Finite Group Databasebeta

← #26113698

Subgroups — #26113698

Order 12032.

450 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 119 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#20248600C211yesmaximal, characteristic
2#20243384C211yesmaximal, characteristic
3#20242072C212yesmaximal
4#20241290C212yesmaximal
5C47×#2983C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689147C2212yes—
8C2×#13093943—21no—
9#15689062C414yes—
10#15689030—21no—
11#15689029—22no—
12#15688988—21no—
13C4×C4⋊Dic47C2211yescharacteristic
14#15688892—21no—
15#15688870—24no—
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#446—24no—
18C47×#432—22no—
19C47×#431C2212yes—
20C22×Dic94—21no—
21C2×#10625329—22no—
22#13094024—22no—
23#13094024—22no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47C2×C412yes—
27C2×C4×Dic47—21no—
28C4⋊(C47⋊C8)—22no—
29C4⋊(C47⋊C8)—22no—
30#13093943—42no—
31C47⋊#95—24no—
32C47⋊#95—24no—
33C47⋊#95C2×C412yes—
34C22×Q8×C47D411yescharacteristic
35C4×Q8×C47—22no—
36C4×Q8×C47—22no—
37C2×C4⋊C4×C47C2×C412yes—
38C2×C4⋊C4×C47D411yescharacteristic
39C2×C42×C47D412yes—
40C2×C42×C47C2311yescharacteristic
41C4⋊C8×C47—24no—
42C4⋊C8×C47D414yes—
43C22⋊C8×C47—22no—
44#97×C47—24no—
45C4×C8×C47—22no—
46C2×Q8×C47—22no—
47C2×Q8×C47—21no—
48C2×Q8×C47—21no—
49C2×Q8×C47—22no—
50C22×C4×C47C22⋊C412yes—
51C22×C4×C47C22⋊C412yes—
52C22×C4×C47C22×C411yescharacteristic
53C22×C4×C47C2×D411yescharacteristic
54C22×C4×C47C2×D411yescharacteristic
55C22×Dic47—22no—
56C22×Dic47—22no—
57C2×Dic94—44no—
58C2×Dic94—41no—
59C2×Dic94—41no—
60C2×C8×C47—24no—
61C4⋊C4×C47—24no—
62C4⋊C4×C47—22no—
63C42×C47—22no—
64C42×C47—22no—
65C42×C47C2×D412yes—
66C42×C47#4112yes—
67C4⋊Dic47—24no—
68C4⋊Dic47—42no—
69C4⋊Dic47—42no—
70C4×Dic47—41no—
71C4×Dic47—41no—
72#10625329—42no—
73#10625329—42no—
74C2×C47⋊C8—42no—
75C23×C47C2×C22⋊C411yescharacteristic
76Q8×C47—42no—
77Q8×C47—42no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—41no—
84C2×C4×C47—42no—
85C2×C4×C47C4×D412yes—
86C2×C4×C47#12011yescharacteristic
87C2×C4×C47#12112yes—
88C2×C4×C47#12311yescharacteristic
89C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
90C2×C4×C47#13712yes—
91C2×C4×C47#13711yescharacteristic
92C2×Dic47—42no—
93C2×Dic47—44no—
94C2×Dic47—42no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97Dic94—82no—
98Dic94—82no—
99C8×C47—44no—
100C47⋊C8—82no—
101#9404—471nomaximal, Sylow
102C22×C47—21no—
103C22×C47—21no—
104C22×C47#38611yescharacteristic
105C22×C47#41711yescharacteristic
106C22×C47#41911yescharacteristic
107C4×C47—21no—
108C4×C47—22no—
109C4×C47—42no—
110C4×C47—42no—
111C4×C47#45412yes—
112C4×C47#46812yes—
113C4×C47#47012yes—
114Dic47—82no—
115Dic47—82no—
116#2983D4711yescharacteristic
117#2568—471no—
118#1801—471no—
119#1549—472no—
120#1303—472no—
121C2×C47—21no—
122C2×C47—21no—
123C2×C47#188811yescharacteristic
124C2×C47#189411yescharacteristic
125C2×C47#191511yescharacteristic
126C2×C4⋊Q8—471no—
127C2×C4×Q8C2×D4711yescharacteristic
128#446—24no—
129#432—22no—
130#431C2×D4712yes—
131#423—472no—
132C2×#101—941no—
133#400—474no—
134#391—941no—
135#391—942no—
136#382—941no—
137C4×C4⋊C4—471no—
138#343—941no—
139#332—944no—
140C47#940411yescharacteristic, complemented, Sylow
141C22×Q8—941no—
142C22×Q8D18811yescharacteristic
143C2×M16—942no—
144C4⋊Q8—942no—
145C4⋊Q8—942no—
146C4×Q8—22no—
147C4×Q8—22no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4—941no—
150C2×C4⋊C4—941no—
151C2×C4⋊C4C4×D4712yes—
152C2×C4⋊C4D18811yescharacteristic
153C2×C42—941no—
154C2×C42C22⋊D4712yes—
155C2×C42C22×D4711yescharacteristic
156C4⋊C8—24no—
157C4⋊C8—942no—
158C4⋊C8—942no—
159C4⋊C8C22⋊D4714yes—
160#101—1882no—
161C22⋊C8—22no—
162#97—24no—
163C4×C8—22no—
164#95—472no—
165#95—944no—
166#95—944no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—22no—
171C2×Q8—1884no—
172C2×Q8—1881no—
173C2×Q8—1881no—
174C22×C4—942no—
175C22×C4—942no—
176C22×C4(C2×D47)⋊C412yes—
177C22×C4(C2×D47)⋊C412yes—
178C22×C4C2×C4×D4711yescharacteristic
179C22×C4C2×D18811yescharacteristic
180C22×C4C2×C22⋊D4711yescharacteristic
181M16—1882no—
182M16—1882no—
183C2×C8—24no—
184C2×C8—1882no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—944no—
188C4⋊C4—1882no—
189C4⋊C4—1882no—
190C42—22no—
191C42—22no—
192C42—1881no—
193C42—1881no—
194C42#1062535012yes—
195C42C2×C22⋊D4712yes—
196C23C2×(C2×D47)⋊C411yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—3762no—
200Q8—3762no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—1882no—
209C2×C4—1882no—
210C2×C4—1884no—
211C2×C4—1882no—
212C2×C4—1882no—
213C2×C4C4×C22⋊D4712yes—
214C2×C4#1309399311yescharacteristic
215C2×C4#1309399812yes—
216C2×C4#1309400711yescharacteristic
217C2×C4#1309405211yescharacteristic
218C2×C4#1309405712yes—
219C2×C4#1309405711yescharacteristic
220C8—44no—
221C8—3762no—
222C22—21no—
223C22—21no—
224C22#1568900211yescharacteristic
225C22#1568912511yescharacteristic
226C22#1568913311yescharacteristic
227C4—21no—
228C4—22no—
229C4—42no—
230C4—42no—
231C4—3762no—
232C4—3762no—
233C4#1568929612yes—
234C4#1568936912yes—
235C4#1568938112yes—
236C2—21no—
237C2—21no—
238C2#2024379111yescharacteristic
239C2#2024382111yescharacteristic
240C2#2024394011yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2983C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2983D47
hypocenterC47#9404
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
140. C47#9404semidirect

Maximal subgroups

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

subgroupindex
#202486002
#202433842
#202420722
#202412902
C47×#29832
#940447