Finite Group Databasebeta

← #26117130

Subgroups — #26117130

Order 12032.

566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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#20253415C212yesmaximal
2#20246681C211yesmaximal, characteristic, complemented
3#20241816C212yesmaximal, complemented
4#20241217C211yesmaximal, characteristic, complemented
5C47×#1963C211yesmaximal, characteristic
6C2×C4×Dic94C2212yes—
7#15689439—22no—
8#15689405—22no—
9#15689320—22no—
10#15689261—22no—
11C4×#10625335—24no—
12#15689176C2212yes—
13#15689055—22no—
14#15689044—22no—
15C4×C4⋊Dic47—22no—
16#15688853—24no—
17C47×#532C2211yescharacteristic
18C47×#423C2211yescharacteristic
19C2×#104×C47—22no—
20C47×#376C2211yescharacteristic
21C22×Dic94D412yes—
22C2×#10625335—24no—
23C4×Dic94—22no—
24C4×Dic94—22no—
25C4×Dic94—22no—
26C4×Dic94—22no—
27C2×C4⋊Dic47—24no—
28C2×C4⋊Dic47D412yes—
29C2×Dic47⋊C4—22no—
30C2×C4×Dic47—22no—
31#13093955—24no—
32C4⋊(C47⋊C8)—22no—
33#13093947—24no—
34#13093945—24no—
35C22⋊(C47⋊C8)—22no—
36C4×C47⋊C8D414yes—
37C47⋊#95—22no—
38C47⋊#95—22no—
39C2×#41×C47—21no—
40C2×M16×C47—21no—
41C4⋊Q8×C47D411yescharacteristic
42#127×C47D411yescharacteristic
43#124×C47—21no—
44#121×C47—22no—
45C4×D4×C47—22no—
46C2×C42×C47D412yes—
47C2×C42×C47C2311yescharacteristic
48C4⋊C8×C47—22no—
49#104×C47—44no—
50#95×C47—22no—
51#41×C47—42no—
52#41×C47—42no—
53C2×Q8×C47—21no—
54C2×D4×C47—22no—
55C2×D4×C47—21no—
56C2×D4×C47—41no—
57C22×C4×C47—22no—
58C22×C4×C47—41no—
59C22×C4×C47C2×D412yes—
60C22×C4×C47C2×D411yescharacteristic
61C22×Dic47—22no—
62C22×Dic47—22no—
63C2×Dic94—22no—
64C2×Dic94—22no—
65C2×Dic94—44no—
66M16×C47—42no—
67C2×C8×C47—41no—
68C4⋊C4×C47—22no—
69C22⋊C4×C47—42no—
70C42×C47—22no—
71C42×C47SD1614yescomplemented
72C42×C47C2×D411yescharacteristic
73C42×C47C2×D412yes—
74C42×C47#4111yescharacteristic
75#10625335—48no—
76C4⋊Dic47—22no—
77C4⋊Dic47—22no—
78C4⋊Dic47—48no—
79Dic47⋊C4—42no—
80Dic47⋊C4—42no—
81C4×Dic47—42no—
82C4×Dic47—42no—
83C2×C47⋊C8—24no—
84C23×C47—41no—
85C23×C47#12011yescharacteristic
86Q8×C47—42no—
87D4×C47—44no—
88D4×C47—42no—
89D4×C47—82no—
90C2×C4×C47—24no—
91C2×C4×C47—42no—
92C2×C4×C47—44no—
93C2×C4×C47—41no—
94C2×C4×C47—81no—
95C2×C4×C47—81no—
96C2×C4×C47#12012yes—
97C2×C4×C47#12112yes—
98C2×C4×C47#12111yescharacteristic
99C2×C4×C47#12711yescharacteristic
100C2×C4×C47C2×SD1612yes—
101C2×C4×C47#13712yes—
102C2×Dic47—24no—
103C2×Dic47—42no—
104C2×Dic47—42no—
105C2×Dic47—44no—
106C2×Dic47—42no—
107Dic94—24no—
108Dic94—24no—
109Dic94—42no—
110Dic94—42no—
111C8×C47—81no—
112C47⋊C8—44no—
113#10014—471nomaximal, Sylow
114C22×C47—22no—
115C22×C47—82no—
116C22×C47—81no—
117C22×C47#39211yescharacteristic
118C22×C47#44812yes—
119C4×C47—22no—
120C4×C47—22no—
121C4×C47—44no—
122C4×C47—81no—
123C4×C47#46112yes—
124C4×C47#49211yescharacteristic
125C4×C47#49711yescharacteristic
126Dic47—44no—
127Dic47—82no—
128#3103—472no—
129#2399—471no—
