Finite Group Databasebeta

← #14771467

Subgroups — #14771467

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic
2#13071481C212yesmaximal
3#13069354C211yesmaximal, characteristic, complemented
4#13069352C211yesmaximal, characteristic, complemented
5#13069208C212yesmaximal, complemented
6#13069206C212yesmaximal, complemented
7#13068701C212yesmaximal
8#13068638C211yesmaximal, characteristic
9#13068515C211yesmaximal, characteristic, complemented
10#13068393C211yesmaximal, characteristic
11C11×#1776C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2212yes—
14C2×#66925—22no—
15C2×C11×#107C2211yescharacteristic
16C2×C11×#106C2211yescharacteristic
17C2×C11×#97C2211yescharacteristic
18C4×C11×C4⋊C4C2212yes—
19C2×(C2×D11)⋊C8C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21C2×#66881C2211yescharacteristic
22C2×#66879C2211yescharacteristic
23#10622600C2212yes—
24C4⋊C4×Dic11C2212yes—
25#10622586C2212yes—
26C2×#66871C2212yes—
27C4×(C2×D11)⋊C4C2211yescharacteristic
28#10622546—22no—
29#10622541C2212yes—
30D11×#107C418yescomplemented
31#10622277—22no—
32#10622265—22no—
33C11×#340C2212yes—
34#10622189C2212yes—
35#10622188C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622162C2211yescharacteristic
40C22×C4×D11—22no—
41C22×C4×D11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11—22no—
47C2×C42×C11C2311yescharacteristic
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4D412yes—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11C2311yescharacteristic
57C22×C11⋊C8C2311yescharacteristic
58C22×C11⋊C8C2311yescharacteristic
59C2×C8×D11—22no—
60C2×C8×D11—22no—
61C2×C8×D11C2×C414yes—
62C4⋊C4×D11—24no—
63C4⋊C4×D11C2×C418yes—
64#66925—48no—
65C11×#107C2×C414yes—
66C11×#106—22no—
67C11×#97—22no—
68C11×#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95D412yes—
74(C2×D11)⋊C8—22no—
75#66882C2×C414yes—
76#66881—22no—
77#66879—22no—
78#66871C2×C418yes—
79#22617—111nomaximal, Sylow
80C23×D11C2×D411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11C2×D412yes—
88C22×Dic11C2×D411yescharacteristic
89C2×C4×D11—28no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—44no—
95C2×C4×D11—44no—
96C2×C4×D11C22×C412yes—
97C2×C4×D11#4112yes—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11C22×C412yes—
102C2×C8×C11#4112yes—
103C2×C8×C11#4112yes—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4C22×C414yes—
108C42×C11—21no—
109C42×C11—21no—
110C42×C11—44no—
111(C2×D11)⋊C4—24no—
112(C2×D11)⋊C4—44no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11C22×C414yes—
117Dic11⋊C4—28no—
118Dic11⋊C4—44no—
119Dic11⋊C4—44no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—44no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8C22×C412yes—
129C8×D11—28no—
130C22×#107—111no—
131#2344—112no—
132#1943—111no—
133#1943—111no—
134#1921—112no—
135#1921—112no—
136#1823—112no—
137#1807—111no—
138#1776—111no—
139#1776D1111yescharacteristic, complemented
140#1752—111no—
141C23×C11C22×D411yescharacteristic
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—22no—
145C22×D11C4×D412yes—
146C22×D11AGL(1,ℤ/8)14yes—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C23×C411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C112−1+411yescharacteristic
161C2×C4×C112−1+411yescharacteristic
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—24no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11C4×D412yes—
174C4×D11—22no—
175C4×D11—22no—
176C4×D11—22no—
177C4×D11—22no—
178C4×D11—416no—
179C8×C11—41no—
180C8×C11#11714yescomplemented
181C11⋊C8—22no—
182C11⋊C8—41no—
183C23×C8—111no—
184C2×#117—222no—
185C22×C4⋊C4—112no—
186C2×#107—111no—
187C2×#107—112no—
188C2×#107—118no—
189C2×#107C2×D1111yescharacteristic
190C2×#106—111no—
191C2×#106C2×D1111yescharacteristic
192C2×C22⋊C8—111no—
193C2×#97—111no—
194C2×#97C2×D1111yescharacteristic
195#389—112no—
196#389—112no—
197#387—222no—
198#387—222no—
199#381—222no—
200#380—112no—
201C4×C4⋊C4—112no—
202C4×C4⋊C4C2×D1112yes—
203C4×C22⋊C4—111no—
204#340—112no—
205#340—112no—
206#340—112no—
207#340—112no—
208#340C2×D1112yes—
209#336—111no—
210#336—111no—
