Finite Group Databasebeta

← #24985440

Subgroups — #24985440

Order 11008.

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

normal subgroups only

This group has 424 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#19135928C212yesmaximal
2#19135694C211yesmaximal, characteristic
3#19132421C211yesmaximal, characteristic
4#19132418C212yesmaximal
5C43×#2809C211yesmaximal, characteristic
6C22×#10621885—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063256—22no—
9C2×#13063248—21no—
10#14582661—22no—
11#14582654C2211yescharacteristic
12#14582654C2212yes—
13C43×#400—21no—
14C43×#398—22no—
15C43×#391—21no—
16C43×#391C2211yescharacteristic
17C43×#389C2212yes—
18C43×#387—22no—
19C22×Dic86—21no—
20C2×#10621885—42no—
21C2×#10621885—42no—
22C2×#10621885—42no—
23C22×C43⋊C8—21no—
24C22×C43⋊C8—22no—
25#13063325—42no—
26C2×C4⋊Dic43—22no—
27#13063256—44no—
28#13063248—42no—
29C22×Q8×C43D411yescharacteristic
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43D412yes—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C4⋊C4×C43D412yes—
36C2×C42×C43—21no—
37C2×C42×C43C2311yescharacteristic
38#95×C43—21no—
39#95×C43—22no—
40#95×C43—22no—
41#95×C43—22no—
42#95×C43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43SD1612yes—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—41no—
54C2×Dic86—22no—
55C2×Dic86—41no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86—41no—
59C2×Dic86—41no—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—42no—
66C4⋊C4×C43—81no—
67C4⋊C4×C43—81no—
68C42×C43—41no—
69C42×C43—81no—
70#10621885—48no—
71C4⋊Dic43—24no—
72C4⋊Dic43—42no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—24no—
75C2×C43⋊C8—42no—
76C2×C43⋊C8—41no—
77C2×C43⋊C8—41no—
78C2×C43⋊C8—42no—
79C23×C43#12011yescharacteristic
80Q8×C43—42no—
81Q8×C43—81no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43C2×SD1611yescharacteristic
98C2×C4×C43#13512yes—
99C2×C4×C43#13712yes—
100C2×C4×C43#13711yescharacteristic
101C2×Dic43—42no—
102C2×Dic43—81no—
103C2×Dic43—81no—
104Dic86—42no—
105Dic86—42no—
106Dic86—81no—
107Dic86—81no—
108C43⋊C8—44no—
109C43⋊C8—42no—
110#7760—431nomaximal, Sylow
111C22×C43#44811yescharacteristic
112C22×C43#45212yes—
113C22×C43#45311yescharacteristic
114C22×C43#45612yes—
115C22×C43B(4,𝔽2)11yescharacteristic
116C4×C43—21no—
117C4×C43—21no—
118C4×C43—22no—
119C4×C43—22no—
120C4×C43—42no—
121C4×C43—82no—
122C4×C43—82no—
123C4×C43—81no—
124Dic43—82no—
125#2809D4311yescharacteristic
126#2058—432no—
127#2016—431no—
128#1272—431no—
129#1271—432no—
130C2×C43#159611yescharacteristic
131C2×C43#160312yes—
132C2×C43#163411yescharacteristic
133C2×C43#165312yes—
134C2×C43#166011yescharacteristic
135C22×Q16—861no—
136C2×C4⋊Q8—431no—
137C2×#106—862no—
138C2×#103—861no—
139#400—21no—
140#398—22no—
141#391—21no—
142#391C2×D4311yescharacteristic
143#389C2×D4312yes—
144#387—22no—
145#340—862no—
146#336—432no—
147#336—431no—
148C43#776011yescharacteristic, complemented, Sylow
149C22×Q8—861no—
150C22×Q8C22⋊D4311yescharacteristic
151C2×Q16—1722no—
152C2×Q16—1722no—
153C2×Q16—1722no—
154C22×C8—861no—
155C22×C8—862no—
156C4⋊Q8—1722no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—862no—
161C2×C4⋊C4C22⋊D4312yes—
162C2×C4⋊C4C22⋊D4312yes—
163C2×C4⋊C4C22⋊D4311yescharacteristic
164C2×C42—21no—
165C2×C42C22×D4311yescharacteristic
166#106—1724no—
167#103—1722no—
168#95—21no—
169#95—22no—
170#95—22no—
171#95—22no—
172#95—22no—
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—862no—
177C2×Q8—1721no—
178C2×Q8—1721no—
179C2×Q8—1721no—
180C2×Q8—1721no—
181C2×Q8—1721no—
182C2×Q8#1062188412yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—1721no—
188C22×C4C2×C22⋊D4311yescharacteristic
189C22×C4C2×C22⋊D4312yes—
190Q16—1728no—
191C2×C8—862no—
192C2×C8—864no—
193C2×C8—1722no—
194C2×C8—1721no—
195C2×C8—1721no—
196C2×C8—1722no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—864no—
206C4⋊C4—1722no—
207C42—41no—
208C42—81no—
209C23#1306329411yescharacteristic
210Q8—42no—
211Q8—81no—
212Q8—3441no—
213Q8—3441no—
214Q8—1722no—
215Q8—1722no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—3441no—
232C2×C4—3441no—
233C2×C4—1722no—
234C2×C4C2×#1062188411yescharacteristic
235C2×C4#1306334512yes—
236C2×C4#1306335512yes—
237C2×C4#1306335611yescharacteristic
238C8—1722no—
239C8—1724no—
240C22#1458303811yescharacteristic
241C22#1458306112yes—
242C22#1458306711yescharacteristic
243C22#1458308212yes—
244C22#1458308611yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—82no—
251C4—82no—
252C4—81no—
253C4—3442no—
254C2#1913351811yescharacteristic
255C2#1913355812yes—
256C2#1913374011yescharacteristic
257C2#1913387212yes—
258C2#1913390611yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2809C2
socle, prime radicalC23×C43#120
hypercenter#2809D43
hypocenterC43#7760
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
148. C43#7760semidirect

Maximal subgroups

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

subgroupindex
#191359282
#191356942
#191324212
#191324182
C43×#28092
#776043