Finite Group Databasebeta

← D11×#2584 #14925002

Subgroups — D11×#2584 #14925002

Order 2816.

2574 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×#125C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic
3#13074005C211yesmaximal, characteristic, complemented
4#13074004C211yesmaximal, characteristic, complemented
5#13074003C212yesmaximal, complemented
6#13074002C214yesmaximal, complemented
7#13074001C212yesmaximal, complemented
8#13074000C212yesmaximal, complemented
9#13073999C211yesmaximal, characteristic, complemented
10#13073998C212yesmaximal, complemented
11D11×#398C212yesmaximal
12D11×#395C212yesmaximal
13D11×#389C212yesmaximal
14D11×#389C212yesmaximal
15D11×#389C214yesmaximal
16C4×C4⋊C4×D11C211yesmaximal, characteristic
17C11×#2584C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22D11×#125—28no—
23C4×Q8×D11—28no—
24C2×C4⋊C4×D11C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×C4⋊C4×D11C2212yes—
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2214yes—
31C2×C4⋊C4×D11C2214yes—
32C2×C4⋊C4×D11C2212yes—
33C2×#66943C2211yescharacteristic
34C2×#66943C2211yescharacteristic
35C2×#66942C2212yes—
36C2×#66942C2212yes—
37C2×#66940C2211yescharacteristic
38C2×#66940C2212yes—
39C2×C42×D11C2212yes—
40C2×C42×D11C2212yes—
41C2×C42×D11C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2212yes—
45C11×#398C2212yes—
46C11×#395C2212yes—
47C11×#389C2212yes—
48C11×#389C2214yes—
49C11×#389C2212yes—
50C4×C11×C4⋊C4C2211yescharacteristic
51#10622842C2212yes—
52#10622598C2214yes—
53#10622598C2212yes—
54#10622598C2212yes—
55#10622597C2214yes—
56#10622596C2212yes—
57#10622593C2212yes—
58#10622592C2212yes—
59#10622592C2214yes—
60C4⋊C4×Dic11C2212yes—
61#10622586C2214yes—
62#10622586C2212yes—
63#10622586C2212yes—
64#10622585C2214yes—
65#10622585C2214yes—
66#10622585C2214yes—
67#10622585C2214yes—
68C4×C4⋊Dic11C2211yescharacteristic
69C4×Dic11⋊C4C2212yes—
70#10622541C2214yes—
71#10622541C2212yes—
72#10622541C2212yes—
73D11×#95C2212yes—
74D11×#95C2214yes—
75D11×#95C2214yes—
76#10622274C2212yes—
77#10622270C2214yes—
78#10622269C2212yes—
79#10622269C2214yes—
80#10622262C2212yes—
81#10622260C2214yes—
82#10622260C2214yes—
83#10622260C2214yes—
84#10622260C2214yes—
85C22×Q8×C11C2311yescharacteristic
86C2×Q8×D11—24no—
87C2×Q8×D11—28no—
88C22×C4×D11C2312yes—
89C22×C4×D11C2312yes—
90C22×C4×D11C2312yes—
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2314yes—
94C22×C4×D11C2312yes—
95C22×C4×D11C2311yescharacteristic
96C22×Dic22C2312yes—
97C22×Dic22C2311yescharacteristic
98C11×#125—24no—
99C4×Q8×C11—24no—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C42×C11C2312yes—
110C2×C42×C11C2312yes—
111C2×C42×C11C2311yescharacteristic
112Q8×Dic11—24no—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2314yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2314yes—
121C2×C4⋊Dic11C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C4⋊C4×D11—24no—
145C4⋊C4×D11—28no—
146C4⋊C4×D11—24no—
147C4⋊C4×D11—24no—
148C4⋊C4×D11—28no—
149C4⋊C4×D11—28no—
150C4⋊C4×D11—216no—
151C4⋊C4×D11—48no—
152C4⋊C4×D11Q8116yescomplemented
153#66943—24no—
154#66943—24no—
155#66942—28no—
156#66942—28no—
157#66940—24no—
158#66940—28no—
159C42×D11—28no—
160C42×D11—44no—
161C42×D11D418yes—
162#66923—24no—
163C4×Dic22—24no—
164C4×Dic22—28no—
165C11×#95C2314yes—
166C11×#95C2314yes—
167C11×#95C2312yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C2×#2584—111nomaximal, Sylow
