Finite Group Databasebeta

← #14912228

Subgroups — #14912228

Order 2816.

3902 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic, complemented
3C23×C4×Dic11C211yesmaximal, characteristic, complemented
4#13071144C214yesmaximal, complemented
5#13071133C214yesmaximal, complemented
6#13071122C214yesmaximal, complemented
7#13071115C214yesmaximal, complemented
8#13071104C211yesmaximal, characteristic, complemented
9#13071098C211yesmaximal, characteristic, complemented
10#13071055C214yesmaximal, complemented
11C4×(C22⋊D11)⋊C4C214yesmaximal, complemented
12#117×Dic11C211yesmaximal, characteristic, complemented
13C11×#2280C211yesmaximal, characteristic, complemented
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2212yes—
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#67006C2212yes—
20#10623322C4116yescomplemented
21C2×#66983C2212yes—
22C2×#66982C2212yes—
23C2×C4×C22⋊D11C2214yes—
24C2×#66979C2211yescharacteristic
25C2×#66977C2212yes—
26C22×C4×Dic11—28no—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2214yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2212yes—
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10623053—28no—
34C2×#66946C2212yescomplemented
35C2×#66940C2212yescomplemented
36C2×(C22⋊D11)⋊C4C2218yes—
37C2×(C22⋊D11)⋊C4C2214yes—
38C2×#66925C2212yescomplemented
39C2×C42×D11C2212yescomplemented
40C11×#381C2212yes—
41C11×#380C2214yes—
42C11×#379C2212yes—
43C4×C11×C22⋊C4C2214yes—
44#10622601C2212yescomplemented
45C4⋊C4×Dic11C2214yescomplemented
46#10622587C2212yescomplemented
47#10622586C2214yescomplemented
48#10622571C2214yes—
49#10622571C2218yes—
50#10622559C2214yes—
51#10622559C2218yes—
52C22⋊C4×Dic11C2214yes—
53C22⋊C4×Dic11C2218yes—
54C4×(C2×D11)⋊C4C2214yescomplemented
55#10622545C2212yescomplemented
56C4×Dic11⋊C4C2214yescomplemented
57C42×Dic11C2212yescomplemented
58#10622282C2218yescomplemented
59#10622279C2218yescomplemented
60#10622265C2218yescomplemented
61#10622262C2218yescomplemented
62C25×C11C2311yescharacteristic
63C23×C4×C11—24no—
64C23×C4×C11—24no—
65C23×C4×C11C2×C418yescomplemented
66C23×C4×C11C2312yes—
67C23×C4×C11C2312yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2312yes—
72C23×Dic11—28no—
73C23×Dic11—216no—
74C23×Dic11C2314yes—
75C23×Dic11C2312yes—
76C23×Dic11C2312yes—
77C23×Dic11C2314yes—
78C2×#4339—24no—
79C2×#4339—24no—
80C2×#4339C2×C418yescomplemented
81C22×D44C2311yescharacteristic
82C22×C4×D11C2314yes—
83C22×C4×D11C2312yes—
84C22×Dic22C2311yescharacteristic
85C11×#117—24no—
86C11×#117—24no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2318yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2312yes—
94#67006C2×C4116yescomplemented
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2312yes—
97#66983C2×C4116yescomplemented
98#66982C2×C4116yescomplemented
99C4×C22⋊D11C2×C4132yescomplemented
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2314yes—
103#66979C2×C418yescomplemented
104C2×C4⋊Dic11C2312yes—
105#66977C2×C4116yescomplemented
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2318yes—
108C2×Dic11⋊C4C2314yes—
109C2×C4×Dic11—24no—
110C2×C4×Dic11—28no—
111C2×C4×Dic11—28no—
112C2×C4×Dic11—28no—
113C2×C4×Dic11—216no—
114C2×C4×Dic11D418yescomplemented
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2318yes—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2311yescharacteristic
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2312yes—
125#66946—28no—
126#66940—28no—
127(C22⋊D11)⋊C4—216no—
128(C22⋊D11)⋊C4—232no—
129#66925—28no—
130C42×D11—28no—
131C11×#95C2318yes—
132C11⋊#95C2318yes—
133C11⋊#95C2318yes—
134C11⋊#95C2318yes—
135C4×#525—111nomaximal, Sylow
136C24×C11—22no—
137C24×C11—28no—
