Finite Group Databasebeta

← #26103559

Subgroups — #26103559

Order 12032.

518 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 79 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#20243312C212yesmaximal
2C47×#1446C211yesmaximal, characteristic
3C2×#13093943—22no—
4C2×#13093943C414yescomplemented
5#15689087—22no—
6C23×Q8×C47C2211yescharacteristic
7C2×#95×C47—22no—
8C2×#95×C47C412yes—
9C2×#10625329—24no—
10#13093943—44no—
11#13093943—44no—
12C22⋊(C47⋊C8)—44no—
13C22×Q8×C47—42no—
14C22×Q8×C47—44no—
15C22×Q8×C47C2×C412yes—
16C22×Q8×C47D411yescharacteristic
17C22×Q8×C47Q811yescharacteristic
18C23×C4×C47—22no—
19C23×C4×C47C2×C411yescharacteristic
20C23×C4×C47D412yes—
21#95×C47—44no—
22#95×C47—42no—
23C24×C47C22⋊C411yescharacteristic
24C2×Q8×C47—24no—
25C2×Q8×C47—24no—
26C2×Q8×C47—42no—
27C2×Q8×C47—42no—
28C2×Q8×C47—41no—
29C2×Q8×C47—41no—
30C2×Q8×C47—42no—
31C2×Q8×C47—416no—
32C22×C4×C47—22no—
33C22×C4×C47—24no—
34C22×C4×C47—24no—
35C22×C4×C47—24no—
36C22×C4×C47—42no—
37C22×C4×C47—42no—
38C22×C4×C47—42no—
39C22×C4×C47—44no—
40C22×C4×C47—44no—
41C22×C4×C47—42no—
42C22×C4×C47C4211yescharacteristic
43C22×C4×C47C22⋊C412yes—
44C22×C4×C47C4⋊C412yes—
45C22×C4×C47C4⋊C411yescharacteristic
46#10625329—44no—
47#10625329—44no—
48C2×C47⋊C8—44no—
49C23×C47—22no—
50C23×C47—22no—
51C23×C47—22no—
52C23×C47#9511yescharacteristic
53C23×C47#9912yes—
54Q8×C47—44no—
55Q8×C47—48no—
56Q8×C47—44no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—21no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—48no—
67C2×C4×C47—44no—
68C2×C4×C47—48no—
69C2×C4×C47—44no—
70C2×C4×C47—84no—
71C2×C4×C47—82no—
72C2×C4×C47—82no—
73C2×C4×C47#9914yes—
74C47⋊C8—84no—
75#7308—471nomaximal, Sylow
76C22×C47—24no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—22no—
80C22×C47—22no—
81C22×C47—22no—
82C22×C47#34212yes—
83C22×C47#34211yescharacteristic
84C22×C47#35512yes—
85C22×C47#35612yes—
86C4×C47—24no—
87C4×C47—41no—
88C4×C47—42no—
89C4×C47—41no—
90C4×C47—84no—
91#1784—472no—
92#1446D4711yescharacteristic
93C2×C47—22no—
94C2×C47—22no—
95C2×C47—22no—
96C2×C47#130411yescharacteristic
97C2×C47#139412yes—
98C23×Q8C2×D4711yescharacteristic
99C2×#101—474no—
100C2×#101—942no—
101#407—942no—
102C2×#95—22no—
103C2×#95Dic4712yes—
104C47#730811yescharacteristic, complemented, Sylow
105C22×Q8—42no—
106C22×Q8—44no—
107C22×Q8Dic9411yescharacteristic
108C22×Q8C4×D4712yes—
109C22×Q8D18811yescharacteristic
110C23×C4—22no—
111C23×C4C2×Dic4711yescharacteristic
112C23×C4C22⋊D4712yes—
113C2×M16—944no—
114#101—1884no—
115#101—1884no—
116C22⋊C8—1884no—
117#95—42no—
118#95—44no—
119C24C22⋊Dic4711yescharacteristic
120C2×Q8—24no—
121C2×Q8—24no—
122C2×Q8—42no—
123C2×Q8—41no—
124C2×Q8—42no—
125C2×Q8—42no—
126C2×Q8—41no—
127C2×Q8—416no—
128C22×C4—22no—
129C22×C4—24no—
130C22×C4—24no—
131C22×C4—24no—
132C22×C4—42no—
133C22×C4—42no—
134C22×C4—44no—
135C22×C4—42no—
136C22×C4—44no—
137C22×C4—42no—
138C22×C4C4×Dic4711yescharacteristic
139C22×C4Dic47⋊C412yes—
140C22×C4C4⋊Dic4711yescharacteristic
141C22×C4(C2×D47)⋊C412yes—
142M16—1884no—
143M16—1884no—
144C2×C8—1884no—
145C23—22no—
146C23—22no—
147C23—22no—
148C23C47⋊#9511yescharacteristic
149C23#1309393912yes—
150Q8—44no—
151Q8—48no—
152Q8—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—48no—
163C2×C4—44no—
164C2×C4—48no—
165C2×C4—44no—
166C2×C4—84no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4#1309393814yes—
170C8—3764no—
171C22—24no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22#1568888912yes—
178C22#1568889011yescharacteristic
179C22#1568892012yes—
180C22#1568892212yes—
181C4—24no—
182C4—42no—
183C4—41no—
184C4—41no—
185C4—84no—
186C2—22no—
187C2—22no—
188C2—22no—
189C2C47⋊#130411yescharacteristic
190C2#2024151512yes—
subgroupG/H
centerC22#15688890
commutatorC22×C4×C47C42
FrattiniC23×Q8C2×D47
FittingC47×#1446C2
socleC22×C47#342
prime radicalC24×C47C22⋊C4
cosocleC23×Q8×C47C22
hypercenter#1446D47
hypocenterC47#7308
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1446

Complements

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

NH ≅ G/Ntype
4. C2×#13093943C4semidirect
104. C47#7308semidirect

Maximal subgroups

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

subgroupindex
#202433122
C47×#14462
#730847