Finite Group Databasebeta

← #14913874

Subgroups — #14913874

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3C2×#10623053C211yesmaximal, characteristic
4#13071530C214yesmaximal, complemented
5#13071517C214yesmaximal, complemented
6#13071514C218yesmaximal, complemented
7#13071241C212yesmaximal, complemented
8#13071239C211yesmaximal, characteristic, complemented
9#13071237C212yesmaximal, complemented
10#13071022C212yesmaximal, complemented
11#13071019C211yesmaximal, characteristic, complemented
12C2×#10622589C211yesmaximal, characteristic, complemented
13D11×#384C212yesmaximal, complemented
14C11×#2317C211yesmaximal, characteristic, complemented
15C22×#4339C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×C4×C22⋊D11C2214yes—
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2214yes—
23C22×C4×Dic11C2211yescharacteristic
24#10623054—28no—
25#10623053C4116yescomplemented
26#10623035—28no—
27C2×#66946C2212yes—
28C2×#66946C2212yes—
29C2×#66945C2212yes—
30C2×#66945C2212yes—
31C2×C4⋊C4×D11C2212yes—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2218yes—
34C2×#66940C2212yes—
35C2×#66940C2212yes—
36C2×(C22⋊D11)⋊C4C2214yes—
37C2×(C22⋊D11)⋊C4C2214yes—
38C2×C4×D44C2212yes—
39C2×#66925C2212yes—
40C2×C42×D11C2212yes—
41C2×C4×Dic22C2212yes—
42C11×#389C2214yes—
43C11×#385C2214yes—
44C11×#384C2212yes—
45C11×#382C2212yes—
46#10622602C2218yes—
47#10622598C2214yes—
48#10622590C2211yescharacteristic
49#10622590C2211yescharacteristic
50#10622589C2212yes—
51#10622589C2218yes—
52#10622589C2214yes—
53#10622589C2211yescharacteristic
54#10622589C2212yes—
55#10622589C2211yescharacteristic
56#10622585C2218yes—
57#10622563C2214yes—
58#10622555C2214yes—
59#10622549C2212yes—
60#10622548C2212yes—
61C4×Dic11⋊C4C2214yes—
62#10622281C2218yes—
63#10622280C2218yes—
64#10622262C2218yes—
65#10622260C2218yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C2×#4339C2×C418yes—
72C2×#4339D418yes—
73C2×#4339Q818yes—
74C22×D44C2311yescharacteristic
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2312yes—
79C22×Dic22C2311yescharacteristic
80C11×#117—24no—
81C11×#117C2×C418yescomplemented
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2318yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C4×C22⋊D11—216no—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98#66979—24no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2318yes—
105C2×Dic11⋊C4—48no—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2318yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2318yes—
112C2×Dic11⋊C4C2314yes—
113C2×C4×Dic11C2×C418yescomplemented
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2312yes—
121#66946—28no—
122#66946C2×C4116yescomplemented
123#66945—28no—
124#66945—28no—
125C4⋊C4×D11—28no—
126C4⋊C4×D11—28no—
127C4⋊C4×D11—416no—
128#66940—28no—
129#66940C2×C4116yescomplemented
130(C22⋊D11)⋊C4—216no—
131(C22⋊D11)⋊C4C2×C4132yescomplemented
132C4×D44—28no—
133#66925C2×C4116yescomplemented
134C42×D11C2×C4116yescomplemented
135C4×Dic22—28no—
136C11×#95C2318yes—
137C11⋊#95C2314yes—
138C11⋊#95C2318yes—
139C11⋊#95C2314yes—
140#34183—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11C2412yes—
143C22×C4×C11—24no—