177C23×D11C2411yescharacteristic
178C2×Q8×C11—22no—
179C2×Q8×C11—24no—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2414yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2411yescharacteristic
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C22×Dic11C2411yescharacteristic
192C22×Dic11C2411yescharacteristic
193C22×Dic11C2414yes—
194C22×Dic11C2412yes—
195C22×Dic11C2411yescharacteristic
196Q8×D11—232no—
197C2×C4×D11—24no—
198C2×C4×D11—24no—
199C2×C4×D11—24no—
200C2×C4×D11—24no—
201C2×C4×D11—28no—
202C2×C4×D11—24no—
203C2×C4×D11—24no—
204C2×C4×D11—28no—
205C2×C4×D11—22no—
206C2×C4×D11—28no—
207C2×C4×D11—24no—
208C2×C4×D11—24no—
209C2×C4×D11—22no—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11C2×D414yes—
213C2×C4×D11C2×D414yes—
214C2×C4×D11C2×D414yes—
215C2×C4×D11C2×Q8116yes—
216C2×C4×D11C2×Q818yes—
217C2×C4×D11#4118yes—
218C2×Dic22—24no—
219C2×Dic22—24no—
220C2×Dic22—24no—
221C2×Dic22—22no—
222C2×Dic22—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—28no—
230C11×C4⋊C4—44no—
231C11×C4⋊C4C2×Q818yescomplemented
232C42×C11—24no—
233C42×C11—42no—
234C42×C11C2×D414yes—
235C4⋊Dic11—24no—
236C4⋊Dic11—24no—
237C4⋊Dic11—24no—
238C4⋊Dic11—28no—
239C4⋊Dic11—22no—
240C4⋊Dic11—22no—
241C4⋊Dic11—22no—
242C4⋊Dic11—44no—
243C4⋊Dic11C2×Q818yescomplemented
244Dic11⋊C4—24no—
245Dic11⋊C4—24no—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—28no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—28no—
255Dic11⋊C4—44no—
256Dic11⋊C4—44no—
257Dic11⋊C4C2×Q8116yescomplemented
258C4×Dic11—24no—
259C4×Dic11—24no—
260C4×Dic11—24no—
261C4×Dic11—42no—
262C4×Dic11—44no—
263C4×Dic11C2×D414yes—
264C4×Dic11C2×D414yes—
265C4×Dic11C2×D414yes—
266C22×#125—111no—
267C22×C4×Q8—111no—
268#2584—112no—
269#2584—112no—
270#2584—112no—
271#2584—114no—
272#2584—112no—
273#2584—111no—
274#2584—111no—
275#2584—111no—
276#2584D1111yescharacteristic, direct product factor
277C2×#398—112no—
278C2×#395—112no—
279C2×#389—112no—
280C2×#389—112no—
281C2×#389—114no—
282C2×C4×C4⋊C4—111no—
283C23×C11C2511yescharacteristic
284C22×D11C22×D412yes—
285C22×D11C22×Q814yes—
286C22×D11C2×#4114yes—
287C22×D11H(5,𝔽2)12yes—
288C22×D112−1+412yes—
289Q8×C11—28no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—24no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×Q818yes—
309C2×C4×C11C22×Q814yes—
310C2×C4×C11C2×#4114yes—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—24no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11C22×D412yes—
327C2×Dic11C22×D412yes—
328C2×Dic11C22×D412yes—
329C2×Dic11C22×Q818yes—
330C2×Dic11C22×Q814yes—
331C2×Dic11C2×#4114yes—
332C4×D11—28no—
333C4×D11—216no—
334C4×D11—28no—
335C4×D11—232no—
336C4×D11—48no—
337C4×D11—48no—
338C4×D11—48no—
339C4×D11C4⋊Q8116yes—
340Dic22—216no—
341Dic22—28no—
342C23×Q8—111no—
343C2×#125—112no—
344C2×#125—112no—
345C2×#125—111no—
346C2×#125—111no—
347C2×#125—111no—
348C2×#125—228no—
349C2×#125C2×D1111yescharacteristic
350C2×C4×Q8—111no—
351C2×C4×Q8—111no—
352C2×C4×Q8—112no—
353C2×C4×Q8—112no—
354C2×C4×Q8—111no—
355C2×C4×Q8—228no—
356C2×C4×Q8C2×D1111yescharacteristic
357C22×C4⋊C4—112no—
358C22×C4⋊C4—112no—
359C22×C4⋊C4—114no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—112no—
362C22×C4⋊C4—111no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—112no—
365C22×C4⋊C4—114no—
366C22×C42—111no—
367C22×C42—112no—
368C22×C42—112no—
369#398—112no—
370#398—112no—
371#398—114no—
372#398—114no—