138C24×C11—22no—
139C24×C11C22×C414yes—
140C24×C11C2411yescharacteristic
141C24×C11C2412yes—
142C23×D11C2412yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—232no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11C22×C418yes—
151C22×C4×C11C22×C418yes—
152C22×C4×C11C22×C414yes—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—24no—
164C2×C22⋊D11C22×C4116yes—
165C2×C22⋊D11C22×C418yes—
166C22×Dic11—264no—
167C22×Dic11—28no—
168C22×Dic11—28no—
169C22×Dic11—28no—
170C22×Dic11—28no—
171C22×Dic11—28no—
172C22×Dic11—28no—
173C22×Dic11—24no—
174C22×Dic11—28no—
175C22×Dic11C2×D418yes—
176C22×Dic11#41116yescomplemented
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2414yes—
181C22×Dic11C2412yes—
182#4339—232no—
183C2×D44—22no—
184C2×D44—22no—
185C2×D44C22×C414yescomplemented
186C2×C4×D11—28no—
187C2×C4×D11—216no—
188C2×C4×D11—24no—
189C2×C4×D11—24no—
190C2×C4×D11C22×C418yescomplemented
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22C22×C414yescomplemented
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—216no—
198C11×C22⋊C4—24no—
199C42×C11—24no—
200C42×C11—24no—
201C22⋊Dic11C22×C4116yes—
202C22⋊Dic11C22×C418yes—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4C22×C4116yescomplemented
206C4⋊Dic11C22×C418yescomplemented
207Dic11⋊C4—28no—
208Dic11⋊C4—216no—
209Dic11⋊C4C22×C4116yescomplemented
210C4×Dic11—28no—
211C4×Dic11—28no—
212C4×Dic11—28no—
213C4×Dic11—216no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11C22×C418yescomplemented
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2×D418yes—
220C2×#525—111no—
221C2×C4×#41—111no—
222C23×C42—111no—
223C4×C22⋊Q8—114no—
224C4×#123—114no—
225C4×#121—114no—
226C4×#120—114no—
227#2297—111no—
228#2296—111no—
229#2290—114no—
230#2280D1111yescharacteristic, complemented
231C42×D4—114no—
232C4×#117—111no—
233C23×C11—216no—
234C23×C11—216no—
235C23×C11—28no—
236C23×C11—216no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—22no—
241C23×C11C23×C412yes—
242C23×C11C23×C414yes—
243C23×C11C22×D412yes—
244C23×C11C2×#4112yes—
245C23×C11C2×#4118yes—
246C23×C11C2511yescharacteristic
247C22×D11—22no—
248C22×D11—28no—
249C22×D11—22no—
250C22×D11C23×C414yes—
251C2×C4×C11—28no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—216no—
255C2×C4×C11—216no—
256C2×C4×C11—24no—
257C2×C4×C11—28no—
258C2×C4×C11—28no—
259C2×C4×C11—24no—
260C2×C4×C11C4×D4116yescomplemented
261C2×C4×C11C23×C414yes—
262C2×C4×C11C23×C412yes—
263C2×C4×C11C23×C412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C2×#4112yes—
267C2×C4×C11C2×#4112yes—
268C22⋊D11—216no—
269C22⋊D11—232no—
270C2×Dic11—232no—
271C2×Dic11—216no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—28no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—216no—
279C2×Dic11—232no—
280C2×Dic11C23×C418yes—
281C2×Dic11C23×C414yes—
282C2×Dic11C22×D414yes—
283C2×Dic11C22×D414yes—
284C2×Dic11C2×#4118yes—
285C2×Dic11C2×#4118yes—
286D44—28no—
287C4×D11—216no—
288C4×D11—416no—
289Dic22—28no—
290C22×#41—111no—
291C24×C4—112no—
292C24×C4C2×D1111yescharacteristic
293#525—1116no—
294C2×#123—112no—
295C2×C22⋊Q8—112no—
296C2×#121—112no—
297C2×#120—112no—
298C4×#41—228no—
299C2×C4×Q8—112no—
300C2×C4×D4—114no—
301C2×C4×D4—112no—
302C2×C4×D4—114no—
303C2×C4×D4—118no—
304C2×#117—111no—
305C2×#117—112no—
306C2×#117C2×D1111yescharacteristic
307C2×#117C2×D1111yescharacteristic
308C22×C42—111no—
309C22×C42—112no—
310C22×C42—112no—
311C22×C42—111no—
312C22×C42—114no—
313C22×C42—112no—
314C22×C42—112no—
315C22×C42—228no—
316#391—112no—
317#390—112no—
318#389—114no—
319#388—118no—
320#387—118no—
321#386—118no—
322#386—114no—
323#385—118no—
324#385—114no—
325#381C2×D1112yes—
326#380C2×D1114yes—
