Finite Group Databasebeta

← #26113818

Subgroups — #26113818

Order 12032.

422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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#20253768C211yesmaximal, characteristic
2#20246569C211yesmaximal, characteristic
3#20241940C212yesmaximal
4#20241254C212yesmaximal
5C47×#1558C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689491—22no—
8#15689473C414yescomplemented
9#15689132—22no—
10C4×#10625329C2211yescharacteristic
11#15689030—22no—
12#15689009—24no—
13#15688991C2212yes—
14#15688861—24no—
15C2×C4⋊Q8×C47C2211yescharacteristic
16C47×#432C2212yes—
17C47×#333—22no—
18C2×#10625329—21no—
19#13094024C2×C412yes—
20#13094016—21no—
21#13094003—22no—
22C4×Dic94—22no—
23#13093983—21no—
24C2×C4⋊Dic47—22no—
25C2×C4×Dic47—22no—
26#13093948—28no—
27#13093935—21no—
28C4×C47⋊C8C2×C412yes—
29C47⋊#95—24no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C47⋊#95D414yes—
33C22×Q8×C47D412yes—
34C4⋊Q8×C47—22no—
35C4⋊Q8×C47C2×C412yes—
36C4⋊Q8×C47D412yes—
37C2×C4⋊C4×C47—22no—
38C2×C42×C47C2311yescharacteristic
39C4⋊C8×C47—22no—
40C22⋊C8×C47—22no—
41#97×C47—22no—
42C2×Q8×C47—22no—
43C2×Q8×C47—42no—
44C2×Q8×C47—42no—
45C2×Q8×C47C22⋊C414yes—
46C22×C4×C47—22no—
47C22×C4×C47C2×D411yescharacteristic
48C22×C4×C47C2×D412yes—
49C22×Dic47—24no—
50C2×Dic94—22no—
51C2×C8×C47—42no—
52C4⋊C4×C47—24no—
53C4⋊C4×C47—24no—
54C42×C47C22×C411yescharacteristic
55C42×C47C2×D411yescharacteristic
56C42×C47#4112yes—
57C22⋊Dic47—41no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47—82no—
61Dic47⋊C4—42no—
62C4×Dic47—41no—
63C4×Dic47—82no—
64#10625329—42no—
65C2×C47⋊C8—22no—
66C23×C47#12011yescharacteristic
67Q8×C47—44no—
68Q8×C47—82no—
69C2×C4×C47—22no—
70C2×C4×C47—24no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47C2×C22⋊C411yescharacteristic
75C2×C4×C47C4×D412yes—
76C2×C4×C47#12112yes—
77C2×C4×C47#12311yescharacteristic
78C2×Dic47—48no—
79C2×Dic47—42no—
80C2×Dic47—44no—
81Dic94—82no—
82C8×C47—82no—
83C47⋊C8—42no—
84#9426—471nomaximal, Sylow
85C22×C47—22no—
86C22×C47#38611yescharacteristic
87C22×C47#45512yes—
88C4×C47—21no—
89C4×C47—21no—
90C4×C47—22no—
91C4×C47—22no—
92C4×C47—44no—
93Dic47—84no—
94Dic47—82no—
95#3139—471no—
96#2381—471no—
97#1558D4711yescharacteristic
98#1515—472no—
99#1288—472no—
100C2×C47—22no—
101C2×C47#188511yescharacteristic
102C2×C47#190512yes—
103#533—471no—
104C2×C4⋊Q8C2×D4711yescharacteristic
105#491—942no—
106#487—474no—
107#432C2×D4712yes—
108#419—942no—
109C4×M16—471no—
110#391—942no—
111#387—944no—
112#383—472no—
113#333—22no—
114#328—944no—
115C47#942611yescharacteristic, complemented, Sylow
116C22×Q8D18812yes—
117C2×M16—941no—
118C4⋊Q8—22no—
119C4⋊Q8—472no—
120C4⋊Q8C4×D4712yes—
121C4⋊Q8C22⋊D4712yes—
122#125—941no—
123C22⋊Q8—942no—
124C4×Q8—942no—
125#117—941no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—942no—
128C2×C42—942no—
129C2×C42C22×D4711yescharacteristic
130C4⋊C8—22no—
131#103—948no—
132C22⋊C8—22no—
133#97—22no—
134#97—941no—
135C4×C8—472no—
136#95—474no—
137#95—944no—
138#95—942no—
139#95—942no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—942no—
144C2×Q8(C2×D47)⋊C414yes—
145C22×C4—22no—
146C22×C4—944no—
147C22×C4C2×D18811yescharacteristic
148C22×C4D4×D4712yes—
149M16—1882no—
150C2×C8—42no—
151C2×C8—942no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4—3762no—
157C4⋊C4—1882no—
158C22⋊C4—1881no—
159C42—3762no—
160C42—1881no—
161C42C2×C4×D4711yescharacteristic
162C42#1062535212yes—
163C42C2×C22⋊D4711yescharacteristic
164C23#1309399411yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—3762no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—1888no—
174C2×C4—1882no—
175C2×C4—1884no—
176C2×C4C2×(C2×D47)⋊C411yescharacteristic
177C2×C4(C22⋊D47)⋊C412yes—
178C2×C4#1309399612yes—
179C2×C4#1309400811yescharacteristic
180C8—82no—
181C8—1882no—
182C22—22no—
183C22#1568900011yescharacteristic
184C22#1568930312yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—3764no—
191C4—3762no—
192C2—22no—
193C2#2024377411yescharacteristic
194C2#2024388012yes—
subgroupG/H
centerC22#15689000
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1558C2
socleC22×C47#386
prime radicalC23×C47#120
cosocleC2×C42×C47C23
hypercenter#1558D47
hypocenterC47#9426
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
8. #15689473C4semidirect
115. C47#9426semidirect

Maximal subgroups

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

subgroupindex
#202537682
#202465692
#202419402
#202412542
C47×#15582
#942647