Finite Group Databasebeta

← #14920355

Subgroups — #14920355

Order 2816.

2794 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C212yesmaximal, complemented
2#13074764C214yesmaximal, complemented
3#13074742C214yesmaximal, complemented
4#13074730C211yesmaximal, characteristic, complemented
5#13074718C211yesmaximal, characteristic, complemented
6#13074544C212yesmaximal, complemented
7#13074350C214yesmaximal, complemented
8#13071876C214yesmaximal, complemented
9#13071832C214yesmaximal, complemented
10C4×#66983C214yesmaximal, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C42×C11C2212yes—
16C2×#67006C2214yes—
17#10623322—216no—
18C2×#66983C2212yes—
19C2×#66983C2212yes—
20C2×#66983C2214yes—
21C2×#66982C2214yes—
22C2×C4×C22⋊D11C2214yes—
23C2×C4×C22⋊D11C2214yes—
24C2×#66979C2212yes—
25C2×#66977C2212yes—
26C2×#66977C2212yes—
27C2×C4×D44C2214yescomplemented
28C4×C11×C22⋊C4C2214yes—
29C4×C11×C22⋊C4C2214yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32#10622826C2218yes—
33#10622825C2214yes—
34#10622574C2218yes—
35#10622574C2218yes—
36#10622573C2218yes—
37#10622566C2218yes—
38#10622553C2218yescomplemented
39#10622552C2214yescomplemented
40C4×(C2×D11)⋊C4C2218yescomplemented
41C4×C4⋊Dic11C2214yescomplemented
42#10622541C2214yescomplemented
43#10622290C2214yescomplemented
44#10622287C2214yescomplemented
45#10622286C2214yescomplemented
46#10622285C2214yescomplemented
47#10622284C2214yescomplemented
48#10622274C2214yescomplemented
49#10622272C2214yescomplemented
50#10622269C2214yescomplemented
51C25×C11C2311yescharacteristic
52C23×C4×C11—44no—
53C23×C4×C11D418yescomplemented
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C22×C22⋊D11C2314yes—
61C22×C22⋊D11C2314yes—
62C22×C22⋊D11C2314yes—
63C2×#4339—28no—
64C2×#4339—48no—
65C22×D44C2314yes—
66C22×D44C2312yes—
67C22×C4×D11C2314yes—
68C22×Dic22C2312yes—
69C2×C11×C22⋊C4—28no—
70C2×C11×C22⋊C4C2318yes—
71C2×C42×C11—44no—
72C2×C42×C11C2314yes—
73C2×C42×C11C2314yes—
74#67006—216no—
75C2×C22⋊Dic11C2314yes—
76C2×C22⋊Dic11C2314yes—
77C2×C22⋊Dic11C2314yes—
78#66983—28no—
79#66983—28no—
80#66983—216no—
81#66982—216no—
82C4×C22⋊D11—216no—
83C4×C22⋊D11—216no—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89#66979—28no—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95#66977—28no—
96#66977—28no—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×C4×Dic11C2314yes—
100C4×D44—48no—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106#34575—111nomaximal, Sylow
107C24×C11—24no—
108C24×C11—42no—
109C24×C11—41no—
110C24×C11—41no—
111C24×C11C2×D414yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C23×D11C2414yes—
115C22×C4×C11—24no—
116C22×C4×C11—28no—
117C22×C4×C11—24no—
118C22×C4×C11—416no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—44no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C2×D418yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D418yes—
129C22×C4×C11#4118yescomplemented
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2411yescharacteristic
133C22×C4×C11C2414yes—
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—28no—
136C2×C22⋊D11—28no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—216no—
139C2×C22⋊D11—48no—
140C2×C22⋊D11—44no—
141C2×C22⋊D11—44no—
142C22×Dic11C2414yes—
143C22×Dic11C2414yes—
144C22×Dic11C2414yes—
145#4339—432no—
146C2×D44—24no—
147C2×D44—28no—
148C2×D44—44no—
149C2×D44—44no—
150C2×D44—44no—
151C2×C4×D11—28no—
152C2×C4×D11—216no—
153C2×Dic22—24no—
154C2×Dic22—44no—
155C11×C22⋊C4—216no—
156C42×C11—28no—
157C42×C11—44no—
158C22⋊Dic11—28no—
159C22⋊Dic11—28no—
160C22⋊Dic11—28no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—48no—
165(C2×D11)⋊C4—48no—
166C4⋊Dic11—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—28no—
169C4⋊Dic11—44no—
170C4⋊Dic11—44no—
