Finite Group Databasebeta

← #15618341

Subgroups — #15618341

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077621C218yesmaximal, complemented
2#13077612C218yesmaximal, complemented
3#13077557C211yesmaximal, characteristic, complemented
4#13077551C211yesmaximal, characteristic, complemented
5#13077334C211yesmaximal, characteristic, complemented
6#13077328C211yesmaximal, characteristic, complemented
7#13077320C212yesmaximal, complemented
8#13077311C212yesmaximal, complemented
9#13077260C212yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11#13077044C212yesmaximal, complemented
12C2×#10622610C211yesmaximal, characteristic, complemented
13C11×#3455C211yesmaximal, characteristic
14C11×#542C414yes—
15C11×#541C412yes—
16C11×#540C412yes—
17C11×#539C414yes—
18C11×#538C414yes—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C11×#529C2218yes—
22C11×#525C2212yes—
23C4×C11×#41C2212yes—
24C2×C11×#117C2211yescharacteristic
25C2×#67001C2212yes—
26C2×#67001C2212yes—
27C22×#4318C2211yescharacteristic
28C23×C11⋊C8C2211yescharacteristic
29#10622847C2212yes—
30#10622847C2212yes—
31#10622820C2212yes—
32#10622637C2214yescomplemented
33#10622637C2218yescomplemented
34Q8×C11⋊C8C2214yescomplemented
35#10622625C2218yes—
36#10622625C2214yescomplemented
37#10622624C2218yes—
38#10622624C2218yes—
39#10622624C2218yescomplemented
40D4×C11⋊C8C2218yes—
41D4×C11⋊C8C2214yescomplemented
42#10622613C2218yes—
43#10622613C2218yescomplemented
44#10622612C2212yes—
45#10622612C2212yes—
46#10622610C2214yes—
47#10622610C2214yes—
48#10622610C2212yes—
49#10622610C2212yes—
50#10622610C2214yescomplemented
51#10622610C2214yescomplemented
52#10622538C2218yescomplemented
53#10622537C2211yescharacteristic
54#10622537C2211yescharacteristic
55C4×#4318C2212yes—
56C4×#4318C2214yescomplemented
57C2×#66867C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59C2×#66867C2214yescomplemented
60C2×C4×C11⋊C8C2211yescharacteristic
61C2×C4×C11⋊C8C2211yescharacteristic
62C2×C11×#41C2312yes—
63C23×C4×C11C2311yescharacteristic
64C11×C4⋊Q8C2×C411yescharacteristic
65C11×C4⋊Q8C2×C412yes—
66C11×#127C2×C411yescharacteristic
67C11×#126C2×C418yes—
68C11×#126C2×C418yes—
69C11×#125C2×C418yes—
70C11×#125C2×C412yes—
71C11×#124C2×C418yes—
72C11×#124C2×C412yes—
73C11×#123C2×C414yes—
74C11×#123C2×C418yes—
75C11×#123C2×C418yes—
76C11×C22⋊Q8C2×C414yes—
77C11×C22⋊Q8C2×C418yes—
78C11×C22⋊Q8C2×C414yes—
79C11×#121C2×C414yes—
80C11×#121C2×C418yes—
81C11×#121C2×C414yes—
82C11×#120C2×C414yes—
83C4×Q8×C11C2×C414yes—
84C4×Q8×C11C2314yes—
85C4×D4×C11C2×C418yes—
86C4×D4×C11C2×C414yes—
87C4×D4×C11C2318yes—
88C4×D4×C11C2314yes—
89C11×#117C2×C412yes—
90C11×#117C2×C412yes—
91C11×#117C2314yes—
92C11×#117C2312yes—
93C11×#117C2314yes—
94C2×C11×C4⋊C4C2×C412yes—
95C2×C11×C22⋊C4C2×C412yes—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2314yes—
99#67001—28no—
100#67001—28no—
101C2×#4318—24no—
102C2×#4318C2312yes—
103C2×#4318C2312yes—
104C2×#4318C2314yes—
105C2×#4318C2314yes—
106C2×#4318C2312yes—
107C2×#4318C2312yes—
