Finite Group Databasebeta

← #26109688

Subgroups — #26109688

Order 12032.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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#20243150C212yesmaximal
2#20241269C214yesmaximal, complemented
3C47×#2285C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)—22no—
5C2×#13093935C2214yes—
6#15688878—22no—
7C2×#117×C47C412yes—
8C22×C42×C47C2211yescharacteristic
9C47×#384C411yescharacteristic
10C47×#384C411yescharacteristic
11C47×#382C2212yes—
12C47×#380—22no—
13C4×C4⋊C4×C47—22no—
14C22×C47⋊C8—24no—
15C22⋊(C47⋊C8)—28no—
16#13093935—28no—
17C23×C4×C47C2×C411yescharacteristic
18C23×C4×C47D412yes—
19#117×C47—44no—
20C2×C4⋊C4×C47—22no—
21C2×C4⋊C4×C47—22no—
22C2×C4⋊C4×C47C2×C412yes—
23C2×C4⋊C4×C47C2×C412yes—
24C2×C22⋊C4×C47—22no—
25C2×C42×C47—24no—
26C2×C42×C47—22no—
27C2×C42×C47C2×C411yescharacteristic
28C2×C42×C47D412yes—
29C2×C42×C47C2311yescharacteristic
30#95×C47—24no—
31C24×C47C22⋊C411yescharacteristic
32C22×C4×C47—22no—
33C22×C4×C47—22no—
34C22×C4×C47—22no—
35C22×C4×C47—24no—
36C22×C4×C47—24no—
37C22×C4×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47—42no—
40C22×C4×C47C22⋊C411yescharacteristic
41C22×C4×C47C22⋊C412yes—
42C22×C4×C47C22×C411yescharacteristic
43C22×C4×C47C2×D412yes—
44C4⋊C4×C47—44no—
45C4⋊C4×C47—42no—
46C4⋊C4×C47—42no—
47C4⋊C4×C47—44no—
48C22⋊C4×C47—44no—
49C42×C47—22no—
50C42×C47—24no—
51C42×C47—44no—
52C42×C47#4114yes—
53C2×C47⋊C8—28no—
54C2×C47⋊C8—44no—
55C2×C47⋊C8—44no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—22no—
59C23×C47—22no—
60C23×C47#10112yes—
61C23×C47C2×C22⋊C411yescharacteristic
62C2×C4×C47—28no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—48no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47—44no—
75C2×C4×C47—44no—
76C2×C4×C47#10012yes—
77C2×C4×C47#10414yes—
78C2×C4×C47#11712yes—
79C2×C4×C47#12314yes—
80C47⋊C8—48no—
81#8721—471nomaximal, Sylow
82C22×C47—22no—
83C22×C47—24no—
84C22×C47—41no—
85C22×C47—42no—
86C22×C47—41no—
87C22×C47#38111yescharacteristic
88C22×C47C2×#10011yescharacteristic
89C22×C47C2×#10111yescharacteristic
90C22×C47C2×#10412yes—
91C22×C47#42112yes—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—24no—
95C4×C47—24no—
96C4×C47—82no—
97C4×C47—82no—
98#2285D4711yescharacteristic
99#1749—472no—
100#1295—474no—
101C2×C47—42no—
102C2×C47#152511yescharacteristic
103C2×C47#153112yes—
104C2×C47#153611yescharacteristic
105C2×C47#182111yescharacteristic
106C2×C47#182612yes—
107C2×#117Dic4712yes—
108C22×C42C2×D4711yescharacteristic
109C2×C22⋊C8—942no—
110C2×#97—474no—
111#384Dic4711yescharacteristic
112#384Dic4711yescharacteristic
113#382C2×D4712yes—
114#380—22no—
115C4×C4⋊C4—22no—
116#336—942no—
117C47#872111yescharacteristic, complemented, Sylow
118C23×C4C2×Dic4711yescharacteristic
119C23×C4C22⋊D4712yes—
120C22×C8—944no—
121#117—44no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4C2×Dic4712yes—
125C2×C4⋊C4C2×Dic4712yes—
126C2×C22⋊C4—22no—
127C2×C42—24no—
128C2×C42—22no—
129C2×C42C2×Dic4711yescharacteristic
130C2×C42C22⋊D4712yes—
131C2×C42C22×D4711yescharacteristic
132C22⋊C8—948no—
133#97—948no—
134#95—24no—
135C24C22⋊Dic4711yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4C22⋊Dic4711yescharacteristic
145C22×C4C22⋊Dic4712yes—
146C22×C4C22×Dic4711yescharacteristic
147C22×C4C2×C22⋊D4712yes—
148C2×C8—948no—
149C2×C8—1884no—
150C2×C8—1884no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C22⋊C4—44no—
156C42—22no—
157C42—24no—
158C42—44no—
159C42#1062535014yes—
160C23—21no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23#1309394312yes—
165C23C2×C22⋊Dic4711yescharacteristic
166C2×C4—28no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—48no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4#1309394112yes—
181C2×C4#1309395114yes—
182C2×C4#1309398312yes—
183C2×C4#1309400714yes—
184C8—1888no—
185C22—22no—
186C22—24no—
187C22—42no—
188C22—41no—
189C22—41no—
190C22#1568898611yescharacteristic
191C22C2×#1309394111yescharacteristic
192C22C2×#1309394311yescharacteristic
193C22C2×#1309395112yes—
194C22#1568914012yes—
195C4—22no—
196C4—22no—
197C4—24no—
198C4—24no—
199C4—82no—
200C4—82no—
201C2—42no—
202C2#2024198011yescharacteristic
203C2#2024200312yes—
204C2#2024202311yescharacteristic
205C2#2024346811yescharacteristic
206C2#2024348712yes—
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2285C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2285D47
hypocenterC47#8721
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #20241269C2semidirect
117. C47#8721semidirect

Maximal subgroups

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

subgroupindex
#202431502
#202412692
C47×#22852
#872147