Finite Group Databasebeta

← D11×#1468 #14719713

Subgroups — D11×#1468 #14719713

Order 2816.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#123C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic, complemented
3C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
4#13066965C211yesmaximal, characteristic, complemented
5#13066964C211yesmaximal, characteristic, complemented
6#13066963C212yesmaximal, complemented
7#13066962C211yesmaximal, characteristic, complemented
8#13066961C212yesmaximal, complemented
9D11×#324C212yesmaximal, complemented
10D11×#323C212yesmaximal, complemented
11C11×#1468C211yesmaximal, characteristic, complemented
12C22×D4×D11C411yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C11×#123C2211yescharacteristic
15C2×#66988C411yescharacteristic
16C2×#66982C2211yescharacteristic
17C2×M16×D11—21no—
18C22×C8×D11—21no—
19D11×#123—21no—
20D11×#123—21no—
21D11×#123—21no—
22D11×#123—21no—
23D11×#123—21no—
24D11×#123—21no—
25D11×#123—21no—
26D11×#123—21no—
27C2×#66947C411yescharacteristic
28C2×#66947C2211yescharacteristic
29C2×C4⋊C4×D11C411yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66939C411yescharacteristic
32C2×#66936C411yescharacteristic
33C2×#66936C2211yescharacteristic
34C2×C22⋊C4×D11C411yescharacteristic
35C2×C22⋊C4×D11C411yescharacteristic
36C2×C22⋊C4×D11C2211yescharacteristic
37C11×#407C2211yescharacteristic, complemented
38C2×C11×C22⋊C8C2211yescharacteristic, complemented
39#10622820C2211yescharacteristic, complemented
40C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
41#10622739—21no—
42C2×(C2×D11)⋊C8—21no—
43#10622339—21no—
44#10622339C2212yescomplemented
45D11×C22⋊C8—21no—
46D11×C22⋊C8—21no—
47D11×C22⋊C8—21no—
48D11×C22⋊C8C2212yes—
49D11×C22⋊C8C2212yes—
50D11×C22⋊C8C2212yescomplemented
51C11×#324C2212yescomplemented
52C11×#323C2212yescomplemented
53#10622166C2212yescomplemented
54#10622163C2212yescomplemented
55#10622107C2212yescomplemented
56#10622107C2212yescomplemented
57#10622106C2212yescomplemented
58#10622106C2212yescomplemented
59C24×D11C2×C411yescharacteristic
60C24×D11C2×C411yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C23×Dic11C2×C411yescharacteristic
66C2×D4×D11—21no—
67C2×D4×D11—21no—
68C2×D4×D11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—44no—
71C22×D44C2×C411yescharacteristic
72C22×C4×D11—44no—
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2×C411yescharacteristic
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11D411yescharacteristic
79C22×C4×D11D411yescharacteristic
80C22×C4×D11D411yescharacteristic
81C22×C4×D11D411yescharacteristic
82C22×C4×D11D411yescharacteristic
83C22×C4×D11D411yescharacteristic
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C2×C11×M16—21no—
89C22×C8×C11—21no—
90C11×#123—21no—
91C11×#123—21no—
92C11×#123—21no—
93C11×#123—21no—
94C2×C11×C4⋊C4C2×C411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2311yescharacteristic
99C2×C22⋊Dic11C2×C411yescharacteristic
100C2×C22⋊Dic11C2×C411yescharacteristic
101C2×C22⋊Dic11C2×C411yescharacteristic
102#66988—21no—
103#66988—21no—
104#66988—21no—
105#66988—21no—
106#66982—21no—
107#66982—21no—