171Dic11⋊C4—28no—
172Dic11⋊C4—28no—
173C4×Dic11—28no—
174C2×#525—112no—
175#2663—114no—
176#2661—114no—
177#2659—111no—
178#2656—111no—
179#2639—112no—
180#2617—114no—
181#2395—114no—
182#2388—114no—
183C4×#121—114no—
184C2×C4×C22⋊C4D1111yescharacteristic, complemented
185C23×C11—22no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—28no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11C22×D414yes—
198C23×C11C22×D412yes—
199C23×C11C2×#4114yes—
200C23×C11C2511yescharacteristic
201C22×D11—24no—
202C22×D11—28no—
203C22×D11—28no—
204C22×D11—24no—
205C22×D11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—216no—
211C2×C4×C11—28no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—48no—
216C2×C4×C11—44no—
217C2×C4×C11—48no—
218C2×C4×C11—48no—
219C2×C4×C11C22×D412yes—
220C2×C4×C11C22×D414yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C2×#4118yes—
223C2×C4×C11H(5,𝔽2)14yes—
224C22⋊D11—416no—
225C22⋊D11—416no—
226C22⋊D11—416no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—28no—
231C2×Dic11—28no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234D44—416no—
235D44—48no—
236C4×D11—416no—
237Dic22—48no—
238C22×#41—112no—
239C24×C4C2×D1111yescharacteristic
240#525—2216no—
241C2×#123—114no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×#121—114no—
245C2×#121—112no—
246C2×#121—112no—
247C2×#120—114no—
248C2×C4×D4—114no—
249C2×C4×D4—114no—
250C2×C4×D4—114no—
251C2×#117—112no—
252C22×C22⋊C4C2×D1112yes—
253C22×C42C2×D1112yes—
254#400—114no—
255#399—114no—
256#398—114no—
257#397—118no—
258#397—114no—
259#395—114no—
260#394—118no—
261#394—118no—
262#394—114no—
263#393—114no—
264#392—118no—
265#392—114no—
266#390—114no—
267#389—114no—
268#388—118no—
269#386—118no—
270#380—114no—
271C4×C4⋊C4—114no—
272C4×C22⋊C4—118no—
273C4×C22⋊C4C2×D1114yes—
274C4×C22⋊C4C2×D1114yes—
275C2×#95C2×D1111yescharacteristic
276C2×#95C2×D1111yescharacteristic
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—416no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11#53214yes—
288C22×C11C23×D411yescharacteristic
289C22×C11C22×#4112yes—
290C22×C11C2×H(5,𝔽2)12yes—
291C22×C11#58511yescharacteristic
292C22×C11#58511yescharacteristic
293C2×D11—44no—
294C2×D11—44no—
295C2×D11—44no—
296C2×D11—48no—
297C2×D11—48no—
298C4×C11—22no—
299C4×C11—24no—
300C4×C11—28no—
301C4×C11—44no—
302C4×C11#53414yes—
303Dic11—44no—
304Dic11—44no—
305Dic11—44no—
306C25C22×D1111yescharacteristic
307C2×#41—228no—
308C2×#41—448no—
309C22×Q8—112no—
310C22×D4—114no—
311C22×D4—114no—
312C22×D4—114no—
313C22×D4—114no—
314C22×D4—112no—
315C23×C4—44no—
316C23×C4—114no—
317C23×C4D4418yescomplemented
318C23×C4C22×D1112yes—
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1112yes—
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1112yes—
323C23×C4C22×D1112yes—
324#123—2216no—
325C22⋊Q8—228no—
326C22⋊Q8—228no—
327#121—228no—
328#121—228no—
329#121—2216no—
330#120—2216no—
331C4×D4—2216no—
332C4×D4—2216no—
333C4×D4—448no—
334#117—228no—
335C2×C4⋊C4—112no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—114no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—114no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—114no—
344C2×C22⋊C4—114no—
345C2×C22⋊C4—114no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—114no—
348C2×C22⋊C4—118no—
349C2×C22⋊C4—118no—
350C2×C22⋊C4—118no—
351C2×C22⋊C4C22×D1118yes—
352C2×C42—44no—
353C2×C42—114no—
354C2×C42C22×D1114yes—
355C2×C42C22×D1114yes—
356#95—118no—
357#95—118no—
358#95—118no—
359#95C22×D1114yes—
360#95C22×D1114yes—
361C2×C11—24no—
362C2×C11—44no—
363C2×C11C2×#53211yescharacteristic
364C2×C11C2×#53411yescharacteristic
365C2×C11#344911yescharacteristic
366C2×C11#345912yes—
367C2×C11#346012yes—
368D11—84no—
369C24—24no—
370C24—42no—
371C24—41no—
