Finite Group Databasebeta

← #26111592

Subgroups — #26111592

Order 12032.

404 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 103 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#20252490C211yesmaximal, characteristic
3#20241810C212yesmaximal
4#20241226C212yesmaximal
5C47×#1526C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689526C412yes—
8#15689522—22no—
9#15689519C412yes—
10#15689254—22no—
11Q8×C47⋊C8—22no—
12#15689184—22no—
13#15689176C2212yes—
14#15689159—22no—
15C2×C4×C47⋊C8C2211yescharacteristic
16#15688855—22no—
17#15688855—22no—
18C47×#533C2211yescharacteristic
19C4×M16×C47C2212yes—
20C47×#330—22no—
21C22×C47⋊C8—21no—
22#13094024C2×C412yes—
23#13094016—21no—
24#13094003—22no—
25C4×Dic94—22no—
26#13093983—21no—
27#13093957—24no—
28#13093955—24no—
29C4⋊(C47⋊C8)—24no—
30C4⋊(C47⋊C8)D412yes—
31C4⋊(C47⋊C8)D412yes—
32C22⋊(C47⋊C8)—22no—
33#13093935—22no—
34C4×C47⋊C8—22no—
35C4×C47⋊C8—22no—
36C4×C47⋊C8—21no—
37C4×C47⋊C8C2×C411yescharacteristic
38C4×C47⋊C8C2×C411yescharacteristic
39C2×M16×C47—22no—
40C4⋊Q8×C47C2×C412yes—
41#125×C47D412yes—
42C22⋊Q8×C47—22no—
43C4×Q8×C47—22no—
44#117×C47D412yes—
45C2×C42×C47C2311yescharacteristic
46#97×C47—22no—
47C4×C8×C47—22no—
48C2×Q8×C47—22no—
49C22×C4×C47C2×D411yescharacteristic
50C22×C4×C47#4112yes—
51C2×Dic94—22no—
52M16×C47—24no—
53M16×C47—42no—
54C2×C8×C47—42no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—24no—
57C4⋊C4×C47C22⋊C414yes—
58C22⋊C4×C47—22no—
59C42×C47—22no—
60C42×C47C22×C411yescharacteristic
61C42×C47C2×D411yescharacteristic
62C42×C47C2×D412yes—
63C22⋊Dic47—41no—
64C4⋊Dic47—22no—
65C4⋊Dic47—22no—
66Dic47⋊C4—42no—
67C4×Dic47—41no—
68C2×C47⋊C8—24no—
69C2×C47⋊C8—21no—
70C2×C47⋊C8—21no—
71C2×C47⋊C8—22no—
72C2×C47⋊C8—22no—
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—44no—
88C47⋊C8—22no—
89C47⋊C8—22no—
90C47⋊C8—42no—
91C47⋊C8—42no—
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#2986—471no—
105#1526D4711yescharacteristic
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—942no—
117C8×Q8—942no—
118#433—942no—
119#431—472no—
120#427—942no—
121C4×M16C2×D4712yes—
122C2×C4×C8—471no—
123#330—22no—
124Q8⋊C8—942no—
125Q8⋊C8—942no—
126C47#906811yescharacteristic, complemented, Sylow
127C2×M16—22no—
128C22×C8—941no—
129C4⋊Q8—472no—
130C4⋊Q8C4×D4712yes—
131#125—941no—
132#125C22⋊D4712yes—
133C22⋊Q8—22no—
134C22⋊Q8—942no—
135C4×Q8—22no—
136C4×Q8—942no—
137#117—941no—
138#117D18812yes—
139C2×C42C22×D4711yescharacteristic
140#107—944no—
141#106—944no—
142C4⋊C8—472no—
143C4⋊C8—472no—
144C4⋊C8—944no—
145C22⋊C8—942no—
146#97—22no—
147#97—942no—
148C4×C8—22no—
149C4×C8—471no—
150C4×C8—471no—
151C4×C8—942no—
152C4×C8—942no—
153C4×C8—941no—
154C2×Q8—22no—
155C2×Q8—942no—
156C22×C4C2×D18811yescharacteristic
157C22×C4#1062535212yes—
158M16—24no—
159M16—42no—
160C2×C8—42no—
161C2×C8—944no—
162C2×C8—941no—
163C2×C8—941no—
164C2×C8—942no—
165C2×C8—942no—
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
177C42D4×D4712yes—
178C42C2×C22⋊D4711yescharacteristic
179C23#1309400811yescharacteristic
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×C4(C22⋊D47)⋊C412yes—
191C2×C4#1309399411yescharacteristic
192C2×C4#1309399612yes—
193C8—44no—
194C8—942no—
195C8—942no—
196C8—1882no—
197C8—1882no—
198C22—22no—
199C22—21no—
200C22#1568900011yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—3762no—
205C4#1568923712yes—
206C4#1568924212yes—
207C4#1568930812yes—
208C2—41no—
209C2#2024371312yes—
210C2#2024377911yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1526C2
socleC22×C47#386
prime radicalC23×C47#123
cosocleC2×C42×C47C23
hypercenter#1526D47
hypocenterC47#9068
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

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
#202524902
#202418102
#202412262
C47×#15262
#906847