Finite Group Databasebeta

← #24984698

Subgroups — #24984698

Order 11008.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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#19134575C212yesmaximal
2#19132418C214yesmaximal, complemented
3C43×#2296C211yesmaximal, characteristic
4C2×C4⋊(C43⋊C8)—22no—
5C2×C22⋊(C43⋊C8)—22no—
6#14582654C2214yes—
7C2×#117×C43C411yescharacteristic
8C2×#117×C43C411yescharacteristic
9C22×C42×C43C2211yescharacteristic
10C43×#389C412yes—
11C43×#389C2212yes—
12C43×#385—22no—
13C4×C4⋊C4×C43—22no—
14C22×C43⋊C8—24no—
15C4⋊(C43⋊C8)—44no—
16C22⋊(C43⋊C8)—44no—
17C23×C4×C43C2×C411yescharacteristic
18C23×C4×C43D412yes—
19#117×C43—22no—
20#117×C43—42no—
21#117×C43C814yescomplemented
22C2×C4⋊C4×C43—22no—
23C2×C4⋊C4×C43—22no—
24C2×C4⋊C4×C43C2×C412yes—
25C2×C4⋊C4×C43C2×C412yes—
26C2×C22⋊C4×C43—21no—
27C2×C22⋊C4×C43—21no—
28C2×C42×C43—21no—
29C2×C42×C43—21no—
30C2×C42×C43—42no—
31C2×C42×C43C2×C411yescharacteristic
32C2×C42×C43D412yes—
33C2×C42×C43C2311yescharacteristic
34#95×C43—22no—
35#95×C43—22no—
36C24×C43C22⋊C411yescharacteristic
37C22×C4×C43—22no—
38C22×C4×C43—22no—
39C22×C4×C43—22no—
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43—22no—
43C22×C4×C43—42no—
44C22×C4×C43—42no—
45C22×C4×C43C22⋊C412yes—
46C22×C4×C43C22⋊C411yescharacteristic
47C22×C4×C43C2×C812yes—
48C22×C4×C43M1612yes—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D412yes—
51C4⋊C4×C43—22no—
52C4⋊C4×C43—42no—
53C4⋊C4×C43—44no—
54C4⋊C4×C43—42no—
55C4⋊C4×C43—42no—
56C4⋊C4×C43C2×C814yes—
57C22⋊C4×C43—24no—
58C22⋊C4×C43—42no—
59C42×C43—24no—
60C42×C43—24no—
61C42×C43—41no—
62C42×C43—41no—
63C42×C43—42no—
64C2×C43⋊C8—44no—
65C2×C43⋊C8—44no—
66C2×C43⋊C8—44no—
67C23×C43—21no—
68C23×C43—21no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43C22⋊C812yes—
72C23×C43C2×C22⋊C411yescharacteristic
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—24no—
78C2×C4×C43—24no—
79C2×C4×C43—24no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—44no—
84C2×C4×C43—44no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43C22⋊C812yes—
91C2×C4×C43#9912yes—
92C2×C4×C43#10112yes—
93C2×C4×C43C22×C811yescharacteristic
94C2×C4×C43C2×M1611yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)12yes—
96C2×C4×C43#13712yes—
97C43⋊C8—84no—
98#7598—431nomaximal, Sylow
99C22×C43—22no—
100C22×C43—24no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43—42no—
104C22×C43C2×C22⋊C811yescharacteristic
105C22×C43C2×#9911yescharacteristic
106C22×C43C2×#10111yescharacteristic
107C22×C43#41712yes—
108C22×C43#42112yes—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—22no—
112C4×C43—22no—
113C4×C43—44no—
114C4×C43—42no—
115C4×C43—82no—
116C4×C43#32414yes—
117#2296D4311yescharacteristic
118#1797—432no—
119#1271—434no—
120C2×C43—42no—
121C2×C43C2×#32411yescharacteristic
122C2×C43#147712yes—
123C2×C43#151312yes—
124C2×C43#153711yescharacteristic
125C2×C43#156111yescharacteristic
126C2×#117Dic4311yescharacteristic
127C2×#117Dic4311yescharacteristic
128C22×C42C2×D4311yescharacteristic
129C2×C4⋊C8—862no—
130C2×C22⋊C8—862no—
131#389Dic4312yes—
132#389C2×D4312yes—
133#385—22no—
134C4×C4⋊C4—22no—
135#336—434no—
136C43#759811yescharacteristic, complemented, Sylow
137C23×C4C2×Dic4311yescharacteristic
138C23×C4C22⋊D4312yes—
139C22×C8—864no—
140#117—22no—
141#117—42no—
142#117C43⋊C814yescomplemented
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4C2×Dic4312yes—
146C2×C4⋊C4C2×Dic4312yes—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42—42no—
152C2×C42C2×Dic4311yescharacteristic
153C2×C42C22⋊D4312yes—
154C2×C42C22×D4311yescharacteristic
155C4⋊C8—1724no—
156C22⋊C8—1724no—
157#95—22no—
158#95—22no—
159C24C22⋊Dic4311yescharacteristic
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4C2×C43⋊C812yes—
169C22×C4#1062187712yes—
170C22×C4C22⋊Dic4312yes—
171C22×C4C22⋊Dic4311yescharacteristic
172C22×C4C22×Dic4311yescharacteristic
173C22×C4C2×C22⋊D4312yes—
174C2×C8—1724no—
175C2×C8—1724no—
176C2×C8—1724no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—44no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4C2×C43⋊C814yes—
183C22⋊C4—24no—
184C22⋊C4—42no—
185C42—24no—
186C42—24no—
187C42—41no—
188C42—41no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—22no—
194C23C22⋊(C43⋊C8)12yes—
195C23C2×C22⋊Dic4311yescharacteristic
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—44no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4C22⋊(C43⋊C8)12yes—
214C2×C4#1306324012yes—
215C2×C4#1306324412yes—
216C2×C4C22×C43⋊C811yescharacteristic
217C2×C4C2×#1062187711yescharacteristic
218C2×C4#1306335012yes—
219C2×C4#1306335512yes—
220C8—3444no—
221C22—24no—
222C22—22no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22C2×C22⋊(C43⋊C8)11yescharacteristic
227C22C2×#1306324011yescharacteristic
228C22C2×#1306324411yescharacteristic
229C22#1458290012yes—
230C22#1458291612yes—
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—44no—
236C4—42no—
237C4—82no—
238C4#1458262514yes—
239C2—42no—
240C2C2×#1458262511yescharacteristic
241C2#1913298212yes—
242C2#1913313812yes—
243C2#1913323311yescharacteristic
244C2#1913333311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#2296C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2296D43
hypocenterC43#7598
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #19132418C2semidirect
21. #117×C43C8semidirect
136. C43#7598semidirect
142. #117C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
#191345752
#191324182
C43×#22962
#759843