Finite Group Databasebeta

← #14685128

Subgroups — #14685128

Order 2816.

1770 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 1770 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
1C22×#66929C211yesmaximal, characteristic
2C2×C42×Dic11C211yesmaximal, characteristic, complemented
3#13066852C216yesmaximal
4#13066851C216yesmaximal, complemented
5C2×C11×#383C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C22×(C2×D11)⋊C4C2214yes—
8C22×(C2×D11)⋊C4C2213yes—
9C22×Dic11⋊C4C2213yes—
10C22×C4×Dic11C2216yes—
11C2×#66929—24no—
12C2×#66929—24no—
13C2×#66929C418yescomplemented
14C11×#383—24no—
15C2×C11×#95C2216yes—
16C2×C11⋊#95C22112yes—
17C42×Dic11—24no—
18C24×D11C2311yescharacteristic
19C23×C4×C11C2314yes—
20C23×C4×C11C2313yes—
21C23×Dic11C2313yes—
22C23×Dic11C2314yes—
23C2×C42×C11C2×C414yes—
24C2×C42×C11D414yes—
25C2×C42×C11D414yes—
26C2×(C2×D11)⋊C4—26no—
27C2×(C2×D11)⋊C4—26no—
28C2×(C2×D11)⋊C4—224no—
29C2×(C2×D11)⋊C4C2×C4112yes—
30C2×Dic11⋊C4—26no—
31C2×Dic11⋊C4—26no—
32C2×Dic11⋊C4C2×C4112yes—
33C2×C4×Dic11—212no—
34C2×C4×Dic11—224no—
35#66929—232no—
36C11×#95—212no—
37C11⋊#95—224no—
38#14711—111nomaximal, Sylow
39C24×C11C2411yescharacteristic
40C23×D11—21no—
41C23×D11—21no—
42C23×D11—212no—
43C23×D11C22×C412yes—
44C22×C4×C11—212no—
45C22×C4×C11—24no—
46C22×C4×C11—212no—
47C22×C4×C11—212no—
48C22×C4×C11C22×C416yes—
49C22×C4×C11C2×D416yes—
50C22×C4×C11C2×D416yes—
51C22×Dic11—24no—
52C22×Dic11—23no—
53C22×Dic11—23no—
54C22×Dic11—212no—
55C22×Dic11—212no—
56C22×Dic11C22×C416yes—
57C22×Dic11#41124yes—
58C42×C11C22⋊C4116yescomplemented
59(C2×D11)⋊C4—224no—
60(C2×D11)⋊C4—416no—
61Dic11⋊C4—224no—
62C4×Dic11—248no—
63C22×#126—111no—
64C2×#383D1111yescharacteristic, complemented
65C2×C43—111no—
66#1437—116no—
67#1436—116no—
68C23×C11C23×C411yescharacteristic
69C23×C11C22×D411yescharacteristic
70C23×C11C22×D411yescharacteristic
71C23×C11C2×#41112yes—
72C22×D11—22no—
73C22×D11—212no—
74C22×D11—46no—
75C22×D11—44no—
76C22×D11—412no—
77C22×D11—46no—
78C2×C4×C11—212no—
79C2×C4×C11—212no—
80C2×C4×C11—212no—
81C2×C4×C11—44no—
82C2×C4×C11—412no—
83C2×C4×C11—412no—
84C2×C4×C11C2×C22⋊C4112yes—
85C2×Dic11—224no—
86C2×Dic11—224no—
87C2×Dic11—26no—
88C2×Dic11—212no—
89C2×Dic11—46no—
90C2×Dic11—46no—
91C2×Dic11#126116yescomplemented
92C2×#126—118no—
93C2×#126—224no—
94C2×#126—224no—
95C22×C4⋊C4—113no—
96C22×C22⋊C4—113no—
97C22×C22⋊C4—114no—
98C22×C42—116no—
99C22×C42C2×D1111yescharacteristic
100#383—24no—
101C2×#95—1112no—
102C2×#95C2×D1116yes—
103C43—224no—
104C22×C11C22×C22⋊C411yescharacteristic
105C22×C11C4×#4116yes—
106C22×C11#52516yes—
