Finite Group Databasebeta

← #14756456

Subgroups — #14756456

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622744C211yesmaximal, characteristic
2C22×#66873C211yesmaximal, characteristic
3C2×#10622735C211yesmaximal, characteristic, complemented
4#13071240C211yesmaximal, characteristic, complemented
5#13071196C211yesmaximal, characteristic
6#13069311C214yesmaximal, complemented
7#13069297C214yesmaximal, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10622823—22no—
18#10622744C418yescomplemented
19#10622735—24no—
20C2×#66885C2214yes—
21C2×#66879C2212yescomplemented
22C2×C8×Dic11C2212yescomplemented
23#10622601C2214yes—
24#10622590—21no—
25#10622589—21no—
26#10622586C2214yescomplemented
27C2×#66873—24no—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30#10622568—22no—
31#10622552—21no—
32#10622552—21no—
33C11×#340C2214yescomplemented
34#10622167C2212yescomplemented
35#10622167C2212yescomplemented
36C24×D11—21no—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×D44—22no—
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—22no—
45C22×D44C2×C414yes—
46C22×D44C2312yes—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16C2×C414yes—
50C22×C8×C11C2312yes—
51C11×#117—22no—
52C11×#117—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D412yes—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64#66979—22no—
65#66979—22no—
66#66979—22no—
67#66979C2×C414yes—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—24no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8D414yes—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79C11⋊#95—24no—
80#66885C2×C4116yescomplemented
81#66879—24no—
82C8×Dic11—24no—
83#66873—24no—
84#66873—24no—
85#21091—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C23×D11—22no—
88C23×D11—24no—
89C23×D11—42no—
90C23×D11—42no—
91C23×D11—82no—
92C23×D11—82no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—82no—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C22×C4×C11#4112yes—
103C22×C4×C11#4112yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11C2×D412yes—
107C22×Dic11C2×D412yes—
108C2×D44—28no—
109C2×D44—24no—
110C2×D44—28no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—42no—
117C2×D44—44no—
118C2×D44—42no—
119C2×D44—44no—
120C2×D44C22×C414yes—
121C11×M16—28no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11C22×C414yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—42no—
131C42×C11—42no—
132C22⋊Dic11—24no—
133C22⋊Dic11—24no—
134(C2×D11)⋊C4—84no—
135(C2×D11)⋊C4—84no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11C22×C414yes—
140Dic11⋊C4—84no—
141C4×Dic11—24no—
142C4×Dic11—22no—
143C4×Dic11—22no—
144C2×C11⋊C8—28no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8C2×D412yes—
150C2×C11⋊C8C2×D412yes—
151C2×#418—111no—
152C22×#102—111no—
153C2×#405—111no—
154#2317—111no—
155#2309—111no—
156#1936—114no—
157#1934—114no—
158#1736D1111yescharacteristic, complemented
159#1735—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11C4×D412yes—
163C23×C11#12112yes—
164C23×C11#12412yes—
165C23×C11C22×D411yescharacteristic
166C22×D11—24no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—44no—
170C22×D11—44no—
171C22×D11—48no—
172C22×D11—88no—
173C22×D11—88no—
174C22×D11—84no—
175C22×D11—84no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—84no—
182C2×C4×C11#11714yes—
183C2×C4×C11C4×D414yes—
184C2×C4×C11C4×D412yes—
185C2×C4×C11#12112yes—
186C2×C4×C11#12314yes—
187C2×C4×C11#12412yes—
188C2×C4×C11#12614yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×Dic11—24no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202D44—24no—
203D44—24no—
204D44—42no—
205D44—42no—
206D44—48no—
207C8×C11—24no—
208C11⋊C8—22no—
209C11⋊C8—22no—
210C23×D4—111no—
211C22×M16C2×D1111yescharacteristic
212C23×C8—111no—
213C2×#117—111no—
214C2×#117—111no—
215C2×#117C2×D1111yescharacteristic
216C22×C4⋊C4C2×D1111yescharacteristic
217#418—118no—
218C2×#102—114no—
219C2×#102—112no—
220C2×#102—112no—
221C2×#102—224no—
222#405—224no—
223C2×#97—112no—
224C2×C4×C8—112no—
225#390—114no—
226#390—221no—
227#390—221no—
228#389—114no—
229#385—222no—
230#384—221no—
231#382—221no—
232#379—222no—
233#340—112no—
234#340—112no—
235#340C2×D1114yescomplemented
236C22×C11—24no—
237C22×C11—24no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11#38814yes—
241C22×C11C2×C4×D411yescharacteristic
242C22×C11C2×#12111yescharacteristic
243C22×C11C2×#12411yescharacteristic
244C22×C11#57612yes—
245C22×C11#57712yes—
246C2×D11—48no—
247C2×D11—44no—
248C2×D11—816no—
249C2×D11—84no—
250C2×D11—82no—
251C2×D11—82no—
252C4×C11—82no—
253C4×C11—82no—
