Finite Group Databasebeta

← #14771462

Subgroups — #14771462

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071509C211yesmaximal, characteristic
2#13071501C211yesmaximal, characteristic
3#13069360C212yesmaximal, complemented
4#13069210C212yesmaximal, complemented
5#13069189C212yesmaximal, complemented
6#13068711C211yesmaximal, characteristic
7#13068711C211yesmaximal, characteristic
8#13068645C211yesmaximal, characteristic
9#13068516C212yesmaximal, complemented
10#13068392C211yesmaximal, characteristic
11C2×C11×#427C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#427C418yescomplemented
16C2×C11×#107C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20#10622825C2211yescharacteristic
21#10622825C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66882C2212yes—
25C2×#66879C2212yes—
26#10622598C2212yes—
27#10622598C2212yes—
28C4⋊C4×Dic11C2212yes—
29C4⋊C4×Dic11C2212yes—
30#10622564—22no—
31#10622564—22no—
32#10622550—21no—
33#10622549—21no—
34C4×C4⋊Dic11—21no—
35#10622545—21no—
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C8×C11—24no—
44C22×C8×C11C2×C414yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#117—22no—
48C11×#117—22no—
49C11×#117C2×C414yes—
50C11×#117C2×C414yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D412yes—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2312yes—
69C22×C11⋊C8C2312yes—
70C11×#107C2×C414yes—
71C11×#107C2×C414yes—
72C11×#106C2×C414yes—
73C11×#106C2×C414yes—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D411yescharacteristic
81C11⋊#95D411yescharacteristic
82C22⋊(C11⋊C8)—22no—
83#66882—24no—
84#66879—24no—
85#22616—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4112yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11C2×D412yes—
100C22×Dic11C2×D412yes—
101C2×C8×C11—28no—
102C2×C8×C11—22no—
103C2×C8×C11C22×C412yes—
104C2×C8×C11C22×C412yes—
105C2×C8×C11#4114yes—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4C22×C412yes—
111C11×C4⋊C4C22×C412yes—
112C11×C4⋊C4C22×C412yes—
113C11×C4⋊C4C22×C412yes—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C42×C11—24no—
117C42×C11—24no—
118C22⋊Dic11—42no—
119C22⋊Dic11—81no—
120C22⋊Dic11—81no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—44no—
126C4⋊Dic11—82no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—44no—
130C4×Dic11—82no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×#427D1111yescharacteristic
135#2347—111no—
136#2346—111no—
137#1944—112no—
138#1921—112no—
139#1918—112no—
140#1825—111no—
141#1825—111no—
142#1808—111no—
143#1776—112no—
144#1752—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11C4×D412yes—
150C23×C11C22×D411yescharacteristic
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11C4×D412yes—
166C2×C4×C11C23×C411yescharacteristic
167C2×C4×C11C2×#4112yes—
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C112−1+412yes—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C8×C11—22no—
183C8×C11#11714yes—
184C11⋊C8—42no—
185C23×C8C2×D1111yescharacteristic
186C2×#117C2×D1111yescharacteristic
187C2×#117C2×D1111yescharacteristic
188#427Dic1118yescomplemented
189C2×#107—112no—
190C2×#107C2×D1111yescharacteristic
191C2×#107C2×D1111yescharacteristic
192C2×#106C2×D1111yescharacteristic
193C2×#106C2×D1111yescharacteristic
194C2×C22⋊C8—111no—
195C2×#97—112no—
196#389—112no—
197#389—112no—
198#388—222no—
199#388—222no—
200#383—221no—
201#382—221no—
202#380—111no—
203#380—111no—
204C4×C4⋊C4—112no—
205C4×C4⋊C4—112no—
206C4×C4⋊C4—221no—
207C4×C22⋊C4—111no—
208#376—221no—
209#340—112no—
210#340—112no—
211#340—112no—
212#340—112no—
213#340—112no—
214#336—112no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11C2×C4×D411yescharacteristic
