Finite Group Databasebeta

← #14914156

Subgroups — #14914156

Order 2816.

3054 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10623105C212yesmaximal, complemented
3#13071662C218yesmaximal, complemented
4#13071540C218yesmaximal, complemented
5#13071341C211yesmaximal, characteristic, complemented
6#13071339C211yesmaximal, characteristic, complemented
7#13071336C211yesmaximal, characteristic, complemented
8#13071207C212yesmaximal, complemented
9C4×#67000C212yesmaximal, complemented
10#13071159C212yesmaximal, complemented
11D11×#382C211yesmaximal, characteristic, complemented
12#13070955C211yesmaximal, characteristic, complemented
13C11×#2327C211yesmaximal, characteristic, complemented
14C22×#4343C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2212yes—
17C2×#67000C2212yes—
18C2×Q8×Dic11C2212yes—
19#10623256C4116yescomplemented
20#10623105—216no—
21C2×#66948C2214yes—
22C2×#66946C2214yes—
23C2×#66946C2212yes—
24C2×#66946C2214yes—
25C2×C4⋊C4×D11C2212yes—
26C2×C4⋊C4×D11C2214yes—
27C2×#66927C2211yescharacteristic
28C2×C4×D44C2214yes—
29C2×C4×D44C2212yes—
30C2×#66925C2211yescharacteristic
31C2×#66925C2214yes—
32C2×#66925C2211yescharacteristic
33C2×C42×D11C2211yescharacteristic
34C11×#391C2212yes—
35C11×#387C2218yes—
36C11×#382C2211yescharacteristic
37C11×#376C2211yescharacteristic
38#10622843C2212yes—
39#10622603C2218yes—
40#10622601C2212yes—
41#10622594C2218yes—
42#10622590C2212yes—
43#10622552C2212yes—
44C4×(C2×D11)⋊C4C2218yes—
45#10622549C2211yescharacteristic
46#10622545C2211yescharacteristic
47C42×Dic11C2211yescharacteristic
48C42×Dic11C2211yescharacteristic
49#10622283C2218yes—
50#10622280C2218yes—
51#10622279C2214yes—
52#10622279C2218yes—
53#10622278C2218yes—
54#10622278C2218yes—
55#10622278C2218yes—
56D11×#95C2214yes—
57#10622263C2214yes—
58#10622262C2214yes—
59C22×Q8×C11C2312yes—
60C2×#4343—28no—
61C2×#4343—28no—
62C2×#4343C2×C4116yescomplemented
63C22×D44C2312yes—
64C22×D44C2314yes—
65C22×D44C2314yes—
66C22×C4×D11C2314yes—
67C22×C4×D11C2314yes—
68C22×C4×D11C2314yes—
69C22×C4×D11C2314yes—
70C22×C4×D11C2312yes—
71C22×C4×D11C2311yescharacteristic
72C11×C4⋊Q8C2×C418yescomplemented
73C4×Q8×C11—28no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C42×C11C2314yes—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81#67000C2×C4116yescomplemented
82Q8×Dic11—28no—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2312yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2312yes—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2312yes—
92C2×Dic11⋊C4C2312yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2312yes—
95C2×C4×Dic11C2314yes—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2314yes—
98C2×C4×Dic11C2314yes—
99C2×C4×Dic11C2312yes—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102#66948C2×C4132yescomplemented
103#66946—216no—
104#66946—28no—
105#66946C2×C4132yescomplemented
106C4⋊C4×D11—28no—
107C4⋊C4×D11—216no—
108#66927C2×C418yescomplemented
109C4×D44—28no—
110C4×D44—216no—
111#66925—24no—
112#66925—216no—
113#66925D418yescomplemented
114C42×D11C2×C418yescomplemented
115C11×#95C2314yes—
116C11×#95C2314yes—
117C11×#95C2318yes—
118C11⋊#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2318yes—
121C11⋊#95C2318yes—
122#34208—111nomaximal, Sylow
123C23×D11C2414yes—
124C23×D11C2411yescharacteristic
125C2×Q8×C11—24no—
126C2×Q8×C11—24no—
127C2×Q8×C11C22×C418yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11C2412yes—
135C22×Dic11C2414yes—
136C22×Dic11C2412yes—
137C22×Dic11C2412yes—
138C22×Dic11C2411yescharacteristic
139#4343—264no—
140C2×D44—28no—
141C2×D44—28no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—48no—
145C2×D44C22×C418yes—
146C2×D44C22×C4116yes—
147C2×D44C22×C4116yes—
148C2×C4×D11—28no—
149C2×C4×D11—28no—
150C2×C4×D11—28no—
151C2×C4×D11—28no—
152C2×C4×D11—28no—
153C2×C4×D11—44no—
