Finite Group Databasebeta

← #14923633

Subgroups — #14923633

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2#13072927C212yesmaximal, complemented
3#13072918C212yesmaximal, complemented
4#13072907C214yesmaximal, complemented
5#13072899C212yesmaximal, complemented
6#13072894C212yesmaximal, complemented
7#13072886C212yesmaximal, complemented
8#13071943C212yesmaximal
9#13071873C214yesmaximal, complemented
10C4×#66982C214yesmaximal, complemented
11#13071098C212yesmaximal, complemented
12#13070999C211yesmaximal, characteristic, complemented
13#13070995C212yesmaximal, complemented
14C22×C11×#117C211yesmaximal, characteristic, complemented
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#117—28no—
19C2×C11×#117C2212yes—
20C2×C11×#117C2212yes—
21C2×C11×#117C2212yescomplemented
22C2×C11×#117C2212yescomplemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2212yes—
26C22×C42×C11C2212yescomplemented
27C22×C22⋊Dic11C2211yescharacteristic
28C2×#66982C2214yes—
29C2×C4×C22⋊D11—28no—
30C2×C4×C22⋊D11C2212yes—
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C2×#66979C2212yes—
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38#10622860C2212yes—
39#10622826C2214yes—
40#10622825C2212yescomplemented
41#10622825C2212yescomplemented
42#10622824C2212yes—
43#10622824C2214yescomplemented
44#10622823C2214yescomplemented
45C4×C22⋊Dic11C2212yescomplemented
46C4×C22⋊Dic11C2212yescomplemented
47#10622606C2214yescomplemented
48#10622605C2214yescomplemented
49#10622600C2214yescomplemented
50#10622600C2214yescomplemented
51#10622595C2214yescomplemented
52#10622593C2214yescomplemented
53#10622586C2214yescomplemented
54#10622586C2214yescomplemented
55#10622572C2218yes—
56#10622568C2214yes—
57#10622565C2218yescomplemented
58#10622559C2214yes—
59#10622559C2214yes—
60#10622556C2214yes—
61#10622553C2218yescomplemented
62C4×(C2×D11)⋊C4C2218yescomplemented
63#10622546C2218yescomplemented
64C4×Dic11⋊C4C2218yescomplemented
65C25×C11C2311yescharacteristic
66C24×D11C2311yescharacteristic
67C23×C4×C11—28no—
68C23×C4×C11D418yes—
69C23×C4×C11C2312yes—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2312yes—
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—24no—
78C22×C22⋊D11—28no—
79C22×C22⋊D11C2312yes—
80C22×C22⋊D11C2312yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×C4×D11—24no—
85C22×C4×D11—28no—
86C22×C4×D11C2312yes—
87C22×C4×D11C2312yes—
88C11×#117—28no—
89C11×#117—28no—
90C11×#117—28no—
91C11×#117—28no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4—28no—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C42×C11—28no—
102C2×C42×C11C2314yes—
103C2×C42×C11C2314yes—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2312yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110#66982—216no—
111C4×C22⋊D11—28no—
112C4×C22⋊D11—28no—
113C4×C22⋊D11—28no—
114C4×C22⋊D11—28no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2318yes—
119C2×(C2×D11)⋊C4C2318yes—
120#66979—28no—
121C2×C4⋊Dic11C2314yes—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4C2318yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2318yes—
127C2×C4×Dic11—24no—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2312yes—
131C11⋊#95C2318yes—
132C11⋊#95C2318yes—
133C11⋊#95C2314yes—
134C11⋊#95C2318yes—
135C11⋊#95C2318yes—
136C11⋊#95C2314yes—
137#34809—111nomaximal, Sylow
138C24×C11—24no—
139C24×C11—24no—
140C24×C11—42no—
141C24×C11C2×D414yes—
142C24×C11C2411yescharacteristic
