Finite Group Databasebeta

← #14914918

Subgroups — #14914918

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
2C2×#10623329C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071664C214yesmaximal, complemented
5#13071627C214yesmaximal, complemented
6#13071604C214yesmaximal, complemented
7#13071595C214yesmaximal, complemented
8#13071290C212yesmaximal, complemented
9#13071279C212yesmaximal, complemented
10#13071191C211yesmaximal, characteristic, complemented
11#13071141C212yesmaximal, complemented
12#13071121C212yesmaximal, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14#13070969C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yescomplemented
22C2×#67006C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yescomplemented
27#10623335C4116yescomplemented
28C2×#66992C2214yes—
29C2×#66990C2212yes—
30#10623329—28no—
31C2×#66988C2212yes—
32C2×D4×Dic11C2212yes—
33C2×D4×Dic11C2212yes—
34C2×D4×Dic11C2212yescomplemented
35C2×D4×Dic11C2212yescomplemented
36C2×#66982C2212yes—
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2214yes—
39C2×C4×C22⋊D11C2214yescomplemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×#66979C2212yescomplemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2212yescomplemented
44C22×C4×Dic11C2211yescharacteristic, complemented
45C2×(C22⋊D11)⋊C4C2214yescomplemented
46C11×#386C2212yes—
47C11×#386C2212yes—
48C11×#386C2214yescomplemented
49C2×C11×#95C2212yescomplemented
50#10622826C2214yes—
51#10622823C2212yescomplemented
52#10622823C2212yescomplemented
53#10622823C2214yescomplemented
54C4×C22⋊Dic11C2214yescomplemented
55C2×C11⋊#95C2212yescomplemented
56#10622571C2212yescomplemented
57#10622571C2212yescomplemented
58#10622571C2214yescomplemented
59#10622570C2214yescomplemented
60#10622569C2214yescomplemented
61#10622568C2212yescomplemented
62#10622559C2214yescomplemented
63#10622558C2214yescomplemented
64#10622557C2214yescomplemented
65#10622556C2212yescomplemented
66C22⋊C4×Dic11C2214yescomplemented
67C22⋊C4×Dic11C2212yescomplemented
68C22⋊C4×Dic11C2214yescomplemented
69C22⋊C4×Dic11C2212yescomplemented
70#10622283C2214yescomplemented
71#10622282C2214yescomplemented
72#10622281C2214yescomplemented
73#10622279C2214yescomplemented
74#10622268C2214yescomplemented
75#10622265C2214yescomplemented
76#10622262C2214yescomplemented
77#10622260C2214yescomplemented
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×C11—24no—
87C23×C4×C11—44no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2312yes—
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2312yes—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11C2×C418yescomplemented
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2312yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2312yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C22×C4×D11—24no—
109C22×C4×D11—44no—
110C22×C4×D11C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—44no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117#67006C2×C4116yescomplemented
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—28no—
120C2×C22⋊Dic11C2×C418yescomplemented
121C2×C22⋊Dic11D418yescomplemented
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2312yes—
131#66992C2×C4132yescomplemented
132#66990C2×C4116yescomplemented
133#66988C2×C4116yescomplemented
134D4×Dic11—28no—
135D4×Dic11—28no—
136D4×Dic11—28no—
137D4×Dic11—28no—
138#66982C2×C4116yescomplemented
139C4×C22⋊D11—216no—
140C4×C22⋊D11—216no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146#66979—28no—
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4—44no—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2314yes—
160C2×C4×Dic11C2314yes—
161(C22⋊D11)⋊C4—48no—
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—24no—
202C22×C4×C11—22no—
203C22×C4×C11—24no—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—42no—
209C22×C4×C11—42no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11—42no—
213C22×C4×C11—416no—
214C22×C4×C11C22×C414yescomplemented
215C22×C4×C11C2414yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C2×C22⋊D11—232no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11C22×C418yes—
227C2×C22⋊D11C22×C418yes—
228C2×C22⋊D11C22×C4116yescomplemented
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11—42no—
238C22×Dic11—42no—
239C22×Dic11—44no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—44no—
243C22×Dic11C22×C414yes—
244C22×Dic11C22×C418yescomplemented
245C22×Dic11C2×D414yes—
246C22×Dic11C2×D414yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2414yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—44no—
256C2×C4×D11—416no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—44no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C22×C418yes—
