Finite Group Databasebeta

← #14914910

Subgroups — #14914910

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×#10623024C211yesmaximal, characteristic
2C2×#10623017C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071663C214yesmaximal, complemented
5#13071632C214yesmaximal, complemented
6#13071606C214yesmaximal, complemented
7#13071592C214yesmaximal, complemented
8#13071284C212yesmaximal, complemented
9#13071273C212yesmaximal, complemented
10#13071191C211yesmaximal, characteristic, complemented
11#13071135C212yesmaximal, complemented
12#13071117C212yesmaximal, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14#13070969C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic, complemented
20C22×C11×C4⋊C4C2212yescomplemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×#66983C2214yes—
26C2×C4×C22⋊D11—28no—
27C2×C4×C22⋊D11C2214yes—
28C2×C4×C22⋊D11C2212yescomplemented
29C2×C4×C22⋊D11C2214yescomplemented
30C2×C4×C22⋊D11C2212yescomplemented
31C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
32C22×(C2×D11)⋊C4C2212yescomplemented
33C22×Dic11⋊C4C2211yescharacteristic, complemented
34C22×C4×Dic11C2211yescharacteristic, complemented
35C2×#66946C2214yescomplemented
36#10623024C4116yescomplemented
37C2×#66939C2212yes—
38C2×#66939C2212yes—
39C2×#66935C2212yes—
40C2×#66935C2212yes—
41#10623017—28no—
42C2×(C22⋊D11)⋊C4C2212yes—
43C2×(C22⋊D11)⋊C4C2212yes—
44C2×C22⋊C4×D11C2212yescomplemented
45C2×#66930C2212yescomplemented
46C11×#385C2212yescomplemented
47C11×#385C2212yescomplemented
48C11×#385C2214yescomplemented
49C2×C11×#95C2212yescomplemented
50#10622826C2212yes—
51#10622826C2212yes—
52#10622826C2212yescomplemented
53#10622826C2214yescomplemented
54#10622826C2212yescomplemented
55C4×C22⋊Dic11C2214yescomplemented
56C2×C11⋊#95C2212yescomplemented
57#10622603C2214yescomplemented
58#10622603C2214yescomplemented
59#10622602C2214yescomplemented
60#10622602C2214yescomplemented
61#10622601C2214yescomplemented
62C4⋊C4×Dic11C2214yescomplemented
63#10622586C2214yescomplemented
64#10622571C2214yes—
65#10622568C2212yescomplemented
66#10622556C2212yescomplemented
67C22⋊C4×Dic11C2212yescomplemented
68C22⋊C4×Dic11C2212yescomplemented
69C22⋊C4×Dic11C2214yescomplemented
70#10622282C2214yescomplemented
71#10622282C2214yescomplemented
72#10622279C2214yescomplemented
73#10622279C2214yescomplemented
74#10622278C2214yescomplemented
75#10622278C2214yescomplemented
76#10622267C2214yescomplemented
77#10622267C2214yescomplemented
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C23×C4×C11—24no—
82C23×C4×C11—44no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2312yes—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11C2×C418yescomplemented
95C22×C22⋊D11C2×C418yescomplemented
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2312yes—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—44no—
108C22×C4×D11C2314yes—
109C22×C4×D11C2312yes—
110C22×C4×D11C2312yes—
111C2×C11×C4⋊C4—44no—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4C2×C418yescomplemented
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11D418yescomplemented
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126#66983C2×C4132yescomplemented
127C4×C22⋊D11—28no—
128C4×C22⋊D11—28no—
129C4×C22⋊D11—216no—
130C4×C22⋊D11—216no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—44no—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2314yes—
147C2×C4×Dic11—24no—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2314yes—
153#66946—48no—
154#66939C2×C4116yescomplemented
155#66939C2×C4116yescomplemented
156#66935C2×C4116yescomplemented
157#66935C2×C4116yescomplemented
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—42no—
172C24×C11—42no—
173C24×C11C22×C414yes—
174C24×C11C2×D414yes—
175C24×C11#4114yes—
176C24×C11C2411yescharacteristic
177C24×C11C2411yescharacteristic
178C24×C11C2411yescharacteristic
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—42no—
184C23×D11—42no—
185C23×D11—42no—
186C23×D11—42no—
187C23×D11C22×C414yes—