327#379C2×D1112yes—
328C4×C4⋊C4—114no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4—118no—
331C4×C22⋊C4—114no—
332C4×C22⋊C4—118no—
333C4×C22⋊C4—114no—
334C4×C22⋊C4—118no—
335C4×C22⋊C4C2×D1114yes—
336#376—112no—
337C43—112no—
338C22×C11—232no—
339C22×C11—24no—
340C22×C11—24no—
341C22×C11—24no—
342C22×C11—24no—
343C22×C11—28no—
344C22×C11—24no—
345C22×C11—28no—
346C22×C11C2×C4×D414yes—
347C22×C11C4×#4118yescomplemented
348C22×C11C24×C411yescharacteristic
349C22×C11C23×D411yescharacteristic
350C22×C11C22×#4111yescharacteristic
351C22×C11C22×#4114yes—
352C2×D11—24no—
353C2×D11—28no—
354C2×D11—44no—
355C2×D11—44no—
356C4×C11—24no—
357C4×C11—44no—
358C4×C11—44no—
359C4×C11C2×C4×D414yes—
360C4×C11C2×C4×D414yes—
361Dic11—24no—
362Dic11—28no—
363Dic11—24no—
364Dic11—28no—
365Dic11#52518yescomplemented
366C25C22×D1111yescharacteristic
367C2×#41—118no—
368C2×#41—224no—
369C2×#41—224no—
370C22×Q8—111no—
371C22×D4—114no—
372C22×D4—112no—
373C22×D4—111no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—112no—
377C23×C4—114no—
378C23×C4—112no—
379C23×C4—114no—
380C23×C4—112no—
381C23×C4—114no—
382C23×C4—2216no—
383C23×C4—228no—
384C23×C4C4×D1118yescomplemented
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1112yes—
388C23×C4C22×D1111yescharacteristic
389#123—1116no—
390C22⋊Q8—1116no—
391#121—1116no—
392#120—1116no—
393C4×Q8—228no—
394C4×D4—1132no—
395C4×D4—228no—
396C4×D4—2216no—
397C4×D4—2232no—
398#117—24no—
399#117—24no—
400#117—118no—
401#117—228no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4C22×D1112yes—
407C2×C4⋊C4C22×D1112yes—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4C22×D1112yes—
414C2×C22⋊C4C22×D1112yes—
415C2×C22⋊C4C22×D1118yes—
416C2×C42—118no—
417C2×C42—112no—
418C2×C42—111no—
419C2×C42—112no—
420C2×C42—111no—
421C2×C42—114no—
422C2×C42—118no—
423C2×C42—114no—
424C2×C42—114no—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—228no—
428C2×C42—228no—
429C2×C42—228no—
430C2×C42—2216no—
431C2×C42—228no—
432C2×C42—224no—
433C2×C42C22×D1112yes—
434C2×C42C22×D1112yes—
435#95—118no—
436#95—118no—
437#95—118no—
438#95C22×D1118yes—
439C2×C11—24no—
440C2×C11—28no—
441C2×C11C22×C4×D411yescharacteristic
442C2×C11C2×C4×#4112yes—
443C2×C11C2×#52512yes—
444C2×C11#344412yes—
445D11—44no—
446C24—22no—
447C24—22no—
448C24—28no—
449C24—112no—
450C24C2×C4×D1114yes—
451C24C23×D1111yescharacteristic
452C24C23×D1112yes—
453#41—2232no—
454C2×Q8—114no—
455C2×Q8—222no—
456C2×Q8—222no—
457C2×D4—1116no—
458C2×D4—118no—
459C2×D4—114no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—2216no—
463C2×D4—222no—
464C2×D4—222no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—232no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—112no—
473C22×C4—118no—
474C22×C4—1116no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—112no—
479C22×C4—118no—
480C22×C4—228no—
481C22×C4—2216no—
482C22×C4—228no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—228no—
487C22×C4—228no—
488C22×C4—2264no—
489C22×C4—224no—
490C22×C4—228no—
491C22×C4—224no—
492C22×C4—224no—
493C22×C4C2×C4×D1118yes—
494C22×C4C2×C4×D1118yes—
495C22×C4C2×C4×D1114yes—
496C22×C4C2×C4×D1114yes—
497C22×C4D4×D1114yes—
498C22×C4#434114yes—
499C22×C4C23×D1114yes—
500C22×C4C23×D1114yes—
501C22×C4C23×D1112yes—
502C22×C4C23×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—118no—
507C4⋊C4—1116no—
508C4⋊C4—228no—
509C4⋊C4—2216no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—216no—
513C22⋊C4—118no—
514C22⋊C4—1116no—
515C22⋊C4—1116no—
516C22⋊C4—228no—
517C22⋊C4—2216no—
518C42—24no—
519C42—24no—
520C42—118no—
521C42—114no—
522C42—114no—
523C42—118no—
524C42—228no—
525C42—228no—
526C42—228no—
527C42—2216no—
528C42—224no—