130#1963D4711yescharacteristic
131#1487—472no—
132#1274—471no—
133C2×C47—22no—
134C2×C47—161no—
135C2×C47#201012yes—
136C2×C47#201311yescharacteristic
137#532C2×D4711yescharacteristic
138C2×C4×Q8—472no—
139#481—942no—
140#475—942no—
141#460—942no—
142#448—942no—
143C4×SD16—944no—
144#431—472no—
145#423C2×D4711yescharacteristic
146C2×#104—22no—
147#398—942no—
148#395—942no—
149C4×C4⋊C4—942no—
150#376C2×D4711yescharacteristic
151Q8⋊C8—944no—
152C47#1001411yescharacteristic, complemented, Sylow
153C2×#41—21no—
154C22×Q8—472no—
155C2×SD16—944no—
156C2×M16—21no—
157C4⋊Q8D18811yescharacteristic
158#127D18811yescharacteristic
159#124—21no—
160#121—22no—
161C4×Q8—942no—
162C4×Q8—942no—
163C4×Q8—942no—
164C4×Q8—942no—
165C4×D4—22no—
166C2×C4⋊C4—472no—
167C2×C4⋊C4—944no—
168C2×C4⋊C4—942no—
169C2×C42—942no—
170C2×C42C22⋊D4712yes—
171C2×C42C22×D4711yescharacteristic
172#106—944no—
173C4⋊C8—22no—
174C4⋊C8—942no—
175#104—44no—
176#103—944no—
177#102—944no—
178C22⋊C8—942no—
179C4×C8—474no—
180#95—22no—
181#95—942no—
182#95—942no—
183#41—42no—
184#41—42no—
185C2×Q8—21no—
186C2×Q8—942no—
187C2×Q8—942no—
188C2×Q8—1884no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—942no—
195C22×C4—942no—
196C22×C4D4×D4712yes—
197C22×C4C2×C22⋊D4711yescharacteristic
198SD16—1888no—
199M16—42no—
200C2×C8—41no—
201C2×C8—944no—
202C4⋊C4—22no—
203C4⋊C4—942no—
204C4⋊C4—942no—
205C4⋊C4—1888no—
206C4⋊C4—1882no—
207C4⋊C4—1882no—
208C22⋊C4—42no—
209C42—22no—
210C42—1882no—
211C42—1882no—
212C42#1062533514yescomplemented
213C42C2×D18811yescharacteristic
214C42#1062535011yescharacteristic
215C42D4×D4712yes—
216C23—41no—
217C23#1309399211yescharacteristic
218Q8—42no—
219Q8—944no—
220Q8—944no—
221Q8—1882no—
222Q8—1882no—
223D4—44no—
224D4—42no—
225D4—82no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—944no—
233C2×C4—1884no—
234C2×C4—1882no—
235C2×C4—1882no—
236C2×C4—1882no—
237C2×C4#1309399412yes—
238C2×C4#1309399712yes—
239C2×C4#1309399811yescharacteristic
240C2×C4#1309402011yescharacteristic
241C2×C4C2×#1062533512yes—
242C2×C4#1309405412yes—
243C8—81no—
244C8—1884no—
245C22—22no—
246C22—82no—
247C22—81no—
248C22#1568903211yescharacteristic
249C22#1568926112yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—81no—
254C4—3762no—
255C4—1884no—
256C4#1568932812yes—
257C4#1568949511yescharacteristic
258C4#1568951811yescharacteristic
259C2—22no—
260C2—161no—
261C2#2024445412yes—
262C2#2024447011yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1963C2
socleC22×C47#392
prime radicalC47×#532C22
hypercenter#1963D47
hypocenterC47#10014
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #20246681C2semidirect
3. #20241816C2semidirect
4. #20241217C2semidirect
71. C42×C47SD16semidirect
152. C47#10014semidirect
212. C42#10625335semidirect

Maximal subgroups

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

subgroupindex
#202534152
#202466812
#202418162
#202412172
C47×#19632
#1001447