Finite Group Databasebeta

← #25005871

Subgroups — #25005871

Order 11008.

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

normal subgroups only

This group has 460 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, complemented
2#19132539C212yesmaximal, complemented
3#19132527C212yesmaximal
4C4×#124×C43C211yesmaximal, characteristic
5#14582952—22no—
6#14582625—22no—
7#14582625C2214yes—
8C2×#124×C43C411yescharacteristic
9C2×C4×Q8×C43C2211yescharacteristic
10C2×C4×D4×C43C411yescharacteristic
11C43×#391C411yescharacteristic
12C43×#390C2211yescharacteristic
13C43×#388—22no—
14C43×#382C2211yescharacteristic
15C4×C22⋊C4×C43—22no—
16C43×C43C411yescharacteristic
17C4⋊(C43⋊C8)—42no—
18C22⋊(C43⋊C8)—24no—
19C4×C43⋊C8—42no—
20C22×Q8×C43C2×C411yescharacteristic
21C22×D4×C43C2×C411yescharacteristic
22C23×C4×C43—21no—
23#124×C43—22no—
24#124×C43C814yescomplemented
25C4×Q8×C43—41no—
26C4×Q8×C43—41no—
27C4×D4×C43—41no—
28C4×D4×C43—41no—
29C2×C4⋊C4×C43C2×C411yescharacteristic
30C2×C4⋊C4×C43D412yes—
31C2×C4⋊C4×C43C2311yescharacteristic
32C2×C22⋊C4×C43—22no—
33C2×C22⋊C4×C43—21no—
34C2×C22⋊C4×C43—22no—
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—
43C24×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43C2×C812yes—
47C2×Q8×C43M1612yes—
48C2×D4×C43—21no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43C2×C812yes—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—44no—
56C22×C4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43C22⋊C412yes—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D412yes—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C22⋊C4×C43—28no—
67C22⋊C4×C43—44no—
68C22⋊C4×C43—42no—
69C42×C43—21no—
70C42×C43—21no—
71C42×C43—22no—
72C42×C43—22no—
73C42×C43—21no—
74C42×C43—41no—
75C42×C43—42no—
76C42×C43—42no—
77C42×C43C2×C812yes—
78C2×C43⋊C8—44no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43—42no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43C2×C22⋊C411yescharacteristic
85Q8×C43—42no—
86Q8×C43—42no—
87D4×C43—42no—
88D4×C43—42no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—82no—
107C2×C4×C43—82no—
108C2×C4×C43C22⋊C814yes—
109C2×C4×C43#9911yescharacteristic
110C2×C4×C43#9911yescharacteristic
111C2×C4×C43C22×C811yescharacteristic
112C2×C4×C43C2×M1611yescharacteristic
113C43⋊C8—84no—
114#11476—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43—44no—
118C22×C43—42no—
119C22×C43—82no—
120C22×C43—81no—
121C22×C43—81no—
122C22×C43C2×C22⋊C811yescharacteristic
123C22×C43C2×#9911yescharacteristic
124C22×C43#41311yescharacteristic
125C4×C43—21no—
126C4×C43—24no—
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—42no—
130C4×C43—42no—
131C4×C43—42no—
132C4×C43—41no—
133C4×C43—81no—
134C4×C43#35512yes—
135C4×#124D4311yescharacteristic
136#1461—432no—
137#1324—432no—
138#1318—432no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43—82no—
142C2×C43#145911yescharacteristic
143C2×C43#212611yescharacteristic
144C2×C43C2×#35511yescharacteristic
145C2×#124Dic4311yescharacteristic
146C2×C4×Q8C2×D4311yescharacteristic
147C2×C4×D4Dic4311yescharacteristic
148#431—862no—
149#391Dic4311yescharacteristic
150#390C2×D4311yescharacteristic
151#388—22no—
152#382C2×D4311yescharacteristic
153C4×C22⋊C4—22no—
154C43Dic4311yescharacteristic
155#324—434no—
156#324—862no—
157C43#1147611yescharacteristic, complemented, Sylow
158C22×Q8C2×Dic4311yescharacteristic
159C22×D4C2×Dic4311yescharacteristic
160C23×C4—21no—
161#124—22no—
162#124C43⋊C814yescomplemented
163C4×Q8—41no—
164C4×Q8—41no—
165C4×D4—41no—
166C4×D4—41no—
167C2×C4⋊C4C2×Dic4311yescharacteristic
168C2×C4⋊C4C22⋊D4312yes—
169C2×C4⋊C4C22×D4311yescharacteristic
170C2×C22⋊C4—22no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—22no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42C2×Dic4311yescharacteristic
176C2×C42C2×Dic4311yescharacteristic
177C2×C42C2×Dic4311yescharacteristic
178C2×C42C22⋊D4312yes—
179C4⋊C8—1722no—
180C22⋊C8—864no—
181C4×C8—1722no—
182#95—22no—
183#95—22no—
184C24—21no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8C2×C43⋊C812yes—
188C2×Q8#1062187712yes—
189C2×D4—21no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4C2×C43⋊C812yes—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—44no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4C22⋊Dic4312yes—
200C22×C4C22⋊Dic4311yescharacteristic
201C22×C4C22⋊Dic4311yescharacteristic
202C22×C4C22×Dic4311yescharacteristic
203C22×C4C2×C22⋊D4312yes—
204C2×C8—1724no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C22⋊C4—28no—
209C22⋊C4—42no—
210C22⋊C4—44no—
211C42—22no—
212C42—21no—
213C42—22no—
214C42—21no—
215C42—21no—
216C42—41no—
217C42—42no—
218C42—42no—
219C42C2×C43⋊C812yes—
220C23—22no—
221C23—42no—
222C23—42no—
223C23—41no—
224C23—41no—
225C23C2×C22⋊Dic4311yescharacteristic
226Q8—42no—
227Q8—42no—
228D4—42no—
229D4—42no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4C22⋊(C43⋊C8)14yes—
250C2×C4#1306324011yescharacteristic
251C2×C4#1306324011yescharacteristic
252C2×C4C22×C43⋊C811yescharacteristic
253C2×C4C2×#1062187711yescharacteristic
254C8—3444no—
255C22—21no—
256C22—21no—
257C22—44no—
258C22—42no—
259C22—82no—
260C22—81no—
261C22—81no—
262C22C2×C22⋊(C43⋊C8)11yescharacteristic
263C22C2×#1306324011yescharacteristic
264C22#1458288311yescharacteristic
265C4—21no—
266C4—24no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—42no—
272C4—41no—
273C4—81no—
274C4#1458269612yes—
275C2—21no—
276C2—21no—
277C2—82no—
278C2#1913291311yescharacteristic
279C2#1913626011yescharacteristic
280C2C2×#1458269611yescharacteristic
subgroupG/H
centerC2×C4#13063240
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC4×#124×C43C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenterC4×#124D43
hypocenterC43#11476
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #19132919C2semidirect
2. #19132539C2semidirect
24. #124×C43C8semidirect
157. C43#11476semidirect
162. #124C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
#191329192
#191325392
#191325272
C4×#124×C432
#1147643