Finite Group Databasebeta

← #14914043

Subgroups — #14914043

Order 2816.

3190 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2C2×#10623017C211yesmaximal, characteristic
3#13071608C218yesmaximal, complemented
4#13071486C214yesmaximal, complemented
5#13071466C214yesmaximal, complemented
6#13071285C214yesmaximal, complemented
7#13071228C211yesmaximal, characteristic, complemented
8#13071191C211yesmaximal, characteristic
9C4×#66982C214yesmaximal, complemented
10C2×#10622824C211yesmaximal, characteristic, complemented
11#13070969C211yesmaximal, characteristic, complemented
12C22×C11×#117C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C2×C11×#117—28no—
16C2×C11×#117C2214yes—
17C2×C11×#117C2214yescomplemented
18C22×C11×C4⋊C4C2212yescomplemented
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2212yescomplemented
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×#66982C4116yescomplemented
26C2×#66982C2212yes—
27C2×#66982C2212yes—
28C2×#66982C2214yes—
29C2×C4×C22⋊D11C2214yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32#10623017—28no—
33C2×(C22⋊D11)⋊C4C2214yes—
34C2×C22⋊C4×D11C2212yes—
35C2×#66930C2212yes—
36#10622826C2214yes—
37#10622824C2214yes—
38#10622824C2212yescomplemented
39#10622824C2212yescomplemented
40#10622823C2214yescomplemented
41C4×C22⋊Dic11C2214yescomplemented
42C2×C11⋊#95C2214yescomplemented
43#10622603C2218yescomplemented
44#10622602C2218yescomplemented
45#10622591C2218yescomplemented
46#10622585C2218yescomplemented
47#10622571C2214yes—
48#10622568C2212yes—
49#10622559C2214yescomplemented
50#10622556C2212yes—
51#10622555C2214yes—
52C22⋊C4×Dic11C2214yes—
53C22⋊C4×Dic11C2214yescomplemented
54#10622553C2218yescomplemented
55C4×(C2×D11)⋊C4C2218yescomplemented
56#10622546C2218yescomplemented
57C4×Dic11⋊C4C2218yescomplemented
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—24no—
61C23×C4×C11—24no—
62C23×C4×C11C2×C418yescomplemented
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2312yes—
68C23×C4×C11C2312yes—
69C22×C22⋊D11—24no—
70C22×C22⋊D11—24no—
71C22×C22⋊D11C2×C418yes—
72C22×C22⋊D11C2312yes—
73C22×C22⋊D11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2312yes—
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C22×C4×D11C2314yes—
79C11×#117—216no—
80C11×#117—216no—
81C2×C11×C4⋊C4—28no—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4D418yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C11×C22⋊C4C2312yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C42×C11—28no—
90C2×C42×C11C2318yes—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11C2×C418yescomplemented
94C2×C22⋊Dic11C2312yes—
95C2×C22⋊Dic11C2312yes—
96C2×C22⋊Dic11C2312yes—
97C2×C22⋊Dic11C2312yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100#66982C2×C4116yescomplemented
101#66982C2×C4116yescomplemented
102#66982C2×C4132yescomplemented
103C4×C22⋊D11—216no—
104C2×(C2×D11)⋊C4C2×C4116yescomplemented
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2318yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×Dic11⋊C4C2×C4116yescomplemented
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2318yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2318yes—
116(C22⋊D11)⋊C4—216no—
117C22⋊C4×D11—28no—
