Finite Group Databasebeta

← C4×#15688922 #26131460

Subgroups — C4×#15688922 #26131460

Order 12032.

500 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#15688922C212yesmaximal
2C4×#13093943C212yesmaximal
3#20241515C212yesmaximal
4C4×C4⋊Q8×C47C211yesmaximal, characteristic
5C2×#13093943C2214yes—
6C4×#10625329—22no—
7#15688922C418yesdirect product factor
8#15688892—22no—
9C2×C4⋊Q8×C47C2211yescharacteristic
10C2×C4×Q8×C47C411yescharacteristic
11C2×C4×Q8×C47C2211yescharacteristic
12C47×#391C411yescharacteristic
13C47×#391C2211yescharacteristic
14C47×#389—22no—
15C47×#384C411yescharacteristic
16C4×C4⋊C4×C47—22no—
17C43×C47C411yescharacteristic
18C2×#10625329—24no—
19#13093943—24no—
20#13093943C2×C418yes—
21#13093935—42no—
22C4×C47⋊C8—42no—
23C22×Q8×C47C2×C411yescharacteristic
24C22×Q8×C47C2311yescharacteristic
25C4⋊Q8×C47—22no—
26C4⋊Q8×C47C2×C414yes—
27C4×Q8×C47—41no—
28C4×Q8×C47—41no—
29C4×Q8×C47—41no—
30C4×Q8×C47—41no—
31C2×C4⋊C4×C47—22no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47C2×C411yescharacteristic
35C2×C4⋊C4×C47C2×C411yescharacteristic
36C2×C4⋊C4×C47D412yes—
37C2×C42×C47—21no—
38C2×C42×C47—21no—
39C2×C42×C47—21no—
40C2×C42×C47C2×C411yescharacteristic
41C2×C42×C47C2×C411yescharacteristic
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47D412yes—
44#95×C47—22no—
45#95×C47—22no—
46C2×Q8×C47—21no—
47C2×Q8×C47—41no—
48C2×Q8×C47—41no—
49C2×Q8×C47—41no—
50C2×Q8×C47—41no—
51C2×Q8×C47C4212yes—
52C2×Q8×C47C22×C412yes—
53C2×Q8×C47#4112yes—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C412yes—
61C22×C4×C47C22×C411yescharacteristic
62C22×C4×C47C2×D412yes—
63C4⋊C4×C47—28no—
64C4⋊C4×C47—41no—
65C4⋊C4×C47—42no—
66C4⋊C4×C47—44no—
67C4⋊C4×C47—42no—
68C4⋊C4×C47—41no—
69C42×C47—24no—
70C42×C47—21no—
71C42×C47—21no—
72C42×C47—22no—
73C42×C47—22no—
74C42×C47—21no—
75C42×C47—42no—
76C42×C47—41no—
77C42×C47—41no—
78C42×C47—41no—
79C42×C47C4212yes—
80#10625329—28no—
81#10625329—44no—
82C2×C47⋊C8—44no—
83C23×C47C2×C22⋊C411yescharacteristic
84Q8×C47—42no—
85Q8×C47—42no—
86Q8×C47—42no—
87Q8×C47—42no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—22no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—42no—
106C2×C4×C47—42no—
107C2×C4×C47—41no—
108C2×C4×C47#9911yescharacteristic
109C2×C4×C47#9911yescharacteristic
110C2×C4×C47C2×C4211yescharacteristic
111C2×C4×C47#11711yescharacteristic
112C2×C4×C47C4×D414yes—
113C47⋊C8—48no—
114C4×#356—471nomaximal, Sylow
115C22×C47—21no—
116C22×C47—21no—
117C22×C47C4×C22⋊C411yescharacteristic
118C22×C47C2×#9911yescharacteristic
119C22×C47#41011yescharacteristic
120C4×C47—24no—
121C4×C47—21no—
122C4×C47—24no—
123C4×C47—21no—
124C4×C47—21no—
125C4×C47—42no—
126C4×C47—41no—
127C4×C47—42no—
128C4×C47—42no—
129C4×C47—81no—
130C4×C47#35612yescomplemented
131C4×C4⋊Q8D4711yescharacteristic
132C2×#356—472no—
133C4×#101—472no—
134#1394—472no—
135C2×C47—21no—
