Finite Group Databasebeta

← C47×#9425 #26049123

Subgroups — C47×#9425 #26049123

Order 12032.

534 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C47×#3138C211yesmaximal, characteristic
2C47×#2380C211yesmaximal, characteristic
3C47×#1555C211yesmaximal, characteristic
4C47×#1515C212yesmaximal, complemented
5C47×#1288C212yesmaximal, complemented
6C47×#533C2211yescharacteristic
7C2×#127×C47C2211yescharacteristic
8C47×#490—22no—
9C47×#486C414yescomplemented
10C47×#432C2212yes—
11C47×#418—22no—
12C4×M16×C47C2211yescharacteristic
13C47×#386—24no—
14C47×#386—22no—
15C47×#383C2212yes—
16C47×#331—22no—
17C47×#328—24no—
18C22×D4×C47—22no—
19C22×D4×C47D412yes—
20C23×C4×C47—22no—
21C2×M16×C47—21no—
22C4⋊Q8×C47C2×C412yescomplemented
23#127×C47—22no—
24#127×C47C2×C412yes—
25#127×C47D412yes—
26#125×C47—21no—
27C22⋊Q8×C47—22no—
28C4×Q8×C47—22no—
29#117×C47—21no—
30C2×C22⋊C4×C47—24no—
31C2×C22⋊C4×C47—22no—
32C2×C42×C47C2311yescharacteristic
33C4⋊C8×C47—22no—
34#102×C47—28no—
35C22⋊C8×C47—22no—
36#97×C47—21no—
37#97×C47—22no—
38C4×C8×C47C2×C412yescomplemented
39#95×C47—22no—
40#95×C47—22no—
41#95×C47D414yes—
42C24×C47—22no—
43C2×Q8×C47—22no—
44C2×D4×C47—24no—
45C2×D4×C47—24no—
46C2×D4×C47—22no—
47C2×D4×C47—42no—
48C2×D4×C47—42no—
49C2×D4×C47—82no—
50C2×D4×C47—82no—
51C2×D4×C47C22⋊C414yes—
52C22×C4×C47—24no—
53C22×C4×C47—84no—
54C22×C4×C47—82no—
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47C2×D412yes—
57M16×C47—42no—
58C2×C8×C47—22no—
59C2×C8×C47—42no—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62C4⋊C4×C47—42no—
63C22⋊C4×C47—41no—
64C22⋊C4×C47—84no—
65C22⋊C4×C47—82no—
66C42×C47—41no—
67C42×C47C22×C411yescharacteristic
68C42×C47C2×D411yescharacteristic
69C42×C47#4112yes—
70C23×C47—24no—
71C23×C47—44no—
72C23×C47—44no—
73C23×C47—42no—
74C23×C47—42no—
75C23×C47#12011yescharacteristic
76Q8×C47—82no—
77D4×C47—44no—
78D4×C47—82no—
79D4×C47—84no—
80D4×C47—84no—
81C2×C4×C47—22no—
82C2×C4×C47—42no—
83C2×C4×C47—48no—
84C2×C4×C47—42no—
85C2×C4×C47—44no—
86C2×C4×C47—88no—
87C2×C4×C47C2×C22⋊C411yescharacteristic
88C2×C4×C47C4×D412yes—
89C2×C4×C47#12112yes—
90C2×C4×C47#12311yescharacteristic
91C8×C47—42no—
92C8×C47—82no—
93#9425C4711yesmaximal, characteristic, direct product factor, Sylow
94C22×C47—22no—
95C22×C47—44no—
96C22×C47—48no—
97C22×C47—82no—
98C22×C47—82no—
99C22×C47—84no—
100C22×C47#38611yescharacteristic
101C22×C47#45512yes—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—84no—
107C4×C47—82no—
108#3138C2×C4711yescharacteristic
109#2380C2×C4711yescharacteristic
110#1555C2×C4711yescharacteristic
111#1515C2×C4712yescomplemented
112#1288C2×C4712yescomplemented
113C2×C47—22no—
114C2×C47—84no—
115C2×C47#188511yescharacteristic
116C2×C47#190412yes—
117#533C22×C4711yescharacteristic
118C2×#127C22×C4711yescharacteristic
119#490—22no—
120#486C4×C4714yescomplemented
121#432C22×C4712yes—
122#418—22no—
123C4×M16C22×C4711yescharacteristic
124#386—22no—
125#386—24no—
126#383C22×C4712yes—
127#331—22no—
128#328—24no—
129C47#942511yescharacteristic, direct product factor, Sylow
130C22×D4—22no—
131C22×D4D4×C4712yes—
132C23×C4—22no—
133C2×M16—21no—
134C4⋊Q8C2×C4×C4712yescomplemented
135#127—22no—
136#127C2×C4×C4712yes—
137#127D4×C4712yes—
138#125—21no—
139C22⋊Q8—22no—
140C4×Q8—22no—
141#117—21no—
142C2×C22⋊C4—24no—
143C2×C22⋊C4—22no—
144C2×C42C23×C4711yescharacteristic
145C4⋊C8—22no—
146#102—28no—
147C22⋊C8—22no—
148#97—21no—
149#97—22no—
150C4×C8C2×C4×C4712yescomplemented
151#95—22no—
152#95—22no—
153#95D4×C4714yes—
154C24—22no—
155C2×Q8—22no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—42no—
160C2×D4—42no—
161C2×D4—82no—
162C2×D4—82no—
163C2×D4C22⋊C4×C4714yes—
164C22×C4—24no—
165C22×C4—84no—
166C22×C4—82no—
167C22×C4C2×D4×C4711yescharacteristic
168C22×C4C2×D4×C4712yes—
169M16—42no—
170C2×C8—22no—
171C2×C8—42no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C22⋊C4—41no—
176C22⋊C4—84no—
177C22⋊C4—82no—
178C42—41no—
179C42C22×C4×C4711yescharacteristic
180C42C2×D4×C4711yescharacteristic
181C42#41×C4712yes—
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#120×C4711yescharacteristic
188Q8—82no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—48no—
196C2×C4—44no—
197C2×C4—42no—
198C2×C4—88no—
199C2×C4C2×C22⋊C4×C4711yescharacteristic
200C2×C4C4×D4×C4712yes—
201C2×C4#121×C4712yes—
202C2×C4#123×C4711yescharacteristic
203C8—42no—
204C8—82no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22C47×#38611yescharacteristic
212C22C47×#45512yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—84no—
218C4—82no—
219C2—22no—
220C2—84no—
221C2C47×#188511yescharacteristic
222C2C47×#190412yes—
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC2×#127×C47C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1515C2semidirect
5. C47×#1288C2semidirect
9. C47×#486C4semidirect
22. C4⋊Q8×C47C2×C4semidirect
38. C4×C8×C47C2×C4semidirect
93. #9425C47direct (N × H)
111. #1515C2×C47semidirect
112. #1288C2×C47semidirect
120. #486C4×C47semidirect
129. C47#9425direct (N × H)
134. C4⋊Q8C2×C4×C47semidirect
150. C4×C8C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31382
C47×#23802
C47×#15552
C47×#15152
C47×#12882
#942547