Finite Group Databasebeta

← #26109804

Subgroups — #26109804

Order 12032.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#20245991C211yesmaximal, characteristic
2#20243468C211yesmaximal, characteristic
3#20241297C214yesmaximal
4C47×#1821C211yesmaximal, characteristic
5#15689087C2212yes—
6#15689009—22no—
7#15689009—22no—
8#15688986C2212yes—
9#15688983C412yes—
10C4×C22⋊Dic47C412yes—
11#15688892—22no—
12C22×C4⋊C4×C47C2211yescharacteristic
13C47×#407C2212yes—
14C47×#343—22no—
15C2×#10625329—22no—
16C2×C4⋊Dic47—22no—
17C2×C22⋊Dic47C2×C414yes—
18C2×C4×Dic47—22no—
19C22⋊(C47⋊C8)—24no—
20C47⋊#95—22no—
21C47⋊#95—22no—
22C47⋊#95—22no—
23C47⋊#95—22no—
24C23×C4×C47C2×C411yescharacteristic
25C23×C4×C47C2×C411yescharacteristic
26C23×C4×C47C2311yescharacteristic
27C2×M16×C47—22no—
28C2×C4⋊C4×C47—24no—
29C2×C4⋊C4×C47D412yes—
30C2×C4⋊C4×C47D412yes—
31C22⋊C8×C47—24no—
32C24×C47C22×C411yescharacteristic
33C22×C4×C47—22no—
34C22×C4×C47—22no—
35C22×C4×C47—42no—
36C22×C4×C47—81no—
37C22×C4×C47—81no—
38C22×C4×C47C22⋊C412yes—
39C22×C4×C47C22⋊C412yes—
40C22×C4×C47C2×D411yescharacteristic
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47#4114yes—
43C22×Dic47—24no—
44M16×C47—44no—
45C2×C8×C47—42no—
46C4⋊C4×C47—24no—
47C4⋊C4×C47—24no—
48C22⋊Dic47—44no—
49C4⋊Dic47—82no—
50C4×Dic47—82no—
51#10625329—44no—
52C2×C47⋊C8—42no—
53C23×C47—22no—
54C23×C47—41no—
55C23×C47—41no—
56C23×C47C2×C22⋊C411yescharacteristic
57C23×C47#11712yes—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—44no—
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47—82no—
66C2×C4×C47—82no—
67C2×C4×C47#12312yes—
68C2×C4×C47#12312yes—
69C2×Dic47—44no—
70C2×Dic47—44no—
71C2×Dic47—44no—
72C8×C47—82no—
73C47⋊C8—82no—
74#8755—471nomaximal, Sylow
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—22no—
80C22×C47—44no—
81C22×C47#38111yescharacteristic
82C22×C47#41012yes—
83C4×C47—22no—
84C4×C47—22no—
85C4×C47—42no—
86C4×C47—42no—
87Dic47—84no—
88#2313—471no—
89#1821—471no—
90#1821D4711yescharacteristic
91#1306—474no—
92C2×C47—22no—
93C2×C47—42no—
94C2×C47#182011yescharacteristic
95C2×C47#182911yescharacteristic
96C2×C47#183011yescharacteristic
97C22×C4⋊C4C2×D4711yescharacteristic
98#407—472no—
99#407C2×D4712yes—
100#387—942no—
101#387—942no—
102#381—472no—
103#380—472no—
104C4×C22⋊C4—472no—
105#343—22no—
106#343—942no—
107C47#875511yescharacteristic, complemented, Sylow
108C23×C4C4×D4711yescharacteristic
109C23×C4C4×D4711yescharacteristic
110C23×C4C22×D4711yescharacteristic
111C2×M16—22no—
112C2×M16—942no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—942no—
115C2×C4⋊C4D18812yes—
116C2×C4⋊C4C22⋊D4712yes—
117C2×C22⋊C4—474no—
118C2×C42—942no—
119C22⋊C8—24no—
120C22⋊C8—944no—
121#95—942no—
122#95—942no—
123#95—942no—
124#95—942no—
125C24C2×C4×D4711yescharacteristic
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—42no—
129C22×C4—81no—
130C22×C4—81no—
131C22×C4—944no—
132C22×C4(C2×D47)⋊C412yes—
133C22×C4(C2×D47)⋊C412yes—
134C22×C4C2×D18811yescharacteristic
135C22×C4#1062535214yes—
136C22×C4C2×C22⋊D4711yescharacteristic
137M16—44no—
138M16—1884no—
139C2×C8—42no—
140C2×C8—1882no—
141C4⋊C4—24no—
142C4⋊C4—24no—
143C4⋊C4—3762no—
144C22⋊C4—1884no—
145C42—3762no—
146C23—22no—
147C23—41no—
148C23—41no—
149C23C2×(C2×D47)⋊C411yescharacteristic
150C23#1309398012yes—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—1884no—
161C2×C4—1884no—
162C2×C4—1884no—
163C2×C4#1309400512yes—
164C2×C4#1309400812yes—
165C8—82no—
166C8—3762no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—44no—
173C22#1568898411yescharacteristic
174C22#1568909612yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—3764no—
180C2—22no—
181C2—42no—
182C2#2024346311yescharacteristic
183C2#2024349711yescharacteristic
184C2#2024350011yescharacteristic
subgroupG/H
centerC22#15688984
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1821C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#1821D47
hypocenterC47#8755
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
107. C47#8755semidirect

Maximal subgroups

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

subgroupindex
#202459912
#202434682
#202412972
C47×#18212
#875547