Finite Group Databasebeta

← #14914908

Subgroups — #14914908

Order 2816.

3658 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13071661C214yesmaximal, complemented
4#13071633C214yesmaximal, complemented
5#13071608C214yesmaximal, complemented
6#13071595C214yesmaximal, complemented
7#13071281C212yesmaximal, complemented
8#13071270C212yesmaximal, complemented
9#13071191C211yesmaximal, characteristic, complemented
10C4×#66988C212yesmaximal, complemented
11C4×#66990C212yesmaximal, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14#13070969C211yesmaximal, characteristic, complemented
15C2×C11×#518C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic, complemented
20C11×#518—28no—
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2212yes—
23C2×C4×D4×C11C2212yescomplemented
24C2×C4×D4×C11C2212yescomplemented
25C2×C11×#117C2212yescomplemented
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2212yescomplemented
29C2×#67006C2212yes—
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2212yescomplemented
33#10623335C4116yescomplemented
34C2×#66992C2214yes—
35C2×#66990C2212yes—
36C2×#66988C2212yes—
37C2×#66982C2212yes—
38C2×C4×C22⋊D11C2214yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41C22×Dic11⋊C4C2212yescomplemented
42C22×C4×Dic11C2211yescharacteristic, complemented
43C2×(C22⋊D11)⋊C4—28no—
44C2×(C22⋊D11)⋊C4C2214yes—
45C2×(C22⋊D11)⋊C4C2214yescomplemented
46#10622833C2212yes—
47#10622833C2212yes—
48#10622833C2214yescomplemented
49#10622826C2212yescomplemented
50#10622826C2212yescomplemented
51#10622826C2214yescomplemented
52#10622823C2214yescomplemented
53C4×C22⋊Dic11C2212yescomplemented
54C4×C22⋊Dic11C2214yescomplemented
55C4×C22⋊Dic11C2212yescomplemented
56C2×C11⋊#95C2212yescomplemented
57C2×C11⋊#95C2212yescomplemented
58#10622603C2214yescomplemented
59#10622602C2214yescomplemented
60#10622591C2214yescomplemented
61#10622585C2214yescomplemented
62#10622571C2214yes—
63#10622570C2214yescomplemented
64#10622569C2214yescomplemented
65#10622568C2212yescomplemented
66#10622559C2212yescomplemented
67#10622559C2212yescomplemented
68#10622559C2214yescomplemented
69#10622558C2214yescomplemented
70#10622557C2214yescomplemented
71#10622556C2212yescomplemented
72C22⋊C4×Dic11C2214yescomplemented
73C22⋊C4×Dic11C2214yescomplemented
74#10622553C2214yescomplemented
75C4×(C2×D11)⋊C4C2214yescomplemented
76#10622546C2214yescomplemented
77C4×Dic11⋊C4C2214yescomplemented
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11C2×C418yescomplemented
84C22×D4×C11C2312yes—
85C22×D4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11C2×C418yescomplemented
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2314yes—
99C23×Dic11—24no—
100C23×Dic11—44no—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2312yes—
103C23×Dic11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2312yes—
107C23×Dic11C2312yes—
108C22×C4×D11—24no—
109C22×C4×D11—44no—
110C22×C4×D11C2314yes—
111C4×D4×C11—28no—
112C4×D4×C11—28no—
113C4×D4×C11—28no—
114C4×D4×C11—28no—
115C11×#117—28no—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—28no—
120C2×C11×C22⋊C4D418yescomplemented
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C11×C22⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C42×C11C2312yes—
128C2×C42×C11C2312yes—
129#67006C2×C4116yescomplemented
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—44no—
132C2×C22⋊Dic11C2×C418yescomplemented
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2314yes—
140#66992C2×C4132yescomplemented
