Finite Group Databasebeta

← #26129659

Subgroups — #26129659

Order 12032.

274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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#20245605C212yesmaximal
2#20244963C211yesmaximal, characteristic
3#20241376C212yesmaximal
4#20241339C211yesmaximal, characteristic
5C47×#3255C211yesmaximal, characteristic
6#15689172C2211yescharacteristic
7#15688945—22no—
8#15688939—22no—
9#15688905C2212yes—
10#15688895—21no—
11#15688883—21no—
12#15688880C2211yescharacteristic
13C47×#533—21no—
14C47×#475—22no—
15C47×#470—21no—
16C47×#470C2212yes—
17C47×#462—22no—
18C47×#423C2211yescharacteristic
19C2×#10625329—21no—
20#13093983—21no—
21#13093964—22no—
22#13093960—22no—
23C2×Q16×C47—21no—
24C2×Q16×C47D412yes—
25C2×M16×C47D411yescharacteristic
26C2×M16×C47C2311yescharacteristic
27C4⋊Q8×C47—21no—
28C4⋊Q8×C47—21no—
29#125×C47—41no—
30C22⋊Q8×C47—22no—
31C22⋊Q8×C47—41no—
32C4×Q8×C47—22no—
33C4×Q8×C47—41no—
34#117×C47—41no—
35C2×C42×C47D411yescharacteristic
36#106×C47—21no—
37#106×C47D412yes—
38C4⋊C8×C47—22no—
39#103×C47—22no—
40#103×C47—22no—
41C2×Q8×C47—22no—
42C2×Q8×C47—41no—
43C22×C4×C47—21no—
44C22×C4×C47C2×D411yescharacteristic
45Q16×C47—42no—
46Q16×C47—81no—
47M16×C47—41no—
48M16×C47—41no—
49C2×C8×C47—21no—
50C2×C8×C47C2×D412yes—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—41no—
53C4⋊C4×C47—41no—
54C4⋊C4×C47—42no—
55C4⋊C4×C47—41no—
56C4⋊C4×C47—42no—
57C22⋊C4×C47—42no—
58C42×C47—21no—
59C42×C47—42no—
60C42×C47SD1611yescharacteristic
61C42×C47SD1611yescharacteristic
62C22⋊Dic47—41no—
63C4⋊Dic47—41no—
64C4×Dic47—41no—
65#10625329—41no—
66#10625329—41no—
67C2×C47⋊C8—41no—
68C47⋊C16—42no—
69C23×C47AGL(1,ℤ/8)11yescharacteristic
70Q8×C47—42no—
71Q8×C47—42no—
72Q8×C47—82no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47#12011yescharacteristic
81C2×C4×C47C2×SD1611yescharacteristic
82C2×Dic47—81no—
83C8×C47—22no—
84C8×C47—41no—
85C47⋊C8—81no—
86#12308—471nomaximal, Sylow
87C22×C47—21no—
88C22×C47—41no—
89C22×C47#45011yescharacteristic
90C4×C47—22no—
91C4×C47—21no—
92C4×C47—41no—
93C4×C47—82no—
94C4×C47—82no—
95C4×C47#45411yescharacteristic
96C4×C47#45811yescharacteristic
97Dic47—161no—
98#3255D4711yescharacteristic
99#2239—472no—
100#2102—471no—
101#1340—472no—
102#1327—471no—
103C2×C47—21no—
104C2×C47—41no—
105C2×C47#161611yescharacteristic
106#533—21no—
107#475—22no—
108#470—21no—
109#470C2×D4712yes—
110#462—22no—
111#430—471no—
112#423C2×D4711yescharacteristic
113#365—942no—
114#362—942no—
115#349—472no—
116#344—941no—
117#339—941no—
118H(3,ℤ/4)—471no—
119C47#1230811yescharacteristic, complemented, Sylow
120C2×Q16—21no—
121C2×Q16C22⋊D4712yes—
122C2×M16—941no—
123C2×M16C22⋊D4711yescharacteristic
124C2×M16C22×D4711yescharacteristic
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127#125—41no—
128C22⋊Q8—22no—
129C22⋊Q8—41no—
130C4×Q8—22no—
131C4×Q8—41no—
132#117—41no—
133#117—941no—
134C2×C42C22⋊D4711yescharacteristic
135M32—942no—
136#108—942no—
137#106—21no—
138#106C22⋊D4712yes—
139C4⋊C8—22no—
140#103—22no—
141#103—22no—
142C2×Q8—22no—
143C2×Q8—41no—
144C22×C4—21no—
145C22×C4C2×C22⋊D4711yescharacteristic
146Q16—42no—
147Q16—81no—
148M16—41no—
149M16—41no—
150M16—1881no—
151M16—1881no—
152C2×C8—21no—
153C2×C8—1881no—
154C2×C8C2×C22⋊D4712yes—
155C4⋊C4—22no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—1881no—
162C22⋊C4—42no—
163C22⋊C4—1881no—
164C42—21no—
165C42—42no—
166C42—1881no—
167C42#1062533511yescharacteristic
168C42#1062533511yescharacteristic
169C16—1882no—
170C23#1309405011yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—3761no—
182C2×C4#1309399311yescharacteristic
183C2×C4C2×#1062533511yescharacteristic
184C8—22no—
185C8—41no—
186C8—3761no—
187C22—21no—
188C22—41no—
189C22#1568927411yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—82no—
194C4—82no—
195C4—7521no—
196C4#1568929611yescharacteristic
197C4#1568931311yescharacteristic
198C2—21no—
199C2—41no—
200C2#2024242511yescharacteristic
subgroupG/H
centerC2#20242425
commutator, cosocleC2×M16×C47C23
FrattiniC2×M16C22×D47
FittingC47×#3255C2
socleC2×C47#1616
prime radicalC23×C47AGL(1,ℤ/8)
hypercenter#3255D47
hypocenterC47#12308
LCSG ▷ C2×M16×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3255

Complements

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

NH ≅ G/Ntype
119. C47#12308semidirect

Maximal subgroups

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

subgroupindex
#202456052
#202449632
#202413762
#202413392
C47×#32552
#1230847