Finite Group Databasebeta

← #14914703

Subgroups — #14914703

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623052C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic
3C22×#66946C211yesmaximal, characteristic
4#13071525C214yesmaximal, complemented
5#13071524C214yesmaximal, complemented
6#13071517C214yesmaximal, complemented
7#13071516C214yesmaximal, complemented
8#13071240C211yesmaximal, characteristic, complemented
9#13071227C214yesmaximal, complemented
10#13071100C211yesmaximal, characteristic, complemented
11#13071098C211yesmaximal, characteristic, complemented
12D11×#385C214yesmaximal, complemented
13C11×#2317C211yesmaximal, characteristic, complemented
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23#10623052—28no—
24#10623052C4116yescomplemented
25C2×#66946—28no—
26C2×#66946C2212yes—
27C2×#66946C2214yes—
28C2×#66946C2214yes—
29C2×#66946C2212yes—
30C2×#66946C2214yes—
31C2×C4⋊C4×D11C2218yescomplemented
32C2×C22⋊C4×D11C2214yes—
33C2×C22⋊C4×D11C2214yes—
34C2×C4×D44C2212yes—
35C2×C4×D44C2212yes—
36C2×C4×D44C2214yes—
37C11×#389C2214yescomplemented
38C11×#385C2214yes—
39C11×#384C2212yescomplemented
40C11×#382C2212yescomplemented
41#10622823C2214yes—
42#10622602C2218yescomplemented
43#10622602C2218yescomplemented
44#10622600C2218yescomplemented
45#10622598C2212yescomplemented
46#10622598C2212yescomplemented
47#10622590C2212yescomplemented
48#10622589C2212yescomplemented
49#10622586C2214yescomplemented
50#10622586C2212yescomplemented
51#10622586C2212yescomplemented
52#10622563C2212yes—
53#10622563C2212yes—
54#10622559C2212yes—
55#10622559C2212yes—
56C4×C4⋊Dic11C2214yescomplemented
57C4×Dic11⋊C4C2214yescomplemented
58#10622281C2218yescomplemented
59#10622281C2218yescomplemented
60#10622280C2218yescomplemented
61D11×#95C2218yescomplemented
62C24×D11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×D44C2×C418yes—
68C22×D44D418yes—
69C22×D44Q818yes—
70C22×D44C2312yes—
71C22×D44C2312yes—
72C22×C4×D11—28no—
73C22×C4×D11—48no—
74C22×C4×D11C2318yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2318yes—
78C11×#117—24no—
79C11×#117C2×C418yescomplemented
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C42×C11C2312yes—
90C2×C42×C11C2312yes—
91C2×C22⋊Dic11C2312yes—
92C2×C22⋊Dic11C2312yes—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98#66979—24no—
99#66979C2×C418yescomplemented
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2314yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2312yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2318yes—
107C2×Dic11⋊C4C2314yes—
108C2×C4×Dic11—24no—
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113#66946—216no—
114#66946—216no—
115#66946—28no—
116#66946—28no—
117#66946C2×C4132yescomplemented
118C4⋊C4×D11—416no—
119C22⋊C4×D11—216no—
120C22⋊C4×D11C2×C4132yescomplemented
121C4×D44—28no—
122C4×D44—28no—
123C4×D44C2×C4132yescomplemented
124C11×#95C2318yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2318yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130#34248—111nomaximal, Sylow
131C24×C11C2411yescharacteristic
132C23×D11—44no—
133C23×D11—44no—
134C23×D11C22×C418yes—
135C23×D11C2×D418yes—
136C23×D11C2×Q818yes—
137C23×D11C2414yes—
138C22×C4×C11—24no—
139C22×C4×C11—44no—
