Finite Group Databasebeta

← #14649496

Subgroups — #14649496

Order 2816.

694 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076955C211yesmaximal, characteristic
2C2×#10622545C211yesmaximal, characteristic
3C2×#10622105C212yesmaximal
4#13066496C212yesmaximal
5C11×#1817C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C22×C4×Dic11—21no—
9C2×C11×C22⋊C8C2212yes—
10#10622825C2211yescharacteristic
11#10622824—21no—
12#10622823—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622546—22no—
16#10622545—24no—
17#10622542C412yescomplemented
18#10622541C412yescomplemented
19C11×#336—22no—
20#10622105—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—22no—
25C22×Dic22C2×C411yescharacteristic
26C22×C8×C11—22no—
27C2×C42×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11C2×C412yes—
30C2×C42×C11D412yes—
31C2×C22⋊Dic11—21no—
32C2×C22⋊Dic11—21no—
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11C2×C412yes—
35#66977—22no—
36#66977—22no—
37C2×Dic11⋊C4—22no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—24no—
40C2×C4×Dic11—28no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8—22no—
43C11⋊#95—24no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95D414yes—
50#9145—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—24no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—42no—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×C4×C11#4112yes—
66C22×Dic11—28no—
67C22×Dic11—22no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—24no—
71C22×Dic11—44no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C2×Dic22—22no—
75C2×Dic22—42no—
76C2×C8×C11—44no—
77C2×C8×C11—42no—
78C42×C11—24no—
79C42×C11—24no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82C22⋊Dic11—42no—
83C4⋊Dic11—22no—
84C4⋊Dic11—42no—
85Dic11⋊C4—44no—
86Dic11⋊C4—42no—
87C4×Dic11—216no—
88#2855—111no—
89C2×#376—111no—
90#1817D1111yescharacteristic
91C2×#328—112no—
92#1294—112no—
93C23×C11—22no—
94C23×C11—22no—
95C23×C11C2×C22⋊C411yescharacteristic
96C23×C11#12011yescharacteristic
97C23×C11#12311yescharacteristic
98C23×C11#13512yes—
99C23×C11#13712yes—
100C2×C4×C11—24no—
101C2×C4×C11—24no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11#10414yes—
114C2×C4×C11C4×D412yes—
115C2×C4×C11#12112yes—
116C2×Dic11—28no—
117C2×Dic11—44no—
118C2×Dic11—48no—
119C2×Dic11—48no—
120C2×Dic11—44no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128Dic22—82no—
129C8×C11—82no—
130C2×C22⋊Q8—111no—
131C22×C42—221no—
132C22×C42C2×D1111yescharacteristic
133C2×C22⋊C8C2×D1112yes—
134#391—112no—
135#389—112no—
136#387—222no—
137#385—221no—
138#381—221no—
139#380—111no—
140#376—224no—
141C2×#95—112no—
142C2×#95—221no—
143#336—22no—
144#328—224no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—24no—
150C22×C11—24no—
151C22×C11#38611yescharacteristic
152C22×C11#41012yes—
153C22×C11#41611yescharacteristic
154C22×C11#41911yescharacteristic
155C22×C11C2×#10412yes—
156C22×C11#45212yes—
157C22×C11#48512yes—
158C4×C11—24no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—42no—
162Dic11—48no—
163Dic11—81no—
164Dic11—81no—
165Dic11—82no—
166C22×Q8—111no—
167C23×C4—222no—
168C23×C4D4411yescharacteristic
169C23×C4D4411yescharacteristic
170C23×C4C22×D1111yescharacteristic
171C22×C8—22no—
172C22⋊Q8—222no—
173C22⋊Q8—222no—
174C2×C4⋊C4—111no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4—222no—
177C2×C4⋊C4—221no—
178C2×C22⋊C4—221no—
179C2×C22⋊C4—221no—
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—224no—
183C2×C42—228no—
184C2×C42C4×D1112yes—
185C2×C42C22⋊D1112yes—
186C22⋊C8—22no—
187C22⋊C8—22no—
188#95—114no—
189#95—224no—
190#95—222no—
191#95—222no—
192#95—222no—
193#95—222no—
194#95—221no—
195C2×C11—22no—
196C2×C11—22no—
197C2×C11#150012yes—
198C2×C11#150612yes—
199C2×C11#187311yescharacteristic
200C2×C11#189611yescharacteristic
201C2×C11#189911yescharacteristic
202C24C2×D4411yescharacteristic
203C2×Q8—222no—
204C2×Q8—442no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—24no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—228no—
214C22×C4—224no—
215C22×C4—222no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4—444no—
219C22×C4—442no—
220C22×C4—442no—
221C22×C4(C2×D11)⋊C412yes—
222C22×C4(C2×D11)⋊C412yes—
223C22×C4C2×C4×D1111yescharacteristic
224C22×C4D4×D1112yes—
225C22×C4#434112yes—
226C22×C4C2×C22⋊D1111yescharacteristic
227C2×C8—44no—
228C2×C8—42no—
229C4⋊C4—222no—
230C4⋊C4—442no—
231C4⋊C4—444no—
232C4⋊C4—442no—
233C22⋊C4—441no—
234C22⋊C4—441no—
235C22⋊C4—442no—
236C42—24no—
237C42—24no—
238C42—2216no—
239C11#914511yescharacteristic, complemented, Sylow
240C23—22no—
241C23—22no—
242C23#6693511yescharacteristic
243C23#6693911yescharacteristic
244C23#6695712yes—
245C23#6696212yes—
246C23C2×(C2×D11)⋊C411yescharacteristic
247Q8—882no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—228no—
262C2×C4—444no—
263C2×C4—448no—
264C2×C4—448no—
265C2×C4—444no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4#6688914yes—
274C2×C4(C22⋊D11)⋊C412yes—
275C2×C4#6699212yes—
276C8—82no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—24no—
282C22—24no—
283C22#1062233612yes—
284C22#1062234612yes—
285C22#1062257111yescharacteristic
286C22#1062261912yes—
287C22#1062272611yescharacteristic
288C22#1062273311yescharacteristic
289C22C2×#6688912yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—448no—
295C4—881no—
296C4—881no—
297C4—882no—
298C2—22no—
299C2—22no—
300C2#1306710312yes—
301C2#1306712912yes—
302C2#1306892611yescharacteristic
303C2#1306905711yescharacteristic
304C2#1306907211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1817D11
hypocenterC11#9145
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
17. #10622542C4semidirect
18. #10622541C4semidirect
239. C11#9145semidirect

Maximal subgroups

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

subgroupindex
#130769552
C2×#106225452
C2×#106221052
#130664962
C11×#18172
#914511