372C24—41no—
373C24—114no—
374C24C2×D4414yes—
375C24C23×D1112yes—
376C24C23×D1111yescharacteristic
377#41—4432no—
378C2×Q8—224no—
379C2×Q8—444no—
380C2×D4—228no—
381C2×D4—228no—
382C2×D4—228no—
383C2×D4—2216no—
384C2×D4—224no—
385C2×D4—228no—
386C2×D4—444no—
387C2×D4—444no—
388C2×D4—444no—
389C2×D4—448no—
390C2×D4—444no—
391C2×D4—444no—
392C22×C4—24no—
393C22×C4—28no—
394C22×C4—24no—
395C22×C4—416no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—44no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—228no—
406C22×C4—2216no—
407C22×C4C2×D4418yes—
408C22×C4C2×D4414yes—
409C22×C4C2×D4414yes—
410C22×C4C2×D4418yes—
411C22×C4#433918yescomplemented
412C22×C4C23×D1114yes—
413C22×C4C23×D1112yes—
414C22×C4C23×D1111yescharacteristic
415C22×C4C23×D1114yes—
416C22×C4C23×D1111yescharacteristic
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—228no—
420C4⋊C4—228no—
421C4⋊C4—228no—
422C4⋊C4—444no—
423C4⋊C4—444no—
424C22⋊C4—216no—
425C22⋊C4—228no—
426C22⋊C4—228no—
427C22⋊C4—228no—
428C22⋊C4—228no—
429C22⋊C4—228no—
430C22⋊C4—2216no—
431C22⋊C4—448no—
432C22⋊C4—448no—
433C42—28no—
434C42—44no—
435C42—228no—
436C11#3457511yescharacteristic, complemented, Sylow
437C23—22no—
438C23—21no—
439C23—21no—
440C23—28no—
441C23—24no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—44no—
446C23—44no—
447C23—48no—
448C23—48no—
449C23—224no—
450C23—228no—
451C23—228no—
452C23—224no—
453C23—224no—
454C23C22×D4414yes—
455C23C22×D4412yes—
456C23C2×#433914yes—
457C23C24×D1111yescharacteristic
458Q8—448no—
459D4—448no—
460D4—4416no—
461D4—4416no—
462D4—4416no—
463D4—4416no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—28no—
469C2×C4—216no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—44no—
474C2×C4—48no—
475C2×C4—48no—
476C2×C4—48no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—228no—
481C2×C4—228no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—4416no—
485C2×C4C22×D4412yes—
486C2×C4C22×D4414yes—
487C2×C4C22×D4412yes—
488C2×C4C2×#433918yes—
489C2×C4#6703714yes—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—24no—
496C22—24no—
497C22—416no—
498C22—44no—
499C22—44no—
500C22—444no—
501C22—444no—
502C22—444no—
503C22—448no—
504C22—448no—
505C22#1062300814yes—
506C22C23×D4411yescharacteristic
507C22C22×#433912yes—
508C22C2×#6703712yes—
509C22#1062345311yescharacteristic
510C22#1062345311yescharacteristic
511C4—24no—
512C4—22no—
513C4—28no—
514C4—44no—
515C4—444no—
516C4—444no—
517C4—444no—
518C4#1062302414yes—
519C2—24no—
520C2—44no—
521C2—884no—
522C2C2×#1062300811yescharacteristic
523C2C2×#1062302411yescharacteristic
524C2#1308194911yescharacteristic
525C2#1308202512yes—
526C2#1308203812yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#34575
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13074764C2semidirect
3. #13074742C2semidirect
4. #13074730C2semidirect
5. #13074718C2semidirect
6. #13074544C2semidirect
7. #13074350C2semidirect
8. #13071876C2semidirect
9. #13071832C2semidirect
10. C4×#66983C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
27. C2×C4×D44C22semidirect
38. #10622553C22semidirect
39. #10622552C22semidirect
40. C4×(C2×D11)⋊C4C22semidirect
41. C4×C4⋊Dic11C22semidirect
42. #10622541C22semidirect
43. #10622290C22semidirect
44. #10622287C22semidirect
45. #10622286C22semidirect
46. #10622285C22semidirect
47. #10622284C22semidirect
48. #10622274C22semidirect
49. #10622272C22semidirect
50. #10622269C22semidirect
53. C23×C4×C11D4semidirect
129. C22×C4×C11#41semidirect
184. C2×C4×C22⋊C4D11semidirect
317. C23×C4D44semidirect
411. C22×C4#4339semidirect
436. C11#34575semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130747642
#130747422
#130747302
#130747182
#130745442
#130743502
#130718762
#130718322
C4×#669832
C2×C4×C11×C22⋊C42
#3457511