136C2×C47—21no—
137C2×C47C4×#9911yescharacteristic
138C2×C47C2×#35611yescharacteristic
139C2×C47#213211yescharacteristic
140C2×C4⋊Q8C2×D4711yescharacteristic
141C2×C4×Q8Dic4711yescharacteristic
142C2×C4×Q8C2×D4711yescharacteristic
143C2×#101—474no—
144C4×M16—942no—
145#391Dic4711yescharacteristic
146#391C2×D4711yescharacteristic
147#389—22no—
148#384Dic4711yescharacteristic
149C4×C4⋊C4—22no—
150C43Dic4711yescharacteristic
151#356—478no—
152#343—942no—
153C47C4×#35611yescharacteristic, complemented, Sylow
154C22×Q8C2×Dic4711yescharacteristic
155C22×Q8C22×D4711yescharacteristic
156C2×M16—944no—
157C4⋊Q8—22no—
158C4⋊Q8C4×D4714yes—
159C4×Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×Dic4711yescharacteristic
167C2×C4⋊C4C2×Dic4711yescharacteristic
168C2×C4⋊C4C22⋊D4712yes—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42C2×Dic4711yescharacteristic
173C2×C42C2×Dic4711yescharacteristic
174C2×C42C2×Dic4711yescharacteristic
175C2×C42C22⋊D4712yes—
176#101—478no—
177#101—944no—
178#97—1882no—
179C4×C8—1882no—
180#95—22no—
181#95—22no—
182C2×Q8—21no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8C4×Dic4712yes—
188C2×Q8C2×C4×D4712yes—
189C2×Q8#1062535012yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22⋊Dic4712yes—
195C22×C4C22⋊Dic4711yescharacteristic
196C22×C4C22⋊Dic4711yescharacteristic
197C22×C4C22×Dic4711yescharacteristic
198C22×C4C2×C22⋊D4712yes—
199M16—948no—
200M16—1884no—
201C2×C8—1884no—
202C4⋊C4—28no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—44no—
207C4⋊C4—42no—
208C42—24no—
209C42—22no—
210C42—21no—
211C42—22no—
212C42—21no—
213C42—21no—
214C42—41no—
215C42—42no—
216C42—41no—
217C42—41no—
218C42C4×Dic4712yes—
219C23C2×C22⋊Dic4711yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—42no—
223Q8—42no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4#1309393911yescharacteristic
245C2×C4#1309393911yescharacteristic
246C2×C4C2×C4×Dic4711yescharacteristic
247C2×C4#1309398311yescharacteristic
248C2×C4C4×C22⋊D4714yes—
249C8—1888no—
250C22—21no—
251C22—21no—
252C22C4×C22⋊Dic4711yescharacteristic
253C22C2×#1309393911yescharacteristic
254C22#1568909711yescharacteristic
255C4—24no—
256C4—21no—
257C4—24no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4#1568892212yesdirect product factor
266C2—21no—
267C2—21no—
268C2C4×#1309393911yescharacteristic
269C2C2×#1568892211yescharacteristic
270C2#2024507311yescharacteristic
subgroupG/H
centerC2×C4#13093939
commutatorC2×C4×C47C2×C42
FrattiniC22×Q8C22×D47
FittingC4×C4⋊Q8×C47C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC22×Q8×C47C23
hypercenterC4×C4⋊Q8D47
hypocenterC47C4×#356
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
7. #15688922C4direct (N × H)
130. C4×C47#356semidirect
153. C47C4×#356semidirect
265. C4#15688922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156889222
C4×#130939432
#202415152
C4×C4⋊Q8×C472
C4×#35647