Finite Group Databasebeta

← #14913886

Subgroups — #14913886

Order 2816.

2914 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2#13071559C214yesmaximal, complemented
3#13071553C214yesmaximal, complemented
4#13071546C214yesmaximal, complemented
5#13071538C214yesmaximal, complemented
6#13071216C212yesmaximal, complemented
7#13071212C212yesmaximal, complemented
8#13071192C212yesmaximal
9#13071011C212yesmaximal, complemented
10#13070999C211yesmaximal, characteristic, complemented
11D11×#380C212yesmaximal, complemented
12#13070968C212yesmaximal, complemented
13C11×#2280C211yesmaximal, characteristic, complemented
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C2×C11×#117C2212yescomplemented
18C22×C22⋊Dic11C2211yescharacteristic
19C2×C4×C22⋊D11C4116yescomplemented
20C2×C4×C22⋊D11C2212yes—
21C2×C4×C22⋊D11C2212yes—
22C2×C4×C22⋊D11C2212yes—
23C2×C4×C22⋊D11C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C2×#66979C2212yescomplemented
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C2×C4⋊C4×D11C2214yescomplemented
29C2×C22⋊C4×D11C2214yes—
30C11×#381C2212yescomplemented
31C11×#380C2212yes—
32C11×#380C2212yescomplemented
33C11×#379C2212yes—
34C4×C11×C22⋊C4C2212yes—
35C4×C11×C22⋊C4C2212yescomplemented
36#10622860C2212yes—
37#10622825C2212yes—
38#10622825C2212yescomplemented
39#10622824C2212yescomplemented
40C4×C22⋊Dic11C2212yes—
41C4×C22⋊Dic11C2212yescomplemented
42#10622600C2214yescomplemented
43#10622590C2214yescomplemented
44C4⋊C4×Dic11C2214yescomplemented
45#10622569C2218yes—
46#10622569C2218yes—
47#10622558C2218yescomplemented
48#10622557C2218yescomplemented
49#10622556C2214yes—
50#10622555C2214yes—
51C22⋊C4×Dic11C2214yes—
52C4×(C2×D11)⋊C4C2218yescomplemented
53#10622546C2218yescomplemented
54#10622280C2214yescomplemented
55#10622279C2218yescomplemented
56D11×#95C2214yescomplemented
57#10622265C2218yescomplemented
58#10622264C2214yescomplemented
59#10622261C2214yescomplemented
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—44no—
63C23×C4×C11C2×C418yescomplemented
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—28no—
71C22×C22⋊D11C2×C418yes—
72C22×C22⋊D11C2312yes—
73C22×C22⋊D11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×C4×D11—44no—
78C22×C4×D11C2×C418yes—
79C22×C4×D11C2312yes—
80C22×C4×D11C2318yes—
81C22×C4×D11C2312yes—
82C11×#117—44no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C42×C11C2314yes—
88C2×C22⋊Dic11C2×C418yescomplemented
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C4×C22⋊D11C2×C4116yescomplemented
95C4×C22⋊D11C2×C4116yescomplemented
96C4×C22⋊D11C2×C4116yescomplemented
97C4×C22⋊D11C2×C4116yescomplemented
98C2×(C2×D11)⋊C4C2×C418yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2312yes—
101C2×(C2×D11)⋊C4C2312yes—
102#66979—44no—
103C2×C4⋊Dic11C2314yes—
104C2×Dic11⋊C4C2×C418yescomplemented
105C2×Dic11⋊C4C2318yes—
106C2×Dic11⋊C4C2312yes—
107C2×Dic11⋊C4C2312yes—
108C2×C4×Dic11C2×C418yescomplemented
109C2×C4×Dic11C2318yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113C4⋊C4×D11—48no—
114C22⋊C4×D11—216no—
115C11×#95C2314yes—
116C11×#95C2314yes—
117C11⋊#95C2314yes—
118C11⋊#95C2318yes—
119C11⋊#95C2318yes—
120C11⋊#95C2318yes—
121C11⋊#95C2318yes—
122C11⋊#95C2314yes—
123#34185—111nomaximal, Sylow
124C24×C11—24no—
125C24×C11—42no—
126C24×C11—42no—
127C24×C11C22×C414yes—
