Finite Group Databasebeta

← #14914162

Subgroups — #14914162

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10623103C212yesmaximal
3#13071676C211yesmaximal, characteristic, complemented
4#13071674C211yesmaximal, characteristic, complemented
5#13071673C212yesmaximal, complemented
6#13071672C211yesmaximal, characteristic, complemented
7#13071670C212yesmaximal, complemented
8#13071484C212yesmaximal
9#13071482C214yesmaximal
10#13071481C212yesmaximal
11#13071331C214yesmaximal, complemented
12#13071199C212yesmaximal
13#13071187C212yesmaximal, complemented
14C4×#66941C212yesmaximal, complemented
15#13071020C211yesmaximal, characteristic
16C4×#66945C211yesmaximal, characteristic
17C11×#2365C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2212yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2212yes—
21C2×Q8×Dic11C2212yes—
22C2×#66997C2212yes—
23D11×C4⋊Q8C4116yescomplemented
24#10623103—216no—
25C2×#66945C2211yescharacteristic
26C2×#66945C2214yes—
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66941C2212yes—
31C2×#66941C2212yes—
32C2×#66940C2212yes—
33C2×#66940C2214yes—
34C2×#66925C2212yes—
35C2×#66925C2214yes—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2212yes—
39C2×C4×Dic22C2214yes—
40C11×#391C2212yes—
41C11×#389C2212yes—
42C11×#387C2214yes—
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2212yes—
46#10622843C2212yes—
47#10622600C2211yescharacteristic
48#10622600C2211yescharacteristic
49#10622598C2212yes—
50#10622594C2214yes—
51#10622591C2214yes—
52#10622589C2211yescharacteristic
53#10622589C2211yescharacteristic
54C4⋊C4×Dic11C2211yescharacteristic
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2211yescharacteristic
57C4⋊C4×Dic11C2212yes—
58#10622587C2212yes—
59#10622586C2212yes—
60#10622585C2214yes—
61C4×(C2×D11)⋊C4C2212yes—
62C4×C4⋊Dic11C2211yescharacteristic
63C4×C4⋊Dic11C2211yescharacteristic
64C4×C4⋊Dic11C2212yes—
65#10622546C2214yes—
66C4×Dic11⋊C4C2212yes—
67C4×Dic11⋊C4C2214yes—
68C42×Dic11C2212yes—
69#10622542C2212yes—
70#10622541C2212yes—
71#10622280C2212yes—
72#10622279C2212yes—
73#10622277C2214yes—
74#10622277C2214yes—
75#10622268C2214yes—
76#10622267C2214yes—
77#10622266C2214yes—
78#10622265C2214yes—
79#10622263C2212yes—
80#10622262C2214yes—
81#10622261C2212yes—
82#10622260C2214yes—
83#10622259C2214yes—
84#10622259C2214yes—
85C22×Q8×C11C2312yes—
86C2×Q8×D11—28no—
87C2×Q8×D11—28no—
88C2×Q8×D11C2×C4116yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2314yes—
92C22×C4×D11C2311yescharacteristic
93C22×Dic22C2312yes—
94C22×Dic22C2314yes—
95C11×C4⋊Q8C2×C418yes—
96C4×Q8×C11—28no—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C42×C11C2312yes—
105C2×C42×C11C2314yes—
106C2×C42×C11C2312yes—
107C2×C42×C11C2311yescharacteristic
108Q8×Dic11—28no—
109#66997C2×C4116yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2312yes—
141#66945—24no—
142#66945—216no—
143#66945D418yes—
144C4⋊C4×D11C2×C4116yes—
145C4⋊C4×D11C2×C4116yes—
146#66941C2×C4116yes—
147#66941C2×C4116yes—
148#66940—28no—
149#66940—216no—
150#66925—28no—
151#66925—216no—
152C42×D11C2×C418yes—
153#66922C2×C418yes—
154C4×Dic22—28no—
155C4×Dic22—216no—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C11×#95C2312yes—
159C11×#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2312yes—
167C11⋊#95C2312yes—
168C11⋊#95C2312yes—
169C11⋊#95C2312yes—
170C11⋊#95C2312yes—
