Finite Group Databasebeta

← #14914616

Subgroups — #14914616

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13071732C214yesmaximal, complemented
3#13071654C212yesmaximal
4#13071643C212yesmaximal, complemented
5#13071575C211yesmaximal, characteristic, complemented
6#13071567C211yesmaximal, characteristic, complemented
7#13071560C212yesmaximal, complemented
8#13071538C212yesmaximal, complemented
9#13071528C211yesmaximal, characteristic, complemented
10#13071516C211yesmaximal, characteristic, complemented
11#13071402C214yesmaximal, complemented
12#13071221C212yesmaximal, complemented
13#13071171C212yesmaximal, complemented
14#13071155C212yesmaximal, complemented
15#13070970C212yesmaximal, complemented
16C4×#66979C211yesmaximal, characteristic, complemented
17C11×#2285C211yesmaximal, characteristic, complemented
18C2×C11×#117C2212yes—
19C22×C42×C11C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66982C2212yes—
22C2×C4×C22⋊D11C2212yes—
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C2×#66946C2212yes—
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66940C2212yes—
30#10623010C4116yescomplemented
31C2×#66929C2212yes—
32C2×#66928C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66925C2212yes—
35C2×#66923C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#384C2211yescharacteristic
38C11×#384C2211yescharacteristic
39C11×#382C2212yes—
40C11×#380C2212yes—
41C11×#380C2212yes—
42C4×C11×C4⋊C4C2212yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C22⋊Dic11C2212yes—
45C4×C22⋊Dic11C2212yes—
46#10622603C2214yes—
47#10622602C2214yes—
48#10622601C2212yes—
49#10622600C2212yes—
50#10622600C2212yes—
51#10622591C2214yes—
52#10622590C2212yes—
53#10622589C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2212yes—
58#10622587C2212yes—
59#10622586C2212yes—
60#10622586C2212yes—
61#10622585C2214yes—
62#10622570C2214yes—
63#10622569C2214yes—
64#10622558C2214yes—
65#10622557C2214yes—
66#10622553C2214yes—
67C4×(C2×D11)⋊C4C2214yes—
68C4×C4⋊Dic11C2211yescharacteristic
69C4×C4⋊Dic11C2211yescharacteristic
70C4×C4⋊Dic11C2211yescharacteristic
71C4×C4⋊Dic11C2211yescharacteristic
72#10622546C2214yes—
73#10622545C2212yes—
74C4×Dic11⋊C4C2214yes—
75C42×Dic11C2212yes—
76#10622282C2214yes—
77#10622282C2214yes—
78#10622279C2214yes—
79#10622279C2214yes—
80#10622265C2214yes—
81#10622265C2214yes—
82#10622262C2214yes—
83#10622262C2214yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11C2312yes—
88C22×D44C2311yescharacteristic
89C22×C4×D11C2312yes—
90C22×C4×D11C2314yes—
91C22×Dic22C2311yescharacteristic
92C11×#117—44no—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C42×C11C2×C418yescomplemented
101C2×C42×C11C2314yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2312yes—
108C2×C22⋊Dic11C2312yes—
109#66983C2×C418yes—
110#66982C2×C4116yescomplemented
111C4×C22⋊D11C2×C4116yescomplemented
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119#66979—24no—
120#66979—24no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127#66977C2×C418yescomplemented
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145#66946—44no—
146#66945—28no—
147C4⋊C4×D11—28no—
148#66940—44no—
149#66929C2×C4116yescomplemented
150#66928C2×C418yes—
151C4×D44C2×C418yes—
152#66925C2×C4116yescomplemented
153#66923C2×C418yescomplemented
154C4×Dic22C2×C418yescomplemented
155C11×#95C2314yes—
156C11×#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165C11⋊#95C2312yes—