108#66982—21no—
109#66982—21no—
110C2×(C2×D11)⋊C4C2×C411yescharacteristic
111C2×(C2×D11)⋊C4C2×C411yescharacteristic
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×(C2×D11)⋊C4C2×C411yescharacteristic
114C2×(C2×D11)⋊C4C2×C411yescharacteristic
115C2×(C2×D11)⋊C4C2311yescharacteristic
116C2×C4⋊Dic11C2×C411yescharacteristic
117C2×C4⋊Dic11C2×C411yescharacteristic
118C2×Dic11⋊C4C2×C411yescharacteristic
119C2×Dic11⋊C4C2×C411yescharacteristic
120C2×Dic11⋊C4C2×C411yescharacteristic
121C2×Dic11⋊C4C2311yescharacteristic
122C2×#4318—21no—
123C22×C11⋊C8—21no—
124M16×D11—44no—
125C2×#4313—22no—
126C2×C8×D11—22no—
127C2×C8×D11—22no—
128C2×C8×D11—22no—
129C2×C8×D11—44no—
130#66947—21no—
131#66947—21no—
132#66947—21no—
133#66947—21no—
134#66947—21no—
135#66947—21no—
136#66947—21no—
137#66947—21no—
138C4⋊C4×D11—21no—
139C4⋊C4×D11—21no—
140C4⋊C4×D11—21no—
141C4⋊C4×D11—21no—
142C4⋊C4×D11—21no—
143C4⋊C4×D11—21no—
144C4⋊C4×D11—21no—
145C4⋊C4×D11—21no—
146#66939—21no—
147#66939—21no—
148#66939—21no—
149#66939—21no—
150#66936—21no—
151#66936—21no—
152#66936—21no—
153#66936—21no—
154#66936—21no—
155#66936—21no—
156#66936—21no—
157#66936—21no—
158C22⋊C4×D11—21no—
159C22⋊C4×D11—21no—
160C22⋊C4×D11—21no—
161C22⋊C4×D11—21no—
162C22⋊C4×D11—21no—
163C22⋊C4×D11—21no—
164C22⋊C4×D11—21no—
165C22⋊C4×D11—21no—
166C22⋊C4×D11—21no—
167C22⋊C4×D11—21no—
168C22⋊C4×D11—21no—
169C22⋊C4×D11—21no—
170C11×C22⋊C8—21no—
171C11×C22⋊C8—21no—
172C11×C22⋊C8C2312yes—
173C11×C22⋊C8C2312yes—
174C22⋊(C11⋊C8)—21no—
175C22⋊(C11⋊C8)—21no—
176C22⋊(C11⋊C8)C2312yes—
177C22⋊(C11⋊C8)C2312yes—
178(C2×D11)⋊C8—22no—
179(C2×D11)⋊C8—22no—
180(C2×D11)⋊C8—22no—
181(C2×D11)⋊C8—22no—
182C2×#1468—111nomaximal, Sylow
183C24×C11C22×C411yescharacteristic
184C24×C11C22×C411yescharacteristic
185C23×D11—24no—
186C23×D11—24no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—42no—
191C23×D11—42no—
192C23×D11—42no—
193C23×D11C22⋊C411yescharacteristic
194C23×D11C22⋊C411yescharacteristic
195C23×D11C22⋊C411yescharacteristic
196C23×D11C22⋊C411yescharacteristic
197C23×D11C22×C411yescharacteristic
198C23×D11C22×C411yescharacteristic
199C23×D11C22×C411yescharacteristic
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—21no—
214C2×C22⋊D11—21no—
215C2×C22⋊D11—21no—
216C2×C22⋊D11—21no—
217C2×C22⋊D11—42no—
218C2×C22⋊D11—42no—
219C22×Dic11—42no—
220C22×Dic11C22⋊C411yescharacteristic
221C22×Dic11C22⋊C411yescharacteristic
222C22×Dic11C22⋊C411yescharacteristic
223C22×Dic11C22⋊C411yescharacteristic
224C22×Dic11C22×C411yescharacteristic
225C22×Dic11C22×C411yescharacteristic
226C22×Dic11C22×C411yescharacteristic
227C22×Dic11C22×C411yescharacteristic
228C22×Dic11C22×C411yescharacteristic
229D4×D11—44no—
230D4×D11—44no—
231D4×D11—44no—
232D4×D11—44no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—42no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—24no—
245C2×C4×D11—42no—
246C2×C4×D11—42no—
247C2×C4×D11—42no—
248C2×C4×D11—42no—
249C2×C4×D11—42no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C2×C4×D11C22⋊C411yescharacteristic
258C2×C4×D11C22⋊C411yescharacteristic
259C2×C4×D11C22⋊C411yescharacteristic
260C2×C4×D11C22⋊C411yescharacteristic
