Finite Group Databasebeta

← #26113882

Subgroups — #26113882

Order 12032.

400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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#20242126C211yesmaximal, characteristic
3#20242072C212yesmaximal
4#20241279C212yesmaximal
5C47×#2986C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689493C414yes—
8#15689475—22no—
9#15689147C2212yes—
10#15689131—22no—
11C4×#10625329C2211yescharacteristic
12#15688870—22no—
13#15688870—22no—
14#15688869—22no—
15C47×#533C2211yescharacteristic
16C47×#446—22no—
17C8×Q8×C47—22no—
18C47×#433—22no—
19C47×#431C2212yes—
20C22×Dic94—21no—
21C2×#10625329—21no—
22C2×#10625329—22no—
23#13094024—22no—
24#13094024—21no—
25#13094024C2×C412yes—
26C2×C4⋊Dic47—22no—
27C4⋊(C47⋊C8)—22no—
28C4⋊(C47⋊C8)—22no—
29#13093947—28no—
30#13093935C2×C412yes—
31C4×C47⋊C8—21no—
32C4⋊Q8×C47D412yes—
33#125×C47C2×C412yes—
34C22⋊Q8×C47—22no—
35C4×Q8×C47—22no—
36#117×C47D412yes—
37C2×C42×C47C2311yescharacteristic
38C4⋊C8×C47—24no—
39C4⋊C8×C47D412yes—
40C4⋊C8×C47D412yes—
41C22⋊C8×C47—22no—
42#97×C47—22no—
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—
52C2×C8×C47—22no—
53C2×C8×C47—22no—
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—
65#10625329—82no—
66C2×C47⋊C8—22no—
67C2×C47⋊C8—42no—
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—42no—
84C8×C47—42no—
85C47⋊C8—42no—
86C47⋊C8—82no—
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#2986D4711yescharacteristic
100#1561—471no—
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—22no—
111C8×Q8—22no—
112#433—22no—
113#431C2×D4712yes—
114#423—472no—
115#419—942no—
116C4×M16—471no—
117#332—942no—
118#332—942no—
119#332—942no—
120C47#943611yescharacteristic, complemented, Sylow
121C22×Q8—941no—
122C2×M16—941no—
123C2×M16—942no—
124C4⋊Q8—472no—
125C4⋊Q8—941no—
126C4⋊Q8—942no—
127C4⋊Q8D18812yes—
128#125C4×D4712yes—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117C22⋊D4712yes—
132C2×C4⋊C4—942no—
133C2×C42C22×D4711yescharacteristic
134C4⋊C8—24no—
135C4⋊C8—942no—
136C4⋊C8—942no—
137C4⋊C8C22⋊D4712yes—
138C4⋊C8C22⋊D4712yes—
139#103—948no—
140C22⋊C8—22no—
141#97—22no—
142#97—472no—
143C4×C8—22no—
144C4×C8—22no—
145C4×C8—941no—
146C2×Q8—22no—
147C2×Q8—942no—
148C2×Q8—1884no—
149C2×Q8—1881no—
150C22×C4—1881no—
151C22×C4#1062535012yes—
152C22×C4C2×C22⋊D4711yescharacteristic
153M16—3762no—
154M16—1882no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—942no—
158C2×C8—1882no—
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
167C42C2×D18811yescharacteristic
168C42C2×C22⋊D4712yes—
169C23#1309400711yescharacteristic
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×C4C4×C22⋊D4712yes—
182C2×C4#1309399311yescharacteristic
183C2×C4#1309399812yes—
184C8—42no—
185C8—42no—
186C8—3762no—
187C8—1882no—
188C22—21no—
189C22—22no—
190C22#1568900211yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—3762no—
195C4#1568929612yes—
196C4#1568938612yes—
197C4#1568939812yes—
198C2—41no—
199C2#2024379111yescharacteristic
200C2#2024390312yes—
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2986C2
socleC22×C47#386
prime radicalC23×C47#123
cosocleC2×C42×C47C23
hypercenter#2986D47
hypocenterC47#9436
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2986

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
#202421262
#202420722
#202412792
C47×#29862
#943647