Finite Group Databasebeta

← D11×#2552 #14925589

Subgroups — D11×#2552 #14925589

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C212yesmaximal
2#13073653C212yesmaximal, complemented
3#13073652C211yesmaximal, characteristic, complemented
4#13073651C211yesmaximal, characteristic, complemented
5#13073650C212yesmaximal, complemented
6#13073649C212yesmaximal, complemented
7#13073648C212yesmaximal, complemented
8#13073647C211yesmaximal, characteristic, complemented
9#13073646C214yesmaximal, complemented
10D11×#398C214yesmaximal
11D11×#389C212yesmaximal
12D11×#389C212yesmaximal
13D11×#384C212yesmaximal
14D11×#384C211yesmaximal, characteristic
15C4×C4⋊C4×D11C211yesmaximal, characteristic
16C4×C4⋊C4×D11C211yesmaximal, characteristic
17C11×#2552C211yesmaximal, characteristic, complemented
18C2×C11×#125C2212yes—
19D11×#125—216no—
20C2×C4⋊C4×D11C2212yes—
21C2×C4⋊C4×D11C2214yes—
22C2×C4⋊C4×D11C2214yes—
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C4⋊C4×D11C2211yescharacteristic
25C2×C4⋊C4×D11C2212yes—
26C2×C4⋊C4×D11C2214yes—
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66943C2212yes—
31C2×#66943C2212yes—
32C2×#66942C2214yes—
33C2×#66942C2214yes—
34C2×C42×D11C2212yes—
35C2×C42×D11C2212yes—
36C2×C42×D11C2211yescharacteristic
37C2×#66923C2212yes—
38C11×#398C2214yes—
39C11×#389C2212yes—
40C11×#389C2212yes—
41C11×#384C2212yes—
42C11×#384C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45#10622598C2212yes—
46#10622598C2212yes—
47#10622597C2214yes—
48#10622597C2214yes—
49#10622596C2214yes—
50#10622593C2214yes—
51#10622589C2212yes—
52#10622589C2214yes—
53#10622589C2214yes—
54#10622589C2212yes—
55#10622589C2212yes—
56#10622589C2212yes—
57#10622589C2212yes—
58C4⋊C4×Dic11C2211yescharacteristic
59C4⋊C4×Dic11C2211yescharacteristic
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2211yescharacteristic
62#10622586C2212yes—
63#10622586C2212yes—
64#10622585C2214yes—
65#10622585C2214yes—
66#10622548C2212yes—
67#10622548C2211yescharacteristic
68C4×C4⋊Dic11C2211yescharacteristic
69C4×C4⋊Dic11C2211yescharacteristic
70C4×Dic11⋊C4C2212yes—
71C4×Dic11⋊C4C2212yes—
72#10622541C2212yes—
73#10622541C2212yes—
74D11×#95C2212yes—
75D11×#95C2212yes—
76D11×#95C2214yes—
77#10622274C2214yes—
78#10622270C2214yes—
79#10622270C2214yes—
80#10622262C2212yes—
81#10622262C2212yes—
82#10622260C2214yes—
83#10622260C2214yes—
84C22×C4×D11C2312yes—
85C22×C4×D11C2312yes—
86C22×C4×D11C2314yes—
87C22×C4×D11C2312yes—
88C22×C4×D11C2312yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C11×#125—28no—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C42×C11C2312yes—
104C2×C42×C11C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C4⋊C4×D11—216no—
139C4⋊C4×D11—216no—
140C4⋊C4×D11—28no—
141C4⋊C4×D11—24no—
142C4⋊C4×D11—24no—
143C4⋊C4×D11—28no—
144C4⋊C4×D11—48no—
145C4⋊C4×D11—44no—
146C4⋊C4×D11D418yes—
147C4⋊C4×D11Q818yes—
148#66943—28no—
149#66943—28no—
150#66942—216no—
151#66942—216no—
152C42×D11—28no—
153C42×D11—28no—
154C42×D11Q818yes—
155#66923—28no—
156C11×#95C2314yes—
157C11×#95C2312yes—
158C11×#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165C11⋊#95C2312yes—
166C11⋊#95C2312yes—
167C11⋊#95C2314yes—
168C2×#2552—111nomaximal, Sylow
169C23×D11C2411yescharacteristic
170C22×C4×C11C2412yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2414yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2412yes—
176C22×C4×C11C2411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2414yes—
