Finite Group Databasebeta

← #14651292

Subgroups — #14651292

Order 2816.

384 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 89 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#13078996C211yesmaximal, characteristic
2#13077721C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic
4#13067253C211yesmaximal, characteristic
5#13066489C211yesmaximal, characteristic
6#13066487C211yesmaximal, characteristic
7C11×#1556C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622838—22no—
13#10622695—22no—
14#10622694C412yes—
15#10622694C412yes—
16#10622539C2211yescharacteristic
17#10622539C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622441—22no—
20#10622333—22no—
21#10622314—22no—
22C11×#332—22no—
23#10622185—22no—
24#10622103—22no—
25C22×Q8×C11—21no—
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8C2×C412yes—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33#66979D412yes—
34#66977—21no—
35#66977—21no—
36C2×#4318—21no—
37#66923D412yes—
38#66922C2×C411yescharacteristic
39#66922C2×C411yescharacteristic
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D412yes—
44C11×C22⋊C8—21no—
45C11×C22⋊C8—21no—
46C11×#97—21no—
47C11×#97—21no—
48#66899—24no—
49#66899—24no—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52#66879—22no—
53Dic11⋊C8—24no—
54C8×Dic11—22no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57#66867—21no—
58#66867—21no—
59#66867—21no—
60C4×C11⋊C8C2×C412yes—
61#9422—111nomaximal, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—44no—
64C2×Q8×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C42×C11C22×C411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C22⋊Dic11—22no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11C22⋊C412yes—
85C4⋊Dic11C22⋊C412yes—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88C4×Dic11—22no—
89#4318—42no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—41no—
93#3139—111no—
94#2987—111no—
95#1556—111no—
96#1556D1111yescharacteristic
97#1537—111no—
98#1291—111no—
99#1291—111no—
100C23×C11#12311yescharacteristic
101Q8×C11—44no—
102Q8×C11—82no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—82no—
108C2×C4×C11C2×C22⋊C411yescharacteristic
109C2×C4×C11C4×D411yescharacteristic
110C2×C4×C11C4×D411yescharacteristic
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12111yescharacteristic
114C2×Dic11—22no—
115C2×Dic11—22no—
116Dic22—81no—
117Dic22—81no—
118C8×C11—42no—
119C8×C11—81no—
120C11⋊C8—42no—
121C11⋊C8—42no—
122C11⋊C8—81no—
123#533—111no—
124C2×C4⋊Q8C2×D1111yescharacteristic
125#491—222no—
126#487—112no—
127#487—112no—
128#446—222no—
129#446—222no—
130#433—222no—
131#432—111no—
132#432—111no—
133#432C2×D1111yescharacteristic
134#432C2×D1111yescharacteristic
135#419—222no—
136C4×M16—111no—
137#332—22no—
138#332—222no—
139#330—222no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#38611yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—82no—
150C4×C11#45412yes—
151Dic11—42no—
152Dic11—42no—
153C22×Q8—21no—
154C2×M16—221no—
155C4⋊Q8—21no—
156C4⋊Q8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—111no—
159C4⋊Q8—111no—
160C4⋊Q8C4×D1112yes—
161#125—112no—
162C22⋊Q8—221no—
163C22⋊Q8—221no—
164C4×Q8—221no—
165C4×Q8—221no—
166#117—112no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C42C22×D1111yescharacteristic
170C4⋊C8—21no—
171C4⋊C8—112no—
172C4⋊C8—224no—
173C4⋊C8—221no—
174C4⋊C8C22⋊D1112yes—
175#103—224no—
176#103—224no—
177C22⋊C8—21no—
178C22⋊C8—21no—
179C22⋊C8—221no—
180C22⋊C8—221no—
181#97—21no—
182#97—21no—
183#97—222no—
184#97—221no—
185#97—221no—
186#97—221no—
187C4×C8—112no—
188C4×C8—222no—
189C2×C11—41no—
190C2×C11#188811yescharacteristic
191C2×C11#190211yescharacteristic
192C2×C11#190211yescharacteristic
193C2×Q8—22no—
194C2×Q8—44no—
195C2×Q8—41no—
196C2×Q8—221no—
197C2×Q8—221no—
198C22×C4—41no—
199C22×C4#433911yescharacteristic
200C22×C4D4×D1111yescharacteristic
201C22×C4#434111yescharacteristic
202M16—442no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—222no—
206C2×C8—222no—
207C2×C8—441no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—112no—
213C4⋊C4—112no—
214C4⋊C4—221no—
215C4⋊C4—222no—
216C4⋊C4—221no—
217C4⋊C4—222no—
218C22⋊C4—222no—
219C42—222no—
220C42C2×C4×D1111yescharacteristic
221C42D4×D1111yescharacteristic
222C42D4×D1111yescharacteristic
223C42C2×C22⋊D1111yescharacteristic
224C11#942211yescharacteristic, complemented, Sylow
225C23#6693611yescharacteristic
226Q8—44no—
227Q8—82no—
228Q8—881no—
229Q8—881no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—82no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4C22⋊C4×D1111yescharacteristic
238C2×C4(C22⋊D11)⋊C411yescharacteristic
239C2×C4#6693711yescharacteristic
240C2×C4C4×C22⋊D1111yescharacteristic
241C2×C4#6699011yescharacteristic
242C2×C4#6699111yescharacteristic
243C8—42no—
244C8—81no—
245C8—442no—
246C8—442no—
247C8—881no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22#1062256911yescharacteristic
252C4—21no—
253C4—21no—
254C4—21no—
255C4—21no—
256C4—21no—
257C4—82no—
258C4—442no—
259C4—442no—
260C4#1062281412yes—
261C2—41no—
262C2#1306901611yescharacteristic
263C2#1306908611yescharacteristic
264C2#1306909211yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1556C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1556D11
hypocenterC11#9422
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
224. C11#9422semidirect

Maximal subgroups

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

subgroupindex
#130789962
#130777212
#130673332
#130672532
#130664892
#130664872
C11×#15562
#942211