Finite Group Databasebeta

← #26120378

Subgroups — #26120378

Order 12032.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#20243507C211yesmaximal, characteristic
3#20242089C212yesmaximal
4#20241901C212yesmaximal
5C47×#1290C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689419—22no—
8#15689364—22no—
9#15689334—22no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11#15688969C2211yescharacteristic
12#15688877—22no—
13#15688870—22no—
14#15688868—22no—
15#15688861—24no—
16C47×#432C2212yes—
17C2×C4⋊C8×C47C2211yescharacteristic
18C2×Dic188—22no—
19C22×C47⋊C8—21no—
20#13094024D412yes—
21#13094024D412yes—
22#13094016—22no—
23#13094003—22no—
24#13094003—22no—
25C4×Dic94—22no—
26C4×Dic94—22no—
27#13093983—22no—
28C2×C4×Dic47—21no—
29#13093958—22no—
30C4⋊(C47⋊C8)—22no—
31#13093949—24no—
32C47⋊#95—21no—
33C47⋊#95D412yes—
34C22×C8×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36C4⋊C8×C47—22no—
37C4⋊C8×C47—22no—
38C22⋊C8×C47—22no—
39#97×C47—22no—
40C22×C4×C47C2×D411yescharacteristic
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47#4111yescharacteristic
43C22×Dic47—22no—
44C2×Dic94—22no—
45C2×Dic94—22no—
46C2×C8×C47—22no—
47C2×C8×C47—42no—
48C2×C8×C47—42no—
49C42×C47C2×D412yes—
50C42×C47#4112yes—
51C22⋊Dic47—42no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56Dic47⋊C4—42no—
57Dic47⋊C4—42no—
58C4×Dic47—41no—
59C4×Dic47—41no—
60C4×Dic47—42no—
61C2×C47⋊C8—42no—
62C2×C47⋊C8—41no—
63Dic188—82no—
64C23×C47#12111yescharacteristic
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—41no—
69C2×C4×C47#12011yescharacteristic
70C2×C4×C47#12112yes—
71C2×C4×C47#12312yes—
72C2×C4×C47#12411yescharacteristic
73C2×Dic47—42no—
74C2×Dic47—42no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78Dic94—42no—
79Dic94—42no—
80Dic94—82no—
81C8×C47—42no—
82C8×C47—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#45411yescharacteristic
93C4×C47#45511yescharacteristic
94Dic47—82no—
95Dic47—82no—
96Dic47—82no—
97#3249—471no—
98#1832—471no—
99#1552—472no—
100#1506—472no—
101#1290D4711yescharacteristic
102C2×C47—22no—
103C2×C47#204011yescharacteristic
104C2×C47#204711yescharacteristic
105C2×C47#205311yescharacteristic
106#533—472no—
107#477—942no—
108#467—942no—
109#462—942no—
110#432C2×D4712yes—
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—942no—
120C22×C8—941no—
121C22×C8D18812yes—
122C4⋊Q8—472no—
123C4⋊Q8—472no—
124#125—942no—
125C22⋊Q8—942no—
126C22⋊Q8—942no—
127C4×Q8—942no—
128C4×Q8—942no—
129#117—942no—
130C2×C42—941no—
131C2×C42C22×D4711yescharacteristic
132#107—942no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—942no—
136#103—944no—
137C22⋊C8—22no—
138#97—22no—
139#95—472no—
140#95—941no—
141C2×Q8—942no—
142C2×Q8—942no—
143C22×C4—942no—
144C22×C4C2×D18811yescharacteristic
145C22×C4D4×D4711yescharacteristic
146C22×C4#1062535411yescharacteristic
147Q16—3762no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—1882no—
152C2×C8—1881no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C22⋊C4—1882no—
160C42—1881no—
161C42—1881no—
162C42—1882no—
163C42#1062535012yes—
164C42D4×D4712yes—
165C23#1309399911yescharacteristic
166Q8—3762no—
167Q8—1882no—
168Q8—1882no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—1882no—
174C2×C4—1882no—
175C2×C4—1882no—
176C2×C4—1882no—
177C2×C4—1882no—
178C2×C4#1309399411yescharacteristic
179C2×C4#1309399712yes—
180C2×C4#1309400912yes—
181C2×C4#1309401211yescharacteristic
182C8—42no—
183C8—82no—
184C8—3761no—
185C22—21no—
186C22—21no—
187C22#1568904111yescharacteristic
188C22#1568939912yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—3762no—
193C4—3762no—
194C4—3762no—
195C4#1568929811yescharacteristic
196C4#1568930311yescharacteristic
197C2—22no—
198C2#2024461811yescharacteristic
199C2#2024465711yescharacteristic
200C2#2024469511yescharacteristic
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1290C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1290D47
hypocenterC47#10517
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

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
#202547332
#202435072
#202420892
#202419012
C47×#12902
#1051747