Finite Group Databasebeta

← #26113880

Subgroups — #26113880

Order 12032.

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

normal subgroups only

This group has 400 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#20253770C211yesmaximal, characteristic
2#20252490C211yesmaximal, characteristic
3#20242074C212yesmaximal
4#20241277C212yesmaximal
5C47×#1561C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689493C414yes—
8#15689475—22no—
9#15689254—22no—
10Q8×C47⋊C8—22no—
11#15689184—22no—
12#15689176C2212yes—
13#15689131—22no—
14C4×#10625329C2211yescharacteristic
15#15688868—22no—
16#15688868—22no—
17C47×#533C2211yescharacteristic
18C47×#423C2212yes—
19C47×#332—22no—
20C22×Dic94—21no—
21C2×#10625329—21no—
22#13094024—22no—
23#13094024—21no—
24#13094024C2×C412yes—
25C2×C4⋊Dic47—22no—
26C4⋊(C47⋊C8)—24no—
27C4⋊(C47⋊C8)D412yes—
28C4⋊(C47⋊C8)D412yes—
29#13093947—28no—
30C22⋊(C47⋊C8)—22no—
31#13093935—22no—
32#13093935C2×C412yes—
33C4×C47⋊C8—22no—
34C4×C47⋊C8—21no—
35C4×C47⋊C8—22no—
36C2×M16×C47—22no—
37C4⋊Q8×C47D412yes—
38#125×C47C2×C412yes—
39C22⋊Q8×C47—22no—
40C4×Q8×C47—22no—
41#117×C47D412yes—
42C2×C42×C47C2311yescharacteristic
43C4⋊C8×C47—22no—
44C4⋊C8×C47—22no—
45C2×Q8×C47—22no—
46C22×C4×C47C2×D411yescharacteristic
47C22×C4×C47#4112yes—
48C22×Dic47—41no—
49C2×Dic94—22no—
50C2×Dic94—44no—
51C2×Dic94—41no—
52M16×C47—82no—
53C2×C8×C47—42no—
54C4⋊C4×C47—24no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47C22⋊C414yes—
57C22⋊C4×C47—22no—
58C42×C47—22no—
59C42×C47C22×C411yescharacteristic
60C42×C47C2×D411yescharacteristic
61C42×C47C2×D412yes—
62C4⋊Dic47—24no—
63C4⋊Dic47—42no—
64#10625329—42no—
65C2×C47⋊C8—22no—
66C2×C47⋊C8—22no—
67C2×C47⋊C8—22no—
68C23×C47#12311yescharacteristic
69Q8×C47—42no—
70Q8×C47—42no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47C2×C22⋊C411yescharacteristic
76C2×C4×C47C4×D412yes—
77C2×C4×C47#12011yescharacteristic
78C2×C4×C47#12112yes—
79C2×Dic47—42no—
80C2×Dic47—82no—
81Dic94—44no—
82Dic94—82no—
83C8×C47—82no—
84C47⋊C8—42no—
85C47⋊C8—42no—
86C47⋊C8—42no—
87#9436—471nomaximal, Sylow
88C22×C47—21no—
89C22×C47—22no—
90C22×C47#38611yescharacteristic
91C4×C47—21no—
92C4×C47—22no—
93C4×C47—44no—
94C4×C47#45412yes—
95C4×C47#47112yes—
96C4×C47#47312yes—
97Dic47—82no—
98#3139—471no—
99#2986—471no—
100#1561D4711yescharacteristic
101#1549—472no—
102#1299—472no—
103C2×C47—41no—
104C2×C47#188811yescharacteristic
105C2×C47#190812yes—
106#533C2×D4711yescharacteristic
107C2×C4⋊Q8—471no—
108#491—474no—
109#487—942no—
110#446—942no—
111C8×Q8—942no—
112#433—942no—
113#431—472no—
114#423C2×D4712yes—
115#419—942no—
116C4×M16—471no—
117#332—22no—
118#332—942no—
119#332—942no—
120C47#943611yescharacteristic, complemented, Sylow
121C22×Q8—941no—
122C2×M16—22no—
123C2×M16—941no—
124C4⋊Q8—472no—
125C4⋊Q8—942no—
126C4⋊Q8—941no—
127C4⋊Q8C22⋊D4712yes—
128#125C4×D4712yes—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117D18812yes—
132C2×C4⋊C4—942no—
133C2×C42C22×D4711yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—472no—
137C4⋊C8—472no—
138C4⋊C8—944no—
139#103—948no—
140C22⋊C8—942no—
141#97—472no—
142#97—942no—
143C4×C8—942no—
144C4×C8—942no—
145C4×C8—941no—
146C2×Q8—22no—
147C2×Q8—942no—
148C2×Q8—1884no—
149C2×Q8—1881no—
150C22×C4—1881no—
151C22×C4C2×D18811yescharacteristic
152C22×C4#1062535212yes—
153M16—82no—
154M16—1882no—
155C2×C8—42no—
156C2×C8—942no—
157C2×C8—942no—
158C2×C8—942no—
159C4⋊C4—24no—
160C4⋊C4—22no—
161C4⋊C4—944no—
162C4⋊C4—1882no—
163C4⋊C4(C2×D47)⋊C414yes—
164C22⋊C4—22no—
165C42—22no—
166C42C2×C4×D4711yescharacteristic
167C42D4×D4712yes—
168C42C2×C22⋊D4711yescharacteristic
169C23#1309400811yescharacteristic
170Q8—42no—
171Q8—42no—
172Q8—3762no—
173Q8—1884no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—3762no—
179C2×C4—1882no—
180C2×C4C2×(C2×D47)⋊C411yescharacteristic
181C2×C4(C22⋊D47)⋊C412yes—
182C2×C4#1309399411yescharacteristic
183C2×C4#1309399612yes—
184C8—82no—
185C8—1882no—
186C8—1882no—
187C8—1882no—
188C22—21no—
189C22—22no—
190C22#1568900011yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—3762no—
195C4#1568929812yes—
196C4#1568938412yes—
197C4#1568939612yes—
198C2—41no—
199C2#2024378911yescharacteristic
200C2#2024390112yes—
subgroupG/H
centerC22#15689000
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1561C2
socleC22×C47#386
prime radicalC23×C47#123
cosocleC2×C42×C47C23
hypercenter#1561D47
hypocenterC47#9436
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
120. C47#9436semidirect

Maximal subgroups

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

subgroupindex
#202537702
#202524902
#202420742
#202412772
C47×#15612
#943647