Finite Group Databasebeta

← #26109799

Subgroups — #26109799

Order 12032.

566 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 87 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#20245973C211yesmaximal, characteristic
2#20243311C212yesmaximal
3#20241297C212yesmaximal
4#20241296C211yesmaximal, characteristic
5C47×#1306C211yesmaximal, characteristic
6C23×Dic94C2211yescharacteristic
7C2×#13093980C412yes—
8C2×#13093942—24no—
9#15689087C2212yes—
10#15689027—24no—
11#15688986C2211yescharacteristic
12#15688984C412yes—
13C47×#407C2212yes—
14C47×#381C2211yescharacteristic
15C22×Dic94—22no—
16C22×Dic94—21no—
17C22×Dic94—21no—
18C22×Dic94—44no—
19C22×Dic94D414yes—
20C23×Dic47C2×C411yescharacteristic
21C23×Dic47C2×C411yescharacteristic
22C2×#10625329—22no—
23#13093980—44no—
24C2×Dic47⋊C4—22no—
25C2×C22⋊Dic47C2×C412yes—
26C2×C4×Dic47—22no—
27#13093942—48no—
28C22⋊(C47⋊C8)—22no—
29C22⋊(C47⋊C8)—22no—
30C47⋊#95—22no—
31C47⋊#95—24no—
32C23×C4×C47C2311yescharacteristic
33C2×M16×C47—22no—
34C2×C22⋊C4×C47C2×C412yes—
35C22⋊C8×C47—22no—
36C22⋊C8×C47—22no—
37#95×C47—22no—
38C24×C47C22×C411yescharacteristic
39C22×C4×C47—22no—
40C22×C4×C47—42no—
41C22×C4×C47C2×D412yes—
42C22×C4×C47#4112yes—
43C22×C4×C47#4111yescharacteristic
44C22×C4×C47#4111yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C22×Dic47—24no—
48C22×Dic47—21no—
49C22×Dic47—21no—
50C22×Dic47—22no—
51C22×Dic47—42no—
52C22×Dic47C22⋊C412yes—
53C22×Dic47C22⋊C412yes—
54C2×Dic94—24no—
55C2×Dic94—24no—
56C2×Dic94—28no—
57C2×Dic94—44no—
58C2×Dic94—44no—
59C2×Dic94—48no—
60C2×Dic94—44no—
61M16×C47—44no—
62C2×C8×C47—42no—
63C22⋊C4×C47—42no—
64C22⋊Dic47—42no—
65Dic47⋊C4—44no—
66C4×Dic47—44no—
67#10625329—44no—
68C2×C47⋊C8—42no—
69C23×C47—22no—
70C23×C47—42no—
71C23×C47C2×C22⋊C411yescharacteristic
72C23×C47#11711yescharacteristic
73C23×C47#11711yescharacteristic
74C2×C4×C47—24no—
75C2×C4×C47—42no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—44no—
79C2×C4×C47—42no—
80C2×C4×C47#12312yes—
81C2×C4×C47#12312yes—
82C2×Dic47—24no—
83C2×Dic47—24no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—24no—
88C2×Dic47—42no—
89C2×Dic47—42no—
90C2×Dic47—44no—
91C2×Dic47—42no—
92C2×Dic47#9914yes—
93Dic94—48no—
94Dic94—48no—
95C8×C47—82no—
96C47⋊C8—82no—
97#8753—471nomaximal, Sylow
98C22×C47—22no—
99C22×C47—21no—
100C22×C47—21no—
101C22×C47—22no—
102C22×C47—22no—
103C22×C47—44no—
104C22×C47#38111yescharacteristic
105C22×C47C2×#9912yes—
106C4×C47—22no—
107C4×C47—22no—
108C4×C47—82no—
109Dic47—24no—
110Dic47—42no—
111Dic47—82no—
112#2310—471no—
113#1784—472no—
114#1306—472no—
115#1306—471no—
116#1306D4711yescharacteristic
117C2×C47—22no—
118C2×C47—41no—
119C2×C47—41no—
120C2×C47#181911yescharacteristic
121C2×C47#183012yes—
122C23×Q8—471no—
123C2×#117—472no—
124C2×#101—944no—
125#407—472no—
126#407C2×D4712yes—
127#391—944no—
128#381—471no—
129#381—472no—
130#381C2×D4711yescharacteristic
131C47#875311yescharacteristic, complemented, Sylow
132C22×Q8—474no—
133C22×Q8—942no—
134C22×Q8—941no—
135C22×Q8—941no—
136C22×Q8—1884no—
137C23×C4—471no—
138C23×C4—471no—
139C23×C4C22×D4711yescharacteristic
140C2×M16—22no—
141C2×M16—942no—
142#117—1884no—
143C2×C4⋊C4—942no—
144C2×C22⋊C4—472no—
145C2×C22⋊C4C4×D4712yes—
146C2×C42—942no—
147#101—1888no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150C22⋊C8—942no—
151C22⋊C8—942no—
152#95—22no—
153#95—944no—
154#95—942no—
155C24C2×C4×D4711yescharacteristic
156C2×Q8—948no—
157C2×Q8—944no—
158C2×Q8—944no—
159C2×Q8—1884no—
160C2×Q8—1888no—
161C2×Q8—1884no—
162C2×Q8—1884no—
163C22×C4—22no—
164C22×C4—42no—
165C22×C4—472no—
166C22×C4—472no—
167C22×C4—944no—
168C22×C4—941no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4—941no—
172C22×C4—942no—
173C22×C4—1882no—
174C22×C4#1062535012yes—
175C22×C4D4×D4712yes—
176C22×C4#1062535211yescharacteristic
177C22×C4#1062535411yescharacteristic
178M16—44no—
179M16—1884no—
180C2×C8—42no—
181C2×C8—1882no—
182C4⋊C4—1884no—
183C22⋊C4—42no—
184C22⋊C4—1882no—
185C42—1884no—
186C23—22no—
187C23—42no—
188C23C22⋊C4×D4711yescharacteristic
189C23#1309398111yescharacteristic
190C23#1309398211yescharacteristic
191Q8—1888no—
192Q8—1888no—
193C2×C4—24no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—44no—
198C2×C4—42no—
199C2×C4—474no—
200C2×C4—944no—
201C2×C4—944no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—944no—
206C2×C4—1884no—
207C2×C4—1882no—
208C2×C4—1882no—
209C2×C4—1882no—
210C2×C4#1309400612yes—
211C2×C4#1309400912yes—
212C8—82no—
213C8—3762no—
214C22—22no—
215C22—21no—
216C22—21no—
217C22—22no—
218C22—22no—
219C22—44no—
220C22#1568898511yescharacteristic
221C22#99×D4712yes—
222C4—22no—
223C4—22no—
224C4—82no—
225C4—944no—
226C4—3762no—
227C4—1882no—
228C2—22no—
229C2—41no—
230C2—41no—
231C2#2024346111yescharacteristic
232C2#2024350112yes—
subgroupG/H
centerC22#15688985
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1306C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#1306D47
hypocenterC47#8753
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
131. C47#8753semidirect

Maximal subgroups

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

subgroupindex
#202459732
#202433112
#202412972
#202412962
C47×#13062
#875347