Finite Group Databasebeta

← C47×#9429 #26049127

Subgroups — C47×#9429 #26049127

Order 12032.

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

normal subgroups only

This group has 508 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×#3152C211yesmaximal, characteristic
2C47×#2381C211yesmaximal, characteristic, complemented
3C47×#1558C211yesmaximal, characteristic, complemented
4C47×#1514C212yesmaximal
5C47×#1288C212yesmaximal, complemented
6C2×#137×C47—22no—
7C47×#532C2211yescharacteristic
8C2×C4⋊Q8×C47C2211yescharacteristic
9C47×#497—22no—
10C47×#494C412yescomplemented
11C47×#492C412yescomplemented
12C47×#432C2212yes—
13C4×M16×C47C2211yescharacteristic
14C47×#391—22no—
15C47×#387—24no—
16C47×#383C2212yes—
17C47×#333—22no—
18C47×#327—24no—
19C2×#41×C47—21no—
20C22×Q8×C47D412yes—
21#137×C47—44no—
22#137×C47—44no—
23C2×Q16×C47—24no—
24C2×SD16×C47—24no—
25C2×M16×C47—21no—
26C4⋊Q8×C47—22no—
27C4⋊Q8×C47C2×C411yescharacteristic
28C4⋊Q8×C47C2×C412yes—
29C4⋊Q8×C47D412yes—
30#127×C47C2×C411yescharacteristic
31#124×C47—21no—
32#121×C47—22no—
33C4×D4×C47—22no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47—22no—
36C2×C42×C47—22no—
37C2×C42×C47C2311yescharacteristic
38C4⋊C8×C47—22no—
39C22⋊C8×C47—22no—
40#97×C47—21no—
41#97×C47—22no—
42C4×C8×C47C2×C412yes—
43#95×C47—24no—
44#95×C47—22no—
45#95×C47—22no—
46#95×C47D414yes—
47#41×C47—42no—
48#41×C47—42no—
49C2×Q8×C47—22no—
50C2×Q8×C47—21no—
51C2×Q8×C47—42no—
52C2×Q8×C47—42no—
53C2×Q8×C47C22⋊C414yes—
54C2×D4×C47—21no—
55C2×D4×C47—22no—
56C2×D4×C47—41no—
57C22×C4×C47—22no—
58C22×C4×C47—24no—
59C22×C4×C47—41no—
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47C2×D412yes—
62Q16×C47—48no—
63SD16×C47—48no—
64M16×C47—24no—
65C2×C8×C47—22no—
66C2×C8×C47—42no—
67C4⋊C4×C47—24no—
68C4⋊C4×C47—24no—
69C4⋊C4×C47—22no—
70C4⋊C4×C47—82no—
71C22⋊C4×C47—42no—
72C42×C47—82no—
73C42×C47C22×C411yescharacteristic
74C42×C47C2×D411yescharacteristic
75C42×C47#4112yes—
76C23×C47—41no—
77C23×C47#12011yescharacteristic
78Q8×C47—44no—
79Q8×C47—42no—
80Q8×C47—82no—
81D4×C47—42no—
82D4×C47—82no—
83D4×C47—82no—
84C2×C4×C47—22no—
85C2×C4×C47—24no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—42no—
89C2×C4×C47—48no—
90C2×C4×C47—41no—
91C2×C4×C47—44no—
92C2×C4×C47—81no—
93C2×C4×C47—81no—
94C2×C4×C47C2×C22⋊C411yescharacteristic
95C2×C4×C47C4×D412yes—
96C2×C4×C47#12112yes—
97C2×C4×C47#12311yescharacteristic
98C8×C47—24no—
99C8×C47—82no—
100#9429C4711yesmaximal, characteristic, direct product factor, Sylow
101C22×C47—22no—
102C22×C47—81no—
103C22×C47—82no—
104C22×C47#38611yescharacteristic
105C22×C47#45312yes—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—22no—
109C4×C47—22no—
110C4×C47—44no—
111C4×C47—84no—
112C4×C47—81no—
113#3152C2×C4711yescharacteristic
114#2381C2×C4711yescharacteristic, complemented
