Finite Group Databasebeta

← #24983949

Subgroups — #24983949

Order 11008.

324 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 39 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#19134518C211yesmaximal, characteristic
2#19132531C211yesmaximal, characteristic
3C43×#1320C211yesmaximal, characteristic
4C23×Dic86C411yescharacteristic
5C2×#13063243—21no—
6C2×#13063243—21no—
7#14582863C411yescharacteristic
8#14582681—21no—
9C43×#407C2211yescharacteristic
10C43×#349—21no—
11C22×Dic86—21no—
12C22×Dic86—21no—
13C22×Dic86—42no—
14C22×Dic86—42no—
15C22×Dic86—41no—
16C22×Dic86—41no—
17C23×Dic43C812yes—
18C2×#10621877—21no—
19#13063265—41no—
20#13063243—42no—
21#13063243—42no—
22C22⋊(C43⋊C8)—41no—
23C23×C4×C43C2×C411yescharacteristic
24C2×M16×C43D411yescharacteristic
25C2×M16×C43D411yescharacteristic
26M32×C43—41no—
27C22⋊C8×C43—41no—
28C24×C43C2×C811yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43—21no—
31C22×C4×C43—41no—
32C22×C4×C43—41no—
33C22×C4×C43C22⋊C411yescharacteristic
34C22×C4×C43M1611yescharacteristic
35C22×Dic43—22no—
36C22×Dic43—42no—
37C22×Dic43—44no—
38C2×Dic86—22no—
39C2×Dic86—22no—
40C2×Dic86—44no—
41C2×Dic86—41no—
42C2×Dic86—41no—
43C2×Dic86—42no—
44C2×Dic86—48no—
45C2×Dic86—42no—
46C2×Dic86—42no—
47C2×Dic86—41no—
48C2×Dic86—41no—
49C2×Dic86—42no—
50C2×Dic86—42no—
51M16×C43—41no—
52M16×C43—41no—
53C2×C8×C43—21no—
54C2×C8×C43—21no—
55#10621877—41no—
56#10621877—41no—
57C2×C43⋊C8—41no—
58C16×C43—81no—
59C43⋊C16—81no—
60C23×C43—21no—
61C23×C43—41no—
62C23×C43—42no—
63C23×C43C22⋊C811yescharacteristic
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—42no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43#9911yescharacteristic
72C2×C4×C43#10011yescharacteristic
73C2×Dic43—24no—
74C2×Dic43—42no—
75C2×Dic43—44no—
76C2×Dic43—42no—
77C2×Dic43—44no—
78Dic86—42no—
79Dic86—42no—
80Dic86—44no—
81Dic86—44no—
82Dic86—42no—
83Dic86—42no—
84C8×C43—41no—
85C8×C43—41no—
86C43⋊C8—81no—
87#7341—431nomaximal, Sylow
88C22×C43—22no—
89C22×C43—21no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—42no—
93C22×C43—42no—
94C22×C43—41no—
95C22×C43#32311yescharacteristic
96C4×C43—21no—
97C4×C43—41no—
98C4×C43AΣL(1,𝔽16)11yescharacteristic
99C4×C43AΣL(1,𝔽16)11yescharacteristic
100Dic43—44no—
101#1784—431no—
102#1320—431no—
103#1320D4311yescharacteristic
104C2×C43—21no—
105C2×C43—42no—
106C2×C43—41no—
107C2×C43#131611yescharacteristic
108C23×Q8—431no—
109C2×#101—861no—
110C2×#101—861no—
111#407—431no—
112#407C2×D4311yescharacteristic
113#349—21no—
114#349—861no—
115C43#734111yescharacteristic, complemented, Sylow
116C22×Q8—861no—
117C22×Q8—861no—
118C22×Q8—1721no—
119C22×Q8—1721no—
120C22×Q8—1722no—
121C22×Q8—1722no—
122C23×C4—432no—
123C23×C4C4×D4311yescharacteristic
124C2×M16—861no—
125C2×M16D17211yescharacteristic
126C2×M16C22⋊D4311yescharacteristic
127M32—41no—
128M32—1721no—
129#101—1722no—
130#101—1722no—
131C22⋊C8—41no—
132C22⋊C8—1721no—
133C24C8×D4311yescharacteristic
134C2×Q8—862no—
135C2×Q8—862no—
136C2×Q8—1721no—
137C2×Q8—1721no—
138C2×Q8—1722no—
139C2×Q8—1724no—
140C2×Q8—1722no—
141C2×Q8—1722no—
142C2×Q8—1728no—
143C2×Q8—1722no—
144C2×Q8—1722no—
145C2×Q8—1721no—
146C2×Q8—1721no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—862no—
152C22×C4—1724no—
153C22×C4—1722no—
154C22×C4#1062187211yescharacteristic
155C22×C4(C2×D43)⋊C411yescharacteristic
156M16—41no—
157M16—41no—
158M16—1721no—
159M16—1721no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1721no—
163C16—81no—
164C16—3441no—
165C23—21no—
166C23—41no—
167C23—42no—
168C23(C2×D43)⋊C811yescharacteristic
169Q8—1722no—
170Q8—1722no—
171Q8—1724no—
172Q8—1724no—
173Q8—1722no—
174Q8—1722no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—864no—
183C2×C4—1722no—
184C2×C4—1724no—
185C2×C4—1722no—
186C2×C4—1724no—
187C2×C4#1306323911yescharacteristic
188C2×C4#1306324111yescharacteristic
189C8—41no—
190C8—41no—
191C8—3441no—
192C22—22no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—42no—
197C22—42no—
198C22—41no—
199C22#1458262211yescharacteristic
200C4—21no—
201C4—41no—
202C4—1724no—
203C4#1458268511yescharacteristic
204C4#1458268711yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2#1913252211yescharacteristic
subgroupG/H
centerC2#19132522
commutator, prime radicalC24×C43C2×C8
Frattini#407C2×D43
FittingC43×#1320C2
socleC2×C43#1316
cosocleC43×#407C22
hypercenter#1320D43
hypocenterC43#7341
LCSG ▷ C24×C43 ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1320

Complements

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

NH ≅ G/Ntype
115. C43#7341semidirect

Maximal subgroups

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

subgroupindex
#191345182
#191325312
C43×#13202
#734143