141#66990C2×C4116yescomplemented
142#66988C2×C4116yescomplemented
143#66982C2×C4116yescomplemented
144C4×C22⋊D11—48no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4—44no—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×C4×Dic11—24no—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159C2×C4×Dic11C2314yes—
160(C22⋊D11)⋊C4—216no—
161(C22⋊D11)⋊C4—216no—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170#34264—111nomaximal, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11—42no—
176C24×C11—42no—
177C24×C11C22×C414yes—
178C24×C11C22×C414yescomplemented
179C24×C11C2×D414yes—
180C24×C11#4114yes—
181C24×C11C2412yes—
182C24×C11C2411yescharacteristic
183C24×C11C2411yescharacteristic
184C24×C11C2411yescharacteristic
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—42no—
188C23×D11—42no—
189C23×D11C22×C414yes—
190C23×D11C2412yes—
191C2×D4×C11—232no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11C22×C418yes—
197C2×D4×C11C22×C418yescomplemented
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11—42no—
210C22×C4×C11C22×C414yescomplemented
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C2×C22⋊D11—232no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11C22×C418yes—
226C2×C22⋊D11C22×C418yes—
227C2×C22⋊D11C22×C4116yescomplemented
228C22×Dic11—24no—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—24no—
234C22×Dic11—24no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—24no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11—42no—
244C22×Dic11—42no—
245C22×Dic11—416no—
246C22×Dic11C22×C414yes—
247C22×Dic11C22×C418yescomplemented
248C22×Dic11C2414yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2414yes—
252C22×Dic11C2412yes—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—44no—
256C2×C4×D11—416no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4C2×D418yes—
264C11×C22⋊C4C2×D418yes—
265C42×C11—24no—
266C42×C11—24no—
267C22⋊Dic11—28no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—44no—
271C22⋊Dic11C22×C418yes—
272C22⋊Dic11C22×C418yescomplemented
273C22⋊Dic11C22×C4116yescomplemented
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4C22×C4116yescomplemented
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—44no—
281Dic11⋊C4C22×C4116yescomplemented
282C4×Dic11—28no—
283C4×Dic11—44no—
284C4×Dic11—44no—
285C2×#534—111no—
286C2×#518D1111yescharacteristic, complemented
287C22×C4×D4—111no—
288#2364—114no—
289#2361—114no—
290#2359—114no—
291#2358—114no—
292#2322—112no—
293#2321—112no—
294#2308—111no—
295C4×#123—112no—
296C4×#120—112no—
297C2×#386—111no—
298C2×#385—111no—
299#2273—111no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—24no—
309C23×C11—24no—
310C23×C11—28no—
311C23×C11—44no—
312C23×C11—48no—
313C23×C11—44no—
314C23×C11—48no—
315C23×C11—48no—
316C23×C11—82no—
317C23×C11—82no—
318C23×C11—84no—
319C23×C11C4×D4116yescomplemented
320C23×C11C23×C414yes—
321C23×C11C23×C412yes—
322C23×C11C23×C412yes—
323C23×C11C23×C412yes—
324C23×C11C22×D412yes—
325C23×C11C22×D412yes—
326C23×C11C22×D412yes—
327C23×C11C2×#4112yes—
328C23×C11C2×#4112yes—
329C23×C11C2×#4112yes—
330C23×C11C2511yescharacteristic
331C22×D11—28no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—24no—
335C22×D11—24no—
336C22×D11—48no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—48no—
340C22×D11C23×C414yes—
341D4×C11—216no—
342D4×C11—216no—
343C2×C4×C11—28no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—44no—
353C2×C4×C11—44no—
354C2×C4×C11—84no—
355C2×C4×C11—84no—
