Finite Group Databasebeta

← #15617566

Subgroups — #15617566

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081817C211yesmaximal, characteristic
2#13077281C218yesmaximal, complemented
3#13077273C218yesmaximal, complemented
4#13077266C214yesmaximal, complemented
5#13077259C214yesmaximal, complemented
6#13077180C211yesmaximal, characteristic, complemented
7#13077060C211yesmaximal, characteristic
8C2×#10622723C211yesmaximal, characteristic
9#13077034C211yesmaximal, characteristic, complemented
10C2×#10622714C211yesmaximal, characteristic, complemented
11C2×C11×#424C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10623054C414yes—
20#10623053C2214yes—
21#10623052C412yes—
22D11×#117C2214yes—
23#10623047C412yes—
24#10623035C414yes—
25#10623017C414yes—
26C4×#4339C2214yes—
27C11×#424C2214yes—
28C11×#424C2212yescomplemented
29C11×#424C2212yescomplemented
30C2×C11×C4⋊C8C2214yescomplemented
31#10622742C2214yes—
32#10622739C2214yes—
33#10622735C2214yes—
34M16×Dic11C2214yescomplemented
35#10622723C2212yes—
36#10622723C2212yes—
37#10622723C2214yes—
38#10622723C2214yes—
39C2×(C2×D11)⋊C8C2214yes—
40#10622714C2214yes—
41#10622714C2214yescomplemented
42#10622714C2214yescomplemented
43C2×#66879C2212yescomplemented
44C2×C8×Dic11C2212yescomplemented
45#10622612C2214yes—
46#10622612C2214yescomplemented
47#10622537C2214yescomplemented
48#10622453C22116yescomplemented
49#10622453C22116yescomplemented
50#10622448C22116yescomplemented
51#10622446C22116yescomplemented
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11C2×C412yes—
54C2×#4339—24no—
55C2×#4339—24no—
56C2×#4339C2×C412yes—
57C2×#4339C2×C412yes—
58C2×#4339C2312yes—
59C2×#4339C2312yes—
60C22×D44C2×C411yescharacteristic
61C22×C4×D11C2312yes—
62C22×Dic22C2×C411yescharacteristic
63C2×C11×M16—24no—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C22×C8×C11—24no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117C2×C412yes—
73C11×#117C2×C412yes—
74C11×#117C2312yes—
75C11×#117C2312yes—
76C2×C11×C4⋊C4C2×C412yes—
77C2×C11×C22⋊C4C2×C412yes—
78C2×C42×C11C2312yes—
79C2×C22⋊Dic11C2×C412yes—
80C4×C22⋊D11C2×C4116yes—
81#66979C2×C412yes—
82#66979C2×C412yes—
83#66979C2312yes—
84#66979C2312yes—
85C2×C4⋊Dic11C2×C412yes—
86C2×C4×Dic11C2312yes—
87C2×#4318—24no—
88C2×#4318—24no—
89C2×#4318C2312yes—
90C2×#4318C2312yes—
91C2×#4318C2312yes—
92C2×#4318C2312yes—
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2312yes—
95#66946C2×C418yes—
96#66945C2×C418yes—
97C4⋊C4×D11C2×C418yes—
98#66940C2×C418yes—
99(C22⋊D11)⋊C4C2×C4116yes—
100C22⋊C4×D11C2×C418yes—
101#66930C2×C418yes—
102C4×D44C2×C418yes—
103#66925C2318yes—
104C42×D11C2318yes—
105C4×Dic22C2×C418yes—
106C11×C4⋊C8C2318yes—
107C11×C4⋊C8C2318yes—
108(C2×D11)⋊C8C2318yes—
109(C2×D11)⋊C8C2318yes—
110(C2×D11)⋊C8C23116yes—
111#66879C2318yes—
112#66879C2318yes—
113C8×Dic11C2318yes—
114C8×Dic11C2318yes—
115C4⋊(C11⋊C8)C23116yes—
116#60126—111nomaximal, Sylow