118#66930—28no—
119C11⋊#95C2318yes—
120C11⋊#95C2318yes—
121C11⋊#95C2318yes—
122C11⋊#95C2318yes—
123C11⋊#95C2318yes—
124#34199—111nomaximal, Sylow
125C24×C11—44no—
126C24×C11C22×C414yes—
127C24×C11C2×D414yes—
128C24×C11#4114yes—
129C24×C11C2411yescharacteristic
130C24×C11C2411yescharacteristic
131C24×C11C2411yescharacteristic
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—44no—
135C23×D11C22×C414yes—
136C23×D11C2412yes—
137C22×C4×C11—232no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11C22×C418yes—
150C22×C4×C11C22×C418yes—
151C22×C4×C11C22×C414yes—
152C22×C4×C11C22×C414yes—
153C22×C4×C11C2×D418yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C2×C22⋊D11—232no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11C22×C418yes—
164C2×C22⋊D11C22×C418yes—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—44no—
170C22×Dic11—44no—
171C22×Dic11—44no—
172C22×Dic11C22×C414yes—
173C22×Dic11C22×C418yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C2×C4×D11—28no—
179C2×C4×D11—48no—
180C11×C4⋊C4—216no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4C2×D418yes—
184C11×C22⋊C4C2×D418yes—
185C42×C11—216no—
186C22⋊Dic11—24no—
187C22⋊Dic11—24no—
188C22⋊Dic11—24no—
189C22⋊Dic11—24no—
190C22⋊Dic11C22×C418yes—
191C22⋊Dic11C22×C418yes—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—48no—
194(C2×D11)⋊C4C22×C4116yes—
195(C2×D11)⋊C4C22×C4116yes—
196Dic11⋊C4—28no—
197Dic11⋊C4—48no—
198Dic11⋊C4C22×C4116yes—
199Dic11⋊C4C22×C4116yes—
200C4×Dic11—28no—
201C4×Dic11—48no—
202C22×#123—111no—
203C2×#518—111no—
204C22×#117D1111yescharacteristic, complemented
205#2359—118no—
206#2344—114no—
207#2342—114no—
208#2322—114no—
209#2315—111no—
210#2308—111no—
211C4×#123—114no—
212C2×#381—111no—
213#2273—111no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—48no—
218C23×C11—48no—
219C23×C11—48no—
220C23×C11C4×D4116yes—
221C23×C11C23×C412yes—
222C23×C11C23×C412yes—
223C23×C11C23×C412yes—
224C23×C11C22×D412yes—
225C23×C11C22×D412yes—
226C23×C11C22×D412yes—
227C23×C11C2×#4112yes—
228C23×C11C2×#4112yes—
229C23×C11C2×#4112yes—
230C23×C11C2511yescharacteristic
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—48no—
236C22×D11—84no—
237C22×D11—84no—
238C22×D11C23×C414yes—
239C2×C4×C11—216no—
240C2×C4×C11—28no—
241C2×C4×C11—28no—
242C2×C4×C11—216no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—28no—
250C2×C4×C11—48no—
251C2×C4×C11—48no—
252C2×C4×C11C23×C414yes—
253C2×C4×C11C23×C414yes—
254C2×C4×C11C22×D418yes—
255C22⋊D11—216no—
256C22⋊D11—216no—
257C2×Dic11—28no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—48no—
266C2×Dic11—84no—
267C2×Dic11—84no—
268C2×Dic11C23×C414yes—
269C2×Dic11C23×C418yes—
270C4×D11—88no—
271C23×D4—111no—
272C24×C4C2×D1111yescharacteristic
273C2×#123—112no—
274C2×#123—114no—
275C2×#123—112no—
276C2×#123—1116no—
277#518—228no—
278C2×C4×D4—114no—
279C2×C4×D4—114no—
280C2×#117—28no—
281C2×#117—112no—
282C2×#117C2×D1114yes—
283C2×#117C2×D1114yescomplemented
284C22×C4⋊C4—112no—
285C22×C4⋊C4C2×D1112yescomplemented
286C22×C22⋊C4—111no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C42C2×D1112yescomplemented
294#389—118no—
295#388—118no—
296#388—118no—
297#387—118no—
298#387—118no—
299#386—114no—