261C2×C4×D11C22⋊C411yescharacteristic
262C2×C4×D11C22⋊C411yescharacteristic
263C2×C4×D11C22⋊C411yescharacteristic
264C2×C4×D11C22⋊C411yescharacteristic
265C2×C4×D11C2×D411yescharacteristic
266C2×C4×D11C2×D411yescharacteristic
267C2×C4×D11C2×D411yescharacteristic
268C2×C4×D11C2×D411yescharacteristic
269C2×C4×D11C2×D411yescharacteristic
270C2×C4×D11C2×D411yescharacteristic
271C2×C4×D11C2×D411yescharacteristic
272C2×C4×D11C2×D411yescharacteristic
273C11×M16—42no—
274C2×C8×C11—22no—
275C2×C8×C11—22no—
276C2×C8×C11—42no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—21no—
283C11×C22⋊C4—21no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C22⋊Dic11—21no—
288C22⋊Dic11—21no—
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291C22⋊Dic11—21no—
292C22⋊Dic11—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—21no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305C4⋊Dic11—21no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11—21no—
309Dic11⋊C4—21no—
310Dic11⋊C4—21no—
311Dic11⋊C4—21no—
312Dic11⋊C4—21no—
313Dic11⋊C4—21no—
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317#4318—42no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8—22no—
320C2×C11⋊C8—42no—
321#4313—44no—
322C8×D11—44no—
323C8×D11—44no—
324C8×D11—44no—
325C22×#123—111no—
326C2×#407—111no—
327C22×C22⋊C8—111no—
328#1468—111no—
329#1468—111no—
330#1468—112no—
331#1468—112no—
332#1468—111no—
333#1468D1111yescharacteristic, direct product factor
334C2×#324—112no—
335C2×#323—112no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—21no—
339C23×C11—22no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11C2×C22⋊C411yescharacteristic
344C23×C11C2×C22⋊C411yescharacteristic
345C23×C11C23×C411yescharacteristic
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—21no—
360C22×D11—22no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—416no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—88no—
374C22×D11#9914yes—
375C22×D11C2×C22⋊C411yescharacteristic
376C22×D11C2×C22⋊C411yescharacteristic
377C22×D11C2×C22⋊C411yescharacteristic
378C22×D11C2×C22⋊C411yescharacteristic
379C22×D11#13114yes—
380D4×C11—42no—
381D4×C11—42no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11C2×C22⋊C411yescharacteristic
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C22⋊D11—42no—
399C22⋊D11—42no—
400C22⋊D11—42no—
401C22⋊D11—42no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—22no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11C2×C22⋊C411yescharacteristic
415C2×Dic11C2×C22⋊C411yescharacteristic
416C2×Dic11C2×C22⋊C411yescharacteristic
417C2×Dic11C2×C22⋊C411yescharacteristic
418D44—42no—
419D44—42no—
420C4×D11—22no—
421C4×D11—22no—
422C4×D11—22no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—22no—
426C4×D11—22no—
427C4×D11—22no—
428C4×D11—41no—
429C4×D11—41no—
430C4×D11—41no—
431C4×D11—41no—
432C4×D11—41no—
433C4×D11—41no—
434C4×D11—41no—
435C4×D11—41no—
436C4×D11—42no—
437C4×D11—42no—
438C4×D11—42no—
439C4×D11—42no—
440C4×D11—42no—
441C4×D11—42no—
442C8×C11—42no—
443C8×C11—42no—
444C11⋊C8—42no—
445C11⋊C8—42no—
446C23×D4—111no—
447C24×C4—111no—
448C22×M16—221no—