128C24×C11C2411yescharacteristic
129C24×C11C2411yescharacteristic
130C24×C11C2411yescharacteristic
131C23×D11—42no—
132C23×D11—42no—
133C23×D11C22×C414yes—
134C23×D11#4118yes—
135C23×D11C2412yes—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—416no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C414yes—
147C22×C4×C11C22×C414yes—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C2418yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—232no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11C22×C418yes—
160C2×C22⋊D11C22×C418yes—
161C22×Dic11—24no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11C22×C414yes—
165C22×Dic11C22×C414yes—
166C22×Dic11C22×C414yes—
167C22×Dic11C2418yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C2×C4×D11—216no—
172C2×C4×D11—28no—
173C2×C4×D11—44no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11—416no—
177C2×C4×D11C22×C418yes—
178C2×C4×D11C22×C418yes—
179C11×C4⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—44no—
183C42×C11—44no—
184C22⋊Dic11—28no—
185C22⋊Dic11—44no—
186C22⋊Dic11—44no—
187C22⋊Dic11C22×C418yes—
188C22⋊Dic11C22×C418yes—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4C22×C418yes—
191(C2×D11)⋊C4C22×C418yes—
192C4⋊Dic11—28no—
193Dic11⋊C4—48no—
194Dic11⋊C4C22×C418yes—
195Dic11⋊C4C22×C418yes—
196C4×Dic11—48no—
197C4×Dic11—44no—
198C4×Dic11C22×C418yes—
199C4×Dic11C22×C418yes—
200C22×C4×D4—111no—
201#2353—114no—
202#2353—114no—
203#2352—114no—
204#2352—114no—
205#2313—112no—
206#2312—112no—
207#2308—112no—
208#2283—112no—
209#2280—111no—
210#2280D1111yescharacteristic, complemented
211C2×#380—112no—
212#2273—112no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—28no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—416no—
225C23×C11C23×C412yes—
226C23×C11C23×C412yes—
227C23×C11C23×C412yes—
228C23×C11C2×#4114yes—
229C23×C11C2511yescharacteristic
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—416no—
235C22×D11#117116yescomplemented
236C22×D11C23×C414yes—
237C22×D11C2×#4114yes—
238C22×D11C2×#4114yes—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—28no—
243C2×C4×C11—28no—
244C2×C4×C11—28no—
245C2×C4×C11—28no—
246C2×C4×C11—28no—
247C2×C4×C11—28no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11C23×C412yes—
252C2×C4×C11C23×C412yes—
253C2×C4×C11C23×C412yes—
254C2×C4×C11C23×C412yes—
255C2×C4×C11H(5,𝔽2)14yes—
256C22⋊D11—216no—
257C22⋊D11—216no—
258C2×Dic11—28no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—28no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11C23×C414yes—
269C2×Dic11C23×C414yes—
270C2×Dic11C23×C414yes—
271C4×D11—216no—
272C4×D11—48no—
273C4×D11—816no—
274C23×D4—111no—
275C24×C4—111no—
276C24×C4C2×D1111yescharacteristic
277C2×C4×D4—112no—
278C2×C4×D4—112no—
279C2×C4×D4—112no—
280C2×C4×D4—112no—
281C2×C4×D4—1116no—
282C2×#117—112no—
283C2×#117C2×D1112yescomplemented
284C22×C4⋊C4—111no—
285C22×C4⋊C4—114no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—111no—
288C22×C22⋊C4—114no—
289C22×C42—111no—
290#388—118no—
291#388—118no—
292#387—118no—
293#387—118no—
294#386—118no—
295#386—118no—
296#383—114no—
297#382—114no—
298#381—112no—
299#381—114no—
300#381C2×D1112yescomplemented
301#380—112no—
302#380—112no—
303#380—114no—
304#380—114no—
305#380—114no—
306#380C2×D1112yes—
307#380C2×D1112yescomplemented
