Finite Group Databasebeta

← #26120441

Subgroups — #26120441

Order 12032.

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

normal subgroups only

This group has 342 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#20243562C211yesmaximal, characteristic
3#20242119C212yesmaximal
4#20242004C212yesmaximal
5C47×#1307C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689409—22no—
8#15689381—22no—
9#15689334—22no—
10C2×#13093959—22no—
11#15689147C2211yescharacteristic
12C2×#13093935C2211yescharacteristic
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#13093959—44no—
30#13093956—22no—
31C4⋊(C47⋊C8)—22no—
32#13093949—24no—
33#13093935—21no—
34#13093935D412yes—
35C2×M16×C47D412yes—
36C2×C42×C47C2311yescharacteristic
37C4⋊C8×C47—22no—
38C4⋊C8×C47—22no—
39C22⋊C8×C47—22no—
40#97×C47—22no—
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47#4112yes—
43C2×Dic94—22no—
44C2×Dic94—22no—
45M16×C47—42no—
46C2×C8×C47—22no—
47C2×C8×C47—42no—
48C42×C47C2×D412yes—
49C42×C47C2×D411yescharacteristic
50C42×C47#4111yescharacteristic
51C22⋊Dic47—42no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56Dic47⋊C4—42no—
57Dic47⋊C4—42no—
58C4×Dic47—42no—
59#10625329—42no—
60C2×C47⋊C8—22no—
61C2×C47⋊C8—22no—
62C2×C47⋊C8—22no—
63C2×C47⋊C8—41no—
64Dic188—82no—
65C23×C47#12411yescharacteristic
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—42no—
69C2×C4×C47#12011yescharacteristic
70C2×C4×C47#12112yes—
71C2×C4×C47#12111yescharacteristic
72C2×C4×C47#12312yes—
73C2×Dic47—42no—
74C2×Dic47—42no—
75Dic94—42no—
76Dic94—42no—
77Dic94—82no—
78C8×C47—42no—
79C8×C47—82no—
80C47⋊C8—24no—
81C47⋊C8—81no—
82#10528—471nomaximal, Sylow
83C22×C47—22no—
84C22×C47—21no—
85C22×C47#39411yescharacteristic
86C4×C47—22no—
87C4×C47—22no—
88C4×C47—21no—
89C4×C47#45311yescharacteristic
90C4×C47#45611yescharacteristic
91Dic47—82no—
92Dic47—82no—
93#3255—471no—
94#1849—471no—
95#1559—472no—
96#1531—472no—
97#1307D4711yescharacteristic
98C2×C47—41no—
99C2×C47#203911yescharacteristic
100C2×C47#204912yes—
101#533—472no—
102#475—942no—
103#470—942no—
104#462—942no—
105#432C2×D4712yes—
106C2×#108—942no—
107#423—471no—
108#423C2×D4711yescharacteristic
109C2×#97—471no—
110#333—942no—
111#332—942no—
112#330—944no—
113C47#1052811yescharacteristic, complemented, Sylow
114C2×Q16—942no—
115C2×M16—941no—
116C2×M16D18812yes—
117C22×C8—941no—
118C4⋊Q8—472no—
119C4⋊Q8—472no—
120#125—942no—
121C22⋊Q8—942no—
122C22⋊Q8—942no—
123C4×Q8—942no—
124C4×Q8—942no—
125#117—942no—
126C2×C42C22×D4711yescharacteristic
127#108—1884no—
128#106—942no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—942no—
132#103—944no—
133C22⋊C8—22no—
134#97—22no—
135#97—472no—
136#97—941no—
137C2×Q8—942no—
138C2×Q8—942no—
139C22×C4C2×D18811yescharacteristic
140C22×C4#1062535012yes—
141Q16—3762no—
142M16—42no—
143M16—1882no—
144C2×C8—22no—
145C2×C8—42no—
146C2×C8—942no—
147C2×C8—942no—
148C2×C8—942no—
149C2×C8—1881no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—1882no—
155C4⋊C4—1882no—
156C22⋊C4—1882no—
157C42—1882no—
158C42D4×D4712yes—
159C42D4×D4711yescharacteristic
160C42#1062535411yescharacteristic
161C23#1309401211yescharacteristic
162Q8—3762no—
163Q8—1882no—
164Q8—1882no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4#1309399411yescharacteristic
171C2×C4#1309399712yes—
172C2×C4#1309399911yescharacteristic
173C2×C4#1309400912yes—
174C8—42no—
175C8—82no—
176C8—944no—
177C8—3761no—
178C22—21no—
179C22—22no—
180C22#1568904111yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—3762no—
185C4—3762no—
186C4#1568929311yescharacteristic
187C4#1568930811yescharacteristic
188C2—41no—
189C2#2024461311yescharacteristic
190C2#2024467112yes—
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1307C2
socleC22×C47#394
prime radicalC23×C47#124
hypercenter#1307D47
hypocenterC47#10528
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
113. C47#10528semidirect

Maximal subgroups

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

subgroupindex
#202547822
#202435622
#202421192
#202420042
C47×#13072
#1052847