Finite Group Databasebeta

← #14914938

Subgroups — #14914938

Order 2816.

2946 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623057C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3C22×C4×Dic22C211yesmaximal, characteristic, complemented
4#13071685C214yesmaximal, complemented
5#13071672C214yesmaximal, complemented
6#13071642C214yesmaximal, complemented
7#13071620C214yesmaximal, complemented
8#13071284C214yesmaximal, complemented
9#13071200C211yesmaximal, characteristic, complemented
10#13071135C214yesmaximal, complemented
11#13071106C211yesmaximal, characteristic
12#13070972C211yesmaximal, characteristic, complemented
13C11×#2296C211yesmaximal, characteristic, complemented
14C22×#4339C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2212yes—
23#10623057C4116yescomplemented
24#10623054—28no—
25C2×#66950C2214yes—
26C2×#66945C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66939C2214yes—
29C2×(C22⋊D11)⋊C4C2214yes—
30C2×#66928C2212yes—
31C2×C4×D44C2212yes—
32C2×#66922C2212yes—
33C2×C4×Dic22—28no—
34C2×C4×Dic22C2214yes—
35C2×C4×Dic22C2212yes—
36C2×C4×Dic22C2214yes—
37C11×#389C2212yes—
38C11×#389C2212yes—
39C11×#385C2212yes—
40C11×#385C2212yes—
41C4×C11×C4⋊C4C2214yes—
42#10622826C2212yes—
43#10622826C2212yes—
44#10622603C2218yes—
45#10622602C2218yes—
46C4⋊C4×Dic11C2214yes—
47C4⋊C4×Dic11C2218yes—
48#10622587C2212yes—
49#10622587C2212yes—
50#10622586C2218yes—
51#10622556C2214yes—
52C22⋊C4×Dic11C2214yes—
53#10622552C2212yes—
54C4×(C2×D11)⋊C4C2214yes—
55C4×C4⋊Dic11C2214yes—
56#10622542C2212yes—
57#10622542C2214yes—
58#10622282C2218yes—
59#10622279C2218yes—
60#10622267C2218yes—
61#10622267C2218yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339C2×C418yes—
71C22×D44C2311yescharacteristic
72C22×C4×D11C2312yes—
73C22×C4×D11C2314yes—
74C22×Dic22—24no—
75C22×Dic22—24no—
76C22×Dic22C2×C418yescomplemented
77C22×Dic22C2311yescharacteristic
78C22×Dic22C2312yes—
79C22×Dic22C2312yes—
80C11×#117—24no—
81C11×#117C2×C418yescomplemented
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C42×C11—24no—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2312yes—
94C2×C22⋊Dic11C2312yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99#66979—24no—
100C2×C4⋊Dic11D418yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2318yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×Dic11⋊C4—28no—
106C2×Dic11⋊C4C2318yes—
107C2×Dic11⋊C4C2314yes—
108C2×C4×Dic11—28no—
109C2×C4×Dic11C2318yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2318yes—
113#66950C2×C4132yescomplemented
114#66945—28no—
115C4⋊C4×D11—28no—
116#66939C2×C4132yescomplemented
117(C22⋊D11)⋊C4—216no—
118#66928C2×C4116yescomplemented
119C4×D44—28no—
120#66922C2×C4116yescomplemented
121C4×Dic22—216no—
122C4×Dic22—216no—
123C4×Dic22—28no—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2318yes—
129C11⋊#95C2318yes—
130C11⋊#95C2318yes—
131#34266—111nomaximal, Sylow
132C24×C11C2411yescharacteristic
133C23×D11C2412yes—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—42no—
138C22×C4×C11C22×C414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11#4114yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—24no—
150C2×C22⋊D11C22×C418yes—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—44no—
154C22×Dic11C22×C418yes—
155C22×Dic11C2×D418yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160#4339—232no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44C22×C414yes—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—24no—
167C2×C4×D11—48no—
168C2×C4×D11C22×C418yes—
169C2×Dic22—232no—
170C2×Dic22—24no—
171C2×Dic22—24no—
172C2×Dic22—22no—
173C2×Dic22—24no—
174C2×Dic22—24no—
175C2×Dic22—22no—
176C2×Dic22C22×C414yes—
177C2×Dic22C22×C418yes—
178C2×Dic22C22×C418yes—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—44no—
183C11×C4⋊C4C22×C418yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4C22×C418yes—
186C42×C11—24no—