108C22×C11⋊C8—24no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2314yes—
112C22×C11⋊C8C2314yes—
113C22×C11⋊C8C2314yes—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22⋊(C11⋊C8)C2318yes—
117C22⋊(C11⋊C8)C2318yes—
118C22⋊(C11⋊C8)C2318yes—
119C4⋊(C11⋊C8)C2314yes—
120C4⋊(C11⋊C8)C2314yes—
121C4⋊(C11⋊C8)C2318yes—
122C4⋊(C11⋊C8)C2318yes—
123#66867C2312yes—
124#66867C2312yes—
125#66867C2314yes—
126#66867C2314yes—
127#66867C2314yes—
128#66867C2314yes—
129C4×C11⋊C8C2314yes—
130C4×C11⋊C8C2312yes—
131C4×C11⋊C8C2312yes—
132C4×C11⋊C8C2314yes—
133C4×C11⋊C8C2314yes—
134C4×C11⋊C8C2314yes—
135#60209—111nomaximal, Sylow
136C24×C11C22×C411yescharacteristic
137C11×#41—24no—
138C11×#41—24no—
139C2×Q8×C11C22×C412yes—
140C2×Q8×C11C22×C414yes—
141C2×D4×C11C22×C414yes—
142C2×D4×C11C22×C412yes—
143C2×D4×C11C22×C418yes—
144C2×D4×C11C22×C414yes—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C22×C418yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C11×C4⋊C4C22×C414yes—
156C11×C4⋊C4C22×C414yes—
157C11×C4⋊C4C22×C414yes—
158C11×C4⋊C4C22×C418yes—
159C11×C4⋊C4C22×C414yes—
160C11×C4⋊C4C22×C418yes—
161C11×C4⋊C4C22×C418yes—
162C11×C4⋊C4C22×C414yes—
163C11×C22⋊C4C22×C414yes—
164C11×C22⋊C4C22×C414yes—
165C11×C22⋊C4C22×C414yes—
166C11×C22⋊C4C22×C418yes—
167C11×C22⋊C4C22×C418yes—
168C11×C22⋊C4C22×C418yes—
169C11×C22⋊C4C22×C418yes—
170C42×C11C22×C412yes—
171C42×C11C22×C411yescharacteristic
172C42×C11C22×C411yescharacteristic
173C42×C11C22×C418yes—
174C42×C11C2412yes—
175C42×C11C2412yes—
176C42×C11C2414yes—
177#4318—24no—
178#4318—24no—
179#4318—28no—
180#4318—28no—
181#4318—24no—
182#4318—24no—
183C2×C11⋊C8—28no—
184C2×C11⋊C8—28no—
185C2×C11⋊C8—28no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8#4114yes—
189C2×C11⋊C8#4114yes—
190C2×C11⋊C8C2412yes—
191C2×C11⋊C8C2412yes—
192C2×C11⋊C8C2414yes—
193C2×C11⋊C8C2414yes—
194C2×C11⋊C8C2411yescharacteristic
195C2×C11⋊C8C2411yescharacteristic
196C2×C11⋊C8C2412yes—
197#3455D1111yescharacteristic
198#2969—118no—
199#2968—118no—
200#2961—111no—
201#2960—111no—
202#2932—111no—
203#2931—111no—
204#2930—112no—
205#2929—112no—
206#2922—112no—
207#2921—111no—
208#2875—112no—
209C2×#405—111no—
210C23×C11—22no—
211C23×C11—42no—
212C23×C11C23×C412yes—
213C23×C11C23×C414yes—
214C23×C11C23×C411yescharacteristic
215Q8×C11—24no—
216Q8×C11—44no—
217D4×C11—28no—
218D4×C11—24no—
219D4×C11—44no—
220D4×C11—48no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—42no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11C23×C414yes—
231C2×C4×C11C23×C414yes—
232C2×C4×C11C23×C412yes—
233C2×C4×C11C23×C418yes—
234C2×C4×C11C23×C412yes—
235C2×C4×C11C23×C412yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C2×#4112yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11C2511yescharacteristic
240C11⋊C8—22no—
241C11⋊C8—24no—
242C11⋊C8—24no—
243C11⋊C8—22no—
244C11⋊C8C2×#4114yes—
245C11⋊C8C2×#4112yes—
246C11⋊C8C2×#4112yes—
247C2×#131—112no—
248C2×#131—112no—
249C22×M16—111no—
250C23×C8—111no—
251#542Dic1114yes—
252#541Dic1112yes—
253#540Dic1112yes—
254#539Dic1114yes—
255#538Dic1114yes—