188C23×D11C22×C414yescomplemented
189C23×D11C2412yes—
190C23×D11C2412yes—
191C22×C4×C11—22no—
192C22×C4×C11—24no—
193C22×C4×C11—22no—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—416no—
208C22×C4×C11C22×C418yescomplemented
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2414yes—
213C22×C4×C11C2412yes—
214C2×C22⋊D11—232no—
215C2×C22⋊D11—232no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11C22×C418yes—
225C2×C22⋊D11C22×C418yes—
226C2×C22⋊D11C22×C418yes—
227C2×C22⋊D11C22×C418yescomplemented
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—24no—
233C22×Dic11—42no—
234C22×Dic11—42no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11C22×C414yes—
238C22×Dic11C22×C414yescomplemented
239C22×Dic11C2×D414yes—
240C22×Dic11C2×D414yes—
241C22×Dic11C2414yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C2×D44—44no—
247C2×D44—44no—
248C2×D44C22×C4116yescomplemented
249C2×C4×D11—28no—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—28no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—416no—
257C11×C4⋊C4—28no—
258C11×C4⋊C4—44no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4C22×C418yes—
262C11×C22⋊C4C22×C418yescomplemented
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D418yes—
266C22⋊Dic11C2×D418yes—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4C22×C4116yescomplemented
275(C2×D11)⋊C4C22×C4116yescomplemented
276C4⋊Dic11C22×C4116yescomplemented
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—28no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11—28no—
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×#386—111no—
298C2×#385D1111yescharacteristic, complemented
299#2273—111no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—44no—
307C23×C11—48no—
308C23×C11—44no—
309C23×C11—48no—
310C23×C11C4×D4116yescomplemented
311C23×C11C23×C412yes—
312C23×C11C23×C412yes—
313C23×C11C23×C412yes—
314C23×C11C22×D412yes—
315C23×C11C22×D412yes—
316C23×C11C22×D412yes—
317C23×C11C2×#4112yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11C2511yescharacteristic
321C22×D11—28no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—24no—
327C22×D11—24no—
328C22×D11—24no—
329C22×D11—24no—
330C22×D11—28no—
331C22×D11—48no—
332C22×D11—48no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—48no—
336C22×D11—82no—
337C22×D11—82no—
338C22×D11—84no—
339C22×D11C23×C414yes—
340C22×D11C23×C414yes—
341C2×C4×C11—28no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—48no—
354C2×C4×C11—48no—
355C2×C4×C11—48no—
356C2×C4×C11—44no—
357C2×C4×C11—82no—
358C2×C4×C11—82no—
359C2×C4×C11C23×C418yes—
360C2×C4×C11H(5,𝔽2)14yes—
361C22⋊D11—216no—
362C22⋊D11—216no—
363C22⋊D11—216no—
364C22⋊D11—216no—
365C2×Dic11—28no—
366C2×Dic11—28no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—24no—
372C2×Dic11—24no—
373C2×Dic11—24no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—44no—
377C2×Dic11—44no—
378C2×Dic11—84no—
379C2×Dic11C23×C414yes—
380C2×Dic11C23×C414yes—
381C2×Dic11C22×D414yes—
382C2×Dic11C22×D414yes—
383D44—416no—
384C4×D11—416no—
385C4×D11—84no—
386C4×D11—84no—
387C23×D4—111no—
388C23×D4—111no—
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—114no—
399C2×C4×D4—112no—
400C2×C4×D4—114no—
401C2×C4×D4—112no—
402C2×C4×D4—114no—
403C2×C4×D4—112no—
404C2×C4×D4—112no—
405C2×C4×D4—228no—
406C2×#117—112no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4C2×D1112yescomplemented
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
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—112no—
427#386—112no—
428#386—114no—
429#386—112no—
430#386—114no—
431#386—114no—
432#386—114no—
433#385—114no—
434#385—114no—
435#385C2×D1112yescomplemented
436#385C2×D1114yescomplemented
437#385C2×D1112yescomplemented
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—416no—
462C22×C11C2×C4×D414yes—
463C22×C11C2×C4×D414yes—
464C22×C11C2×C4×D414yes—
465C22×C11C24×C411yescharacteristic
466C22×C11C23×D411yescharacteristic
467C22×C11C22×#4111yescharacteristic
468C22×C11C2×H(5,𝔽2)12yes—