187C42×C11—24no—
188C42×C11—24no—
189C42×C11C22×C418yes—
190C22⋊Dic11—24no—
191(C2×D11)⋊C4—28no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—44no—
194(C2×D11)⋊C4C22×C4132yes—
195C4⋊Dic11—24no—
196C4⋊Dic11C22×C4132yes—
197C4⋊Dic11C2×D418yes—
198C4⋊Dic11C2×D418yes—
199Dic11⋊C4—216no—
200Dic11⋊C4—28no—
201C4×Dic11—216no—
202C4×Dic11—28no—
203C4×Dic11—24no—
204C4×Dic11—48no—
205C2×#536—111no—
206C2×#520—111no—
207C22×C4×Q8—111no—
208#2367—114no—
209#2365—114no—
210#2362—114no—
211#2360—114no—
212#2322—114no—
213#2310—111no—
214C4×#123—114no—
215#2297—111no—
216#2296D1111yescharacteristic, complemented
217#2274—111no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11C23×C412yes—
221C23×C11C22×D412yes—
222C23×C11C2×#4112yes—
223C23×C11C2511yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11C23×C414yes—
229C2×C4×C11—28no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11C4×D4116yes—
243C2×C4×C11C23×C418yes—
244C2×C4×C11C23×C412yes—
245C2×C4×C11C23×C412yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4112yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C112−1+414yes—
251C22⋊D11—216no—
252C2×Dic11—216no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—28no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—48no—
262C2×Dic11C23×C414yes—
263C2×Dic11C23×C418yes—
264C2×Dic11C22×D418yes—
265D44—28no—
266C4×D11—216no—
267C4×D11—88no—
268Dic22—216no—
269Dic22—216no—
270Dic22—28no—
271C22×#41—111no—
272C23×Q8—111no—
273#536—1116no—
274C2×C4⋊Q8—112no—
275C2×#124—112no—
276C2×#123—114no—
277C2×C22⋊Q8—114no—
278#520—228no—
279C2×C4×Q8—114no—
280C2×C4×Q8—112no—
281C2×C4×Q8—114no—
282C2×C4×Q8—228no—
283C2×C4×D4—114no—
284C2×C4×D4—112no—
285C2×#117—111no—
286C2×#117—112no—
287C2×#117C2×D1111yescharacteristic
288C2×#117C2×D1111yescharacteristic
289C22×C4⋊C4—111no—
290C22×C4⋊C4—112no—
291C22×C4⋊C4—112no—
292C22×C42—112no—
293C22×C42C2×D1111yescharacteristic
294#391—112no—
295#391—112no—
296#391—114no—
297#391—112no—
298#390—112no—
299#389—118no—
300#389C2×D1112yes—
301#389C2×D1112yes—
302#388—118no—
303#388—118no—
304#387—118no—
305#387—118no—
306#386—112no—
307#386—112no—
308#385—118no—
309#385C2×D1112yes—
310#385C2×D1112yes—
311#381—114no—
312C4×C4⋊C4—114no—
313C4×C4⋊C4—118no—
314C4×C4⋊C4—114no—
315C4×C4⋊C4C2×D1114yes—
316C4×C22⋊C4—114no—
317C4×C22⋊C4—114no—
318C4×C22⋊C4—118no—
319C22×C11—24no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—24no—
323C22×C11C2×C4×D414yes—
324C22×C11C24×C411yescharacteristic
325C22×C11C23×D411yescharacteristic
326C22×C11C22×#4111yescharacteristic
327C22×C11C2×2−1+412yes—
328C22×C11#58512yes—
329C2×D11—24no—
330C2×D11—28no—
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—44no—
334C4×C11—28no—
335C4×C11—24no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11C2×C4×D414yes—
340C4×C11C2×C4×D414yes—
341Dic11—28no—
342Dic11—24no—
343Dic11—28no—
344Dic11—44no—
345C2×#41—118no—
346C2×#41—224no—
347C2×#41—224no—
348C22×Q8—118no—
349C22×Q8—112no—
350C22×Q8—112no—
351C22×Q8—111no—
352C22×Q8—224no—
353C22×Q8—224no—
354C22×D4—112no—
355C22×D4—111no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—114no—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C4⋊Q8—1116no—
364#124—1116no—
365#123—1132no—
366C22⋊Q8—1132no—
367C4×Q8—2216no—
368C4×Q8—2216no—
369C4×Q8—228no—
370C4×D4—228no—
371C4×D4—2216no—
372#117—24no—
373#117—228no—
374#117—224no—
375#117C4×D1118yescomplemented
376C2×C4⋊C4—118no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—118no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—228no—
384C2×C4⋊C4—228no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1114yes—
388C2×C4⋊C4C22×D1114yes—
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4C22×D1112yes—
396C2×C22⋊C4C22×D1112yes—
397C2×C42—24no—
398C2×C42—114no—
399C2×C42—112no—
400C2×C42—118no—
401C2×C42—118no—
402C2×C42—228no—
403C2×C42C22×D1112yes—
404C2×C42C22×D1112yes—