107C22×C11C2×#12614yes—
108C22×C11#529112yes—
109C22×C11#53216yes—
110C2×D11—48no—
111C2×D11—46no—
112C2×D11—84no—
113C2×D11—84no—
114C4×C11—212no—
115C4×C11—84no—
116Dic11—216no—
117Dic11—46no—
118C25—111no—
119C23×C4—114no—
120C23×C4—113no—
121C23×C4C22×D1114yes—
122C23×C4C22×D1113yes—
123#126—2232no—
124C2×C4⋊C4—1112no—
125C2×C4⋊C4—226no—
126C2×C4⋊C4—226no—
127C2×C22⋊C4—1112no—
128C2×C22⋊C4—226no—
129C2×C22⋊C4—226no—
130C2×C22⋊C4—2224no—
131C2×C42—2224no—
132C2×C42—2212no—
133C2×C42C4×D1114yes—
134C2×C42D4414yes—
135C2×C42C22⋊D1114yes—
136#95—212no—
137#95—2224no—
138C2×C11#229713yes—
139C2×C11C4×#12614yes—
140C2×C11#285214yes—
141C2×C11#286014yes—
142D11—82no—
143C24—112no—
144C24—221no—
145C24—2212no—
146C24—221no—
147C24C23×D1111yescharacteristic
148C22×C4—212no—
149C22×C4—212no—
150C22×C4—212no—
151C22×C4—24no—
152C22×C4—1124no—
153C22×C4—116no—
154C22×C4—224no—
155C22×C4—2212no—
156C22×C4—223no—
157C22×C4—2212no—
158C22×C4—223no—
159C22×C4C2×C4×D1116yes—
160C22×C4C2×D4416yes—
161C22×C4C2×C22⋊D1116yes—
162C4⋊C4—2224no—
163C22⋊C4—2224no—
164C22⋊C4—4416no—
165C42—2248no—
166C42(C2×D11)⋊C4116yescomplemented
167C11#1471111yescharacteristic, complemented, Sylow
168C23—2212no—
169C23—222no—
170C23—444no—
171C23—4412no—
172C23—446no—
173C23—446no—
174C23C22×C4×D1111yescharacteristic
175C23C22×D4411yescharacteristic
176C23#41×D11112yes—
177C23C22×C22⋊D1111yescharacteristic
178C2×C4—212no—
179C2×C4—212no—
180C2×C4—212no—
181C2×C4—44no—
182C2×C4—412no—
183C2×C4—412no—
184C2×C4—1116no—
185C2×C4—2224no—
186C2×C4—2224no—
187C2×C4—2212no—
188C2×C4—226no—
189C2×C4—446no—
190C2×C4—446no—
191C2×C4C2×(C2×D11)⋊C4112yes—
192C22—446no—
193C22—448no—
194C22—884no—
195C22—884no—
196C22#1062305316yes—
197C22#1062305516yes—
198C22D11×#12614yes—
199C22#10623237112yes—
200C22C22×(C2×D11)⋊C411yescharacteristic
201C22#1062336316yes—
202C4—212no—
203C4—84no—
204C4—2216no—
205C4—446no—
206C2—882no—
207C2#1307110413yes—
208C2#1307116414yes—
209C2#1307693214yes—
210C2#1307698114yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#383C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#383D11
hypocenterC11#14711
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. C2×C42×Dic11C2semidirect
4. #13066851C2semidirect
5. C2×C11×#383C2semidirect
13. C2×#66929C4semidirect
58. C42×C11C22⋊C4semidirect
64. C2×#383D11semidirect
91. C2×Dic11#126semidirect
166. C42(C2×D11)⋊C4semidirect
167. C11#14711semidirect

Maximal subgroups

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

subgroupindex
C22×#669292
C2×C42×Dic112
#130668522
#130668512
C2×C11×#3832
#1471111