Finite Group Databasebeta

← #24990048

Subgroups — #24990048

Order 11008.

404 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 99 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#19137092C211yesmaximal, characteristic
2#19132907C212yesmaximal
3#19132428C211yesmaximal, characteristic, complemented
4#19132423C212yesmaximal, complemented
5C43×#1276C211yesmaximal, characteristic, complemented
6C2×#13063282C2211yescharacteristic
7#14582952C2212yes—
8#14582790—22no—
9#14582783—22no—
10C4×Dic43⋊C4C412yes—
11C4×(C2×D43)⋊C4C412yes—
12#14582745C2211yescharacteristic
13#14582624—22no—
14#14582622—22no—
15C43×#431C2212yes—
16C43×C43C2211yescharacteristic
17C22×C4×D43C2×C411yescharacteristic
18#13063282—22no—
19#13063282—21no—
20#13063282—21no—
21C2×Dic43⋊C4—22no—
22C2×Dic43⋊C4D412yes—
23C2×(C2×D43)⋊C4—22no—
24C2×(C2×D43)⋊C4D412yes—
25C2×C4×Dic43C2×C412yes—
26C2×C4×Dic43C2×C411yescharacteristic
27C4⋊(C43⋊C8)—22no—
28C22⋊(C43⋊C8)—22no—
29C4×C43⋊C8—22no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C2×C42×C43—22no—
34C2×C42×C43C2×C412yes—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C22⋊C8×C43—22no—
38C4×C8×C43—22no—
39C23×D43C22⋊C411yescharacteristic
40C22×C4×C43—22no—
41C22×C4×C43C22×C411yescharacteristic
42C22×C4×C43C2×D412yes—
43C22×Dic43—22no—
44C22×Dic43C22⋊C411yescharacteristic
45C22×Dic43C22⋊C412yes—
46C2×C4×D43—21no—
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×C8×C43—42no—
51C42×C43—22no—
52C42×C43—22no—
53C42×C43—44no—
54C42×C43#4112yes—
55C42×C43#4111yescharacteristic
56C42×C43#4111yescharacteristic
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—44no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62Dic43⋊C4—44no—
63C4×Dic43—21no—
64C4×Dic43—21no—
65C4×Dic43—22no—
66C4×Dic43—22no—
67C2×C43⋊C8—42no—
68C23×C43C2×C22⋊C411yescharacteristic
69C22×D43—21no—
70C22×D43—22no—
71C22×D43—42no—
72C2×C4×C43—24no—
73C2×C4×C43—42no—
74C2×C4×C43—42no—
75C2×C4×C43—42no—
76C2×C4×C43#11711yescharacteristic
77C2×C4×C43#11711yescharacteristic
78C2×C4×C43#12312yes—
79C2×C4×C43#12312yes—
80C2×C4×C43#13112yes—
81C2×C4×C43#13112yes—
82C2×Dic43—22no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—42no—
86C2×Dic43—42no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C4×D43—41no—
90C4×D43—42no—
91C4×D43—41no—
92C8×C43—82no—
93C43⋊C8—82no—
94#8732—431nomaximal, Sylow
95C22×C43—22no—
96C22×C43#38111yescharacteristic
97C22×C43#40812yes—
98C2×D43—41no—
99C2×D43—42no—
100C2×D43—82no—
101C4×C43—22no—
102C4×C43—22no—
103C4×C43—44no—
104C4×C43#43311yescharacteristic
105C4×C43#43312yes—
106C4×C43#43311yescharacteristic
107Dic43—41no—
108Dic43—42no—
109Dic43—82no—
110#2298—431no—
111#1458—432no—
112#1276—431no—
113#1276D4311yescharacteristic, complemented
114#1274—432no—
115C2×C43—22no—
116C2×C43#181811yescharacteristic
117C2×C43#182712yes—
118D43—81no—
119C2×#117—431no—
120#431—432no—
121#431C2×D4312yes—
122#388—862no—
123#387—862no—
124C4×C4⋊C4—432no—
125C4×C22⋊C4—432no—
126#376—431no—
127C43C2×D4311yescharacteristic
128#324—862no—
129#323—862no—
130C43#873211yescharacteristic, complemented, Sylow
131C23×C4—431no—
132#117—862no—
133#117—861no—
134#117—861no—
135C2×C4⋊C4—432no—
136C2×C4⋊C4—862no—
137C2×C22⋊C4—432no—
138C2×C22⋊C4—862no—
139C2×C42—22no—
140C2×C42—431no—
141C2×C42—432no—
142C2×C42C4×D4312yes—
143C2×C42C22×D4311yescharacteristic
144C4⋊C8—22no—
145C4⋊C8—862no—
146C22⋊C8—22no—
147C22⋊C8—862no—
148C4×C8—22no—
149C4×C8—862no—
150#95—862no—
151#95—862no—
152#95—862no—
153C24—431no—
154C22×C4—22no—
155C22×C4—431no—
156C22×C4—432no—
157C22×C4—861no—
158C22×C4—861no—
159C22×C4—862no—
160C22×C4—862no—
161C22×C4—862no—
162C22×C4C2×C4×D4311yescharacteristic
163C22×C4D4×D4312yes—
164C2×C8—42no—
165C2×C8—1722no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—1724no—
169C22⋊C4—862no—
170C22⋊C4—862no—
171C22⋊C4—1724no—
172C42—22no—
173C42—22no—
174C42—44no—
175C42—861no—
176C42—861no—
177C42—862no—
178C42—862no—
179C42#1062189812yes—
180C42#1062190011yescharacteristic
181C42#1062190211yescharacteristic
182C23—862no—
183C23—861no—
184C23—1722no—
185C23C22⋊C4×D4311yescharacteristic
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—861no—
193C2×C4—1722no—
194C2×C4—1722no—
195C2×C4—1722no—
196C2×C4—1721no—
197C2×C4—1722no—
198C2×C4—1721no—
199C2×C4—1722no—
200C2×C4#1306328211yescharacteristic
201C2×C4#1306328311yescharacteristic
202C2×C4#1306330712yes—
203C2×C4#1306331012yes—
204C2×C4#1306333112yes—
205C2×C4#1306333312yes—
206C8—82no—
207C8—3442no—
208C22—22no—
209C22—3442no—
210C22—1721no—
211C22—1722no—
212C22#1458276111yescharacteristic
213C22#1458286412yes—
214C4—22no—
215C4—22no—
216C4—44no—
217C4—3442no—
218C4—1721no—
219C4—1722no—
220C4#1458295811yescharacteristic
221C4#1458295912yes—
222C4#1458296111yescharacteristic
223C2—22no—
224C2—3441no—
225C2#1913466511yescharacteristic
226C2#1913469812yes—
subgroupG/H
centerC2×C4#13063283
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1276C2
socleC22×C43#381
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1276D43
hypocenterC43#8732
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
3. #19132428C2semidirect
4. #19132423C2semidirect
5. C43×#1276C2semidirect
113. #1276D43semidirect
130. C43#8732semidirect

Maximal subgroups

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

subgroupindex
#191370922
#191329072
#191324282
#191324232
C43×#12762
#873243