405C2×C42C22×D1112yes—
406C2×C42C22×D1112yes—
407#95—118no—
408#95—114no—
409#95—118no—
410#95—114no—
411#95—118no—
412#95C22×D1114yes—
413#95C22×D1114yes—
414C2×C11—24no—
415C2×C11C22×C4×D411yescharacteristic
416C2×C11C4×2−1+412yes—
417C2×C11#348511yescharacteristic
418C2×C11#348611yescharacteristic
419C2×C11#350712yes—
420D11—44no—
421C24—112no—
422C24C23×D1111yescharacteristic
423#41—2232no—
424C2×Q8—118no—
425C2×Q8—118no—
426C2×Q8—114no—
427C2×Q8—2232no—
428C2×Q8—224no—
429C2×Q8—224no—
430C2×Q8—222no—
431C2×Q8—224no—
432C2×Q8—224no—
433C2×Q8—222no—
434C2×D4—118no—
435C2×D4—114no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—222no—
439C2×D4—222no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4—118no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—114no—
448C22×C4—118no—
449C22×C4—118no—
450C22×C4—114no—
451C22×C4—228no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—448no—
457C22×C4—444no—
458C22×C4C2×C4×D1114yes—
459C22×C4D4×D1114yes—
460C22×C4#434314yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—28no—
471C4⋊C4—44no—
472C4⋊C4—1132no—
473C4⋊C4—118no—
474C4⋊C4—118no—
475C4⋊C4—228no—
476C4⋊C4—2216no—
477C4⋊C4—224no—
478C4⋊C4C2×C4×D1118yes—
479C22⋊C4—24no—
480C22⋊C4—1132no—
481C22⋊C4—228no—
482C22⋊C4—224no—
483C22⋊C4—228no—
484C22⋊C4—444no—
485C22⋊C4C2×C4×D1118yes—
486C42—24no—
487C42—24no—
488C42—24no—
489C42—2216no—
490C42—228no—
491C42—224no—
492C42—448no—
493C42C2×C4×D1118yes—
494C11#3426611yescharacteristic, complemented, Sylow
495C23—22no—
496C23—22no—
497C23—114no—
498C23—222no—
499C23—222no—
500C23—224no—
501C23—224no—
502C23C22×C4×D1112yes—
503C23C2×D4×D1112yes—
504C23C2×#434312yes—
505C23C24×D1111yescharacteristic
506Q8—2216no—
507Q8—2216no—
508Q8—228no—
509D4—2216no—
510D4—228no—
511C2×C4—28no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—44no—
524C2×C4—118no—
525C2×C4—114no—
526C2×C4—118no—
527C2×C4—2216no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—228no—
533C2×C4—2216no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—448no—
538C2×C4—888no—
539C2×C4#66946116yes—
540C2×C4C22×C4×D1118yes—
541C2×C4C22×C4×D1112yes—
542C2×C4C22×C4×D1112yes—
543C2×C4C2×D4×D1112yes—
544C2×C4C2×D4×D1112yes—
545C2×C4C2×#434312yes—
546C2×C4C2×#434312yes—
547C2×C4#6704314yes—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—224no—
553C22—228no—
554C22—444no—
555C22—442no—
556C22—442no—
557C22C2×#6694614yes—
558C22C23×C4×D1111yescharacteristic
559C22C22×D4×D1111yescharacteristic
560C22C22×#434311yescharacteristic
561C22C2×#6704312yes—
562C22#1062345312yes—
563C4—24no—
564C4—28no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—228no—
569C4—224no—
570C4—228no—
571C4—444no—
572C4C2×#6694614yes—
573C4C2×#6694614yes—
574C2—24no—
575C2—444no—
576C2C22×#6694611yescharacteristic
577C2C4×#6704312yes—
578C2#1308225811yescharacteristic
579C2#1308226311yescharacteristic
580C2#1308248312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2296C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2296D11
hypocenterC11#34266
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2296

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic22C2semidirect
4. #13071685C2semidirect
5. #13071672C2semidirect
6. #13071642C2semidirect
7. #13071620C2semidirect
8. #13071284C2semidirect
9. #13071200C2semidirect
10. #13071135C2semidirect
12. #13070972C2semidirect
13. C11×#2296C2semidirect
23. #10623057C4semidirect
76. C22×Dic22C2×C4semidirect
81. C11×#117C2×C4semidirect
113. #66950C2×C4semidirect
116. #66939C2×C4semidirect
118. #66928C2×C4semidirect
120. #66922C2×C4semidirect
216. #2296D11semidirect
375. #117C4×D11semidirect
494. C11#34266semidirect

Maximal subgroups

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

subgroupindex
C2×#106230572
C2×#106230542
C22×C4×Dic222
#130716852
#130716722
#130716422
#130716202
#130712842
#130712002
#130711352
#130711062
#130709722
C11×#22962
#3426611