Finite Group Databasebeta

← #14771475

Subgroups — #14771475

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic
2#13071489C212yesmaximal
3#13069354C211yesmaximal, characteristic, complemented
4#13069352C211yesmaximal, characteristic, complemented
5#13069187C212yesmaximal, complemented
6#13069185C212yesmaximal, complemented
7#13068705C212yesmaximal
8#13068638C211yesmaximal, characteristic
9#13068515C211yesmaximal, characteristic, complemented
10#13068393C211yesmaximal, characteristic
11C11×#1776C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2212yes—
14C2×C11×#107C2211yescharacteristic
15C2×C11×#106C2211yescharacteristic
16C2×C11×#97C2211yescharacteristic
17C4×C11×C4⋊C4C2212yes—
18C2×(C2×D11)⋊C8C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66881C2211yescharacteristic
21C2×#66879C2211yescharacteristic
22#10622600C2212yes—
23C4⋊C4×Dic11C2212yes—
24#10622586C2212yes—
25C2×#66871C2212yes—
26C4×(C2×D11)⋊C4—22no—
27C4×(C2×D11)⋊C4C2211yescharacteristic
28#10622546—22no—
29#10622541C2212yes—
30D11×#107C418yescomplemented
31#10622280—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—
64C11×#107C2×C414yes—
65C11×#106—22no—
66C11×#97—22no—
67C11×#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95D412yes—
73(C2×D11)⋊C8—22no—
74#66882C2×C414yes—
75#66881—22no—
76#66879—22no—
77#66871C2×C418yes—
78#22618—111nomaximal, Sylow
79C23×D11C2×D411yescharacteristic
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11C2×D412yes—
87C22×Dic11C2×D411yescharacteristic
88C2×C4×D11—28no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—82no—
94C2×C4×D11—82no—
95C2×C4×D11C22×C412yes—
96C2×C4×D11#4112yes—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11C22×C412yes—
101C2×C8×C11#4112yes—
102C2×C8×C11#4112yes—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4C22×C414yes—
107C42×C11—21no—
108C42×C11—21no—
109C42×C11—82no—
110(C2×D11)⋊C4—24no—
111(C2×D11)⋊C4—44no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11C22×C414yes—
116Dic11⋊C4—28no—
117Dic11⋊C4—82no—
118Dic11⋊C4—82no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—82no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8C22×C412yes—
128C8×D11—28no—
129C22×#107—111no—
130#2345—112no—
131#1943—111no—
132#1943—111no—
133#1918—112no—
134#1918—112no—
135#1824—112no—
136#1807—111no—
137#1776—111no—
138#1776D1111yescharacteristic, complemented
139#1752—111no—
140C23×C11C22×D411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—22no—
144C22×D11C4×D412yes—
145C22×D11#13714yes—
146C2×C4×C11—24no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×C4×C112−1+411yescharacteristic
160C2×C4×C112−1+411yescharacteristic
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11C4×D412yes—
173C4×D11—22no—
174C4×D11—22no—
175C4×D11—22no—
176C4×D11—22no—
177C4×D11—88no—
178C8×C11—41no—
179C8×C11#11714yes—
180C11⋊C8—22no—
181C11⋊C8—41no—
182C23×C8—111no—
183C22×C4⋊C4—112no—
184C2×#107—111no—
185C2×#107—112no—
186C2×#107—118no—
187C2×#107C2×D1111yescharacteristic
188C2×#106—111no—
189C2×#106C2×D1111yescharacteristic
190C2×C22⋊C8—111no—
191C2×#97—111no—
192C2×#97C2×D1111yescharacteristic
193#389—112no—
194#389—112no—
195#387—222no—
196#387—222no—
197#380—112no—
198#380—222no—
199C4×C4⋊C4—112no—
200C4×C4⋊C4C2×D1112yes—
201C4×C22⋊C4—111no—
202C4×C22⋊C4—222no—
203#340—112no—
204#340—112no—
205#340—112no—
206#340—112no—
207#340C2×D1112yes—
208#336—111no—
209#336—111no—
210C22×C11C2×C4×D411yescharacteristic
211C22×C11#54711yescharacteristic
212C22×C11#54711yescharacteristic
213C22×C11C2×#13712yes—
214C22×C11#57612yes—
215C2×D11—24no—
216C2×D11—24no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11#44114yes—
