Finite Group Databasebeta

← #26109807

Subgroups — #26109807

Order 12032.

398 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 99 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#20243468C212yesmaximal
2#20241296C214yesmaximal
3C47×#2313C211yesmaximal, characteristic
4#15689087C2214yes—
5#15688892—24no—
6C22×C4⋊C4×C47C2211yescharacteristic
7C47×#387—24no—
8C47×#381C2212yes—
9C47×#380C412yes—
10C4×C22⋊C4×C47C412yes—
11C2×#10625329—24no—
12C22⋊(C47⋊C8)—28no—
13C23×C4×C47C2×C411yescharacteristic
14C23×C4×C47C2×C411yescharacteristic
15C23×C4×C47C2311yescharacteristic
16C2×C4⋊C4×C47—24no—
17C2×C4⋊C4×C47—22no—
18C2×C4⋊C4×C47D414yes—
19C2×C22⋊C4×C47C2×C414yes—
20C2×C42×C47—22no—
21#95×C47—22no—
22#95×C47—22no—
23#95×C47—24no—
24C24×C47C22×C411yescharacteristic
25C22×C4×C47—22no—
26C22×C4×C47—22no—
27C22×C4×C47—24no—
28C22×C4×C47—42no—
29C22×C4×C47—81no—
30C22×C4×C47—81no—
31C22×C4×C47C22⋊C412yes—
32C22×C4×C47C22⋊C412yes—
33C22×C4×C47C2×D412yes—
34C22×C4×C47#4114yes—
35C4⋊C4×C47—28no—
36C4⋊C4×C47—82no—
37C22⋊C4×C47—44no—
38C42×C47—82no—
39#10625329—48no—
40C2×C47⋊C8—44no—
41C23×C47—22no—
42C23×C47—41no—
43C23×C47—41no—
44C23×C47C2×C22⋊C411yescharacteristic
45C23×C47#11712yes—
46C2×C4×C47—24no—
47C2×C4×C47—22no—
48C2×C4×C47—22no—
49C2×C4×C47—44no—
50C2×C4×C47—42no—
51C2×C4×C47—42no—
52C2×C4×C47—44no—
53C2×C4×C47—44no—
54C2×C4×C47—44no—
55C2×C4×C47—82no—
56C2×C4×C47—82no—
57C2×C4×C47#12314yes—
58C47⋊C8—84no—
59#8755—471nomaximal, Sylow
60C22×C47—21no—
61C22×C47—21no—
62C22×C47—22no—
63C22×C47—22no—
64C22×C47—22no—
65C22×C47—44no—
66C22×C47#38111yescharacteristic
67C22×C47#41012yes—
68C4×C47—24no—
69C4×C47—42no—
70C4×C47—42no—
71C4×C47—84no—
72#2313D4711yescharacteristic
73#1821—472no—
74#1306—474no—
75C2×C47—22no—
76C2×C47—42no—
77C2×C47#182011yescharacteristic
78C2×C47#182911yescharacteristic
79C2×C47#183011yescharacteristic
80C22×C4⋊C4C2×D4711yescharacteristic
81#407—474no—
82#387—24no—
83#381C2×D4712yes—
84#380Dic4712yes—
85C4×C22⋊C4Dic4712yes—
86#343—944no—
87C47#875511yescharacteristic, complemented, Sylow
88C23×C4C2×Dic4711yescharacteristic
89C23×C4C2×Dic4711yescharacteristic
90C23×C4C22×D4711yescharacteristic
91C2×M16—944no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4C22⋊D4714yes—
95C2×C22⋊C4C2×Dic4714yes—
96C2×C42—22no—
97C22⋊C8—948no—
98#95—22no—
99#95—22no—
100#95—24no—
101C24C22×Dic4711yescharacteristic
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—24no—
105C22×C4—42no—
106C22×C4—81no—
107C22×C4—81no—
108C22×C4C22⋊Dic4712yes—
109C22×C4C22⋊Dic4712yes—
110C22×C4#1062535014yes—
111C22×C4C2×C22⋊D4712yes—
112M16—1888no—
113C2×C8—1884no—
114C4⋊C4—28no—
115C4⋊C4—82no—
116C22⋊C4—44no—
117C42—82no—
118C23—22no—
119C23—41no—
120C23—41no—
121C23C2×C22⋊Dic4711yescharacteristic
122C23#1309398312yes—
123C2×C4—24no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—44no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—44no—
130C2×C4—44no—
131C2×C4—44no—
132C2×C4—82no—
133C2×C4—82no—
134C2×C4#1309400714yes—
135C8—3764no—
136C22—21no—
137C22—21no—
138C22—22no—
139C22—22no—
140C22—22no—
141C22—44no—
142C22#1568898611yescharacteristic
143C22#1568909712yes—
144C4—24no—
145C4—42no—
146C4—42no—
147C4—84no—
148C2—22no—
149C2—42no—
150C2#2024346511yescharacteristic
151C2#2024349911yescharacteristic
152C2#2024350211yescharacteristic
subgroupG/H
centerC22#15688986
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2313C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#2313D47
hypocenterC47#8755
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
87. C47#8755semidirect

Maximal subgroups

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

subgroupindex
#202434682
#202412962
C47×#23132
#875547