449C23×C8—221no—
450C2×#123—111no—
451C2×#123—111no—
452C2×#123—111no—
453C2×#123—111no—
454C2×#123—111no—
455C2×#123—111no—
456C2×#123—111no—
457C2×#123—221no—
458C2×#123—221no—
459C2×#123—221no—
460C2×#123—221no—
461C2×#123—221no—
462C2×#123—221no—
463C2×#123—221no—
464C2×#123—221no—
465C2×#123C2×D1111yescharacteristic
466C22×C4⋊C4—111no—
467C22×C4⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471#407—111no—
472#407—112no—
473#407—221no—
474#407—221no—
475#407C2×D1111yescharacteristic, complemented
476C2×C22⋊C8—111no—
477C2×C22⋊C8—112no—
478C2×C22⋊C8—112no—
479C2×C22⋊C8—112no—
480C2×C22⋊C8—221no—
481C2×C22⋊C8—221no—
482C2×C22⋊C8—221no—
483C2×C22⋊C8—221no—
484C2×C22⋊C8C2×D1111yescharacteristic, complemented
485#324—112no—
486#324—112no—
487#324—112no—
488#324C2×D1112yescomplemented
489#323—112no—
490#323—112no—
491#323—112no—
492#323C2×D1112yescomplemented
493C22×C11—21no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—44no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—82no—
505C22×C11C2×#9912yes—
506C22×C11C22×C22⋊C411yescharacteristic
507C22×C11C2×#13112yes—
508C2×D11—21no—
509C2×D11—21no—
510C2×D11—21no—
511C2×D11—21no—
512C2×D11—28no—
513C2×D11—28no—
514C2×D11—21no—
515C2×D11—21no—
516C2×D11—21no—
517C2×D11—44no—
518C2×D11—44no—
519C2×D11—44no—
520C2×D11—44no—
521C2×D11—41no—
522C2×D11—41no—
523C2×D11—41no—
524C2×D11—84no—
525C2×D11—84no—
526C2×D11—82no—
527C2×D11#40812yes—
528C2×D11#40812yes—
529C2×D11C2×#9912yes—
530C2×D11C2×#9912yes—
531C2×D11#41312yes—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11—41no—
539Dic11—21no—
540Dic11—21no—
541Dic11—21no—
542Dic11—21no—
543Dic11—41no—
544Dic11—41no—
545Dic11—41no—
546C25—111no—
547C25—111no—
548C22×D4—111no—
549C22×D4—111no—
550C22×D4—111no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4—444no—
556C22×D4C4×D1111yescharacteristic
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—444no—
574C23×C4C22×D1111yescharacteristic
575C2×M16—21no—
576C2×M16—222no—
577C2×M16—221no—
578C2×M16—444no—
579C22×C8—21no—
580C22×C8—222no—
581C22×C8—222no—
582C22×C8—222no—
583C22×C8—221no—
584C22×C8—444no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—221no—
590#123—221no—
591#123—221no—
592#123—221no—
593#123—221no—
594#123—221no—
595#123—221no—
596#123—221no—
597#123—221no—
598#123—221no—
599#123—221no—
600#123—221no—
601#123—221no—
602#123—221no—
603#123—221no—
604#123—221no—
605#123—221no—
606#123—221no—
607#123—221no—
608#123—221no—
609#123—221no—
610#123—221no—
611#123—221no—
612#123—221no—
613#123—221no—
614#123—221no—
615#123—221no—
616#123—221no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—111no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—221no—
624C2×C4⋊C4—221no—
625C2×C4⋊C4—221no—
626C2×C4⋊C4—221no—
627C2×C4⋊C4—221no—
628C2×C4⋊C4—221no—
629C2×C4⋊C4—221no—
630C2×C4⋊C4—221no—
631C2×C4⋊C4C4×D1111yescharacteristic
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C22⋊C4—111no—
634C2×C22⋊C4—111no—
635C2×C22⋊C4—111no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—111no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—111no—