266C22⋊Dic11C22×C418yescomplemented
267C22⋊Dic11C22×C4116yescomplemented
268C22⋊Dic11C2×D418yes—
269C22⋊Dic11C2×D418yes—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4C22×C4116yescomplemented
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276Dic11⋊C4—28no—
277Dic11⋊C4—28no—
278Dic11⋊C4—44no—
279Dic11⋊C4C22×C4116yescomplemented
280C4×Dic11—28no—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—44no—
284C4×Dic11—44no—
285C2×#534—111no—
286C2×#518—111no—
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×#386D1111yescharacteristic, complemented
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—28no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—24no—
355C2×C4×C11—48no—
356C2×C4×C11—48no—
357C2×C4×C11—44no—
358C2×C4×C11—84no—
359C2×C4×C11C23×C414yes—
360C2×C4×C11H(5,𝔽2)14yes—
361C22⋊D11—216no—
362C22⋊D11—216no—
363C22⋊D11—416no—
364C2×Dic11—28no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11—24no—
369C2×Dic11—24no—
370C2×Dic11—24no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—24no—
374C2×Dic11—24no—
375C2×Dic11—44no—
376C2×Dic11—48no—
377C2×Dic11—44no—
378C2×Dic11—84no—
379C2×Dic11—84no—
380C2×Dic11—82no—
381C2×Dic11—82no—
382C2×Dic11C23×C414yes—
383C2×Dic11C23×C418yes—
384C2×Dic11C22×D414yes—
385C2×Dic11C22×D414yes—
386C4×D11—416no—
387C23×D4—111no—
388C23×D4C2×D1111yescharacteristic
389C24×C4—111no—
390C24×C4C2×D1111yescharacteristic
391#534—1116no—
392C2×#123—112no—
393C2×#123—112no—
394C2×#121—114no—
395C2×#120—112no—
396C2×#120—112no—
397#518—228no—
398C2×C4×D4—112no—
399C2×C4×D4—112no—
400C2×C4×D4—112no—
401C2×C4×D4—112no—
402C2×C4×D4—114no—
403C2×C4×D4—114no—
404C2×C4×D4—114no—
405C2×C4×D4—228no—
406C2×#117—112no—
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⋊C4—111no—
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—114no—
426#386—112no—
427#386—112no—
428#386—114no—
429#386—114no—
430#386C2×D1112yes—
431#386C2×D1112yes—
432#386C2×D1114yescomplemented
433#385—112no—
434#385—114no—
435#385—112no—
436#385—114no—
437#385—114no—
438#381—112no—
439#379—112no—
440C4×C4⋊C4—114no—
441C4×C22⋊C4—114no—
442C4×C22⋊C4—112no—
443C4×C22⋊C4—112no—
444C4×C22⋊C4—114no—
445C4×C22⋊C4—114no—
446C4×C22⋊C4—114no—
447C2×#95—112no—
448C2×#95C2×D1112yescomplemented
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—42no—
485C4×C11—44no—
486Dic11—24no—
487Dic11—28no—
488Dic11—24no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
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—24no—
507C23×C4—44no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—112no—
512C23×C4—111no—
513C23×C4—112no—
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—114no—
517C23×C4—224no—
518C23×C4—444no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1112yes—
521C23×C4C22×D1112yes—
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1112yes—
525#123—1116no—
526#123—1116no—
527#121—1132no—
528#120—1116no—
529#120—1116no—
530C4×D4—2216no—
531C4×D4—2216no—
532C4×D4—228no—
533C4×D4—228no—
534C4×D4—228no—
535C4×D4—228no—
536C4×D4—448no—
537#117—228no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—444no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—44no—
548C2×C22⋊C4—118no—
549C2×C22⋊C4—118no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—228no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4C22×D1112yes—
567C2×C22⋊C4C22×D1112yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—112no—
571C2×C42—112no—
572C2×C42—114no—
573C2×C42—114no—
574C2×C42—114no—
575C2×C42—224no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95C22×D1114yes—
583#95C22×D1114yes—
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
608C24D4×D1114yes—
609C24#434114yes—
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—24no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—416no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—118no—
653C22×C4—114no—
654C22×C4—114no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—228no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—228no—
665C22×C4—444no—
666C22×C4—4416no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—444no—
673C22×C4—444no—
674C22×C4—442no—
675C22×C4C2×C4×D1114yescomplemented
676C22×C4C23×D1114yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C4⋊C4—1116no—
681C4⋊C4—228no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—228no—
685C4⋊C4—444no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—118no—
691C22⋊C4—118no—
692C22⋊C4—1116no—
693C22⋊C4—118no—
694C22⋊C4—118no—
695C22⋊C4—1116no—
696C22⋊C4—228no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—228no—
704C42—224no—
705C42—224no—
706C42—444no—
707C42—444no—