308#379—112no—
309#379C2×D1112yes—
310C4×C4⋊C4—114no—
311C4×C22⋊C4—112no—
312C4×C22⋊C4—112no—
313C4×C22⋊C4—114no—
314C4×C22⋊C4—118no—
315C4×C22⋊C4—118no—
316C4×C22⋊C4C2×D1112yes—
317C4×C22⋊C4C2×D1112yescomplemented
318#376—114no—
319C2×#95—114no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—28no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—416no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11C2×#11714yes—
333C22×C11C24×C411yescharacteristic
334C22×C11C22×#4112yes—
335C22×C11C2×H(5,𝔽2)12yes—
336C22×C11#58512yes—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—28no—
340C2×D11—28no—
341C2×D11—416no—
342C2×D11C2×#11718yes—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—48no—
347C4×C11#51814yes—
348Dic11—24no—
349Dic11—24no—
350Dic11—24no—
351Dic11—48no—
352C25—111no—
353C25C22×D1111yescharacteristic
354C22×D4—118no—
355C22×D4—112no—
356C22×D4—112no—
357C22×D4—228no—
358C23×C4—44no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—112no—
363C23×C4—118no—
364C23×C4—112no—
365C23×C4—118no—
366C23×C4—444no—
367C23×C4C4×D1118yescomplemented
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C4×D4—1116no—
375C4×D4—1116no—
376C4×D4—1116no—
377C4×D4—1116no—
378#117—44no—
379#117—444no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—448no—
386C2×C4⋊C4C22×D1114yes—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—112no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—2216no—
398C2×C22⋊C4C22×D1114yes—
399C2×C22⋊C4C22×D1114yes—
400C2×C22⋊C4C22×D1114yes—
401C2×C42—118no—
402C2×C42—112no—
403C2×C42—112no—
404C2×C42—114no—
405C2×C42—118no—
406C2×C42C22×D1114yes—
407#95—114no—
408#95—118no—
409#95—118no—
410#95—114no—
411#95—118no—
412#95—118no—
413#95C22×D1114yes—
414#95C22×D1114yes—
415C2×C11—24no—
416C2×C11—42no—
417C2×C11—42no—
418C2×C11C22×#11711yescharacteristic
419C2×C11C2×#51811yescharacteristic
420C2×C11#342811yescharacteristic
421C2×C11#350514yes—
422D11—28no—
423C24—24no—
424C24—42no—
425C24—42no—
426C24—112no—
427C24—114no—
428C24—118no—
429C24—442no—
430C24—442no—
431C24C2×C4×D1114yes—
432C24C23×D1111yescharacteristic
433C24C23×D1111yescharacteristic
434C24C23×D1111yescharacteristic
435C2×D4—118no—
436C2×D4—118no—
437C2×D4—2232no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—224no—
441C2×D4—224no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—416no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—114no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—118no—
456C22×C4—118no—
457C22×C4—118no—
458C22×C4—2216no—
459C22×C4—224no—
460C22×C4—228no—
461C22×C4—4416no—
462C22×C4—444no—
463C22×C4—448no—
464C22×C4—448no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4C2×C4×D1114yes—
468C22×C4C2×C4×D1114yes—
469C22×C4C2×C4×D1114yes—
470C22×C4C2×C4×D1114yes—
471C22×C4C2×C4×D1114yes—
472C22×C4C2×C4×D1114yes—
473C22×C4C23×D1118yes—
474C22×C4C23×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477C22×C4C23×D1111yescharacteristic
478C4⋊C4—28no—
479C4⋊C4—118no—
480C4⋊C4—118no—
481C4⋊C4—228no—
482C4⋊C4—448no—
483C22⋊C4—28no—
484C22⋊C4—44no—
485C22⋊C4—44no—
486C22⋊C4—118no—
487C22⋊C4—118no—
488C22⋊C4—118no—
489C22⋊C4—118no—
490C22⋊C4—2216no—
491C22⋊C4—228no—
492C22⋊C4—444no—
493C22⋊C4—444no—
494C42—44no—
495C42—118no—
496C42—118no—
497C42—444no—
498C42—448no—
