Finite Group Databasebeta

← #26120446

Subgroups — #26120446

Order 12032.

326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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#20254782C211yesmaximal, characteristic
2#20243528C211yesmaximal, characteristic
3#20242119C212yesmaximal
4#20242004C212yesmaximal
5C47×#1307C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689409—22no—
8#15689381—22no—
9#15689334—22no—
10#15689147C2211yescharacteristic
11C2×#13093935C2211yescharacteristic
12#15688887—22no—
13#15688871—22no—
14#15688868—22no—
15#15688864—24no—
16C47×#432C2212yes—
17C47×#423C2211yescharacteristic
18C2×Dic188—22no—
19C2×#10625329—21no—
20C22×C47⋊C8—21no—
21#13094024D412yes—
22#13094024D412yes—
23#13094016—22no—
24#13094003—22no—
25#13094003—22no—
26C4×Dic94—22no—
27C4×Dic94—22no—
28#13093983—22no—
29#13093956—22no—
30C4⋊(C47⋊C8)—22no—
31#13093949—24no—
32#13093935—21no—
33#13093935D412yes—
34C2×M16×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36C4⋊C8×C47—22no—
37C4⋊C8×C47—22no—
38C22⋊C8×C47—22no—
39#97×C47—22no—
40C22×C4×C47C2×D411yescharacteristic
41C22×C4×C47#4112yes—
42C2×Dic94—22no—
43C2×Dic94—22no—
44M16×C47—42no—
45C2×C8×C47—22no—
46C2×C8×C47—42no—
47C42×C47C2×D412yes—
48C42×C47C2×D411yescharacteristic
49C42×C47#4111yescharacteristic
50C22⋊Dic47—42no—
51C4⋊Dic47—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55Dic47⋊C4—42no—
56Dic47⋊C4—42no—
57C4×Dic47—42no—
58#10625329—42no—
59C2×C47⋊C8—22no—
60C2×C47⋊C8—41no—
61C2×C47⋊C8—41no—
62C2×C47⋊C8—41no—
63Dic188—82no—
64C23×C47#12411yescharacteristic
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—42no—
68C2×C4×C47#12011yescharacteristic
69C2×C4×C47#12112yes—
70C2×C4×C47#12111yescharacteristic
71C2×C4×C47#12312yes—
72C2×Dic47—42no—
73C2×Dic47—42no—
74Dic94—42no—
75Dic94—42no—
76Dic94—82no—
77C8×C47—42no—
78C8×C47—82no—
79C47⋊C8—42no—
80C47⋊C8—81no—
81#10529—471nomaximal, Sylow
82C22×C47—22no—
83C22×C47—21no—
84C22×C47#39411yescharacteristic
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—21no—
88C4×C47#45411yescharacteristic
89C4×C47#45511yescharacteristic
90Dic47—82no—
91Dic47—82no—
92#3255—471no—
93#1838—471no—
94#1559—472no—
95#1531—472no—
96#1307D4711yescharacteristic
97C2×C47—41no—
98C2×C47#204011yescharacteristic
99C2×C47#204912yes—
100#533—472no—
101#475—942no—
102#470—942no—
103#462—942no—
104#432C2×D4712yes—
105#423—471no—
106#423C2×D4711yescharacteristic
107C2×#97—471no—
108#341—942no—
109#333—942no—
110#332—942no—
111#330—944no—
112C47#1052911yescharacteristic, complemented, Sylow
113C2×Q16—942no—
114C2×M16—941no—
115C2×M16D18812yes—
116C22×C8—941no—
117C4⋊Q8—472no—
118C4⋊Q8—472no—
119#125—942no—
120C22⋊Q8—942no—
121C22⋊Q8—942no—
122C4×Q8—942no—
123C4×Q8—942no—
124#117—942no—
125C2×C42C22×D4711yescharacteristic
126#106—942no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—942no—
130#103—944no—
131C22⋊C8—22no—
132#97—22no—
133#97—472no—
134#97—941no—
135C2×Q8—942no—
136C2×Q8—942no—
137C22×C4C2×D18811yescharacteristic
138C22×C4#1062535012yes—
139Q16—3762no—
140M16—42no—
141M16—1882no—
142C2×C8—22no—
143C2×C8—42no—
144C2×C8—942no—
145C2×C8—1881no—
146C2×C8—1881no—
147C2×C8—1881no—
148C4⋊C4—942no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—1882no—
153C4⋊C4—1882no—
154C22⋊C4—1882no—
155C42—1882no—
156C42D4×D4712yes—
157C42D4×D4711yescharacteristic
158C42#1062535411yescharacteristic
159C23#1309401211yescharacteristic
160Q8—3762no—
161Q8—1882no—
162Q8—1882no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—1882no—
167C2×C4—1882no—
168C2×C4#1309399411yescharacteristic
169C2×C4#1309399712yes—
170C2×C4#1309399911yescharacteristic
171C2×C4#1309400912yes—
172C8—42no—
173C8—82no—
174C8—3761no—
175C8—1882no—
176C22—21no—
177C22—22no—
178C22#1568904111yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—3762no—
183C4—3762no—
184C4#1568929811yescharacteristic
185C4#1568930311yescharacteristic
186C2—41no—
187C2#2024461811yescharacteristic
188C2#2024467112yes—
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1307C2
socleC22×C47#394
prime radicalC23×C47#124
hypercenter#1307D47
hypocenterC47#10529
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
112. C47#10529semidirect

Maximal subgroups

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

subgroupindex
#202547822
#202435282
#202421192
#202420042
C47×#13072
#1052947