144C22×C4×C11—44no—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×Q814yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11C22×C418yes—
155C2×C22⋊D11C2×D418yes—
156C2×C22⋊D11C2×Q818yes—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—44no—
161C22×Dic11C22×C418yes—
162C22×Dic11C2412yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168#4339C4⋊C4164yescomplemented
169C2×D44C22×C414yes—
170C2×D44C2×D414yes—
171C2×D44C2×Q814yes—
172C2×C4×D11—28no—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11—48no—
177C2×C4×D11—48no—
178C2×C4×D11C22×C4116yes—
179C2×C4×D11C22×C418yes—
180C2×C4×D11C2×D418yes—
181C2×C4×D11C2×Q818yes—
182C2×Dic22C22×C414yes—
183C2×Dic22C2×D414yes—
184C2×Dic22C2×Q814yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—48no—
190C11×C4⋊C4C22×C418yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4C22×C418yes—
193C42×C11—24no—
194C42×C11C22×C418yes—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4C22×C4116yes—
199C4⋊Dic11—24no—
200C4⋊Dic11—22no—
201C4⋊Dic11—24no—
202C4⋊Dic11—22no—
203C4⋊Dic11—48no—
204Dic11⋊C4—28no—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207Dic11⋊C4—216no—
208Dic11⋊C4—28no—
209Dic11⋊C4—48no—
210Dic11⋊C4C22×C4116yes—
211C4×Dic11—28no—
212C4×Dic11—28no—
213C4×Dic11—24no—
214C4×Dic11C22×C414yes—
215C4×Dic11C22×C4116yes—
216C4×Dic11C22×C414yes—
217C4×Dic11C22×C418yes—
218C2×#520—111no—
219C2×#520—111no—
220C2×C4×#41—111no—
221Q8×C4⋊C4—114no—
222D4×C4⋊C4—114no—
223D4×C4⋊C4—118no—
224#2317—112no—
225#2317—112no—
226#2317—111no—
227#2317D1111yescharacteristic, complemented
228#2285—112no—
229#2285—111no—
230C2×#384—112no—
231C2×#384—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11C23×C412yes—
235C23×C11C22×D412yes—
236C23×C11C22×Q812yes—
237C23×C11C2511yescharacteristic
238C22×D11—24no—
239C22×D11—24no—
240C22×D11C23×C414yes—
241C22×D11C22×D414yes—
242C22×D11C22×Q814yes—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—28no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—84no—
252C2×C4×C11C2×C4⋊C4116yescomplemented
253C2×C4×C11C23×C418yes—
254C2×C4×C11C23×C412yes—
255C2×C4×C11C23×C412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×Q812yes—
259C2×C4×C11C22×Q812yes—
260C22⋊D11C2×C4⋊C4132yescomplemented
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—216no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—28no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—84no—
271C2×Dic11C23×C414yes—
272C2×Dic11C23×C414yes—
273C2×Dic11C23×C414yes—
274C2×Dic11C22×D414yes—
275C2×Dic11C22×Q814yes—
276C2×Dic11H(5,𝔽2)14yes—
277C2×Dic112−1+414yes—
278D44C2×C4⋊C4116yescomplemented
279C4×D11—232no—
280C4×D11—88no—
281C4×D11—88no—
282C4×D11C2×C4⋊C4132yescomplemented
283Dic22C2×C4⋊C4116yescomplemented
284C22×#41—111no—
285#520—228no—
286#520—228no—
287C4×#41—1116no—
288C2×C4×Q8—112no—
289C2×C4×Q8—112no—
290C2×C4×Q8—112no—
291C2×C4×D4—114no—
292C2×C4×D4—112no—
293C2×C4×D4—112no—
294C2×C4×D4—114no—
295C2×C4×D4—114no—
296C2×C4×D4—112no—
297C2×#117—111no—
298C2×#117—112no—
299C2×#117—112no—
300C2×#117—112no—
301C2×#117C2×D1111yescharacteristic
302C2×#117C2×D1111yescharacteristic
303C22×C4⋊C4—111no—
304C22×C4⋊C4—114no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4—112no—
307C22×C4⋊C4—118no—
308C22×C4⋊C4C2×D1111yescharacteristic
