Finite Group Databasebeta

← #24989098

Subgroups — #24989098

Order 11008.

818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#14583504C211yesmaximal, characteristic
2#19134678C211yesmaximal, characteristic, complemented
3#19133123C214yesmaximal, complemented
4C43×#1820C211yesmaximal, characteristic, complemented
5#14583504—28no—
6C2×#13063322C411yescharacteristic, complemented
7C2×#13063317C411yescharacteristic, complemented
8C2×#13063310—22no—
9C2×#13063299C2212yes—
10C2×#13063298—22no—
11C2×C4×D172C412yescomplemented
12#14582863C2212yes—
13#14582668—22no—
14#14582632—28no—
15C2×#117×C43C2211yescharacteristic
16C43×#381C2212yes—
17C43×#342—22no—
18C22×D172—22no—
19C22×D172C2×C412yes—
20C22×C22⋊D43—22no—
21C22×C4×D43—22no—
22C2×#10621877—22no—
23#13063322—24no—
24#13063317—24no—
25#13063310—216no—
26#13063299—24no—
27#13063299D418yes—
28#13063298—216no—
29C4×D172—24no—
30C4×D172—24no—
31C2×C4⋊Dic43C2×C412yes—
32C2×Dic43⋊C4—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×(C2×D43)⋊C4—22no—
35C22⋊(C43⋊C8)—24no—
36C23×C4×C43C2311yescharacteristic
37#117×C43—24no—
38C2×C4⋊C4×C43D412yes—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43D412yes—
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43#95×C43—24no—
44C24×C43C2×D411yescharacteristic
45C23×D43—22no—
46C22×C4×C43—42no—
47C22×C4×C43—42no—
48C22×C4×C43C22⋊C412yes—
49C22×C4×C43C22⋊C412yes—
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D414yes—
53C2×C22⋊D43—28no—
54C2×C22⋊D43—84no—
55C22×Dic43—22no—
56C2×D172—22no—
57C2×D172—28no—
58C2×D172—44no—
59C2×D172—84no—
60C2×D172C22⋊C414yes—
61C2×C4×D43—28no—
62C2×C4×D43—84no—
63C4⋊C4×C43—24no—
64C22⋊C4×C43—24no—
65C22⋊C4×C43—44no—
66C42×C43—22no—
67C42×C43—22no—
68(C2×D43)⋊C4—28no—
69(C2×D43)⋊C4—28no—
70C4⋊Dic43—22no—
71C4⋊Dic43C22⋊C414yes—
72Dic43⋊C4—28no—
73#10621877—44no—
74C2×C43⋊C8—42no—
75C23×C43—22no—
76C23×C43—42no—
77C23×C43C2×C22⋊C411yescharacteristic
78C23×C43#12012yes—
79C22×D43—24no—
80C22×D43—44no—
81C22×D43—44no—
82C22×D43—44no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—44no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—82no—
91C2×C4×C43—84no—
92C2×C4×C43C2×C22⋊C412yes—
93C2×C4×C43#12012yes—
94C22⋊D43—88no—
95C2×Dic43—24no—
96C2×Dic43—44no—
97D172—44no—
98D172—44no—
99D172—88no—
100C4×D43—88no—
101C43⋊C8—82no—
102#8518—431nomaximal, Sylow
103C22×C43—22no—
104C22×C43—24no—
105C22×C43—22no—
106C22×C43—82no—
107C22×C43#37911yescharacteristic
108C22×C43#41012yes—
109C2×D43—44no—
110C2×D43—44no—
111C2×D43—44no—
112C2×D43—88no—
113C4×C43—22no—
114C4×C43—22no—
115C4×C43—42no—
116C4×C43—42no—
117C4×C43—162no—
118Dic43—44no—
119C2×#540—431no—
120#1822—431no—
121#1820D4311yescharacteristic, complemented
122#1510—434no—
123C2×C43—22no—
124C2×C43—42no—
125C2×C43#178211yescharacteristic
126C2×C43#179512yes—
127D43—84no—
128#540—868no—
129C2×#127—431no—
130C2×#125—431no—
131C2×#123—862no—
132C2×#121—432no—
133C2×#121—862no—
134C2×C4×D4—432no—
135C2×#117C2×D4311yescharacteristic
136#407—432no—
137#381C2×D4312yes—
138#343—862no—
139#342—22no—
140#327—868no—
141C43#851811yescharacteristic, complemented, Sylow
142C22×D4—432no—
143C22×D4—862no—
144C22×D4—862no—
145C23×C4—862no—
146C23×C4C22×D4311yescharacteristic
147C2×M16—862no—
148#127—864no—
149#125—864no—
150#123—8616no—
151#121—438no—
152#121—8616no—
153#121—864no—
154C4×D4—864no—
155C4×D4—864no—
156#117—24no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—862no—
159C2×C4⋊C4D17212yes—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—862no—
162C2×C22⋊C4—862no—
163C2×C22⋊C4C22⋊D4312yes—
164C2×C42C4×D4311yescharacteristic
165C2×C42C4×D4311yescharacteristic
166C22⋊C8—864no—
167#95—24no—
168C24—862no—
169C24C2×C22⋊D4311yescharacteristic
170C2×D4—434no—
171C2×D4—868no—
172C2×D4—868no—
173C2×D4—862no—
174C2×D4—3444no—
175C2×D4—3444no—
176C2×D4—1724no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—868no—
180C22×C4—862no—
181C22×C4—3444no—
182C22×C4(C2×D43)⋊C412yes—
183C22×C4(C2×D43)⋊C412yes—
184C22×C4C2×C4×D4311yescharacteristic
185C22×C4C2×D17211yescharacteristic
186C22×C4D4×D4314yes—
187M16—1724no—
188C2×C8—1722no—
189C4⋊C4—24no—
190C4⋊C4—434no—
191C4⋊C4—868no—
192C4⋊C4—862no—
193C22⋊C4—24no—
194C22⋊C4—44no—
195C22⋊C4—868no—
196C22⋊C4—868no—
197C42—22no—
198C42—22no—
199C23—22no—
200C23—42no—
201C23—864no—
202C23—1724no—
203C23—1724no—
204C23—1724no—
205C23C2×(C2×D43)⋊C411yescharacteristic
206C23#1306329312yes—
207D4—3448no—
208D4—3448no—
209D4—1724no—
210D4—1724no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—82no—
219C2×C4—84no—
220C2×C4—864no—
221C2×C4—3448no—
222C2×C4—1724no—
223C2×C4C22⋊C4×D4312yes—
224C2×C4#1306329512yes—
225C8—3442no—
226C22—22no—
227C22—22no—
228C22—24no—
229C22—82no—
230C22—3448no—
231C22—1724no—
232C22—1724no—
233C22—1724no—
234C22#1458275411yescharacteristic
235C22#1458287212yes—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—162no—
241C4—1724no—
242C2—22no—
243C2—42no—
244C2—3444no—
245C2#1913451211yescharacteristic
246C2#1913456312yes—
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1820C2
socleC22×C43#379
prime radicalC2×#14583504C2
cosocleC23×C4×C43C23
hypercenter#1820D43
hypocenterC43#8518
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #19134678C2semidirect
3. #19133123C2semidirect
4. C43×#1820C2semidirect
6. C2×#13063322C4semidirect
7. C2×#13063317C4semidirect
11. C2×C4×D172C4semidirect
121. #1820D43semidirect
141. C43#8518semidirect

Maximal subgroups

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

subgroupindex
C2×#145835042
#191346782
#191331232
C43×#18202
#851843