Finite Group Databasebeta

← #26119004

Subgroups — #26119004

Order 12032.

504 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 113 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#20254541C212yesmaximal
2#20251766C211yesmaximal, characteristic
3#20244365C211yesmaximal, characteristic
4#20242072C212yesmaximal
5C47×#1276C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7C2×#13094024C2212yes—
8#15689528—22no—
9#15689474—22no—
10#15689459—24no—
11#15689419—24no—
12#15689147C2211yescharacteristic
13#15689029—24no—
14#15688989—22no—
15#15688883—22no—
16#15688870—24no—
17C47×#431C2212yes—
18C43×C47C2211yescharacteristic
19C22×Dic94—22no—
20C2×#10625329—21no—
21#13094024—22no—
22#13094024—22no—
23#13094024—22no—
24#13094024—22no—
25#13094024D412yes—
26#13094016—21no—
27#13094003—22no—
28C4×Dic94—22no—
29#13093983—21no—
30C2×C4⋊Dic47—22no—
31C2×C4⋊Dic47D414yes—
32#13093958—28no—
33C4⋊(C47⋊C8)—22no—
34#13093949—28no—
35C47⋊#95—28no—
36C2×C42×C47—22no—
37C2×C42×C47D412yes—
38C2×C42×C47C2311yescharacteristic
39C4⋊C8×C47D414yes—
40C22⋊C8×C47—22no—
41C4×C8×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47C2×D412yes—
44C22×C4×C47C2×D411yescharacteristic
45C22×Dic47—24no—
46C2×Dic94—22no—
47C2×Dic94—48no—
48C2×Dic94—42no—
49C2×Dic94—42no—
50C2×C8×C47—24no—
51C42×C47—22no—
52C42×C47—44no—
53C42×C47Q1614yes—
54C42×C47C2×D411yescharacteristic
55C42×C47C2×D412yes—
56C42×C47#4111yescharacteristic
57C22⋊Dic47—41no—
58C4⋊Dic47—24no—
59C4⋊Dic47—22no—
60C4⋊Dic47—24no—
61C4⋊Dic47—22no—
62C4⋊Dic47—42no—
63C4⋊Dic47—42no—
64Dic47⋊C4—42no—
65C4×Dic47—41no—
66#10625329—42no—
67C2×C47⋊C8—41no—
68C23×C47#12011yescharacteristic
69C2×C4×C47—24no—
70C2×C4×C47—24no—
71C2×C4×C47—44no—
72C2×C4×C47#12012yes—
73C2×C4×C47#12112yes—
74C2×C4×C47#12111yescharacteristic
75C2×C4×C47#12711yescharacteristic
76C2×C4×C47C2×Q1612yes—
77C2×C4×C47#13712yes—
78C2×Dic47—48no—
79C2×Dic47—42no—
80C2×Dic47—44no—
81Dic94—44no—
82Dic94—84no—
83Dic94—84no—
84C8×C47—44no—
85C47⋊C8—81no—
86#10295—471nomaximal, Sylow
87C22×C47—22no—
88C22×C47#39211yescharacteristic
89C22×C47#45112yes—
90C4×C47—22no—
91C4×C47—44no—
92C4×C47#45414yes—
93C4×C47#46212yes—
94C4×C47#49411yescharacteristic
95C4×C47#49711yescharacteristic
96Dic47—82no—
97Dic47—84no—
98#3230—472no—
99#2862—471no—
100#1994—471no—
101#1549—472no—
102#1276D4711yescharacteristic
103C2×C47—22no—
104C2×C47#200312yes—
105C2×C47#201611yescharacteristic
106#533—471no—
107C2×C4⋊Q8—472no—
108#500—942no—
109#487—942no—
110#484—944no—
111#477—944no—
112#431C2×D4712yes—
113#423—471no—
114#391—944no—
115#382—942no—
116C43C2×D4711yescharacteristic
117#339—942no—
118#332—944no—
119C47#1029511yescharacteristic, complemented, Sylow
120C22×Q8—942no—
121C2×M16—941no—
122C4⋊Q8—472no—
123C4⋊Q8—942no—
124C4⋊Q8—942no—
125C4⋊Q8—942no—
126C4⋊Q8—942no—
127#125—941no—
128C22⋊Q8—942no—
129C4×Q8—942no—
130#117—941no—
131C2×C4⋊C4—474no—
132C2×C4⋊C4—942no—
133C2×C42—22no—
134C2×C42D18812yes—
135C2×C42C22×D4711yescharacteristic
136#107—948no—
137C4⋊C8—942no—
138C4⋊C8D18814yes—
139#103—948no—
140C22⋊C8—22no—
141C4×C8—22no—
142#95—948no—
143C2×Q8—942no—
144C2×Q8—1888no—
145C2×Q8—1882no—
146C2×Q8—1882no—
147C22×C4—22no—
148C22×C4—944no—
149C22×C4C2×D18811yescharacteristic
150C22×C4D4×D4712yes—
151M16—1882no—
152C2×C8—24no—
153C2×C8—1881no—
154C4⋊C4—944no—
155C4⋊C4—942no—
156C4⋊C4—944no—
157C4⋊C4—942no—
158C4⋊C4—1882no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C22⋊C4—1881no—
162C42—22no—
163C42—44no—
164C42—1881no—
165C42Dic18814yes—
166C42C2×D18812yes—
167C42D4×D4711yescharacteristic
168C42#1062535411yescharacteristic
169C23#1309399411yescharacteristic
170Q8—3764no—
171Q8—3764no—
172Q8—1884no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—1888no—
177C2×C4—1882no—
178C2×C4—1884no—
179C2×C4#1309399412yes—
180C2×C4#1309399912yes—
181C2×C4#1309399911yescharacteristic
182C2×C4#1309402111yescharacteristic
183C2×C4C2×Dic18812yes—
184C2×C4#1309405712yes—
185C8—44no—
186C8—3761no—
187C22—22no—
188C22#1568903311yescharacteristic
189C22#1568928112yes—
190C4—22no—
191C4—44no—
192C4—3764no—
193C4—3762no—
194C4#1568929714yes—
195C4#1568933412yes—
196C4#1568950311yescharacteristic
197C4#1568951711yescharacteristic
198C2—22no—
199C2#2024441312yes—
200C2#2024449011yescharacteristic
subgroupG/H
centerC22#15689033
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1276C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1276D47
hypocenterC47#10295
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
119. C47#10295semidirect

Maximal subgroups

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

subgroupindex
#202545412
#202517662
#202443652
#202420722
C47×#12762
#1029547