Finite Group Databasebeta

← #25009389

Subgroups — #25009389

Order 11008.

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

normal subgroups only

This group has 400 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#19135762C211yesmaximal, characteristic
2#19133551C212yesmaximal
3#19132616C212yesmaximal
4#19132525C211yesmaximal, characteristic
5C43×#2607C211yesmaximal, characteristic
6#14583525C2211yescharacteristic
7#14583055—22no—
8#14582762—21no—
9#14582666C2211yescharacteristic
10#14582665—21no—
11#14582635—22no—
12#14582623C2212yes—
13C43×#399—21no—
14C43×#393C2212yes—
15C43×#391—22no—
16C43×#387—22no—
17C43×#381C2211yescharacteristic
18C4×C22⋊C4×C43—21no—
19C2×#10621885—42no—
20#13063304—22no—
21#13063302—42no—
22C2×C22⋊Dic43—21no—
23C2×C22⋊Dic43—21no—
24#13063249—42no—
25C22⋊(C43⋊C8)—22no—
26C43⋊#95—42no—
27C22×Q8×C43D412yes—
28C23×C4×C43D411yescharacteristic
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—21no—
31C2×C22⋊C4×C43—22no—
32C2×C22⋊C4×C43D411yescharacteristic
33C2×C22⋊C4×C43C2311yescharacteristic
34C2×C42×C43—21no—
35C2×C42×C43—21no—
36#95×C43—22no—
37#95×C43—21no—
38#95×C43—22no—
39#95×C43—22no—
40#95×C43D412yes—
41C24×C43C2×D411yescharacteristic
42C2×Q8×C43—44no—
43C2×Q8×C43—42no—
44C22×C4×C43—21no—
45C22×C4×C43—22no—
46C22×C4×C43—21no—
47C22×C4×C43—22no—
48C22×C4×C43—21no—
49C22×C4×C43—41no—
50C22×C4×C43—41no—
51C22×C4×C43Q1612yescomplemented
52C22×C4×C43C2×D412yes—
53C22×Dic43—22no—
54C22×Dic43—41no—
55C2×Dic86—22no—
56C4⋊C4×C43—44no—
57C4⋊C4×C43—81no—
58C22⋊C4×C43—41no—
59C22⋊C4×C43—41no—
60C22⋊C4×C43—44no—
61C42×C43—81no—
62C42×C43—81no—
63C22⋊Dic43—41no—
64C22⋊Dic43—41no—
65C22⋊Dic43—41no—
66C22⋊Dic43—41no—
67#10621885—84no—
68C4⋊Dic43—22no—
69Dic43⋊C4—42no—
70C2×C43⋊C8—42no—
71C23×C43—21no—
72C23×C43—21no—
73C23×C43—42no—
74C23×C43#12011yescharacteristic
75C23×C43C2×Q1611yescharacteristic
76C23×C43#13711yescharacteristic
77Q8×C43—44no—
78Q8×C43—82no—
79C2×C4×C43—24no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—42no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—41no—
93C2×C4×C43—81no—
94C2×Dic43—42no—
95C2×Dic43—82no—
96C2×Dic43—81no—
97C2×Dic43—82no—
98Dic86—82no—
99C43⋊C8—82no—
100#12215—431nomaximal, Sylow
101C22×C43—22no—
102C22×C43—21no—
103C22×C43—21no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—42no—
107C22×C43—81no—
108C22×C43#45111yescharacteristic
109C22×C43#45511yescharacteristic
110C22×C43B(4,𝔽2)11yescharacteristic
111C4×C43—42no—
112C4×C43—42no—
113C4×C43—44no—
114C4×C43—82no—
115C4×C43—81no—
116Dic43—82no—
117Dic43—161no—
118#2607D4311yescharacteristic
119#2030—431no—
120#1602—432no—
121#1351—432no—
122#1317—431no—
123C2×C43—21no—
124C2×C43—21no—
125C2×C43—41no—
126C2×C43—41no—
127C2×C43#160211yescharacteristic
128C2×C43#219712yes—
129#543—431no—
130#451—862no—
131#399—21no—
132#393C2×D4312yes—
133#391—22no—
134#387—22no—
135#381—861no—
136#381C2×D4311yescharacteristic
137C4×C22⋊C4—21no—
138#342—431no—
139#342—861no—
140#328—862no—
141#323—432no—
142C43#1221511yescharacteristic, complemented, Sylow
143C22×Q8C22⋊D4312yes—
144C23×C4C22⋊D4311yescharacteristic
145C2×Q16—1722no—
146C22⋊Q8—862no—
147C22⋊Q8—1722no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—861no—
152C2×C22⋊C4—861no—
153C2×C22⋊C4C22⋊D4311yescharacteristic
154C2×C22⋊C4C22×D4311yescharacteristic
155C2×C42—21no—
156C2×C42—21no—
157#103—1722no—
158C22⋊C8—862no—
159#95—22no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—1722no—
164#95C22⋊D4312yes—
165C24C2×C22⋊D4311yescharacteristic
166C2×Q8—44no—
167C2×Q8—42no—
168C2×Q8—862no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—862no—
177C22×C4—1721no—
178C22×C4#1062188512yescomplemented
179C22×C4C2×C22⋊D4312yes—
180Q16—3444no—
181C2×C8—1722no—
182C4⋊C4—44no—
183C4⋊C4—81no—
184C4⋊C4—862no—
185C4⋊C4—1722no—
186C22⋊C4—41no—
187C22⋊C4—44no—
188C22⋊C4—41no—
189C22⋊C4—1721no—
190C22⋊C4—1721no—
191C22⋊C4—1721no—
192C22⋊C4—1721no—
193C42—81no—
194C42—81no—
195C23—21no—
196C23—21no—
197C23—42no—
198C23#1306329411yescharacteristic
199C23C2×#1062188511yescharacteristic
200C23#1306335611yescharacteristic
201Q8—44no—
202Q8—82no—
203Q8—3442no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—3442no—
220C2×C4—3441no—
221C2×C4—3442no—
222C2×C4—1722no—
223C8—3442no—
224C22—22no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—81no—
231C22#1458305511yescharacteristic
232C22#1458307711yescharacteristic
233C22#1458308611yescharacteristic
234C4—42no—
235C4—44no—
236C4—42no—
237C4—82no—
238C4—81no—
239C4—3442no—
240C4—6881no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2#1913355211yescharacteristic
246C2#1913658512yes—
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2607C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#2607D43
hypocenterC43#12215
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
51. C22×C4×C43Q16semidirect
142. C43#12215semidirect
178. C22×C4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191357622
#191335512
#191326162
#191325252
C43×#26072
#1221543