140C22×C4×C11C22×C414yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×Q814yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C2×D44C4⋊C4164yescomplemented
159C2×D44C22×C418yes—
160C2×D44C22×C418yes—
161C2×D44C2×D418yes—
162C2×D44C2×D418yes—
163C2×D44C2×Q818yes—
164C2×D44C2×Q818yes—
165C2×C4×D11—216no—
166C2×C4×D11—216no—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—48no—
174C2×C4×D11—432no—
175C2×C4×D11C22×C4132yescomplemented
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—48no—
181C11×C4⋊C4C22×C418yescomplemented
182C11×C22⋊C4—24no—
183C11×C22⋊C4C22×C418yes—
184C42×C11—24no—
185C42×C11C22×C418yescomplemented
186C22⋊Dic11—24no—
187C22⋊Dic11C22×C418yes—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4C22×C4132yescomplemented
192C4⋊Dic11—28no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—44no—
196C4⋊Dic11C22×C418yescomplemented
197Dic11⋊C4—28no—
198Dic11⋊C4—48no—
199Dic11⋊C4—44no—
200C4×Dic11—24no—
201C4×Dic11—24no—
202C4×Dic11—24no—
203C4×Dic11C22×C418yescomplemented
204C2×#518—111no—
205C2×#518—111no—
206C22×C4×D4—111no—
207#2349—114no—
208#2349—114no—
209D4×C4⋊C4—114no—
210D4×C4⋊C4—114no—
211#2317—111no—
212#2317D1111yescharacteristic, complemented
213#2315—114no—
214#2296—111no—
215#2296—111no—
216C2×#385—114no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11C23×C412yes—
220C23×C11C22×D412yes—
221C23×C11C22×Q812yes—
222C23×C11C2511yescharacteristic
223C22×D11—28no—
224C22×D11—28no—
225C22×D11—48no—
226C22×D11—416no—
227C22×D11—48no—
228C22×D11—416no—
229C22×D11C2×C4⋊C4132yescomplemented
230C22×D11C23×C418yes—
231C22×D11C22×D418yes—
232C22×D11C22×Q818yes—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—28no—
240C2×C4×C11—24no—
241C2×C4×C11—48no—
242C2×C4×C11C2×C4⋊C4116yescomplemented
243C2×C4×C11C23×C418yes—
244C2×C4×C11C23×C412yes—
245C2×C4×C11C23×C412yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×Q812yes—
249C2×C4×C11C22×Q812yes—
250C2×Dic11—28no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—44no—
263C2×Dic11C23×C418yes—
264C2×Dic11H(5,𝔽2)14yes—
265D44C2×C4⋊C4132yescomplemented
266D44C2×C4⋊C4132yescomplemented
267C4×D11—432no—
268C4×D11—432no—
269C4×D11—88no—
270C4×D11—88no—
271C23×D4—111no—
272C24×C4—112no—
273#518—1116no—
274#518—228no—
275C2×C4×D4—114no—
276C2×C4×D4—112no—
277C2×C4×D4—114no—
278C2×C4×D4—114no—
279C2×C4×D4—112no—
280C2×C4×D4—114no—
281C2×C4×D4—112no—
282C2×C4×D4—112no—
283C2×C4×D4—228no—
284C2×#117—111no—
285C2×#117—111no—
286C2×#117C2×D1111yescharacteristic
287C2×#117C2×D1111yescharacteristic
288C22×C4⋊C4—118no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4—114no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—114no—
293C22×C42—111no—
294#389—114no—
295#389—112no—
296#389—112no—
297#389—112no—
298#389—112no—
299#389C2×D1114yescomplemented
300#385—114no—
301#385—118no—
302#385—118no—
303#385—112no—
304#385—112no—
305#385—112no—
306#385—112no—
307#385—118no—
308#385—118no—
309#385C2×D1114yes—
310#384—112no—
311#384C2×D1112yescomplemented
312#382—112no—
313#382C2×D1112yescomplemented
314#380—118no—
315#380—118no—
316C4×C4⋊C4—114no—
317C4×C4⋊C4—114no—
318C2×#95—118no—
319C22×C11—24no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—24no—
323C22×C11C22×C4⋊C414yes—
324C22×C11C24×C411yescharacteristic