309C22×C42—111no—
310C22×C42—112no—
311#389—118no—
312#389—114no—
313#389—118no—
314#389C2×D1114yes—
315#385—118no—
316#385—114no—
317#385—118no—
318#385C2×D1114yes—
319#384—112no—
320#384—118no—
321#384—114no—
322#384—111no—
323#384—112no—
324#384—111no—
325#384—112no—
326#384C2×D1112yes—
327#382—111no—
328#382—111no—
329#382—112no—
330#382C2×D1112yes—
331#380—114no—
332#380—118no—
333C4×C4⋊C4—114no—
334C4×C4⋊C4—118no—
335C22×C11—24no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—24no—
339C22×C11C22×C4⋊C414yes—
340C22×C11C24×C411yescharacteristic
341C22×C11C23×D411yescharacteristic
342C22×C11C23×Q811yescharacteristic
343C22×C11C2×H(5,𝔽2)12yes—
344C22×C11C2×2−1+412yes—
345C2×D11—28no—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—28no—
349C2×D11C22×C4⋊C418yes—
350C4×C11—28no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11C22×C4⋊C414yes—
355C4×C11C22×C4⋊C414yes—
356Dic11—24no—
357Dic11—42no—
358Dic11—44no—
359Dic11—42no—
360Dic11C22×C4⋊C418yes—
361Dic11#52018yescomplemented
362C2×#41—118no—
363C2×#41—118no—
364C2×#41—118no—
365C22×Q8—111no—
366C22×D4—112no—
367C22×D4—111no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—114no—
371C23×C4—112no—
372C23×C4—114no—
373C23×C4—114no—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C4×Q8—1116no—
377C4×Q8—228no—
378C4×Q8—228no—
379C4×D4—1116no—
380C4×D4—1132no—
381C4×D4—228no—
382C4×D4—2216no—
383C4×D4—228no—
384C4×D4—2216no—
385#117—24no—
386#117—1116no—
387#117—228no—
388#117—228no—
389#117—224no—
390#117C4×D1118yescomplemented
391C2×C4⋊C4—24no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—118no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—118no—
404C2×C4⋊C4—228no—
405C2×C4⋊C4—228no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—4416no—
408C2×C4⋊C4—448no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1112yes—
411C2×C4⋊C4C22×D1112yes—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1118yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4C22×D1112yes—
420C2×C22⋊C4C22×D1112yes—
421C2×C42—118no—
422C2×C42—111no—
423C2×C42—114no—
424C2×C42—112no—
425C2×C42—111no—
426C2×C42—1116no—
427C2×C42—114no—
428C2×C42—114no—
429C2×C42—112no—
430C2×C42C22×D1112yes—
431C2×C42C22×D1112yes—
432#95—114no—
433#95—114no—
434#95—118no—
435#95C22×D1118yes—
436C2×C11—24no—
437C2×C11C23×C4⋊C411yescharacteristic
438C2×C11C2×#52012yes—
439C2×C11#349811yescharacteristic
440C2×C11#349911yescharacteristic
441C2×C11#350312yes—
442D11—28no—
443C24—112no—
444C24C23×D1111yescharacteristic
445#41—1164no—
446C2×Q8—114no—
447C2×Q8—114no—
448C2×Q8—114no—
449C2×D4—118no—
450C2×D4—118no—
451C2×D4—118no—
452C2×D4—114no—
453C2×D4—114no—
454C2×D4—114no—
455C22×C4—24no—
456C22×C4—44no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—118no—
460C22×C4—118no—
461C22×C4—118no—
462C22×C4—118no—
463C22×C4—112no—
464C22×C4—1116no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—228no—
469C22×C4—228no—
470C22×C4—228no—
471C22×C4—228no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—448no—
476C22×C4—448no—
477C22×C4—444no—
478C22×C4C2×C4×D1114yes—
479C22×C4D4×D1114yes—
480C22×C4Q8×D1114yes—
481C22×C4C23×D1112yes—
482C22×C4C23×D1112yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—48no—