254C4×C11#38814yes—
255C4×C11C2×#11711yescharacteristic
256C4×C11C2×C4×D411yescharacteristic
257C4×C11C2×#12311yescharacteristic
258C4×C11C2×#12611yescharacteristic
259Dic11—44no—
260Dic11—42no—
261Dic11—42no—
262C25—221no—
263C22×D4—114no—
264C22×D4—112no—
265C22×D4—222no—
266C22×D4—222no—
267C22×D4—222no—
268C22×D4—221no—
269C22×D4—222no—
270C22×D4—222no—
271C23×C4—21no—
272C23×C4C22×D1111yescharacteristic
273C2×M16—22no—
274C2×M16—22no—
275C2×M16C4×D1114yes—
276C22×C8—114no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—222no—
280C22×C8—222no—
281C22×C8C22×D1112yes—
282#117—22no—
283#117—22no—
284#117—114no—
285#117—222no—
286#117—222no—
287#117—222no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4C22×D1112yes—
296C2×C4⋊C4C22×D1112yes—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—112no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—224no—
301C2×C22⋊C4—224no—
302C2×C42—21no—
303C2×C42—112no—
304C2×C42—221no—
305#102—1116no—
306#102—224no—
307#102—224no—
308#97—224no—
309C4×C8—224no—
310#95—224no—
311C2×C11—24no—
312C2×C11C2×#38811yescharacteristic
313C2×C11#294612yes—
314C2×C11#305711yescharacteristic
315C2×C11#305811yescharacteristic
316C2×C11#313612yes—
317D11—84no—
318C24—222no—
319C24—224no—
320C24—442no—
321C24—442no—
322C24—882no—
323C24—882no—
324C24D4×D1111yescharacteristic
325C2×D4—114no—
326C2×D4—228no—
327C2×D4—228no—
328C2×D4—224no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—442no—
335C2×D4—442no—
336C2×D4—444no—
337C2×D4—444no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—82no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—222no—
345C22×C4C2×C4×D1112yes—
346C22×C4#433912yes—
347C22×C4#433912yes—
348C22×C4D4×D1112yes—
349C22×C4D4×D1111yescharacteristic
350C22×C4#434112yes—
351C22×C4#434312yes—
352C22×C4C23×D1111yescharacteristic
353M16—28no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—228no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8C2×C4×D1114yes—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—42no—
369C4⋊C4—114no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—884no—
374C22⋊C4—42no—
375C22⋊C4—224no—
376C22⋊C4—224no—
377C22⋊C4—884no—
378C22⋊C4—884no—
379C42—42no—
380C42—224no—
381C42—222no—
382C42—222no—
383C11#2109111yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—224no—
387C23—442no—
388C23—442no—
389C23—444no—
390C23—448no—
391C23—444no—
392C23—888no—
393C23—888no—
394C23—884no—
395C23—884no—
396C23#6693712yes—
397C23#6693812yes—
398C23#6694612yes—
399C23C2×D4×D1111yescharacteristic
400D4—224no—
401D4—224no—
402D4—442no—
403D4—442no—
404D4—448no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—224no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4#6692514yes—
419C2×C4(C22⋊D11)⋊C414yes—
420C2×C4#6693712yes—
421C2×C4#6693812yes—
422C2×C4#6694612yes—
423C2×C4#6694714yes—
424C2×C4#6695114yes—
425C2×C4C22×C4×D1111yescharacteristic
426C2×C4C2×#433911yescharacteristic
427C2×C4C2×#433911yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4C2×#434111yescharacteristic
430C2×C4C2×#434311yescharacteristic
431C8—24no—
432C8—222no—
433C8—222no—
434C22—24no—
435C22—24no—
436C22—22no—
437C22—22no—
438C22—444no—
439C22—448no—
440C22—8816no—
441C22—884no—
442C22—882no—
443C22—882no—
444C22#1062228214yes—
445C22C2×#6693711yescharacteristic
446C22C2×#6693811yescharacteristic
447C22C2×#6694611yescharacteristic
448C22#1062330512yes—
449C22#1062330912yes—
450C4—82no—
451C4—82no—
452C4—444no—
453C4—442no—
454C4—442no—
455C4#1062228214yes—
456C4C2×#6692511yescharacteristic
457C4C2×(C22⋊D11)⋊C411yescharacteristic
458C4C2×#6694711yescharacteristic
459C4C2×#6695111yescharacteristic
460C2—24no—
461C2—884no—
462C2C2×#1062228211yescharacteristic
463C2#1307744612yes—
464C2#1307825811yescharacteristic
465C2#1307826311yescharacteristic
466C2#1307897312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#21091
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. C2×#10622735C2semidirect
4. #13071240C2semidirect
6. #13069311C2semidirect
7. #13069297C2semidirect
8. #13068332C2semidirect
9. C11×#1736C2semidirect
18. #10622744C4semidirect
21. C2×#66879C22semidirect
22. C2×C8×Dic11C22semidirect
26. #10622586C22semidirect
33. C11×#340C22semidirect
34. #10622167C22semidirect
35. #10622167C22semidirect
80. #66885C2×C4semidirect
158. #1736D11semidirect
235. #340C2×D11semidirect
383. C11#21091semidirect

Maximal subgroups

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

subgroupindex
C2×#106227442
C22×#668732
C2×#106227352
#130712402
#130711962
#130693112
#130692972
#130683322
C11×#17362
#2109111