Finite Group Databasebeta

← #26104513

Subgroups — #26104513

Order 12032.

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

normal subgroups only

This group has 658 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#20241214C214yesmaximal, complemented
3C2×C47×#391C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)—22no—
5C2×#13093935—22no—
6#15688878C2214yes—
7C23×Q8×C47C411yescharacteristic
8C22×C4⋊C4×C47C411yescharacteristic
9C22×C42×C47C2211yescharacteristic
10C47×#391—22no—
11C47×#391C412yes—
12C47×#391C2212yes—
13C2×#95×C47—22no—
14C22×C47⋊C8—24no—
15C22⋊(C47⋊C8)—28no—
16#13093935—44no—
17C22×Q8×C47—24no—
18C22×Q8×C47—21no—
19C22×Q8×C47—42no—
20C22×Q8×C47—42no—
21C22×Q8×C47C2×C412yes—
22C23×C4×C47—21no—
23C23×C4×C47—21no—
24C23×C4×C47C2×C411yescharacteristic
25C23×C4×C47D412yes—
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47—42no—
28C2×C4⋊C4×C47C2×C412yes—
29C2×C42×C47—42no—
30C2×C42×C47C2×C411yescharacteristic
31C2×C42×C47D412yes—
32C2×C42×C47C2311yescharacteristic
33#95×C47—24no—
34#95×C47—24no—
35C24×C47C22⋊C411yescharacteristic
36C2×Q8×C47—24no—
37C2×Q8×C47—22no—
38C2×Q8×C47—416no—
39C2×Q8×C47—42no—
40C2×Q8×C47—42no—
41C2×Q8×C47—42no—
42C2×Q8×C47—42no—
43C2×Q8×C47M1614yes—
44C22×C4×C47—22no—
45C22×C4×C47—22no—
46C22×C4×C47—22no—
47C22×C4×C47—24no—
48C22×C4×C47—24no—
49C22×C4×C47—22no—
50C22×C4×C47—24no—
51C22×C4×C47—22no—
52C22×C4×C47—42no—
53C22×C4×C47—42no—
54C22×C4×C47—42no—
55C22×C4×C47—42no—
56C22×C4×C47—44no—
57C22×C4×C47C22⋊C412yes—
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22×C411yescharacteristic
60C22×C4×C47C2×D412yes—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—42no—
63C42×C47—24no—
64C42×C47—41no—
65C42×C47—41no—
66C2×C47⋊C8—28no—
67C2×C47⋊C8—44no—
68C2×C47⋊C8—44no—
69C23×C47—21no—
70C23×C47—21no—
71C23×C47—22no—
72C23×C47#10012yes—
73C23×C47#10414yes—
74C23×C47C2×C22⋊C411yescharacteristic
75Q8×C47—44no—
76Q8×C47—48no—
77Q8×C47—44no—
78C2×C4×C47—28no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—24no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—48no—
90C2×C4×C47—48no—
91C2×C4×C47—42no—
92C2×C4×C47—42no—
93C2×C4×C47—42no—
94C2×C4×C47—44no—
95C2×C4×C47—84no—
96C2×C4×C47#9912yes—
97C2×C4×C47C2×M1612yes—
98C2×C4×C47#13714yes—
99C47⋊C8—48no—
100#7629—471nomaximal, Sylow
101C22×C47—22no—
102C22×C47—22no—
103C22×C47—24no—
104C22×C47—24no—
105C22×C47#32914yes—
106C22×C47#40711yescharacteristic
107C22×C47C2×#9911yescharacteristic
108C22×C47C2×#10011yescharacteristic
109C22×C47#41912yes—
110C22×C47C2×#10412yes—
111C4×C47—22no—
112C4×C47—22no—
113C4×C47—24no—
114C4×C47—44no—
115C4×C47—42no—
116C4×C47—82no—
117C2×#391D4711yescharacteristic
118#1749—472no—
119#1272—474no—
120C2×C47—24no—
121C2×C47#146211yescharacteristic
122C2×C47#149112yes—
123C2×C47#150812yes—
124C2×C47C2×#32911yescharacteristic
125C2×C47#155811yescharacteristic
126C23×Q8Dic4711yescharacteristic
127C22×C4⋊C4Dic4711yescharacteristic
128C22×C42C2×D4711yescharacteristic
129C2×C22⋊C8—942no—
130C2×#97—942no—
131#391—22no—
132#391Dic4712yes—
133#391C2×D4712yes—
134C2×#95—22no—
135#336—474no—
136C47#762911yescharacteristic, complemented, Sylow
137C22×Q8—24no—
138C22×Q8—21no—
139C22×Q8—42no—
140C22×Q8—42no—
141C22×Q8C2×Dic4712yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4C2×Dic4711yescharacteristic
145C23×C4C22⋊D4712yes—
146C22×C8—944no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4C2×Dic4712yes—
150C2×C42—42no—
151C2×C42C2×Dic4711yescharacteristic
152C2×C42C22⋊D4712yes—
153C2×C42C22×D4711yescharacteristic
154C22⋊C8—948no—
155#97—1884no—
156#95—24no—
157#95—24no—
158C24C22⋊Dic4711yescharacteristic
159C2×Q8—24no—
160C2×Q8—22no—
161C2×Q8—416no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8#1062532914yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—24no—
171C22×C4—24no—
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—44no—
180C22×C4C22⋊Dic4712yes—
181C22×C4C22⋊Dic4711yescharacteristic
182C22×C4C22×Dic4711yescharacteristic
183C22×C4C2×C22⋊D4712yes—
184C2×C8—948no—
185C2×C8—1884no—
186C2×C8—1884no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C42—24no—
190C42—41no—
191C42—41no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23#1309394112yes—
196C23#1309395114yes—
197C23C2×C22⋊Dic4711yescharacteristic
198Q8—44no—
199Q8—48no—
200Q8—44no—
201C2×C4—28no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—48no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—44no—
218C2×C4—84no—
219C2×C4#1309393912yes—
220C2×C4C2×#1062532912yes—
221C2×C4#1309405514yes—
222C8—1888no—
223C22—22no—
224C22—24no—
225C22—22no—
226C22—24no—
227C22#1568886314yes—
228C22#1568908711yescharacteristic
229C22C2×#1309393911yescharacteristic
230C22C2×#1309394111yescharacteristic
231C22#1568913212yes—
232C22C2×#1309395112yes—
233C4—22no—
234C4—22no—
235C4—24no—
236C4—44no—
237C4—42no—
238C4—82no—
239C2—24no—
240C2#2024171511yescharacteristic
241C2#2024183512yes—
242C2#2024190812yes—
243C2C2×#1568886311yescharacteristic
244C2#2024211411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#391C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#391D47
hypocenterC47#7629
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. #20241214C2semidirect
136. C47#7629semidirect

Maximal subgroups

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

subgroupindex
#202431502
#202412142
C2×C47×#3912
#762947