Finite Group Databasebeta

← #26120374

Subgroups — #26120374

Order 12032.

344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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#20243507C211yesmaximal, characteristic
2#20242088C212yesmaximal
3#20241900C212yesmaximal
4#20241258C211yesmaximal, characteristic
5C47×#3249C211yesmaximal, characteristic
6#15689180C2212yes—
7C2×C4⋊(C47⋊C8)C2211yescharacteristic
8#15688969C2211yescharacteristic
9#15688877—22no—
10#15688869—22no—
11#15688869—22no—
12#15688860—24no—
13C47×#533C2212yes—
14C47×#477—22no—
15C47×#467—22no—
16C47×#462—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C22×C47⋊C8—21no—
19C2×C4×Dic47—21no—
20C4⋊(C47⋊C8)—22no—
21C4⋊(C47⋊C8)—22no—
22C22⋊(C47⋊C8)—22no—
23#13093935—22no—
24C47⋊#95—21no—
25C47⋊#95D412yes—
26C2×Q16×C47—22no—
27C22×C8×C47D412yes—
28C4⋊Q8×C47D412yes—
29C4⋊Q8×C47D412yes—
30#125×C47—22no—
31C22⋊Q8×C47—22no—
32C22⋊Q8×C47—22no—
33C4×Q8×C47—22no—
34C4×Q8×C47—22no—
35#117×C47—22no—
36C2×C42×C47C2311yescharacteristic
37#107×C47—22no—
38C4⋊C8×C47—22no—
39#103×C47—24no—
40C2×Q8×C47—22no—
41C2×Q8×C47—22no—
42C22×C4×C47C2×D411yescharacteristic
43C22×C4×C47C2×D411yescharacteristic
44C22×C4×C47#4111yescharacteristic
45C22×Dic47—22no—
46Q16×C47—82no—
47C2×C8×C47—22no—
48C2×C8×C47—42no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—42no—
54C4⋊C4×C47—42no—
55C22⋊C4×C47—42no—
56C42×C47—42no—
57C42×C47C2×D412yes—
58C42×C47#4112yes—
59C4×Dic47—41no—
60C4×Dic47—41no—
61C2×C47⋊C8—42no—
62C2×C47⋊C8—41no—
63C2×C47⋊C8—42no—
64C23×C47#12111yescharacteristic
65Q8×C47—42no—
66Q8×C47—42no—
67Q8×C47—82no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47#12011yescharacteristic
75C2×C4×C47#12112yes—
76C2×C4×C47#12312yes—
77C2×C4×C47#12411yescharacteristic
78C2×Dic47—42no—
79C2×Dic47—42no—
80C2×Dic47—42no—
81C8×C47—42no—
82C47⋊C8—82no—
83C47⋊C8—81no—
84#10517—471nomaximal, Sylow
85C22×C47—21no—
86C22×C47—21no—
87C22×C47#39411yescharacteristic
88C22×C47#47312yes—
89C4×C47—22no—
90C4×C47—21no—
91C4×C47—22no—
92C4×C47—82no—
93C4×C47—82no—
94C4×C47#45411yescharacteristic
95C4×C47#45511yescharacteristic
96Dic47—82no—
97#3249D4711yescharacteristic
98#1832—471no—
99#1552—472no—
100#1506—472no—
101#1290—471no—
102C2×C47—22no—
103C2×C47#204011yescharacteristic
104C2×C47#204711yescharacteristic
105C2×C47#205311yescharacteristic
106#533C2×D4712yes—
107#477—22no—
108#467—22no—
109#462—22no—
110#432—472no—
111C2×C4⋊C8—471no—
112C2×C4⋊C8C2×D4711yescharacteristic
113#376—471no—
114#336—942no—
115#332—942no—
116#332—942no—
117#328—944no—
118C47#1051711yescharacteristic, complemented, Sylow
119C2×Q16—22no—
120C22×C8—941no—
121C22×C8C22⋊D4712yes—
122C4⋊Q8C22⋊D4712yes—
123C4⋊Q8C22⋊D4712yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42—941no—
131C2×C42C22×D4711yescharacteristic
132#107—22no—
133C4⋊C8—22no—
134C4⋊C8—942no—
135C4⋊C8—942no—
136#103—24no—
137C22⋊C8—942no—
138#97—942no—
139#95—472no—
140#95—941no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—942no—
144C22×C4D4×D4711yescharacteristic
145C22×C4#1062535211yescharacteristic
146C22×C4C2×C22⋊D4711yescharacteristic
147Q16—82no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—1882no—
151C2×C8—1881no—
152C2×C8—1882no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—42no—
161C42—1881no—
162C42—1881no—
163C42#1062535212yes—
164C42C2×C22⋊D4712yes—
165C23#1309399511yescharacteristic
166Q8—42no—
167Q8—42no—
168Q8—82no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—1882no—
176C2×C4—1882no—
177C2×C4—1882no—
178C2×C4#1309399311yescharacteristic
179C2×C4#1309399612yes—
180C2×C4#1309400512yes—
181C2×C4#1309401111yescharacteristic
182C8—42no—
183C8—3762no—
184C8—3761no—
185C22—21no—
186C22—21no—
187C22#1568903711yescharacteristic
188C22#1568939512yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—82no—
193C4—82no—
194C4—3762no—
195C4#1568929611yescharacteristic
196C4#1568930111yescharacteristic
197C2—22no—
198C2#2024461411yescharacteristic
199C2#2024465311yescharacteristic
200C2#2024469111yescharacteristic
subgroupG/H
centerC22#15689037
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#3249C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#3249D47
hypocenterC47#10517
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
118. C47#10517semidirect

Maximal subgroups

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

subgroupindex
#202435072
#202420882
#202419002
#202412582
C47×#32492
#1051747