642C2×C22⋊C4—221no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—221no—
645C2×C22⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C22⋊C4—221no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4C4×D1111yescharacteristic
655C2×C22⋊C4C4×D1111yescharacteristic
656C2×C22⋊C4C22×D1111yescharacteristic
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—112no—
660C22⋊C8—112no—
661C22⋊C8—222no—
662C22⋊C8—222no—
663C22⋊C8—222no—
664C22⋊C8—222no—
665C22⋊C8—221no—
666C22⋊C8—221no—
667C22⋊C8C22×D1112yes—
668C22⋊C8C22×D1112yes—
669C2×C11—22no—
670C2×C11—22no—
671C2×C11—41no—
672C2×C11—81no—
673C2×C11C2×#40811yescharacteristic
674C2×C11C22×#9911yescharacteristic
675C2×C11C2×#41311yescharacteristic
676D11—22no—
677D11—22no—
678D11—41no—
679D11—81no—
680D11#146814yesdirect product factor
681C24—111no—
682C24—111no—
683C24—111no—
684C24—111no—
685C24—111no—
686C24—111no—
687C24—111no—
688C24—224no—
689C24—224no—
690C24—221no—
691C24—221no—
692C24—224no—
693C24—442no—
694C24—442no—
695C24—442no—
696C24C2×C4×D1111yescharacteristic
697C24C2×C4×D1111yescharacteristic
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—221no—
702C2×D4—221no—
703C2×D4—221no—
704C2×D4—221no—
705C2×D4—221no—
706C2×D4—221no—
707C2×D4—442no—
708C2×D4—444no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4—444no—
712C2×D4—442no—
713C2×D4—442no—
714C22×C4—42no—
715C22×C4—111no—
716C22×C4—111no—
717C22×C4—111no—
718C22×C4—111no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—111no—
726C22×C4—111no—
727C22×C4—111no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—224no—
741C22×C4—224no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—224no—
749C22×C4—442no—
750C22×C4—442no—
751C22×C4—442no—
752C22×C4—442no—
753C22×C4—442no—
754C22×C4—442no—
755C22×C4—442no—
756C22×C4—442no—
757C22×C4—442no—
758C22×C4—442no—
759C22×C4—442no—
760C22×C4—442no—
761C22×C4—442no—
762C22×C4C2×C4×D1111yescharacteristic
763C22×C4C2×C4×D1111yescharacteristic
764C22×C4C2×C4×D1111yescharacteristic
765C22×C4C2×C4×D1111yescharacteristic
766C22×C4D4×D1111yescharacteristic
767C22×C4D4×D1111yescharacteristic
768C22×C4D4×D1111yescharacteristic
769C22×C4D4×D1111yescharacteristic
770C22×C4C23×D1111yescharacteristic
771M16—42no—
772M16—444no—
773M16—442no—
774C2×C8—22no—
775C2×C8—22no—
776C2×C8—42no—
777C2×C8—222no—
778C2×C8—222no—
779C2×C8—444no—
780C2×C8—444no—
781C2×C8—444no—
782C2×C8—442no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—221no—
788C4⋊C4—221no—
789C4⋊C4—221no—
790C4⋊C4—221no—
791C4⋊C4—221no—
792C4⋊C4—221no—
793C4⋊C4—221no—
794C4⋊C4—221no—
795C4⋊C4—221no—
796C4⋊C4—221no—
797C4⋊C4—221no—
798C4⋊C4—221no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—221no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—221no—
813C22⋊C4—221no—
814C22⋊C4—221no—
815C22⋊C4—221no—
816C22⋊C4—221no—
817C22⋊C4—221no—
818C22⋊C4—221no—
819C22⋊C4—221no—
820C22⋊C4—221no—
821C22⋊C4—221no—
822C22⋊C4—221no—
823C11C2×#146811yescharacteristic, complemented, Sylow
824C23—22no—
825C23—22no—
826C23—21no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—111no—
832C23—111no—
833C23—111no—
834C23—114no—
835C23—114no—