708C11#3426411yescharacteristic, complemented, Sylow
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—24no—
719C23—28no—
720C23—44no—
721C23—48no—
722C23—44no—
723C23—48no—
724C23—48no—
725C23—84no—
726C23—82no—
727C23—82no—
728C23—114no—
729C23—228no—
730C23—222no—
731C23—222no—
732C23—224no—
733C23—224no—
734C23—448no—
735C23—444no—
736C23—448no—
737C23—444no—
738C23(C22⋊D11)⋊C4116yescomplemented
739C23C22×C4×D1114yes—
740C23C22×C4×D1112yes—
741C23C22×C4×D1112yes—
742C23C22×C4×D1112yes—
743C23C2×D4×D1112yes—
744C23C2×D4×D1112yes—
745C23C2×D4×D1112yes—
746C23C2×#434112yes—
747C23C2×#434112yes—
748C23C2×#434112yes—
749C23C24×D1111yescharacteristic
750D4—216no—
751D4—216no—
752D4—2216no—
753D4—2216no—
754D4—4416no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—44no—
770C2×C4—84no—
771C2×C4—118no—
772C2×C4—114no—
773C2×C4—114no—
774C2×C4—114no—
775C2×C4—228no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—224no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—224no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—224no—
785C2×C4—224no—
786C2×C4—4416no—
787C2×C4—444no—
788C2×C4—444no—
789C2×C4—448no—
790C2×C4—884no—
791C2×C4—884no—
792C2×C4—882no—
793C2×C4—882no—
794C2×C4C22×C4×D1114yes—
795C2×C4#6703714yes—
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×(C22⋊D11)⋊C414yes—
822C22C2×(C22⋊D11)⋊C414yes—
823C22C2×(C22⋊D11)⋊C414yes—
824C22C23×C4×D1111yescharacteristic
825C22C22×D4×D1111yescharacteristic
826C22C22×#434111yescharacteristic
827C22C2×#6703712yes—
828C22#1062345312yes—
829C4—24no—
830C4—24no—
831C4—44no—
832C4—42no—
833C4—224no—
834C4—224no—
835C4—224no—
836C4—228no—
837C4—442no—
838C4—442no—
839C2—24no—
840C2—24no—
841C2—24no—
842C2—44no—
843C2—444no—
844C2C22×(C22⋊D11)⋊C411yescharacteristic
845C2C4×#6703712yes—
846C2#1308224511yescharacteristic
847C2#1308225411yescharacteristic
848C2#1308245012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#386C2
socle, cosocleC23×C11C25
prime radicalC2×#10623335C2
hypercenterC2×#386D11
hypocenterC11#34264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10623329C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13071664C2semidirect
5. #13071627C2semidirect
6. #13071604C2semidirect
7. #13071595C2semidirect
8. #13071290C2semidirect
9. #13071279C2semidirect
10. #13071191C2semidirect
11. #13071141C2semidirect
12. #13071121C2semidirect
13. C2×#10622823C2semidirect
14. #13070969C2semidirect
15. C2×C11×#386C2semidirect
19. C23×C4×D11C22semidirect
21. C22×C11×C22⋊C4C22semidirect
26. C22×C22⋊Dic11C22semidirect
27. #10623335C4semidirect
34. C2×D4×Dic11C22semidirect
35. C2×D4×Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C2×#66979C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×C4×Dic11C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
48. C11×#386C22semidirect
49. C2×C11×#95C22semidirect
51. #10622823C22semidirect
52. #10622823C22semidirect
53. #10622823C22semidirect
54. C4×C22⋊Dic11C22semidirect
55. C2×C11⋊#95C22semidirect
56. #10622571C22semidirect
57. #10622571C22semidirect
58. #10622571C22semidirect
59. #10622570C22semidirect
60. #10622569C22semidirect
61. #10622568C22semidirect
62. #10622559C22semidirect
63. #10622558C22semidirect
64. #10622557C22semidirect
65. #10622556C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. C22⋊C4×Dic11C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. C22⋊C4×Dic11C22semidirect
70. #10622283C22semidirect
71. #10622282C22semidirect
72. #10622281C22semidirect
73. #10622279C22semidirect
74. #10622268C22semidirect
75. #10622265C22semidirect
76. #10622262C22semidirect
77. #10622260C22semidirect
83. C22×D4×C11C2×C4semidirect
96. C22×C22⋊D11C2×C4semidirect
117. #67006C2×C4semidirect
120. C2×C22⋊Dic11C2×C4semidirect
121. C2×C22⋊Dic11D4semidirect
131. #66992C2×C4semidirect
132. #66990C2×C4semidirect
133. #66988C2×C4semidirect
138. #66982C2×C4semidirect
178. C24×C11C22×C4semidirect
197. C2×D4×C11C22×C4semidirect
214. C22×C4×C11C22×C4semidirect
228. C2×C22⋊D11C22×C4semidirect
244. C22×Dic11C22×C4semidirect
266. C22⋊Dic11C22×C4semidirect
267. C22⋊Dic11C22×C4semidirect
273. (C2×D11)⋊C4C22×C4semidirect
279. Dic11⋊C4C22×C4semidirect
297. C2×#386D11semidirect
319. C23×C11C4×D4semidirect
415. C22×C22⋊C4C2×D11semidirect
432. #386C2×D11semidirect
448. C2×#95C2×D11semidirect
503. C22×D4C4×D11semidirect
607. C24C2×C4×D11semidirect
630. C2×D4C2×C4×D11semidirect
675. C22×C4C2×C4×D11semidirect
708. C11#34264semidirect
738. C23(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C2×#106233292
C22×C4×C22⋊D112
#130716642
#130716272
#130716042
#130715952
#130712902
#130712792
#130711912
#130711412
#130711212
C2×#106228232
#130709692
C2×C11×#3862
#3426411