154C2×C4×D11—48no—
155C2×C4×D11—48no—
156C2×C4×D11—48no—
157C2×C4×D11C22×C4116yes—
158C2×C4×D11C22×C418yes—
159C2×C4×D11C22×C414yes—
160C2×C4×D11C2×D414yes—
161C2×C4×D11#4114yes—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4C22×C4116yes—
165C42×C11—28no—
166C42×C11—22no—
167C42×C11C22×C414yes—
168C42×C11C2×D414yes—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4C22×C4132yes—
175(C2×D11)⋊C4C2×D418yes—
176C4⋊Dic11—28no—
177C4⋊Dic11—24no—
178Dic11⋊C4—28no—
179Dic11⋊C4—24no—
180Dic11⋊C4C2×D418yes—
181C4×Dic11—28no—
182C4×Dic11—22no—
183C4×Dic11—44no—
184C4×Dic11—44no—
185C4×Dic11C22×C418yes—
186C4×Dic11C22×C414yes—
187C4×Dic11C2×D414yes—
188C2×#532—111no—
189C2×#520—112no—
190#2364—118no—
191#2352—118no—
192#2328—111no—
193#2328—111no—
194#2327—111no—
195#2327D1111yescharacteristic, complemented
196#2311—112no—
197C4×#124—112no—
198C4×#124—112no—
199C2×#382—111no—
200C4×#117—111no—
201C23×C11C2511yescharacteristic
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—28no—
206C22×D11—28no—
207C22×D11C23×C418yes—
208C22×D11C23×C412yes—
209C22×D11C22×D412yes—
210C22×D11C2×#4112yes—
211Q8×C11—216no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—28no—
220C2×C4×C11C23×C414yes—
221C2×C4×C11C23×C418yes—
222C2×C4×C11C23×C412yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C2×#4112yes—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—28no—
232C2×Dic11C23×C414yes—
233C2×Dic11C23×C412yes—
234C2×Dic11C22×D414yes—
235C2×Dic11C22×D412yes—
236C2×Dic11C2×#4112yes—
237D44—232no—
238D44—216no—
239D44—416no—
240C4×D11—232no—
241C4×D11—48no—
242C4×D11—88no—
243C4×D11—88no—
244C4×D11—88no—
245C4×D11C4×D4116yes—
246C22×#41—112no—
247#532—1116no—
248C2×C4⋊Q8C2×D1111yescharacteristic
249C2×#127—111no—
250C2×#124—112no—
251C2×#121—114no—
252#520—2216no—
253C2×C4×Q8—112no—
254C2×C4×Q8C2×D1112yes—
255C2×C4×D4—114no—
256C2×C4×D4—112no—
257C2×C4×D4—114no—
258C2×C4×D4—112no—
259C2×C4×D4—114no—
260C2×#117—111no—
261C2×#117—111no—
262C2×#117—114no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—114no—
265C22×C42—111no—
266#391—112no—
267#391C2×D1112yes—
268#390—112no—
269#390—112no—
270#388—118no—
271#388—118no—
272#387—118no—
273#387C2×D1118yes—
274#386—118no—
275#386—118no—
276#386—118no—
277#382—112no—
278#382—111no—
279#382—114no—
280#382C2×D1111yescharacteristic
281#380—118no—
282C4×C4⋊C4—114no—
283C4×C22⋊C4—118no—
284C4×C22⋊C4—118no—
285C4×C22⋊C4—114no—
286#376—111no—
287#376C2×D1111yescharacteristic
288C2×#95—114no—
289C43—111no—
290C43—111no—
291C22×C11C24×C411yescharacteristic
292C22×C11C23×D411yescharacteristic
293C22×C11C22×#4111yescharacteristic
294C22×C11#58514yes—
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—28no—
299C2×D11—216no—
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—48no—
303C2×D11C2×C4×D414yes—
304C4×C11—28no—
305C4×C11—24no—
306C4×C11—24no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11C2×C4×D414yes—
310Dic11—24no—
311Dic11—24no—
312Dic11—44no—
313Dic11—42no—
314Dic11C2×C4×D414yes—
315C2×#41—1116no—
316C2×#41—228no—
317C2×#41—228no—
318C22×Q8C22×D1112yes—
319C22×D4—114no—
320C22×D4—112no—
321C22×D4—114no—
322C23×C4—111no—
323C23×C4—114no—
324C23×C4—112no—
325C23×C4—114no—
326C23×C4—114no—
327C23×C4—114no—
328C4⋊Q8C4×D1118yescomplemented
329#127—118no—
330#124—1116no—
331#121—1132no—
332C4×Q8—28no—
333C4×Q8—228no—
334C4×D4—1132no—
335C4×D4—2216no—
336C4×D4—228no—
337C4×D4—2216no—
338C4×D4—228no—
339#117—118no—
340#117—2216no—
341#117—224no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—2216no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4C22×D1112yes—
350C2×C4⋊C4C22×D1114yes—
351C2×C4⋊C4C22×D1114yes—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—118no—
354C2×C22⋊C4—114no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—118no—
359C2×C42—111no—
360C2×C42—112no—
