Finite Group Databasebeta

← #26119378

Subgroups — #26119378

Order 12032.

400 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 101 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#20244365C211yesmaximal, characteristic
2#20241951C212yesmaximal
3#20241246C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#2859C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689176C2212yes—
8#15689147C2211yescharacteristic
9#15688883—21no—
10#15688883—21no—
11#15688859—24no—
12C2×#125×C47—21no—
13C47×#389—24no—
14C47×#384—21no—
15C47×#382C2212yes—
16C43×C47C2211yescharacteristic
17C2×#10625329—21no—
18#13094024Q812yes—
19#13094016—21no—
20#13094003—22no—
21C4×Dic94—22no—
22#13093983—21no—
23C4⋊(C47⋊C8)—22no—
24C4⋊(C47⋊C8)—22no—
25C22⋊(C47⋊C8)—22no—
26C4×C47⋊C8—22no—
27#125×C47—42no—
28#125×C47—42no—
29C2×C4⋊C4×C47—24no—
30C2×C4⋊C4×C47—24no—
31C2×C4⋊C4×C47—22no—
32C2×C42×C47—22no—
33C2×C42×C47D411yescharacteristic
34C2×C42×C47D411yescharacteristic
35C2×C42×C47C2311yescharacteristic
36#95×C47—22no—
37#95×C47D414yes—
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47—24no—
41C22×C4×C47C2×D412yes—
42C22×C4×C47C2×D411yescharacteristic
43C2×Dic94—22no—
44C4⋊C4×C47—48no—
45C4⋊C4×C47—48no—
46C4⋊C4×C47—42no—
47C4⋊C4×C47—42no—
48C42×C47—21no—
49C42×C47—21no—
50C42×C47—44no—
51C42×C47SD1612yes—
52C42×C47Q1612yes—
53C42×C47C2×Q811yescharacteristic
54C42×C47#4111yescharacteristic
55C42×C47#4112yes—
56C22⋊Dic47—41no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59Dic47⋊C4—42no—
60C4×Dic47—41no—
61#10625329—41no—
62#10625329—41no—
63C2×C47⋊C8—42no—
64C2×C47⋊C8—41no—
65C23×C47#12011yescharacteristic
66C2×C4×C47—24no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47—48no—
72C2×C4×C47—44no—
73C2×C4×C47C22⋊Q812yes—
74C2×C4×C47C22⋊Q811yescharacteristic
75C2×C4×C47#12412yes—
76C2×C4×C47#12411yescharacteristic
77C2×C4×C47C2×SD1611yescharacteristic
78C2×C4×C47C2×Q1611yescharacteristic
79C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C47#13711yescharacteristic
81C2×Dic47—42no—
82Dic94—82no—
83C47⋊C8—82no—
84C47⋊C8—81no—
85#10365—471nomaximal, Sylow
86C22×C47—22no—
87C22×C47#39311yescharacteristic
88C22×C47#45011yescharacteristic
89C22×C47#45111yescharacteristic
90C4×C47—24no—
91C4×C47—22no—
92C4×C47—22no—
93C4×C47—42no—
94C4×C47—84no—
95C4×C47#47511yescharacteristic
96C4×C47#47711yescharacteristic
97C4×C47#48711yescharacteristic
98C4×C47#48911yescharacteristic
99Dic47—82no—
100#2859D4711yescharacteristic
101#1994—471no—
102#1518—472no—
103#1286—472no—
104#1276—471no—
105C2×C47—21no—
106C2×C47—21no—
107C2×C47#202411yescharacteristic
108C2×C47#203112yes—
109#533—471no—
110C2×#125—21no—
111#431—472no—
112#423—471no—
113#389—24no—
114#384—21no—
115#382C2×D4712yes—
116C43C2×D4711yescharacteristic
117#339—941no—
118#339—941no—
119#328—944no—
120C47#1036511yescharacteristic, complemented, Sylow
121C2×M16—941no—
122C4⋊Q8—472no—
123#125—42no—
124#125—42no—
125#125—941no—
126C22⋊Q8—942no—
127C4×Q8—942no—
128#117—941no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C42—22no—
133C2×C42C22⋊D4711yescharacteristic
134C2×C42C22⋊D4711yescharacteristic
135C2×C42C22×D4711yescharacteristic
136C4⋊C8—942no—
137C4⋊C8—942no—
138C22⋊C8—942no—
139C4×C8—942no—
140#95—22no—
141#95C22⋊D4714yes—
142C2×Q8—942no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—24no—
146C22×C4C2×C22⋊D4712yes—
147C22×C4C2×C22⋊D4711yescharacteristic
148M16—1881no—
149M16—1881no—
150C2×C8—1882no—
151C2×C8—1881no—
152C4⋊C4—48no—
153C4⋊C4—48no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—1882no—
159C22⋊C4—1881no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—1881no—
164C42#1062533512yes—
165C42#1062533712yes—
166C42Q8×D4711yescharacteristic
167C42#1062535411yescharacteristic
168C42#1062535412yes—
169C23#1309399311yescharacteristic
170Q8—3762no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—1882no—
179C2×C4#1309400012yes—
180C2×C4#1309400011yescharacteristic
181C2×C4#1309401312yes—
182C2×C4#1309401311yescharacteristic
183C2×C4C2×#1062533511yescharacteristic
184C2×C4C2×#1062533711yescharacteristic
185C2×C4#1309405011yescharacteristic
186C2×C4#1309405511yescharacteristic
187C8—3762no—
188C8—3761no—
189C22—22no—
190C22#1568903411yescharacteristic
191C22#1568927411yescharacteristic
192C22#1568927911yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—84no—
198C4—3762no—
199C4#1568940511yescharacteristic
200C4#1568941511yescharacteristic
201C4#1568947511yescharacteristic
202C4#1568948511yescharacteristic
203C2—21no—
204C2—21no—
205C2#2024452611yescharacteristic
206C2#2024455712yes—
subgroupG/H
centerC22#15689034
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2859C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#2859D47
hypocenterC47#10365
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2859

Complements

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

NH ≅ G/Ntype
120. C47#10365semidirect

Maximal subgroups

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

subgroupindex
#202443652
#202419512
#202412462
#202412212
C47×#28592
#1036547