Finite Group Databasebeta

← #26109062

Subgroups — #26109062

Order 12032.

456 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 113 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#20245943C211yesmaximal, characteristic
2#20243242C212yesmaximal
3C2×#15688864C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#1295C211yesmaximal, characteristic
6C2×#13094016C2211yescharacteristic
7C2×Dic47⋊C8—22no—
8C2×#13093935C2212yes—
9#15689019C412yes—
10#15689005—22no—
11C4⋊C4×Dic47C412yes—
12#15688974—22no—
13C42×Dic47C2211yescharacteristic
14#15688877—22no—
15#15688864—24no—
16C2×#97×C47C2212yes—
17C47×#382C2211yescharacteristic
18C22×C47⋊C8—22no—
19#13094016—22no—
20#13094016D412yes—
21#13094016Q812yes—
22C2×C4⋊Dic47C2×C412yes—
23C2×Dic47⋊C4—22no—
24C2×Dic47⋊C4—22no—
25C2×C4×Dic47—22no—
26C2×C4×Dic47C2×C411yescharacteristic
27C2×C4×Dic47C2×C411yescharacteristic
28C2×C4×Dic47D412yes—
29C2×C4×Dic47D412yes—
30Dic47⋊C8—28no—
31#13093935—22no—
32#13093935—22no—
33C47⋊#95—22no—
34C47⋊#95—22no—
35C22×C8×C47—22no—
36C2×C4⋊C4×C47C2×C412yes—
37C2×C42×C47C2311yescharacteristic
38#97×C47—22no—
39#97×C47—22no—
40#95×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47C22×C411yescharacteristic
43C22×C4×C47C2×D412yes—
44C22×Dic47—22no—
45C22×Dic47C22⋊C411yescharacteristic
46C22×Dic47C22⋊C411yescharacteristic
47C22×Dic47C22⋊C412yes—
48C2×C8×C47—24no—
49C2×C8×C47—42no—
50C2×C8×C47—42no—
51C4⋊C4×C47—42no—
52C42×C47C2×D411yescharacteristic
53C42×C47C2×Q811yescharacteristic
54C42×C47#4112yes—
55C4⋊Dic47—22no—
56C4⋊Dic47C4⋊C414yes—
57Dic47⋊C4—24no—
58Dic47⋊C4—24no—
59Dic47⋊C4—44no—
60C4×Dic47—22no—
61C4×Dic47—24no—
62C4×Dic47—41no—
63C4×Dic47—42no—
64C4×Dic47—44no—
65C2×C47⋊C8—24no—
66C2×C47⋊C8—42no—
67C2×C47⋊C8—42no—
68C23×C47C2×C22⋊C411yescharacteristic
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47C2×C4⋊C411yescharacteristic
77C2×C4×C47#11711yescharacteristic
78C2×C4×C47#12112yes—
79C2×C4×C47C22⋊Q812yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—24no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47#10112yes—
89C2×Dic47#10414yes—
90C8×C47—44no—
91C47⋊C8—44no—
92#8584—471nomaximal, Sylow
93C22×C47#38011yescharacteristic
94C22×C47C2×#10111yescharacteristic
95C22×C47#41311yescharacteristic
96C22×C47C2×#10412yes—
97C22×C47#42112yes—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—22no—
101C4×C47—22no—
102C4×C47—82no—
103Dic47—24no—
104Dic47—22no—
105Dic47—44no—
106Dic47—41no—
107C4×#125—471no—
108#1767—472no—
109C2×#330—472no—
110#1295—471no—
111#1295D4711yescharacteristic
112C2×C47#152611yescharacteristic
113C2×C47#153212yes—
114C2×C47#153411yescharacteristic
115C2×C47#180111yescharacteristic
116C2×C47#180612yes—
117C2×#125—471no—
118C2×C4⋊C8—942no—
119C2×#97—472no—
120C2×#97C2×D4712yes—
121#389—472no—
122#387—942no—
123#382C2×D4711yescharacteristic
124C4×C4⋊C4—472no—
125C4×C4⋊C4—942no—
126C43—471no—
127#336—942no—
128#330—944no—
129C47#858411yescharacteristic, complemented, Sylow
130C22×C8—22no—
131C22×C8—942no—
132#125—472no—
133#125—472no—
134#125—942no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4—942no—
137C2×C4⋊C4—942no—
138C2×C4⋊C4C4×D4712yes—
139C2×C42—471no—
140C2×C42—472no—
141C2×C42—471no—
142C2×C42—472no—
143C2×C42—942no—
144C2×C42C22×D4711yescharacteristic
145C4⋊C8—948no—
146#97—22no—
147#97—22no—
148#97—942no—
149#97—942no—
150#95—22no—
151#95—942no—
152#95—942no—
153C22×C4—22no—
154C22×C4—472no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—942no—
158C22×C4C2×C4×D4711yescharacteristic
159C22×C4D4×D4712yes—
160C2×C8—24no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—944no—
164C2×C8—1882no—
165C2×C8—1882no—
166C4⋊C4—42no—
167C4⋊C4—474no—
168C4⋊C4—942no—
169C4⋊C4—944no—
170C4⋊C4—944no—
171C4⋊C4—1884no—
172C42—944no—
173C42—942no—
174C42—1881no—
175C42—1882no—
176C42—1884no—
177C42#1062535012yes—
178C42D4×D4711yescharacteristic
179C42Q8×D4711yescharacteristic
180C23C22⋊C4×D4711yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—472no—
189C2×C4—474no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—944no—
194C2×C4—941no—
195C2×C4—942no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4C4⋊C4×D4711yescharacteristic
199C2×C4#1309398111yescharacteristic
200C2×C4#1309399712yes—
201C2×C4#1309400212yes—
202C8—44no—
203C8—1884no—
204C22#1568898211yescharacteristic
205C22#101×D4711yescharacteristic
206C22#1568910411yescharacteristic
207C22#104×D4712yes—
208C22#1568913812yes—
209C4—21no—
210C4—21no—
211C4—22no—
212C4—22no—
213C4—82no—
214C4—944no—
215C4—942no—
216C4—1881no—
217C4—1884no—
218C2#2024198111yescharacteristic
219C2#2024200512yes—
220C2#2024201311yescharacteristic
221C2#2024338311yescharacteristic
222C2#2024340712yes—
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1295D47
hypocenterC47#8584
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
129. C47#8584semidirect

Maximal subgroups

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

subgroupindex
#202459432
#202432422
C2×#156888642
#202412692
C47×#12952
#858447