469C22×C11#58512yes—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—28no—
473C2×D11—28no—
474C2×D11—416no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—44no—
480C2×D11—44no—
481C2×D11—88no—
482C4×C11—28no—
483C4×C11—24no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487Dic11—24no—
488Dic11—24no—
489Dic11—24no—
490Dic11—24no—
491Dic11—44no—
492C25—111no—
493C25—111no—
494C25C22×D1111yescharacteristic
495C22×D4—118no—
496C22×D4—118no—
497C22×D4—112no—
498C22×D4—112no—
499C22×D4—112no—
500C22×D4—112no—
501C22×D4—114no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C23×C4—24no—
507C23×C4—44no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—112no—
513C23×C4—114no—
514C23×C4—112no—
515C23×C4—112no—
516C23×C4—224no—
517C23×C4—444no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1112yes—
520C23×C4C22×D1112yes—
521C23×C4C22×D1111yescharacteristic
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—228no—
531C4×D4—228no—
532C4×D4—2216no—
533C4×D4—2216no—
534C4×D4—228no—
535C4×D4—228no—
536C4×D4—448no—
537#117—228no—
538C2×C4⋊C4—44no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4C22×D1114yes—
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—114no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—228no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—444no—
565C2×C22⋊C4C4×D1118yescomplemented
566C2×C22⋊C4C22×D1112yes—
567C2×C22⋊C4C22×D1112yes—
568C2×C22⋊C4C22×D1112yes—
569C2×C22⋊C4C22×D1112yes—
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×C11C22×C4×D411yescharacteristic
588C2×C11C4×H(5,𝔽2)12yes—
589C2×C11#348411yescharacteristic
590C2×C11#348511yescharacteristic
591C2×C11#350512yes—
592D11—44no—
593D11—44no—
594C24—42no—
595C24—42no—
596C24—112no—
597C24—112no—
598C24—114no—
599C24—114no—
600C24—222no—
601C24—222no—
602C24—222no—
603C24—222no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24C2×C4×D1114yes—
609C24D4×D1114yes—
610C24#434314yes—
611C24C23×D1111yescharacteristic
612C24C23×D1111yescharacteristic
613C24C23×D1111yescharacteristic
614C2×D4—118no—
615C2×D4—118no—
616C2×D4—118no—
617C2×D4—118no—
618C2×D4—1116no—
619C2×D4—2232no—
620C2×D4—2232no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—444no—
630C2×D4—444no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—416no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—114no—
655C22×C4—114no—
656C22×C4—114no—
657C22×C4—228no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—224no—
665C22×C4—228no—
666C22×C4—444no—
667C22×C4—444no—
668C22×C4—444no—
669C22×C4—4416no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—442no—
674C22×C4C2×C4×D1118yescomplemented
675C22×C4C23×D1112yes—
676C22×C4C23×D1112yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1114yes—
679C22×C4C23×D1112yes—
680C4⋊C4—28no—
681C4⋊C4—44no—
682C4⋊C4—1116no—
683C4⋊C4—228no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—118no—
689C22⋊C4—118no—
690C22⋊C4—1116no—
691C22⋊C4—1116no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—228no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—228no—
698C22⋊C4—444no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4C2×C4×D1118yes—
702C22⋊C4C2×C4×D1118yescomplemented
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—44no—
716C23—48no—
717C23—44no—
718C23—48no—
719C23—114no—
720C23—114no—
721C23—228no—
722C23—222no—
723C23—222no—
724C23—224no—
725C23—224no—
726C23—222no—
727C23—222no—
728C23—224no—
729C23—224no—
730C23—228no—
731C23—448no—
732C23—448no—
733C23—444no—
734C23—448no—
735C23—444no—
736C23—884no—
737C23—882no—
738C23—882no—
739C23#66946116yescomplemented
740C23C22×C4×D1112yes—
741C23C22×C4×D1112yes—
742C23C22×C4×D1112yes—
743C23C2×D4×D1112yes—
744C23C2×D4×D1112yes—
745C23C2×D4×D1112yes—
746C23C2×#434312yes—
747C23C2×#434312yes—
748C23C2×#434312yes—
749C23C24×D1111yescharacteristic
750D4—2216no—
751D4—2216no—
752D4—2216no—
753D4—2216no—
754D4—4416no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—44no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—114no—
774C2×C4—114no—
775C2×C4—114no—