492C4⋊C4—1116no—
493C4⋊C4—228no—
494C4⋊C4—228no—
495C4⋊C4—228no—
496C4⋊C4—2216no—
497C4⋊C4—228no—
498C4⋊C4—222no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—222no—
502C4⋊C4—448no—
503C4⋊C4—448no—
504C4⋊C4C2×C4×D1118yes—
505C22⋊C4—24no—
506C22⋊C4—1116no—
507C22⋊C4—228no—
508C22⋊C4—228no—
509C22⋊C4—224no—
510C22⋊C4C2×C4×D1118yes—
511C42—24no—
512C42—114no—
513C42—114no—
514C42—1116no—
515C42—118no—
516C42—228no—
517C42—228no—
518C42—224no—
519C42C2×C4×D1118yes—
520C11#3418311yescharacteristic, complemented, Sylow
521C23—22no—
522C23—22no—
523C23—114no—
524C23—114no—
525C23—114no—
526C23—224no—
527C23—224no—
528C23C22×C4×D1112yes—
529C23C2×D4×D1112yes—
530C23C2×Q8×D1112yes—
531C23C24×D1111yescharacteristic
532Q8—1116no—
533D4—1132no—
534D4—1116no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—84no—
544C2×C4—114no—
545C2×C4—114no—
546C2×C4—114no—
547C2×C4—114no—
548C2×C4—114no—
549C2×C4—114no—
550C2×C4—1132no—
551C2×C4—114no—
552C2×C4—2232no—
553C2×C4—2216no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—228no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—888no—
563C2×C4—888no—
564C2×C4—884no—
565C2×C4C4⋊C4×D11116yescomplemented
566C2×C4C22×C4×D1118yes—
567C2×C4C22×C4×D1112yes—
568C2×C4C22×C4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1112yes—
571C2×C4C2×Q8×D1112yes—
572C2×C4C2×Q8×D1112yes—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—24no—
577C22—118no—
578C22—224no—
579C22—224no—
580C22—228no—
581C22—228no—
582C22C2×C4⋊C4×D1114yes—
583C22C23×C4×D1111yescharacteristic
584C22C22×D4×D1111yescharacteristic
585C22C22×Q8×D1111yescharacteristic
586C22D11×H(5,𝔽2)12yes—
587C22D11×2−1+412yes—
588C4—28no—
589C4—44no—
590C4—42no—
591C4—42no—
592C4—118no—
593C4—118no—
594C4—224no—
595C4—442no—
596C4—444no—
597C4—442no—
598C4C2×C4⋊C4×D1114yes—
599C4C2×C4⋊C4×D1114yes—
600C2—24no—
601C2—228no—
602C2C22×C4⋊C4×D1111yescharacteristic
603C2D11×#52012yes—
604C2#1308239111yescharacteristic
605C2#1308239811yescharacteristic
606C2#1308243112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2317C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2317D11
hypocenterC11#34183
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. #13071530C2semidirect
5. #13071517C2semidirect
6. #13071514C2semidirect
7. #13071241C2semidirect
8. #13071239C2semidirect
9. #13071237C2semidirect
10. #13071022C2semidirect
11. #13071019C2semidirect
12. C2×#10622589C2semidirect
13. D11×#384C2semidirect
14. C11×#2317C2semidirect
25. #10623053C4semidirect
81. C11×#117C2×C4semidirect
113. C2×C4×Dic11C2×C4semidirect
122. #66946C2×C4semidirect
129. #66940C2×C4semidirect
131. (C22⋊D11)⋊C4C2×C4semidirect
133. #66925C2×C4semidirect
134. C42×D11C2×C4semidirect
168. #4339C4⋊C4semidirect
227. #2317D11semidirect
252. C2×C4×C11C2×C4⋊C4semidirect
260. C22⋊D11C2×C4⋊C4semidirect
278. D44C2×C4⋊C4semidirect
282. C4×D11C2×C4⋊C4semidirect
283. Dic22C2×C4⋊C4semidirect
361. Dic11#520semidirect
390. #117C4×D11semidirect
520. C11#34183semidirect
565. C2×C4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
C2×#106230542
C2×#106230532
#130715302
#130715172
#130715142
#130712412
#130712392
#130712372
#130710222
#130710192
C2×#106225892
D11×#3842
C11×#23172
#3418311