Finite Group Databasebeta

← #14664939

Subgroups — #14664939

Order 2816.

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

normal subgroups only

This group has 388 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#13073821C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066645C214yesmaximal
4C11×#1801C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C11×#423—21no—
8C2×C11×#101—21no—
9#10622843—21no—
10#10622592C412yes—
11#10622592C2212yes—
12#10622589—21no—
13C4×C4⋊Dic11C411yescharacteristic
14#10622541—21no—
15#10622541—21no—
16#10622538—21no—
17C11×#343C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×Dic22C2×C412yes—
22C2×C11×M16—22no—
23C4×Q8×C11—41no—
24C4×Q8×C11—41no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—22no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37#66922—41no—
38#66922—41no—
39C11×C4⋊C8—41no—
40C11×C4⋊C8—41no—
41C11×#101—42no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95C2×C412yes—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47C4×C11⋊C8—41no—
48#11908—111nomaximal, Sylow
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C2×Q8×C11SD1612yes—
52C2×Q8×C11Q1612yes—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—22no—
62C2×Dic22—42no—
63C2×Dic22—82no—
64C11×M16—42no—
65C11×M16—42no—
66C2×C8×C11—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C4⋊Dic11—24no—
77C4⋊Dic11—42no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—82no—
81Dic11⋊C4—82no—
82C4×Dic11—42no—
83C2×C11⋊C8—42no—
84#2567—111no—
85#1801D1111yescharacteristic
86#1461—111no—
87#1354—114no—
88C23×C11C2×C22⋊C411yescharacteristic
89Q8×C11—42no—
90Q8×C11—42no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11#9911yescharacteristic
105C2×C4×C11#9911yescharacteristic
106C2×C4×C11#10312yes—
107C2×C4×C11#10312yes—
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11C2×Q1611yescharacteristic
110C2×Dic11—24no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116Dic22—84no—
117C8×C11—82no—
118C11⋊C8—82no—
119C2×C4⋊Q8—111no—
120C2×C4×Q8C2×D1111yescharacteristic
121#431—221no—
122#423—21no—
123C2×#101—21no—
124#395—112no—
125#395—112no—
126#391—221no—
127#389—221no—
128#389—221no—
129#384—221no—
130C4×C4⋊C4—111no—
131#343C2×D1112yes—
132#324—112no—
133#324—221no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11C2×#9911yescharacteristic
137C22×C11C2×#10311yescharacteristic
138C22×C11#42111yescharacteristic
139C4×C11—21no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11#35612yes—
148Dic11—44no—
149Dic11—82no—
150C22×Q8—112no—
151C22×Q8C22⋊D1111yescharacteristic
152C2×M16—22no—
153C4⋊Q8—441no—
154C4⋊Q8—441no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—221no—
158C2×C4⋊C4—221no—
159C2×C4⋊C4—221no—
160C2×C4⋊C4—222no—
161C2×C4⋊C4—222no—
162C2×C4⋊C4C4×D1111yescharacteristic
163C2×C4⋊C4D4411yescharacteristic
164C2×C4⋊C4C22×D1111yescharacteristic
165C2×C42—221no—
166C2×C42C4×D1111yescharacteristic
167C2×C42D4411yescharacteristic
168C2×C42C22⋊D1111yescharacteristic
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—441no—
172#101—42no—
173C22⋊C8—222no—
174C4×C8—441no—
175#95—112no—
176#95—222no—
177#95—222no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11#152011yescharacteristic
181C2×C11#212211yescharacteristic
182C2×C11C2×#35611yescharacteristic
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—442no—
186C2×Q8—882no—
187C2×Q8#432412yes—
188C2×Q8#432612yes—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4(C2×D11)⋊C411yescharacteristic
192C22×C4(C2×D11)⋊C411yescharacteristic
193C22×C4(C2×D11)⋊C411yescharacteristic
194C22×C4(C2×D11)⋊C411yescharacteristic
195C22×C4C2×C4×D1111yescharacteristic
196C22×C4C2×D4411yescharacteristic
197C22×C4C2×C22⋊D1111yescharacteristic
198M16—42no—
199M16—42no—
200C2×C8—42no—
201C2×C8—442no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—224no—
206C4⋊C4—442no—
207C4⋊C4—441no—
208C4⋊C4—441no—
209C4⋊C4—882no—
210C4⋊C4—882no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—442no—
218C11#1190811yescharacteristic, complemented, Sylow
219C23C2×(C2×D11)⋊C411yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—884no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—224no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4#6687011yescharacteristic
243C2×C4#6687011yescharacteristic
244C2×C4#6687412yes—
245C2×C4#6687412yes—
246C2×C4C2×#432411yescharacteristic
247C2×C4C2×#432611yescharacteristic
248C8—82no—
249C8—882no—
250C22—21no—
251C22—21no—
252C22C2×#6687011yescharacteristic
253C22C2×#6687411yescharacteristic
254C22#1062261811yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—444no—
264C4—882no—
265C4#1062211612yes—
266C2—21no—
267C2—21no—
268C2#1306718711yescharacteristic
269C2#1307026711yescharacteristic
270C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1801D11
hypocenterC11#11908
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
218. C11#11908semidirect

Maximal subgroups

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

subgroupindex
#130738212
#130669402
#130666452
C11×#18012
#1190811