171C11⋊#95C2312yes—
172#34209—111nomaximal, Sylow
173C23×D11C2411yescharacteristic
174C2×Q8×C11—24no—
175C2×Q8×C11—24no—
176C2×Q8×C11C22×C418yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188C22×Dic11C2411yescharacteristic
189C22×Dic11C2414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2411yescharacteristic
192C22×Dic11C2411yescharacteristic
193Q8×D11—264no—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—28no—
197C2×C4×D11—28no—
198C2×C4×D11—22no—
199C2×C4×D11—22no—
200C2×C4×D11C22×C414yes—
201C2×C4×D11C22×C414yes—
202C2×C4×D11C22×C4116yes—
203C2×C4×D11C22×C414yes—
204C2×C4×D11C2×D414yes—
205C2×C4×D11#4114yes—
206C2×Dic22—28no—
207C2×Dic22—28no—
208C2×Dic22—24no—
209C2×Dic22—24no—
210C2×Dic22C22×C418yes—
211C2×Dic22C22×C4116yes—
212C11×C4⋊C4—28no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4C22×C418yes—
217C11×C4⋊C4C22×C418yes—
218C11×C4⋊C4C2×D414yes—
219C42×C11—28no—
220C42×C11—24no—
221C42×C11—24no—
222C42×C11C22×C414yes—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4C2×D418yes—
227C4⋊Dic11—28no—
228C4⋊Dic11—22no—
229C4⋊Dic11—22no—
230C4⋊Dic11—22no—
231C4⋊Dic11C22×C418yes—
232C4⋊Dic11C22×C418yes—
233C4⋊Dic11C2×D414yes—
234Dic11⋊C4—28no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—24no—
238Dic11⋊C4—24no—
239Dic11⋊C4—28no—
240Dic11⋊C4C22×C4116yes—
241Dic11⋊C4C22×C4116yes—
242C4×Dic11—28no—
243C4×Dic11—28no—
244C4×Dic11—24no—
245C4×Dic11—24no—
246C4×Dic11—24no—
247C4×Dic11—28no—
248C4×Dic11—24no—
249C4×Dic11—24no—
250C4×Dic11C22×C414yes—
251C4×Dic11C22×C414yes—
252C4×Dic11C22×C414yes—
253C4×Dic11C2×D418yes—
254C22×C4⋊Q8—111no—
255C2×#519—112no—
256#2365—112no—
257#2365—111no—
258#2365—111no—
259#2365—111no—
260#2365—112no—
261#2365D1111yescharacteristic, complemented
262#2344—112no—
263#2344—114no—
264#2344—112no—
265#2327—114no—
266#2310—112no—
267C4×C4⋊Q8—112no—
268C4×C4⋊Q8—112no—
269#2285—111no—
270C4×#117—111no—
271C23×C11C2511yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11C23×C412yes—
277C22×D11C22×D412yes—
278C22×D11C2×#4112yes—
279Q8×C11—216no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11C23×C412yes—
296C2×C4×C11C23×C418yes—
297C2×C4×C11C23×C412yes—
298C2×C4×C11C23×C412yes—
299C2×C4×C11C22×D414yes—
300C2×C4×C11C22×D412yes—
301C2×C4×C11C2×#4112yes—
302C2×C4×C112−1+412yes—
303C2×C4×C112−1+412yes—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11C23×C412yes—
320C2×Dic11C23×C418yes—
321C2×Dic11C23×C412yes—
322C2×Dic11C23×C412yes—
323C2×Dic11C22×D414yes—
324C2×Dic11C22×D412yes—
325C2×Dic11C2×#4112yes—
326C2×Dic112−1+412yes—
327C2×Dic112−1+412yes—
328C4×D11—232no—
329C4×D11—28no—
330C4×D11—28no—
331C4×D11C4×D4116yes—
332Dic22—216no—
333Dic22—232no—
334C23×Q8—112no—
335C2×C4⋊Q8—112no—
336C2×C4⋊Q8—1116no—
337C2×C4⋊Q8—112no—
338C2×C4⋊Q8—112no—
339C2×C4⋊Q8—111no—
340C2×C4⋊Q8C2×D1111yescharacteristic
341#519—2216no—
342C2×C4×Q8—112no—
343C2×C4×Q8—114no—
344C2×C4×Q8—112no—
345C2×C4×Q8—114no—
346C2×C4×Q8—112no—
347C2×C4×Q8C2×D1112yes—
348C2×#117—111no—
349C2×#117—111no—
350C2×#117—114no—
351C2×#117—112no—
352C2×#117—114no—
353C22×C4⋊C4—112no—
354C22×C4⋊C4—112no—
355C22×C42—111no—
356#391—112no—
357#391—112no—
358#391—112no—
359#391—114no—
360#391—114no—
361#391C2×D1112yes—
362#389—114no—
363#389—112no—
364#389—112no—
365#389—112no—
366#389—114no—
367#389C2×D1112yes—
368#387—114no—
369#387—114no—
370#387—114no—