166C11⋊#95C2312yes—
167#34242—111nomaximal, Sylow
168C24×C11C2411yescharacteristic
169C23×D11C2412yes—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11C22×C414yes—
177C22×C4×C11C22×C414yes—
178C22×C4×C11C22×C414yes—
179C22×C4×C11C2414yes—
180C22×C4×C11C2414yes—
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11C22×C418yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C2×D44—22no—
198C2×D44—22no—
199C2×D44C22×C414yes—
200C2×C4×D11—28no—
201C2×C4×D11—24no—
202C2×C4×D11—24no—
203C2×C4×D11—44no—
204C2×C4×D11—44no—
205C2×C4×D11C22×C418yes—
206C2×Dic22—22no—
207C2×Dic22—22no—
208C2×Dic22C22×C414yes—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C22⋊C4—44no—
216C42×C11—44no—
217C42×C11C22×C414yes—
218C42×C11C22×C414yes—
219C42×C11C22×C414yes—
220C42×C11C22×C414yes—
221C22⋊Dic11—24no—
222C22⋊Dic11—24no—
223C22⋊Dic11C22×C418yes—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—44no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4C22×C418yes—
228(C2×D11)⋊C4C22×C418yes—
229(C2×D11)⋊C4C22×C418yes—
230(C2×D11)⋊C4C22×C418yes—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11C22×C414yes—
234C4⋊Dic11C22×C414yes—
235C4⋊Dic11#4114yes—
236C4⋊Dic11#4114yes—
237Dic11⋊C4—28no—
238Dic11⋊C4—44no—
239Dic11⋊C4—44no—
240Dic11⋊C4C22×C418yes—
241Dic11⋊C4C22×C418yes—
242Dic11⋊C4C22×C418yes—
243Dic11⋊C4C22×C418yes—
244C4×Dic11—28no—
245C4×Dic11—24no—
246C4×Dic11—24no—
247C4×Dic11—24no—
248C4×Dic11—24no—
249C4×Dic11—44no—
250C4×Dic11—42no—
251C4×Dic11—42no—
252C4×Dic11—44no—
253C4×Dic11C22×C418yes—
254C2×#529—111no—
255#2373—114no—
256#2363—112no—
257#2362—112no—
258#2355—111no—
259#2354—111no—
260#2354—112no—
261#2352—112no—
262Q8×C4⋊C4—111no—
263D4×C4⋊C4—111no—
264#2335—114no—
265#2314—112no—
266C4×#125—112no—
267C4×#124—112no—
268#2285D1111yescharacteristic, complemented
269#2274—112no—
270C4×#117—111no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11C23×C412yes—
278C23×C11C2511yescharacteristic
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11C23×C414yes—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—28no—
295C2×C4×C11—28no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—44no—
303C2×C4×C11C23×C412yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C23×C412yes—
309C2×C4×C11C2×#4112yes—
310C2×C4×C11C2×#4112yes—
311C2×C4×C11H(5,𝔽2)12yes—
312C2×C4×C112−1+412yes—
313C22⋊D11—48no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11C23×C414yes—
331C2×Dic11C23×C414yes—
332C2×Dic11C23×C414yes—
333C2×Dic11C2×#4114yes—
334C2×Dic11C2×#4114yes—
335D44—28no—
336C4×D11—216no—
337C4×D11—88no—
338Dic22—28no—
339#529—1116no—
340C2×#126—112no—
341C2×#125—111no—
342C2×#124—111no—
343C2×#123—112no—
344C2×C22⋊Q8—111no—
345C2×#121—111no—
346C2×C4×Q8—112no—
347C2×C4×Q8—111no—
348C2×C4×D4—112no—
349C2×C4×D4—112no—
350C2×C4×D4—111no—
351C2×#117—111no—
352C2×#117—111no—
353C2×#117—112no—
354C2×#117—112no—
355C2×#117C2×D1112yes—
356C22×C4⋊C4—112no—
357C22×C42C2×D1111yescharacteristic
358#391—112no—
359#390—112no—
360#390—114no—
361#389—112no—
362#389—112no—
363#389—114no—
364#388—114no—
365#388—114no—
366#388—114no—
367#388—114no—
368#388—114no—
369#388—114no—
370#387—114no—
371#387—114no—
372#387—114no—
373#387—114no—
374#386—114no—
375#385—114no—
376#384—112no—
377#384C2×D1111yescharacteristic
378#384C2×D1111yescharacteristic
379#382—112no—
380#382C2×D1112yes—
