Finite Group Databasebeta

← #14685131

Subgroups — #14685131

Order 2816.

1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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×#10622550C211yesmaximal, characteristic, complemented
2C2×C42×Dic11C211yesmaximal, characteristic, complemented
3#13066853C216yesmaximal
4#13066848C216yesmaximal, complemented
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⋊#95C22112yes—
15C2×C11⋊#95C2216yes—
16#10622550—24no—
17C42×Dic11—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—224no—
34C2×C4×Dic11—212no—
35C2×C4×Dic11—224no—
36C11⋊#95—212no—
37C11⋊#95—224no—
38#14711—111nomaximal, Sylow
39C24×C11—21no—
40C24×C11—21no—
41C24×C11—212no—
42C24×C11C22×C412yes—
43C24×C11C2411yescharacteristic
44C22×C4×C11—212no—
45C22×C4×C11—23no—
46C22×C4×C11—23no—
47C22×C4×C11—212no—
48C22×C4×C11C22×C416yes—
49C22×C4×C11C22×C416yes—
50C22×C4×C11C2×D416yes—
51C22×C4×C11C2×D416yes—
52C22×Dic11—24no—
53C22×Dic11—24no—
54C22×Dic11—212no—
55C22×Dic11—212no—
56C22×Dic11—212no—
57C22×Dic11#41124yes—
58C11×C4⋊C4—224no—
59C11×C22⋊C4—224no—
60C42×C11C22⋊C4116yescomplemented
61C22⋊Dic11—416no—
62C4×Dic11—248no—
63C22×#126D1111yescharacteristic
64C2×#383—111no—
65C2×C43—111no—
66#1437—116no—
67#1436—116no—
68C23×C11—22no—
69C23×C11—212no—
70C23×C11—46no—
71C23×C11—44no—
72C23×C11—412no—
73C23×C11—46no—
74C23×C11C23×C411yescharacteristic
75C23×C11C22×D411yescharacteristic
76C23×C11C22×D411yescharacteristic
77C23×C11C2×#41112yes—
78C2×C4×C11—212no—
79C2×C4×C11—212no—
80C2×C4×C11—212no—
81C2×C4×C11—26no—
82C2×C4×C11—212no—
83C2×C4×C11—46no—
84C2×C4×C11—46no—
85C2×C4×C11C2×C22⋊C4112yes—
86C2×Dic11—224no—
87C2×Dic11—224no—
88C2×Dic11—44no—
89C2×Dic11—412no—
90C2×Dic11—412no—
91C2×Dic11#126116yescomplemented
92C2×#126—24no—
93C2×#126—24no—
94C2×#126Dic1118yescomplemented
95C22×C4⋊C4C2×D1113yes—
96C22×C22⋊C4—114no—
97C22×C22⋊C4C2×D1113yes—
98C22×C42—116no—
99C22×C42C2×D1111yescharacteristic
100#383—224no—
101C2×#95—1112no—
102C2×#95—116no—
103C43—224no—
104C22×C11—48no—
105C22×C11—46no—
106C22×C11—84no—
107C22×C11—84no—
108C22×C11C22×C22⋊C411yescharacteristic
109C22×C11C4×#4116yes—
110C22×C11#52516yes—
111C22×C11C2×#12614yes—
112C22×C11#529112yes—
113C22×C11#53216yes—
114C4×C11—212no—
115C4×C11—46no—
116Dic11—216no—
117Dic11—84no—
118C25C22×D1111yescharacteristic
119C23×C4—114no—
120C23×C4—114no—
121C23×C4C22×D1113yes—
122C23×C4C22×D1113yes—
123#126—232no—
124C2×C4⋊C4—26no—
125C2×C4⋊C4—26no—
126C2×C4⋊C4C2×Dic11112yes—
127C2×C22⋊C4—26no—
128C2×C22⋊C4—26no—
129C2×C22⋊C4—2224no—
130C2×C22⋊C4C2×Dic11112yes—
131C2×C42—2224no—
132C2×C42—2212no—
133C2×C42C2×Dic1114yes—
134C2×C42C22⋊D1114yes—
135C2×C42C22⋊D1114yes—
136#95—2224no—
137#95—2212no—
138C2×C11—82no—
139C2×C11#229713yes—
140C2×C11C4×#12614yes—
141C2×C11#285214yes—
142C2×C11#286014yes—
143C24—212no—
144C24—21no—
145C24—21no—
146C24C22×Dic1112yes—
147C24C23×D1111yescharacteristic
148C22×C4—212no—
149C22×C4—212no—
150C22×C4—23no—
151C22×C4—23no—
152C22×C4—1124no—
153C22×C4—2212no—
154C22×C4—224no—
155C22×C4—2212no—
156C22×C4—2212no—
157C22×C4—224no—
158C22×C4C22×Dic1116yes—
159C22×C4C22×Dic1116yes—
160C22×C4C2×C22⋊D1116yes—
161C22×C4C2×C22⋊D1116yes—
162C4⋊C4—224no—
163C22⋊C4—224no—
164C22⋊C4—4416no—
165C42—2248no—
166C42C22⋊Dic11116yescomplemented
167C11#1471111yescharacteristic, complemented, Sylow
168C23—212no—
169C23—22no—
170C23—44no—
171C23—412no—
172C23—46no—
173C23—46no—
174C23#41×D11112yes—
175C23C23×Dic1111yescharacteristic
176C23C22×C22⋊D1111yescharacteristic
177C23C22×C22⋊D1111yescharacteristic
178C2×C4—212no—
179C2×C4—212no—
180C2×C4—212no—
181C2×C4—212no—
182C2×C4—26no—
183C2×C4—46no—
184C2×C4—46no—
185C2×C4—1116no—
186C2×C4—2224no—
187C2×C4—2224no—
188C2×C4—444no—
189C2×C4—4412no—
190C2×C4—4412no—
191C2×C4C2×C22⋊Dic11112yes—
192C22—46no—
193C22—48no—
194C22—84no—
195C22—84no—
196C22D11×#12614yes—
197C22#10623237112yes—
198C22#41×Dic1116yes—
199C22#1062335916yes—
200C22#1062336316yes—
201C22C22×C22⋊Dic1111yescharacteristic
202C4—212no—
203C4—46no—
204C4—2216no—
205C4—884no—
206C2—82no—
207C2#1307110713yes—
208C2#126×Dic1114yes—
209C2#1307692814yes—
210C2#1307698114yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#126C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#126D11
hypocenterC11#14711
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C2×#10622550C2semidirect
2. C2×C42×Dic11C2semidirect
4. #13066848C2semidirect
8. C2×C11×#126C4semidirect
60. C42×C11C22⋊C4semidirect
91. C2×Dic11#126semidirect
94. C2×#126Dic11semidirect
166. C42C22⋊Dic11semidirect
167. C11#14711semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
C2×C42×Dic112
#130668532
#130668482
C22×C11×#1262
#1471111