Finite Group Databasebeta

← #25009353

Subgroups — #25009353

Order 11008.

404 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135751C211yesmaximal, characteristic
2#19133602C212yesmaximal, complemented
3#19132601C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic
5C43×#2724C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583229—22no—
8#14582904—21no—
9#14582668C2211yescharacteristic
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yes—
13C2×#123×C43—21no—
14C43×#398C2212yes—
15C43×#397—22no—
16C43×#390C2211yescharacteristic
17C43×#389—21no—
18C43×#385—22no—
19C2×#10621877—21no—
20#13063324—41no—
21#13063316—41no—
22#13063304—22no—
23#13063284—21no—
24#13063256—42no—
25#13063248—42no—
26#13063246—41no—
27#13063246—41no—
28C22⋊(C43⋊C8)—22no—
29C22×D4×C43D411yescharacteristic
30C23×C4×C43—21no—
31#123×C43—42no—
32#123×C43—42no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43D412yes—
37C2×C4⋊C4×C43C2311yescharacteristic
38C2×C22⋊C4×C43—22no—
39C2×C22⋊C4×C43—21no—
40C2×C22⋊C4×C43—22no—
41C2×C42×C43D411yescharacteristic
42#95×C43—22no—
43#95×C43—22no—
44#95×C43D412yes—
45C24×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×D4×C43SD1612yes—
50C22×C4×C43—21no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—42no—
54C22×C4×C43—81no—
55C22×C4×C43—81no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D412yes—
58C2×Dic86—22no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—42no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—81no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—44no—
67C22⋊C4×C43—44no—
68C42×C43—41no—
69C22⋊Dic43—41no—
70C4⋊Dic43—21no—
71C4⋊Dic43—21no—
72C4⋊Dic43—22no—
73Dic43⋊C4—42no—
74C4×Dic43—41no—
75#10621877—41no—
76#10621877—41no—
77C2×C43⋊C8—42no—
78C2×C43⋊C8—41no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43—42no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43#12011yescharacteristic
85D4×C43—42no—
86D4×C43—81no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—84no—
101C2×C4×C43C2×SD1611yescharacteristic
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C2×Dic43—41no—
104C2×Dic43—41no—
105Dic86—82no—
106C43⋊C8—81no—
107C43⋊C8—82no—
108#12209—431nomaximal, Sylow
109C22×C43—21no—
110C22×C43—21no—
111C22×C43—44no—
112C22×C43—42no—
113C22×C43—82no—
114C22×C43—81no—
115C22×C43—81no—
116C22×C43#45011yescharacteristic
117C22×C43#45511yescharacteristic
118C22×C43B(4,𝔽2)11yescharacteristic
119C4×C43—21no—
120C4×C43—21no—
121C4×C43—42no—
122C4×C43—42no—
123C4×C43—82no—
124C4×C43—82no—
125Dic43—81no—
126Dic43—81no—
127#2724D4311yescharacteristic
128#2027—431no—
129#1611—432no—
130#1346—432no—
131#1318—431no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43—82no—
135C2×C43#160111yescharacteristic
136C2×C43#219811yescharacteristic
137C2×C43#220311yescharacteristic
138#544—431no—
139C2×#123—21no—
140#483—862no—
141#418—861no—
142#398C2×D4312yes—
143#397—22no—
144#390C2×D4311yescharacteristic
145#389—21no—
146#385—22no—
147#343—431no—
148#339—861no—
149#328—862no—
150#324—432no—
151C43#1220911yescharacteristic, complemented, Sylow
152C22×D4C22⋊D4311yescharacteristic
153C23×C4—21no—
154C2×M16—861no—
155C4⋊Q8—1721no—
156#125—1721no—
157#123—42no—
158#123—42no—
159C22⋊Q8—862no—
160#117—861no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4C22⋊D4312yes—
165C2×C4⋊C4C22×D4311yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—22no—
169C2×C42C22⋊D4311yescharacteristic
170#106—1722no—
171#103—1722no—
172#102—1721no—
173#102—1721no—
174C22⋊C8—862no—
175#95—22no—
176#95—22no—
177#95C22⋊D4312yes—
178C24—21no—
179C2×Q8—862no—
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4#1062188312yes—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4C2×C22⋊D4311yescharacteristic
191C22×C4C2×C22⋊D4312yes—
192M16—1721no—
193M16—1721no—
194C2×C8—1722no—
195C2×C8—1721no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—81no—
202C4⋊C4—861no—
203C4⋊C4—861no—
204C4⋊C4—862no—
205C4⋊C4—1722no—
206C22⋊C4—44no—
207C22⋊C4—42no—
208C22⋊C4—44no—
209C22⋊C4—1721no—
210C42—41no—
211C42—1721no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23—41no—
216C23—41no—
217C23#1306329411yescharacteristic
218Q8—3442no—
219D4—42no—
220D4—81no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—1721no—
236C2×C4—1721no—
237C2×C4C2×#1062188311yescharacteristic
238C2×C4#1306335111yescharacteristic
239C8—3441no—
240C8—3442no—
241C22—21no—
242C22—21no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1458305011yescharacteristic
249C22#1458307711yescharacteristic
250C22#1458308611yescharacteristic
251C4—21no—
252C4—21no—
253C4—42no—
254C4—42no—
255C4—82no—
256C4—82no—
257C4—3441no—
258C4—3441no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#1913354711yescharacteristic
263C2#1913659111yescharacteristic
264C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2724C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#2724D43
hypocenterC43#12209
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2724

Complements

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

NH ≅ G/Ntype
2. #19133602C2semidirect
3. #19132601C2semidirect
151. C43#12209semidirect

Maximal subgroups

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

subgroupindex
#191357512
#191336022
#191326012
#191325272
C43×#27242
#1220943