356C2×C4×C11—82no—
357C2×C4×C11—82no—
358C2×C4×C11C23×C414yes—
359C2×C4×C11C22×D414yes—
360C2×C4×C11C22×D414yes—
361C22⋊D11—216no—
362C22⋊D11—216no—
363C22⋊D11—416no—
364C2×Dic11—28no—
365C2×Dic11—28no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—24no—
370C2×Dic11—22no—
371C2×Dic11—24no—
372C2×Dic11—22no—
373C2×Dic11—24no—
374C2×Dic11—24no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—24no—
378C2×Dic11—48no—
379C2×Dic11—48no—
380C2×Dic11—48no—
381C2×Dic11—44no—
382C2×Dic11—84no—
383C2×Dic11C23×C414yes—
384C2×Dic11C23×C418yes—
385C2×Dic11H(5,𝔽2)14yes—
386C4×D11—416no—
387C23×D4—111no—
388C23×D4C2×D1111yescharacteristic
389C24×C4—111no—
390C24×C4—111no—
391#534—1116no—
392C2×#123—112no—
393C2×#123—112no—
394C2×#121—114no—
395C2×#120—112no—
396C2×#120—112no—
397#518—28no—
398C2×C4×D4—114no—
399C2×C4×D4—114no—
400C2×C4×D4—114no—
401C2×C4×D4—228no—
402C2×C4×D4C2×D1112yes—
403C2×C4×D4C2×D1112yes—
404C2×C4×D4C2×D1112yescomplemented
405C2×C4×D4C2×D1112yescomplemented
406C2×#117C2×D1112yescomplemented
407C22×C4⋊C4—111no—
408C22×C4⋊C4—112no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4C2×D1111yescharacteristic
414C22×C22⋊C4C2×D1111yescharacteristic
415C22×C22⋊C4C2×D1112yescomplemented
416C22×C42—111no—
417#390—114no—
418#389—114no—
419#388—114no—
420#388—114no—
421#388—114no—
422#388—114no—
423#387—114no—
424#387—114no—
425#386—112no—
426#386—114no—
427#386—112no—
428#386—112no—
429#386—112no—
430#386—114no—
431#386—114no—
432#386—114no—
433#385—114no—
434#385—114no—
435#385—112no—
436#385—114no—
437#385—112no—
438#381—112no—
439#379—112no—
440C4×C4⋊C4—114no—
441C4×C22⋊C4—112no—
442C4×C22⋊C4—112no—
443C4×C22⋊C4—114no—
444C4×C22⋊C4—114no—
445C4×C22⋊C4—114no—
446C4×C22⋊C4—114no—
447C2×#95—112no—
448C2×#95—112no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—28no—
463C22×C11—416no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—44no—
467C22×C11—88no—
468C22×C11C2×C4×D414yes—
469C22×C11C2×C4×D414yes—
470C22×C11C2×C4×D414yes—
471C22×C11C24×C411yescharacteristic
472C22×C11C23×D411yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C2×H(5,𝔽2)12yes—
475C22×C11#58512yes—
476C2×D11—24no—
477C2×D11—28no—
478C2×D11—416no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—44no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—42no—
486C4×C11—42no—
487Dic11—24no—
488Dic11—28no—
489Dic11—24no—
490Dic11—42no—
491Dic11—44no—
492C25—111no—
493C25C22×D1111yescharacteristic
494C25C22×D1111yescharacteristic
495C22×D4—24no—
496C22×D4—24no—
497C22×D4—118no—
498C22×D4—112no—
499C22×D4—112no—
500C22×D4—114no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4C4×D1118yescomplemented
504C22×D4C22×D1112yes—
505C22×D4C22×D1112yes—
506C23×C4—111no—
507C23×C4—112no—
508C23×C4—111no—
509C23×C4—112no—
510C23×C4—112no—
511C23×C4—112no—
512C23×C4—111no—
513C23×C4—114no—
514C23×C4—224no—
515C23×C4—224no—
516C23×C4—444no—
517C23×C4—444no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1112yes—
522C23×C4C22×D1112yes—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525#123—1116no—
526#123—1116no—
527#121—1132no—
528#120—1116no—
529#120—1116no—
530C4×D4—28no—
531C4×D4—28no—
532C4×D4—28no—
533C4×D4—28no—
534C4×D4—2216no—
535C4×D4—2216no—
536C4×D4—448no—
537#117—28no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—444no—
544C2×C4⋊C4C22×D1112yes—
545C2×C4⋊C4C22×D1112yes—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—28no—
548C2×C22⋊C4—118no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—444no—