300#386—114no—
301#385—114no—
302#385—118no—
303#385—114no—
304#381—112no—
305#381—114no—
306#381—112no—
307#381—112no—
308#380—114no—
309#379—112no—
310C4×C4⋊C4—118no—
311C4×C22⋊C4—114no—
312C4×C22⋊C4—114no—
313C4×C22⋊C4—114no—
314C4×C22⋊C4—118no—
315C2×#95—114no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11—416no—
326C22×C11C2×C4×D414yes—
327C22×C11C2×C4×D414yes—
328C22×C11C2×C4×D414yes—
329C22×C11C24×C411yescharacteristic
330C22×C11C23×D411yescharacteristic
331C22×C11C22×#4111yescharacteristic
332C22×C11#58514yes—
333C2×D11—24no—
334C2×D11—28no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—88no—
338C4×C11—24no—
339C4×C11—24no—
340C4×C11—28no—
341C4×C11—44no—
342Dic11—24no—
343Dic11—28no—
344Dic11—44no—
345Dic11—44no—
346C25—111no—
347C25C22×D1111yescharacteristic
348C22×D4—118no—
349C22×D4—112no—
350C22×D4—112no—
351C22×D4—224no—
352C22×D4—224no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—111no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—114no—
360C23×C4C4×D1118yescomplemented
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1112yes—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1112yes—
366C23×C4C22×D1112yes—
367#123—1116no—
368#123—1132no—
369#123—1116no—
370C4×D4—2216no—
371C4×D4—2216no—
372#117—216no—
373#117—216no—
374#117—228no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—1116no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4C22×D1118yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—112no—
386C2×C22⋊C4—1116no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—112no—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4C22⋊D1118yes—
399C2×C22⋊C4C22×D1112yes—
400C2×C22⋊C4C22×D1112yes—
401C2×C22⋊C4C22×D1112yes—
402C2×C22⋊C4C22×D1112yes—
403C2×C42—28no—
404C2×C42—114no—
405C2×C42—118no—
406C2×C42C22×D1118yes—
407#95—118no—
408#95—118no—
409#95—118no—
410#95—118no—
411#95—118no—
412C2×C11—24no—
413C2×C11—24no—
414C2×C11—24no—
415C2×C11C22×C4×D411yescharacteristic
416C2×C11#342812yes—
417C2×C11#348512yes—
418C2×C11#349112yes—
419D11—44no—
420C24—44no—
421C24—112no—
422C24—114no—
423C24—222no—
424C24—222no—
425C24—444no—
426C24C2×C4×D1114yes—
427C24#433914yes—
428C24C2×C22⋊D1114yes—
429C24C23×D1111yescharacteristic
430C24C23×D1111yescharacteristic
431C24C23×D1111yescharacteristic
432C2×D4—118no—
433C2×D4—118no—
434C2×D4—2232no—
435C2×D4—224no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—224no—
439C22×C4—232no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—112no—
454C22×C4—118no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—228no—
462C22×C4—448no—
463C22×C4—444no—
464C22×C4—444no—
465C22×C4—444no—
466C22×C4C2×C4×D1118yes—
467C22×C4C2×C4×D1114yes—
468C22×C4C2×C4×D1118yes—
469C22×C4C2×C4×D1114yes—
470C22×C4C2×C22⋊D1118yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1112yes—
474C22×C4C23×D1114yes—
475C4⋊C4—216no—
476C4⋊C4—1116no—
477C4⋊C4—1116no—
478C4⋊C4—228no—
479C4⋊C4—448no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—118no—
483C22⋊C4—118no—
484C22⋊C4—1116no—
485C22⋊C4—1116no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C22⋊C4—228no—
491C22⋊C4—448no—
492C22⋊C4C2×C22⋊D1118yes—
493C22⋊C4C2×C22⋊D1118yes—
494C42—216no—
