Finite Group Databasebeta

← #26111594

Subgroups — #26111594

Order 12032.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#20253898C211yesmaximal, characteristic
2#20241983C211yesmaximal, characteristic
3#20241808C212yesmaximal
4#20241224C212yesmaximal
5C47×#2986C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689526C412yes—
8#15689522—22no—
9#15689519C412yes—
10#15689159—22no—
11C4×#10625329C2212yes—
12C2×C4×C47⋊C8C2211yescharacteristic
13#15688865—22no—
14#15688853—22no—
15#15688853—22no—
16C47×#533C2211yescharacteristic
17C47×#446—22no—
18C8×Q8×C47—22no—
19C47×#433—22no—
20C47×#431C2212yes—
21C2×#10625329—22no—
22C22×C47⋊C8—21no—
23#13094024C2×C412yes—
24#13094016—21no—
25#13094003—22no—
26C4×Dic94—22no—
27#13093983—21no—
28#13093957—24no—
29#13093955—24no—
30#13093935—22no—
31C4×C47⋊C8—21no—
32C4×C47⋊C8—22no—
33C4×C47⋊C8C2×C411yescharacteristic
34C4×C47⋊C8C2×C411yescharacteristic
35C4⋊Q8×C47C2×C412yes—
36#125×C47D412yes—
37C22⋊Q8×C47—22no—
38C4×Q8×C47—22no—
39#117×C47D412yes—
40C2×C42×C47C2311yescharacteristic
41C4⋊C8×C47—24no—
42C4⋊C8×C47D412yes—
43C4⋊C8×C47D412yes—
44C22⋊C8×C47—22no—
45#97×C47—22no—
46C4×C8×C47—22no—
47C4×C8×C47—22no—
48C2×Q8×C47—22no—
49C22×C4×C47C2×D411yescharacteristic
50C22×C4×C47#4112yes—
51C2×Dic94—22no—
52C2×C8×C47—22no—
53C2×C8×C47—22no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—24no—
56C4⋊C4×C47C22⋊C414yes—
57C22⋊C4×C47—22no—
58C42×C47—22no—
59C42×C47C22×C411yescharacteristic
60C42×C47C2×D411yescharacteristic
61C42×C47C2×D412yes—
62C22⋊Dic47—41no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65Dic47⋊C4—42no—
66C4×Dic47—41no—
67#10625329—24no—
68#10625329—42no—
69C2×C47⋊C8—24no—
70C2×C47⋊C8—21no—
71C2×C47⋊C8—21no—
72C2×C47⋊C8—42no—
73C23×C47#12311yescharacteristic
74Q8×C47—42no—
75Q8×C47—42no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—24no—
80C2×C4×C47C2×C22⋊C411yescharacteristic
81C2×C4×C47C4×D412yes—
82C2×C4×C47#12011yescharacteristic
83C2×C4×C47#12112yes—
84C2×Dic47—42no—
85Dic94—42no—
86Dic94—42no—
87C8×C47—42no—
88C8×C47—42no—
89C47⋊C8—22no—
90C47⋊C8—22no—
91C47⋊C8—44no—
92#9068—471nomaximal, Sylow
93C22×C47—22no—
94C22×C47—21no—
95C22×C47#38611yescharacteristic
96C4×C47—22no—
97C4×C47—21no—
98C4×C47—44no—
99C4×C47#44312yes—
100C4×C47#44412yes—
101C4×C47#45612yes—
102Dic47—82no—
103#3160—471no—
104#2986D4711yescharacteristic
105#1526—471no—
106#1485—472no—
107#1278—472no—
108C2×C47—41no—
109C2×C47#187612yes—
110C2×C47#188611yescharacteristic
111#533—471no—
112#533C2×D4711yescharacteristic
113#500—472no—
114#499—942no—
115#498—472no—
116#446—22no—
117C8×Q8—22no—
118#433—22no—
119#431C2×D4712yes—
120#427—942no—
121C4×M16—472no—
122C2×C4×C8—471no—
123#330—942no—
124Q8⋊C8—942no—
125Q8⋊C8—942no—
126C47#906811yescharacteristic, complemented, Sylow
127C2×M16—942no—
128C22×C8—941no—
129C4⋊Q8—472no—
130C4⋊Q8C4×D4712yes—
131#125—941no—
132#125D18812yes—
133C22⋊Q8—22no—
134C22⋊Q8—942no—
135C4×Q8—22no—
136C4×Q8—942no—
137#117—941no—
138#117C22⋊D4712yes—
139C2×C42C22×D4711yescharacteristic
140#107—944no—
141#106—944no—
142C4⋊C8—24no—
143C4⋊C8C22⋊D4712yes—
144C4⋊C8C22⋊D4712yes—
145C22⋊C8—22no—
146#97—22no—
147#97—942no—
148C4×C8—22no—
149C4×C8—22no—
150C4×C8—471no—
151C4×C8—471no—
152C4×C8—941no—
153C4×C8—942no—
154C2×Q8—22no—
155C2×Q8—942no—
156C22×C4#1062535012yes—
157C22×C4C2×C22⋊D4711yescharacteristic
158M16—944no—
159M16—1882no—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—944no—
163C2×C8—941no—
164C2×C8—941no—
165C2×C8—1882no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C4⋊C4—1882no—
171C4⋊C4(C2×D47)⋊C414yes—
172C22⋊C4—22no—
173C22⋊C4—1881no—
174C42—22no—
175C42—1881no—
176C42C2×C4×D4711yescharacteristic
177C42C2×D18811yescharacteristic
178C42C2×C22⋊D4712yes—
179C23#1309400711yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—1882no—
183Q8—1882no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—1882no—
189C2×C4C2×(C2×D47)⋊C411yescharacteristic
190C2×C4C4×C22⋊D4712yes—
191C2×C4#1309399311yescharacteristic
192C2×C4#1309399812yes—
193C8—42no—
194C8—42no—
195C8—942no—
196C8—942no—
197C8—1884no—
198C22—22no—
199C22—21no—
200C22#1568900211yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—3762no—
205C4#1568923812yes—
206C4#1568924312yes—
207C4#1568930612yes—
208C2—41no—
209C2#2024371512yes—
210C2#2024378111yescharacteristic
subgroupG/H
centerC2×C4#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2986C2
socleC22×C47#386
prime radicalC23×C47#123
cosocleC2×C42×C47C23
hypercenter#2986D47
hypocenterC47#9068
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
126. C47#9068semidirect

Maximal subgroups

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

subgroupindex
#202538982
#202419832
#202418082
#202412242
C47×#29862
#906847