Finite Group Databasebeta

← #14754389

Subgroups — #14754389

Order 2816.

758 conjugacy classes of subgroups; only the 255 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 255 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#13077248C212yesmaximal
2C2×#10622320C211yesmaximal, characteristic
3#13068790C212yesmaximal, complemented
4#13068757C211yesmaximal, characteristic, complemented
5#13068657C214yesmaximal
6#13068517C214yesmaximal, complemented
7C11×#1838C211yesmaximal, characteristic, complemented
8C22×#4313C2212yes—
9C2×C42×D11C2211yescharacteristic
10C11×#423C2212yes—
11C2×C11×#97C2211yescharacteristic
12#10622739C2214yes—
13C2×#66886C2218yes—
14M16×Dic11C2214yes—
15C2×C8×Dic11C2212yes—
16#10622537C2212yes—
17C2×#66867C2211yescharacteristic
18#10622448—24no—
19#10622446—24no—
20#10622320C418yes—
21C11×#341C2214yes—
22#10622190C2214yes—
23C22×C4×D11Q812yes—
24C22×C4×D11C2311yescharacteristic
25C2×C11×M16C2314yes—
26C22×C8×C11C2312yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4×Dic11Q812yes—
29C2×C4×Dic11C2311yescharacteristic
30C2×#4318C2314yes—
31C22×C11⋊C8C2312yes—
32C2×#4313—28no—
33C2×#4313C2×C418yes—
34C42×D11C2×C414yes—
35C42×D11D412yes—
36C42×D11D412yes—
37C11×C4⋊C8—24no—
38C11×#97C2×C414yes—
39#66886—216no—
40(C2×D11)⋊C8—28no—
41#66879—24no—
42C8×Dic11—24no—
43C8×Dic11C2×C418yes—
44C4⋊(C11⋊C8)—24no—
45#66867C2×C414yes—
46#20827—111nomaximal, Sylow
47C23×D11C2×Q811yescharacteristic
48C22×C4×C11C2×Q812yes—
49C22×C4×C11C2411yescharacteristic
50C22×Dic11C2×Q811yescharacteristic
51C22×Dic11C2×Q812yes—
52C2×C4×D11—24no—
53C2×C4×D11—44no—
54C2×C4×D11C4⋊C414yes—
55C2×C4×D11C4⋊C414yes—
56C2×C4×D11C22×C412yes—
57C2×C4×D11C2×D412yes—
58C11×M16—28no—
59C2×C8×C11—24no—
60C2×C8×C11—24no—
61C2×C8×C11C22×C414yes—
62C42×C11C22×C412yes—
63C42×C11C2×D412yes—
64C4×Dic11C4⋊C414yes—
65C4×Dic11C4⋊C414yes—
66C4×Dic11C22×C412yes—
67C4×Dic11C2×D411yescharacteristic
68C4×Dic11C2×D411yescharacteristic
69#4318—28no—
70C2×C11⋊C8—24no—
71C2×C11⋊C8C22×C414yes—
72C2×C11⋊C8#4118yes—
73#4313—216no—
74#2920—112no—
75C2×C4×M16—111no—
76#1849—112no—
77#1838—111no—
78#1838D1111yescharacteristic, complemented
79#1811—114no—
80C4×#108—114no—
81C23×C11C22×Q811yescharacteristic
82C22×D11—22no—
83C22×D11—42no—
84C22×D11C2×C4⋊C412yes—
85C2×C4×C11—42no—
86C2×C4×C11C2×C4⋊C414yes—
87C2×C4×C11C23×C411yescharacteristic
88C2×C4×C11C22×D411yescharacteristic
89C2×C4×C11C2×#4114yes—
90C2×Dic11—22no—
91C2×Dic11—24no—
92C2×Dic11C2×C4⋊C412yes—
93C2×Dic11C2×C4⋊C412yes—
94C2×Dic11C2×C4⋊C412yes—
95C4×D11—24no—
96C4×D11—24no—
97C4×D11—28no—
98C4×D11—44no—
99C8×C11—24no—
100C8×C11—44no—
101C11⋊C8—44no—
102C11⋊C8#11718yes—
103C22×M16—112no—
104C22×C42—111no—
105#432—224no—
106#431—224no—
