Finite Group Databasebeta

← #26119522

Subgroups — #26119522

Order 12032.

406 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 77 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#20243488C212yesmaximal
2#20243463C211yesmaximal, characteristic
3#20241296C211yesmaximal, characteristic
4#20241241C212yesmaximal
5C47×#2608C211yesmaximal, characteristic
6C2×#13093983C2211yescharacteristic
7#15689087C2212yes—
8#15688986C2211yescharacteristic
9#15688889—22no—
10#15688883—22no—
11#15688883—22no—
12C47×#396—22no—
13C47×#389—22no—
14C47×#387—22no—
15C47×#381C2211yescharacteristic
16C4×C22⋊C4×C47C2212yes—
17C2×#10625329—22no—
18#13093983—22no—
19#13093983—22no—
20C2×C4⋊Dic47Q812yes—
21C2×C22⋊Dic47—21no—
22C2×C22⋊Dic47—21no—
23C2×C4×Dic47—21no—
24C22⋊(C47⋊C8)—22no—
25C22⋊(C47⋊C8)—22no—
26C47⋊#95—22no—
27C23×C4×C47C2311yescharacteristic
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—22no—
30C2×C4⋊C4×C47—22no—
31C2×C22⋊C4×C47—22no—
32C2×C22⋊C4×C47D412yes—
33C2×C42×C47D412yes—
34C2×C42×C47D412yes—
35#95×C47—22no—
36#95×C47—22no—
37#95×C47—22no—
38C24×C47C2×D411yescharacteristic
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47—42no—
43C22×C4×C47C2×D412yes—
44C22×C4×C47C2×Q811yescharacteristic
45C22×C4×C47#4112yes—
46C22×C4×C47#4111yescharacteristic
47C22×Dic47—22no—
48C22×Dic47—41no—
49C4⋊C4×C47—44no—
50C4⋊C4×C47—44no—
51C4⋊C4×C47—82no—
52C22⋊C4×C47—44no—
53C22⋊C4×C47—42no—
54C42×C47—42no—
55C42×C47—42no—
56C22⋊Dic47—41no—
57C22⋊Dic47—41no—
58C22⋊Dic47—42no—
59C4⋊Dic47—24no—
60C4×Dic47—42no—
61#10625329—42no—
62#10625329—42no—
63C2×C47⋊C8—42no—
64C23×C47—22no—
65C23×C47—42no—
66C23×C47#12011yescharacteristic
67C23×C47C22⋊Q811yescharacteristic
68C23×C47#12411yescharacteristic
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—24no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47C22⋊Q812yes—
84C2×C4×C47#12412yes—
85C2×Dic47—42no—
86C2×Dic47—82no—
87C2×Dic47—81no—
88C2×Dic47—82no—
89C47⋊C8—82no—
90#10389—471nomaximal, Sylow
91C22×C47—22no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—22no—
95C22×C47—22no—
96C22×C47—82no—
97C22×C47#39311yescharacteristic
98C22×C47#45812yes—
99C4×C47—22no—
100C4×C47—22no—
101C4×C47—44no—
102C4×C47—82no—
103C4×C47—82no—
104Dic47—82no—
105Dic47—161no—
106#2608D4711yescharacteristic
107#1826—472no—
108#1820—471no—
109#1306—471no—
110#1284—472no—
111C2×C47—22no—
112C2×C47—41no—
113C2×C47—41no—
114C2×C47#203011yescharacteristic
115C2×C47#203112yes—
116C2×#117—471no—
117#407—472no—
118#396—22no—
119#389—22no—
120#387—22no—
121#381—471no—
122#381C2×D4711yescharacteristic
123C4×C22⋊C4C2×D4712yes—
124#342—942no—
125#339—942no—
126#339—942no—
127C47#1038911yescharacteristic, complemented, Sylow
128C23×C4C22×D4711yescharacteristic
129C2×M16—942no—
130#117—942no—
131#117—942no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—472no—
136C2×C22⋊C4—22no—
137C2×C22⋊C4—941no—
138C2×C22⋊C4—941no—
139C2×C22⋊C4C22⋊D4712yes—
140C2×C42—941no—
141C2×C42C22⋊D4712yes—
142C2×C42C22⋊D4712yes—
143C22⋊C8—942no—
144C22⋊C8—942no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—942no—
149C24C2×C22⋊D4711yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—42no—
154C22×C4—942no—
155C22×C4—1881no—
156C22×C4Q8×D4711yescharacteristic
157C22×C4#1062535412yes—
158C22×C4#1062535411yescharacteristic
159C22×C4C2×C22⋊D4712yes—
160M16—1882no—
161M16—1882no—
162C2×C8—1882no—
163C4⋊C4—44no—
164C4⋊C4—44no—
165C4⋊C4—82no—
166C4⋊C4—944no—
167C22⋊C4—44no—
168C22⋊C4—42no—
169C22⋊C4—1882no—
170C22⋊C4—1881no—
171C22⋊C4—1881no—
172C42—42no—
173C42—42no—
174C42—1882no—
175C23—22no—
176C23—42no—
177C23#1309399311yescharacteristic
178C23#1309400011yescharacteristic
179C23#1309401311yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—3762no—
195C2×C4—3761no—
196C2×C4—3762no—
197C2×C4—1882no—
198C2×C4#1309400012yes—
199C2×C4#1309401312yes—
200C8—3762no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1568903411yescharacteristic
208C22#1568931312yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—3762no—
215C4—7521no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2024455411yescharacteristic
220C2#2024455712yes—
subgroupG/H
centerC22#15689034
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#2608C2
socleC22×C47#393
prime radicalC24×C47C2×D4
hypercenter#2608D47
hypocenterC47#10389
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

Complements

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

NH ≅ G/Ntype
127. C47#10389semidirect

Maximal subgroups

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

subgroupindex
#202434882
#202434632
#202412962
#202412412
C47×#26082
#1038947