Finite Group Databasebeta

← #26119525

Subgroups — #26119525

Order 12032.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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#20249058C211yesmaximal, characteristic
2#20243487C212yesmaximal
3#20241296C211yesmaximal, characteristic
4#20241240C212yesmaximal
5C47×#1820C211yesmaximal, characteristic
6#15689087C2212yes—
7#15689046—22no—
8#15689020—22no—
9#15689006—22no—
10C4×C22⋊Dic47C2212yes—
11#15688882—22no—
12#15688882—22no—
13C2×#117×C47C2211yescharacteristic
14C47×#381C2211yescharacteristic
15C47×#381C2211yescharacteristic
16C47×#342—22no—
17C2×#10625329—22no—
18C2×C4⋊Dic47—22no—
19C2×Dic47⋊C4—22no—
20C2×Dic47⋊C4—22no—
21C2×C22⋊Dic47—22no—
22C2×C4×Dic47D412yes—
23C2×C4×Dic47D412yes—
24C22⋊(C47⋊C8)—22no—
25C22⋊(C47⋊C8)—22no—
26C47⋊#95—22no—
27C47⋊#95—22no—
28C23×C4×C47C2311yescharacteristic
29#117×C47—22no—
30#117×C47—22no—
31C2×C4⋊C4×C47Q812yes—
32C2×C22⋊C4×C47—21no—
33C2×C22⋊C4×C47—21no—
34C2×C22⋊C4×C47D412yes—
35C2×C42×C47—21no—
36#95×C47—22no—
37#95×C47—22no—
38C24×C47C2×D411yescharacteristic
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—42no—
42C22×C4×C47—41no—
43C22×C4×C47C2×D412yes—
44C22×C4×C47C2×Q811yescharacteristic
45C22×C4×C47#4112yes—
46C22×C4×C47#4111yescharacteristic
47C22×Dic47—22no—
48C22×Dic47—22no—
49C4⋊C4×C47—24no—
50C22⋊C4×C47—41no—
51C22⋊C4×C47—41no—
52C22⋊C4×C47—42no—
53C22⋊C4×C47—42no—
54C42×C47—42no—
55C22⋊Dic47—44no—
56C4⋊Dic47—44no—
57Dic47⋊C4—44no—
58Dic47⋊C4—82no—
59C4×Dic47—42no—
60C4×Dic47—42no—
61#10625329—42no—
62#10625329—42no—
63C2×C47⋊C8—42no—
64C23×C47—22no—
65C23×C47—42no—
66C23×C47#12011yescharacteristic
67C23×C47C22⋊Q811yescharacteristic
68C23×C47#12411yescharacteristic
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—82no—
79C2×C4×C47—81no—
80C2×C4×C47—82no—
81C2×C4×C47C22⋊Q812yes—
82C2×C4×C47#12412yes—
83C2×Dic47—24no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C47⋊C8—82no—
90#10389—471nomaximal, Sylow
91C22×C47—22no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—22no—
95C22×C47—22no—
96C22×C47—82no—
97C22×C47#39311yescharacteristic
98C22×C47#45812yes—
99C4×C47—22no—
100C4×C47—22no—
101C4×C47—82no—
102C4×C47—82no—
103C4×C47—161no—
104Dic47—44no—
105Dic47—82no—
106#2608—471no—
107#1826—472no—
108#1820D4711yescharacteristic
109#1306—471no—
110#1284—472no—
111C2×C47—22no—
112C2×C47—41no—
113C2×C47—41no—
114C2×C47#203011yescharacteristic
115C2×C47#203112yes—
116C2×#117C2×D4711yescharacteristic
117#407—472no—
118#396—942no—
119#389—942no—
120#387—942no—
121#381C2×D4711yescharacteristic
122#381C2×D4711yescharacteristic
123C4×C22⋊C4—472no—
124#342—22no—
125#339—942no—
126#339—942no—
127C47#1038911yescharacteristic, complemented, Sylow
128C23×C4C22×D4711yescharacteristic
129C2×M16—942no—
130#117—22no—
131#117—22no—
132C2×C4⋊C4—942no—
133C2×C4⋊C4—942no—
134C2×C4⋊C4—942no—
135C2×C4⋊C4Dic9412yes—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—942no—
139C2×C22⋊C4C22⋊D4712yes—
140C2×C42—21no—
141C2×C42—472no—
142C2×C42—472no—
143C22⋊C8—942no—
144C22⋊C8—942no—
145#95—22no—
146#95—22no—
147#95—942no—
148#95—942no—
149C24C2×C22⋊D4711yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—41no—
154C22×C4—942no—
155C22×C4—942no—
156C22×C4C2×Dic9411yescharacteristic
157C22×C4#1062535011yescharacteristic
158C22×C4D4×D4712yes—
159C22×C4#1062535212yes—
160M16—1882no—
161M16—1882no—
162C2×C8—1882no—
163C4⋊C4—24no—
164C4⋊C4—3762no—
165C4⋊C4—1884no—
166C4⋊C4—1884no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C22⋊C4—1884no—
172C42—42no—
173C42—1882no—
174C42—1882no—
175C23—22no—
176C23—42no—
177C23#1309399211yescharacteristic
178C23#1309400311yescharacteristic
179C23#1309401111yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4—82no—
192C2×C4—944no—
193C2×C4—1882no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4#1309400112yes—
199C2×C4#1309401012yes—
200C8—3762no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1568903511yescharacteristic
208C22#1568931212yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—82no—
213C4—161no—
214C4—3762no—
215C4—1884no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2024455511yescharacteristic
220C2#2024456212yes—
subgroupG/H
centerC22#15689035
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#1820C2
socleC22×C47#393
prime radicalC24×C47C2×D4
hypercenter#1820D47
hypocenterC47#10389
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
127. C47#10389semidirect

Maximal subgroups

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

subgroupindex
#202490582
#202434872
#202412962
#202412402
C47×#18202
#1038947