107C2×#108—118no—
108#423—112no—
109#423C2×D1112yes—
110#407—114no—
111C4×M16—118no—
112C4×M16—114no—
113C2×#97—111no—
114C2×#97C2×D1111yescharacteristic
115C2×C4×C8—112no—
116#341—114no—
117#341C2×D1114yes—
118C22×C11—22no—
119C22×C11C22×C4⋊C411yescharacteristic
120C22×C11#53312yes—
121C2×D11—24no—
122C2×D11—22no—
123C2×D11—44no—
124C4×C11—24no—
125C4×C11C2×#11712yes—
126C4×C11#53212yes—
127Dic11—22no—
128Dic11—22no—
129Dic11#43014yes—
130C23×C4—111no—
131C23×C4—112no—
132C2×M16—118no—
133C2×M16—114no—
134C2×M16—228no—
135C2×M16C22×D1114yes—
136C22×C8—112no—
137C22×C8C22×D1112yes—
138C2×C42—112no—
139C2×C42—111no—
140C2×C42—114no—
141C2×C42—112no—
142C2×C42—112no—
143C2×C42C22×D1111yescharacteristic
144#108—2216no—
145C4⋊C8—24no—
146C4⋊C8—224no—
147C22⋊C8—228no—
148#97—114no—
149#97—224no—
150#97C4×D1114yes—
151C4×C8—118no—
152C4×C8—224no—
153C2×C11—22no—
154C2×C11#228511yescharacteristic
155C2×C11C2×#43012yes—
156D11—42no—
157C24—111no—
158C22×C4—112no—
159C22×C4—111no—
160C22×C4—114no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—114no—
164C22×C4—224no—
165C22×C4—444no—
166C22×C4Q8×D1112yes—
167C22×C4C23×D1111yescharacteristic
168M16—28no—
169M16—2216no—
170M16—228no—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—114no—
174C2×C8—118no—
175C2×C8—224no—
176C2×C8C2×C4×D1114yes—
177C42—114no—
178C42—114no—
179C42—112no—
180C42—111no—
181C42—111no—
182C42C2×C4×D1112yes—
183C42D4×D1112yes—
184C11#2082711yescharacteristic, complemented, Sylow
185C23—112no—
186C23—222no—
187C23—442no—
188C23C2×Q8×D1111yescharacteristic
189C2×C4—42no—
190C2×C4—112no—
191C2×C4—112no—
192C2×C4—112no—
193C2×C4—228no—
194C2×C4—224no—
195C2×C4—222no—
196C2×C4—224no—
197C2×C4—224no—
198C2×C4—444no—
199C2×C4C4⋊C4×D1114yes—
200C2×C4C22×C4×D1111yescharacteristic
201C2×C4C2×D4×D1111yescharacteristic
202C2×C4#41×D1114yes—
203C8—24no—
204C8—44no—
205C8—118no—
206C8—444no—
207C22—22no—
208C22—222no—
209C22—224no—
210C22—444no—
211C22C2×C4⋊C4×D1111yescharacteristic
212C22#1062321912yes—
213C4—24no—
214C4—114no—
215C4—222no—
216C4—222no—
217C4D11×#11712yes—
218C4#1062319912yes—
219C2—22no—
220C2—442no—
221C2#1307102211yescharacteristic
222C2D11×#43012yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1838C2
socleC22×C11C22×C4⋊C4
prime radicalC23×D11C2×Q8
cosocleC22×C4×C11C24
hypercenter#1838D11
hypocenterC11#20827
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
3. #13068790C2semidirect
4. #13068757C2semidirect
6. #13068517C2semidirect
7. C11×#1838C2semidirect
78. #1838D11semidirect
184. C11#20827semidirect

Maximal subgroups

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

subgroupindex
#130772482
C2×#106223202
#130687902
#130687572
#130686572
#130685172
C11×#18382
#2082711