Finite Group Databasebeta

← #24990076

Subgroups — #24990076

Order 11008.

418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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#19134678C211yesmaximal, characteristic
2#19134672C211yesmaximal, characteristic
3#19132448C214yesmaximal
4C43×#2298C211yesmaximal, characteristic
5#14582863C2212yes—
6#14582762C2212yes—
7#14582668—22no—
8#14582666—22no—
9C2×#117×C43C2211yescharacteristic
10C43×#388—22no—
11C43×#387—22no—
12C4×C4⋊C4×C43C412yescomplemented
13C4×C22⋊C4×C43C2212yes—
14C43×#376C411yescharacteristic, complemented
15C43×C43C411yescharacteristic, complemented
16C2×#10621877—22no—
17C2×C22⋊Dic43—22no—
18C22⋊(C43⋊C8)—24no—
19C43⋊#95—24no—
20C23×C4×C43C2311yescharacteristic
21#117×C43—24no—
22C2×C4⋊C4×C43—22no—
23C2×C4⋊C4×C43D412yes—
24C2×C22⋊C4×C43—22no—
25C2×C22⋊C4×C43D412yes—
26C2×C42×C43—22no—
27C2×C42×C43C2×C411yescharacteristic
28C2×C42×C43C2×C411yescharacteristic
29C2×C42×C43C2×C412yes—
30C2×C42×C43C2×C412yes—
31#95×C43—22no—
32#95×C43—22no—
33#95×C43—22no—
34C24×C43C2×D411yescharacteristic
35C22×C4×C43—22no—
36C22×C4×C43—22no—
37C22×C4×C43—42no—
38C22×C4×C43C22⋊C412yes—
39C22×C4×C43C22⋊C412yes—
40C22×C4×C43C22×C411yescharacteristic
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43#4114yes—
43C22×Dic43—42no—
44C4⋊C4×C43—24no—
45C4⋊C4×C43—44no—
46C22⋊C4×C43—24no—
47C22⋊C4×C43—44no—
48C42×C43—22no—
49C42×C43—22no—
50C42×C43—42no—
51C42×C43—42no—
52C42×C43—44no—
53C22⋊Dic43—44no—
54#10621877—44no—
55C2×C43⋊C8—42no—
56C23×C43—22no—
57C23×C43—42no—
58C23×C43C2×C22⋊C411yescharacteristic
59C23×C43#12312yes—
60C2×C4×C43—22no—
61C2×C4×C43—22no—
62C2×C4×C43—24no—
63C2×C4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—44no—
66C2×C4×C43—42no—
67C2×C4×C43—42no—
68C2×C4×C43—42no—
69C2×C4×C43—42no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43#11712yes—
74C2×C4×C43#12312yes—
75C2×Dic43—82no—
76C2×Dic43—84no—
77C43⋊C8—82no—
78#8740—431nomaximal, Sylow
79C22×C43—22no—
80C22×C43—22no—
81C22×C43—24no—
82C22×C43—82no—
83C22×C43#38111yescharacteristic
84C22×C43#41012yes—
85C4×C43—22no—
86C4×C43—22no—
87C4×C43—44no—
88C4×C43—42no—
89C4×C43—42no—
90C4×C43—82no—
91Dic43—162no—
92#2298D4311yescharacteristic
93#1822—431no—
94#1820—431no—
95#1284—434no—
96C2×C43—22no—
97C2×C43—42no—
98C2×C43#182011yescharacteristic
99C2×C43#182712yes—
100C2×#117C2×D4311yescharacteristic
101#407—432no—
102#388—22no—
103#387—22no—
104#381—432no—
105C4×C4⋊C4Dic4312yescomplemented
106C4×C22⋊C4C2×D4312yes—
107#376Dic4311yescharacteristic, complemented
108C43Dic4311yescharacteristic, complemented
109#343—862no—
110#342—862no—
111C43#874011yescharacteristic, complemented, Sylow
112C23×C4C22×D4311yescharacteristic
113C2×M16—862no—
114#117—24no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4C22⋊D4312yes—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—862no—
119C2×C22⋊C4C22⋊D4312yes—
120C2×C42—22no—
121C2×C42C2×Dic4311yescharacteristic
122C2×C42C2×Dic4311yescharacteristic
123C2×C42C2×Dic4312yes—
124C2×C42C2×Dic4312yes—
125C22⋊C8—864no—
126#95—22no—
127#95—22no—
128#95—22no—
129#95—864no—
130C24C2×C22⋊D4311yescharacteristic
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—1722no—
135C22×C4C22⋊Dic4312yes—
136C22×C4C22⋊Dic4312yes—
137C22×C4#1062189814yes—
138C22×C4C22×Dic4311yescharacteristic
139C22×C4C2×C22⋊D4311yescharacteristic
140M16—1724no—
141C2×C8—1722no—
142C4⋊C4—24no—
143C4⋊C4—44no—
144C22⋊C4—24no—
145C22⋊C4—44no—
146C22⋊C4—1724no—
147C42—22no—
148C42—22no—
149C42—42no—
150C42—42no—
151C42—44no—
152C23—22no—
153C23—42no—
154C23C2×C22⋊Dic4311yescharacteristic
155C23#1306330812yes—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—3442no—
170C2×C4—3444no—
171C2×C4#1306328412yes—
172C2×C4#1306330812yes—
173C8—3442no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—82no—
178C22#1458276211yescharacteristic
179C22#1458287312yes—
180C4—22no—
181C4—22no—
182C4—44no—
183C4—42no—
184C4—42no—
185C4—82no—
186C4—6882no—
187C2—22no—
188C2—42no—
189C2#1913467211yescharacteristic
190C2#1913469912yes—
subgroupG/H
centerC22#14582762
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2298C2
socleC22×C43#381
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2298D43
hypocenterC43#8740
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
12. C4×C4⋊C4×C43C4semidirect
14. C43×#376C4semidirect
15. C43×C43C4semidirect
105. C4×C4⋊C4Dic43semidirect
107. #376Dic43semidirect
108. C43Dic43semidirect
111. C43#8740semidirect

Maximal subgroups

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

subgroupindex
#191346782
#191346722
#191324482
C43×#22982
#874043