Finite Group Databasebeta

← #14755399

Subgroups — #14755399

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×#10622853C211yesmaximal, characteristic, complemented
3#13070995C212yesmaximal, complemented
4#13069029C214yesmaximal, complemented
5#13069024C214yesmaximal, complemented
6#13068349C212yesmaximal, complemented
7C11×#3428C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C11×#520—24no—
11C11×#519—21no—
12C11×#518—21no—
13C11×#518C2214yes—
14C4×C11×#41—24no—
15C2×C11×#117—22no—
16C2×C11×#117C2212yes—
17#10623359—24no—
18#10623359C418yescomplemented
19C2×#66999—21no—
20C2×#66991—21no—
21C2×#66990C2212yes—
22C2×#66988C2212yes—
23C2×C4×C22⋊D11—22no—
24C2×#66979C2212yes—
25C2×#66979C2211yescharacteristic
26#10622853—24no—
27C2×#66898C2214yes—
28#10622600—24no—
29#10622568C2214yes—
30#10622556C2214yes—
31C4×(C2×D11)⋊C4—24no—
32#10622164C2218yes—
33C24×D11C2311yescharacteristic
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—24no—
37C2×C11×#41C2×C414yes—
38C2×C11×#41D414yes—
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2312yes—
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C23×Dic11C2311yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—24no—
52C22×C4×D11C2×C414yescomplemented
53C4×Q8×C11—28no—
54C4×D4×C11—28no—
55C4×D4×C11—216no—
56C11×#117—24no—
57C11×#117—24no—
58C11×#117—22no—
59C11×#117—24no—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4D414yescomplemented
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4C2314yes—
67C2×C42×C11—24no—
68C2×C42×C11D414yescomplemented
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11C2314yes—
71C2×C22⋊Dic11C2312yes—
72#66999—28no—
73#66991—28no—
74#66990—24no—
75#66990C2×C418yescomplemented
76#66988—24no—
77#66988C2×C418yescomplemented
78C4×C22⋊D11—216no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—28no—
81#66979—22no—
82#66979—24no—
83#66979—24no—
84#66979C2×C414yescomplemented
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—22no—
90#66898—28no—
91C11⋊#95—28no—
92#20959—111nomaximal, Sylow
93C24×C11C2×D412yes—
94C24×C11C2411yescharacteristic
95C23×D11—22no—
96C23×D11—21no—
97C23×D11—21no—
98C23×D11—22no—
99C23×D11—44no—
100C23×D11C22×C412yes—
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22⋊C414yescomplemented
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yescomplemented
113C2×D4×C11C22×C414yes—
114C2×D4×C11C2×D414yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—28no—
119C22×C4×C11C22⋊C418yescomplemented
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D418yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4114yes—
129C2×C22⋊D11—28no—
130C2×C22⋊D11—48no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11C22×C412yes—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—28no—
141C2×C4×D11—28no—
142C2×C4×D11—42no—
143C2×C4×D11—41no—
144C2×C4×D11—41no—
145C2×C4×D11—44no—
146C2×C4×D11—44no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C42×C11—28no—
156C42×C11—24no—
157C42×C11—24no—
158C22⋊Dic11—28no—
159C22⋊Dic11—22no—
160C22⋊Dic11—24no—
161C22⋊Dic11—24no—
162C22⋊Dic11C22×C414yes—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—416no—
165C4⋊Dic11—24no—
166C4⋊Dic11—44no—
167Dic11⋊C4—28no—
168C4×Dic11—24no—
169C4×Dic11—44no—
170C2×#525—111no—
171#3428D1111yescharacteristic, complemented
172C2×#410—111no—
173#2280—112no—
174#1890—114no—
175#1889—114no—
176#1740—112no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—44no—
181C23×C11C2×C22⋊C414yes—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C22×D412yes—
186C23×C11C2×#4112yes—
187C22×D11—28no—
188C22×D11—24no—
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—44no—
