Finite Group Databasebeta

← #14684829

Subgroups — #14684829

Order 2816.

1530 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 411 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×#10622548C211yesmaximal, characteristic, complemented
2C2×#10622550C211yesmaximal, characteristic, complemented
3#13066869C216yesmaximal, complemented
4#13066861C216yesmaximal
5C22×C11×#126C211yesmaximal, characteristic
6C2×C11×#126—24no—
7C2×C11×#126—24no—
8C2×C11×#126C418yescomplemented
9C22×C11×C4⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C22×C42×C11C2211yescharacteristic
12C22×C22⋊Dic11C2214yes—
13C22×C4⋊Dic11C2216yes—
14C2×C11⋊#95C2216yes—
15C2×C11⋊#95C22112yes—
16#10622550—24no—
17#10622548—24no—
18C25×C11C2311yescharacteristic
19C23×C4×C11C2313yes—
20C23×C4×C11C2313yes—
21C23×Dic11C2314yes—
22C23×Dic11C2314yes—
23C11×#126—232no—
24C2×C11×C4⋊C4—26no—
25C2×C11×C4⋊C4—26no—
26C2×C11×C4⋊C4C2×C4112yes—
27C2×C11×C22⋊C4—26no—
28C2×C11×C22⋊C4—26no—
29C2×C11×C22⋊C4C2×C4112yes—
30C2×C42×C11C2×C414yes—
31C2×C42×C11D414yes—
32C2×C42×C11D414yes—
33C2×C22⋊Dic11—412no—
34C2×C4⋊Dic11—212no—
35C2×C4⋊Dic11—412no—
36C11⋊#95—212no—
37C11⋊#95—412no—
38#14665—111nomaximal, Sylow
39C24×C11—21no—
40C24×C11—21no—
41C24×C11—26no—
42C24×C11—26no—
43C24×C11C22×C412yes—
44C24×C11C2411yescharacteristic
45C22×C4×C11—26no—
46C22×C4×C11—26no—
47C22×C4×C11—23no—
48C22×C4×C11—23no—
49C22×C4×C11—26no—
50C22×C4×C11—26no—
51C22×C4×C11C22×C416yes—
52C22×C4×C11C22×C416yes—
53C22×C4×C11C2×D416yes—
54C22×C4×C11C2×D416yes—
55C22×Dic11—24no—
56C22×Dic11—24no—
57C22×Dic11—212no—
58C22×Dic11—212no—
59C22×Dic11—212no—
60C22×Dic11—212no—
61C11×C4⋊C4—224no—
62C11×C22⋊C4—224no—
63C42×C11C22⋊C4116yescomplemented
64C22⋊Dic11—416no—
65C4⋊Dic11—424no—
66C22×#126D1111yescharacteristic
67C2×#384—111no—
68C2×#383—111no—
69#1441—116no—
70#1439—116no—
71C23×C11—22no—
72C23×C11—212no—
73C23×C11—43no—
74C23×C11—43no—
75C23×C11—46no—
76C23×C11—44no—
77C23×C11—412no—
78C23×C11C23×C411yescharacteristic
79C23×C11C22×D411yescharacteristic
80C23×C11C22×D411yescharacteristic
81C23×C11H(5,𝔽2)16yes—
82C23×C112−1+416yes—
83C2×C4×C11—212no—
84C2×C4×C11—26no—
85C2×C4×C11—26no—
86C2×C4×C11—212no—
87C2×C4×C11—26no—
88C2×C4×C11—212no—
89C2×C4×C11—43no—
90C2×C4×C11—43no—
91C2×C4×C11—46no—
92C2×C4×C11C2×C22⋊C4112yes—
93C2×Dic11—412no—
94C2×Dic11—412no—
95C2×Dic11—44no—
96C2×Dic11—44no—
97C2×Dic11—412no—
98C2×Dic11—412no—
99C2×#126—24no—
100C2×#126—24no—
101C2×#126Dic1118yescomplemented
102C22×C4⋊C4—116no—
103C22×C4⋊C4C2×D1113yes—
104C22×C22⋊C4—114no—
105C22×C22⋊C4C2×D1113yes—
106C22×C42C2×D1111yescharacteristic
107#384—224no—
108#383—224no—
109C2×#95—116no—
110C2×#95—1112no—
111C22×C11—46no—
112C22×C11—48no—
113C22×C11—81no—
114C22×C11—83no—
115C22×C11—84no—
116C22×C11C22×C22⋊C411yescharacteristic