181C22×Dic11C2412yes—
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2412yes—
184C22×Dic11C2411yescharacteristic
185C22×Dic11C2411yescharacteristic
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—28no—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—24no—
193C2×C4×D11—28no—
194C2×C4×D11—22no—
195C2×C4×D11—24no—
196C2×C4×D11—24no—
197C2×C4×D11—28no—
198C2×C4×D11—22no—
199C2×C4×D11—24no—
200C2×C4×D11—24no—
201C2×C4×D11C2×D418yes—
202C2×C4×D11C2×D414yes—
203C2×C4×D11C2×Q814yes—
204C2×C4×D11C2×Q818yes—
205C2×C4×D11C2×Q814yes—
206C2×C4×D11C2×Q814yes—
207C2×C4×D11C2×Q814yes—
208C2×C4×D11#4114yes—
209C2×C4×D11#4114yes—
210C11×C4⋊C4—28no—
211C11×C4⋊C4—28no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—44no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4C2×D414yes—
219C11×C4⋊C4C2×Q814yes—
220C42×C11—24no—
221C42×C11—24no—
222C42×C11C2×Q814yes—
223C4⋊Dic11—28no—
224C4⋊Dic11—24no—
225C4⋊Dic11—28no—
226C4⋊Dic11—22no—
227C4⋊Dic11—24no—
228C4⋊Dic11—22no—
229C4⋊Dic11—44no—
230C4⋊Dic11—42no—
231C4⋊Dic11C2×D414yes—
232C4⋊Dic11C2×Q814yes—
233Dic11⋊C4—28no—
234Dic11⋊C4—28no—
235Dic11⋊C4—28no—
236Dic11⋊C4—28no—
237Dic11⋊C4—24no—
238Dic11⋊C4—28no—
239Dic11⋊C4—24no—
240Dic11⋊C4—28no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243Dic11⋊C4—44no—
244Dic11⋊C4C2×D418yes—
245Dic11⋊C4C2×Q818yes—
246C4×Dic11—24no—
247C4×Dic11—24no—
248C4×Dic11—24no—
249C4×Dic11—24no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C4×Dic11C2×Q814yes—
253C4×Dic11C2×Q814yes—
254C4×Dic11C2×Q814yes—
255C22×#125—112no—
256#2552—114no—
257#2552—112no—
258#2552—112no—
259#2552—112no—
260#2552—111no—
261#2552—111no—
262#2552—111no—
263#2552—112no—
264#2552D1111yescharacteristic, direct product factor
265C2×#398—114no—
266C2×#389—112no—
267C2×#389—112no—
268C2×#384—112no—
269C2×#384—111no—
270C2×C4×C4⋊C4—111no—
271C2×C4×C4⋊C4—111no—
272C23×C11C2511yescharacteristic
273C22×D11C22×D412yes—
274C22×D11C22×Q812yes—
275C22×D11C22×Q812yes—
276C22×D11C2×#4112yes—
277C22×D11C2×#4112yes—
278C22×D11H(5,𝔽2)12yes—
279C22×D112−1+412yes—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11C22×D414yes—
296C2×C4×C11C22×D412yes—
297C2×C4×C11C22×Q812yes—
298C2×C4×C11C22×Q814yes—
299C2×C4×C11C22×Q812yes—
300C2×C4×C11C22×Q812yes—
301C2×C4×C11C22×Q812yes—
302C2×C4×C11C2×#4112yes—
303C2×C4×C11C2×#4112yes—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—21no—
307C2×Dic11—22no—
308C2×Dic11—21no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—22no—
319C2×Dic11C22×D414yes—
320C2×Dic11C22×D412yes—
321C2×Dic11C22×Q812yes—
322C2×Dic11C22×Q814yes—
323C2×Dic11C22×Q812yes—
324C2×Dic11C22×Q812yes—
325C2×Dic11C22×Q812yes—
326C2×Dic11C2×#4112yes—
327C2×Dic11C2×#4112yes—
328C4×D11—28no—
329C4×D11—216no—
330C4×D11—216no—
331C4×D11—48no—
332C4×D11—48no—
333C4×D11—416no—
334C4×D11#125116yescomplemented
335C4×D11C4⋊Q8116yes—
336C2×#125—114no—
337C2×#125—114no—
338C2×#125—112no—
339C2×#125—112no—
340C2×#125—112no—
341C2×#125—2216no—
342C2×#125C2×D1112yes—
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—114no—
346C22×C4⋊C4—114no—
347C22×C4⋊C4—112no—
348C22×C4⋊C4—111no—
349C22×C4⋊C4—111no—
350C22×C4⋊C4—112no—
351C22×C4⋊C4—112no—
352C22×C4⋊C4—114no—
353C22×C42—111no—
354C22×C42—112no—
355C22×C42—112no—
356#398—114no—
357#398—114no—
358#398—114no—
359#398—114no—
360#398—114no—
361#398—114no—
362#398—114no—
363#398C2×D1114yes—
364#389—114no—
365#389—114no—
366#389—112no—
367#389—112no—
368#389—112no—
369#389—112no—