836C23—111no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—221no—
851C23—222no—
852C23—441no—
853C23—441no—
854C23—441no—
855C23—441no—
856C23—441no—
857C23—442no—
858C23—442no—
859C23—442no—
860C23—442no—
861C23—4416no—
862C23—442no—
863C23—442no—
864C23—888no—
865C23C22⋊C4×D1111yescharacteristic
866C23C22⋊C4×D1111yescharacteristic
867C23C22×C4×D1111yescharacteristic
868D4—42no—
869D4—42no—
870D4—442no—
871D4—442no—
872D4—442no—
873D4—442no—
874D4—442no—
875D4—442no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—111no—
889C2×C4—111no—
890C2×C4—111no—
891C2×C4—111no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—221no—
905C2×C4—222no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—442no—
915C2×C4—442no—
916C2×C4—442no—
917C2×C4—442no—
918C2×C4—442no—
919C2×C4—442no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4C22⋊C4×D1111yescharacteristic
927C2×C4C22⋊C4×D1111yescharacteristic
928C2×C4C2×D4×D1111yescharacteristic
929C2×C4C2×D4×D1111yescharacteristic
930C8—42no—
931C8—42no—
932C8—442no—
933C8—442no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—44no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—82no—
946C22—112no—
947C22—112no—
948C22—112no—
949C22—112no—
950C22—112no—
951C22—228no—
952C22—228no—
953C22—221no—
954C22—221no—
955C22—221no—
956C22—221no—
957C22—221no—
958C22—221no—
959C22—221no—
960C22—444no—
961C22—444no—
962C22—444no—
963C22—444no—
964C22—441no—
965C22—441no—
966C22—441no—
967C22—882no—
968C22—884no—
969C22—884no—
970C22D11×#9912yes—
971C22C2×C22⋊C4×D1111yescharacteristic
972C22D11×#13112yes—
973C4—21no—
974C4—21no—
975C4—21no—
976C4—21no—
977C4—41no—
978C4—41no—
979C4—41no—
980C4—221no—
981C4—221no—
982C4—221no—
983C4—221no—
984C4—441no—
985C4—441no—
986C4—441no—
987C2—22no—
988C2—22no—
989C2—41no—
990C2—81no—
991C2—114no—
992C2—222no—
993C2—222no—
994C2—441no—
995C2—881no—
996C2D11×#40811yescharacteristic
997C2C2×D11×#9911yescharacteristic
998C2D11×#41311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1468C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1468D11
hypocenterC11C2×#1468
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. C2×D11×C22⋊C8C2semidirect
4. #13066965C2semidirect
5. #13066964C2semidirect
6. #13066963C2semidirect
7. #13066962C2semidirect
8. #13066961C2semidirect
9. D11×#324C2semidirect
10. D11×#323C2semidirect
11. C11×#1468C2semidirect
37. C11×#407C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. #10622820C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
44. #10622339C22semidirect
50. D11×C22⋊C8C22semidirect
51. C11×#324C22semidirect
52. C11×#323C22semidirect
53. #10622166C22semidirect
54. #10622163C22semidirect
55. #10622107C22semidirect
56. #10622107C22semidirect
57. #10622106C22semidirect
58. #10622106C22semidirect
333. #1468D11direct (N × H)
475. #407C2×D11semidirect
484. C2×C22⋊C8C2×D11semidirect
488. #324C2×D11semidirect
492. #323C2×D11semidirect
680. D11#1468direct (N × H)
823. C11C2×#1468semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1232
D11×#4072
C2×D11×C22⋊C82
#130669652
#130669642
#130669632
#130669622
#130669612
D11×#3242
D11×#3232
C11×#14682
C2×#146811