Finite Group Databasebeta

← #26119016

Subgroups — #26119016

Order 12032.

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

normal subgroups only

This group has 528 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#20254338C212yesmaximal
2#20251766C211yesmaximal, characteristic
3#20244365C211yesmaximal, characteristic
4#20242068C212yesmaximal
5C47×#1276C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7C2×#13094024C2212yes—
8#15689503—22no—
9#15689474—22no—
10#15689334—24no—
11#15689281—24no—
12#15689147C2211yescharacteristic
13#15689029—24no—
14#15688989—22no—
15#15688883—22no—
16#15688871—24no—
17C47×#431C2212yes—
18C43×C47C2211yescharacteristic
19C22×Dic94D414yes—
20C2×Dic188—28no—
21C2×#10625329—21no—
22#13094024—22no—
23#13094024—22no—
24#13094024—22no—
25#13094024—22no—
26#13094024D412yes—
27#13094016—21no—
28#13094003—22no—
29C4×Dic94—22no—
30#13093983—21no—
31C2×C4⋊Dic47—22no—
32C2×C4⋊Dic47—22no—
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—24no—
47C2×Dic94—22no—
48C2×Dic94—24no—
49C2×Dic94—48no—
50C2×C8×C47—24no—
51C42×C47—22no—
52C42×C47—44no—
53C42×C47Q1614yescomplemented
54C42×C47C2×D411yescharacteristic
55C42×C47C2×D412yes—
56C42×C47#4111yescharacteristic
57C22⋊Dic47—41no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47—42no—
61C4⋊Dic47—42no—
62C4⋊Dic47—42no—
63C4⋊Dic47—42no—
64Dic47⋊C4—42no—
65C4×Dic47—41no—
66#10625329—42no—
67C2×C47⋊C8—41no—
68Dic188—88no—
69C23×C47#12011yescharacteristic
70C2×C4×C47—24no—
71C2×C4×C47—24no—
72C2×C4×C47—44no—
73C2×C4×C47#12012yes—
74C2×C4×C47#12112yes—
75C2×C4×C47#12111yescharacteristic
76C2×C4×C47#12711yescharacteristic
77C2×C4×C47C2×Q1612yes—
78C2×C4×C47#13712yes—
79C2×Dic47—48no—
80C2×Dic47—42no—
81C2×Dic47—44no—
82Dic94—44no—
83Dic94—48no—
84Dic94—84no—
85C8×C47—44no—
86C47⋊C8—81no—
87#10297—471nomaximal, Sylow
88C22×C47—22no—
89C22×C47#39211yescharacteristic
90C22×C47#45112yes—
91C4×C47—22no—
92C4×C47—44no—
93C4×C47#45514yes—
94C4×C47#46212yes—
95C4×C47#49411yescharacteristic
96C4×C47#49711yescharacteristic
97Dic47—84no—
98Dic47—82no—
99#3209—472no—
100#2862—471no—
101#1994—471no—
102#1548—472no—
103#1276D4711yescharacteristic
104C2×C47—22no—
105C2×C47#200412yes—
106C2×C47#201611yescharacteristic
107#533—471no—
108C2×C4⋊Q8—472no—
109#494—942no—
110#487—942no—
111#462—944no—
112#451—944no—
113#431C2×D4712yes—
114#423—471no—
115#391—944no—
116#382—942no—
117C43C2×D4711yescharacteristic
118#339—942no—
119#333—944no—
120C47#1029711yescharacteristic, complemented, Sylow
121C22×Q8—474no—
122C2×Q16—948no—
123C2×M16—941no—
124C4⋊Q8—472no—
125C4⋊Q8—942no—
126C4⋊Q8—942no—
127C4⋊Q8—942no—
128C4⋊Q8—942no—
129#125—941no—
130C22⋊Q8—942no—
131C4×Q8—942no—
132#117—941no—
133C2×C4⋊C4—942no—
134C2×C4⋊C4—942no—
135C2×C42—22no—
136C2×C42D18812yes—
137C2×C42C22×D4711yescharacteristic
138C4⋊C8—942no—
139C4⋊C8D18814yes—
140#103—948no—
141C22⋊C8—22no—
142C4×C8—22no—
143#95—948no—
144C2×Q8—944no—
145C2×Q8—942no—
146C2×Q8—944no—
147C2×Q8—1888no—
148C22×C4—22no—
149C22×C4—944no—
150C22×C4C2×D18811yescharacteristic
151C22×C4D4×D4712yes—
152Q16—3768no—
153M16—1882no—
154C2×C8—24no—
155C2×C8—1881no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—1882no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C4⋊C4—1882no—
163C22⋊C4—1881no—
164C42—22no—
165C42—44no—
166C42—1881no—
167C42Dic18814yescomplemented
168C42C2×D18812yes—
169C42D4×D4711yescharacteristic
170C42#1062535411yescharacteristic
171C23#1309399411yescharacteristic
172Q8—3764no—
173Q8—1884no—
174Q8—1888no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—1888no—
179C2×C4—1882no—
180C2×C4—1884no—
181C2×C4#1309399412yes—
182C2×C4#1309399912yes—
183C2×C4#1309399911yescharacteristic
184C2×C4#1309402111yescharacteristic
185C2×C4C2×Dic18812yes—
186C2×C4#1309405712yes—
187C8—44no—
188C8—3761no—
189C22—22no—
190C22#1568903311yescharacteristic
191C22#1568928112yes—
192C4—22no—
193C4—44no—
194C4—3764no—
195C4—3762no—
196C4#1568930214yes—
197C4#1568933412yes—
198C4#1568950311yescharacteristic
199C4#1568951711yescharacteristic
200C2—22no—
201C2#2024442012yes—
202C2#2024449011yescharacteristic
subgroupG/H
centerC22#15689033
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1276C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1276D47
hypocenterC47#10297
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
53. C42×C47Q16semidirect
120. C47#10297semidirect
167. C42Dic188semidirect

Maximal subgroups

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

subgroupindex
#202543382
#202517662
#202443652
#202420682
C47×#12762
#1029747