373#398—112no—
374#398C2×D1112yes—
375#395—112no—
376#395—114no—
377#395—112no—
378#395—114no—
379#395—112no—
380#395C2×D1112yes—
381#389—114no—
382#389—114no—
383#389—114no—
384#389—114no—
385#389—112no—
386#389—114no—
387#389—112no—
388#389—112no—
389#389—114no—
390#389—112no—
391#389—112no—
392#389—114no—
393#389—112no—
394#389—114no—
395#389—114no—
396#389—114no—
397#389—114no—
398#389C2×D1112yes—
399#389C2×D1114yes—
400#389C2×D1112yes—
401C4×C4⋊C4—112no—
402C4×C4⋊C4—112no—
403C4×C4⋊C4—111no—
404C4×C4⋊C4—112no—
405C4×C4⋊C4C2×D1111yescharacteristic
406C2×#95—112no—
407C2×#95—114no—
408C2×#95—114no—
409C22×C11C23×D411yescharacteristic
410C22×C11C23×Q812yes—
411C22×C11C22×#4112yes—
412C22×C11C2×H(5,𝔽2)11yescharacteristic
413C22×C11C2×2−1+411yescharacteristic
414C2×D11#52514yes—
415C2×D11C2×C4⋊Q814yes—
416C2×D11#53714yes—
417C2×D11#55418yes—
418C2×D11#55718yes—
419C4×C11—22no—
420C4×C11—24no—
421C4×C11—22no—
422C4×C11—28no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11C2×C4⋊Q814yes—
427Dic11—22no—
428Dic11—24no—
429Dic11—22no—
430Dic11—28no—
431Dic11—42no—
432Dic11—42no—
433Dic11—42no—
434Dic11C2×C4⋊Q814yes—
435C22×Q8—111no—
436C22×Q8—112no—
437C22×Q8—224no—
438C22×Q8—228no—
439C22×Q8C22×D1111yescharacteristic
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—112no—
444C23×C4—114no—
445C23×C4—112no—
446C23×C4—112no—
447C23×C4—112no—
448#125—24no—
449#125—228no—
450#125—228no—
451#125—224no—
452#125—224no—
453#125—224no—
454C4×Q8—24no—
455C4×Q8—228no—
456C4×Q8—224no—
457C4×Q8—228no—
458C4×Q8—224no—
459C4×Q8—224no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—1116no—
463C2×C4⋊C4—112no—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—112no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—112no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—114no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—224no—
485C2×C4⋊C4—228no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—228no—
489C2×C4⋊C4—228no—
490C2×C4⋊C4—2216no—
491C2×C4⋊C4—448no—
492C2×C4⋊C4C22×D1112yes—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1112yes—
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C4⋊C4C22×D1111yescharacteristic
497C2×C4⋊C4C22×D1112yes—
498C2×C4⋊C4C22×D1114yes—
499C2×C4⋊C4C22×D1114yes—
500C2×C4⋊C4C22×D1112yes—
501C2×C42—111no—
502C2×C42—111no—
503C2×C42—111no—
504C2×C42—118no—
505C2×C42—112no—
506C2×C42—112no—
507C2×C42—112no—
508C2×C42—112no—
509C2×C42—114no—
510C2×C42—228no—
511C2×C42—444no—
512C2×C42C22×D1112yes—
513C2×C42C22×D1112yes—
514C2×C42C22×D1111yescharacteristic
515#95—112no—
516#95—114no—
517#95—114no—
518#95—114no—
519#95—114no—
520#95—114no—
521#95—114no—
522#95—114no—
523#95C22×D1112yes—
524#95C22×D1114yes—
525#95C22×D1114yes—
526C2×C11C2×#52511yescharacteristic
527C2×C11C22×C4⋊Q811yescharacteristic
528C2×C11C2×#53711yescharacteristic
529C2×C11C2×#55412yes—
530C2×C11C2×#55712yes—
531D11#258418yesdirect product factor
532C24—111no—
533C2×Q8—22no—
534C2×Q8—24no—
535C2×Q8—224no—
536C2×Q8—224no—
537C2×Q8—224no—
538C2×Q8—2232no—
539C2×Q8—222no—
540C2×Q8—224no—
541C22×C4—111no—
542C22×C4—114no—
543C22×C4—118no—
544C22×C4—114no—
545C22×C4—111no—
546C22×C4—112no—
547C22×C4—111no—
548C22×C4—114no—
549C22×C4—114no—
550C22×C4—1116no—
551C22×C4—118no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—224no—
556C22×C4—222no—
557C22×C4—228no—
558C22×C4—228no—
559C22×C4—224no—
560C22×C4—224no—
561C22×C4—222no—
