Finite Group Databasebeta

← #26107200

Subgroups — #26107200

Order 12032.

528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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#20243137C212yesmaximal, complemented
2C2×#15688863C212yesmaximal
3#20241269C212yesmaximal, complemented
4C4×#124×C47C211yesmaximal, characteristic
5C2×#13093935C2214yes—
6#15688878—22no—
7#15688878—22no—
8#15688863C418yescomplemented
9C2×#124×C47C2211yescharacteristic
10C2×C4×Q8×C47C411yescharacteristic
11C2×C4×D4×C47C411yescharacteristic
12C47×#391C411yescharacteristic
13C47×#390C411yescharacteristic
14C47×#388—22no—
15C47×#382C2211yescharacteristic
16C4×C22⋊C4×C47—22no—
17C43×C47C2211yescharacteristic
18C22×C47⋊C8—24no—
19#13093935—24no—
20#13093935C2×C418yescomplemented
21C22×Q8×C47C2×C411yescharacteristic
22C22×D4×C47C2×C411yescharacteristic
23C23×C4×C47—21no—
24#124×C47—22no—
25#124×C47C2×C414yes—
26C4×Q8×C47—42no—
27C4×D4×C47—42no—
28C2×C4⋊C4×C47—21no—
29C2×C4⋊C4×C47C2×C411yescharacteristic
30C2×C4⋊C4×C47C2×C411yescharacteristic
31C2×C22⋊C4×C47—22no—
32C2×C22⋊C4×C47—21no—
33C2×C22⋊C4×C47—22no—
34C2×C42×C47—21no—
35C2×C42×C47C2×C411yescharacteristic
36C2×C42×C47C2×C411yescharacteristic
37C2×C42×C47D412yes—
38C2×C42×C47D412yes—
39C2×C42×C47C2311yescharacteristic
40#95×C47—22no—
41#95×C47—22no—
42C24×C47—21no—
43C2×Q8×C47—21no—
44C2×Q8×C47—41no—
45C2×Q8×C47—41no—
46C2×Q8×C47C4212yes—
47C2×D4×C47—21no—
48C2×D4×C47—41no—
49C2×D4×C47—41no—
50C2×D4×C47C4212yes—
51C22×C4×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—44no—
55C22×C4×C47—42no—
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22⋊C412yes—
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22×C411yescharacteristic
60C22×C4×C47C2×D412yes—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—41no—
64C22⋊C4×C47—28no—
65C22⋊C4×C47—44no—
66C22⋊C4×C47—42no—
67C42×C47—22no—
68C42×C47—41no—
69C42×C47—42no—
70C42×C47—42no—
71C42×C47—42no—
72C42×C47C22×C412yes—
73C42×C47#4112yes—
74C2×C47⋊C8—28no—
75C2×C47⋊C8—44no—
76C2×C47⋊C8—44no—
77C23×C47—22no—
78C23×C47—41no—
79C23×C47—41no—
80C23×C47—42no—
81C23×C47—42no—
82C23×C47C2×C22⋊C411yescharacteristic
83Q8×C47—42no—
84Q8×C47—42no—
85D4×C47—42no—
86D4×C47—42no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—41no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—84no—
105C2×C4×C47#10012yes—
106C2×C4×C47C2×C4211yescharacteristic
107C2×C4×C47#11711yescharacteristic
108C2×C4×C47C4×D414yes—
109C47⋊C8—48no—
110#8224—471nomaximal, Sylow
111C22×C47—42no—
112C22×C47—44no—
113C22×C47—81no—
114C22×C47—81no—
115C22×C47—82no—
116C22×C47C4×C22⋊C411yescharacteristic
117C22×C47C2×#10011yescharacteristic
118C22×C47#41311yescharacteristic
119C22×C47#42112yes—
120C22×C47#42112yes—
121C4×C47—21no—
122C4×C47—21no—
123C4×C47—24no—
124C4×C47—22no—
125C4×C47—41no—
126C4×C47—42no—
127C4×C47—42no—
128C4×C47—81no—
129C4×C47—81no—
130C4×#124D4711yescharacteristic
131#1745—472no—
132C2×#329—472no—
133#1295—472no—
134C2×C47—82no—
135C2×C47#153311yescharacteristic
136C2×C47#153512yes—
137C2×C47#153611yescharacteristic