381#380—112no—
382#380—112no—
383#380C2×D1112yes—
384#380C2×D1112yes—
385C4×C4⋊C4—112no—
386C4×C4⋊C4—112no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4—112no—
389C4×C4⋊C4—111no—
390C4×C4⋊C4—111no—
391C4×C4⋊C4—111no—
392C4×C4⋊C4—114no—
393C4×C4⋊C4—111no—
394C4×C4⋊C4—114no—
395C4×C4⋊C4—114no—
396C4×C4⋊C4C2×D1112yes—
397C4×C4⋊C4C2×D1112yes—
398C4×C22⋊C4—112no—
399C4×C22⋊C4—112no—
400C4×C22⋊C4—114no—
401C4×C22⋊C4—114no—
402C4×C22⋊C4—114no—
403#376—112no—
404C43—112no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11C24×C411yescharacteristic
413C22×C11C22×#4111yescharacteristic
414C22×C11C22×#4111yescharacteristic
415C22×C11C2×H(5,𝔽2)11yescharacteristic
416C22×C11C2×2−1+411yescharacteristic
417C22×C11#58511yescharacteristic
418C22×C11#58511yescharacteristic
419C2×D11—24no—
420C2×D11—24no—
421C2×D11—24no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C4×C11—22no—
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—44no—
431C4×C11—44no—
432C4×C11C4×#4114yes—
433C4×C11#52014yes—
434Dic11—24no—
435Dic11—24no—
436Dic11—24no—
437Dic11—24no—
438Dic11—24no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—111no—
442C22×D4—112no—
443C22×D4—111no—
444C23×C4—112no—
445C23×C4—114no—
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449#126—1116no—
450#125—118no—
451#124—118no—
452#123—1116no—
453C22⋊Q8—118no—
454#121—118no—
455C4×Q8—118no—
456C4×Q8—444no—
457C4×D4—1116no—
458C4×D4—118no—
459C4×D4—444no—
460#117—44no—
461#117—1116no—
462#117—228no—
463#117—224no—
464#117—224no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—112no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—114no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—228no—
479C2×C4⋊C4C22×D1112yes—
480C2×C4⋊C4C22×D1112yes—
481C2×C4⋊C4C22×D1112yes—
482C2×C4⋊C4C22×D1112yes—
483C2×C4⋊C4C22×D1112yes—
484C2×C4⋊C4C22×D1112yes—
485C2×C22⋊C4—112no—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4C22×D1114yes—
496C2×C42—112no—
497C2×C42—112no—
498C2×C42—112no—
499C2×C42—114no—
500C2×C42—112no—
501C2×C42—112no—
502C2×C42—114no—
503C2×C42—112no—
504C2×C42—112no—
505C2×C42—114no—
506C2×C42C4×D1118yescomplemented
507C2×C42C22×D1114yes—
508C2×C42C22×D1111yescharacteristic
509C2×C42C22×D1111yescharacteristic
510C2×C42C22×D1111yescharacteristic
511C2×C42C22×D1111yescharacteristic
512#95—112no—
513#95—112no—
514#95—112no—
515#95—112no—
516#95—114no—
517#95—114no—
518#95—114no—
519#95—114no—
520#95—114no—
521#95—114no—
522#95C22×D1114yes—
523#95C22×D1114yes—
524C2×C11—42no—
525C2×C11C2×C4×#4111yescharacteristic
526C2×C11C2×#52011yescharacteristic
527C2×C11#342811yescharacteristic
528C2×C11#351411yescharacteristic
529C2×C11#351511yescharacteristic
530C2×C11#351711yescharacteristic
531C2×C11#351811yescharacteristic
532D11—44no—
533C24—112no—
534C24C23×D1111yescharacteristic
535C2×Q8—114no—
536C2×Q8—222no—
537C2×Q8—222no—
538C2×D4—118no—
539C2×D4—114no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—442no—
543C2×D4—442no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—118no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—228no—
559C22×C4—224no—
560C22×C4—224no—
561C22×C4—444no—
562C22×C4—444no—
563C22×C4C2×C4×D1114yes—
564C22×C4C2×C4×D1114yes—
565C22×C4C2×C4×D1114yes—
566C22×C4C23×D1114yes—
567C22×C4C23×D1114yes—
568C22×C4C23×D1111yescharacteristic
569C22×C4C23×D1111yescharacteristic