115#1558C2×C4711yescharacteristic, complemented
116#1514C2×C4712yes—
117#1288C2×C4712yescomplemented
118C2×C47—22no—
119C2×C47—161no—
120C2×C47#188711yescharacteristic
121C2×C47#190512yes—
122C2×#137—22no—
123#532C22×C4711yescharacteristic
124C2×C4⋊Q8C22×C4711yescharacteristic
125#497—22no—
126#494C4×C4712yescomplemented
127#492C4×C4712yescomplemented
128#432C22×C4712yes—
129C4×M16C22×C4711yescharacteristic
130#391—22no—
131#387—24no—
132#383C22×C4712yes—
133#333—22no—
134#327—24no—
135C47#942911yescharacteristic, direct product factor, Sylow
136C2×#41—21no—
137C22×Q8D4×C4712yes—
138#137—44no—
139#137—44no—
140C2×Q16—24no—
141C2×SD16—24no—
142C2×M16—21no—
143C4⋊Q8—22no—
144C4⋊Q8C2×C4×C4711yescharacteristic
145C4⋊Q8C2×C4×C4712yes—
146C4⋊Q8D4×C4712yes—
147#127C2×C4×C4711yescharacteristic
148#124—21no—
149#121—22no—
150C4×D4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C42—22no—
154C2×C42C23×C4711yescharacteristic
155C4⋊C8—22no—
156C22⋊C8—22no—
157#97—21no—
158#97—22no—
159C4×C8C2×C4×C4712yes—
160#95—24no—
161#95—22no—
162#95—22no—
163#95D4×C4714yes—
164#41—42no—
165#41—42no—
166C2×Q8—22no—
167C2×Q8—21no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8C22⋊C4×C4714yes—
171C2×D4—21no—
172C2×D4—22no—
173C2×D4—41no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—41no—
177C22×C4C2×D4×C4711yescharacteristic
178C22×C4C2×D4×C4712yes—
179Q16—48no—
180SD16—48no—
181M16—24no—
182C2×C8—22no—
183C2×C8—42no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—82no—
188C22⋊C4—42no—
189C42—82no—
190C42C22×C4×C4711yescharacteristic
191C42C2×D4×C4711yescharacteristic
192C42#41×C4712yes—
193C23—41no—
194C23#120×C4711yescharacteristic
195Q8—44no—
196Q8—42no—
197Q8—82no—
198D4—42no—
199D4—82no—
200D4—82no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—48no—
207C2×C4—44no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4C2×C22⋊C4×C4711yescharacteristic
212C2×C4C4×D4×C4712yes—
213C2×C4#121×C4712yes—
214C2×C4#123×C4711yescharacteristic
215C8—24no—
216C8—82no—
217C22—22no—
218C22—81no—
219C22—82no—
220C22C47×#38611yescharacteristic
221C22C47×#45312yes—
222C4—21no—
223C4—21no—
224C4—22no—
225C4—22no—
226C4—44no—
227C4—84no—
228C4—81no—
229C2—22no—
230C2—161no—
231C2C47×#188711yescharacteristic
232C2C47×#190512yes—
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
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
2. C47×#2381C2semidirect
3. C47×#1558C2semidirect
5. C47×#1288C2semidirect
10. C47×#494C4semidirect
11. C47×#492C4semidirect
100. #9429C47direct (N × H)
114. #2381C2×C47semidirect
115. #1558C2×C47semidirect
117. #1288C2×C47semidirect
126. #494C4×C47semidirect
127. #492C4×C47semidirect
135. C47#9429direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31522
C47×#23812
C47×#15582
C47×#15142
C47×#12882
#942947