138C2×C47C4×#10011yescharacteristic
139C2×C47#175912yes—
140C2×#124C2×D4711yescharacteristic
141C2×C4×Q8Dic4711yescharacteristic
142C2×C4×D4Dic4711yescharacteristic
143C2×#97—474no—
144#391Dic4711yescharacteristic
145#390Dic4711yescharacteristic
146#388—22no—
147#382C2×D4711yescharacteristic
148C4×C22⋊C4—22no—
149C43C2×D4711yescharacteristic
150#336—942no—
151#336—942no—
152#329—478no—
153C47#822411yescharacteristic, complemented, Sylow
154C22×Q8C2×Dic4711yescharacteristic
155C22×D4C2×Dic4711yescharacteristic
156C23×C4—21no—
157C22×C8—944no—
158#124—22no—
159#124C4×D4714yes—
160C4×Q8—42no—
161C4×D4—42no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4C2×Dic4711yescharacteristic
164C2×C4⋊C4C2×Dic4711yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—21no—
167C2×C22⋊C4—22no—
168C2×C42—21no—
169C2×C42C2×Dic4711yescharacteristic
170C2×C42C2×Dic4711yescharacteristic
171C2×C42C22⋊D4712yes—
172C2×C42C22⋊D4712yes—
173C2×C42C22×D4711yescharacteristic
174#97—478no—
175#97—944no—
176#95—22no—
177#95—22no—
178C24—21no—
179C2×Q8—21no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8C4×Dic4712yes—
183C2×D4—21no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4C4×Dic4712yes—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—44no—
191C22×C4—42no—
192C22×C4C22⋊Dic4712yes—
193C22×C4C22⋊Dic4711yescharacteristic
194C22×C4C22⋊Dic4711yescharacteristic
195C22×C4C22×Dic4711yescharacteristic
196C22×C4C2×C22⋊D4712yes—
197C2×C8—948no—
198C2×C8—1884no—
199C2×C8—1884no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C22⋊C4—28no—
204C22⋊C4—44no—
205C22⋊C4—42no—
206C42—22no—
207C42—41no—
208C42—42no—
209C42—42no—
210C42—42no—
211C42C2×C4×D4712yes—
212C42#1062535012yes—
213C23—22no—
214C23—41no—
215C23—41no—
216C23—42no—
217C23—42no—
218C23C2×C22⋊Dic4711yescharacteristic
219Q8—42no—
220Q8—42no—
221D4—42no—
222D4—42no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—84no—
241C2×C4#1309394112yes—
242C2×C4C2×C4×Dic4711yescharacteristic
243C2×C4#1309398311yescharacteristic
244C2×C4C4×C22⋊D4714yes—
245C8—1888no—
246C22—42no—
247C22—44no—
248C22—81no—
249C22—82no—
250C22—81no—
251C22C4×C22⋊Dic4711yescharacteristic
252C22C2×#1309394111yescharacteristic
253C22#1568910711yescharacteristic
254C22#1568914012yes—
255C22#1568914012yes—
256C4—22no—
257C4—21no—
258C4—21no—
259C4—24no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—81no—
264C4—81no—
265C2—82no—
266C2#2024201211yescharacteristic
267C2#2024201912yes—
268C2#2024202311yescharacteristic
269C2C4×#1309394111yescharacteristic
270C2#2024319812yes—
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC4×#124×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D4×C47C2×C4
cosocleC2×C42×C47C23
hypercenterC4×#124D47
hypocenterC47#8224
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #20243137C2semidirect
3. #20241269C2semidirect
8. #15688863C4semidirect
20. #13093935C2×C4semidirect
153. C47#8224semidirect

Maximal subgroups

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

subgroupindex
#202431372
C2×#156888632
#202412692
C4×#124×C472
#822447