Finite Group Databasebeta

← #26117268

Subgroups — #26117268

Order 12032.

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

normal subgroups only

This group has 528 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#20253912C211yesmaximal, characteristic, complemented
2#20253396C212yesmaximal
3#20241790C212yesmaximal, complemented
4#20241219C211yesmaximal, characteristic, complemented
5C47×#1955C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689532—22no—
8#15689532—22no—
9#15689453—22no—
10#15689413—22no—
11#15689328—22no—
12#15689274—22no—
13C4×#10625335—24no—
14#15689176C2212yes—
15#15689161—22no—
16#15688853—24no—
17C2×C4×D4×C47C2211yescharacteristic
18C2×C4⋊C8×C47C2211yescharacteristic
19C2×C22⋊C8×C47—22no—
20C2×#97×C47C2211yescharacteristic
21C2×#10625335—24no—
22#13094024D412yes—
23#13094024D412yes—
24#13094016—22no—
25#13094003—22no—
26#13094003—22no—
27C4×Dic94—22no—
28C4×Dic94—22no—
29#13093983—22no—
30#13093958—22no—
31#13093958—22no—
32#13093956—24no—
33#13093955—24no—
34C4⋊(C47⋊C8)—22no—
35#13093947—24no—
36#13093945—24no—
37C22⋊(C47⋊C8)—22no—
38C4×C47⋊C8D414yes—
39C22×D4×C47D411yescharacteristic
40C23×C4×C47—21no—
41C22×C8×C47—21no—
42C22×C8×C47D412yes—
43C4×D4×C47—22no—
44C4×D4×C47—22no—
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C22⋊C4×C47—21no—
47C2×C42×C47C2311yescharacteristic
48C4⋊C8×C47—22no—
49C22⋊C8×C47—44no—
50#97×C47—22no—
51C24×C47—21no—
52C2×D4×C47—22no—
53C2×D4×C47—42no—
54C22×C4×C47—21no—
55C22×C4×C47—41no—
56C22×C4×C47—41no—
57C22×C4×C47—42no—
58C22×C4×C47—42no—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47#4111yescharacteristic
62C2×Dic94—22no—
63C2×Dic94—22no—
64C2×C8×C47—22no—
65C2×C8×C47—22no—
66C2×C8×C47—41no—
67C2×C8×C47—42no—
68C2×C8×C47SD1614yescomplemented
69C4⋊C4×C47—22no—
70C22⋊C4×C47—42no—
71C42×C47C2×D412yes—
72C42×C47C2×D412yes—
73C22⋊Dic47—42no—
74#10625335—48no—
75C4⋊Dic47—22no—
76C4⋊Dic47—22no—
77C4⋊Dic47—22no—
78C4⋊Dic47—22no—
79Dic47⋊C4—42no—
80Dic47⋊C4—42no—
81C4×Dic47—42no—
82C2×C47⋊C8—24no—
83C23×C47—22no—
84C23×C47—41no—
85C23×C47—42no—
86C23×C47—41no—
87C23×C47—42no—
88C23×C47#12111yescharacteristic
89D4×C47—24no—
90D4×C47—42no—
91C2×C4×C47—41no—
92C2×C4×C47—41no—
93C2×C4×C47—41no—
94C2×C4×C47—42no—
95C2×C4×C47—82no—
96C2×C4×C47—81no—
97C2×C4×C47—81no—
98C2×C4×C47#12011yescharacteristic
99C2×C4×C47#12012yes—
100C2×C4×C47#12112yes—
101C2×C4×C47#12711yescharacteristic
102C2×C4×C47C2×SD1612yes—
103C2×C4×C47#13712yes—
104C2×Dic47—42no—
105C2×Dic47—42no—
106Dic94—44no—
107Dic94—44no—
108C8×C47—24no—
109C8×C47—81no—
110C47⋊C8—44no—
111#10036—471nomaximal, Sylow
112C22×C47—21no—
113C22×C47—21no—
114C22×C47—44no—
115C22×C47—42no—
116C22×C47—82no—
117C22×C47—81no—
118C22×C47—81no—
119C22×C47#39211yescharacteristic
120C22×C47#46112yes—
121C4×C47—22no—
122C4×C47—22no—
123C4×C47—81no—
124C4×C47#44812yes—
125C4×C47#49211yescharacteristic
126C4×C47#49711yescharacteristic
127Dic47—82no—
128Dic47—82no—
129#3162—471no—