776C2×C4—114no—
777C2×C4—228no—
778C2×C4—228no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—224no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—224no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—224no—
788C2×C4—4416no—
789C2×C4—444no—
790C2×C4—444no—
791C2×C4—884no—
792C2×C4—884no—
793C2×C4—884no—
794C2×C4C22×C4×D1118yes—
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—416no—
809C22—224no—
810C22—224no—
811C22—228no—
812C22—228no—
813C22—4416no—
814C22—444no—
815C22—444no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—888no—
821C22C2×#6694614yes—
822C22C2×#6694614yes—
823C22C2×#6694614yes—
824C22C23×C4×D1111yescharacteristic
825C22C22×D4×D1111yescharacteristic
826C22C2×#6703712yes—
827C22C22×#434311yescharacteristic
828C22#1062345312yes—
829C4—24no—
830C4—28no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—224no—
835C4—224no—
836C4—224no—
837C4—224no—
838C4—444no—
839C2—24no—
840C2—24no—
841C2—24no—
842C2—444no—
843C2—444no—
844C2C22×#6694611yescharacteristic
845C2C4×#6703712yes—
846C2#1308224511yescharacteristic
847C2#1308225411yescharacteristic
848C2#1308245712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#385C2
socle, cosocleC23×C11C25
prime radicalC2×#10623024C2
hypercenterC2×#385D11
hypocenterC11#34264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#10623017C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13071663C2semidirect
5. #13071632C2semidirect
6. #13071606C2semidirect
7. #13071592C2semidirect
8. #13071284C2semidirect
9. #13071273C2semidirect
10. #13071191C2semidirect
11. #13071135C2semidirect
12. #13071117C2semidirect
13. C2×#10622826C2semidirect
14. #13070969C2semidirect
15. C2×C11×#385C2semidirect
19. C23×C4×D11C22semidirect
20. C22×C11×C4⋊C4C22semidirect
28. C2×C4×C22⋊D11C22semidirect
29. C2×C4×C22⋊D11C22semidirect
30. C2×C4×C22⋊D11C22semidirect
31. C22×(C2×D11)⋊C4C22semidirect
32. C22×(C2×D11)⋊C4C22semidirect
33. C22×Dic11⋊C4C22semidirect
34. C22×C4×Dic11C22semidirect
35. C2×#66946C22semidirect
36. #10623024C4semidirect
44. C2×C22⋊C4×D11C22semidirect
45. C2×#66930C22semidirect
46. C11×#385C22semidirect
47. C11×#385C22semidirect
48. C11×#385C22semidirect
49. C2×C11×#95C22semidirect
52. #10622826C22semidirect
53. #10622826C22semidirect
54. #10622826C22semidirect
55. C4×C22⋊Dic11C22semidirect
56. C2×C11⋊#95C22semidirect
57. #10622603C22semidirect
58. #10622603C22semidirect
59. #10622602C22semidirect
60. #10622602C22semidirect
61. #10622601C22semidirect
62. C4⋊C4×Dic11C22semidirect
63. #10622586C22semidirect
65. #10622568C22semidirect
66. #10622556C22semidirect
67. C22⋊C4×Dic11C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. C22⋊C4×Dic11C22semidirect
70. #10622282C22semidirect
71. #10622282C22semidirect
72. #10622279C22semidirect
73. #10622279C22semidirect
74. #10622278C22semidirect
75. #10622278C22semidirect
76. #10622267C22semidirect
77. #10622267C22semidirect
94. C22×C22⋊D11C2×C4semidirect
95. C22×C22⋊D11C2×C4semidirect
115. C2×C11×C22⋊C4C2×C4semidirect
121. C2×C22⋊Dic11D4semidirect
126. #66983C2×C4semidirect
154. #66939C2×C4semidirect
155. #66939C2×C4semidirect
156. #66935C2×C4semidirect
157. #66935C2×C4semidirect
188. C23×D11C22×C4semidirect
208. C22×C4×C11C22×C4semidirect
227. C2×C22⋊D11C22×C4semidirect
238. C22×Dic11C22×C4semidirect
248. C2×D44C22×C4semidirect
262. C11×C22⋊C4C22×C4semidirect
274. (C2×D11)⋊C4C22×C4semidirect
275. (C2×D11)⋊C4C22×C4semidirect
276. C4⋊Dic11C22×C4semidirect
298. C2×#385D11semidirect
310. C23×C11C4×D4semidirect
408. C22×C4⋊C4C2×D11semidirect
435. #385C2×D11semidirect
436. #385C2×D11semidirect
437. #385C2×D11semidirect
448. C2×#95C2×D11semidirect
565. C2×C22⋊C4C4×D11semidirect
674. C22×C4C2×C4×D11semidirect
702. C22⋊C4C2×C4×D11semidirect
708. C11#34264semidirect
739. C23#66946semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106230172
C22×C4×C22⋊D112
#130716632
#130716322
#130716062
#130715922
#130712842
#130712732
#130711912
#130711352
#130711172
C2×#106228262
#130709692
C2×C11×#3852
#3426411