Finite Group Databasebeta

← #24994461

Subgroups — #24994461

Order 11008.

454 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 115 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#19139957C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19133025C212yesmaximal
4#19132454C212yesmaximal
5C43×#2983C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14582923C2212yes—
8C2×#13063244—21no—
9#14582838C412yes—
10#14582819C412yes—
11#14582806—21no—
12#14582795—21no—
13#14582783—22no—
14#14582765C2211yescharacteristic
15#14582668—21no—
16#14582631—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C43×#446—24no—
19C43×#432—22no—
20C43×#431C2212yes—
21C22×Dic86C2×C411yescharacteristic
22C2×#10621877—22no—
23C4×Dic86—22no—
24C4×Dic86—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—21no—
29C2×C4×Dic43—21no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32#13063244—42no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—21no—
37C43⋊#95C2×C412yes—
38C22×Q8×C43D411yescharacteristic
39C4×Q8×C43—22no—
40C4×Q8×C43—22no—
41C2×C4⋊C4×C43C2×C412yes—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43D412yes—
44C2×C42×C43C2311yescharacteristic
45C4⋊C8×C43—24no—
46C4⋊C8×C43—22no—
47C22⋊C8×C43—22no—
48#97×C43—24no—
49C4×C8×C43D414yes—
50C2×Q8×C43—22no—
51C2×Q8×C43—21no—
52C2×Q8×C43—21no—
53C2×Q8×C43—22no—
54C22×C4×C43C22⋊C412yes—
55C22×C4×C43C22⋊C412yes—
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×Dic43—21no—
60C22×Dic43—22no—
61C22×Dic43—21no—
62C2×Dic86—22no—
63C2×Dic86—42no—
64C2×C8×C43—24no—
65C4⋊C4×C43—24no—
66C4⋊C4×C43—22no—
67C42×C43—22no—
68C42×C43—22no—
69C42×C43C2×D412yes—
70C42×C43#4112yes—
71C4⋊Dic43—22no—
72C4⋊Dic43—41no—
73C4⋊Dic43—41no—
74Dic43⋊C4—44no—
75Dic43⋊C4—41no—
76Dic43⋊C4—41no—
77C4×Dic43—42no—
78#10621877—42no—
79#10621877—42no—
80C2×C43⋊C8—42no—
81C23×C43C2×C22⋊C411yescharacteristic
82Q8×C43—42no—
83Q8×C43—42no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43C4×D412yes—
92C2×C4×C43#12011yescharacteristic
93C2×C4×C43#12112yes—
94C2×C4×C43#12311yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C43#13712yes—
97C2×C4×C43#13711yescharacteristic
98C2×Dic43—22no—
99C2×Dic43—41no—
100C2×Dic43—41no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—41no—
105C2×Dic43—42no—
106Dic86—24no—
107Dic86—42no—
108C8×C43—44no—
109C43⋊C8—82no—
110#9488—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—21no—
113C22×C43#38611yescharacteristic
114C22×C43#41711yescharacteristic
115C22×C43#41911yescharacteristic
116C4×C43—22no—
117C4×C43—21no—
118C4×C43—21no—
119C4×C43—42no—
120C4×C43—42no—
121C4×C43#46812yes—
122C4×C43#47012yes—
123Dic43—42no—
124Dic43—82no—
125Dic43—81no—
126#2983D4311yescharacteristic
127#2581—431no—
128#1801—431no—
129#1487—432no—
130#1286—432no—
131C2×C43—21no—
132C2×C43—21no—
133C2×C43#189111yescharacteristic
134C2×C43#189411yescharacteristic
135C2×C43#191211yescharacteristic
136C2×C4×Q8—431no—
137C2×C4×Q8C2×D4311yescharacteristic
138#446—24no—
139#432—22no—
140#431C2×D4312yes—
141#423—432no—
142C2×#101—861no—
143#400—432no—
144#395—432no—
145#391—861no—
146#389—861no—
147#387—862no—
148#382—431no—
149#343—861no—
150Q8⋊C8—864no—
151C43#948811yescharacteristic, complemented, Sylow
152C22×Q8—431no—
153C22×Q8D17211yescharacteristic
154C2×M16—862no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—862no—
158C4×Q8—862no—
159C2×C4⋊C4—431no—
160C2×C4⋊C4—862no—
161C2×C4⋊C4—861no—
162C2×C4⋊C4—861no—
163C2×C4⋊C4C4×D4312yes—
164C2×C4⋊C4D17211yescharacteristic
165C2×C42—861no—
166C2×C42C22⋊D4312yes—
167C2×C42C22×D4311yescharacteristic
168C4⋊C8—24no—
169C4⋊C8—22no—
170C4⋊C8—862no—
171C4⋊C8—862no—
172#101—1722no—
173C22⋊C8—22no—
174#97—24no—
175C4×C8C22⋊D4314yes—
176#95—432no—
177#95—862no—
178#95—862no—
179#95—862no—
180#95—861no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—862no—
186C2×Q8—1722no—
187C22×C4—861no—
188C22×C4—862no—
189C22×C4—861no—
190C22×C4(C2×D43)⋊C412yes—
191C22×C4(C2×D43)⋊C412yes—
192C22×C4C2×C4×D4311yescharacteristic
193C22×C4C2×D17211yescharacteristic
194C22×C4C2×C22⋊D4311yescharacteristic
195M16—1722no—
196M16—1722no—
197C2×C8—24no—
198C2×C8—1722no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—862no—
202C4⋊C4—1724no—
203C4⋊C4—1721no—
204C4⋊C4—1721no—
205C4⋊C4—1721no—
206C4⋊C4—1721no—
207C42—22no—
208C42—22no—
209C42—1722no—
210C42#1062189812yes—
211C42C2×C22⋊D4312yes—
212C23C2×(C2×D43)⋊C411yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—864no—
216Q8—1722no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—862no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4—1721no—
230C2×C4—1721no—
231C2×C4—1721no—
232C2×C4C4×C22⋊D4312yes—
233C2×C4#1306329411yescharacteristic
234C2×C4#1306329912yes—
235C2×C4#1306330811yescharacteristic
236C2×C4#1306335311yescharacteristic
237C2×C4#1306335812yes—
238C2×C4#1306335811yescharacteristic
239C8—44no—
240C8—3442no—
241C22—21no—
242C22—21no—
243C22#1458277811yescharacteristic
244C22#1458290111yescharacteristic
245C22#1458290911yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—3442no—
252C4—3441no—
253C4—1722no—
254C4#1458314512yes—
255C4#1458315712yes—
256C2—21no—
257C2—21no—
258C2#1913501311yescharacteristic
259C2#1913502811yescharacteristic
260C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2983C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2983D43
hypocenterC43#9488
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
151. C43#9488semidirect

Maximal subgroups

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

subgroupindex
#191399572
#191345912
#191330252
#191324542
C43×#29832
#948843