117C24×C11C22×C411yescharacteristic
118C23×D11C22×C412yes—
119C22×C4×C11C22×C414yes—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11#4114yes—
124C22×C4×C11#4114yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—28no—
129C2×C22⋊D11C22×C414yes—
130C2×C22⋊D11C22×C414yes—
131C22×Dic11C22×C412yes—
132C22×Dic11C22×C414yes—
133#4339—28no—
134#4339—28no—
135#4339—24no—
136#4339—24no—
137#4339—24no—
138#4339—24no—
139C2×D44—24no—
140C2×D44C22×C412yes—
141C2×D44C22×C412yes—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11C22×C414yes—
145C2×C4×D11C22×C4116yes—
146C2×C4×D11C2414yes—
147C2×Dic22—24no—
148C2×Dic22C22×C412yes—
149C2×Dic22C22×C412yes—
150C11×M16—24no—
151C11×M16—24no—
152C2×C8×C11—24no—
153C2×C8×C11—24no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—24no—
157C2×C8×C11C2412yes—
158C2×C8×C11C2414yes—
159C2×C8×C11C2412yes—
160C11×C4⋊C4C22×C414yes—
161C11×C4⋊C4C22×C414yes—
162C11×C22⋊C4C22×C414yes—
163C11×C22⋊C4C22×C414yes—
164C42×C11C22×C414yes—
165C42×C11C2414yes—
166C22⋊Dic11C22×C414yes—
167C22⋊Dic11C22×C414yes—
168(C2×D11)⋊C4C22×C4116yes—
169C4⋊Dic11C22×C414yes—
170C4⋊Dic11C22×C414yes—
171Dic11⋊C4C22×C4116yes—
172C4×Dic11C22×C4116yes—
173C4×Dic11C22×C414yes—
174C4×Dic11C2414yes—
175#4318—24no—
176#4318—24no—
177#4318—24no—
178#4318—24no—
179C2×C11⋊C8—24no—
180C2×C11⋊C8—24no—
181C2×C11⋊C8C2414yes—
182C2×C11⋊C8C2414yes—
183#3428—111no—
184#2925—118no—
185#2924—118no—
186#2923—114no—
187#2922—114no—
188#2905—111no—
189C2×#424D1111yescharacteristic, complemented
190#2879—111no—
191C2×#408—111no—
192#2873—111no—
193C2×#405—111no—
194C23×C11—42no—
195C23×C11#11714yes—
196C23×C11C23×C411yescharacteristic
197C23×C11C23×C411yescharacteristic
198C23×C11C23×C411yescharacteristic
199C22×D11—24no—
200C22×D11—44no—
201C22×D11C23×C414yes—
202C2×C4×C11—44no—
203C2×C4×C11#11714yes—
204C2×C4×C11#11714yes—
205C2×C4×C11#11714yes—
206C2×C4×C11C23×C418yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C2×#4112yes—
211C2×C4×C11C2×#4112yes—
212C2×C4×C11C2×#4112yes—
213C2×C4×C11C2×#4112yes—
214C2×C4×C11C2×#4112yes—
215C2×C4×C11C2×#4112yes—
216C2×C4×C11C2511yescharacteristic
217C22⋊D11—28no—
218C22⋊D11—28no—
219C2×Dic11—24no—
220C2×Dic11—44no—
221C2×Dic11C23×C414yes—
222C2×Dic11C23×C418yes—
223D44—24no—
224D44—24no—
225C4×D11—28no—
226C4×D11—24no—
227C4×D11—24no—
228C4×D11—416no—
229Dic22—24no—
230Dic22—24no—
231C8×C11—22no—
232C8×C11—22no—
233C8×C11—24no—
234C11⋊C8—24no—
235C11⋊C8—24no—
236C22×#41—111no—
237C22×M16—111no—
238C22×M16—111no—
239C22×M16C2×D1111yescharacteristic
240C23×C8C2×D1111yescharacteristic
241#520—114no—
242#520—114no—
243#519—112no—
244#518—112no—
245#518—114no—
246C4×#41—114no—
247C4×#41—114no—
248C2×#117—111no—
249C2×#117—114no—
250C2×#117C2×D1111yescharacteristic
251#433—1116no—
252#433—1116no—
253#432—1116no—
254#431—1116no—
255#424—114no—
256#424—114no—
257#424C2×D1114yes—
258#424C2×D1112yescomplemented