529C42—224no—
530C11C4×#52511yescharacteristic, complemented, Sylow
531C23—216no—
532C23—216no—
533C23—28no—
534C23—216no—
535C23—22no—
536C23—22no—
537C23—24no—
538C23—24no—
539C23—114no—
540C23—222no—
541C23—222no—
542C23—228no—
543C23C22×C4×D1112yes—
544C23C22×C4×D1114yes—
545C23C2×D4×D1112yes—
546C23C2×#434112yes—
547C23#41×D1118yes—
548C23C24×D1111yescharacteristic
549Q8—228no—
550D4—2216no—
551D4—2232no—
552D4—228no—
553C2×C4—28no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—216no—
557C2×C4—216no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—28no—
561C2×C4—28no—
562C2×C4—114no—
563C2×C4—118no—
564C2×C4—118no—
565C2×C4—114no—
566C2×C4—114no—
567C2×C4—118no—
568C2×C4—2216no—
569C2×C4—2232no—
570C2×C4—2216no—
571C2×C4—2232no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—228no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—2216no—
579C2×C4—4416no—
580C2×C4(C22⋊D11)⋊C4116yescomplemented
581C2×C4C22×C4×D1114yes—
582C2×C4C22×C4×D1112yes—
583C2×C4C22×C4×D1112yes—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×D4×D1112yes—
586C2×C4C2×#434112yes—
587C2×C4C2×#434112yes—
588C22—232no—
589C22—24no—
590C22—28no—
591C22—24no—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—28no—
596C22—224no—
597C22—228no—
598C22—444no—
599C22—444no—
600C22C2×(C22⋊D11)⋊C414yes—
601C22#1062305318yescomplemented
602C22C23×C4×D1111yescharacteristic
603C22C22×D4×D1111yescharacteristic
604C22C22×#434111yescharacteristic
605C22C2×#41×D1114yes—
606C4—24no—
607C4—44no—
608C4—44no—
609C4—118no—
610C4—224no—
611C4—228no—
612C4—224no—
613C4—228no—
614C4C2×(C22⋊D11)⋊C414yes—
615C4C2×(C22⋊D11)⋊C414yes—
616C2—24no—
617C2—28no—
618C2—444no—
619C2C22×(C22⋊D11)⋊C411yescharacteristic
620C2C2×#1062305312yes—
621C2D11×#52512yes—
622C2#1308190812yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2280C2
socle, cosocleC23×C11C25
prime radicalC2×#10623322C2
hypercenter#2280D11
hypocenterC11C4×#525
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. C23×C4×Dic11C2semidirect
4. #13071144C2semidirect
5. #13071133C2semidirect
6. #13071122C2semidirect
7. #13071115C2semidirect
8. #13071104C2semidirect
9. #13071098C2semidirect
10. #13071055C2semidirect
11. C4×(C22⋊D11)⋊C4C2semidirect
12. #117×Dic11C2semidirect
13. C11×#2280C2semidirect
20. #10623322C4semidirect
34. C2×#66946C22semidirect
35. C2×#66940C22semidirect
38. C2×#66925C22semidirect
39. C2×C42×D11C22semidirect
44. #10622601C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622587C22semidirect
47. #10622586C22semidirect
54. C4×(C2×D11)⋊C4C22semidirect
55. #10622545C22semidirect
56. C4×Dic11⋊C4C22semidirect
57. C42×Dic11C22semidirect
58. #10622282C22semidirect
59. #10622279C22semidirect
60. #10622265C22semidirect
61. #10622262C22semidirect
65. C23×C4×C11C2×C4semidirect
80. C2×#4339C2×C4semidirect
94. #67006C2×C4semidirect
97. #66983C2×C4semidirect
98. #66982C2×C4semidirect
99. C4×C22⋊D11C2×C4semidirect
103. #66979C2×C4semidirect
105. #66977C2×C4semidirect
114. C2×C4×Dic11D4semidirect
176. C22×Dic11#41semidirect
185. C2×D44C22×C4semidirect
190. C2×C4×D11C22×C4semidirect
193. C2×Dic22C22×C4semidirect
205. (C2×D11)⋊C4C22×C4semidirect
206. C4⋊Dic11C22×C4semidirect
209. Dic11⋊C4C22×C4semidirect
216. C4×Dic11C22×C4semidirect
230. #2280D11semidirect
260. C2×C4×C11C4×D4semidirect
347. C22×C11C4×#41semidirect
365. Dic11#525semidirect
384. C23×C4C4×D11semidirect
530. C11C4×#525semidirect
580. C2×C4(C22⋊D11)⋊C4semidirect
601. C22#10623053semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106230532
C23×C4×Dic112
#130711442
#130711332
#130711222
#130711152
#130711042
#130710982
#130710552
C4×(C22⋊D11)⋊C42
#117×Dic112
C11×#22802
C4×#52511