371#387—114no—
372#387—114no—
373#387—114no—
374#387—114no—
375#387C2×D1114yes—
376#384—111no—
377#384—111no—
378#382—112no—
379#381—114no—
380#381—114no—
381#380—111no—
382#380—111no—
383#380—112no—
384C4×C4⋊C4—112no—
385C4×C4⋊C4—112no—
386C4×C4⋊C4—111no—
387C4×C4⋊C4—111no—
388C4×C4⋊C4—114no—
389C4×C4⋊C4—112no—
390C4×C4⋊C4—112no—
391C4×C4⋊C4—111no—
392C4×C4⋊C4—111no—
393C4×C4⋊C4—114no—
394C4×C4⋊C4C2×D1112yes—
395C4×C4⋊C4C2×D1111yescharacteristic
396C4×C4⋊C4C2×D1111yescharacteristic
397C4×C22⋊C4—112no—
398C4×C22⋊C4—112no—
399#376—112no—
400C43—112no—
401C22×C11C24×C411yescharacteristic
402C22×C11C23×D411yescharacteristic
403C22×C11C22×#4111yescharacteristic
404C22×C11C2×2−1+411yescharacteristic
405C22×C11C2×2−1+411yescharacteristic
406C22×C11C2×2−1+411yescharacteristic
407C22×C11C2×2−1+411yescharacteristic
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11C2×C4×D414yes—
415C4×C11—28no—
416C4×C11—22no—
417C4×C11—24no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11C2×C4×D414yes—
422C4×C11#51914yescomplemented
423Dic11—28no—
424Dic11—22no—
425Dic11—24no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11C2×C4×D414yes—
430Dic11#51914yescomplemented
431C22×Q8—1116no—
432C22×Q8—114no—
433C22×Q8—112no—
434C22×Q8—228no—
435C22×Q8—228no—
436C22×Q8C22×D1112yes—
437C23×C4—111no—
438C23×C4—114no—
439C23×C4—111no—
440C23×C4—111no—
441C4⋊Q8—1116no—
442C4⋊Q8—1116no—
443C4⋊Q8—1116no—
444C4⋊Q8—118no—
445C4⋊Q8C4×D1118yes—
446C4×Q8—28no—
447C4×Q8—2216no—
448C4×Q8—228no—
449C4×Q8—2216no—
450C4×Q8—228no—
451C4×Q8—228no—
452#117—118no—
453#117—2216no—
454#117—228no—
455#117—2216no—
456#117—224no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—114no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—1116no—
463C2×C4⋊C4—1116no—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—112no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4C22×D1114yes—
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1112yes—
479C2×C4⋊C4C22×D1112yes—
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—112no—
482C2×C22⋊C4—112no—
483C2×C22⋊C4—112no—
484C2×C22⋊C4—112no—
485C2×C42—112no—
486C2×C42—111no—
487C2×C42—111no—
488C2×C42—111no—
489C2×C42—118no—
490C2×C42—114no—
491C2×C42—114no—
492C2×C42—114no—
493C2×C42—112no—
494C2×C42—112no—
495C2×C42—112no—
496C2×C42—112no—
497C2×C42—112no—
498C2×C42C22×D1114yes—
499C2×C42C22×D1112yes—
500C2×C42C22×D1112yes—
501C2×C42C22×D1111yescharacteristic
502#95—112no—
503#95—112no—
504#95—112no—
505#95—112no—
506#95—112no—
507#95—112no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95C22×D1112yes—
515#95C22×D1114yes—
516#95C22×D1112yes—
517#95C22×D1114yes—
518C2×C11C22×C4×D411yescharacteristic
519C2×C11C2×#51911yescharacteristic
520C2×C11C2×#51911yescharacteristic
521C2×C11#349911yescharacteristic
522C2×C11#349911yescharacteristic
523C2×C11#350911yescharacteristic
524C2×C11#350911yescharacteristic
525D11—24no—
526C24—111no—
527C2×Q8—24no—
528C2×Q8—24no—
529C2×Q8—1116no—
530C2×Q8—118no—
531C2×Q8—228no—
532C2×Q8—228no—
533C2×Q8—2264no—
534C2×Q8—224no—
535C2×Q8—224no—
536C2×Q8C2×C4×D1118yes—
537C22×C4—111no—
538C22×C4—111no—
539C22×C4—114no—
540C22×C4—114no—
541C22×C4—114no—
542C22×C4—111no—
543C22×C4—114no—
544C22×C4—112no—
545C22×C4—114no—
546C22×C4—114no—
547C22×C4—1116no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—228no—
