Finite Group Databasebeta

← #26109680

Subgroups — #26109680

Order 12032.

554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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
3C2×C47×#382C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)—22no—
5C2×#13093935C2214yes—
6#15688878—22no—
7C22×C4⋊C4×C47C412yes—
8C22×C42×C47C2211yescharacteristic
9C47×#382—22no—
10C47×#382C412yes—
11C47×#382C2212yes—
12C2×#95×C47—22no—
13C22×C47⋊C8—24no—
14C22⋊(C47⋊C8)—28no—
15#13093935—28no—
16C23×C4×C47—22no—
17C23×C4×C47C2×C411yescharacteristic
18C23×C4×C47D412yes—
19C2×C4⋊C4×C47—22no—
20C2×C4⋊C4×C47—44no—
21C2×C4⋊C4×C47C2×C414yes—
22C2×C42×C47—24no—
23C2×C42×C47C2×C411yescharacteristic
24C2×C42×C47D412yes—
25C2×C42×C47C2311yescharacteristic
26#95×C47—24no—
27#95×C47—24no—
28C24×C47C22⋊C411yescharacteristic
29C22×C4×C47—22no—
30C22×C4×C47—22no—
31C22×C4×C47—22no—
32C22×C4×C47—24no—
33C22×C4×C47—24no—
34C22×C4×C47—24no—
35C22×C4×C47—42no—
36C22×C4×C47—44no—
37C22×C4×C47—44no—
38C22×C4×C47—44no—
39C22×C4×C47C22⋊C412yes—
40C22×C4×C47C22⋊C411yescharacteristic
41C22×C4×C47C22×C411yescharacteristic
42C22×C4×C47C2×D412yes—
43C4⋊C4×C47—44no—
44C4⋊C4×C47—44no—
45C42×C47—22no—
46C42×C47—24no—
47C42×C47#4114yes—
48C2×C47⋊C8—28no—
49C2×C47⋊C8—44no—
50C2×C47⋊C8—44no—
51C23×C47—21no—
52C23×C47—21no—
53C23×C47—22no—
54C23×C47#10112yes—
55C23×C47#10414yes—
56C23×C47C2×C22⋊C411yescharacteristic
57C2×C4×C47—28no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—48no—
68C2×C4×C47—44no—
69C2×C4×C47—44no—
70C2×C4×C47—44no—
71C2×C4×C47—88no—
72C2×C4×C47#10012yes—
73C2×C4×C47#11712yes—
74C2×C4×C47#12314yes—
75C47⋊C8—48no—
76#8719—471nomaximal, Sylow
77C22×C47—22no—
78C22×C47—24no—
79C22×C47—24no—
80C22×C47—22no—
81C22×C47#33014yes—
82C22×C47#38111yescharacteristic
83C22×C47C2×#10011yescharacteristic
84C22×C47C2×#10111yescharacteristic
85C22×C47C2×#10412yes—
86C22×C47#42112yes—
87C4×C47—22no—
88C4×C47—22no—
89C4×C47—24no—
90C4×C47—42no—
91C4×C47—84no—
92C2×#382D4711yescharacteristic
93#1749—472no—
94#1295—474no—
95C2×C47—24no—
96C2×C47C2×#33011yescharacteristic
97C2×C47#152712yes—
98C2×C47#153411yescharacteristic
99C2×C47#182111yescharacteristic
100C2×C47#182612yes—
101C22×C4⋊C4Dic4712yes—
102C22×C42C2×D4711yescharacteristic
103C2×C22⋊C8—942no—
104C2×#97—474no—
105#382—22no—
106#382Dic4712yes—
107#382C2×D4712yes—
108C2×#95—22no—
109#336—942no—
110C47#871911yescharacteristic, complemented, Sylow
111C23×C4—22no—
112C23×C4C2×Dic4711yescharacteristic
113C23×C4C22⋊D4712yes—
114C22×C8—944no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—44no—
117C2×C4⋊C4C2×Dic4714yes—
118C2×C42—24no—
119C2×C42C2×Dic4711yescharacteristic
120C2×C42C22⋊D4712yes—
121C2×C42C22×D4711yescharacteristic
122C22⋊C8—948no—
123#97—948no—
124#95—24no—
125#95—24no—
126C24C22⋊Dic4711yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—24no—
131C22×C4—24no—
132C22×C4—24no—
133C22×C4—42no—
134C22×C4—44no—
135C22×C4—44no—
136C22×C4—44no—
137C22×C4C22⋊Dic4712yes—
138C22×C4C22⋊Dic4711yescharacteristic
139C22×C4C22×Dic4711yescharacteristic
140C22×C4C2×C22⋊D4712yes—
141C2×C8—948no—
142C2×C8—1884no—
143C2×C8—1884no—
144C4⋊C4—44no—
145C4⋊C4—44no—
146C42—22no—
147C42—24no—
148C42#1062535014yes—
149C23—21no—
150C23—21no—
151C23—22no—
152C23#1309394312yes—
153C23#1309395114yes—
154C23C2×C22⋊Dic4711yescharacteristic
155C2×C4—28no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—48no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4—88no—
170C2×C4#1309394112yes—
171C2×C4#1309398312yes—
172C2×C4#1309400714yes—
173C8—1888no—
174C22—22no—
175C22—24no—
176C22—24no—
177C22—22no—
178C22#1568886514yes—
179C22#1568898611yescharacteristic
180C22C2×#1309394111yescharacteristic
181C22C2×#1309394311yescharacteristic
182C22C2×#1309395112yes—
183C22#1568914012yes—
184C4—22no—
185C4—22no—
186C4—24no—
187C4—42no—
188C4—84no—
189C2—24no—
190C2C2×#1568886511yescharacteristic
191C2#2024198612yes—
192C2#2024201511yescharacteristic
193C2#2024346811yescharacteristic
194C2#2024348712yes—
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#382C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#382D47
hypocenterC47#8719
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #20241269C2semidirect
110. C47#8719semidirect

Maximal subgroups

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

subgroupindex
#202431502
#202412692
C2×C47×#3822
#871947