Finite Group Databasebeta

← #26117239

Subgroups — #26117239

Order 12032.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#20254733C211yesmaximal, characteristic
2#20253518C212yesmaximal
3#20242002C212yesmaximal
4#20241258C211yesmaximal, characteristic
5C47×#1985C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689453—22no—
8#15689419—22no—
9#15689408—22no—
10#15689364—22no—
11#15689334—22no—
12#15689333—22no—
13#15689279—22no—
14#15689228—24no—
15#15689180C2212yes—
16#15688864—24no—
17C2×C4×Q8×C47C2211yescharacteristic
18C2×C4⋊C8×C47C2211yescharacteristic
19C2×#97×C47C2211yescharacteristic
20C47×#336—22no—
21C2×Dic188—22no—
22C2×#10625337—24no—
23#13094024D412yes—
24#13094024D412yes—
25#13094016—22no—
26#13094003—22no—
27#13094003—22no—
28C4×Dic94—22no—
29C4×Dic94—22no—
30#13093983—22no—
31#13093958—22no—
32#13093955—24no—
33C4⋊(C47⋊C8)—22no—
34#13093949—24no—
35#13093948—24no—
36#13093947—24no—
37C22⋊(C47⋊C8)—22no—
38#13093935D414yes—
39C22×Q8×C47D411yescharacteristic
40C22×C8×C47—21no—
41C22×C8×C47D412yes—
42C4×Q8×C47—22no—
43C4×Q8×C47—22no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C42×C47—21no—
47C2×C42×C47C2311yescharacteristic
48C4⋊C8×C47—22no—
49#97×C47—22no—
50C2×Q8×C47—22no—
51C2×Q8×C47—42no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47#4111yescharacteristic
57C2×Dic94—22no—
58C2×Dic94—22no—
59C2×C8×C47—22no—
60C2×C8×C47—22no—
61C2×C8×C47—41no—
62C2×C8×C47—41no—
63C2×C8×C47—42no—
64C4⋊C4×C47—22no—
65C4⋊C4×C47—42no—
66C42×C47—41no—
67C42×C47—41no—
68C42×C47C2×D412yes—
69C42×C47C2×D412yes—
70C22⋊Dic47—42no—
71#10625337—48no—
72C4⋊Dic47—22no—
73C4⋊Dic47—22no—
74C4⋊Dic47—22no—
75C4⋊Dic47—22no—
76Dic47⋊C4—42no—
77Dic47⋊C4—42no—
78C4×Dic47—42no—
79C2×C47⋊C8—24no—
80Dic188—82no—
81C23×C47#12111yescharacteristic
82Q8×C47—24no—
83Q8×C47—42no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47—41no—
91C2×C4×C47—41no—
92C2×C4×C47—42no—
93C2×C4×C47#12011yescharacteristic
94C2×C4×C47#12012yes—
95C2×C4×C47#12112yes—
96C2×C4×C47#12711yescharacteristic
97C2×Dic47—42no—
98C2×Dic47—42no—
99Dic94—44no—
100Dic94—42no—
101Dic94—42no—
102C8×C47—42no—
103C8×C47—42no—
104C47⋊C8—44no—
105#10031—471nomaximal, Sylow
106C22×C47—21no—
107C22×C47—21no—
108C22×C47#39211yescharacteristic
109C22×C47#47312yes—
110C4×C47—21no—
111C4×C47—22no—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47—81no—
115C4×C47#45511yescharacteristic
116C4×C47#45611yescharacteristic
117Dic47—82no—
118Dic47—82no—
119#3249—471no—
120#3113—472no—
121#1985D4711yescharacteristic
122#1531—472no—
123#1290—471no—
124C2×C47—22no—
125C2×C47#200711yescharacteristic
126C2×C47#201011yescharacteristic
127C2×C47#202011yescharacteristic
128#533—472no—
129C2×C4×Q8C2×D4711yescharacteristic
130#483—942no—
131#477—942no—
132#475—942no—
133#467—942no—
134#462—942no—
135#462—942no—
136#451—942no—
137#441—944no—
138#432—472no—
139C2×C4⋊C8C2×D4711yescharacteristic
140C2×#97C2×D4711yescharacteristic
141#336—22no—
142#330—944no—
143C47#1003111yescharacteristic, complemented, Sylow
144C22×Q8D18811yescharacteristic
145C2×Q16—942no—
146C2×Q16—944no—
147C22×C8—21no—
148C22×C8C22⋊D4712yes—
149C4⋊Q8—472no—
150C4⋊Q8—472no—
151#125—942no—
152C22⋊Q8—942no—
153C22⋊Q8—942no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—942no—
157C4×Q8—942no—
158#117—942no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4D18811yescharacteristic
161C2×C42—21no—
162C2×C42C22×D4711yescharacteristic
163#107—942no—
164#106—944no—
165C4⋊C8—22no—
166C4⋊C8—942no—
167#103—944no—
168#103—944no—
169#103—944no—
170C22⋊C8—942no—
171#97—22no—
172#97—474no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—942no—
176C2×Q8—942no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×D18811yescharacteristic
180C22×C4#1062535011yescharacteristic
181C22×C4C2×C22⋊D4711yescharacteristic
182Q16—3762no—
183Q16—1888no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—944no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—942no—
193C4⋊C4—942no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—1882no—
197C4⋊C4—1882no—
198C22⋊C4—1882no—
199C42—41no—
200C42—41no—
201C42—1882no—
202C42D4×D4712yes—
203C42D4×D4712yes—
204C23#1309399811yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—1884no—
208Q8—1882no—
209Q8—1882no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—1882no—
220C2×C4—1882no—
221C2×C4#1309399211yescharacteristic
222C2×C4#1309399412yes—
223C2×C4#1309399712yes—
224C2×C4#1309402011yescharacteristic
225C8—42no—
226C8—42no—
227C8—1884no—
228C22—21no—
229C22—21no—
230C22#1568903211yescharacteristic
231C22#1568939812yes—
232C4—22no—
233C4—21no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—3762no—
238C4—3762no—
239C4#1568930011yescharacteristic
240C4#1568930511yescharacteristic
241C2—22no—
242C2#2024443411yescharacteristic
243C2#2024445511yescharacteristic
244C2#2024450911yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1985C2
socleC22×C47#392
prime radicalC23×C47#121
hypercenter#1985D47
hypocenterC47#10031
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
143. C47#10031semidirect

Maximal subgroups

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

subgroupindex
#202547332
#202535182
#202420022
#202412582
C47×#19852
#1003147