143C24×C11C2411yescharacteristic
144C24×C11C2411yescharacteristic
145C23×D11—22no—
146C23×D11—24no—
147C23×D11—24no—
148C23×D11—42no—
149C23×D11C2412yes—
150C22×C4×C11—24no—
151C22×C4×C11—232no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—28no—
159C22×C4×C11—44no—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11#4118yes—
167C22×C4×C11C2414yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C2×C22⋊D11—232no—
174C2×C22⋊D11—24no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—24no—
177C2×C22⋊D11—24no—
178C2×C22⋊D11—24no—
179C2×C22⋊D11#4118yes—
180C22×Dic11—24no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—24no—
185C22×Dic11—42no—
186C22×Dic11C2412yes—
187C22×Dic11C2418yes—
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—416no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—28no—
201C42×C11—28no—
202C42×C11—28no—
203C22⋊Dic11—24no—
204C22⋊Dic11—24no—
205C22⋊Dic11—28no—
206C22⋊Dic11—28no—
207C22⋊Dic11—44no—
208(C2×D11)⋊C4—216no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—48no—
212C4⋊Dic11—28no—
213Dic11⋊C4—216no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216Dic11⋊C4—48no—
217C4×Dic11—24no—
218C4×Dic11—24no—
219C4×Dic11—28no—
220C22×C4×D4—111no—
221C22×#117D1111yescharacteristic, complemented
222#2487—112no—
223#2486—112no—
224#2485—114no—
225#2484—112no—
226#2483—112no—
227#2482—112no—
228#2405—112no—
229#2395—114no—
230C4×#123—114no—
231#2296—112no—
232#2280—111no—
233#2280—112no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—28no—
239C23×C11—28no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—44no—
244C23×C11—416no—
245C23×C11C22×D412yes—
246C23×C11C22×D412yes—
247C23×C11C22×D412yes—
248C23×C11C2×#4114yes—
249C23×C11C2×#4114yes—
250C23×C11C2511yescharacteristic
251C22×D11—28no—
252C22×D11—22no—
253C22×D11—24no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—416no—
257C22×D11—44no—
258C22×D11—44no—
259C22×D11C2×#4114yes—
260C2×C4×C11—28no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—28no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—28no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—28no—
270C2×C4×C11—28no—
271C2×C4×C11—48no—
272C2×C4×C11—48no—
273C2×C4×C11#123116yescomplemented
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C2×#4114yes—
279C2×C4×C11C2×#4114yes—
280C22⋊D11—216no—
281C22⋊D11—216no—
282C2×Dic11—28no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—28no—
288C2×Dic11—28no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—28no—
292C2×Dic11—44no—
293C2×Dic11—44no—
294C2×Dic11C2×#4114yes—
295C4×D11—48no—
296C4×D11—48no—
297C23×D4—111no—
298C24×C4—111no—
299C24×C4C2×D1111yescharacteristic
300C2×#123—114no—
301C2×C4×D4—112no—
302C2×C4×D4—112no—
303C2×C4×D4—112no—
304C2×C4×D4—112no—
305C2×C4×D4—228no—
306C2×#117—28no—
307C2×#117—112no—
308C2×#117C2×D1112yes—
309C2×#117C2×D1112yes—
310C2×#117C2×D1112yescomplemented
311C2×#117C2×D1112yescomplemented
312C22×C4⋊C4—111no—
313C22×C4⋊C4C2×D1111yescharacteristic, complemented
314C22×C4⋊C4C2×D1111yescharacteristic, complemented
315C22×C22⋊C4—111no—
316C22×C22⋊C4—111no—
317C22×C22⋊C4C2×D1112yes—
318C22×C42—111no—
319C22×C42C2×D1112yescomplemented
320#400—114no—
321#399—114no—
322#398—114no—
323#397—114no—
324#397—118no—
325#394—118no—
326#389—114no—
327#389—114no—
328#388—118no—
329#387—118no—
330#386—114no—
331#385—114no—
332#385—114no—
333#385—114no—
334#381—112no—
335#381—114no—