563C2×C22⋊C4C22⋊D1118yescomplemented
564C2×C22⋊C4C22×D1112yes—
565C2×C22⋊C4C22×D1112yes—
566C2×C22⋊C4C22×D1112yes—
567C2×C22⋊C4C22×D1112yes—
568C2×C22⋊C4C22×D1112yes—
569C2×C22⋊C4C22×D1112yes—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42C22×D1112yes—
575C2×C42C22×D1112yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584C2×C11—24no—
585C2×C11—24no—
586C2×C11—24no—
587C2×C11—44no—
588C2×C11C22×C4×D411yescharacteristic
589C2×C11C4×H(5,𝔽2)12yes—
590C2×C11#348411yescharacteristic
591C2×C11#348511yescharacteristic
592C2×C11#350512yes—
593D11—44no—
594C24—22no—
595C24—22no—
596C24—42no—
597C24—42no—
598C24—42no—
599C24—42no—
600C24—112no—
601C24—114no—
602C24—222no—
603C24—222no—
604C24—442no—
605C24—442no—
606C24C2×C4×D1114yes—
607C24C2×C4×D1114yescomplemented
608C24#433914yes—
609C24C2×C22⋊D1114yes—
610C24C23×D1112yes—
611C24C23×D1111yescharacteristic
612C24C23×D1111yescharacteristic
613C24C23×D1111yescharacteristic
614C2×D4—232no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—118no—
620C2×D4—118no—
621C2×D4—1116no—
622C2×D4—2232no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4C2×C4×D1118yes—
630C2×D4C2×C4×D1118yescomplemented
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—42no—
643C22×C4—114no—
644C22×C4—114no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—118no—
648C22×C4—114no—
649C22×C4—112no—
650C22×C4—228no—
651C22×C4—224no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—228no—
662C22×C4—444no—
663C22×C4—4416no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—4416no—
672C22×C4C2×C4×D1114yescomplemented
673C22×C4C2×C22⋊D1114yes—
674C22×C4C2×C22⋊D1114yes—
675C22×C4C23×D1112yes—
676C22×C4C23×D1112yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—1116no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—444no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—118no—
691C22⋊C4—118no—
692C22⋊C4—1116no—
693C22⋊C4—1116no—
694C22⋊C4—228no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—228no—
698C22⋊C4—444no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4C2×C22⋊D1118yes—
702C22⋊C4C2×C22⋊D1118yes—
703C42—24no—
704C42—24no—
705C42—228no—
706C42—444no—
707C42—444no—
708C11#3426411yescharacteristic, complemented, Sylow
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—22no—
719C23—28no—
720C23—44no—
721C23—48no—
722C23—48no—
723C23—44no—
724C23—48no—
725C23—84no—
726C23—82no—
727C23—82no—
728C23—114no—
729C23—228no—
730C23—222no—
731C23—224no—
732C23—224no—
733C23—222no—
734C23—448no—
735C23—444no—
736C23—448no—
737C23—444no—
738C23C4×C22⋊D11116yescomplemented
739C23C22×C4×D1114yes—
740C23C22×C4×D1112yes—
741C23C22×C4×D1112yes—
742C23C22×C4×D1112yes—
743C23C2×#433912yes—
744C23C2×#433912yes—
745C23C2×#433912yes—
746C23C22×C22⋊D1112yes—
747C23C22×C22⋊D1112yes—
748C23C22×C22⋊D1112yes—
749C23C24×D1111yescharacteristic
750D4—216no—
751D4—216no—
752D4—2216no—
753D4—2216no—
754D4—4416no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—118no—
771C2×C4—114no—
772C2×C4—114no—
773C2×C4—228no—
774C2×C4—228no—
775C2×C4—222no—
776C2×C4—224no—
777C2×C4—222no—
778C2×C4—224no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—224no—
782C2×C4—224no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—224no—
786C2×C4—222no—
787C2×C4—4416no—
788C2×C4—448no—
789C2×C4—448no—
790C2×C4—448no—
791C2×C4—444no—
792C2×C4—884no—
793C2×C4C22×C4×D1114yes—
794C2×C4C22×C22⋊D1114yes—
795C2×C4C22×C22⋊D1114yes—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—28no—
