Finite Group Databasebeta

← #14914992

Subgroups — #14914992

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic
2#13071697C214yesmaximal, complemented
3#13071696C214yesmaximal, complemented
4#13071621C214yesmaximal, complemented
5#13071616C214yesmaximal, complemented
6#13071347C214yesmaximal, complemented
7#13071228C211yesmaximal, characteristic
8#13071148C214yesmaximal, complemented
9C2×#10622823C211yesmaximal, characteristic
10#13070969C211yesmaximal, characteristic
11#13070969C211yesmaximal, characteristic
12C2×C4×C22⋊Dic11C211yesmaximal, characteristic
13C2×C11×#385C211yesmaximal, characteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66977C2214yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2212yes—
25C2×#66940C2214yescomplemented
26#10623014C4116yescomplemented
27C2×#66931C2214yes—
28C2×#66931C2214yes—
29C11×#385C2214yes—
30C11×#385C2212yes—
31C11×#385C2212yes—
32C2×C11×#95C2212yes—
33#10622823C2212yes—
34#10622823C2214yes—
35#10622823C2212yes—
36#10622823C2212yes—
37#10622823C2212yes—
38C4×C22⋊Dic11C2214yes—
39C4×C22⋊Dic11C2212yes—
40C4×C22⋊Dic11C2214yes—
41C4×C22⋊Dic11C2214yes—
42C4×C22⋊Dic11C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622591C2214yescomplemented
46#10622591C2214yescomplemented
47C4⋊C4×Dic11C2214yescomplemented
48#10622587C2214yescomplemented
49#10622586C2214yescomplemented
50#10622585C2214yescomplemented
51#10622585C2214yescomplemented
52#10622559C2212yes—
53#10622559C2212yes—
54#10622555C2214yes—
55C22⋊C4×Dic11C2212yes—
56C22⋊C4×Dic11C2214yes—
57C22⋊C4×Dic11C2214yes—
58C22⋊C4×Dic11C2214yes—
59C22⋊C4×Dic11C2212yes—
60#10622266C2214yescomplemented
61#10622266C2214yescomplemented
62#10622265C2214yescomplemented
63#10622265C2214yescomplemented
64#10622262C2214yescomplemented
65#10622262C2214yescomplemented
66#10622259C2214yescomplemented
67#10622259C2214yescomplemented
68C25×C11C2311yescharacteristic
69C23×C4×C11—24no—
70C23×C4×C11—44no—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2312yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2312yes—
81C23×Dic11C2312yes—
82C23×Dic11C2312yes—
83C22×Dic22C2314yes—
84C2×C11×C4⋊C4—44no—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4C2×C418yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11C2×C418yes—
95C2×C22⋊Dic11C2×C418yes—
96C2×C22⋊Dic11Q818yescomplemented
97C2×C22⋊Dic11C2312yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×C22⋊Dic11C2312yes—
103C2×C22⋊Dic11C2312yes—
104C2×C22⋊Dic11C2312yes—
105C2×C4⋊Dic11C2314yes—
106#66977C2×C4132yescomplemented
107C2×Dic11⋊C4—44no—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×C4×Dic11—44no—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2314yes—
121#66940—48no—
122#66931C2×C4132yescomplemented
123#66931C2×C4132yescomplemented
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#34270—111nomaximal, Sylow
137C24×C11—42no—
138C24×C11—42no—
139C24×C11C22×C414yes—
140C24×C11C2×Q814yes—
141C24×C11#4114yes—
142C24×C11C2411yescharacteristic
143C24×C11C2411yescharacteristic
144C24×C11C2411yescharacteristic
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—416no—
162C22×C4×C11C22×C418yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2414yes—
167C22×C4×C11C2412yes—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11C22×C418yes—
179C22×Dic11C22×C418yes—
180C22×Dic11C2×Q818yes—
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C22×Dic11C2414yes—
184C22×Dic11C2414yes—
185C22×Dic11C2414yes—
186C2×Dic22—44no—
187C2×Dic22—44no—
188C2×Dic22C22×C4116yescomplemented
189C11×C4⋊C4—28no—
190C11×C4⋊C4—44no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4C22×C418yes—
194C11×C22⋊C4C22×C418yes—
195C22⋊Dic11—24no—
196C22⋊Dic11—24no—
197C22⋊Dic11C22×C418yes—
198C22⋊Dic11C22×C418yes—
199C22⋊Dic11C22×C418yes—
200C22⋊Dic11C22×C418yes—
201C22⋊Dic11C2×Q818yes—
202C22⋊Dic11C2×Q818yes—
203C4⋊Dic11C22×C4116yescomplemented
204Dic11⋊C4—28no—
205Dic11⋊C4—44no—
206Dic11⋊C4—44no—
207Dic11⋊C4—44no—