570C22×C4C23×D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—118no—
581C4⋊C4—118no—
582C4⋊C4—114no—
583C4⋊C4—118no—
584C4⋊C4—114no—
585C4⋊C4—118no—
586C4⋊C4—114no—
587C4⋊C4—114no—
588C4⋊C4—228no—
589C4⋊C4—222no—
590C4⋊C4—222no—
591C4⋊C4—444no—
592C4⋊C4—444no—
593C22⋊C4—44no—
594C22⋊C4—118no—
595C22⋊C4—118no—
596C22⋊C4—118no—
597C22⋊C4—118no—
598C22⋊C4—118no—
599C22⋊C4—228no—
600C22⋊C4—224no—
601C22⋊C4—224no—
602C22⋊C4—444no—
603C22⋊C4—444no—
604C42—44no—
605C42—118no—
606C42—224no—
607C42—224no—
608C42—228no—
609C42—224no—
610C42—224no—
611C42—444no—
612C42—442no—
613C42—442no—
614C42—444no—
615C42C2×C4×D1114yes—
616C42C2×C4×D1114yes—
617C42C2×C4×D1114yes—
618C42C2×C4×D1114yes—
619C11#3424211yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—114no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23C22×C4×D1112yes—
634C23C24×D1111yescharacteristic
635Q8—228no—
636D4—228no—
637D4—448no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—44no—
655C2×C4—114no—
656C2×C4—114no—
657C2×C4—114no—
658C2×C4—114no—
659C2×C4—114no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—2216no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—888no—
678C2×C4C22×C4×D1112yes—
679C2×C4C22×C4×D1112yes—
680C2×C4C22×C4×D1112yes—
681C2×C4C22×C4×D1112yes—
682C2×C4C22×C4×D1112yes—
683C2×C4C22×C4×D1112yes—
684C2×C4#6703712yes—
685C2×C4#6704012yes—
686C2×C4#41×D1112yes—
687C2×C4#41×D1112yes—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—224no—
696C22—224no—
697C22—224no—
698C22—442no—
699C22—442no—
700C22—442no—
701C22—442no—
702C22C23×C4×D1111yescharacteristic
703C22C2×#6703711yescharacteristic
704C22C2×#6704011yescharacteristic
705C22C2×#41×D1111yescharacteristic
706C22C2×#41×D1111yescharacteristic
707C22#1062345311yescharacteristic
708C22#1062345311yescharacteristic
709C4—22no—
710C4—22no—
711C4—22no—
712C4—22no—
713C4—44no—
714C4—44no—
715C4—224no—
716C4—224no—
717C4—224no—
718C4—224no—
719C4—224no—
720C4—442no—
721C4—442no—
722C4#1062303514yes—
723C4#1062305314yes—
724C2—42no—
725C2—444no—
726C2C2×#1062305311yescharacteristic
727C2C2×#1062303511yescharacteristic
728C2#1308181711yescharacteristic
729C2#1308257211yescharacteristic
730C2#1308258911yescharacteristic
731C2#1308261411yescharacteristic
732C2#1308262511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2285C2
socle, cosocleC23×C11C25
prime radicalC2×#66983C22
hypercenter#2285D11
hypocenterC11#34242
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13071732C2semidirect
4. #13071643C2semidirect
5. #13071575C2semidirect
6. #13071567C2semidirect
7. #13071560C2semidirect
8. #13071538C2semidirect
9. #13071528C2semidirect
10. #13071516C2semidirect
11. #13071402C2semidirect
12. #13071221C2semidirect
13. #13071171C2semidirect
14. #13071155C2semidirect
15. #13070970C2semidirect
16. C4×#66979C2semidirect
17. C11×#2285C2semidirect
30. #10623010C4semidirect
100. C2×C42×C11C2×C4semidirect
110. #66982C2×C4semidirect
111. C4×C22⋊D11C2×C4semidirect
127. #66977C2×C4semidirect
149. #66929C2×C4semidirect
152. #66925C2×C4semidirect
153. #66923C2×C4semidirect
154. C4×Dic22C2×C4semidirect
268. #2285D11semidirect
506. C2×C42C4×D11semidirect
619. C11#34242semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130717322
#130716542
#130716432
#130715752
#130715672
#130715602
#130715382
#130715282
#130715162
#130714022
#130712212
#130711712
#130711552
#130709702
C4×#669792
C11×#22852
#3424211