Finite Group Databasebeta

← #26120782

Subgroups — #26120782

Order 12032.

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

normal subgroups only

This group has 382 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#20243557C212yesmaximal
2#20243521C211yesmaximal, characteristic
3#20241269C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#2845C211yesmaximal, characteristic
6C2×#13093957—22no—
7C2×#13093955—22no—
8C2×#13093935C2211yescharacteristic
9C2×#13093935C2212yes—
10#15688993C2211yescharacteristic
11#15688885—22no—
12C47×#398—22no—
13C47×#398—22no—
14C47×#398—22no—
15C47×#382C2211yescharacteristic
16C47×#382C2212yes—
17C22×C47⋊C8—22no—
18C22×C47⋊C8—21no—
19C2×C4⋊Dic47—21no—
20C2×C4⋊Dic47—22no—
21#13093957—44no—
22#13093955—44no—
23#13093935—22no—
24#13093935—21no—
25#13093935Q814yes—
26#13093935Q812yes—
27C2×C4⋊C4×C47—22no—
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—22no—
30C2×C4⋊C4×C47D412yes—
31C2×C4⋊C4×C47D412yes—
32C2×C4⋊C4×C47D412yes—
33C2×C42×C47C2311yescharacteristic
34#95×C47—22no—
35#95×C47—22no—
36#95×C47—22no—
37#95×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C2×D412yes—
42C22×C4×C47C2×D411yescharacteristic
43C22×Dic47—41no—
44C4⋊C4×C47—42no—
45C4⋊C4×C47—42no—
46C4⋊C4×C47—42no—
47C4⋊C4×C47—82no—
48C4⋊C4×C47—82no—
49C4⋊C4×C47—82no—
50C42×C47C2×Q812yes—
51C42×C47C2×Q811yescharacteristic
52C42×C47#4111yescharacteristic
53C4⋊Dic47—42no—
54C4⋊Dic47—42no—
55C4⋊Dic47—42no—
56C2×C47⋊C8—24no—
57C2×C47⋊C8—24no—
58C2×C47⋊C8—24no—
59C2×C47⋊C8—22no—
60C2×C47⋊C8—41no—
61C2×C47⋊C8—41no—
62C23×C47#12011yescharacteristic
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47C22⋊Q812yes—
77C2×C4×C47C22⋊Q811yescharacteristic
78C2×C4×C47C4⋊Q812yes—
79C2×C4×C47C4⋊Q811yescharacteristic
80C2×Dic47—82no—
81C2×Dic47—81no—
82C47⋊C8—28no—
83C47⋊C8—42no—
84#10585—471nomaximal, Sylow
85C22×C47#39511yescharacteristic
86C22×C47#45312yes—
87C22×C47#45411yescharacteristic
88C22×C47#45511yescharacteristic
89C22×C47#45612yes—
90C4×C47—22no—
91C4×C47—22no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—82no—
95C4×C47—82no—
96C4×C47—82no—
97Dic47—161no—
98#2845D4711yescharacteristic
99#1847—472no—
100#1836—471no—
101#1295—471no—
102#1295—472no—
103C2×C47#165611yescharacteristic
104C2×C47#166112yes—
105C2×C47#166311yescharacteristic
106C2×C47#206012yes—
107C2×C47#206111yescharacteristic
108C2×#107—942no—
109C2×#106—942no—
110C2×#97—471no—
111C2×#97—472no—
112#398—22no—
113#398—22no—
114#398—22no—
115#384—471no—
116#382C2×D4711yescharacteristic
117#382C2×D4712yes—
118#340—942no—
119C47#1058511yescharacteristic, complemented, Sylow
120C22×C8—942no—
121C22×C8—941no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—941no—
126C2×C4⋊C4—942no—
127C2×C4⋊C4C22⋊D4712yes—
128C2×C4⋊C4C22⋊D4712yes—
129C2×C4⋊C4C22⋊D4712yes—
130C2×C42C22×D4711yescharacteristic
131#107—1884no—
132#106—1884no—
133#97—474no—
134#97—472no—
135#97—942no—
136#97—941no—
137#95—22no—
138#95—22no—
139#95—22no—
140#95—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—1881no—
145C22×C4C2×C22⋊D4712yes—
146C22×C4C2×C22⋊D4711yescharacteristic
147C2×C8—944no—
148C2×C8—944no—
149C2×C8—944no—
150C2×C8—942no—
151C2×C8—1881no—
152C2×C8—1881no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—82no—
157C4⋊C4—82no—
158C4⋊C4—82no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C42Q8×D4712yes—
163C42Q8×D4711yescharacteristic
164C42#1062535411yescharacteristic
165C23#1309399311yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—3762no—
180C2×C4—3761no—
181C2×C4#1309400012yes—
182C2×C4#1309400011yescharacteristic
183C2×C4#1309402212yes—
184C2×C4#1309402211yescharacteristic
185C8—948no—
186C8—1882no—
187C22#1568904211yescharacteristic
188C22#1568929112yes—
189C22#1568929611yescharacteristic
190C22#1568930111yescharacteristic
191C22#1568930612yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—7521no—
200C2#2024268111yescharacteristic
201C2#2024270512yes—
202C2#2024271611yescharacteristic
203C2#2024473012yes—
204C2#2024473511yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2845C2
socle, prime radicalC23×C47#120
hypercenter#2845D47
hypocenterC47#10585
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
119. C47#10585semidirect

Maximal subgroups

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

subgroupindex
#202435572
#202435212
#202412692
C47×#28452
#1058547