208Dic11⋊C4C22×C4116yescomplemented
209Dic11⋊C4C22×C4116yescomplemented
210C4×Dic11—28no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C4×Dic11—44no—
214C4×Dic11—44no—
215C4×Dic11—44no—
216C2×#543—111no—
217#2368—114no—
218#2368—114no—
219#2360—114no—
220#2360—114no—
221#2329—114no—
222#2315—111no—
223C4×C22⋊Q8—114no—
224C2×#385—111no—
225C2×#385D1111yescharacteristic
226#2273—111no—
227#2273—111no—
228C2×C4×C22⋊C4—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—44no—
236C23×C11—48no—
237C23×C11—48no—
238C23×C11—44no—
239C23×C11C4×Q8116yescomplemented
240C23×C11C23×C412yes—
241C23×C11C23×C412yes—
242C23×C11C23×C412yes—
243C23×C11C22×Q812yes—
244C23×C11C22×Q812yes—
245C23×C11C22×Q812yes—
246C23×C11C2×#4112yes—
247C23×C11C2×#4112yes—
248C23×C11C2×#4112yes—
249C23×C11C2511yescharacteristic
250C2×C4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—48no—
263C2×C4×C11—48no—
264C2×C4×C11—48no—
265C2×C4×C11—44no—
266C2×C4×C11—82no—
267C2×C4×C11—82no—
268C2×C4×C11C23×C418yes—
269C2×C4×C11H(5,𝔽2)14yes—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—48no—
281C2×Dic11—48no—
282C2×Dic11—48no—
283C2×Dic11—82no—
284C2×Dic11—82no—
285C2×Dic11C23×C418yes—
286C2×Dic11C23×C418yes—
287C2×Dic11C22×Q818yes—
288Dic22—416no—
289C24×C4C2×D1111yescharacteristic
290#543—1116no—
291C2×C22⋊Q8—114no—
292C2×C22⋊Q8—114no—
293C2×C22⋊Q8—114no—
294C2×C4×Q8—114no—
295C22×C4⋊C4—112no—
296C22×C4⋊C4C2×D1112yes—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—111no—
299C22×C22⋊C4—111no—
300C22×C22⋊C4—111no—
301C22×C22⋊C4C2×D1111yescharacteristic
302C22×C22⋊C4C2×D1111yescharacteristic
303C22×C42—112no—
304#391—114no—
305#391—114no—
306#391—114no—
307#389—114no—
308#389—114no—
309#389—114no—
310#387—114no—
311#387—114no—
312#387—114no—
313#387—114no—
314#387—114no—
315#387—114no—
316#385—112no—
317#385—112no—
318#385—112no—
319#385—114no—
320#385—112no—
321#385—112no—
322#385—112no—
323#385C2×D1112yes—
324#385C2×D1114yes—
325#385C2×D1112yes—
326#380—114no—
327C4×C4⋊C4—114no—
328C4×C4⋊C4—114no—
329C4×C4⋊C4—114no—
330C4×C22⋊C4—112no—
331C4×C22⋊C4—114no—
332C4×C22⋊C4—114no—
333C4×C22⋊C4—114no—
334C4×C22⋊C4—112no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—114no—
337C4×C22⋊C4—112no—
338C4×C22⋊C4—114no—
339C4×C22⋊C4—112no—
340C2×#95—112no—
341C2×#95—112no—
342C2×#95C2×D1112yes—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—24no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—24no—
353C22×C11—24no—
354C22×C11—24no—
355C22×C11—416no—
356C22×C11C2×C4×Q814yes—
357C22×C11C2×C4×Q814yes—
358C22×C11C2×C4×Q814yes—
359C22×C11C24×C411yescharacteristic
360C22×C11C23×Q811yescharacteristic
361C22×C11C22×#4111yescharacteristic
362C22×C11C2×H(5,𝔽2)12yes—
363C22×C11#58512yes—
364C4×C11—28no—
365C4×C11—24no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—42no—
369Dic11—28no—
370Dic11—28no—
371Dic11—28no—
372Dic11—42no—
373Dic11—42no—
374C25C22×D1111yescharacteristic
375C22×Q8—114no—
376C23×C4—24no—
377C23×C4—44no—
378C23×C4—112no—
379C23×C4—112no—
380C23×C4—112no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1112yes—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1112yes—
390C22⋊Q8—1132no—
391C22⋊Q8—1132no—
392C22⋊Q8—1132no—
393C4×Q8—448no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—444no—
403C2×C4⋊C4C22×D1114yes—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—118no—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—112no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—112no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—112no—
415C2×C22⋊C4—112no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4C4×D1118yes—
419C2×C22⋊C4C22×D1112yes—
420C2×C22⋊C4C22×D1112yes—
421C2×C22⋊C4C22×D1112yes—
422C2×C22⋊C4C22×D1112yes—
423C2×C42—114no—
424C2×C42—114no—
425C2×C42—114no—
426C2×C42—114no—
427C2×C42—114no—
428C2×C42—114no—
429C2×C42—444no—
430#95—114no—
431#95—114no—
432#95—114no—
433#95—114no—
434#95—114no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95C22×D1114yes—
