Finite Group Databasebeta

← #14651276

Subgroups — #14651276

Order 2816.

424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079009C211yesmaximal, characteristic
2#13067341C211yesmaximal, characteristic, complemented
3#13067332C211yesmaximal, characteristic, complemented
4#13067251C211yesmaximal, characteristic
5#13066487C211yesmaximal, characteristic, complemented
6#13066487C211yesmaximal, characteristic, complemented
7C11×#2980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#435—22no—
11C11×#435—22no—
12C11×#432C2211yescharacteristic
13C11×#432C2211yescharacteristic
14C11×#408—22no—
15#10622845—22no—
16#10622694C412yes—
17#10622683C412yes—
18#10622668—22no—
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21C4×#4318C2211yescharacteristic
22#10622178—22no—
23#10622124—22no—
24#10622119—22no—
25C2×C11×#41D412yes—
26C22×Dic22—21no—
27C2×C11×M16—22no—
28C22×C8×C11—22no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124D412yes—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×#4318—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C412yes—
44C11×C4⋊C8D412yes—
45C11×C4⋊C8D412yes—
46C11×C22⋊C8—24no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#97—21no—
51#66899—24no—
52#66896—24no—
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57#66867—21no—
58#66867—21no—
59#66867—21no—
60C4×C11⋊C8C2×C412yes—
61#9419—111nomaximal, Sylow
62C11×#41—42no—
63C11×#41—42no—
64C2×Q8×C11C22⋊C412yes—
65C2×D4×C11—22no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11C22⋊C412yes—
69C22×C4×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—41no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—82no—
77C11×M16—82no—
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—82no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C42×C11C22×C411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93#4318—42no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97#3141—111no—
98#2980D1111yescharacteristic
99#1558—111no—
100#1556—111no—
101#1536—111no—
102#1291—111no—
103#1291—111no—
104C23×C11—22no—
105C23×C11#12311yescharacteristic
106Q8×C11—42no—
107D4×C11—42no—
108D4×C11—81no—
109D4×C11—81no—
110D4×C11—82no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×Dic11—42no—
124C2×Dic11—82no—
125Dic22—82no—
126Dic22—82no—
127C8×C11—42no—
128C8×C11—42no—
129C11⋊C8—42no—
130C11⋊C8—81no—
131C11⋊C8—81no—
132#532C2×D1111yescharacteristic
133C2×C4⋊Q8—111no—
134#489—222no—
135#487—112no—
136#486—112no—
137#435—22no—
138#435—22no—
139#432—111no—
140#432—111no—
141#432C2×D1111yescharacteristic
142#432C2×D1111yescharacteristic
143#417—222no—
144#408—22no—
145C4×M16—111no—
146#333—222no—
147#332—222no—
148#329—222no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—42no—
155C22×C11#38611yescharacteristic
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—42no—
162C4×C11#45512yes—
163Dic11—82no—
164C2×#41C22⋊D1112yes—
165C22×Q8—221no—
166C2×M16—22no—
167C2×M16—221no—
168C22×C8—22no—
169C4⋊Q8—112no—
170C4⋊Q8—221no—
171C4⋊Q8—221no—
172C4⋊Q8—221no—
173C4⋊Q8C4×D1111yescharacteristic
174#127C4×D1111yescharacteristic
175#124D4412yes—
176#121—21no—
177#121—21no—
178C4×D4—21no—
179C4×D4—21no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—221no—
182C2×C42C22×D1111yescharacteristic
183C4⋊C8—221no—
184C4⋊C8—221no—
185C4⋊C8C22⋊D1112yes—
186C4⋊C8C22⋊D1112yes—
187#103—224no—
188#102—224no—
189C22⋊C8—24no—
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—221no—
193C22⋊C8—221no—
194#97—21no—
195#97—21no—
196#97—221no—
197#97—221no—
198#97—221no—
199C4×C8—112no—
200C2×C11—41no—
201C2×C11—82no—
202C2×C11#188511yescharacteristic
203C2×C11#190211yescharacteristic
204C2×C11#190311yescharacteristic
205#41—42no—
206#41—42no—
207C2×Q8—222no—
208C2×Q8—441no—
209C2×Q8—882no—
210C2×Q8(C2×D11)⋊C412yes—
211C2×D4—22no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4(C2×D11)⋊C412yes—
215C22×C4—22no—
216C22×C4—441no—
217C22×C4#433911yescharacteristic
218C22×C4#433911yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220M16—82no—
221M16—442no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—82no—
225C2×C8—222no—
226C2×C8—441no—
227C2×C8—441no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—222no—
231C4⋊C4—222no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C22⋊C4—22no—
235C22⋊C4—22no—
236C42C2×C4×D1111yescharacteristic
237C42C2×D4411yescharacteristic
238C42C2×C22⋊D1111yescharacteristic
239C42C2×C22⋊D1111yescharacteristic
240C11#941911yescharacteristic, complemented, Sylow
241C23—22no—
242C23#6698211yescharacteristic
243Q8—42no—
244Q8—882no—
245Q8—882no—
246D4—42no—
247D4—81no—
248D4—81no—
249D4—82no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—442no—
257C2×C4—882no—
258C2×C4C2×(C2×D11)⋊C411yescharacteristic
259C2×C4C4×C22⋊D1111yescharacteristic
260C2×C4C4×C22⋊D1111yescharacteristic
261C2×C4#6698311yescharacteristic
262C2×C4#6698311yescharacteristic
263C2×C4#6700611yescharacteristic
264C8—42no—
265C8—42no—
266C8—442no—
267C8—881no—
268C8—881no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22#1062282611yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—42no—
282C4—882no—
283C4#1062285512yes—
284C2—41no—
285C2—82no—
286C2#1306900411yescharacteristic
287C2#1306908911yescharacteristic
288C2#1306909611yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2980C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#2980D11
hypocenterC11#9419
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #13067341C2semidirect
3. #13067332C2semidirect
5. #13066487C2semidirect
6. #13066487C2semidirect
240. C11#9419semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130673412
#130673322
#130672512
#130664872
C11×#29802
#941911