256#533C2×D1111yescharacteristic
257#532C2×D1111yescharacteristic
258#529C2×D1118yes—
259#525C2×D1112yes—
260C4×#41C2×D1112yes—
261C2×#117C2×D1111yescharacteristic
262#446—114no—
263#446—118no—
264C8×Q8—114no—
265#436—118no—
266#436—114no—
267#435—118no—
268#435—118no—
269#435—118no—
270C8×D4—118no—
271C8×D4—114no—
272#433—118no—
273#433—118no—
274#431—118no—
275#424—112no—
276#424—112no—
277#423—111no—
278#423—111no—
279#408—112no—
280#408—112no—
281#407—112no—
282#405—114no—
283#405—114no—
284#405—112no—
285#405—112no—
286#405—114no—
287#405—114no—
288C4×M16—112no—
289C4×M16—114no—
290C2×#97—111no—
291C2×#97—111no—
292C2×#97—114no—
293C2×C4×C8—111no—
294C2×C4×C8—111no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—28no—
299C22×C11—24no—
300C22×C11—44no—
301C22×C11C4×#4112yes—
302C22×C11C24×C411yescharacteristic
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—28no—
308C4×C11—22no—
309C4×C11C4×#4112yes—
310C4×C11C22×#4111yescharacteristic
311C4×C11C22×#4111yescharacteristic
312C2×#41C22×D1112yes—
313C23×C4C22×D1111yescharacteristic
314#131—228no—
315#131—228no—
316C2×M16—112no—
317C2×M16—112no—
318C2×M16—112no—
319C2×M16—112no—
320C2×M16—114no—
321C2×M16—114no—
322C2×M16—224no—
323C22×C8—111no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—114no—
327C22×C8—111no—
328C22×C8—114no—
329C22×C8—114no—
330C22×C8—224no—
331C4⋊Q8C2×Dic1111yescharacteristic
332C4⋊Q8C2×Dic1112yes—
333#127C2×Dic1111yescharacteristic
334#126C2×Dic1118yes—
335#126C2×Dic1118yes—
336#125C2×Dic1118yes—
337#125C2×Dic1112yes—
338#124C2×Dic1118yes—
339#124C2×Dic1112yes—
340#123C2×Dic1114yes—
341#123C2×Dic1118yes—
342#123C2×Dic1118yes—
343C22⋊Q8C2×Dic1114yes—
344C22⋊Q8C2×Dic1118yes—
345C22⋊Q8C2×Dic1114yes—
346#121C2×Dic1114yes—
347#121C2×Dic1118yes—
348#121C2×Dic1114yes—
349#120C2×Dic1114yes—
350C4×Q8C2×Dic1114yes—
351C4×Q8C22×D1114yes—
352C4×D4C2×Dic1118yes—
353C4×D4C2×Dic1114yes—
354C4×D4C22×D1118yes—
355C4×D4C22×D1114yes—
356#117C2×Dic1112yes—
357#117C2×Dic1112yes—
358#117C22×D1114yes—
359#117C22×D1112yes—
360#117C22×D1114yes—
361C2×C4⋊C4C2×Dic1112yes—
362C2×C22⋊C4C2×Dic1112yes—
363C2×C42C22×D1111yescharacteristic
364C2×C42C22×D1111yescharacteristic
365C2×C42C22×D1114yes—
366C4⋊C8—114no—
367C4⋊C8—114no—
368C4⋊C8—118no—
369C4⋊C8—118no—
370C22⋊C8—118no—
371C22⋊C8—118no—
372C22⋊C8—118no—
373#97—112no—
374#97—112no—
375#97—114no—
376#97—114no—
377#97—114no—
378#97—114no—
379C4×C8—114no—
380C4×C8—112no—
381C4×C8—112no—
382C4×C8—114no—
383C4×C8—114no—
384C4×C8—114no—
385C2×C11—22no—
386C2×C11—44no—
387C2×C11—42no—
388C2×C11C2×C4×#4111yescharacteristic
389C2×C11#357312yes—
390C24C22×Dic1111yescharacteristic
391#41—24no—
392#41—24no—
393C2×Q8C22×Dic1112yes—
394C2×Q8C22×Dic1114yes—
395C2×D4C22×Dic1114yes—
396C2×D4C22×Dic1112yes—
397C2×D4C22×Dic1118yes—
398C2×D4C22×Dic1114yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4C22×Dic1111yescharacteristic
402C22×C4C22×Dic1112yes—
403C22×C4C22×Dic1112yes—
404C22×C4C22×Dic1112yes—
405C22×C4C22×Dic1118yes—
406C22×C4C23×D1114yes—
407C22×C4C23×D1112yes—
