Finite Group Databasebeta

← #14914915

Subgroups — #14914915

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×#10623017C211yesmaximal, characteristic, complemented
3#13071661C214yesmaximal, complemented
4#13071633C214yesmaximal, complemented
5#13071602C214yesmaximal, complemented
6#13071593C214yesmaximal, complemented
7#13071285C212yesmaximal, complemented
8#13071274C212yesmaximal, complemented
9#13071194C211yesmaximal, characteristic, complemented
10C4×#66982C212yesmaximal, complemented
11C4×#67006C212yesmaximal, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14#13070969C211yesmaximal, characteristic, complemented
15C22×C4×D4×C11C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic, complemented
19C23×C22⋊D11C2211yescharacteristic
20C2×C4×D4×C11—28no—
21C2×C4×D4×C11C2214yes—
22C2×C4×D4×C11C2214yescomplemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic, complemented
26C22×C42×C11C2211yescharacteristic, complemented
27C2×#67006C2212yes—
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31#10623335C4116yescomplemented
32C2×#66992C2214yes—
33C2×#66990C2212yes—
34C2×#66988C2212yes—
35C2×#66982C2212yes—
36C2×C4×C22⋊D11C2212yes—
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2214yescomplemented
39C22×(C2×D11)⋊C4C2212yescomplemented
40C22×Dic11⋊C4C2212yescomplemented
41#10623017—28no—
42C2×(C22⋊D11)⋊C4C2212yescomplemented
43C2×(C22⋊D11)⋊C4C2212yescomplemented
44C2×C22⋊C4×D11C2212yescomplemented
45C2×#66930C2212yescomplemented
46#10622860C2212yescomplemented
47#10622833C2214yes—
48#10622833C2212yescomplemented
49#10622833C2212yescomplemented
50#10622826C2212yes—
51#10622826C2212yes—
52#10622826C2214yescomplemented
53#10622826C2214yescomplemented
54#10622824C2212yescomplemented
55#10622823C2214yescomplemented
56#10622823C2212yescomplemented
57#10622823C2212yescomplemented
58#10622823C2214yescomplemented
59C4×C22⋊Dic11C2214yescomplemented
60C4×C22⋊Dic11C2212yescomplemented
61C4×C22⋊Dic11C2212yescomplemented
62C2×C11⋊#95C2212yescomplemented
63C2×C11⋊#95C2212yescomplemented
64#10622603C2214yescomplemented
65#10622602C2214yescomplemented
66#10622591C2214yescomplemented
67#10622585C2214yescomplemented
68#10622570C2214yescomplemented
69#10622569C2214yescomplemented
70#10622558C2214yescomplemented
71#10622557C2214yescomplemented
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×C11—24no—
87C23×C4×C11—24no—
88C23×C4×C11—44no—
89C23×C4×C11—44no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2312yes—
92C23×C4×C11C2312yes—
93C23×C4×C11C2314yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11C2×C418yescomplemented
101C22×C22⋊D11C2312yes—
102C22×C22⋊D11C2312yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2312yes—
108C23×Dic11C2312yes—
109C22×C4×D11C2312yes—
110C22×C4×D11C2312yes—
111C4×D4×C11—216no—
112C4×D4×C11—216no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4D418yescomplemented
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C42×C11—24no—
121C2×C42×C11C2314yes—
122#67006C2×C4116yescomplemented
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11C2×C418yescomplemented
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2314yes—
135#66992C2×C4132yescomplemented
136#66990C2×C4116yescomplemented
137#66988C2×C4116yescomplemented
138#66982C2×C4116yescomplemented
139C4×C22⋊D11—28no—
140C4×C22⋊D11—28no—
141C4×C22⋊D11—48no—
142C2×(C2×D11)⋊C4—44no—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×Dic11⋊C4—44no—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158(C22⋊D11)⋊C4—28no—
159(C22⋊D11)⋊C4—28no—
160C22⋊C4×D11—28no—
161#66930—28no—
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×C414yes—
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×C414yescomplemented
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×C418yes—
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—28no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—28no—
209C22×C4×C11—42no—
210C22×C4×C11—44no—
211C22×C4×C11—42no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11—42no—
215C22×C4×C11—416no—
216C22×C4×C11—416no—
217C22×C4×C11C22×C414yes—
218C22×C4×C11C2×D414yes—
219C22×C4×C11C2×D414yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C2×C22⋊D11—232no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11C22×C418yes—
233C2×C22⋊D11C22×C418yescomplemented
234C2×C22⋊D11C22×C4116yescomplemented
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—24no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11—42no—
244C22×Dic11—42no—
245C22×Dic11—42no—
246C22×Dic11C22×C414yescomplemented
247C22×Dic11C22×C418yescomplemented
248C22×Dic11C2414yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2414yes—
253C2×C4×D11—24no—
254C2×C4×D11—24no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C11×C4⋊C4—28no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4C2×D418yes—
