Finite Group Databasebeta

← #14910190

Subgroups — #14910190

Order 2816.

512 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 143 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#13079266C212yesmaximal, complemented
2#13070774C214yesmaximal, complemented
3#13070719C212yesmaximal, complemented
4#13070702C212yesmaximal, complemented
5#13070652C214yesmaximal, complemented
6C11×#2151C211yesmaximal, characteristic, complemented
7#10623066—22no—
8C2×C11×M32C2211yescharacteristic
9C22×C11×C16C2211yescharacteristic
10C11×#405C2211yescharacteristic
11#10622748—22no—
12#10622728C2214yes—
13C2×D176C2212yes—
14C2×D176C2212yes—
15#10622326—22no—
16#10622324—22no—
17#10622308C2212yes—
18C4×D88C2214yes—
19#10622296C2212yes—
20C11×C4⋊C16C2214yes—
21#10622147C2214yes—
22#10622147C2214yes—
23#10622143C2212yes—
24#10622142C2212yes—
25C2×C11×M16D411yescharacteristic
26C22×C8×C11C2311yescharacteristic
27C11×#117D411yescharacteristic
28#66983—24no—
29C2×D88—22no—
30C2×D88C2314yes—
31#66947—44no—
32#66937—44no—
33#66927—22no—
34C4×D44—24no—
35#66923—22no—
36C11×M32—41no—
37C2×C11×C16—41no—
38C2×C11×C16C2312yes—
39C2×C11×C16C2312yes—
40C11×#97D412yes—
41C4×C8×C11C2312yes—
42#66885—24no—
43#66885—24no—
44#66882C2314yes—
45#66881—22no—
46D176—42no—
47D176—42no—
48#33825—111nomaximal, Sylow
49C22×C4×C11C2×D411yescharacteristic
50C2×C22⋊D11—44no—
51C2×D44—24no—
52C2×D44—44no—
53C2×C4×D11—44no—
54C11×M16—41no—
55C2×C8×C11—21no—
56C2×C8×C11—21no—
57C2×C8×C11C2×D412yes—
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11C2411yescharacteristic
60C11×C4⋊C4D812yes—
61C11×C22⋊C4D812yes—
62C42×C11C2×D412yes—
63(C2×D11)⋊C4—44no—
64(C2×D11)⋊C4—44no—
65C4⋊Dic11—24no—
66Dic11⋊C4—44no—
67D88—24no—
68D88—24no—
69D88—44no—
70C11×C16—22no—
71C11×C16—22no—
72#3176—112no—
73#2228—114no—
74#2218—112no—
75#2215—112no—
76#2206—114no—
77#2151D1111yescharacteristic, complemented
78C23×C11C2×D811yescharacteristic
79C22×D11—44no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11C2×D814yes—
83C2×C4×C11C2×D811yescharacteristic
84C2×C4×C11C22×D411yescharacteristic
85C22⋊D11—164no—
86C2×Dic11—44no—
87D44—44no—
88D44—44no—
89D44—164no—
90C4×D11—164no—
91C8×C11—21no—
92C8×C11—22no—
93C8×C11H(5,𝔽2)11yescharacteristic
94C8×C112−1+411yescharacteristic
95#540—222no—
96C2×D16—112no—
97C2×D16—112no—
98C2×M32C2×D1111yescharacteristic
99C22×C16C2×D1111yescharacteristic
100#499—112no—
101#493—112no—
102#490—222no—
103#469—222no—
104#466—114no—
105#442—222no—
106C4×D8—114no—
107#405C2×D1111yescharacteristic
108#367—112no—
109#366—112no—
110C4⋊C16C2×D1114yes—
111#357—114no—
112#357—114no—
113C22×C11—22no—
114C22×C11—21no—
115C22×C11C22×D811yescharacteristic
116C2×D11—84no—
117C2×D11—84no—
118C2×D11—84no—
119C4×C11—24no—
120C4×C11—21no—
121C4×C11#53711yescharacteristic
122C4×C11#57511yescharacteristic
123Dic11—84no—
124C2×D8—114no—
125C2×D8—222no—
126C2×M16D4411yescharacteristic
127C22×C8C22×D1111yescharacteristic
128#127—222no—
129#125—222no—
130#123—444no—
131#121—224no—
132#121—444no—
133C4×D4—224no—
134#117D4411yescharacteristic
135D16—442no—
136D16—442no—
137M32—41no—
138C2×C16—41no—
139C2×C16C22×D1112yes—
140C2×C16C22×D1112yes—
141#107—114no—
142#106—222no—
143#102—224no—
144#102—224no—
145#97D4412yes—
146C4×C8C22×D1112yes—
147C2×C11—41no—
148C2×C11#324511yescharacteristic
149C2×C11#341512yes—
150D11—164no—
151C2×D4—224no—
152C2×D4—444no—
153C2×D4—444no—
154C22×C4—444no—
155C22×C4C2×D4411yescharacteristic
156D8—224no—
157D8—224no—
158D8—444no—
159M16—41no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8C2×D4412yes—
163C2×C8C2×D4411yescharacteristic
164C2×C8C23×D1111yescharacteristic
165C4⋊C4—224no—
166C4⋊C4—444no—
167C4⋊C4D8812yes—
168C22⋊C4—444no—
169C22⋊C4—444no—
170C22⋊C4D8812yes—
171C42C2×D4412yes—
172C16—22no—
173C16—22no—
174C11#3382511yescharacteristic, complemented, Sylow
175C23—444no—
176C23C2×D8811yescharacteristic
177D4—444no—
178D4—444no—
179D4—1764no—
180D4—1764no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—444no—
184C2×C4—1764no—
185C2×C4C2×D8814yes—
186C2×C4C2×D8811yescharacteristic
187C2×C4C22×D4411yescharacteristic
188C8—22no—
189C8—21no—
190C8#6703711yescharacteristic
191C8#6704011yescharacteristic
192C22—21no—
193C22—22no—
194C22—884no—
195C22—884no—
196C22—884no—
197C22C22×D8811yescharacteristic
198C4—21no—
199C4—24no—
200C4—884no—
201C4#1062304111yescharacteristic
202C4#1062327911yescharacteristic
203C2—41no—
204C2—1764no—
205C2#1307992611yescharacteristic
206C2#1308175712yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2151C2
socleC22×C11C22×D8
hypercenter#2151D11
hypocenterC11#33825
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13070774C2semidirect
3. #13070719C2semidirect
4. #13070702C2semidirect
5. #13070652C2semidirect
6. C11×#2151C2semidirect
77. #2151D11semidirect
174. C11#33825semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130707742
#130707192
#130707022
#130706522
C11×#21512
#3382511