Finite Group Databasebeta

← #14767598

Subgroups — #14767598

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622309C211yesmaximal, characteristic
2#13071324C212yesmaximal, complemented
3#13069430C212yesmaximal, complemented
4#13068972C212yesmaximal, complemented
5#13068965C212yesmaximal
6#13068958C212yesmaximal, complemented
7#13068951C212yesmaximal, complemented
8#13068367C211yesmaximal, characteristic, complemented
9C11×#1834C211yesmaximal, characteristic, complemented
10C22×Dic44C2211yescharacteristic
11C22×D88C2211yescharacteristic
12C22×#4314C2212yes—
13C2×#66946C2212yes—
14C2×#66940C2212yes—
15C2×#66928C2212yes—
16C2×C4×C8×C11C2211yescharacteristic
17C11×#384C2212yes—
18#10622603—22no—
19#10622603—22no—
20#10622602—22no—
21#10622602—22no—
22#10622601C2212yes—
23#10622587C2212yes—
24C2×#66874C2212yes—
25C2×#66874C2212yes—
26C2×#66873C2212yes—
27C2×#66873C2212yes—
28#10622545C2211yescharacteristic
29C2×#66867C2211yescharacteristic
30#10622309C418yescomplemented
31C11×#340C2211yescharacteristic
32C11×#340C2212yes—
33C11×#340C2211yescharacteristic
34#10622188C2212yes—
35#10622188C2212yes—
36C22×D44C2312yes—
37C22×C4×D11—22no—
38C22×Dic22C2312yes—
39C22×C8×C11C2311yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C42×C11C2311yescharacteristic
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×Dic11⋊C4—22no—
52C2×C4×Dic11—22no—
53C2×C4×Dic11C2312yes—
54C22×C11⋊C8C2312yes—
55C2×Dic44—42no—
56C2×Dic44C2×C414yescomplemented
57C2×D88—42no—
58C2×D88C2×C414yes—
59C2×#4314—42no—
60C2×#4314—42no—
61C2×#4314C2×C418yescomplemented
62#66946—42no—
63#66946—42no—
64#66940—42no—
65#66940—42no—
66#66928—24no—
67#66928C2×C418yescomplemented
68C4×C8×C11C2×C414yescomplemented
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95D411yescharacteristic
72C11⋊#95D412yes—
73C11⋊#95D411yescharacteristic
74#66874—42no—
75#66874—42no—
76#66873—42no—
77#66873—42no—
78#66867—22no—
79#22274—111nomaximal, Sylow
80C23×D11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—22no—
87C22×Dic11C2×D412yes—
88C22×Dic11C2×D412yes—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44C22×C414yes—
95C2×C4×D11—44no—
96C2×C4×D11—82no—
97C2×C4×D11—82no—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22—22no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22C22×C414yes—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11C22×C412yes—
107C2×C8×C11C22×C412yes—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—82no—
113C11×C4⋊C4—82no—
114C42×C11C22×C412yes—
115C42×C11#4112yes—
116(C2×D11)⋊C4—28no—
117(C2×D11)⋊C4—28no—
118(C2×D11)⋊C4—44no—
119(C2×D11)⋊C4—82no—
120(C2×D11)⋊C4—82no—
121Dic11⋊C4—44no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11—44no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128Dic44—44no—
129D88—44no—
130#4314—48no—
131C2×#495—111no—
132#2326—112no—
133#1959—112no—
134#1880—112no—
135#1879—112no—
136#1878—112no—
137#1877—112no—
138#1834D1111yescharacteristic, complemented
139#1746—111no—
140C23×C11C22×D411yescharacteristic
141C22×D11—24no—
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148C2×C4×C11—21no—
149C2×C4×C11—22no—
150C2×C4×C11—21no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11C4×D412yes—
158C2×C4×C11C4×D412yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×C4×C11H(5,𝔽2)12yes—
162C2×C4×C11H(5,𝔽2)12yes—
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172D44—24no—
173D44—24no—
174D44—42no—
175D44—42no—
176C4×D11—88no—
177Dic22—24no—
178Dic22—24no—
179Dic22—42no—
180Dic22—42no—
181C8×C11—22no—
182C8×C11—22no—
183C11⋊C8—42no—
184C22×Q16—111no—
185C22×SD16—112no—
186C22×D8—111no—
187C2×#124—112no—
188C2×C4×Q8—112no—
189C2×C4×D4—112no—
190#495—118no—
191C2×#103—112no—
192C2×#103—112no—
193C2×#102—112no—
194C2×#102—112no—
195C2×#97—111no—
196C2×C4×C8C2×D1111yescharacteristic
197#391—112no—
198#390—112no—
199#388—222no—
200#388—222no—
201#385—222no—
202#385—222no—
203#384C2×D1112yes—
204#376—111no—
205#340C2×D1111yescharacteristic
206#340C2×D1112yes—
207#340C2×D1111yescharacteristic
208#336—112no—
209#336—112no—
210C22×C11C2×C4×D411yescharacteristic
211C22×C11#53512yes—
