Finite Group Databasebeta

← #25005879

Subgroups — #25005879

Order 11008.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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#19132919C212yesmaximal
2#19132541C212yesmaximal
3#19132529C212yesmaximal
4C4×C4⋊Q8×C43C211yesmaximal, characteristic
5#14582952—22no—
6#14582625—22no—
7#14582625C2214yes—
8C2×C4⋊Q8×C43C411yescharacteristic
9C2×C4×Q8×C43C411yescharacteristic
10C2×C4×Q8×C43C2211yescharacteristic
11C43×#391C411yescharacteristic
12C43×#391C2211yescharacteristic
13C43×#389—22no—
14C43×#384C2211yescharacteristic
15C4×C4⋊C4×C43—22no—
16C43×C43C411yescharacteristic
17C4⋊(C43⋊C8)—42no—
18C22⋊(C43⋊C8)—24no—
19C4×C43⋊C8—42no—
20C22×Q8×C43C2×C411yescharacteristic
21C22×Q8×C43C2×C411yescharacteristic
22C4⋊Q8×C43—22no—
23C4⋊Q8×C43C814yescomplemented
24C4×Q8×C43—41no—
25C4×Q8×C43—41no—
26C4×Q8×C43—41no—
27C4×Q8×C43—41no—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43—21no—
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43C2×C411yescharacteristic
32C2×C4⋊C4×C43D412yes—
33C2×C4⋊C4×C43C2311yescharacteristic
34C2×C42×C43—21no—
35C2×C42×C43—21no—
36C2×C42×C43—21no—
37C2×C42×C43C2×C411yescharacteristic
38C2×C42×C43C2×C411yescharacteristic
39C2×C42×C43C2×C411yescharacteristic
40C2×C42×C43D412yes—
41#95×C43—22no—
42#95×C43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43C2×C812yes—
49C2×Q8×C43C2×C812yes—
50C2×Q8×C43M1612yes—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43C22⋊C412yes—
56C22×C4×C43C22⋊C411yescharacteristic
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D412yes—
60C4⋊C4×C43—28no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C4⋊C4×C43—44no—
65C4⋊C4×C43—42no—
66C42×C43—24no—
67C42×C43—21no—
68C42×C43—21no—
69C42×C43—22no—
70C42×C43—22no—
71C42×C43—21no—
72C42×C43—41no—
73C42×C43—42no—
74C42×C43—41no—
75C42×C43—41no—
76C42×C43C2×C812yes—
77C2×C43⋊C8—44no—
78C23×C43C2×C22⋊C411yescharacteristic
79Q8×C43—42no—
80Q8×C43—42no—
81Q8×C43—42no—
82Q8×C43—42no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—41no—
103C2×C4×C43C22⋊C814yes—
104C2×C4×C43#9911yescharacteristic
105C2×C4×C43#9911yescharacteristic
106C2×C4×C43C22×C811yescharacteristic
107C2×C4×C43C2×M1611yescharacteristic
108C43⋊C8—84no—
109#11478—431nomaximal, Sylow
110C22×C43—21no—
111C22×C43—21no—
112C22×C43C2×C22⋊C811yescharacteristic
113C22×C43C2×#9911yescharacteristic
114C22×C43#41311yescharacteristic
115C4×C43—24no—
116C4×C43—21no—
117C4×C43—24no—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—42no—
121C4×C43—42no—
122C4×C43—41no—
123C4×C43—42no—
124C4×C43—81no—
125C4×C43#35612yes—
126C4×C4⋊Q8D4311yescharacteristic
127#1461—432no—
128#1325—432no—
129#1319—432no—
130C2×C43—21no—
131C2×C43—21no—
132C2×C43#145911yescharacteristic
133C2×C43#212611yescharacteristic
134C2×C43C2×#35611yescharacteristic
135C2×C4⋊Q8Dic4311yescharacteristic
136C2×C4×Q8Dic4311yescharacteristic
137C2×C4×Q8C2×D4311yescharacteristic
138#431—862no—
139#391Dic4311yescharacteristic
140#391C2×D4311yescharacteristic
141#389—22no—
142#384C2×D4311yescharacteristic
143C4×C4⋊C4—22no—
144C43Dic4311yescharacteristic
145#324—434no—
146#324—862no—
147C43#1147811yescharacteristic, complemented, Sylow
148C22×Q8C2×Dic4311yescharacteristic
149C22×Q8C2×Dic4311yescharacteristic
150C4⋊Q8—22no—
151C4⋊Q8C43⋊C814yescomplemented
152C4×Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×Dic4311yescharacteristic
160C2×C4⋊C4C22⋊D4312yes—
161C2×C4⋊C4C22×D4311yescharacteristic
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42C2×Dic4311yescharacteristic
166C2×C42C2×Dic4311yescharacteristic
167C2×C42C2×Dic4311yescharacteristic
168C2×C42C22⋊D4312yes—
169C4⋊C8—1722no—
170C22⋊C8—864no—
171C4×C8—1722no—
172#95—22no—
173#95—22no—
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C2×C43⋊C812yes—
180C2×Q8C2×C43⋊C812yes—
181C2×Q8#1062187712yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4C22⋊Dic4312yes—
187C22×C4C22⋊Dic4311yescharacteristic
188C22×C4C22⋊Dic4311yescharacteristic
189C22×C4C22×Dic4311yescharacteristic
190C22×C4C2×C22⋊D4312yes—
191C2×C8—1724no—
192C4⋊C4—28no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C42—24no—
199C42—22no—
200C42—21no—
201C42—22no—
202C42—21no—
203C42—21no—
204C42—41no—
205C42—42no—
206C42—41no—
207C42—41no—
208C42C2×C43⋊C812yes—
209C23C2×C22⋊Dic4311yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4C22⋊(C43⋊C8)14yes—
235C2×C4#1306324011yescharacteristic
236C2×C4#1306324011yescharacteristic
237C2×C4C22×C43⋊C811yescharacteristic
238C2×C4C2×#1062187711yescharacteristic
239C8—3444no—
240C22—21no—
241C22—21no—
242C22C2×C22⋊(C43⋊C8)11yescharacteristic
243C22C2×#1306324011yescharacteristic
244C22#1458288311yescharacteristic
245C4—24no—
246C4—21no—
247C4—24no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4#1458269812yes—
256C2—21no—
257C2—21no—
258C2#1913291311yescharacteristic
259C2#1913626011yescharacteristic
260C2C2×#1458269811yescharacteristic
subgroupG/H
centerC2×C4#13063240
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC4×C4⋊Q8×C43C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenterC4×C4⋊Q8D43
hypocenterC43#11478
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
23. C4⋊Q8×C43C8semidirect
147. C43#11478semidirect
151. C4⋊Q8C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
#191329192
#191325412
#191325292
C4×C4⋊Q8×C432
#1147843