336#381—114no—
337#380—112no—
338#380—112no—
339#380—114no—
340#380—114no—
341#379—112no—
342#379—114no—
343C4×C4⋊C4—118no—
344C4×C22⋊C4—112no—
345C4×C22⋊C4—112no—
346C4×C22⋊C4—118no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—28no—
352C22×C11—28no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—416no—
357C22×C11—44no—
358C22×C11C2×#12314yes—
359C22×C11#52514yes—
360C22×C11C23×D411yescharacteristic
361C22×C11C22×#4112yes—
362C22×C11C22×#4112yes—
363C22×C11#58512yes—
364C2×D11—24no—
365C2×D11—28no—
366C2×D11—416no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—44no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—44no—
373C4×C11—44no—
374C4×C11C2×#12314yes—
375C4×C11C2×#12314yes—
376Dic11—24no—
377Dic11—42no—
378Dic11—42no—
379Dic11—48no—
380C25—111no—
381C25C22×D1111yescharacteristic
382C22×D4—112no—
383C22×D4—112no—
384C22×D4—228no—
385C22×D4—224no—
386C23×C4—28no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—112no—
391C23×C4—112no—
392C23×C4—228no—
393C23×C4—224no—
394C23×C4C22⋊D1118yes—
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1112yes—
402C23×C4C22×D1111yescharacteristic
403#123—2216no—
404C4×D4—228no—
405C4×D4—228no—
406C4×D4—228no—
407C4×D4—228no—
408#117—28no—
409#117—28no—
410#117—28no—
411#117—28no—
412#117—228no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—118no—
419C2×C4⋊C4—118no—
420C2×C4⋊C4—224no—
421C2×C4⋊C4C22×D1112yes—
422C2×C4⋊C4C22×D1112yes—
423C2×C4⋊C4C22×D1112yes—
424C2×C4⋊C4C22×D1112yes—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—112no—
427C2×C22⋊C4—112no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—112no—
431C2×C22⋊C4—112no—
432C2×C22⋊C4—118no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—118no—
435C2×C22⋊C4—224no—
436C2×C22⋊C4—224no—
437C2×C22⋊C4C22×D1114yes—
438C2×C22⋊C4C22×D1114yes—
439C2×C42—28no—
440C2×C42—112no—
441C2×C42—114no—
442C2×C42—112no—
443C2×C42—224no—
444C2×C42C22×D1114yes—
445C2×C42C22×D1114yes—
446#95—118no—
447#95—118no—
448#95—114no—
449#95—114no—
450#95—118no—
451#95—118no—
452C2×C11—24no—
453C2×C11—24no—
454C2×C11—42no—
455C2×C11C22×#12311yescharacteristic
456C2×C11C2×#52511yescharacteristic
457C2×C11#344911yescharacteristic
458C2×C11#347514yes—
459D11—44no—
460C24—24no—
461C24—24no—
462C24—42no—
463C24—112no—
464C24—224no—
465C24—222no—
466C24—224no—
467C24—442no—
468C24C2×C22⋊D1114yes—
469C24C23×D1111yescharacteristic
470C24C23×D1111yescharacteristic
471C24C23×D1111yescharacteristic
472C2×D4—118no—
473C2×D4—224no—
474C2×D4—224no—
475C2×D4—2232no—
476C2×D4—224no—
477C2×D4—224no—
478C2×D4—224no—
479C22×C4—24no—
480C22×C4—232no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—28no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—44no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—118no—
492C22×C4—112no—
493C22×C4—224no—
494C22×C4—222no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—228no—
499C22×C4—228no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—442no—
503C22×C4—4416no—
504C22×C4#433918yes—
505C22×C4C2×C22⋊D1114yes—
506C22×C4C2×C22⋊D1114yes—
507C22×C4C2×C22⋊D1114yes—
508C22×C4C2×C22⋊D1114yes—
509C22×C4C2×C22⋊D1114yes—
510C22×C4C2×C22⋊D1114yes—
511C22×C4C23×D1114yes—
512C22×C4C23×D1114yes—
513C22×C4C23×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—2216no—
522C4⋊C4—228no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—448no—
526C22⋊C4—28no—
527C22⋊C4—28no—