554C22×C4—228no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4C23×D1112yes—
558C22×C4C23×D1112yes—
559C22×C4C23×D1112yes—
560C22×C4C23×D1111yescharacteristic
561C22×C4C23×D1114yes—
562C22×C4C23×D1112yes—
563C22×C4C23×D1111yescharacteristic
564C22×C4C23×D1111yescharacteristic
565C4⋊C4—28no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—1116no—
570C4⋊C4—1116no—
571C4⋊C4—118no—
572C4⋊C4—118no—
573C4⋊C4—114no—
574C4⋊C4—224no—
575C4⋊C4—228no—
576C4⋊C4—224no—
577C4⋊C4—228no—
578C4⋊C4—224no—
579C4⋊C4—224no—
580C4⋊C4—228no—
581C4⋊C4—222no—
582C4⋊C4—222no—
583C4⋊C4—222no—
584C4⋊C4C2×C4×D1118yes—
585C4⋊C4C2×C4×D1118yes—
586C4⋊C4D4×D1114yes—
587C22⋊C4—118no—
588C22⋊C4—224no—
589C22⋊C4—224no—
590C22⋊C4—224no—
591C42—28no—
592C42—24no—
593C42—24no—
594C42—114no—
595C42—114no—
596C42—114no—
597C42—118no—
598C42—228no—
599C42—228no—
600C42—224no—
601C42—224no—
602C42—224no—
603C42—228no—
604C42—224no—
605C42—224no—
606C42C2×C4×D1114yes—
607C11#3420911yescharacteristic, complemented, Sylow
608C23—112no—
609C23—112no—
610C23—112no—
611C23—221no—
612C23—221no—
613C23—221no—
614C23—221no—
615C23C24×D1111yescharacteristic
616Q8—216no—
617Q8—2232no—
618Q8—2216no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
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—112no—
642C2×C4—118no—
643C2×C4—114no—
644C2×C4—228no—
645C2×C4—2232no—
646C2×C4—224no—
647C2×C4—222no—
648C2×C4—221no—
649C2×C4—224no—
650C2×C4—221no—
651C2×C4—222no—
652C2×C4—228no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4C22×C4×D1112yes—
663C2×C4C22×C4×D1118yes—
664C2×C4C22×C4×D1112yes—
665C2×C4C22×C4×D1112yes—
666C2×C4C2×D4×D1114yes—
667C2×C4C2×D4×D1112yes—
668C2×C4#6704012yes—
669C2×C4#41×D1112yes—
670C2×C4#6704312yes—
671C22—114no—
672C22—222no—
673C22—222no—
674C22—222no—
675C22—222no—
676C22—222no—
677C22—222no—
678C22C23×C4×D1111yescharacteristic
679C22C22×D4×D1111yescharacteristic
680C22C2×#6704011yescharacteristic
681C22C2×#41×D1111yescharacteristic
682C22C2×#6704311yescharacteristic
683C22D11×2−1+411yescharacteristic
684C22D11×2−1+411yescharacteristic
685C4—24no—
686C4—28no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—114no—
692C4—114no—
693C4—224no—
694C4—228no—
695C4—222no—
696C4—442no—
697C4—442no—
698C4—442no—
699C4C4×D4×D1114yes—
700C4#1062310314yescomplemented
701C2—224no—
702C2C2×C4×D4×D1111yescharacteristic
703C2D11×#51911yescharacteristic
704C2C2×#1062310311yescharacteristic
705C2#1308239511yescharacteristic
706C2#1308240011yescharacteristic
707C2#1308249611yescharacteristic
708C2#1308249911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2365C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2365D11
hypocenterC11#34209
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
3. #13071676C2semidirect
4. #13071674C2semidirect
5. #13071673C2semidirect
6. #13071672C2semidirect
7. #13071670C2semidirect
11. #13071331C2semidirect
13. #13071187C2semidirect
14. C4×#66941C2semidirect
17. C11×#2365C2semidirect
23. D11×C4⋊Q8C4semidirect
261. #2365D11semidirect
422. C4×C11#519semidirect
430. Dic11#519semidirect
607. C11#34209semidirect
700. C4#10623103semidirect

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×#106231032
#130716762
#130716742
#130716732
#130716722
#130716702
#130714842
#130714822
#130714812
#130713312
#130711992
#130711872
C4×#669412
#130710202
C4×#669452
C11×#23652
#3420911