260C11×C22⋊C4C2×D418yes—
261C42×C11—28no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11C22×C418yes—
269C22⋊Dic11C22×C418yescomplemented
270C22⋊Dic11C22×C4116yescomplemented
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4C22×C4116yescomplemented
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—28no—
279Dic11⋊C4—44no—
280Dic11⋊C4C22×C4116yescomplemented
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—44no—
284C4×Dic11—44no—
285C2×#534—111no—
286C2×#518—111no—
287C22×C4×D4D1111yescharacteristic, complemented
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—28no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—24no—
310C23×C11—24no—
311C23×C11—44no—
312C23×C11—48no—
313C23×C11—48no—
314C23×C11—44no—
315C23×C11—48no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—48no—
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—22no—
332C22×D11—22no—
333C22×D11—24no—
334C22×D11—24no—
335C22×D11—28no—
336C22×D11—48no—
337C22×D11—82no—
338C22×D11—82no—
339C22×D11—84no—
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—24no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—44no—
355C2×C4×C11—44no—
356C2×C4×C11—416no—
357C2×C4×C11—48no—
358C2×C4×C11—48no—
359C2×C4×C11—44no—
360C2×C4×C11C23×C414yes—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C22×D414yes—
363C2×C4×C11H(5,𝔽2)14yes—
364C22⋊D11—216no—
365C22⋊D11—216no—
366C22⋊D11—416no—
367C2×Dic11—28no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—24no—
371C2×Dic11—24no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—24no—
377C2×Dic11—24no—
378C2×Dic11—24no—
379C2×Dic11—48no—
380C2×Dic11—82no—
381C2×Dic11—82no—
382C2×Dic11—84no—
383C2×Dic11C23×C414yes—
384C2×Dic11C23×C418yes—
385C4×D11—84no—
386C4×D11—84no—
387C23×D4—111no—
388C23×D4C2×D1111yescharacteristic
389C24×C4C2×D1111yescharacteristic
390C24×C4C2×D1111yescharacteristic, complemented
391#534—1116no—
392C2×#123—112no—
393C2×#123—112no—
394C2×#121—114no—
395C2×#120—112no—
396C2×#120—112no—
397#518—228no—
398C2×C4×D4—28no—
399C2×C4×D4—112no—
400C2×C4×D4—112no—
401C2×C4×D4—114no—
402C2×C4×D4—112no—
403C2×C4×D4—112no—
404C2×C4×D4C2×D1114yes—
405C2×C4×D4C2×D1114yescomplemented
406C2×#117—112no—
407C22×C4⋊C4—112no—
408C22×C4⋊C4C2×D1111yescharacteristic, complemented
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4—112no—
414C22×C22⋊C4C2×D1111yescharacteristic
415C22×C22⋊C4C2×D1111yescharacteristic, complemented
416C22×C42C2×D1111yescharacteristic, complemented
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—112no—
429#386—114no—
430#386—114no—
431#386—112no—
432#386—114no—
433#385—112no—
434#385—114no—
435#385—114no—
436#385—112no—
437#385—114no—
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—416no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—44no—
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—42no—
479C2×D11—42no—
480C2×D11—44no—
481C2×D11—88no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—24no—
486C4×C11—42no—
487Dic11—24no—
488Dic11—28no—
489Dic11—42no—
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—24no—
507C23×C4—24no—
508C23×C4—44no—
509C23×C4—44no—
510C23×C4—111no—
511C23×C4—112no—
512C23×C4—112no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—112no—
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1112yes—
519C23×C4C22×D1112yes—
520C23×C4C22×D1114yes—
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525#123—1116no—
526#123—1116no—
527#121—1132no—
528#120—1116no—
529#120—1116no—
530C4×D4—216no—
531C4×D4—216no—
532C4×D4—228no—
533C4×D4—228no—
534C4×D4—228no—
535C4×D4—228no—
536C4×D4—448no—
537#117—228no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—444no—
545C2×C4⋊C4C22×D1114yes—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—118no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—228no—
565C2×C22⋊C4—444no—
566C2×C22⋊C4C22⋊D1118yescomplemented
567C2×C22⋊C4C22×D1114yes—
568C2×C22⋊C4C22×D1112yes—
569C2×C22⋊C4C22×D1112yes—
570C2×C42—24no—
571C2×C42—112no—
572C2×C42—112no—
573C2×C42—114no—
574C2×C42—114no—
575C2×C42C22×D1114yes—
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×D1114yes—
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×D1118yes—
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—28no—
641C22×C4—28no—
642C22×C4—42no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—416no—
649C22×C4—416no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—112no—
653C22×C4—118no—
654C22×C4—114no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—224no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—224no—
663C22×C4—224no—
664C22×C4—444no—
665C22×C4—444no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4C2×C4×D1114yes—
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—28no—
