Finite Group Databasebeta

← #26119382

Subgroups — #26119382

Order 12032.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#20251751C211yesmaximal, characteristic
2#20244365C211yesmaximal, characteristic
3#20241953C212yesmaximal
4#20241247C212yesmaximal
5C47×#1276C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7C2×#13094016—21no—
8#15689147C2211yescharacteristic
9#15689021—24no—
10#15688993—21no—
11#15688989C2212yes—
12#15688883—21no—
13#15688883—21no—
14#15688861—24no—
15C47×#431C2212yes—
16C43×C47C2211yescharacteristic
17C2×#10625329—21no—
18#13094024Q812yes—
19#13094016—21no—
20#13094016—42no—
21#13094016—42no—
22#13094003—22no—
23C4×Dic94—22no—
24#13093983—21no—
25C2×C4⋊Dic47—24no—
26C2×C4⋊Dic47—22no—
27C2×Dic47⋊C4—24no—
28C4⋊(C47⋊C8)—22no—
29C47⋊#95—22no—
30C47⋊#95D414yes—
31C2×C42×C47—22no—
32C2×C42×C47D411yescharacteristic
33C2×C42×C47D411yescharacteristic
34C2×C42×C47C2311yescharacteristic
35C4⋊C8×C47—22no—
36C22⋊C8×C47—22no—
37C4×C8×C47—22no—
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47C2×D412yes—
41C22×C4×C47C2×D411yescharacteristic
42C22×Dic47—24no—
43C2×Dic94—22no—
44C2×C8×C47—42no—
45C42×C47—21no—
46C42×C47—21no—
47C42×C47—44no—
48C42×C47SD1612yes—
49C42×C47Q1612yes—
50C42×C47C2×Q811yescharacteristic
51C42×C47#4112yes—
52C42×C47#4111yescharacteristic
53C22⋊Dic47—41no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47—48no—
57C4⋊Dic47—42no—
58C4⋊Dic47—42no—
59Dic47⋊C4—48no—
60Dic47⋊C4—42no—
61C4×Dic47—41no—
62#10625329—41no—
63#10625329—41no—
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×C47C22⋊Q812yes—
72C2×C4×C47C22⋊Q811yescharacteristic
73C2×C4×C47#12412yes—
74C2×C4×C47#12411yescharacteristic
75C2×C4×C47C2×SD1611yescharacteristic
76C2×C4×C47C2×Q1611yescharacteristic
77C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C47#13711yescharacteristic
79C2×Dic47—48no—
80C2×Dic47—42no—
81C2×Dic47—44no—
82Dic94—82no—
83C8×C47—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#47511yescharacteristic
95C4×C47#47711yescharacteristic
96C4×C47#48711yescharacteristic
97C4×C47#48911yescharacteristic
98Dic47—84no—
99Dic47—82no—
100#2859—471no—
101#1994—471no—
102#1518—472no—
103#1286—472no—
104#1276D4711yescharacteristic
105C2×C47—21no—
106C2×C47—21no—
107C2×C47#202411yescharacteristic
108C2×C47#203112yes—
109#533—471no—
110C2×#125—941no—
111#431C2×D4712yes—
112#423—471no—
113#389—944no—
114#384—941no—
115#382—472no—
116C43C2×D4711yescharacteristic
117#339—941no—
118#339—941no—
119#328—944no—
120C47#1036511yescharacteristic, complemented, Sylow
121C2×M16—941no—
122C4⋊Q8—472no—
123#125—941no—
124#125—1882no—
125#125—1882no—
126C22⋊Q8—942no—
127C4×Q8—942no—
128#117—941no—
129C2×C4⋊C4—944no—
130C2×C4⋊C4—944no—
131C2×C4⋊C4—942no—
132C2×C42—22no—
133C2×C42D18811yescharacteristic
134C2×C42D18811yescharacteristic
135C2×C42C22×D4711yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—942no—
138C22⋊C8—22no—
139C4×C8—22no—
140#95—474no—
141#95—942no—
142C2×Q8—942no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—944no—
146C22×C4C2×D18811yescharacteristic
147C22×C4D4×D4712yes—
148M16—1881no—
149M16—1881no—
150C2×C8—42no—
151C2×C8—1881no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—1888no—
155C4⋊C4—1888no—
156C4⋊C4—1882no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C22⋊C4—1881no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—1881no—
164C42#1062532512yes—
165C42Dic18812yes—
166C42#1062535012yes—
167C42#1062535211yescharacteristic
168C42Q8×D4711yescharacteristic
169C23#1309399411yescharacteristic
170Q8—3762no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—1888no—
177C2×C4—1884no—
178C2×C4—1882no—
179C2×C4#1309400212yes—
180C2×C4#1309400411yescharacteristic
181C2×C4#1309401012yes—
182C2×C4#1309401211yescharacteristic
183C2×C4C2×#1062532511yescharacteristic
184C2×C4C2×Dic18811yescharacteristic
185C2×C4#1309405211yescharacteristic
186C2×C4#1309405711yescharacteristic
187C8—82no—
188C8—3761no—
189C22—22no—
190C22#1568903611yescharacteristic
191C22#1568927611yescharacteristic
192C22#1568928111yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—3764no—
198C4—3762no—
199C4#1568940911yescharacteristic
200C4#1568941911yescharacteristic
201C4#1568947411yescharacteristic
202C4#1568948311yescharacteristic
203C2—21no—
204C2—21no—
205C2#2024453011yescharacteristic
206C2#2024456112yes—
subgroupG/H
centerC22#15689036
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1276C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#1276D47
hypocenterC47#10365
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
120. C47#10365semidirect

Maximal subgroups

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

subgroupindex
#202517512
#202443652
#202419532
#202412472
C47×#12762
#1036547