325C22×C11C23×D411yescharacteristic
326C22×C11C23×Q811yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11#58512yes—
329C2×D11—216no—
330C2×D11—28no—
331C2×D11—28no—
332C2×D11—216no—
333C2×D11—432no—
334C2×D11C22×C4⋊C4116yes—
335C4×C11—28no—
336C4×C11—44no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11C22×C4⋊C414yes—
340C4×C11C22×C4⋊C414yes—
341Dic11—28no—
342Dic11—24no—
343Dic11—42no—
344Dic11—42no—
345Dic11—42no—
346C25—112no—
347C22×D4—118no—
348C22×D4—118no—
349C22×D4—118no—
350C22×D4—112no—
351C22×D4—112no—
352C23×C4—118no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—114no—
357C23×C4—114no—
358C23×C4—228no—
359C23×C4—448no—
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C4×D4—1132no—
363C4×D4—1132no—
364C4×D4—228no—
365C4×D4—228no—
366C4×D4—2216no—
367C4×D4—2216no—
368C4×D4—228no—
369C4×D4—228no—
370#117—24no—
371#117—118no—
372#117—224no—
373#117C4×D1118yescomplemented
374C2×C4⋊C4—24no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—4416no—
384C2×C4⋊C4C22×D1112yes—
385C2×C4⋊C4C22×D1112yes—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1118yes—
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—1132no—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—2216no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4C22×D1112yes—
400C2×C22⋊C4C22×D1112yes—
401C2×C42—112no—
402C2×C42—112no—
403C2×C42—112no—
404C2×C42—112no—
405C2×C42—224no—
406C2×C42C22×D1112yes—
407C2×C42C22×D1112yes—
408#95—114no—
409#95—114no—
410#95—118no—
411#95—114no—
412#95—114no—
413#95C22×D1118yes—
414C2×C11—24no—
415C2×C11C23×C4⋊C411yescharacteristic
416C2×C11C4×H(5,𝔽2)12yes—
417C2×C11#348411yescharacteristic
418C2×C11#348511yescharacteristic
419C2×C11#350112yes—
420D11—216no—
421C24—114no—
422C24—118no—
423C24—118no—
424C24—118no—
425C24—444no—
426C24—444no—
427C24C23×D1111yescharacteristic
428C2×D4—1164no—
429C2×D4—118no—
430C2×D4—118no—
431C2×D4—118no—
432C2×D4—118no—
433C2×D4—118no—
434C2×D4—118no—
435C22×C4—24no—
436C22×C4—44no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—1132no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—2216no—
444C22×C4—2216no—
445C22×C4—228no—
446C22×C4—228no—
447C22×C4—224no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—448no—
451C22×C4—448no—
452C22×C4—448no—
453C22×C4—448no—
454C22×C4—448no—
455C22×C4—4432no—
456C22×C4—442no—
457C22×C4C2×C4×D1114yes—
458C22×C4D4×D1114yes—
459C22×C4Q8×D1114yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1114yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1111yescharacteristic
465C22×C4C23×D1111yescharacteristic
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—48no—
471C4⋊C4—118no—
472C4⋊C4—228no—
473C4⋊C4—228no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—448no—
477C4⋊C4—444no—
478C4⋊C4—444no—
479C4⋊C4C2×C4×D1118yescomplemented
480C22⋊C4—24no—
481C22⋊C4—118no—
482C22⋊C4—1132no—
483C22⋊C4—228no—
484C22⋊C4—228no—
485C22⋊C4—2216no—
486C22⋊C4—224no—
487C22⋊C4C2×C4×D1118yes—
488C42—24no—
489C42—118no—
490C42—224no—
491C42—224no—
492C42—224no—
493C42C2×C4×D1118yescomplemented
494C11#3424811yescharacteristic, complemented, Sylow
495C23—22no—
496C23—22no—
497C23—118no—
498C23—118no—
499C23—118no—
500C23—1132no—
501C23—228no—
502C23—228no—