370#389—112no—
371#389—112no—
372#389—114no—
373#389—114no—
374#389C2×D1112yes—
375#389C2×D1112yes—
376#384—112no—
377#384—112no—
378#384—112no—
379#384—114no—
380#384—112no—
381#384—112no—
382#384—114no—
383#384—112no—
384#384—111no—
385#384C2×D1112yes—
386#384C2×D1111yescharacteristic
387C4×C4⋊C4—111no—
388C4×C4⋊C4—111no—
389C4×C4⋊C4—111no—
390C4×C4⋊C4—111no—
391C4×C4⋊C4—112no—
392C4×C4⋊C4—112no—
393C4×C4⋊C4—111no—
394C4×C4⋊C4—111no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—112no—
397C4×C4⋊C4C2×D1111yescharacteristic
398C4×C4⋊C4C2×D1111yescharacteristic
399C2×#95—112no—
400C2×#95—112no—
401C2×#95—114no—
402C22×C11C23×D411yescharacteristic
403C22×C11C23×Q811yescharacteristic
404C22×C11C23×Q811yescharacteristic
405C22×C11C22×#4111yescharacteristic
406C22×C11C22×#4111yescharacteristic
407C22×C11C2×H(5,𝔽2)11yescharacteristic
408C22×C11C2×2−1+411yescharacteristic
409C2×D11C2×#12514yes—
410C2×D11C2×C4⋊Q814yes—
411C2×D11#54414yes—
412C2×D11#54714yes—
413C2×D11#55014yes—
414C2×D11#55414yes—
415C2×D11#55714yes—
416C4×C11—22no—
417C4×C11—24no—
418C4×C11—24no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—44no—
422C4×C11C2×#12514yescomplemented
423C4×C11C2×C4⋊Q814yes—
424Dic11—22no—
425Dic11—24no—
426Dic11—24no—
427Dic11—42no—
428Dic11—42no—
429Dic11—44no—
430Dic11C2×#12514yescomplemented
431Dic11C2×C4⋊Q814yes—
432C23×C4—111no—
433C23×C4—111no—
434C23×C4—112no—
435C23×C4—112no—
436C23×C4—111no—
437C23×C4—114no—
438C23×C4—112no—
439C23×C4—112no—
440#125—28no—
441#125—228no—
442#125—2216no—
443#125—2216no—
444#125—228no—
445#125—228no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—111no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—118no—
451C2×C4⋊C4—118no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—114no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—228no—
472C2×C4⋊C4—2216no—
473C2×C4⋊C4—2216no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4—228no—
477C2×C4⋊C4—444no—
478C2×C4⋊C4—448no—
479C2×C4⋊C4C22×D1112yes—
480C2×C4⋊C4C22×D1114yes—
481C2×C4⋊C4C22×D1114yes—
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1112yes—
485C2×C4⋊C4C22×D1114yes—
486C2×C4⋊C4C22×D1112yes—
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42—118no—
493C2×C42—112no—
494C2×C42—112no—
495C2×C42—112no—
496C2×C42—112no—
497C2×C42—112no—
498C2×C42—112no—
499C2×C42—228no—
500C2×C42—228no—
501C2×C42C22×D1112yes—
502C2×C42C22×D1112yes—
503C2×C42C22×D1111yescharacteristic
504#95—112no—
505#95—112no—
506#95—112no—
507#95—112no—
508#95—112no—
509#95—112no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95C22×D1112yes—
514#95C22×D1112yes—
515#95C22×D1114yes—
516C2×C11C22×#12511yescharacteristic
517C2×C11C22×C4⋊Q811yescharacteristic
518C2×C11C2×#54411yescharacteristic
519C2×C11C2×#54711yescharacteristic
520C2×C11C2×#55011yescharacteristic
521C2×C11C2×#55411yescharacteristic
522C2×C11C2×#55711yescharacteristic
523D11#255218yesdirect product factor
524C24—111no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—114no—
528C22×C4—114no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—114no—
532C22×C4—114no—
533C22×C4—111no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—118no—
537C22×C4—114no—
538C22×C4—118no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—114no—
542C22×C4—224no—
543C22×C4—224no—
544C22×C4—224no—
545C22×C4—222no—
546C22×C4—224no—
547C22×C4—222no—
548C22×C4—224no—
549C22×C4—224no—
550C22×C4—228no—
551C22×C4—228no—
552C22×C4—224no—