361C2×C42—111no—
362C2×C42—118no—
363C2×C42—114no—
364C2×C42—111no—
365C2×C42—114no—
366C2×C42—114no—
367C2×C42C22×D1114yes—
368C2×C42C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370C2×C42C22×D1111yescharacteristic
371#95—118no—
372#95—114no—
373#95—114no—
374#95—118no—
375#95C22×D1114yes—
376#95C22×D1114yes—
377#95C22×D1118yes—
378C2×C11C22×C4×D411yescharacteristic
379C2×C11#342812yes—
380C2×C11#350012yes—
381C2×C11#351212yes—
382D11—24no—
383D11—48no—
384C24—111no—
385C24—114no—
386#41—2264no—
387C2×Q8—24no—
388C2×Q8—24no—
389C2×Q8C2×C4×D1118yes—
390C2×D4—1116no—
391C2×D4—118no—
392C2×D4—1116no—
393C2×D4—228no—
394C2×D4—228no—
395C2×D4—224no—
396C2×D4—224no—
397C2×D4—448no—
398C22×C4—111no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—1116no—
405C22×C4—118no—
406C22×C4—112no—
407C22×C4—114no—
408C22×C4—228no—
409C22×C4—228no—
410C22×C4—228no—
411C22×C4—228no—
412C22×C4—228no—
413C22×C4—444no—
414C22×C4—448no—
415C22×C4—448no—
416C22×C4—448no—
417C22×C4C23×D1114yes—
418C22×C4C23×D1112yes—
419C22×C4C23×D1112yes—
420C22×C4C23×D1114yes—
421C22×C4C23×D1112yes—
422C22×C4C23×D1111yescharacteristic
423C4⋊C4—28no—
424C4⋊C4—24no—
425C4⋊C4—118no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4C2×C4×D11116yes—
431C22⋊C4—1132no—
432C22⋊C4—118no—
433C22⋊C4—228no—
434C22⋊C4—224no—
435C22⋊C4—228no—
436C22⋊C4—448no—
437C22⋊C4—448no—
438C42—28no—
439C42—22no—
440C42—118no—
441C42—114no—
442C42—114no—
443C42—228no—
444C42—222no—
445C42—444no—
446C42—444no—
447C42C2×C4×D1114yes—
448C42D4×D1114yes—
449C11#3420811yescharacteristic, complemented, Sylow
450C23—112no—
451C23—112no—
452C23—112no—
453C23—118no—
454C23—224no—
455C23—224no—
456C23—224no—
457C23—228no—
458C23—228no—
459C23C24×D1111yescharacteristic
460Q8—216no—
461D4—2232no—
462D4—2216no—
463D4—4416no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—28no—
472C2×C4—112no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—1116no—
476C2×C4—114no—
477C2×C4—114no—
478C2×C4—2232no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—228no—
485C2×C4—448no—
486C2×C4—888no—
487C2×C4—888no—
488C2×C4—888no—
489C2×C4C22×C4×D1114yes—
490C2×C4C22×C4×D1118yes—
491C2×C4C22×C4×D1112yes—
492C2×C4C2×D4×D1114yes—
493C2×C4C2×D4×D1112yes—
494C2×C4#41×D1112yes—
495C22—114no—
496C22—224no—
497C22—224no—
498C22—224no—
499C22—228no—
500C22—2216no—
501C22—444no—
502C22—444no—
503C22—448no—
504C22C23×C4×D1111yescharacteristic
505C22C22×D4×D1111yescharacteristic
506C22C2×#41×D1111yescharacteristic
507C22#1062345714yes—
508C4—24no—
509C4—28no—
510C4—24no—
511C4—44no—
512C4—42no—
513C4—114no—
514C4—224no—
515C4—224no—
516C4—444no—
517C4—442no—
518C4C4×D4×D1114yes—
519C2—224no—
520C2—448no—
521C2C2×C4×D4×D1111yescharacteristic
522C2#1308181812yes—
523C2#1308240512yes—
524C2#1308253912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2327C2
socle, cosocleC23×C11C25
prime radicalC2×#10623256C2
hypercenter#2327D11
hypocenterC11#34208
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2327

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. #13071662C2semidirect
4. #13071540C2semidirect
5. #13071341C2semidirect
6. #13071339C2semidirect
7. #13071336C2semidirect
8. #13071207C2semidirect
9. C4×#67000C2semidirect
10. #13071159C2semidirect
11. D11×#382C2semidirect
12. #13070955C2semidirect
13. C11×#2327C2semidirect
19. #10623256C4semidirect
62. C2×#4343C2×C4semidirect
72. C11×C4⋊Q8C2×C4semidirect
81. #67000C2×C4semidirect
102. #66948C2×C4semidirect
105. #66946C2×C4semidirect
108. #66927C2×C4semidirect
113. #66925D4semidirect
114. C42×D11C2×C4semidirect
195. #2327D11semidirect
328. C4⋊Q8C4×D11semidirect
449. C11#34208semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106231052
#130716622
#130715402
#130713412
#130713392
#130713362
#130712072
C4×#670002
#130711592
D11×#3822
#130709552
C11×#23272
#3420811