221C22×C11#54712yes—
222C22×C11#57512yes—
223C22×C11#57611yescharacteristic
224C22×C11#57811yescharacteristic
225C4×C11—22no—
226C4×C11—42no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11C2×#11711yescharacteristic
231C4×C11#51911yescharacteristic
232C4×C11#55212yes—
233Dic11—42no—
234Dic11—42no—
235Dic11—82no—
236Dic11—82no—
237C23×C4C22×D1111yescharacteristic
238C22×C8—24no—
239C22×C8—112no—
240C22×C8C2×Dic1114yes—
241C22×C8C22×D1111yescharacteristic
242C22×C8C22×D1111yescharacteristic
243#117—22no—
244#117—22no—
245#117C2×Dic1114yes—
246#117C2×Dic1114yes—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—112no—
249C2×C4⋊C4—222no—
250C2×C4⋊C4—222no—
251C2×C4⋊C4C22×D1111yescharacteristic
252C2×C4⋊C4C22×D1111yescharacteristic
253C2×C4⋊C4C22×D1111yescharacteristic
254C2×C4⋊C4C22×D1111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—112no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—112no—
263C2×C42—222no—
264C2×C42—222no—
265#107—224no—
266#107C2×Dic1114yes—
267#107C2×Dic1114yes—
268#106C2×Dic1114yes—
269#106C2×Dic1114yes—
270C22⋊C8—222no—
271#97—224no—
272#95—111no—
273#95—111no—
274#95—222no—
275#95—222no—
276#95—222no—
277#95—222no—
278#95—221no—
279#95—221no—
280C2×C11—42no—
281C2×C11#234411yescharacteristic
282C2×C11#294311yescharacteristic
283C2×C11#295111yescharacteristic
284C2×C11#334712yes—
285C2×C11#334912yes—
286C24D4×D1111yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—112no—
294C22×C4—112no—
295C22×C4—222no—
296C22×C4—222no—
297C22×C4D4×D1111yescharacteristic
298C22×C4#434112yes—
299C22×C4C22×Dic1112yes—
300C22×C4C23×D1111yescharacteristic
301C2×C8—22no—
302C2×C8—28no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8#433914yes—
307C2×C8C22×Dic1112yes—
308C2×C8C22×Dic1112yes—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C4⋊C4—444no—
318C4⋊C4—882no—
319C4⋊C4C22×Dic1112yes—
320C4⋊C4C22×Dic1112yes—
321C4⋊C4C22×Dic1112yes—
322C4⋊C4C22×Dic1112yes—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—442no—
326C22⋊C4—881no—
327C22⋊C4—881no—
328C42—24no—
329C42—24no—
330C42—222no—
331C42—222no—
332C42—444no—
333C42—882no—
334C11#2261611yescharacteristic, complemented, Sylow
335C23—22no—
336C23—22no—
337C23—21no—
338C23—21no—
339C23D4×Dic1112yes—
340C23C2×D4×D1111yescharacteristic
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4D4×Dic1112yes—
368C2×C4C2×#433912yes—
369C2×C4C2×#434111yescharacteristic
370C2×C4#6704012yes—
371C2×C4C23×Dic1111yescharacteristic
372C8—22no—
373C8—442no—
374C8#6697914yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22#1062303812yes—
381C22#1062329912yes—
382C22#1062330011yescharacteristic
383C22#1062330211yescharacteristic
384C22C2×D4×Dic1111yescharacteristic
385C4—22no—
386C4—42no—
387C4—42no—
388C4—42no—
389C4—42no—
390C4—442no—
391C4—442no—
392C4—882no—
393C4—882no—
394C4#1062304412yes—
395C4C2×#6697911yescharacteristic
396C4#1062334311yescharacteristic
397C2—42no—
398C2#1307148511yescharacteristic
399C2#1307741711yescharacteristic
400C2#1307749211yescharacteristic
401C2#1308111212yes—
402C2#1308114212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#427C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#427D11
hypocenterC11#22616
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
3. #13069360C2semidirect
4. #13069210C2semidirect
5. #13069189C2semidirect
9. #13068516C2semidirect
15. C11×#427C4semidirect
188. #427Dic11semidirect
334. C11#22616semidirect

Maximal subgroups

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

subgroupindex
#130715092
#130715012
#130693602
#130692102
#130691892
#130687112
#130686452
#130685162
#130683922
C2×C11×#4272
#2261611