117C22×C11#52016yes—
118C22×C11#53513yes—
119C22×C11#53613yes—
120C22×C11#53716yes—
121C22×C11#56014yes—
122C22×C11#563112yes—
123C4×C11—212no—
124C4×C11—46no—
125Dic11—84no—
126Dic11—84no—
127C25C22×D1111yescharacteristic
128C23×C4—114no—
129C23×C4—114no—
130C23×C4C22×D1113yes—
131C23×C4C22×D1113yes—
132#126—232no—
133C2×C4⋊C4—26no—
134C2×C4⋊C4—26no—
135C2×C4⋊C4—2212no—
136C2×C4⋊C4—4412no—
137C2×C4⋊C4C2×Dic11112yes—
138C2×C22⋊C4—26no—
139C2×C22⋊C4—26no—
140C2×C22⋊C4—4412no—
141C2×C22⋊C4C2×Dic11112yes—
142C2×C42C2×Dic1114yes—
143C2×C42C22⋊D1114yes—
144C2×C42C22⋊D1114yes—
145#95—2212no—
146#95—4412no—
147C2×C11—82no—
148C2×C11#231113yes—
149C2×C11#238314yes—
150C2×C11#281811yescharacteristic
151C2×C11#282113yes—
152C2×C11#282314yes—
153C24—26no—
154C24—26no—
155C24—21no—
156C24—21no—
157C24C22×Dic1112yes—
158C24C23×D1111yescharacteristic
159C22×C4—26no—
160C22×C4—26no—
161C22×C4—26no—
162C22×C4—26no—
163C22×C4—23no—
164C22×C4—23no—
165C22×C4—2212no—
166C22×C4—2212no—
167C22×C4—2212no—
168C22×C4—2212no—
169C22×C4—224no—
170C22×C4—224no—
171C22×C4C22×Dic1116yes—
172C22×C4C22×Dic1116yes—
173C22×C4C2×C22⋊D1116yes—
174C22×C4C2×C22⋊D1116yes—
175C4⋊C4—224no—
176C4⋊C4—4424no—
177C22⋊C4—224no—
178C22⋊C4—4416no—
179C42C22⋊Dic11116yescomplemented
180C11#1466511yescharacteristic, complemented, Sylow
181C23—212no—
182C23—22no—
183C23—44no—
184C23—412no—
185C23—43no—
186C23—43no—
187C23—46no—
188C23#6704216yes—
189C23#6704316yes—
190C23C23×Dic1111yescharacteristic
191C23C22×C22⋊D1111yescharacteristic
192C23C22×C22⋊D1111yescharacteristic
193C2×C4—26no—
194C2×C4—212no—
195C2×C4—26no—
196C2×C4—212no—
197C2×C4—212no—
198C2×C4—26no—
199C2×C4—43no—
200C2×C4—43no—
201C2×C4—46no—
202C2×C4—444no—
203C2×C4—444no—
204C2×C4—4412no—
205C2×C4—4412no—
206C2×C4—4412no—
207C2×C4—4412no—
208C2×C4C2×C22⋊Dic11112yes—
209C22—46no—
210C22—48no—
211C22—81no—
212C22—83no—
213C22—84no—
214C22#1062324214yes—
215C22#10623243112yes—
216C22#1062335613yes—
217C22#1062335816yes—
218C22#1062336113yes—
219C22#1062336416yes—
220C22C22×C22⋊Dic1111yescharacteristic
221C4—212no—
222C4—46no—
223C4—884no—
224C4—884no—
225C2—82no—
226C2#1307120813yes—
227C2#1307180814yes—
228C2#1307665611yescharacteristic
229C2#1307667413yes—
230C2#1307668814yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#126C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#126D11
hypocenterC11#14665
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C2×#10622548C2semidirect
2. C2×#10622550C2semidirect
3. #13066869C2semidirect
8. C2×C11×#126C4semidirect
63. C42×C11C22⋊C4semidirect
101. C2×#126Dic11semidirect
179. C42C22⋊Dic11semidirect
180. C11#14665semidirect

Maximal subgroups

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

subgroupindex
C2×#106225482
C2×#106225502
#130668692
#130668612
C22×C11×#1262
#1466511