Finite Group Databasebeta

← #24983216

Subgroups — #24983216

Order 11008.

476 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 59 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#19132519C212yesmaximal, complemented
2C43×#1779C211yesmaximal, characteristic
3C22⋊(C43⋊C16)—22no—
4C24×C4×C43C411yescharacteristic
5C2×C22⋊C8×C43—22no—
6C2×C22⋊C8×C43C411yescharacteristic
7C2×C22⋊C8×C43C2211yescharacteristic
8C2×C43⋊C16—42no—
9C25×C43C811yescharacteristic
10C23×C4×C43—21no—
11C23×C4×C43—21no—
12C23×C4×C43—44no—
13C23×C4×C43—41no—
14C23×C4×C43—41no—
15C23×C4×C43C811yescharacteristic
16C23×C4×C43C2×C411yescharacteristic
17C22×C8×C43—21no—
18C22×C8×C43D412yes—
19C22⋊C8×C43—41no—
20C22⋊C8×C43—44no—
21C22⋊C8×C43—41no—
22C24×C43—21no—
23C24×C43—21no—
24C24×C43—42no—
25C24×C43—41no—
26C24×C43—42no—
27C24×C43—41no—
28C24×C43C1612yescomplemented
29C24×C43C2×C811yescharacteristic
30C22×C4×C43—24no—
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43—41no—
35C22×C4×C43—42no—
36C22×C4×C43—42no—
37C22×C4×C43—42no—
38C22×C4×C43—42no—
39C22×C4×C43—42no—
40C22×C4×C43—42no—
41C22×C4×C43—44no—
42C22×C4×C43—44no—
43C22×C4×C43—44no—
44C22×C4×C43—44no—
45C22×C4×C43—41no—
46C22×C4×C43—41no—
47C22×C4×C43C22⋊C411yescharacteristic
48C22×C4×C43M1611yescharacteristic
49C2×C8×C43—22no—
50C2×C8×C43—42no—
51C2×C8×C43—42no—
52C2×C8×C43—41no—
53C43⋊C16—82no—
54C23×C43—22no—
55C23×C43—22no—
56C23×C43—21no—
57C23×C43—22no—
58C23×C43—21no—
59C23×C43—41no—
60C23×C43—44no—
61C23×C43—42no—
62C23×C43—41no—
63C23×C43—41no—
64C23×C43—41no—
65C23×C43—44no—
66C23×C43—42no—
67C23×C43—42no—
68C23×C43—42no—
69C23×C43—42no—
70C23×C43—48no—
71C23×C43—42no—
72C23×C43—41no—
73C23×C43—41no—
74C23×C43C22⋊C811yescharacteristic
75C23×C43C2×C1611yescharacteristic
76C23×C43M3211yescharacteristic
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43—44no—
81C2×C4×C43—42no—
82C2×C4×C43—41no—
83C2×C4×C43—42no—
84C2×C4×C43—48no—
85C2×C4×C43—41no—
86C2×C4×C43—44no—
87C2×C4×C43—42no—
88C2×C4×C43—41no—
89C2×C4×C43—42no—
90C2×C4×C43#9911yescharacteristic
91C2×C4×C43#10011yescharacteristic
92C8×C43—42no—
93C8×C43—81no—
94#7054—431nomaximal, Sylow
95C22×C43—21no—
96C22×C43—21no—
97C22×C43—24no—
98C22×C43—21no—
99C22×C43—21no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43—44no—
107C22×C43—44no—
108C22×C43—44no—
109C22×C43—44no—
110C22×C43—42no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43—42no—
114C22×C43—41no—
115C22×C43#32311yescharacteristic
116C22×C43C22⋊C1611yescharacteristic
117C22×C43#34911yescharacteristic
118C4×C43—21no—
119C4×C43—42no—
120C4×C43—41no—
121C4×C43AΣL(1,𝔽16)12yes—
122#1779D4311yescharacteristic
123#1314—432no—
124C2×C43—21no—
125C2×C43—21no—
126C2×C43—44no—
127C2×C43—41no—
128C2×C43—41no—
129C2×C43#131411yescharacteristic
130C2×C43#131611yescharacteristic
131C2×C43#132011yescharacteristic
132C24×C4Dic4311yescharacteristic
133C2×C22⋊C8—22no—
134C2×C22⋊C8Dic4311yescharacteristic
135C2×C22⋊C8C2×D4311yescharacteristic
136C22⋊C16—862no—
137C43#705411yescharacteristic, complemented, Sylow
138C25C43⋊C811yescharacteristic
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—44no—
142C23×C4—41no—
143C23×C4—41no—
144C23×C4C43⋊C811yescharacteristic
145C23×C4C2×Dic4311yescharacteristic
146C22×C8—21no—
147C22×C8C22⋊D4312yes—
148C2×C16—1722no—
149C22⋊C8—41no—
150C22⋊C8—44no—
151C22⋊C8—41no—
152C24—21no—
153C24—21no—
154C24—42no—
155C24—41no—
156C24—42no—
157C24—41no—
158C24C43⋊C1612yescomplemented
159C24C2×C43⋊C811yescharacteristic
160C22×C4—24no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—44no—
171C22×C4—44no—
172C22×C4—44no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—44no—
177C22×C4#1062187711yescharacteristic
178C22×C4C22⋊Dic4311yescharacteristic
179C2×C8—22no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—41no—
183C16—3442no—
184C23—22no—
185C23—22no—
186C23—21no—
187C23—22no—
188C23—21no—
189C23—41no—
190C23—44no—
191C23—42no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—44no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—48no—
201C23—42no—
202C23—41no—
203C23—41no—
204C23C22⋊(C43⋊C8)11yescharacteristic
205C23C2×C43⋊C1611yescharacteristic
206C23#1306326511yescharacteristic
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4#1306324011yescharacteristic
221C2×C4#1306324211yescharacteristic
222C8—42no—
223C8—81no—
224C22—21no—
225C22—21no—
226C22—24no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—44no—
236C22—44no—
237C22—44no—
238C22—44no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22#1458262311yescharacteristic
245C22C22⋊(C43⋊C16)11yescharacteristic
246C22#1458268111yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4#1458268612yes—
251C2—21no—
252C2—21no—
253C2—44no—
254C2—41no—
255C2—41no—
256C2#1913251911yescharacteristic
257C2#1913252311yescharacteristic
258C2#1913253111yescharacteristic
subgroupG/H
centerC2×C4#13063240
commutatorC23×C43C2×C16
FrattiniC2×C22⋊C8C2×D43
FittingC43×#1779C2
socleC22×C43#323
prime radicalC25×C43C8
cosocleC2×C22⋊C8×C43C22
hypercenter#1779D43
hypocenterC43#7054
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. #19132519C2semidirect
28. C24×C43C16semidirect
137. C43#7054semidirect
158. C24C43⋊C16semidirect

Maximal subgroups

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

subgroupindex
#191325192
C43×#17792
#705443