503C23—448no—
504C23—4416no—
505C23—448no—
506C23—4416no—
507C23C22×C4×D1112yes—
508C23C2×D4×D1112yes—
509C23C2×Q8×D1112yes—
510C23C24×D1111yescharacteristic
511D4—1132no—
512D4—1132no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—28no—
520C2×C4—24no—
521C2×C4—48no—
522C2×C4—118no—
523C2×C4—114no—
524C2×C4—228no—
525C2×C4—222no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—4432no—
537C2×C4—4432no—
538C2×C4—444no—
539C2×C4—888no—
540C2×C4—888no—
541C2×C4C4⋊C4×D11116yescomplemented
542C2×C4C22×C4×D1118yes—
543C2×C4C22×C4×D1112yes—
544C2×C4C22×C4×D1112yes—
545C2×C4C2×D4×D1112yes—
546C2×C4C2×D4×D1112yes—
547C2×C4C2×Q8×D1112yes—
548C2×C4C2×Q8×D1112yes—
549C22—24no—
550C22—22no—
551C22—22no—
552C22—24no—
553C22—1116no—
554C22—2216no—
555C22—228no—
556C22—228no—
557C22—2216no—
558C22—4432no—
559C22C2×C4⋊C4×D1114yes—
560C22C23×C4×D1111yescharacteristic
561C22C22×D4×D1111yescharacteristic
562C22C22×Q8×D1111yescharacteristic
563C22D11×H(5,𝔽2)12yes—
564C22#1062345712yes—
565C4—28no—
566C4—44no—
567C4—42no—
568C4—42no—
569C4—224no—
570C4—228no—
571C4—442no—
572C4—442no—
573C4—442no—
574C4C2×C4⋊C4×D1114yes—
575C4C2×C4⋊C4×D1114yes—
576C2—24no—
577C2—2216no—
578C2C22×C4⋊C4×D1111yescharacteristic
579C2#1308182212yes—
580C2#1308225011yescharacteristic
581C2#1308225911yescharacteristic
582C2#1308241812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2317C2
socle, cosocleC23×C11C25
prime radicalC23×D44C22
hypercenter#2317D11
hypocenterC11#34248
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. #13071525C2semidirect
5. #13071524C2semidirect
6. #13071517C2semidirect
7. #13071516C2semidirect
8. #13071240C2semidirect
9. #13071227C2semidirect
10. #13071100C2semidirect
11. #13071098C2semidirect
12. D11×#385C2semidirect
13. C11×#2317C2semidirect
24. #10623052C4semidirect
31. C2×C4⋊C4×D11C22semidirect
37. C11×#389C22semidirect
39. C11×#384C22semidirect
40. C11×#382C22semidirect
42. #10622602C22semidirect
43. #10622602C22semidirect
44. #10622600C22semidirect
45. #10622598C22semidirect
46. #10622598C22semidirect
47. #10622590C22semidirect
48. #10622589C22semidirect
49. #10622586C22semidirect
50. #10622586C22semidirect
51. #10622586C22semidirect
56. C4×C4⋊Dic11C22semidirect
57. C4×Dic11⋊C4C22semidirect
58. #10622281C22semidirect
59. #10622281C22semidirect
60. #10622280C22semidirect
61. D11×#95C22semidirect
79. C11×#117C2×C4semidirect
99. #66979C2×C4semidirect
117. #66946C2×C4semidirect
120. C22⋊C4×D11C2×C4semidirect
123. C4×D44C2×C4semidirect
158. C2×D44C4⋊C4semidirect
175. C2×C4×D11C22×C4semidirect
181. C11×C4⋊C4C22×C4semidirect
185. C42×C11C22×C4semidirect
191. (C2×D11)⋊C4C22×C4semidirect
196. C4⋊Dic11C22×C4semidirect
203. C4×Dic11C22×C4semidirect
212. #2317D11semidirect
229. C22×D11C2×C4⋊C4semidirect
242. C2×C4×C11C2×C4⋊C4semidirect
265. D44C2×C4⋊C4semidirect
266. D44C2×C4⋊C4semidirect
299. #389C2×D11semidirect
311. #384C2×D11semidirect
313. #382C2×D11semidirect
373. #117C4×D11semidirect
479. C4⋊C4C2×C4×D11semidirect
493. C42C2×C4×D11semidirect
494. C11#34248semidirect
541. 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×#106230522
C22×#669462
#130715252
#130715242
#130715172
#130715162
#130712402
#130712272
#130711002
#130710982
D11×#3852
C11×#23172
#3424811