Finite Group Databasebeta

← #25006239

Subgroups — #25006239

Order 11008.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139580C211yesmaximal, characteristic
2#19132939C211yesmaximal, characteristic
3#19132528C214yesmaximal
4C43×#1461C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6C2×#13063323C412yes—
7#14582956—21no—
8#14582829—21no—
9#14582829—21no—
10#14582804C2212yes—
11#14582797—21no—
12#14582797—21no—
13C4×C4⋊Dic43C411yescharacteristic
14#14582625—21no—
15#14582625C2212yes—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#431—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C22×Dic86C2×C412yes—
21#13063325—41no—
22#13063325—41no—
23#13063323—44no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×C4×Dic43C2×C412yes—
30C4⋊(C43⋊C8)—41no—
31C22⋊(C43⋊C8)—22no—
32#13063236—41no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C22×Q8×C43C2×C411yescharacteristic
37C4×Q8×C43—41no—
38C4×Q8×C43—41no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C4⋊C8×C43—41no—
46C22⋊C8×C43—22no—
47C4×C8×C43—41no—
48C2×Q8×C43—22no—
49C2×Q8×C43—22no—
50C2×Q8×C43—41no—
51C22×C4×C43C22⋊C411yescharacteristic
52C22×C4×C43C22⋊C411yescharacteristic
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—22no—
59C22×Dic43—22no—
60C2×Dic86—24no—
61C2×Dic86—42no—
62C2×Dic86—42no—
63C2×C8×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C42×C43—21no—
68C42×C43—21no—
69C42×C43—21no—
70C42×C43—21no—
71C42×C43—21no—
72C42×C43—21no—
73C4⋊Dic43—24no—
74C4⋊Dic43—42no—
75C4⋊Dic43—41no—
76C4⋊Dic43—41no—
77Dic43⋊C4—44no—
78Dic43⋊C4—44no—
79C4×Dic43—42no—
80C2×C43⋊C8—42no—
81C23×C43C2×C22⋊C411yescharacteristic
82Q8×C43—44no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43#9911yescharacteristic
98C2×C4×C43#9911yescharacteristic
99C2×C4×C43#10012yes—
100C2×C4×C43#13112yes—
101C2×Dic43—24no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107Dic86—84no—
108C8×C43—82no—
109C43⋊C8—82no—
110#11568—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—21no—
113C22×C43#40811yescharacteristic
114C22×C43C2×#9911yescharacteristic
115C22×C43C2×#10011yescharacteristic
116C4×C43—21no—
117C4×C43—22no—
118C4×C43—22no—
119C4×C43—41no—
120C4×C43—41no—
121C4×C43—41no—
122C4×C43—41no—
123C4×C43#35612yes—
124Dic43—44no—
125Dic43—82no—
126#2546—431no—
127#1467—431no—
128#1461D4311yescharacteristic
129#1319—434no—
130C2×C43—21no—
131C2×C43—21no—
132C2×C43#147111yescharacteristic
133C2×C43#212911yescharacteristic
134C2×C43C2×#35611yescharacteristic
135C2×C4⋊Q8—432no—
136C2×C4⋊Q8—431no—
137C2×C4×Q8C2×D4311yescharacteristic
138#432—861no—
139#431—21no—
140#398—861no—
141#398—861no—
142#391—432no—
143#389—861no—
144#389—861no—
145C4×C4⋊C4—431no—
146#324—21no—
147#324—432no—
148#324—861no—
149#324C2×D4312yes—
150C43#1156811yescharacteristic, complemented, Sylow
151C22×Q8—432no—
152C22×Q8C4×D4311yescharacteristic
153C4⋊Q8—1721no—
154C4⋊Q8—1721no—
155C4⋊Q8—1724no—
156C4×Q8—41no—
157C4×Q8—41no—
158C2×C4⋊C4—861no—
159C2×C4⋊C4—862no—
160C2×C4⋊C4—862no—
161C2×C4⋊C4—861no—
162C2×C4⋊C4—861no—
163C2×C4⋊C4D17211yescharacteristic
164C2×C4⋊C4C22⋊D4311yescharacteristic
165C2×C4⋊C4C22×D4311yescharacteristic
166C2×C42—432no—
167C2×C42C4×D4311yescharacteristic
168C2×C42D17211yescharacteristic
169C2×C42C22⋊D4311yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—1721no—
172C22⋊C8—22no—
173C22⋊C8—862no—
174#97—1721no—
175C4×C8—41no—
176#95—861no—
177#95—862no—
178#95—862no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—864no—
183C2×Q8—1722no—
184C2×Q8—1722no—
185C22×C4—862no—
186C22×C4—862no—
187C22×C4(C2×D43)⋊C411yescharacteristic
188C22×C4(C2×D43)⋊C411yescharacteristic
189C22×C4(C2×D43)⋊C411yescharacteristic
190C22×C4(C2×D43)⋊C411yescharacteristic
191C22×C4C2×C4×D4311yescharacteristic
192C22×C4C2×D17211yescharacteristic
193C22×C4C2×C22⋊D4311yescharacteristic
194C2×C8—42no—
195C2×C8—1722no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—864no—
200C4⋊C4—1724no—
201C4⋊C4—1722no—
202C4⋊C4—1721no—
203C4⋊C4—1721no—
204C4⋊C4—1724no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—1722no—
212C23C2×(C2×D43)⋊C411yescharacteristic
213Q8—44no—
214Q8—3444no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—864no—
230C2×C4—1722no—
231C2×C4—1722no—
232C2×C4—1722no—
233C2×C4—1722no—
234C2×C4—1722no—
235C2×C4#1306323911yescharacteristic
236C2×C4#1306323911yescharacteristic
237C2×C4#1306324112yes—
238C2×C4#1306333112yes—
239C8—82no—
240C8—3442no—
241C22—21no—
242C22—21no—
243C22#1458286511yescharacteristic
244C22C2×#1306323911yescharacteristic
245C22C2×#1306324111yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—3442no—
254C4—1724no—
255C4#1458269712yes—
256C2—21no—
257C2—21no—
258C2#1913295411yescharacteristic
259C2#1913626911yescharacteristic
260C2C2×#1458269711yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1461C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1461D43
hypocenterC43#11568
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
150. C43#11568semidirect

Maximal subgroups

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

subgroupindex
#191395802
#191329392
#191325282
C43×#14612
#1156843