Finite Group Databasebeta

← #14653252

Subgroups — #14653252

Order 2816.

406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×#10622294C211yesmaximal, characteristic
2#13068788C211yesmaximal, characteristic
3#13067300C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic
6#13067287C211yesmaximal, characteristic
7C11×#1452C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66883—22no—
14C2×#66880—22no—
15#10622537C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622294—22no—
18#10622294C414yes—
19C11×#322—22no—
20#10622124—22no—
21#10622124—22no—
22#10622120—22no—
23#10622119—22no—
24C22×Dic22—21no—
25C22×Dic22—21no—
26C22×C8×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×#4318—21no—
33C2×#4318—21no—
34#66922—21no—
35#66922—21no—
36#66922—21no—
37#66922—21no—
38#66922—21no—
39#66922—21no—
40#66922C2×C412yes—
41#66922C2×C412yes—
42C11×C4⋊C8D412yes—
43C11×C4⋊C8D412yes—
44C11×C22⋊C8—21no—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47C4×C8×C11—21no—
48C4×C8×C11C2×C412yes—
49C4×C8×C11D412yes—
50#66883—44no—
51#66880—28no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56#9775—111nomaximal, Sylow
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11#4111yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—41no—
61C22×Dic11—41no—
62C2×Dic22—22no—
63C2×Dic22—22no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22—42no—
67C2×Dic22—42no—
68C2×Dic22—82no—
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11C22⋊C414yes—
74C42×C11C22×C411yescharacteristic
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D411yescharacteristic
77C42×C11C2×D411yescharacteristic
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81C4⋊Dic11—22no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86#4318—42no—
87#4318—42no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—41no—
90C2×#487—111no—
91#1848—111no—
92#1549—111no—
93#1548—111no—
94#1546—111no—
95#1546—111no—
96#1452D1111yescharacteristic
97C23×C11#12411yescharacteristic
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11C2×C22⋊C411yescharacteristic
101C2×C4×C11C4×D411yescharacteristic
102C2×C4×C11C4×D411yescharacteristic
103C2×C4×C11#12111yescharacteristic
104C2×C4×C11#12111yescharacteristic
105C2×C4×C11#12711yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)12yes—
107C2×C4×C11#13712yes—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—82no—
111C2×Dic11—82no—
112Dic22—44no—
113Dic22—82no—
114Dic22—81no—
115Dic22—81no—
116Dic22—82no—
117C8×C11—24no—
118C8×C11—42no—
119C8×C11—42no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C2×C4⋊Q8—111no—
123C2×C4⋊Q8—111no—
124#487—114no—
125#487—222no—
126#431C2×D1111yescharacteristic
127#431C2×D1111yescharacteristic
128C2×#108—222no—
129#423—111no—
130#423—111no—
131C2×#103—222no—
132C2×C4×C8C2×D1111yescharacteristic
133#333—222no—
134#332—222no—
135#332—222no—
136#332—222no—
137#322—22no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#39011yescharacteristic
141C22×C11#48912yes—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11#41712yes—
145C4×C11#47112yes—
146C4×C11#47312yes—
147C4×C11#49611yescharacteristic
148C4×C11#49711yescharacteristic
149Dic11—82no—
150Dic11—82no—
151C22×Q8—221no—
152C22×Q8—221no—
153C2×M16—221no—
154C2×M16—221no—
155C22×C8D4412yes—
156C4⋊Q8—112no—
157C4⋊Q8—112no—
158C4⋊Q8—221no—
159C4⋊Q8—221no—
160C4⋊Q8—221no—
161C4⋊Q8—221no—
162C4⋊Q8—221no—
163C4⋊Q8—221no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4—221no—
168C2×C42C22×D1111yescharacteristic
169#108—444no—
170C4⋊C8—221no—
171C4⋊C8—221no—
172C4⋊C8—221no—
173C4⋊C8—221no—
174C4⋊C8D4412yes—
175C4⋊C8D4412yes—
176#103—228no—
177C22⋊C8—21no—
178C22⋊C8—21no—
179C4×C8—21no—
180C4×C8—21no—
181C4×C8C4×D1112yes—
182C4×C8C22⋊D1112yes—
183C2×C11—22no—
184C2×C11#195911yescharacteristic
185C2×C11#197711yescharacteristic
186C2×C11#197911yescharacteristic
187C2×Q8—222no—
188C2×Q8—222no—
189C2×Q8—441no—
190C2×Q8—441no—
191C2×Q8—442no—
192C2×Q8—442no—
193C2×Q8—882no—
194C22×C4—441no—
195C22×C4—441no—
196C22×C4C2×D4411yescharacteristic
197C22×C4#433911yescharacteristic
198C22×C4#433911yescharacteristic
199M16—442no—
200M16—442no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—22no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8(C2×D11)⋊C414yes—
208C4⋊C4—222no—
209C4⋊C4—222no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C42C2×C4×D1111yescharacteristic
217C42C2×D4411yescharacteristic
218C42C2×D4411yescharacteristic
219C42C2×C22⋊D1111yescharacteristic
220C11#977511yescharacteristic, complemented, Sylow
221C23#6692811yescharacteristic
222Q8—444no—
223Q8—882no—
224Q8—882no—
225Q8—881no—
226Q8—881no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—882no—
232C2×C4—882no—
233C2×C4C4×D4411yescharacteristic
234C2×C4C4×D4411yescharacteristic
235C2×C4#6692711yescharacteristic
236C2×C4#6696112yes—
237C2×C4#6696212yes—
238C2×C4C2×(C2×D11)⋊C411yescharacteristic
239C2×C4#6698311yescharacteristic
240C2×C4#6698311yescharacteristic
241C8—24no—
242C8—42no—
243C8—42no—
244C8—881no—
245C8—881no—
246C22—21no—
247C22—21no—
248C22#1062232712yes—
249C22#1062255211yescharacteristic
250C4—21no—
251C4—21no—
252C4—882no—
253C4—882no—
254C4#1062232511yescharacteristic
255C4#1062232811yescharacteristic
256C4#1062274612yes—
257C4#1062275412yes—
258C4#1062275612yes—
259C2—22no—
260C2#1306943211yescharacteristic
261C2#1306951911yescharacteristic
262C2#1306953111yescharacteristic
subgroupG/H
centerC22#10622552
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1452C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenter#1452D11
hypocenterC11#9775
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1452

Complements

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

NH ≅ G/Ntype
220. C11#9775semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
#130687882
#130673002
#130672962
#130672872
C11×#14522
#977511