130#3101—472no—
131#1955D4711yescharacteristic
132#1481—472no—
133#1275—471no—
134C2×C47—22no—
135C2×C47—82no—
136C2×C47#201011yescharacteristic
137C2×C47#201311yescharacteristic
138C2×C47#201711yescharacteristic
139#533—472no—
140C2×C4×D4C2×D4711yescharacteristic
141#501—942no—
142#501—942no—
143#483—942no—
144#476—942no—
145#461—942no—
146#450—942no—
147C4×SD16—944no—
148#431—472no—
149#427—942no—
150C2×C4⋊C8C2×D4711yescharacteristic
151C2×C22⋊C8—22no—
152C2×#97C2×D4711yescharacteristic
153Q8⋊C8—944no—
154C47#1003611yescharacteristic, complemented, Sylow
155C22×D4D18811yescharacteristic
156C23×C4—21no—
157C2×SD16—944no—
158C22×C8—21no—
159C22×C8C22⋊D4712yes—
160C4⋊Q8—472no—
161C4⋊Q8—472no—
162#125—942no—
163C22⋊Q8—942no—
164C22⋊Q8—942no—
165C4×Q8—942no—
166C4×Q8—942no—
167C4×D4—22no—
168C4×D4—22no—
169#117—942no—
170C2×C4⋊C4D18811yescharacteristic
171C2×C22⋊C4—21no—
172C2×C42C22×D4711yescharacteristic
173#107—942no—
174#107—942no—
175#106—944no—
176#106—944no—
177C4⋊C8—22no—
178C4⋊C8—942no—
179#103—944no—
180#102—944no—
181C22⋊C8—44no—
182C22⋊C8—942no—
183#97—22no—
184C4×C8—474no—
185C24—21no—
186C2×Q8—942no—
187C2×Q8—942no—
188C2×D4—22no—
189C2×D4—42no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4C2×D18811yescharacteristic
196C22×C4#1062535011yescharacteristic
197C22×C4C2×C22⋊D4711yescharacteristic
198SD16—1888no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—944no—
204C2×C8#1062533514yescomplemented
205C4⋊C4—22no—
206C4⋊C4—942no—
207C4⋊C4—942no—
208C4⋊C4—942no—
209C4⋊C4—942no—
210C4⋊C4—1882no—
211C4⋊C4—1882no—
212C22⋊C4—42no—
213C22⋊C4—1882no—
214C42—1882no—
215C42D4×D4712yes—
216C42D4×D4712yes—
217C23—22no—
218C23—41no—
219C23—42no—
220C23—41no—
221C23—42no—
222C23#1309399811yescharacteristic
223Q8—1884no—
224Q8—1884no—
225D4—24no—
226D4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—1882no—
235C2×C4—1882no—
236C2×C4#1309399211yescharacteristic
237C2×C4#1309399412yes—
238C2×C4#1309399712yes—
239C2×C4#1309402011yescharacteristic
240C2×C4C2×#1062533512yes—
241C2×C4#1309405412yes—
242C8—24no—
243C8—81no—
244C8—1884no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#1568903211yescharacteristic
253C22#1568932812yes—
254C4—22no—
255C4—22no—
256C4—81no—
257C4—3762no—
258C4—3762no—
259C4#1568926112yes—
260C4#1568949511yescharacteristic
261C4#1568951811yescharacteristic
262C2—22no—
263C2—82no—
264C2#2024445511yescharacteristic
265C2#2024447011yescharacteristic
266C2#2024449211yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1955C2
socleC22×C47#392
prime radicalC22×D4×C47D4
hypercenter#1955D47
hypocenterC47#10036
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #20253912C2semidirect
3. #20241790C2semidirect
4. #20241219C2semidirect
68. C2×C8×C47SD16semidirect
154. C47#10036semidirect
204. C2×C8#10625335semidirect

Maximal subgroups

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

subgroupindex
#202539122
#202533962
#202417902
#202412192
C47×#19552
#1003647