212C22×C11#57611yescharacteristic
213C22×C11#57712yes—
214C22×C11#57811yescharacteristic
215C2×D11—44no—
216C2×D11—44no—
217C2×D11—44no—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—82no—
222C4×C11—22no—
223C4×C11—22no—
224C4×C11—82no—
225C4×C11—82no—
226C4×C11#51811yescharacteristic
227C4×C11#51811yescharacteristic
228C4×C11#54012yes—
229Dic11—44no—
230Dic11—42no—
231Dic11—42no—
232C22×Q8—112no—
233C22×D4—112no—
234C23×C4—222no—
235C2×Q16—114no—
236C2×Q16—442no—
237C2×SD16—118no—
238C2×SD16—442no—
239C2×SD16—442no—
240C2×D8—114no—
241C2×D8—442no—
242C22×C8—112no—
243C22×C8C22×D1111yescharacteristic
244C22×C8C22×D1111yescharacteristic
245#124—118no—
246#124—224no—
247C4×Q8—442no—
248C4×Q8—442no—
249C4×D4—442no—
250C4×D4—442no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4C22×D1112yes—
255C2×C4⋊C4C22×D1112yes—
256C2×C22⋊C4—222no—
257C2×C22⋊C4—222no—
258C2×C22⋊C4—222no—
259C2×C22⋊C4—222no—
260C2×C22⋊C4—222no—
261C2×C42—112no—
262C2×C42—222no—
263C2×C42C22×D1111yescharacteristic
264#103—442no—
265#103—442no—
266#102—442no—
267#102—442no—
268#97—222no—
269C4×C8C4×D1114yescomplemented
270#95—111no—
271#95—112no—
272#95—111no—
273#95—222no—
274#95—222no—
275C2×C11#232811yescharacteristic
276C2×C11#295111yescharacteristic
277C2×C11#295211yescharacteristic
278C2×C11#322412yes—
279C2×C11#322512yes—
280D11—84no—
281C24—222no—
282C2×Q8—114no—
283C2×Q8—222no—
284C2×Q8—222no—
285C2×Q8—222no—
286C2×Q8—222no—
287C2×Q8—222no—
288C2×D4—114no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—222no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—112no—
297C22×C4—112no—
298C22×C4—222no—
299C22×C4—444no—
300C22×C4—882no—
301C22×C4—882no—
302C22×C4D4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4C23×D1111yescharacteristic
305Q16—444no—
306SD16—448no—
307D8—444no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8C2×C4×D1112yes—
314C2×C8C2×C4×D1112yes—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—82no—
320C4⋊C4—82no—
321C4⋊C4—444no—
322C22⋊C4—228no—
323C22⋊C4—228no—
324C22⋊C4—444no—
325C22⋊C4—882no—
326C22⋊C4—882no—
327C42—222no—
328C42—222no—
329C42—444no—
330C42C2×C4×D1112yes—
331C42#434312yes—
332C11#2227411yescharacteristic, complemented, Sylow
333C23—224no—
334C23—442no—
335C23—442no—
336C23—442no—
337C23—442no—
338C23—442no—
339C23—442no—
340C23C2×D4×D1111yescharacteristic
341Q8—224no—
342Q8—224no—
343Q8—442no—
344Q8—442no—
345D4—224no—
346D4—224no—
347D4—442no—
348D4—442no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—222no—
359C2×C4—224no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—888no—
368C2×C4#6694612yes—
369C2×C4#6694612yes—
370C2×C4C22×C4×D1111yescharacteristic
371C2×C4C2×#434311yescharacteristic
372C2×C4#6704212yes—
373C2×C4#6704212yes—
374C8—22no—
375C8—22no—
376C8—442no—
377C22—444no—
378C22—444no—
379C22—444no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22—882no—
384C22C2×#6694611yescharacteristic
385C22#1062320512yes—
386C22#1062328811yescharacteristic
387C22#1062329312yes—
388C22#1062329711yescharacteristic
389C4—22no—
390C4—22no—
391C4—82no—
392C4—82no—
393C4—442no—
394C4—442no—
395C4—444no—
396C4#1062305211yescharacteristic
397C4#1062305211yescharacteristic
398C4#1062322912yes—
399C2—884no—
400C2#1307133911yescharacteristic
401C2#1307749011yescharacteristic
402C2#1307749911yescharacteristic
403C2#1307971312yes—
404C2#1307972812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1834C2
socleC23×C11C22×D4
prime radicalC22×D88C22
cosocleC22×C4×C11C24
hypercenter#1834D11
hypocenterC11#22274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #13071324C2semidirect
3. #13069430C2semidirect
4. #13068972C2semidirect
6. #13068958C2semidirect
7. #13068951C2semidirect
8. #13068367C2semidirect
9. C11×#1834C2semidirect
30. #10622309C4semidirect
56. C2×Dic44C2×C4semidirect
61. C2×#4314C2×C4semidirect
67. #66928C2×C4semidirect
68. C4×C8×C11C2×C4semidirect
138. #1834D11semidirect
269. C4×C8C4×D11semidirect
332. C11#22274semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
#130713242
#130694302
#130689722
#130689652
#130689582
#130689512
#130683672
C11×#18342
#2227411