Finite Group Databasebeta

← #24983918

Subgroups — #24983918

Order 11008.

374 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 71 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#19132925C212yesmaximal
2C43×#1445C211yesmaximal, characteristic
3#14582863—22no—
4#14582625—22no—
5#14582625C414yescomplemented
6C22×C4⋊C4×C43C2211yescharacteristic
7C2×#95×C43—22no—
8C2×#95×C43C411yescharacteristic
9C2×#95×C43C411yescharacteristic
10C2×#10621877—42no—
11C22⋊(C43⋊C8)—24no—
12C22⋊(C43⋊C8)—42no—
13C23×C4×C43—21no—
14C23×C4×C43—21no—
15C23×C4×C43C2×C411yescharacteristic
16C23×C4×C43D412yes—
17C2×C4⋊C4×C43—41no—
18C2×C4⋊C4×C43—41no—
19C2×C4⋊C4×C43C2×C412yes—
20C2×C4⋊C4×C43D411yescharacteristic
21C2×C4⋊C4×C43Q811yescharacteristic
22#95×C43—41no—
23#95×C43—41no—
24#95×C43—44no—
25C24×C43C22⋊C411yescharacteristic
26C22×C4×C43—22no—
27C22×C4×C43—22no—
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43—22no—
31C22×C4×C43—22no—
32C22×C4×C43—42no—
33C22×C4×C43—42no—
34C22×C4×C43—42no—
35C22×C4×C43—42no—
36C22×C4×C43—42no—
37C22×C4×C43—42no—
38C22×C4×C43—41no—
39C22×C4×C43—41no—
40C22×C4×C43—42no—
41C22×C4×C43—41no—
42C22×C4×C43—41no—
43C22×C4×C43C4211yescharacteristic
44C22×C4×C43C22⋊C412yes—
45C22×C4×C43C4⋊C412yes—
46C22×C4×C43C4⋊C411yescharacteristic
47C4⋊C4×C43—42no—
48C4⋊C4×C43—41no—
49C4⋊C4×C43—41no—
50#10621877—82no—
51#10621877—82no—
52C2×C43⋊C8—44no—
53C23×C43—22no—
54C23×C43—21no—
55C23×C43—21no—
56C23×C43—21no—
57C23×C43—21no—
58C23×C43#9511yescharacteristic
59C23×C43#9911yescharacteristic
60C23×C43#9911yescharacteristic
61C2×C4×C43—22no—
62C2×C4×C43—21no—
63C2×C4×C43—22no—
64C2×C4×C43—21no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—42no—
68C2×C4×C43—42no—
69C2×C4×C43—42no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43—44no—
74C2×C4×C43—44no—
75C2×C4×C43—42no—
76C2×C4×C43—42no—
77C2×C4×C43—82no—
78C2×C4×C43—82no—
79C2×C4×C43—82no—
80C2×C4×C43—81no—
81C2×C4×C43—81no—
82C2×C4×C43—81no—
83C2×C4×C43—81no—
84C43⋊C8—84no—
85#7326—431nomaximal, Sylow
86C22×C43—22no—
87C22×C43—22no—
88C22×C43—22no—
89C22×C43—22no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—21no—
96C22×C43#34211yescharacteristic
97C22×C43#34412yes—
98C22×C43#35311yescharacteristic
99C22×C43#35411yescharacteristic
100C22×C43#35511yescharacteristic
101C22×C43#35611yescharacteristic
102C4×C43—41no—
103C4×C43—41no—
104C4×C43—42no—
105C4×C43—42no—
106C4×C43—82no—
107C4×C43—82no—
108#1463—432no—
109#1445D4311yescharacteristic
110C2×C43—21no—
111C2×C43—21no—
112C2×C43—22no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#130611yescharacteristic
116C2×C43#139311yescharacteristic
117C2×C43#139411yescharacteristic
118C22×C4⋊C4C2×D4311yescharacteristic
119#407—862no—
120C2×#95—22no—
121C2×#95Dic4311yescharacteristic
122C2×#95Dic4311yescharacteristic
123#324—434no—
124#324—862no—
125C43#732611yescharacteristic, complemented, Sylow
126C23×C4—21no—
127C23×C4—21no—
128C23×C4C2×Dic4311yescharacteristic
129C23×C4C22⋊D4312yes—
130C2×M16—1722no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4Dic8611yescharacteristic
134C2×C4⋊C4C4×D4312yes—
135C2×C4⋊C4D17211yescharacteristic
136C22⋊C8—864no—
137C22⋊C8—1722no—
138#95—41no—
139#95—41no—
140#95—44no—
141C24C22⋊Dic4311yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C4×Dic4311yescharacteristic
160C22×C4Dic43⋊C412yes—
161C22×C4C4⋊Dic4311yescharacteristic
162C22×C4(C2×D43)⋊C412yes—
163M16—3442no—
164M16—3442no—
165C2×C8—1724no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—41no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23C43⋊#9511yescharacteristic
175C23#1306324011yescharacteristic
176C23#1306324011yescharacteristic
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C8—3444no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1458266611yescharacteristic
212C22#1458266912yes—
213C22#1458269211yescharacteristic
214C22#1458269411yescharacteristic
215C22#1458269611yescharacteristic
216C22#1458269811yescharacteristic
217C4—42no—
218C4—42no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—82no—
223C2—21no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—21no—
228C2#1913250311yescharacteristic
229C2#1913272011yescharacteristic
230C2#1913272211yescharacteristic
subgroupG/H
centerC22#14582666
commutatorC22×C4×C43C42
FrattiniC22×C4⋊C4C2×D43
FittingC43×#1445C2
socleC22×C43#342
prime radicalC24×C43C22⋊C4
cosocleC22×C4⋊C4×C43C22
hypercenter#1445D43
hypocenterC43#7326
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
5. #14582625C4semidirect
125. C43#7326semidirect

Maximal subgroups

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

subgroupindex
#191329252
C43×#14452
#732643