259#424C2×D1112yescomplemented
260#423—114no—
261C2×C4⋊C8C2×D1114yescomplemented
262#408—114no—
263#408—112no—
264#408—112no—
265#408—114no—
266#408—114no—
267#407—114no—
268C2×C22⋊C8—114no—
269#405—114no—
270#405—114no—
271#405—114no—
272#405—114no—
273C4×M16—114no—
274C2×#97—112no—
275C2×C4×C8—112no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—44no—
280C22×C11C2×#11712yes—
281C22×C11C2×#11712yes—
282C22×C11C2×#11712yes—
283C22×C11C24×C411yescharacteristic
284C2×D11—24no—
285C2×D11—28no—
286C2×D11—84no—
287C4×C11—28no—
288C4×C11C2×#11712yes—
289C4×C11C2×#11712yes—
290C4×C11C2×#11712yes—
291C4×C11C22×#4111yescharacteristic
292C4×C11C22×#4111yescharacteristic
293Dic11—24no—
294Dic11—28no—
295C2×#41—112no—
296C2×#41—112no—
297C2×#41—112no—
298C2×#41—112no—
299C2×#41—224no—
300C2×#41—224no—
301C22×Q8—111no—
302C22×D4—112no—
303C22×D4—111no—
304C23×C4—112no—
305C23×C4C22×D1111yescharacteristic
306C2×M16—24no—
307C2×M16—112no—
308C2×M16—112no—
309C2×M16—112no—
310C2×M16—112no—
311C2×M16—224no—
312C2×M16—224no—
313C2×M16C22×D1112yes—
314C2×M16C22×D1112yes—
315C22×C8—24no—
316C22×C8—112no—
317C22×C8—112no—
318C22×C8C22×D1111yescharacteristic
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1112yes—
321C22×C8C22×D1112yes—
322C22×C8C22×D1112yes—
323C4×Q8—118no—
324C4×Q8—118no—
325C4×D4—1116no—
326C4×D4—118no—
327C4×D4—1116no—
328C4×D4—118no—
329#117—112no—
330#117—112no—
331#117—112no—
332#117—112no—
333#117—118no—
334#117—118no—
335#117—118no—
336#117C4×D1112yes—
337#117C4×D1112yes—
338#117C22×D1112yes—
339#117C22×D1112yes—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4C4×D1112yes—
343C2×C22⋊C4—112no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4C4×D1112yes—
346C2×C42—112no—
347C2×C42—118no—
348C2×C42C22×D1112yes—
349C4⋊C8—1116no—
350C4⋊C8C22×D1118yes—
351C4⋊C8C22×D1118yes—
352C22⋊C8—118no—
353C22⋊C8—118no—
354C22⋊C8—1116no—
355#97—118no—
356#97—118no—
357C4×C8—118no—
358C4×C8—118no—
359C2×C11—22no—
360C2×C11—22no—
361C2×C11—22no—
362C2×C11C22×#11711yescharacteristic
363C2×C11#357312yes—
364D11—44no—
365C24—112no—
366C24C2×C4×D1111yescharacteristic
367#41—228no—
368#41—228no—
369#41—224no—
370#41—224no—
371#41—224no—
372#41—224no—
373C2×Q8—112no—
374C2×Q8—112no—
375C2×Q8—224no—
376C2×D4—114no—
377C2×D4—114no—
378C2×D4—112no—
379C2×D4—112no—
380C2×D4—228no—
381C2×D4—224no—
382C22×C4—112no—
383C22×C4—114no—
384C22×C4—114no—
385C22×C4—114no—
386C22×C4—1116no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4C2×C4×D1114yes—
390C22×C4C2×C4×D1111yescharacteristic
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4#434114yes—
394C22×C4#434314yes—
395C22×C4C23×D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397C22×C4C23×D1111yescharacteristic
398M16—24no—
399M16—24no—
400M16—224no—
401M16—224no—
402M16—224no—
403M16—224no—
404C2×C8—24no—
405C2×C8—24no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—24no—
409C2×C8—114no—