408C22×C4C23×D1111yescharacteristic
409M16—224no—
410M16—224no—
411M16—228no—
412M16—228no—
413M16—224no—
414M16—224no—
415C2×C8—114no—
416C2×C8—114no—
417C2×C8—111no—
418C2×C8—111no—
419C2×C8—112no—
420C2×C8—112no—
421C2×C8—112no—
422C2×C8—114no—
423C2×C8—114no—
424C2×C8—228no—
425C2×C8—228no—
426C2×C8—228no—
427C2×C8—222no—
428C2×C8—222no—
429C4⋊C4C22×Dic1114yes—
430C4⋊C4C22×Dic1114yes—
431C4⋊C4C22×Dic1114yes—
432C4⋊C4C22×Dic1118yes—
433C4⋊C4C22×Dic1114yes—
434C4⋊C4C22×Dic1118yes—
435C4⋊C4C22×Dic1118yes—
436C4⋊C4C22×Dic1114yes—
437C22⋊C4C22×Dic1114yes—
438C22⋊C4C22×Dic1114yes—
439C22⋊C4C22×Dic1114yes—
440C22⋊C4C22×Dic1118yes—
441C22⋊C4C22×Dic1118yes—
442C22⋊C4C22×Dic1118yes—
443C22⋊C4C22×Dic1118yes—
444C42C22×Dic1112yes—
445C42C22×Dic1111yescharacteristic
446C42C22×Dic1111yescharacteristic
447C42C22×Dic1118yes—
448C42C23×D1112yes—
449C42C23×D1112yes—
450C42C23×D1114yes—
451C11#6020911yescharacteristic, complemented, Sylow
452C23—22no—
453C23—42no—
454C23C23×Dic1112yes—
455C23C23×Dic1114yes—
456C23C23×Dic1111yescharacteristic
457Q8—24no—
458Q8—44no—
459D4—28no—
460D4—24no—
461D4—44no—
462D4—48no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—48no—
471C2×C4—42no—
472C2×C4#41×D1112yes—
473C2×C4#41×D1112yes—
474C2×C4C23×Dic1114yes—
475C2×C4C23×Dic1114yes—
476C2×C4C23×Dic1112yes—
477C2×C4C23×Dic1118yes—
478C2×C4C23×Dic1112yes—
479C2×C4C23×Dic1112yes—
480C2×C4C23×Dic1111yescharacteristic
481C2×C4C24×D1111yescharacteristic
482C8—114no—
483C8—112no—
484C8—112no—
485C8—222no—
486C8—224no—
487C8—224no—
488C8—222no—
489C22—22no—
490C22—28no—
491C22—24no—
492C22—22no—
493C22—24no—
494C22—44no—
495C22#41×Dic1112yes—
496C22C24×Dic1111yescharacteristic
497C4—24no—
498C4—22no—
499C4—28no—
500C4—22no—
501C4—22no—
502C4—24no—
503C4#41×Dic1112yes—
504C4C2×#41×D1111yescharacteristic
505C4C2×#41×D1111yescharacteristic
506C2—22no—
507C2—42no—
508C2—44no—
509C2C2×#41×Dic1111yescharacteristic
510C2#1308332812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
Fitting, prime radicalC11×#3455C2
cosocleC2×C4×C11C25
hypercenter#3455D11
hypocenterC11#60209
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #13077621C2semidirect
2. #13077612C2semidirect
3. #13077557C2semidirect
4. #13077551C2semidirect
5. #13077334C2semidirect
6. #13077328C2semidirect
7. #13077320C2semidirect
8. #13077311C2semidirect
9. #13077260C2semidirect
10. #13077254C2semidirect
11. #13077044C2semidirect
12. C2×#10622610C2semidirect
32. #10622637C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
36. #10622625C22semidirect
39. #10622624C22semidirect
41. D4×C11⋊C8C22semidirect
43. #10622613C22semidirect
50. #10622610C22semidirect
51. #10622610C22semidirect
52. #10622538C22semidirect
56. C4×#4318C22semidirect
59. C2×#66867C22semidirect
451. C11#60209semidirect

Maximal subgroups

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

subgroupindex
#130776212
#130776122
#130775572
#130775512
#130773342
#130773282
#130773202
#130773112
#130772602
#130772542
#130770442
C2×#106226102
C11×#34552
#6020911