Finite Group Databasebeta

← #14909318

Subgroups — #14909318

Order 2816.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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#13079203C212yesmaximal
2#13070869C211yesmaximal, characteristic, complemented
3#13070845C212yesmaximal, complemented
4#13070708C214yesmaximal
5#13070474C214yesmaximal, complemented
6C4×C16×D11C211yesmaximal, characteristic
7C11×#2252C211yesmaximal, characteristic, complemented
8#10623259—22no—
9C11×#500C2212yes—
10#10622706—22no—
11C2×Dic88C2214yes—
12C2×C16×D11C2212yes—
13#10622500—22no—
14#10622500C2214yes—
15#10622486—22no—
16#10622486C2214yes—
17#10622312C2212yes—
18C4×C8×D11C2211yescharacteristic
19C11×#366C2214yes—
20C4×C11×C16C2211yescharacteristic
21C16×Dic11C2212yes—
22#10622130C2218yes—
23C4×C11⋊C16C2211yescharacteristic
24C11×C4⋊Q8—22no—
25#66999—42no—
26Q8×Dic11—42no—
27C2×Dic44—22no—
28C2×Dic44C2314yes—
29C2×C8×D11D411yescharacteristic
30C2×C8×D11C2311yescharacteristic
31#66950—24no—
32#66945—42no—
33#66943—42no—
34#66940—24no—
35C42×D11D411yescharacteristic
36#66922—22no—
37C2×C11×C16C2312yes—
38C11×#107—22no—
39C11×#107C2314yes—
40C4×C8×C11C2311yescharacteristic
41C8×Dic11D411yescharacteristic
42C8×Dic11C2311yescharacteristic
43C2×C11⋊C16C2312yes—
44#66874—24no—
45#66874—24no—
46C4×C11⋊C8D411yescharacteristic
47Dic88—28no—
48C16×D11—24no—
49#33734—111nomaximal, Sylow
50C2×Q8×C11—42no—
51C2×C4×D11D811yescharacteristic
52C2×C4×D11D811yescharacteristic
53C2×C4×D11C2×D411yescharacteristic
54C2×Dic22—24no—
55C2×C8×C11C2×D411yescharacteristic
56C2×C8×C11C2411yescharacteristic
57C11×C4⋊C4—24no—
58C11×C4⋊C4—42no—
59C42×C11C2×D411yescharacteristic
60(C2×D11)⋊C4—44no—
61C4⋊Dic11—44no—
62C4⋊Dic11—42no—
63C4⋊Dic11—42no—
64Dic11⋊C4—44no—
65C4×Dic11—44no—
66C4×Dic11D811yescharacteristic
67C4×Dic11D811yescharacteristic
68C4×Dic11C2×D411yescharacteristic
69C2×C11⋊C8C2×D411yescharacteristic
70C2×C11⋊C8C2×D411yescharacteristic
71Dic44—28no—
72Dic44—44no—
73C8×D11—22no—
74C8×D11—22no—
75C11×C16#4114yes—
76C11⋊C16—22no—
77#3170—112no—
78#2252D1111yescharacteristic, complemented
79#2247—111no—
80#2241—112no—
81#2216—114no—
82C4×Q32—114no—
83C2×C4×C16—111no—
84C22×D11C2×D811yescharacteristic
85Q8×C11—84no—
86C2×C4×C11—44no—
87C2×C4×C11C2×D811yescharacteristic
88C2×C4×C11C2×D811yescharacteristic
89C2×C4×C11C22×D411yescharacteristic
90C2×Dic11—44no—
91C2×Dic11C2×D811yescharacteristic
92C2×Dic11C2×D811yescharacteristic
93C2×Dic11C2×D811yescharacteristic
94C4×D11—21no—
95C4×D11—21no—
96C4×D11—22no—
97C4×D11Q3214yescomplemented
98Dic22—44no—
99Dic22—44no—
100C8×C11#13512yes—
101C8×C11C2×#4112yes—
102C11⋊C8—21no—
103C11⋊C8—21no—
104#533—222no—
105C2×Q32—114no—
106C22×C16—112no—
107#500C2×D1112yes—
108#494—112no—
109#487—222no—
110#467—114no—
111#467—222no—
112C4×Q16—114no—
113C4×Q16—222no—