495C42—228no—
496C42—448no—
497C11#3419911yescharacteristic, complemented, Sylow
498C23—24no—
499C23—24no—
500C23—24no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—114no—
505C23—222no—
506C23—228no—
507C23—222no—
508C23—228no—
509C23—448no—
510C23—884no—
511C23—884no—
512C23C4×C22⋊D11116yes—
513C23C22×C4×D1112yes—
514C23C22×C4×D1112yes—
515C23C22×C4×D1112yes—
516C23C2×#433912yes—
517C23C2×#433912yes—
518C23C2×#433912yes—
519C23C22×C22⋊D1112yes—
520C23C22×C22⋊D1112yes—
521C23C22×C22⋊D1112yes—
522C23C24×D1111yescharacteristic
523D4—2216no—
524D4—2216no—
525C2×C4—216no—
526C2×C4—28no—
527C2×C4—28no—
528C2×C4—216no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—28no—
535C2×C4—24no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—118no—
539C2×C4—114no—
540C2×C4—228no—
541C2×C4—222no—
542C2×C4—228no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—228no—
546C2×C4—228no—
547C2×C4—224no—
548C2×C4—448no—
549C2×C4—888no—
550C2×C4—884no—
551C2×C4—884no—
552C2×C4C22×C4×D1114yes—
553C2×C4C22×C4×D1114yes—
554C2×C4C22×C22⋊D1118yes—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—416no—
565C22—224no—
566C22—228no—
567C22—444no—
568C22—444no—
569C22—888no—
570C22C2×C4×C22⋊D1114yes—
571C22C2×C4×C22⋊D1114yes—
572C22C2×C4×C22⋊D1114yes—
573C22C23×C4×D1111yescharacteristic
574C22C22×#433911yescharacteristic
575C22#1062345314yes—
576C22C23×C22⋊D1111yescharacteristic
577C4—28no—
578C4—24no—
579C4—24no—
580C4—44no—
581C4—224no—
582C4—228no—
583C4—444no—
584C4—444no—
585C2—24no—
586C2—24no—
587C2—24no—
588C2—444no—
589C2C22×C4×C22⋊D1111yescharacteristic
590C2#1308181712yes—
591C2#1308226012yes—
592C2#1308231412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C11×#117C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenterC22×#117D11
hypocenterC11#34199
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #13071608C2semidirect
4. #13071486C2semidirect
5. #13071466C2semidirect
6. #13071285C2semidirect
7. #13071228C2semidirect
9. C4×#66982C2semidirect
10. C2×#10622824C2semidirect
11. #13070969C2semidirect
12. C22×C11×#117C2semidirect
17. C2×C11×#117C22semidirect
18. C22×C11×C4⋊C4C22semidirect
21. C22×C42×C11C22semidirect
25. C2×#66982C4semidirect
38. #10622824C22semidirect
39. #10622824C22semidirect
40. #10622823C22semidirect
41. C4×C22⋊Dic11C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622603C22semidirect
44. #10622602C22semidirect
45. #10622591C22semidirect
46. #10622585C22semidirect
49. #10622559C22semidirect
53. C22⋊C4×Dic11C22semidirect
54. #10622553C22semidirect
55. C4×(C2×D11)⋊C4C22semidirect
56. #10622546C22semidirect
57. C4×Dic11⋊C4C22semidirect
62. C23×C4×C11C2×C4semidirect
93. C2×C22⋊Dic11C2×C4semidirect
100. #66982C2×C4semidirect
101. #66982C2×C4semidirect
102. #66982C2×C4semidirect
104. C2×(C2×D11)⋊C4C2×C4semidirect
109. C2×Dic11⋊C4C2×C4semidirect
204. C22×#117D11semidirect
283. C2×#117C2×D11semidirect
285. C22×C4⋊C4C2×D11semidirect
293. C22×C42C2×D11semidirect
360. C23×C4C4×D11semidirect
497. C11#34199semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
C2×#106230172
#130716082
#130714862
#130714662
#130712852
#130712282
#130711912
C4×#669822
C2×#106228242
#130709692
C22×C11×#1172
#3419911