Finite Group Databasebeta

← #25005759

Subgroups — #25005759

Order 11008.

454 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#14582625C212yesmaximal
2#19132541C212yesmaximal, complemented
3#19132539C212yesmaximal, complemented
4C43×#2317C211yesmaximal, characteristic
5C2×C22⋊(C43⋊C8)—22no—
6#14582625—22no—
7#14582625C2214yes—
8C2×#117×C43C411yescharacteristic
9C2×#117×C43C411yescharacteristic
10C22×C4⋊C4×C43C2211yescharacteristic
11C43×#389—22no—
12C43×#385—22no—
13C43×#384C411yescharacteristic
14C43×#384C2211yescharacteristic
15C43×#382C411yescharacteristic
16C43×#382C2211yescharacteristic
17C22×C43⋊C8—42no—
18C22⋊(C43⋊C8)—24no—
19C22⋊(C43⋊C8)—42no—
20C23×C4×C43C2×C411yescharacteristic
21C23×C4×C43D412yes—
22#117×C43—22no—
23#117×C43—42no—
24#117×C43C814yescomplemented
25C2×C4⋊C4×C43—21no—
26C2×C4⋊C4×C43—22no—
27C2×C4⋊C4×C43—22no—
28C2×C4⋊C4×C43—42no—
29C2×C4⋊C4×C43C2×C411yescharacteristic
30C2×C4⋊C4×C43C2×C411yescharacteristic
31C2×C4⋊C4×C43C2×C411yescharacteristic
32C2×C4⋊C4×C43D412yes—
33C2×C4⋊C4×C43C2311yescharacteristic
34C2×C22⋊C4×C43—21no—
35C2×C22⋊C4×C43—21no—
36C2×C42×C43—21no—
37C2×C42×C43C2×C411yescharacteristic
38C2×C42×C43C2×C411yescharacteristic
39#95×C43—22no—
40#95×C43—22no—
41C24×C43C22⋊C411yescharacteristic
42C22×C4×C43—22no—
43C22×C4×C43—22no—
44C22×C4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—82no—
51C22×C4×C43C22⋊C411yescharacteristic
52C22×C4×C43C22⋊C412yes—
53C22×C4×C43C2×C812yes—
54C22×C4×C43M1612yes—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D412yes—
57C4⋊C4×C43—24no—
58C4⋊C4×C43—41no—
59C4⋊C4×C43—42no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—82no—
64C4⋊C4×C43—82no—
65C22⋊C4×C43—24no—
66C22⋊C4×C43—42no—
67C42×C43—21no—
68C42×C43—21no—
69C42×C43—42no—
70C42×C43C2×C812yescomplemented
71C42×C43C2×C812yescomplemented
72C2×C43⋊C8—44no—
73C2×C43⋊C8—84no—
74C23×C43—41no—
75C23×C43—41no—
76C23×C43C22⋊C812yes—
77C23×C43#9912yes—
78C23×C43#10112yes—
79C23×C43C2×C22⋊C411yescharacteristic
80C2×C4×C43—24no—
81C2×C4×C43—24no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—44no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—82no—
102C2×C4×C43C22⋊C812yes—
103C2×C4×C43C22×C811yescharacteristic
104C2×C4×C43C2×M1611yescharacteristic
105C43⋊C8—84no—
106#11448—431nomaximal, Sylow
107C22×C43—22no—
108C22×C43—21no—
109C22×C43—22no—
110C22×C43—21no—
111C22×C43—42no—
112C22×C43—42no—
113C22×C43#32414yes—
114C22×C43C2×C22⋊C811yescharacteristic
115C22×C43C2×#9911yescharacteristic
116C22×C43C2×#10111yescharacteristic
117C4×C43—22no—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—42no—
121C4×C43—42no—
122C4×C43—42no—
123C4×C43—42no—
124C4×C43—81no—
125C4×C43—81no—
126#2317D4311yescharacteristic
127C2×#324—432no—
128#1325—432no—
129#1324—432no—
130C2×C43—21no—
131C2×C43—24no—
132C2×C43—21no—
133C2×C43C2×#32411yescharacteristic
134C2×C43#212711yescharacteristic
135C2×C43#213311yescharacteristic
136C2×#117Dic4311yescharacteristic
137C2×#117Dic4311yescharacteristic
138C22×C4⋊C4C2×D4311yescharacteristic
139C2×C22⋊C8—862no—
140#389—22no—
141#385—22no—
142#384Dic4311yescharacteristic
143#384C2×D4311yescharacteristic
144#382Dic4311yescharacteristic
145#382C2×D4311yescharacteristic
146#324—434no—
147#324—862no—
148C43#1144811yescharacteristic, complemented, Sylow
149C23×C4C2×Dic4311yescharacteristic
150C23×C4C22⋊D4312yes—
151C22×C8—1722no—
152#117—22no—
153#117—42no—
154#117C43⋊C814yescomplemented
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4C2×Dic4311yescharacteristic
160C2×C4⋊C4C2×Dic4311yescharacteristic
161C2×C4⋊C4C2×Dic4311yescharacteristic
162C2×C4⋊C4C22⋊D4312yes—
163C2×C4⋊C4C22×D4311yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—21no—
166C2×C42—21no—
167C2×C42C2×Dic4311yescharacteristic
168C2×C42C2×Dic4311yescharacteristic
169C22⋊C8—864no—
170C22⋊C8—1722no—
171#95—22no—
172#95—22no—
173C24C22⋊Dic4311yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—82no—
183C22×C4C2×C43⋊C812yes—
184C22×C4#1062187712yes—
185C22×C4C22⋊Dic4311yescharacteristic
186C22×C4C22⋊Dic4312yes—
187C22×C4C22×Dic4311yescharacteristic
188C22×C4C2×C22⋊D4312yes—
189C2×C8—3444no—
190C2×C8—1724no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C22⋊C4—24no—
200C22⋊C4—42no—
201C42—21no—
202C42—21no—
203C42—42no—
204C42C2×C43⋊C812yescomplemented
205C42C2×C43⋊C812yescomplemented
206C23—41no—
207C23—41no—
208C23C22⋊(C43⋊C8)12yes—
209C23#1306324012yes—
210C23#1306324412yes—
211C23C2×C22⋊Dic4311yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4C22⋊(C43⋊C8)12yes—
235C2×C4C22×C43⋊C811yescharacteristic
236C2×C4C2×#1062187711yescharacteristic
237C8—3444no—
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22#1458262514yes—
245C22C2×C22⋊(C43⋊C8)11yescharacteristic
246C22C2×#1306324011yescharacteristic
247C22C2×#1306324411yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—24no—
260C2C2×#1458262511yescharacteristic
261C2#1913626411yescharacteristic
262C2#1913628411yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2317C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2317D43
hypocenterC43#11448
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. #19132541C2semidirect
3. #19132539C2semidirect
24. #117×C43C8semidirect
70. C42×C43C2×C8semidirect
71. C42×C43C2×C8semidirect
148. C43#11448semidirect
154. #117C43⋊C8semidirect
204. C42C2×C43⋊C8semidirect
205. C42C2×C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#145826252
#191325412
#191325392
C43×#23172
#1144843