499C11#3418511yescharacteristic, complemented, Sylow
500C23—22no—
501C23—22no—
502C23—28no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—44no—
510C23—44no—
511C23—416no—
512C23—114no—
513C23—114no—
514C23—114no—
515C23—1116no—
516C23—224no—
517C23—224no—
518C23—444no—
519C23—4416no—
520C23—444no—
521C23C22×C4×D1112yes—
522C23C22×C4×D1112yes—
523C23C22×C4×D1112yes—
524C23#41×D1114yes—
525C23C24×D1111yescharacteristic
526D4—2216no—
527D4—2216no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—28no—
533C2×C4—28no—
534C2×C4—28no—
535C2×C4—28no—
536C2×C4—28no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—114no—
543C2×C4—228no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—2216no—
549C2×C4—228no—
550C2×C4—228no—
551C2×C4—228no—
552C2×C4—448no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—8816no—
556C2×C4C22×C4×D1112yes—
557C2×C4C22×C4×D1112yes—
558C2×C4C22×C4×D1112yes—
559C2×C4C22×C4×D1112yes—
560C2×C4#6703714yes—
561C22—28no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—416no—
571C22—44no—
572C22—44no—
573C22—118no—
574C22—228no—
575C22—228no—
576C22—224no—
577C22—224no—
578C22—4416no—
579C22D11×#11714yes—
580C22C23×C4×D1111yescharacteristic
581C22C2×#6703712yes—
582C22C2×#41×D1112yes—
583C22#1062345312yes—
584C4—22no—
585C4—22no—
586C4—22no—
587C4—48no—
588C4—224no—
589C4—224no—
590C4—224no—
591C4—448no—
592C4#1062301714yes—
593C2—24no—
594C2—42no—
595C2—42no—
596C2—228no—
597C2C2×D11×#11711yescharacteristic
598C2C2×#1062301711yescharacteristic
599C2#1308181711yescharacteristic
600C2#1308244414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2280C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenter#2280D11
hypocenterC11#34185
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #13071559C2semidirect
3. #13071553C2semidirect
4. #13071546C2semidirect
5. #13071538C2semidirect
6. #13071216C2semidirect
7. #13071212C2semidirect
9. #13071011C2semidirect
10. #13070999C2semidirect
11. D11×#380C2semidirect
12. #13070968C2semidirect
13. C11×#2280C2semidirect
17. C2×C11×#117C22semidirect
19. C2×C4×C22⋊D11C4semidirect
25. C2×#66979C22semidirect
28. C2×C4⋊C4×D11C22semidirect
30. C11×#381C22semidirect
32. C11×#380C22semidirect
35. C4×C11×C22⋊C4C22semidirect
38. #10622825C22semidirect
39. #10622824C22semidirect
41. C4×C22⋊Dic11C22semidirect
42. #10622600C22semidirect
43. #10622590C22semidirect
44. C4⋊C4×Dic11C22semidirect
47. #10622558C22semidirect
48. #10622557C22semidirect
52. C4×(C2×D11)⋊C4C22semidirect
53. #10622546C22semidirect
54. #10622280C22semidirect
55. #10622279C22semidirect
56. D11×#95C22semidirect
57. #10622265C22semidirect
58. #10622264C22semidirect
59. #10622261C22semidirect
63. C23×C4×C11C2×C4semidirect
88. C2×C22⋊Dic11C2×C4semidirect
94. C4×C22⋊D11C2×C4semidirect
95. C4×C22⋊D11C2×C4semidirect
96. C4×C22⋊D11C2×C4semidirect
97. C4×C22⋊D11C2×C4semidirect
104. C2×Dic11⋊C4C2×C4semidirect
108. C2×C4×Dic11C2×C4semidirect
210. #2280D11semidirect
235. C22×D11#117semidirect
283. C2×#117C2×D11semidirect
300. #381C2×D11semidirect
307. #380C2×D11semidirect
317. C4×C22⋊C4C2×D11semidirect
367. C23×C4C4×D11semidirect
499. C11#34185semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130715592
#130715532
#130715462
#130715382
#130712162
#130712122
#130711922
#130710112
#130709992
D11×#3802
#130709682
C11×#22802
#3418511