Finite Group Databasebeta

← #26104074

Subgroups — #26104074

Order 12032.

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

normal subgroups only

This group has 274 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#20245053C212yesmaximal
2C47×#1963C211yesmaximal, characteristic
3#15689097—22no—
4#15688918C414yescomplemented
5#15688916—22no—
6C47×#532C2211yescharacteristic
7C47×#423C411yescharacteristic, complemented
8C2×#104×C47—22no—
9C47×#376C411yescharacteristic, complemented
10#13093983—42no—
11#13093939—24no—
12#13093939—42no—
13C2×#41×C47D412yes—
14C2×M16×C47—21no—
15C4⋊Q8×C47Q811yescharacteristic
16#127×C47D411yescharacteristic
17#124×C47C2×C412yes—
18#121×C47—41no—
19C4×D4×C47—41no—
20C2×C42×C47—21no—
21C2×C42×C47C2×C411yescharacteristic
22C4⋊C8×C47—41no—
23#104×C47—44no—
24#95×C47—41no—
25#41×C47—42no—
26#41×C47—42no—
27C2×Q8×C47C4⋊C412yes—
28C2×D4×C47—22no—
29C2×D4×C47—41no—
30C2×D4×C47C22⋊C412yes—
31C22×C4×C47—21no—
32C22×C4×C47—22no—
33C22×C4×C47—41no—
34C22×C4×C47C22⋊C411yescharacteristic
35M16×C47—42no—
36C2×C8×C47—41no—
37C4⋊C4×C47—41no—
38C22⋊C4×C47—42no—
39C42×C47—21no—
40C42×C47—22no—
41C42×C47—41no—
42C42×C47C4211yescharacteristic
43C42×C47C4⋊C411yescharacteristic
44C22⋊Dic47—44no—
45C4⋊Dic47—82no—
46C4×Dic47—82no—
47C23×C47—22no—
48C23×C47#9911yescharacteristic
49Q8×C47—42no—
50D4×C47—42no—
51D4×C47—82no—
52D4×C47—82no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—42no—
59C2×C4×C47—42no—
60C2×C4×C47—42no—
61C2×C4×C47—81no—
62C2×C4×C47—82no—
63C2×C4×C47#9511yescharacteristic
64C2×C4×C47#9911yescharacteristic
65C2×Dic47—84no—
66C8×C47—81no—
67#7506—471nomaximal, Sylow
68C22×C47—21no—
69C22×C47—41no—
70C22×C47—42no—
71C22×C47—82no—
72C22×C47#34211yescharacteristic
73C4×C47—21no—
74C4×C47—41no—
75C4×C47—41no—
76C4×C47—42no—
77C4×C47—82no—
78C4×C47#35311yescharacteristic
79C4×C47#35411yescharacteristic
80Dic47—164no—
81#2126—472no—
82#1963D4711yescharacteristic
83C2×C47—21no—
84C2×C47—41no—
85C2×C47—82no—
86C2×C47#139311yescharacteristic
87#532C2×D4711yescharacteristic
88#423Dic4711yescharacteristic, complemented
89C2×#104—22no—
90#410—942no—
91#376Dic4711yescharacteristic, complemented
92#354—474no—
93#353—942no—
94C47#750611yescharacteristic, complemented, Sylow
95C2×#41C22⋊D4712yes—
96C2×M16—21no—
97C4⋊Q8Dic9411yescharacteristic
98#127D18811yescharacteristic
99#124C4×D4712yes—
100#121—41no—
101C4×D4—41no—
102#117—1882no—
103C2×C42—21no—
104C2×C42C2×Dic4711yescharacteristic
105C4⋊C8—41no—
106#104—44no—
107#99—944no—
108#99—1882no—
109#95—41no—
110#41—42no—
111#41—42no—
112C2×Q8Dic47⋊C412yes—
113C2×D4—22no—
114C2×D4—41no—
115C2×D4(C2×D47)⋊C412yes—
116C22×C4—21no—
117C22×C4—22no—
118C22×C4—41no—
119C22×C4C22⋊Dic4711yescharacteristic
120M16—42no—
121C2×C8—41no—
122C4⋊C4—41no—
123C4⋊C4—3762no—
124C22⋊C4—42no—
125C22⋊C4—1884no—
126C42—21no—
127C42—22no—
128C42—41no—
129C42—3762no—
130C42C4×Dic4711yescharacteristic
131C42C4⋊Dic4711yescharacteristic
132C23—22no—
133C23#1309393911yescharacteristic
134Q8—42no—
135D4—42no—
136D4—82no—
137D4—82no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—81no—
147C2×C4—82no—
148C2×C4—3764no—
149C2×C4C47⋊#9511yescharacteristic
150C2×C4#1309393911yescharacteristic
151C8—81no—
152C22—21no—
153C22—41no—
154C22—42no—
155C22—82no—
156C22#1568889011yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—42no—
161C4—82no—
162C4—7524no—
163C4#1568891611yescharacteristic
164C4#1568891811yescharacteristic
165C2—21no—
166C2—41no—
167C2—82no—
168C2#2024151311yescharacteristic
subgroupG/H
centerC4#15688916
commutatorC42×C47C42
Frattini#532C2×D47
FittingC47×#1963C2
socleC2×C47#1393
prime radical, cosocleC47×#532C22
hypercenter#1963D47
hypocenterC47#7506
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1963

Complements

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

NH ≅ G/Ntype
4. #15688918C4semidirect
7. C47×#423C4semidirect
9. C47×#376C4semidirect
88. #423Dic47semidirect
91. #376Dic47semidirect
94. C47#7506semidirect

Maximal subgroups

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

subgroupindex
#202450532
C47×#19632
#750647