528C22⋊C4—2216no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—448no—
536C22⋊C4—444no—
537C42—28no—
538C42—28no—
539C42—228no—
540C42—224no—
541C42—224no—
542C11#3480911yescharacteristic, complemented, Sylow
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—28no—
548C23—28no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—44no—
553C23—416no—
554C23—114no—
555C23—228no—
556C23—224no—
557C23—222no—
558C23—224no—
559C23—222no—
560C23—4416no—
561C23—444no—
562C23—444no—
563C23C2×#433914yes—
564C23#41×D1114yes—
565C23C22×C22⋊D1112yes—
566C23C22×C22⋊D1112yes—
567C23C22×C22⋊D1112yes—
568C23C24×D1111yescharacteristic
569D4—2216no—
570D4—2216no—
571C2×C4—28no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—48no—
583C2×C4—48no—
584C2×C4—114no—
585C2×C4—228no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—228no—
589C2×C4—224no—
590C2×C4—228no—
591C2×C4—228no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—444no—
596C2×C4—444no—
597C2×C4—448no—
598C2×C4—448no—
599C2×C4#66982116yescomplemented
600C2×C4C2×#433914yes—
601C2×C4C2×#433914yes—
602C2×C4C22×C22⋊D1112yes—
603C2×C4C22×C22⋊D1112yes—
604C2×C4C22×C22⋊D1112yes—
605C2×C4C22×C22⋊D1112yes—
606C22—28no—
607C22—28no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—44no—
617C22—228no—
618C22—224no—
619C22—4416no—
620C22—444no—
621C22—442no—
622C22—442no—
623C22C2×#6698214yes—
624C22#1062335914yes—
625C22C22×#433912yes—
626C22C2×#41×D1112yes—
627C22#1062345312yes—
628C22C23×C22⋊D1111yescharacteristic
629C4—22no—
630C4—22no—
631C4—44no—
632C4—44no—
633C4—224no—
634C4—448no—
635C4—442no—
636C4—442no—
637C4C2×#6698214yes—
638C4C2×#6698214yes—
639C2—24no—
640C2—24no—
641C2—42no—
642C2—444no—
643C2C22×#6698211yescharacteristic
644C2C2×#1062335911yescharacteristic
645C2#1308194511yescharacteristic
646C2#1308217014yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
prime radicalC23×C22⋊D11C22
hypercenterC22×#117D11
hypocenterC11#34809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13072927C2semidirect
3. #13072918C2semidirect
4. #13072907C2semidirect
5. #13072899C2semidirect
6. #13072894C2semidirect
7. #13072886C2semidirect
9. #13071873C2semidirect
10. C4×#66982C2semidirect
11. #13071098C2semidirect
12. #13070999C2semidirect
13. #13070995C2semidirect
14. C22×C11×#117C2semidirect
21. C2×C11×#117C22semidirect
22. C2×C11×#117C22semidirect
23. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C4⋊C4C22semidirect
26. C22×C42×C11C22semidirect
40. #10622825C22semidirect
41. #10622825C22semidirect
43. #10622824C22semidirect
44. #10622823C22semidirect
45. C4×C22⋊Dic11C22semidirect
46. C4×C22⋊Dic11C22semidirect
47. #10622606C22semidirect
48. #10622605C22semidirect
49. #10622600C22semidirect
50. #10622600C22semidirect
51. #10622595C22semidirect
52. #10622593C22semidirect
53. #10622586C22semidirect
54. #10622586C22semidirect
57. #10622565C22semidirect
61. #10622553C22semidirect
62. C4×(C2×D11)⋊C4C22semidirect
63. #10622546C22semidirect
64. C4×Dic11⋊C4C22semidirect
221. C22×#117D11semidirect
273. C2×C4×C11#123semidirect
310. C2×#117C2×D11semidirect
311. C2×#117C2×D11semidirect
313. C22×C4⋊C4C2×D11semidirect
314. C22×C4⋊C4C2×D11semidirect
319. C22×C42C2×D11semidirect
542. C11#34809semidirect
599. C2×C4#66982semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130729272
#130729182
#130729072
#130728992
#130728942
#130728862
#130719432
#130718732
C4×#669822
#130710982
#130709992
#130709952
C22×C11×#1172
#3480911