Finite Group Databasebeta

← #26104367

Subgroups — #26104367

Order 12032.

630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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#20243456C212yesmaximal
2#20241214C214yesmaximal, complemented
3C2×C47×#391C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)—22no—
5#15688878—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)—44no—
16C22×Q8×C47—21no—
17C22×Q8×C47—22no—
18C22×Q8×C47—42no—
19C22×Q8×C47—42no—
20C22×Q8×C47C814yescomplemented
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—48no—
39C2×Q8×C47—42no—
40C2×Q8×C47—42no—
41C2×Q8×C47—48no—
42C2×Q8×C47—42no—
43C2×Q8×C47—42no—
44C2×Q8×C47C2×C814yes—
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—44no—
56C22×C4×C47—42no—
57C22×C4×C47C22⋊C412yes—
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C2×C812yes—
60C22×C4×C47M1612yes—
61C22×C4×C47C22×C411yescharacteristic
62C22×C4×C47C2×D412yes—
63C4⋊C4×C47—42no—
64C4⋊C4×C47—42no—
65C42×C47—41no—
66C42×C47—42no—
67C42×C47—41no—
68C2×C47⋊C8—44no—
69C2×C47⋊C8—44no—
70C2×C47⋊C8—44no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47C22⋊C812yes—
74C23×C47#9912yes—
75C23×C47#10012yes—
76C23×C47C2×C22⋊C411yescharacteristic
77Q8×C47—44no—
78Q8×C47—48no—
79Q8×C47—44no—
80C2×C4×C47—24no—
81C2×C4×C47—24no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—24no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—48no—
93C2×C4×C47—48no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—42no—
97C2×C4×C47—44no—
98C2×C4×C47—84no—
99C2×C4×C47C22⋊C812yes—
100C2×C4×C47C22×C811yescharacteristic
101C2×C4×C47C2×M1611yescharacteristic
102C2×C4×C47#13714yes—
103C47⋊C8—84no—
104#7595—471nomaximal, Sylow
105C22×C47—22no—
106C22×C47—24no—
107C22×C47—24no—
108C22×C47—22no—
109C22×C47#32314yes—
110C22×C47C2×C22⋊C811yescharacteristic
111C22×C47C2×#9911yescharacteristic
112C22×C47C2×#10011yescharacteristic
113C22×C47#41912yes—
114C22×C47#42112yes—
115C4×C47—22no—
116C4×C47—21no—
117C4×C47—21no—
118C4×C47—24no—
119C4×C47—44no—
120C4×C47—42no—
121C4×C47—82no—
122C2×#391D4711yescharacteristic
123#1817—472no—
124#1272—474no—
125C2×C47—24no—
126C2×C47C2×#32311yescharacteristic
127C2×C47#147912yes—
128C2×C47#151112yes—
129C2×C47#153311yescharacteristic
130C2×C47#155811yescharacteristic
131C23×Q8Dic4711yescharacteristic
132C22×C4⋊C4Dic4711yescharacteristic
133C22×C42C2×D4711yescharacteristic
134C2×C22⋊C8—942no—
135#391—22no—
136#391Dic4712yes—
137#391C2×D4712yes—
138C2×#95—22no—
139#336—474no—
140#336—942no—
141C47#759511yescharacteristic, complemented, Sylow
142C22×Q8—22no—
143C22×Q8—21no—
144C22×Q8—42no—
145C22×Q8—42no—
146C22×Q8C47⋊C814yescomplemented
147C22×Q8C2×Dic4712yes—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4C2×Dic4711yescharacteristic
151C23×C4C22⋊D4712yes—
152C22×C8—944no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4C2×Dic4712yes—
156C2×C42—42no—
157C2×C42C2×Dic4711yescharacteristic
158C2×C42C22⋊D4712yes—
159C2×C42C22×D4711yescharacteristic
160C22⋊C8—1884no—
161#95—24no—
162#95—24no—
163C24C22⋊Dic4711yescharacteristic
164C2×Q8—24no—
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—48no—
169C2×Q8—48no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8C2×C47⋊C814yes—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—22no—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—44no—
184C22×C4—42no—
185C22×C4C2×C47⋊C812yes—
186C22×C4#1062532912yes—
187C22×C4C22⋊Dic4712yes—
188C22×C4C22⋊Dic4711yescharacteristic
189C22×C4C22×Dic4711yescharacteristic
190C22×C4C2×C22⋊D4712yes—
191C2×C8—1884no—
192C2×C8—1884no—
193C2×C8—1884no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C42—41no—
197C42—42no—
198C42—41no—
199C23—22no—
200C23—22no—
201C23C22⋊(C47⋊C8)12yes—
202C23#1309393912yes—
203C23#1309394112yes—
204C23C2×C22⋊Dic4711yescharacteristic
205Q8—44no—
206Q8—48no—
207Q8—44no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—48no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—48no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—84no—
227C2×C4C22⋊(C47⋊C8)12yes—
228C2×C4C22×C47⋊C811yescharacteristic
229C2×C4C2×#1062532911yescharacteristic
230C2×C4#1309405514yes—
231C8—3764no—
232C22—24no—
233C22—22no—
234C22—24no—
235C22—22no—
236C22#1568884714yes—
237C22C2×C22⋊(C47⋊C8)11yescharacteristic
238C22C2×#1309393911yescharacteristic
239C22C2×#1309394111yescharacteristic
240C22#1568913212yes—
241C22#1568914012yes—
242C4—24no—
243C4—22no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—44no—
248C4—82no—
249C2—24no—
250C2C2×#1568884711yescharacteristic
251C2#2024178312yes—
252C2#2024192112yes—
253C2#2024201211yescharacteristic
254C2#2024211411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×#391C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#391D47
hypocenterC47#7595
LCSG ▷ C2×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
20. C22×Q8×C47C8semidirect
141. C47#7595semidirect
146. C22×Q8C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
#202434562
#202412142
C2×C47×#3912
#759547