192C22×D11—48no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—42no—
196C22×D11—41no—
197C22×D11—42no—
198C22×D11—41no—
199Q8×C11—28no—
200D4×C11—28no—
201D4×C11—28no—
202D4×C11—28no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—28no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—48no—
209C2×C4×C11—88no—
210C2×C4×C11C2×C22⋊C414yes—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C4×D414yes—
214C2×C4×C11C4×D414yes—
215C2×C4×C11#12012yes—
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12114yes—
219C2×C4×C11#12114yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#12312yes—
222C22⋊D11—416no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—44no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—48no—
231C2×Dic11—44no—
232C4×D11—44no—
233C4×D11—44no—
234C4×D11—48no—
235C22×#41C2×D1111yescharacteristic
236C24×C4—111no—
237#525—118no—
238#525—224no—
239C2×#123—112no—
240C2×C22⋊Q8—221no—
241C2×#121—221no—
242C2×#120—112no—
243#520—24no—
244#519—21no—
245#518—21no—
246#518C2×D1114yes—
247C4×#41—24no—
248C2×C4×D4—222no—
249C2×#117—22no—
250C2×#117—111no—
251C2×#117—112no—
252C2×#117C2×D1112yes—
253#410—224no—
254C2×#99—114no—
255#381—114no—
256#380—224no—
257#379—114no—
258C4×C22⋊C4—224no—
259#342—118no—
260C22×C11—24no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—82no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11C2×C4×D412yes—
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×#12112yes—
273C22×C11C2×#12311yescharacteristic
274C2×D11—28no—
275C2×D11—24no—
276C2×D11—42no—
277C2×D11—48no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—42no—
282C4×C11—24no—
283C4×C11—48no—
284C4×C11#38612yes—
285C4×C11#38612yes—
286C4×C11#38614yes—
287Dic11—44no—
288Dic11—42no—
289Dic11—84no—
290C25—111no—
291C2×#41—24no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41C4×D1114yes—
295C2×#41D4414yes—
296C22×Q8C22⋊D1111yescharacteristic
297C22×D4—222no—
298C22×D4C22⋊D1111yescharacteristic
299C22×D4C22×D1112yes—
300C23×C4—111no—
301C23×C4—114no—
302C23×C4—222no—
303C23×C4—224no—
304C23×C4—221no—
305C23×C4—221no—
306C23×C4—222no—
307C23×C4—222no—
308C23×C4C22⋊D1112yes—
309C23×C4C22×D1111yescharacteristic
310#123—118no—
311#123—224no—
312C22⋊Q8—228no—
313#121—228no—
314#120—118no—
315#120—224no—
316C4×Q8—28no—
317C4×D4—28no—
318C4×D4—216no—
319C4×D4—2216no—
320#117—24no—
321#117—24no—
322#117—22no—
323#117—24no—
324#117—22no—
325#117—22no—
326#117—22no—
327#117—114no—
328#117—222no—
329#117—224no—
330#117—224no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4C22⋊D1114yescomplemented
336C2×C22⋊C4—24no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—114no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—228no—
342C2×C22⋊C4C22×D1114yes—
343C2×C42—24no—
344C2×C42—221no—
345C2×C42—222no—
346C2×C42C22⋊D1114yescomplemented
347#99—228no—
348#95—228no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—22no—
352C2×C11—21no—
353C2×C11—44no—
354C2×C11C2×#38611yescharacteristic
355C2×C11#302512yes—
356D11—44no—
357C24—112no—
358C24—222no—
359C24—221no—
360C24—221no—
361C24—222no—
362C24—444no—
363C24C2×C22⋊D1112yes—
364C24C23×D1111yescharacteristic
365#41—28no—
366#41—28no—
367#41—28no—
368#41—28no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8(C2×D11)⋊C414yescomplemented
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—228no—
377C2×D4—448no—
378C2×D4(C2×D11)⋊C414yescomplemented
379C2×D4C2×C4×D1114yes—
380C2×D4C2×D4414yes—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—28no—
385C22×C4—112no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—221no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—228no—