810C22—416no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—88no—
815C22—224no—
816C22—228no—
817C22—4416no—
818C22—444no—
819C22—442no—
820C22—442no—
821C22C2×C4×C22⋊D1114yes—
822C22C2×C4×C22⋊D1114yes—
823C22C2×C4×C22⋊D1114yes—
824C22C23×C4×D1111yescharacteristic
825C22C22×#433911yescharacteristic
826C22D11×H(5,𝔽2)12yes—
827C22#1062345512yes—
828C22C23×C22⋊D1111yescharacteristic
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—224no—
835C4—224no—
836C4—228no—
837C4—444no—
838C4—442no—
839C2—24no—
840C2—24no—
841C2—24no—
842C2—44no—
843C2—444no—
844C2C22×C4×C22⋊D1111yescharacteristic
845C2#1308182012yes—
846C2#1308224711yescharacteristic
847C2#1308225611yescharacteristic
848C2#1308244612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#518C2
socle, cosocleC23×C11C25
prime radicalC2×#10623335C2
hypercenterC2×#518D11
hypocenterC11#34264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13071661C2semidirect
4. #13071633C2semidirect
5. #13071608C2semidirect
6. #13071595C2semidirect
7. #13071281C2semidirect
8. #13071270C2semidirect
9. #13071191C2semidirect
10. C4×#66988C2semidirect
11. C4×#66990C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622559C2semidirect
14. #13070969C2semidirect
15. C2×C11×#518C2semidirect
19. C23×C4×D11C22semidirect
23. C2×C4×D4×C11C22semidirect
24. C2×C4×D4×C11C22semidirect
25. C2×C11×#117C22semidirect
28. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. #10623335C4semidirect
38. C2×C4×C22⋊D11C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C22×Dic11⋊C4C22semidirect
42. C22×C4×Dic11C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
48. #10622833C22semidirect
49. #10622826C22semidirect
50. #10622826C22semidirect
51. #10622826C22semidirect
52. #10622823C22semidirect
53. C4×C22⋊Dic11C22semidirect
54. C4×C22⋊Dic11C22semidirect
55. C4×C22⋊Dic11C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. #10622603C22semidirect
59. #10622602C22semidirect
60. #10622591C22semidirect
61. #10622585C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622568C22semidirect
66. #10622559C22semidirect
67. #10622559C22semidirect
68. #10622559C22semidirect
69. #10622558C22semidirect
70. #10622557C22semidirect
71. #10622556C22semidirect
72. C22⋊C4×Dic11C22semidirect
73. C22⋊C4×Dic11C22semidirect
74. #10622553C22semidirect
75. C4×(C2×D11)⋊C4C22semidirect
76. #10622546C22semidirect
77. C4×Dic11⋊C4C22semidirect
83. C22×D4×C11C2×C4semidirect
95. C22×C22⋊D11C2×C4semidirect
120. C2×C11×C22⋊C4D4semidirect
129. #67006C2×C4semidirect
132. C2×C22⋊Dic11C2×C4semidirect
140. #66992C2×C4semidirect
141. #66990C2×C4semidirect
142. #66988C2×C4semidirect
143. #66982C2×C4semidirect
178. C24×C11C22×C4semidirect
197. C2×D4×C11C22×C4semidirect
210. C22×C4×C11C22×C4semidirect
227. C2×C22⋊D11C22×C4semidirect
247. C22×Dic11C22×C4semidirect
272. C22⋊Dic11C22×C4semidirect
273. C22⋊Dic11C22×C4semidirect
277. (C2×D11)⋊C4C22×C4semidirect
281. Dic11⋊C4C22×C4semidirect
286. C2×#518D11semidirect
319. C23×C11C4×D4semidirect
404. C2×C4×D4C2×D11semidirect
405. C2×C4×D4C2×D11semidirect
406. C2×#117C2×D11semidirect
415. C22×C22⋊C4C2×D11semidirect
503. C22×D4C4×D11semidirect
563. C2×C22⋊C4C22⋊D11semidirect
607. C24C2×C4×D11semidirect
630. C2×D4C2×C4×D11semidirect
672. C22×C4C2×C4×D11semidirect
708. C11#34264semidirect
738. C23C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C22×(C22⋊D11)⋊C42
#130716612
#130716332
#130716082
#130715952
#130712812
#130712702
#130711912
C4×#669882
C4×#669902
C2×#106228332
C2×#106225592
#130709692
C2×C11×#5182
#3426411