220C4×C11—42no—
221C4×C11—44no—
222C4×C11—82no—
223C4×C11C2×#11711yescharacteristic
224C4×C11#51911yescharacteristic
225C4×C11#55211yescharacteristic
226C4×C11#55211yescharacteristic
227Dic11—22no—
228Dic11—42no—
229Dic11—44no—
230Dic11—82no—
231C23×C4—111no—
232C23×C4—222no—
233C22×C8—111no—
234C22×C8—114no—
235C22×C8—111no—
236C22×C8—222no—
237C22×C8—222no—
238C22×C8C22×D1111yescharacteristic
239C22×C8C22×D1111yescharacteristic
240C2×C4⋊C4—112no—
241C2×C4⋊C4—118no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—224no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4C22×D1112yes—
248C2×C4⋊C4C22×D1112yes—
249C2×C22⋊C4—112no—
250C2×C22⋊C4—222no—
251C2×C42—22no—
252C2×C42—111no—
253C2×C42—222no—
254C2×C42C22×D1111yescharacteristic
255#107—114no—
256#107—118no—
257#107C4×D1114yes—
258#106—22no—
259#106—222no—
260C22⋊C8—222no—
261#97—22no—
262#97—222no—
263#95—22no—
264#95—112no—
265#95—222no—
266#95—222no—
267#95—222no—
268#95—222no—
269C2×C11#234411yescharacteristic
270C2×C11C2×#44111yescharacteristic
271C2×C11#294811yescharacteristic
272C2×C11#334612yes—
273C2×C11#334612yes—
274D11—24no—
275C24—111no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—111no—
279C22×C4—112no—
280C22×C4—112no—
281C22×C4—112no—
282C22×C4—228no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—222no—
289C22×C4—882no—
290C22×C4—882no—
291C22×C4D4×D1112yes—
292C22×C4C23×D1111yescharacteristic
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—112no—
297C2×C8—221no—
298C2×C8—221no—
299C2×C8—228no—
300C2×C8—221no—
301C2×C8—221no—
302C2×C8—221no—
303C2×C8C2×C4×D1112yes—
304C2×C8#433912yes—
305C2×C8#433912yes—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—114no—
310C4⋊C4—228no—
311C4⋊C4—222no—
312C4⋊C4—222no—
313C4⋊C4—222no—
314C4⋊C4—882no—
315C4⋊C4—882no—
316C4⋊C4C2×C4×D1114yes—
317C22⋊C4—224no—
318C22⋊C4—444no—
319C42—21no—
320C42—21no—
321C42—82no—
322C42—221no—
323C42—221no—
324C42—882no—
325C11#2261811yescharacteristic, complemented, Sylow
326C23—114no—
327C23—112no—
328C23—221no—
329C23—222no—
330C23—221no—
331C23C2×D4×D1111yescharacteristic
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—112no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—224no—
351C2×C4—222no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—888no—
358C2×C4C22×C4×D1111yescharacteristic
359C2×C4C2×#433911yescharacteristic
360C2×C4C2×#433911yescharacteristic
361C2×C4#6704011yescharacteristic
362C2×C4#41×D1111yescharacteristic
363C2×C4#6704311yescharacteristic
364C8—41no—
365C8—222no—
366C8—441no—
367C8#6692514yes—
368C22—114no—
369C22—224no—
370C22—224no—
371C22—222no—
372C22—222no—
373C22#1062303811yescharacteristic
374C22C4×D4×D1111yescharacteristic
375C22#1062308211yescharacteristic
376C22#1062330512yes—
377C22D11×#13712yes—
378C4—42no—
379C4—44no—
380C4—82no—
381C4—222no—
382C4—442no—
383C4—444no—
384C4—882no—
385C4C2×#6692511yescharacteristic
386C4#1062306011yescharacteristic
387C4#1062310311yescharacteristic
388C4#1062311211yescharacteristic
389C2—224no—
390C2#1307148111yescharacteristic
391C2D11×#44111yescharacteristic
392C2#1307746511yescharacteristic
393C2#1308110212yes—
394C2#1308110612yes—
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#22618
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. #13069187C2semidirect
6. #13069185C2semidirect
9. #13068515C2semidirect
11. C11×#1776C2semidirect
30. D11×#107C4semidirect
138. #1776D11semidirect
325. C11#22618semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
#130714892
#130693542
#130693522
#130691872
#130691852
#130687052
#130686382
#130685152
#130683932
C11×#17762
#2261811