441#95C22×D1114yes—
442C2×C11—24no—
443C2×C11—24no—
444C2×C11—24no—
445C2×C11C22×C4×Q811yescharacteristic
446C2×C11C4×H(5,𝔽2)12yes—
447C2×C11#349011yescharacteristic
448C2×C11#349111yescharacteristic
449C2×C11#350112yes—
450C24—42no—
451C24—42no—
452C24C2×C4×D1114yes—
453C24#434114yes—
454C24Q8×D1114yes—
455C24C23×D1111yescharacteristic
456C24C23×D1111yescharacteristic
457C24C23×D1111yescharacteristic
458C2×Q8—1116no—
459C2×Q8—444no—
460C2×Q8—444no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—416no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—118no—
482C22×C4—118no—
483C22×C4—118no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4C2×C4×D1118yes—
497C22×C4C23×D1112yes—
498C22×C4C23×D1112yes—
499C22×C4C23×D1112yes—
500C22×C4C23×D1114yes—
501C22×C4C23×D1112yes—
502C4⋊C4—28no—
503C4⋊C4—44no—
504C4⋊C4—1116no—
505C4⋊C4—1116no—
506C4⋊C4—1116no—
507C4⋊C4—228no—
508C4⋊C4—444no—
509C4⋊C4—444no—
510C4⋊C4—444no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—118no—
514C22⋊C4—118no—
515C22⋊C4—118no—
516C22⋊C4—118no—
517C22⋊C4—118no—
518C22⋊C4—118no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C22⋊C4C2×C4×D1118yes—
522C22⋊C4C2×C4×D1118yes—
523C42—228no—
524C42—444no—
525C42—444no—
526C42—444no—
527C42—444no—
528C42—444no—
529C11#3427011yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—44no—
537C23—48no—
538C23—44no—
539C23—48no—
540C23#66940116yescomplemented
541C23C22×C4×D1112yes—
542C23C22×C4×D1112yes—
543C23C22×C4×D1112yes—
544C23C2×#434112yes—
545C23C2×#434112yes—
546C23C2×#434112yes—
547C23C2×Q8×D1112yes—
548C23C2×Q8×D1112yes—
549C23C2×Q8×D1112yes—
550C23C24×D1111yescharacteristic
551Q8—4416no—
552C2×C4—28no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—48no—
565C2×C4—48no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—118no—
571C2×C4—118no—
572C2×C4—118no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—448no—
584C2×C4—448no—
585C2×C4—448no—
586C2×C4—882no—
587C2×C4—882no—
588C2×C4C22×C4×D1118yes—
589C2×C4#6703714yes—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—24no—
600C22—24no—
601C22—24no—
602C22—416no—
603C22C2×#6694014yes—
604C22C2×#6694014yes—
605C22C2×#6694014yes—
606C22C23×C4×D1111yescharacteristic
607C22C22×#434111yescharacteristic
608C22C2×#6703712yes—
609C22C22×Q8×D1111yescharacteristic
610C22#1062345312yes—
611C4—24no—
612C4—28no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—228no—
617C4—228no—
618C4—228no—
619C4—442no—
620C4—442no—
621C2—24no—
622C2—24no—
623C2—24no—
624C2C22×#6694011yescharacteristic
625C2C4×#6703712yes—
626C2#1308230311yescharacteristic
627C2#1308231211yescharacteristic
628C2#1308241212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#385C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#34270
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #13071697C2semidirect
3. #13071696C2semidirect
4. #13071621C2semidirect
5. #13071616C2semidirect
6. #13071347C2semidirect
8. #13071148C2semidirect
25. C2×#66940C22semidirect
26. #10623014C4semidirect
45. #10622591C22semidirect
46. #10622591C22semidirect
47. C4⋊C4×Dic11C22semidirect
48. #10622587C22semidirect
49. #10622586C22semidirect
50. #10622585C22semidirect
51. #10622585C22semidirect
60. #10622266C22semidirect
61. #10622266C22semidirect
62. #10622265C22semidirect
63. #10622265C22semidirect
64. #10622262C22semidirect
65. #10622262C22semidirect
66. #10622259C22semidirect
67. #10622259C22semidirect
96. C2×C22⋊Dic11Q8semidirect
106. #66977C2×C4semidirect
122. #66931C2×C4semidirect
123. #66931C2×C4semidirect
188. C2×Dic22C22×C4semidirect
203. C4⋊Dic11C22×C4semidirect
208. Dic11⋊C4C22×C4semidirect
209. Dic11⋊C4C22×C4semidirect
239. C23×C11C4×Q8semidirect
529. C11#34270semidirect
540. C23#66940semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130716972
#130716962
#130716212
#130716162
#130713472
#130712282
#130711482
C2×#106228232
#130709692
C2×C4×C22⋊Dic112
C2×C11×#3852
#3427011