562C22×C4—224no—
563C22×C4—224no—
564C22×C4—224no—
565C22×C4—228no—
566C22×C4—224no—
567C22×C4—224no—
568C22×C4—224no—
569C22×C4—224no—
570C22×C4C23×D1112yes—
571C22×C4C23×D1112yes—
572C22×C4C23×D1112yes—
573C22×C4C23×D1111yescharacteristic
574C22×C4C23×D1111yescharacteristic
575C22×C4C23×D1114yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1111yescharacteristic
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—28no—
585C4⋊C4—44no—
586C4⋊C4—1116no—
587C4⋊C4—118no—
588C4⋊C4—224no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—224no—
595C4⋊C4—224no—
596C4⋊C4—224no—
597C4⋊C4—228no—
598C4⋊C4—228no—
599C4⋊C4—224no—
600C4⋊C4—222no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—222no—
604C4⋊C4—222no—
605C4⋊C4—228no—
606C4⋊C4—444no—
607C4⋊C4—444no—
608C4⋊C4—444no—
609C4⋊C4Q8×D1118yescomplemented
610C42—24no—
611C42—42no—
612C42—114no—
613C42—114no—
614C42—114no—
615C42—224no—
616C42—224no—
617C42—224no—
618C42—442no—
619C42—444no—
620C42D4×D1114yes—
621C11C2×#258411yescharacteristic, complemented, Sylow
622C23—112no—
623C23—114no—
624C23—114no—
625C23—112no—
626C23—112no—
627C23C24×D1111yescharacteristic
628Q8—28no—
629Q8—228no—
630Q8—2216no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—24no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—112no—
647C2×C4—114no—
648C2×C4—1116no—
649C2×C4—112no—
650C2×C4—112no—
651C2×C4—118no—
652C2×C4—114no—
653C2×C4—228no—
654C2×C4—2216no—
655C2×C4—2232no—
656C2×C4—228no—
657C2×C4—222no—
658C2×C4—224no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—221no—
662C2×C4—224no—
663C2×C4—221no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—224no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—448no—
673C2×C4—448no—
674C2×C4—448no—
675C2×C4C2×D4×D1112yes—
676C2×C4C2×D4×D1112yes—
677C2×C4C2×D4×D1112yes—
678C2×C4C2×Q8×D1118yes—
679C2×C4C2×Q8×D1114yes—
680C2×C4#41×D1114yes—
681C22—118no—
682C22—114no—
683C22—118no—
684C22—114no—
685C22—114no—
686C22C22×D4×D1111yescharacteristic
687C22C22×Q8×D1112yes—
688C22C2×#41×D1112yes—
689C22D11×H(5,𝔽2)11yescharacteristic
690C22D11×2−1+411yescharacteristic
691C4—28no—
692C4—22no—
693C4—22no—
694C4—24no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—114no—
699C4—228no—
700C4—222no—
701C4—222no—
702C4—224no—
703C4—442no—
704C4—442no—
705C4—442no—
706C4D11×C4⋊Q814yes—
707C2—118no—
708C2D11×#52511yescharacteristic
709C2C2×D11×C4⋊Q811yescharacteristic
710C2D11×#53711yescharacteristic
711C2D11×#55412yes—
712C2D11×#55712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2584C2
prime radicalC23×D11C24
hypercenter#2584D11
hypocenterC11C2×#2584
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2584

Complements

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

NH ≅ G/Ntype
3. #13074005C2semidirect
4. #13074004C2semidirect
5. #13074003C2semidirect
6. #13074002C2semidirect
7. #13074001C2semidirect
8. #13074000C2semidirect
9. #13073999C2semidirect
10. #13073998C2semidirect
17. C11×#2584C2semidirect
152. C4⋊C4×D11Q8semidirect
231. C11×C4⋊C4C2×Q8semidirect
243. C4⋊Dic11C2×Q8semidirect
257. Dic11⋊C4C2×Q8semidirect
276. #2584D11direct (N × H)
531. D11#2584direct (N × H)
609. C4⋊C4Q8×D11semidirect
621. C11C2×#2584semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×C4×Q8×D112
#130740052
#130740042
#130740032
#130740022
#130740012
#130740002
#130739992
#130739982
D11×#3982
D11×#3952
D11×#3892
C4×C4⋊C4×D112
C11×#25842
C2×#258411