Finite Group Databasebeta

← #14909389

Subgroups — #14909389

Order 2816.

484 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 139 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#13079276C212yesmaximal
2#13070869C211yesmaximal, characteristic, complemented
3#13070863C212yesmaximal, complemented
4#13070725C212yesmaximal
5#13070708C212yesmaximal
6#13070486C212yesmaximal, complemented
7#13070474C212yesmaximal, complemented
8#13070211C211yesmaximal, characteristic
9C11×#2253C211yesmaximal, characteristic, complemented
10#10623228—22no—
11C11×#499C2212yes—
12#10622682—22no—
13C2×Dic88C2212yes—
14C2×Dic88C2212yes—
15C2×#66862C2211yescharacteristic
16C2×C16×D11C2211yescharacteristic
17#10622500C2214yes—
18#10622486C2214yes—
19#10622481—22no—
20#10622466—22no—
21#10622312C2212yes—
22#10622302C2211yescharacteristic
23C11×#367C2212yes—
24C11×#366C2212yes—
25C4×C11×C16C2211yescharacteristic
26#10622140C2211yescharacteristic
27C16×Dic11C2211yescharacteristic
28#10622130C2214yes—
29#10622130C2214yes—
30#10622099C2211yescharacteristic
31C11×#125—22no—
32C2×Dic44—22no—
33C2×Dic44C2314yes—
34C2×#4313D411yescharacteristic
35C2×C8×D11C2311yescharacteristic
36#66951—44no—
37#66950—24no—
38#66943—44no—
39#66940—24no—
40#66925D411yescharacteristic
41#66922—22no—
42C2×C11×C16C2311yescharacteristic
43C2×C11×C16C2311yescharacteristic
44C11×#107C2314yes—
45C11×#106—22no—
46C4×C8×C11C2311yescharacteristic
47#66879D411yescharacteristic
48C8×Dic11C2311yescharacteristic
49C2×C11⋊C16C2311yescharacteristic
50C2×C11⋊C16C2311yescharacteristic
51#66874—24no—
52#66874—24no—
53#66867D411yescharacteristic
54Dic88—24no—
55Dic88—24no—
56#66862—22no—
57C16×D11—22no—
58#33741—111nomaximal, Sylow
59C2×C4×D11C2×D411yescharacteristic
60C2×Dic22—24no—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2411yescharacteristic
63C11×C4⋊C4—24no—
64C11×C4⋊C4—44no—
65C42×C11C2×D411yescharacteristic
66(C2×D11)⋊C4—44no—
67(C2×D11)⋊C4D812yes—
68C4⋊Dic11—44no—
69C4⋊Dic11—44no—
70Dic11⋊C4—44no—
71Dic11⋊C4D812yes—
72C4×Dic11—44no—
73C4×Dic11C2×D411yescharacteristic
74C2×C11⋊C8C2×D411yescharacteristic
75C2×C11⋊C8C2×D411yescharacteristic
76Dic44—24no—
77Dic44—24no—
78Dic44—44no—
79#4313—22no—
80C8×D11—21no—
81C8×D11—21no—
82C11×C16#4112yes—
83C11×C16#4112yes—
84C11⋊C16—21no—
85C11⋊C16—21no—
86#3177—112no—
87#2253D1111yescharacteristic, complemented
88#2247—111no—
89#2245—112no—
90#2219—112no—
91#2216—112no—
92#2176—112no—
93C4×Q32—112no—
94#2108—111no—
95C22×D11C2×D811yescharacteristic
96C2×C4×C11—44no—
97C2×C4×C11C2×D812yes—
98C2×C4×C11C22×D411yescharacteristic
99C2×Dic11—44no—
100C2×Dic11C2×D812yes—
101C2×Dic11C2×D811yescharacteristic
102C4×D11—21no—
103C4×D11—21no—
104Dic22—44no—
105Dic22—44no—
106C8×C11#13512yes—
107C8×C11C2×#4111yescharacteristic
108C8×C11C2×#4111yescharacteristic
109C11⋊C8—21no—
110C11⋊C8—21no—
111#541—222no—
