Finite Group Databasebeta

← #14647253

Subgroups — #14647253

Order 2816.

418 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 91 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#13071114C211yesmaximal, characteristic
2#13068693C211yesmaximal, characteristic
3#13066470C214yesmaximal
4C11×#1822C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C11×#407C2212yes—
7#10622824C2212yes—
8C4×C22⋊Dic11C2212yes—
9#10622594—22no—
10#10622564—22no—
11C4×C4⋊Dic11C412yescomplemented
12#10622545C411yescharacteristic, complemented
13C42×Dic11C411yescharacteristic, complemented
14C11×#343—22no—
15#10622164—22no—
16C23×C4×C11C2311yescharacteristic
17C2×C11×M16—22no—
18C11×#117—24no—
19C2×C11×C4⋊C4D412yes—
20C2×C11×C22⋊C4D412yes—
21C2×C42×C11C2×C411yescharacteristic
22C2×C42×C11C2×C411yescharacteristic
23C2×C22⋊Dic11—22no—
24C2×C22⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×C4×Dic11—22no—
27C2×C4×Dic11C2×C412yes—
28C2×C4×Dic11C2×C412yes—
29C11×C22⋊C8—24no—
30C11⋊#95—22no—
31C11⋊#95—22no—
32C11⋊#95—22no—
33C11⋊#95—24no—
34#8740—111nomaximal, Sylow
35C24×C11C2×D411yescharacteristic
36C22×C4×C11—42no—
37C22×C4×C11C22⋊C412yes—
38C22×C4×C11C22⋊C412yes—
39C22×C4×C11C22×C411yescharacteristic
40C22×C4×C11C2×D411yescharacteristic
41C22×C4×C11#4114yes—
42C22×Dic11—22no—
43C22×Dic11—22no—
44C22×Dic11—42no—
45C11×M16—44no—
46C2×C8×C11—42no—
47C11×C4⋊C4—24no—
48C11×C22⋊C4—24no—
49C42×C11—22no—
50C42×C11—22no—
51C22⋊Dic11—44no—
52C22⋊Dic11—44no—
53C4⋊Dic11—44no—
54C4×Dic11—42no—
55C4×Dic11—42no—
56C4×Dic11—44no—
57#2298—111no—
58#1822D1111yescharacteristic
59#1820—111no—
60#1284—114no—
61C23×C11—22no—
62C23×C11—42no—
63C23×C11C2×C22⋊C411yescharacteristic
64C23×C11#12312yes—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—44no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11#11712yes—
73C2×C4×C11#12312yes—
74C2×Dic11—24no—
75C2×Dic11—42no—
76C2×Dic11—42no—
77C2×Dic11—42no—
78C2×Dic11—42no—
79C2×Dic11—42no—
80C2×Dic11—82no—
81C2×Dic11—84no—
82C8×C11—82no—
83C2×#117C2×D1111yescharacteristic
84#407C2×D1112yes—
85#388—222no—
86#387—222no—
87#381—112no—
88C4×C4⋊C4—112no—
89C4×C22⋊C4—112no—
90#376—111no—
91C43—111no—
92#343—22no—
93#342—222no—
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—24no—
97C22×C11—82no—
98C22×C11#38111yescharacteristic
99C22×C11#41012yes—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—42no—
103C4×C11—42no—
104Dic11—44no—
105Dic11—82no—
106Dic11—162no—
107C23×C4C22×D1111yescharacteristic
108C2×M16—22no—
109#117—24no—
110C2×C4⋊C4—222no—
111C2×C4⋊C4C22⋊D1112yes—
112C2×C22⋊C4—222no—
113C2×C22⋊C4—222no—
114C2×C22⋊C4D4412yes—
115C2×C42—112no—
116C2×C42—112no—
117C2×C42—222no—
118C2×C42C4×D1111yescharacteristic
119C2×C42C4×D1111yescharacteristic
120C22⋊C8—24no—
121#95—222no—
122#95—222no—
123#95—222no—
124#95—224no—
125C2×C11—22no—
126C2×C11—42no—
127C2×C11#182011yescharacteristic
128C2×C11#182712yes—
129C24C2×D4411yescharacteristic
130C22×C4—42no—
131C22×C4—222no—
132C22×C4—222no—
133C22×C4—442no—
134C22×C4(C2×D11)⋊C412yes—
135C22×C4(C2×D11)⋊C412yes—
136C22×C4C2×C4×D1111yescharacteristic
137C22×C4#434114yes—
138C22×C4C2×C22⋊D1111yescharacteristic
139M16—44no—
140C2×C8—42no—
141C4⋊C4—24no—
142C4⋊C4—444no—
143C22⋊C4—24no—
144C22⋊C4—444no—
145C22⋊C4—444no—
146C42—22no—
147C42—22no—
148C42—442no—
149C42—442no—
150C42—444no—
151C11#874011yescharacteristic, complemented, Sylow
152C23—22no—
153C23—42no—
154C23#6693912yes—
155C23C2×(C2×D11)⋊C411yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—224no—
164C2×C4—442no—
165C2×C4—442no—
166C2×C4—442no—
167C2×C4—442no—
168C2×C4—442no—
169C2×C4—882no—
170C2×C4—884no—
171C2×C4#6693012yes—
172C2×C4#6698812yes—
173C8—82no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—82no—
178C22#1062255611yescharacteristic
179C22#1062261912yes—
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—444no—
185C4—882no—
186C4—1762no—
187C2—22no—
188C2—42no—
189C2#1306869111yescharacteristic
190C2#1306872112yes—
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1822C2
socleC22×C11#381
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1822D11
hypocenterC11#8740
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
11. C4×C4⋊Dic11C4semidirect
12. #10622545C4semidirect
13. C42×Dic11C4semidirect
151. C11#8740semidirect

Maximal subgroups

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

subgroupindex
#130711142
#130686932
#130664702
C11×#18222
#874011