410C2×C8—114no—
411C2×C8—224no—
412C2×C8—224no—
413C2×C8C23×D1112yes—
414C2×C8C23×D1114yes—
415C2×C8C23×D1112yes—
416C4⋊C4—114no—
417C4⋊C4—1116no—
418C4⋊C4—114no—
419C4⋊C4C2×C4×D1114yes—
420C4⋊C4C2×C4×D1114yes—
421C22⋊C4—114no—
422C22⋊C4—114no—
423C22⋊C4—1116no—
424C22⋊C4C2×C4×D1114yes—
425C22⋊C4C2×C4×D1114yes—
426C42—114no—
427C42—1116no—
428C42—114no—
429C42C2×C4×D1114yes—
430C42C23×D1114yes—
431C11#6012611yescharacteristic, complemented, Sylow
432C23—42no—
433C23—114no—
434C23—224no—
435C23—444no—
436C23#6694514yes—
437C23C22×C4×D1111yescharacteristic
438C23C22×C4×D1111yescharacteristic
439C23C22×C4×D1111yescharacteristic
440Q8—224no—
441Q8—224no—
442D4—228no—
443D4—228no—
444D4—224no—
445D4—224no—
446C2×C4—44no—
447C2×C4—118no—
448C2×C4—114no—
449C2×C4—224no—
450C2×C4—228no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—4416no—
454C2×C4—444no—
455C2×C4#6694514yes—
456C2×C4#6694514yes—
457C2×C4#6694514yes—
458C2×C4C22×C4×D1118yes—
459C2×C4C22×C4×D1111yescharacteristic
460C2×C4C22×C4×D1111yescharacteristic
461C2×C4C22×C4×D1111yescharacteristic
462C2×C4C2×#434112yes—
463C2×C4C2×#434112yes—
464C2×C4C2×#434112yes—
465C2×C4C2×#434312yes—
466C2×C4C2×#434312yes—
467C2×C4C2×#434312yes—
468C2×C4C24×D1111yescharacteristic
469C8—22no—
470C8—22no—
471C8—24no—
472C8—224no—
473C8—224no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—44no—
478C22—224no—
479C22—228no—
480C22—884no—
481C22C2×#6694512yes—
482C22C2×#6694512yes—
483C22C2×#6694512yes—
484C22C23×C4×D1111yescharacteristic
485C4—28no—
486C4—224no—
487C4—228no—
488C4C2×#6694512yes—
489C4C2×#6694512yes—
490C4C2×#6694512yes—
491C4C22×#434111yescharacteristic
492C4C22×#434311yescharacteristic
493C2—22no—
494C2—22no—
495C2—22no—
496C2—444no—
497C2C22×#6694511yescharacteristic
498C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#424C2
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#424D11
hypocenterC11#60126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. #13077281C2semidirect
3. #13077273C2semidirect
4. #13077266C2semidirect
5. #13077259C2semidirect
6. #13077180C2semidirect
9. #13077034C2semidirect
10. C2×#10622714C2semidirect
11. C2×C11×#424C2semidirect
28. C11×#424C22semidirect
29. C11×#424C22semidirect
30. C2×C11×C4⋊C8C22semidirect
34. M16×Dic11C22semidirect
41. #10622714C22semidirect
42. #10622714C22semidirect
43. C2×#66879C22semidirect
44. C2×C8×Dic11C22semidirect
46. #10622612C22semidirect
47. #10622537C22semidirect
48. #10622453C22semidirect
49. #10622453C22semidirect
50. #10622448C22semidirect
51. #10622446C22semidirect
189. C2×#424D11semidirect
258. #424C2×D11semidirect
259. #424C2×D11semidirect
261. C2×C4⋊C8C2×D11semidirect
431. C11#60126semidirect

Maximal subgroups

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

subgroupindex
#130818172
#130772812
#130772732
#130772662
#130772592
#130771802
#130770602
C2×#106227232
#130770342
C2×#106227142
C2×C11×#4242
#6012611