Finite Group Databasebeta

← #26109061

Subgroups — #26109061

Order 12032.

456 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 121 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#125×Dic47C211yesmaximal, characteristic
2#20243242C212yesmaximal
3C2×#15688865C211yesmaximal, characteristic
4#20241270C212yesmaximal
5C2×C47×#330C211yesmaximal, characteristic
6C2×Dic47⋊C8—22no—
7C2×#13093935C2212yes—
8#15689022C412yes—
9#15689009—22no—
10#15688989C2211yescharacteristic
11C4⋊C4×Dic47—22no—
12C4⋊C4×Dic47C412yes—
13C42×Dic47C2211yescharacteristic
14#15688877—22no—
15#15688865—22no—
16C2×#125×C47C2211yescharacteristic
17C2×#97×C47C2212yes—
18C47×#330—22no—
19C22×C47⋊C8—22no—
20C2×C4⋊Dic47—22no—
21C2×C4⋊Dic47C2×C412yes—
22C2×C4×Dic47—22no—
23C2×C4×Dic47C2×C411yescharacteristic
24C2×C4×Dic47C2×C411yescharacteristic
25C2×C4×Dic47D412yes—
26C2×C4×Dic47D412yes—
27Dic47⋊C8—28no—
28#13093935—22no—
29#13093935—22no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C47⋊#95—22no—
33C22×C8×C47—22no—
34#125×C47—22no—
35#125×C47D412yes—
36#125×C47Q812yes—
37C2×C4⋊C4×C47—22no—
38C2×C4⋊C4×C47C2×C412yes—
39C2×C42×C47C2311yescharacteristic
40#97×C47—22no—
41#97×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47C22×C411yescharacteristic
44C22×C4×C47C2×D412yes—
45C22×Dic47—22no—
46C22×Dic47C22⋊C411yescharacteristic
47C22×Dic47C22⋊C411yescharacteristic
48C22×Dic47C22⋊C412yes—
49C2×C8×C47—24no—
50C2×C8×C47—42no—
51C2×C8×C47—42no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—24no—
54C4⋊C4×C47—24no—
55C4⋊C4×C47C4⋊C414yes—
56C42×C47C2×D411yescharacteristic
57C42×C47C2×Q811yescharacteristic
58C42×C47#4112yes—
59C4⋊Dic47—44no—
60C4⋊Dic47—42no—
61C4×Dic47—22no—
62C4×Dic47—24no—
63C4×Dic47—41no—
64C4×Dic47—42no—
65C4×Dic47—44no—
66C2×C47⋊C8—24no—
67C2×C47⋊C8—42no—
68C2×C47⋊C8—42no—
69C23×C47C2×C22⋊C411yescharacteristic
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47C2×C4⋊C411yescharacteristic
78C2×C4×C47#11711yescharacteristic
79C2×C4×C47#12112yes—
80C2×C4×C47C22⋊Q812yes—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47#10112yes—
90C2×Dic47#10414yes—
91C8×C47—44no—
92C47⋊C8—44no—
93#8584—471nomaximal, Sylow
94C22×C47#38011yescharacteristic
95C22×C47C2×#10111yescharacteristic
96C22×C47#41311yescharacteristic
97C22×C47C2×#10412yes—
98C22×C47#42112yes—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—44no—
104Dic47—24no—
105Dic47—22no—
106Dic47—41no—
107Dic47—82no—
108C4×#125—471no—
109#1767—472no—
110C2×#330—471no—
111C2×#330D4711yescharacteristic
112#1295—472no—
113C2×C47#152611yescharacteristic
114C2×C47#153212yes—
115C2×C47#153411yescharacteristic
116C2×C47#180111yescharacteristic
117C2×C47#180612yes—
118C2×#125C2×D4711yescharacteristic
119C2×C4⋊C8—942no—
120C2×#97—472no—
121C2×#97C2×D4712yes—
122#389—472no—
123#387—942no—
124#382—471no—
125C4×C4⋊C4—472no—
126C4×C4⋊C4—942no—
127C43—471no—
128#336—942no—
129#330—22no—
130#330—942no—
131C47#858411yescharacteristic, complemented, Sylow
132C22×C8—22no—
133C22×C8—942no—
134#125—22no—
135#125Dic9412yes—
136#125C22⋊D4712yes—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—942no—
140C2×C4⋊C4C4×D4712yes—
141C2×C42—471no—
142C2×C42—472no—
143C2×C42—471no—
144C2×C42—472no—
145C2×C42—942no—
146C2×C42C22×D4711yescharacteristic
147C4⋊C8—948no—
148#97—22no—
149#97—22no—
150#97—942no—
151#97—942no—
152#95—942no—
153#95—942no—
154#95—942no—
155C22×C4—22no—
156C22×C4—472no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—942no—
160C22×C4C2×C4×D4711yescharacteristic
161C22×C4D4×D4712yes—
162C2×C8—24no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—944no—
166C2×C8—1882no—
167C2×C8—1882no—
168C4⋊C4—22no—
169C4⋊C4—24no—
170C4⋊C4—24no—
171C4⋊C4—1882no—
172C4⋊C4—1884no—
173C4⋊C4Dic47⋊C414yes—
174C42—944no—
175C42—942no—
176C42—1881no—
177C42—1882no—
178C42—1884no—
179C42C2×Dic9411yescharacteristic
180C42#1062535212yes—
181C42C2×C22⋊D4711yescharacteristic
182C23C22⋊C4×D4711yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—472no—
191C2×C4—474no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—941no—
196C2×C4—942no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4C2×Dic47⋊C411yescharacteristic
201C2×C4#1309398011yescharacteristic
202C2×C4#1309399612yes—
203C2×C4#1309400112yes—
204C8—44no—
205C8—1884no—
206C22#1568898111yescharacteristic
207C22#101×D4711yescharacteristic
208C22#1568910611yescharacteristic
209C22#104×D4712yes—
210C22#1568913812yes—
211C4—21no—
212C4—21no—
213C4—22no—
214C4—22no—
215C4—44no—
216C4—944no—
217C4—942no—
218C4—3762no—
219C4—1881no—
220C2#2024198111yescharacteristic
221C2#2024200712yes—
222C2#2024201311yescharacteristic
223C2#2024338211yescharacteristic
224C2#2024340612yes—
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#330C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#330D47
hypocenterC47#8584
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
131. C47#8584semidirect

Maximal subgroups

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

subgroupindex
#125×Dic472
#202432422
C2×#156888652
#202412702
C2×C47×#3302
#858447