681C4⋊C4—1116no—
682C4⋊C4—228no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—444no—
686C22⋊C4—28no—
687C22⋊C4—118no—
688C22⋊C4—118no—
689C22⋊C4—1116no—
690C22⋊C4—1116no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—228no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—444no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4C2×C22⋊D1118yes—
702C22⋊C4C2×C22⋊D1118yes—
703C42—28no—
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—28no—
716C23—22no—
717C23—24no—
718C23—24no—
719C23—22no—
720C23—44no—
721C23—48no—
722C23—48no—
723C23—48no—
724C23—44no—
725C23—44no—
726C23—48no—
727C23—44no—
728C23—114no—
729C23—222no—
730C23—224no—
731C23—224no—
732C23—222no—
733C23—228no—
734C23—448no—
735C23—884no—
736C23—882no—
737C23—882no—
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—28no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—416no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—44no—
772C2×C4—118no—
773C2×C4—114no—
774C2×C4—228no—
775C2×C4—222no—
776C2×C4—224no—
777C2×C4—224no—
778C2×C4—222no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—224no—
782C2×C4—224no—
783C2×C4—224no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—448no—
787C2×C4—884no—
788C2×C4—884no—
789C2×C4—884no—
790C2×C4—882no—
791C2×C4—882no—
792C2×C4C22×C4×D1114yes—
793C2×C4#6703714yes—
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—416no—
812C22—44no—
813C22—42no—
814C22—42no—
815C22—224no—
816C22—228no—
817C22—444no—
818C22—442no—
819C22—442no—
820C22—888no—
821C22C2×C4×C22⋊D1114yes—
822C22C2×C4×C22⋊D1114yes—
823C22C2×C4×C22⋊D1114yes—
824C22C23×C4×D1111yescharacteristic
825C22C22×#433911yescharacteristic
826C22C2×#6703712yes—
827C22#1062345312yes—
828C22C23×C22⋊D1111yescharacteristic
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—42no—
834C4—224no—
835C4—228no—
836C4—444no—
837C4—442no—
838C4—442no—
839C2—24no—
840C2—24no—
841C2—24no—
842C2—44no—
843C2—444no—
844C2C22×C4×C22⋊D1111yescharacteristic
845C2C4×#6703712yes—
846C2#1308225111yescharacteristic
847C2#1308226011yescharacteristic
848C2#1308245512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C4×D4×C11C2
socle, cosocleC23×C11C25
prime radicalC2×#10623335C2
hypercenterC22×C4×D4D11
hypocenterC11#34264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10623017C2semidirect
3. #13071661C2semidirect
4. #13071633C2semidirect
5. #13071602C2semidirect
6. #13071593C2semidirect
7. #13071285C2semidirect
8. #13071274C2semidirect
9. #13071194C2semidirect
10. C4×#66982C2semidirect
11. C4×#67006C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622823C2semidirect
14. #13070969C2semidirect
15. C22×C4×D4×C11C2semidirect
18. C24×C4×C11C22semidirect
22. C2×C4×D4×C11C22semidirect
23. C22×C11×C4⋊C4C22semidirect
25. C22×C11×C22⋊C4C22semidirect
26. C22×C42×C11C22semidirect
31. #10623335C4semidirect
38. C2×C4×C22⋊D11C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×Dic11⋊C4C22semidirect
42. C2×(C22⋊D11)⋊C4C22semidirect
43. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×C22⋊C4×D11C22semidirect
45. C2×#66930C22semidirect
46. #10622860C22semidirect
48. #10622833C22semidirect
49. #10622833C22semidirect
52. #10622826C22semidirect
53. #10622826C22semidirect
54. #10622824C22semidirect
55. #10622823C22semidirect
56. #10622823C22semidirect
57. #10622823C22semidirect
58. #10622823C22semidirect
59. C4×C22⋊Dic11C22semidirect
60. C4×C22⋊Dic11C22semidirect
61. C4×C22⋊Dic11C22semidirect
62. C2×C11⋊#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. #10622603C22semidirect
65. #10622602C22semidirect
66. #10622591C22semidirect
67. #10622585C22semidirect
68. #10622570C22semidirect
69. #10622569C22semidirect
70. #10622558C22semidirect
71. #10622557C22semidirect
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
100. C22×C22⋊D11C2×C4semidirect
116. C2×C11×C22⋊C4D4semidirect
122. #67006C2×C4semidirect
125. C2×C22⋊Dic11C2×C4semidirect
135. #66992C2×C4semidirect
136. #66990C2×C4semidirect
137. #66988C2×C4semidirect
138. #66982C2×C4semidirect
189. C23×D11C22×C4semidirect
233. C2×C22⋊D11C22×C4semidirect
234. C2×C22⋊D11C22×C4semidirect
246. C22×Dic11C22×C4semidirect
247. C22×Dic11C22×C4semidirect
269. C22⋊Dic11C22×C4semidirect
270. C22⋊Dic11C22×C4semidirect
275. (C2×D11)⋊C4C22×C4semidirect
280. Dic11⋊C4C22×C4semidirect
287. C22×C4×D4D11semidirect
319. C23×C11C4×D4semidirect
390. C24×C4C2×D11semidirect
405. C2×C4×D4C2×D11semidirect
408. C22×C4⋊C4C2×D11semidirect
415. C22×C22⋊C4C2×D11semidirect
416. C22×C42C2×D11semidirect
503. C22×D4C4×D11semidirect
566. C2×C22⋊C4C22⋊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
C2×#106230172
#130716612
#130716332
#130716022
#130715932
#130712852
#130712742
#130711942
C4×#669822
C4×#670062
C2×#106228262
C2×#106228232
#130709692
C22×C4×D4×C112
#3426411