112C2×Q32—112no—
113C2×Q32—112no—
114C2×M32—111no—
115C22×C16—111no—
116#499C2×D1112yes—
117#494—112no—
118#491—222no—
119#470—222no—
120#467—114no—
121#441—222no—
122C4×Q16—114no—
123#405—111no—
124#367C2×D1112yes—
125#366C2×D1112yes—
126#358—114no—
127#358—114no—
128#346—111no—
129#346—111no—
130C4×C16—111no—
131C4×C16C2×D1111yescharacteristic
132C22×C11C22×D811yescharacteristic
133C2×D11—22no—
134C2×D11—21no—
135C4×C11—22no—
136C4×C11—84no—
137C4×C11#53211yescharacteristic
138C4×C11C2×#13511yescharacteristic
139Dic11—22no—
140Dic11—21no—
141Dic11—84no—
142C2×Q16—114no—
143C2×Q16—222no—
144C2×M16—111no—
145C22×C8—111no—
146C4⋊Q8—222no—
147#126—444no—
148#125—22no—
149#125—444no—
150C22⋊Q8—224no—
151C4×Q8—224no—
152#117—111no—
153Q32—224no—
154Q32—224no—
155M32—222no—
156C2×C16—111no—
157C2×C16—111no—
158C2×C16—222no—
159C2×C16C22×D1111yescharacteristic
160C2×C16C22×D1111yescharacteristic
161#107C22×D1114yes—
162#106—22no—
163#103—224no—
164#103—224no—
165#97—111no—
166#97—111no—
167C4×C8—111no—
168C4×C8C22×D1111yescharacteristic
169C2×C11#316911yescharacteristic
170C2×C11#341712yes—
171D11—41no—
172C2×Q8—224no—
173C22×C4—111no—
174Q16—224no—
175Q16—224no—
176Q16—444no—
177M16—222no—
178C2×C8—111no—
179C2×C8—111no—
180C2×C8—221no—
181C2×C8—221no—
182C2×C8D4×D1111yescharacteristic
183C2×C8C23×D1111yescharacteristic
184C4⋊C4—24no—
185C4⋊C4—44no—
186C4⋊C4—112no—
187C4⋊C4—444no—
188C4⋊C4—444no—
189C4⋊C4—444no—
190C22⋊C4—112no—
191C22⋊C4—444no—
192C42—111no—
193C42—444no—
194C42D4×D1111yescharacteristic
195C16—221no—
196C16—221no—
197C16#434312yes—
198C16#434312yes—
199C11#3374111yescharacteristic, complemented, Sylow
200C23—111no—
201Q8—444no—
202Q8—444no—
203C2×C4—44no—
204C2×C4—112no—
205C2×C4—111no—
206C2×C4—221no—
207C2×C4—221no—
208C2×C4—444no—
209C2×C4D8×D1112yes—
210C2×C4C2×D4×D1111yescharacteristic
211C8—221no—
212C8—221no—
213C8#6697212yes—
214C8C2×#434311yescharacteristic
215C8C2×#434311yescharacteristic
216C22—221no—
217C22—222no—
218C22C2×D8×D1111yescharacteristic
219C4—22no—
220C4—84no—
221C4—221no—
222C4—222no—
223C4—884no—
224C4#1062325611yescharacteristic
225C4C2×#6697211yescharacteristic
226C2—441no—
227C2#1307919611yescharacteristic
228C2#1308176612yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2253C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2253D11
hypocenterC11#33741
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2253

Complements

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

NH ≅ G/Ntype
2. #13070869C2semidirect
3. #13070863C2semidirect
6. #13070486C2semidirect
7. #13070474C2semidirect
9. C11×#2253C2semidirect
87. #2253D11semidirect
199. C11#33741semidirect

Maximal subgroups

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

subgroupindex
#130792762
#130708692
#130708632
#130707252
#130707082
#130704862
#130704742
#130702112
C11×#22532
#3374111