22no—
1014C42—222no—
1015C42—222no—
1016C42—222no—
1017C42—222no—
1018C42—222no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C11C2×#245211yescharacteristic, complemented, Sylow
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—112no—
1031C23—112no—
1032C23—112no—
1033C23—112no—
1034C23—112no—
1035C23—112no—
1036C23—112no—
1037C23—114no—
1038C23—2216no—
1039C23—2216no—
1040C23—2216no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—448no—
1048C23—448no—
1049C23—448no—
1050C23—448no—
1051C23C2×Q8×D1114yes—
1052C23C24×D1111yescharacteristic
1053Q8—48no—
1054Q8—448no—
1055Q8—448no—
1056Q8—448no—
1057D4—28no—
1058D4—2216no—
1059D4—228no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—48no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—1116no—
1087C2×C4—112no—
1088C2×C4—112no—
1089C2×C4—114no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—228no—
1093C2×C4—2216no—
1094C2×C4—228no—
1095C2×C4—228no—
1096C2×C4—228no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—222no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—448no—
1120C2×C4—448no—
1121C2×C4—448no—
1122C2×C4—448no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—448no—
1126C2×C4C2×D4×D1112yes—
1127C2×C4C2×D4×D1112yes—
1128C2×C4C2×D4×D1114yes—
1129C2×C4C2×D4×D1112yes—
1130C2×C4C2×D4×D1112yes—
1131C2×C4C2×Q8×D1112yes—
1132C2×C4#41×D1112yes—
1133C2×C4#41×D1112yes—
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—114no—
1142C22—114no—
1143C22—114no—
1144C22—114no—
1145C22—114no—
1146C22—114no—
1147C22—114no—
1148C22—224no—
1149C22—224no—
1150C22—224no—
1151C22—4432no—
1152C22—442no—
1153C22—442no—
1154C22—442no—
1155C22—442no—
1156C22C22×D4×D1111yescharacteristic
1157C22C22×D4×D1111yescharacteristic
1158C22C22×Q8×D1111yescharacteristic
1159C22C2×#41×D1111yescharacteristic
1160C22C2×#41×D1111yescharacteristic
1161C22D11×H(5,𝔽2)11yescharacteristic
1162C22D11×2−1+411yescharacteristic
1163C4—22no—
1164C4—22no—
1165C4—24no—
1166C4—22no—
1167C4—22no—
1168C4—42no—
1169C4—41no—
1170C4—42no—
1171C4—41no—
1172C4—114no—
1173C4—222no—
1174C4—222no—
1175C4—224no—
1176C4—222no—
1177C4—222no—
1178C4—442no—
1179C4—441no—
1180C4—442no—
1181C4—441no—
1182C4D11×C22⋊Q814yescomplemented
1183C2—44no—
1184C2—118no—
1185C2—444no—
1186C2C2×D11×C22⋊Q811yescharacteristic
1187C2D11×#53211yescharacteristic
1188C2D11×#54211yescharacteristic
1189C2D42×D1111yescharacteristic
1190C2D11×#54811yescharacteristic
1191C2D4×Q8×D1111yescharacteristic
1192C2D11×#55411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2452C2
prime radicalC22×D4×D11C22
hypercenter#2452D11
hypocenterC11C2×#2452
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×D11×C22⋊Q8C2semidirect
4. #13072469C2semidirect
5. #13072468C2semidirect
6. #13072467C2semidirect
7. #13072466C2semidirect
8. #13072465C2semidirect
9. #13072464C2semidirect
10. #13072463C2semidirect
11. #13072462C2semidirect
12. #13072461C2semidirect
13. #13072460C2semidirect
14. #13072459C2semidirect
15. D11×#396C2semidirect
16. D11×#393C2semidirect
19. D11×#389C2semidirect
20. D11×#389C2semidirect
21. D11×#385C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2452C2semidirect
27. C2×C11×C4⋊Q8C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
30. C2×#66999C22semidirect
31. C2×#66997C22semidirect
34. C2×#66977C22semidirect
38. C2×#66950C22semidirect
39. C2×#66949C22semidirect
40. C2×#66949C22semidirect
50. C2×#66941C22semidirect
51. C2×#66941C22semidirect
52. C2×#66941C22semidirect
59. C2×#66931C22semidirect
60. C2×#66931C22semidirect
65. C2×#66922C22semidirect
66. C11×#396C22semidirect
67. C11×#393C22semidirect
70. C11×#389C22semidirect
71. C11×#389C22semidirect
72. C11×#385C22semidirect
73. C4×C11×C4⋊C4C22semidirect
74. #10622844C22semidirect
77. #10622823C22semidirect
78. #10622607C22semidirect
79. #10622607C22semidirect
80. #10622607C22semidirect
81. #10622602C22semidirect
82. #10622602C22semidirect
85. #10622598C22semidirect
86. #10622598C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. C4⋊C4×Dic11C22semidirect
89. #10622586C22semidirect
90. #10622586C22semidirect
91. #10622585C22semidirect
92. #10622585C22semidirect
97. #10622563C22semidirect
98. #10622561C22semidirect
99. #10622561C22semidirect
100. #10622561C22semidirect
101. #10622560C22semidirect
102. #10622560C22semidirect
103. #10622560C22semidirect
104. #10622559C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. #10622541C22semidirect
111. #10622541C22semidirect
112. #10622289C22semidirect
113. #10622286C22semidirect
114. #10622286C22semidirect
115. #10622286C22semidirect
116. #10622281C22semidirect
117. #10622281C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
137. C2×D4×D11Q8semidirect
237. C4⋊C4×D11D4semidirect
286. C2×D4×C11C2×Q8semidirect
302. C2×C22⋊D11C2×Q8semidirect
320. C2×D44C2×Q8semidirect
374. C11×C4⋊C4C2×D4semidirect
405. C4⋊Dic11C2×D4semidirect
417. Dic11⋊C4C2×D4semidirect
418. Dic11⋊C4C2×D4semidirect
442. #2452D11direct (N × H)
557. C4×D11C22⋊Q8semidirect
570. C2×C4⋊Q8C2×D11semidirect
579. C2×C22⋊Q8C2×D11semidirect
610. #396C2×D11semidirect
618. #393C2×D11semidirect
641. #389C2×D11semidirect
642. #389C2×D11semidirect
650. #385C2×D11semidirect
658. C4×C4⋊C4C2×D11semidirect
701. C4×C11C2×C22⋊Q8semidirect
711. Dic11C2×C22⋊Q8semidirect
865. D11#2452direct (N × H)
898. C2×D4Q8×D11semidirect
990. C4⋊C4D4×D11semidirect
1023. C11C2×#2452semidirect
1182. C4D11×C22⋊Q8semidirect

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×D4×D112
#130724692
#130724682
#130724672
#130724662
#130724652
#130724642
#130724632
#130724622
#130724612
#130724602
#130724592
D11×#3962
D11×#3932
D11×#3902
D11×#3892
D11×#3852
C4×C4⋊C4×D112
C11×#24522
C2×#245211