553C22×C4—224no—
554C22×C4—228no—
555C22×C4—224no—
556C22×C4—224no—
557C22×C4C23×D1112yes—
558C22×C4C23×D1112yes—
559C22×C4C23×D1114yes—
560C22×C4C23×D1112yes—
561C22×C4C23×D1111yescharacteristic
562C22×C4C23×D1112yes—
563C22×C4C23×D1111yescharacteristic
564C22×C4C23×D1111yescharacteristic
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—44no—
572C4⋊C4—42no—
573C4⋊C4—118no—
574C4⋊C4—114no—
575C4⋊C4—118no—
576C4⋊C4—114no—
577C4⋊C4—228no—
578C4⋊C4—228no—
579C4⋊C4—228no—
580C4⋊C4—228no—
581C4⋊C4—228no—
582C4⋊C4—224no—
583C4⋊C4—224no—
584C4⋊C4—228no—
585C4⋊C4—228no—
586C4⋊C4—228no—
587C4⋊C4—224no—
588C4⋊C4—222no—
589C4⋊C4—222no—
590C4⋊C4—224no—
591C4⋊C4—444no—
592C4⋊C4—444no—
593C4⋊C4—444no—
594C4⋊C4—444no—
595C4⋊C4—442no—
596C4⋊C4D4×D1114yes—
597C4⋊C4Q8×D1114yes—
598C42—24no—
599C42—24no—
600C42—114no—
601C42—114no—
602C42—114no—
603C42—224no—
604C42—224no—
605C42—224no—
606C42—224no—
607C42—224no—
608C42—224no—
609C42Q8×D1114yes—
610C11C2×#255211yescharacteristic, complemented, Sylow
611C23—112no—
612C23—112no—
613C23—112no—
614C23—112no—
615C23—112no—
616C23—112no—
617C23—112no—
618C23C24×D1111yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—112no—
635C2×C4—112no—
636C2×C4—112no—
637C2×C4—112no—
638C2×C4—112no—
639C2×C4—112no—
640C2×C4—1116no—
641C2×C4—1116no—
642C2×C4—114no—
643C2×C4—112no—
644C2×C4—114no—
645C2×C4—2216no—
646C2×C4—228no—
647C2×C4—2216no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—224no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—224no—
660C2×C4—222no—
661C2×C4—224no—
662C2×C4—222no—
663C2×C4—448no—
664C2×C4—448no—
665C2×C4—4416no—
666C2×C4C2×D4×D1114yes—
667C2×C4C2×D4×D1112yes—
668C2×C4C2×Q8×D1112yes—
669C2×C4C2×Q8×D1114yes—
670C2×C4C2×Q8×D1112yes—
671C2×C4C2×Q8×D1112yes—
672C2×C4C2×Q8×D1112yes—
673C2×C4#41×D1112yes—
674C2×C4#41×D1112yes—
675C22—114no—
676C22—114no—
677C22—114no—
678C22—114no—
679C22—114no—
680C22—114no—
681C22—114no—
682C22C22×D4×D1111yescharacteristic
683C22C22×Q8×D1111yescharacteristic
684C22C22×Q8×D1111yescharacteristic
685C22C2×#41×D1111yescharacteristic
686C22C2×#41×D1111yescharacteristic
687C22D11×H(5,𝔽2)11yescharacteristic
688C22D11×2−1+411yescharacteristic
689C4—24no—
690C4—22no—
691C4—24no—
692C4—42no—
693C4—42no—
694C4—44no—
695C4—114no—
696C4—114no—
697C4—224no—
698C4—222no—
699C4—224no—
700C4—442no—
701C4—442no—
702C4—444no—
703C4D11×#12514yescomplemented
704C4D11×C4⋊Q814yes—
705C2—118no—
706C2C2×D11×#12511yescharacteristic
707C2C2×D11×C4⋊Q811yescharacteristic
708C2D11×#54411yescharacteristic
709C2D11×#54711yescharacteristic
710C2D11×#55011yescharacteristic
711C2D11×#55411yescharacteristic
712C2D11×#55711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2552C2
prime radicalC23×D11C24
hypercenter#2552D11
hypocenterC11C2×#2552
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
2. #13073653C2semidirect
3. #13073652C2semidirect
4. #13073651C2semidirect
5. #13073650C2semidirect
6. #13073649C2semidirect
7. #13073648C2semidirect
8. #13073647C2semidirect
9. #13073646C2semidirect
17. C11×#2552C2semidirect
264. #2552D11direct (N × H)
334. C4×D11#125semidirect
422. C4×C11C2×#125semidirect
430. Dic11C2×#125semidirect
523. D11#2552direct (N × H)
610. C11C2×#2552semidirect
703. C4D11×#125semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130736532
#130736522
#130736512
#130736502
#130736492
#130736482
#130736472
#130736462
D11×#3982
D11×#3892
D11×#3842
C4×C4⋊C4×D112
C11×#25522
C2×#255211