394C22×C4—228no—
395C22×C4—224no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—444no—
399C22×C4—444no—
400C22×C4—442no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4(C2×D11)⋊C418yescomplemented
404C22×C4C2×C4×D1112yes—
405C22×C4C2×D4412yes—
406C22×C4#433914yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1118yes—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1112yes—
412C22×C4C2×C22⋊D1112yes—
413C4⋊C4—28no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—224no—
417C4⋊C4—228no—
418C4⋊C4—444no—
419C22⋊C4—28no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—114no—
423C22⋊C4—228no—
424C22⋊C4—222no—
425C22⋊C4—228no—
426C22⋊C4—224no—
427C22⋊C4—224no—
428C22⋊C4—4416no—
429C42—28no—
430C42—24no—
431C42—24no—
432C42—224no—
433C42—444no—
434C11#2095911yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—42no—
438C23—44no—
439C23—228no—
440C23—224no—
441C23—222no—
442C23—224no—
443C23—444no—
444C23—442no—
445C23—444no—
446C23—444no—
447C23—448no—
448C23—441no—
449C23—442no—
450C23—441no—
451C23C2×(C2×D11)⋊C414yes—
452C23C22×C4×D1111yescharacteristic
453C23C22×D4411yescharacteristic
454C23C2×#433912yes—
455C23C22×C22⋊D1111yescharacteristic
456C23C22×C22⋊D1112yes—
457Q8—28no—
458D4—28no—
459D4—28no—
460D4—28no—
461D4—4416no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—28no—
465C2×C4—28no—
466C2×C4—28no—
467C2×C4—48no—
468C2×C4—88no—
469C2×C4—224no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—444no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4—448no—
479C2×C4—448no—
480C2×C4—444no—
481C2×C4C2×(C2×D11)⋊C414yes—
482C2×C4C2×(C2×D11)⋊C412yes—
483C2×C4C2×(C2×D11)⋊C412yes—
484C2×C4C4×C22⋊D1114yes—
485C2×C4C4×C22⋊D1114yes—
486C2×C4#6698212yes—
487C2×C4#6698212yes—
488C2×C4#6698314yes—
489C2×C4#6698314yes—
490C2×C4#6700612yes—
491C2×C4#6700611yescharacteristic
492C2×C4#6700611yescharacteristic
493C22—24no—
494C22—22no—
495C22—24no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—44no—
500C22—44no—
501C22—82no—
502C22—224no—
503C22—228no—
504C22—442no—
505C22—448no—
506C22—444no—
507C22—444no—
508C22—442no—
509C22—444no—
510C22C22×(C2×D11)⋊C411yescharacteristic
511C22C2×C4×C22⋊D1112yes—
512C22C2×#6698211yescharacteristic
513C22C2×#6698312yes—
514C22C2×#6700611yescharacteristic
515C4—24no—
516C4—48no—
517C4—444no—
518C4—442no—
519C4—884no—
520C4#1062282612yes—
521C4#1062282612yes—
522C4#1062282614yes—
523C2—21no—
524C2—22no—
525C2—21no—
526C2—22no—
527C2—44no—
528C2—444no—
529C2C2×#1062282611yescharacteristic
530C2#1307800812yes—
subgroupG/H
centerC2×C4#67006
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#3428C2
socleC22×C11C2×#120
prime radicalC2×#10623359C2
cosocleC24×C11C24
hypercenter#3428D11
hypocenterC11#20959
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3428

Complements

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

NH ≅ G/Ntype
2. C2×#10622853C2semidirect
3. #13070995C2semidirect
4. #13069029C2semidirect
5. #13069024C2semidirect
6. #13068349C2semidirect
7. C11×#3428C2semidirect
18. #10623359C4semidirect
52. C22×C4×D11C2×C4semidirect
64. C2×C11×C4⋊C4D4semidirect
68. C2×C42×C11D4semidirect
75. #66990C2×C4semidirect
77. #66988C2×C4semidirect
84. #66979C2×C4semidirect
107. C2×Q8×C11C22⋊C4semidirect
112. C2×D4×C11C22⋊C4semidirect
119. C22×C4×C11C22⋊C4semidirect
171. #3428D11semidirect
335. C2×C4⋊C4C22⋊D11semidirect
346. C2×C42C22⋊D11semidirect
371. C2×Q8(C2×D11)⋊C4semidirect
378. C2×D4(C2×D11)⋊C4semidirect
403. C22×C4(C2×D11)⋊C4semidirect
434. C11#20959semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×#106228532
#130709952
#130690292
#130690242
#130683492
C11×#34282
#2095911