114C2×C4×C8—111no—
115#366C2×D1114yes—
116#358—118no—
117C4×C16—112no—
118C4×C16—111no—
119C4×C16C2×D1111yescharacteristic
120C22×C11C22×D811yescharacteristic
121C2×D11—21no—
122C2×D11—21no—
123C2×D11C2×Q3212yes—
124C4×C11—84no—
125C4×C11C2×Q3212yes—
126C4×C11#50812yes—
127C4×C11#53211yescharacteristic
128C4×C11C2×#13511yescharacteristic
129Dic11—21no—
130Dic11—21no—
131Dic11—84no—
132Dic11C2×Q3212yes—
133C2×Q16—114no—
134C2×Q16—222no—
135C22×C8—111no—
136C22×C8—111no—
137C4⋊Q8—22no—
138C4⋊Q8—222no—
139#125—442no—
140C22⋊Q8—224no—
141C22⋊Q8—442no—
142C4×Q8—224no—
143C4×Q8—442no—
144#117—442no—
145C2×C42—111no—
146Q32—228no—
147C2×C16—112no—
148C2×C16—224no—
149C2×C16C22×D1112yes—
150#107—22no—
151#107C22×D1114yes—
152#103—224no—
153#103—224no—
154C4×C8—111no—
155C4×C8—111no—
156C4×C8—111no—
157C4×C8C22×D1111yescharacteristic
158C2×C11#316911yescharacteristic
159C2×C11C22×Q3211yescharacteristic
160C2×C11C2×#50811yescharacteristic
161D11—22no—
162C2×Q8—42no—
163C2×Q8—224no—
164C22×C4—111no—
165C22×C4—111no—
166C22×C4—111no—
167Q16—228no—
168Q16—444no—
169C2×C8—111no—
170C2×C8—111no—
171C2×C8—222no—
172C2×C8—222no—
173C2×C8D4×D1111yescharacteristic
174C2×C8C23×D1111yescharacteristic
175C4⋊C4—24no—
176C4⋊C4—42no—
177C4⋊C4—444no—
178C4⋊C4—444no—
179C4⋊C4—442no—
180C4⋊C4—442no—
181C22⋊C4—444no—
182C42—111no—
183C42—111no—
184C42—111no—
185C42—444no—
186C42D4×D1111yescharacteristic
187C16—222no—
188C16#434314yes—
189C11#3373411yescharacteristic, complemented, Sylow
190C23—111no—
191Q8—84no—
192Q8—444no—
193Q8—444no—
194C2×C4—44no—
195C2×C4—111no—
196C2×C4—114no—
197C2×C4—111no—
198C2×C4—111no—
199C2×C4—221no—
200C2×C4—222no—
201C2×C4—221no—
202C2×C4—444no—
203C2×C4D8×D1111yescharacteristic
204C2×C4D8×D1111yescharacteristic
205C2×C4C2×D4×D1111yescharacteristic
206C8—221no—
207C8—221no—
208C8#6697212yes—
209C8C2×#434312yes—
210C22—112no—
211C22—221no—
212C22—221no—
213C22C2×D8×D1111yescharacteristic
214C4—84no—
215C4—112no—
216C4—221no—
217C4—221no—
218C4—884no—
219C4#1062252512yes—
220C4D11×Q3212yes—
221C4#1062325611yescharacteristic
222C4C2×#6697211yescharacteristic
223C2—222no—
224C2#1307919611yescharacteristic
225C2C2×D11×Q3211yescharacteristic
226C2C2×#1062252511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2252C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2252D11
hypocenterC11#33734
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2252

Complements

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

NH ≅ G/Ntype
2. #13070869C2semidirect
3. #13070845C2semidirect
5. #13070474C2semidirect
7. C11×#2252C2semidirect
78. #2252D11semidirect
97. C4×D11Q32semidirect
189. C11#33734semidirect

Maximal subgroups

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

subgroupindex
#130792032
#130708692
#130708452
#130707082
#130704742
C4×C16×D112
C11×#22522
#3373411