211C22×C11C2×C4×D411yescharacteristic
212C22×C11#54711yescharacteristic
213C22×C11#54711yescharacteristic
214C22×C11C2×AGL(1,ℤ/8)12yes—
215C22×C11#57812yes—
216C2×D11—24no—
217C2×D11—24no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11#44214yes—
221C4×C11—42no—
222C4×C11—44no—
223C4×C11—82no—
224C4×C11C2×#11711yescharacteristic
225C4×C11#51911yescharacteristic
226C4×C11#55211yescharacteristic
227C4×C11#55211yescharacteristic
228Dic11—22no—
229Dic11—42no—
230Dic11—44no—
231Dic11—82no—
232C23×C4—111no—
233C23×C4—222no—
234C22×C8—111no—
235C22×C8—114no—
236C22×C8—111no—
237C22×C8—222no—
238C22×C8—222no—
239C22×C8C22×D1111yescharacteristic
240C22×C8C22×D1111yescharacteristic
241#117—448no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—118no—
244C2×C4⋊C4—112no—
245C2×C4⋊C4—224no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4C22×D1112yes—
250C2×C4⋊C4C22×D1112yes—
251C2×C22⋊C4—112no—
252C2×C22⋊C4—222no—
253C2×C42—22no—
254C2×C42—111no—
255C2×C42—222no—
256C2×C42C22×D1111yescharacteristic
257#107—114no—
258#107—118no—
259#107C4×D1114yes—
260#106—22no—
261#106—222no—
262C22⋊C8—222no—
263#97—22no—
264#97—222no—
265#95—22no—
266#95—112no—
267#95—222no—
268#95—222no—
269#95—222no—
270#95—222no—
271C2×C11#234411yescharacteristic
272C2×C11C2×#44211yescharacteristic
273C2×C11#295011yescharacteristic
274C2×C11#334312yes—
275C2×C11#334312yes—
276D11—24no—
277C24—111no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—111no—
281C22×C4—112no—
282C22×C4—112no—
283C22×C4—112no—
284C22×C4—228no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4—444no—
292C22×C4—444no—
293C22×C4D4×D1112yes—
294C22×C4C23×D1111yescharacteristic
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—112no—
299C2×C8—221no—
300C2×C8—221no—
301C2×C8—228no—
302C2×C8—221no—
303C2×C8—221no—
304C2×C8—221no—
305C2×C8C2×C4×D1112yes—
306C2×C8#433912yes—
307C2×C8#433912yes—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—114no—
312C4⋊C4—228no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—444no—
317C4⋊C4—444no—
318C4⋊C4C2×C4×D1114yes—
319C22⋊C4—224no—
320C22⋊C4—444no—
321C42—21no—
322C42—21no—
323C42—44no—
324C42—221no—
325C42—221no—
326C42—444no—
327C11#2261711yescharacteristic, complemented, Sylow
328C23—114no—
329C23—112no—
330C23—221no—
331C23—222no—
332C23—221no—
333C23C2×D4×D1111yescharacteristic
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—112no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—222no—
352C2×C4—224no—
353C2×C4—222no—
354C2×C4—4416no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4C22×C4×D1111yescharacteristic
361C2×C4C2×#433911yescharacteristic
362C2×C4C2×#433911yescharacteristic
363C2×C4#6704011yescharacteristic
364C2×C4#41×D1111yescharacteristic
365C2×C4#6704311yescharacteristic
366C8—41no—
367C8—222no—
368C8—441no—
369C8#6692514yescomplemented
370C22—114no—
371C22—222no—
372C22—224no—
373C22—224no—
374C22—222no—
375C22#1062303811yescharacteristic
376C22C4×D4×D1111yescharacteristic
377C22#1062308211yescharacteristic
378C22D11×AGL(1,ℤ/8)12yes—
379C22#1062331012yes—
380C4—44no—
381C4—42no—
382C4—82no—
383C4—222no—
384C4—444no—
385C4—442no—
386C4—882no—
387C4C2×#6692511yescharacteristic
388C4#1062306011yescharacteristic
389C4#1062310311yescharacteristic
390C4#1062311211yescharacteristic
391C2—224no—
392C2#1307148111yescharacteristic
393C2D11×#44211yescharacteristic
394C2#1307748111yescharacteristic
395C2#1308105712yes—
396C2#1308106112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1776C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1776D11
hypocenterC11#22617
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
3. #13069354C2semidirect
4. #13069352C2semidirect
5. #13069208C2semidirect
6. #13069206C2semidirect
9. #13068515C2semidirect
11. C11×#1776C2semidirect
30. D11×#107C4semidirect
139. #1776D11semidirect
180. C8×C11#117semidirect
327. C11#22617semidirect
369. C8#66925semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
#130714812
#130693542
#130693522
#130692082
#130692062
#130687012
#130686382
#130685152
#130683932
C11×#17762
#2261711