Finite Group Databasebeta

← C47×#7626 #26047324

Subgroups — C47×#7626 #26047324

Order 12032.

874 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 150 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×C47×#390C211yesmaximal, characteristic
2C47×#1749C212yesmaximal, complemented
3C47×#1270C214yesmaximal, complemented
4C23×D4×C47C411yescharacteristic
5C22×C4⋊C4×C47C411yescharacteristic
6C22×C22⋊C4×C47—22no—
7C22×C42×C47C2211yescharacteristic
8C2×C22⋊C8×C47—22no—
9C2×#97×C47—22no—
10C47×#390—22no—
11C47×#390C412yes—
12C47×#390C2212yes—
13C47×#336C2214yescomplemented
14C25×C47—21no—
15C22×D4×C47—24no—
16C22×D4×C47—21no—
17C22×D4×C47—42no—
18C22×D4×C47—42no—
19C22×D4×C47C2×C412yes—
20C23×C4×C47—21no—
21C23×C4×C47C2×C411yescharacteristic
22C23×C4×C47D412yes—
23C22×C8×C47—24no—
24C2×C4⋊C4×C47—21no—
25C2×C4⋊C4×C47—42no—
26C2×C4⋊C4×C47C2×C412yes—
27C2×C22⋊C4×C47—24no—
28C2×C22⋊C4×C47—24no—
29C2×C22⋊C4×C47—48no—
30C2×C42×C47—42no—
31C2×C42×C47C2×C411yescharacteristic
32C2×C42×C47D412yes—
33C2×C42×C47C2311yescharacteristic
34C22⋊C8×C47—28no—
35#97×C47—44no—
36C24×C47—24no—
37C24×C47—22no—
38C24×C47—44no—
39C24×C47—42no—
40C24×C47—42no—
41C24×C47—44no—
42C24×C47C22⋊C411yescharacteristic
43C2×D4×C47—24no—
44C2×D4×C47—22no—
45C2×D4×C47—416no—
46C2×D4×C47—42no—
47C2×D4×C47—42no—
48C2×D4×C47—42no—
49C2×D4×C47—42no—
50C2×D4×C47M1614yes—
51C22×C4×C47—22no—
52C22×C4×C47—22no—
53C22×C4×C47—22no—
54C22×C4×C47—24no—
55C22×C4×C47—24no—
56C22×C4×C47—22no—
57C22×C4×C47—42no—
58C22×C4×C47—44no—
59C22×C4×C47—42no—
60C22×C4×C47C22⋊C412yes—
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C2×D412yes—
64C2×C8×C47—28no—
65C2×C8×C47—44no—
66C2×C8×C47—44no—
67C4⋊C4×C47—42no—
68C4⋊C4×C47—42no—
69C22⋊C4×C47—48no—
70C22⋊C4×C47—48no—
71C42×C47—24no—
72C42×C47—41no—
73C42×C47—41no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47—22no—
77C23×C47—24no—
78C23×C47—48no—
79C23×C47—416no—
80C23×C47—42no—
81C23×C47—42no—
82C23×C47—44no—
83C23×C47—44no—
84C23×C47—84no—
85C23×C47—88no—
86C23×C47—84no—
87C23×C47#10012yes—
88C23×C47#10414yes—
89C23×C47C2×C22⋊C411yescharacteristic
90D4×C47—44no—
91D4×C47—48no—
92D4×C47—44no—
93C2×C4×C47—28no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—48no—
104C2×C4×C47—42no—
105C2×C4×C47—44no—
106C2×C4×C47—84no—
107C2×C4×C47#9912yes—
108C2×C4×C47C2×M1612yes—
109C2×C4×C47AGL(1,ℤ/8)14yes—
110C8×C47—48no—
111#7626C4711yesmaximal, characteristic, direct product factor, Sylow
112C22×C47—22no—
113C22×C47—22no—
114C22×C47—24no—
115C22×C47—24no—
116C22×C47—44no—
117C22×C47—48no—
118C22×C47—816no—
119C22×C47—82no—
120C22×C47—84no—
121C22×C47—82no—
122C22×C47#32914yes—
123C22×C47#40711yescharacteristic
124C22×C47C2×#9911yescharacteristic
125C22×C47C2×#10011yescharacteristic
126C22×C47#41812yes—
127C22×C47C2×#10412yes—
128C4×C47—22no—
129C4×C47—22no—
130C4×C47—24no—
131C4×C47—42no—
132C4×C47—82no—
133C2×#390C2×C4711yescharacteristic
134#1749C2×C4712yescomplemented
135#1270C2×C4714yescomplemented
136C2×C47—24no—
137C2×C47—84no—
138C2×C47#146211yescharacteristic
139C2×C47#149012yes—
140C2×C47#150712yes—
141C2×C47C2×#32911yescharacteristic
142C2×C47#155511yescharacteristic
143C23×D4C4×C4711yescharacteristic
144C22×C4⋊C4C4×C4711yescharacteristic
145C22×C22⋊C4—22no—
146C22×C42C22×C4711yescharacteristic
147C2×C22⋊C8—22no—
148C2×#97—22no—
149#390—22no—
150#390C4×C4712yes—
151#390C22×C4712yes—
152#336C22×C4714yescomplemented
153C47#762611yescharacteristic, direct product factor, Sylow
154C25—21no—
155C22×D4—24no—
156C22×D4—21no—
157C22×D4—42no—
158C22×D4—42no—
159C22×D4C2×C4×C4712yes—
160C23×C4—21no—
161C23×C4C2×C4×C4711yescharacteristic
162C23×C4D4×C4712yes—
163C22×C8—24no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4C2×C4×C4712yes—
167C2×C22⋊C4—24no—
168C2×C22⋊C4—24no—
169C2×C22⋊C4—48no—
170C2×C42—42no—
171C2×C42C2×C4×C4711yescharacteristic
172C2×C42D4×C4712yes—
173C2×C42C23×C4711yescharacteristic
174C22⋊C8—28no—
175#97—44no—
176C24—24no—
177C24—22no—
178C24—44no—
179C24—42no—
180C24—44no—
181C24—42no—
182C24C22⋊C4×C4711yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—416no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4M16×C4714yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—44no—
199C22×C4—42no—
200C22×C4C22⋊C4×C4712yes—
201C22×C4C22⋊C4×C4711yescharacteristic
202C22×C4C22×C4×C4711yescharacteristic
203C22×C4C2×D4×C4712yes—
204C2×C8—28no—
205C2×C8—44no—
206C2×C8—44no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—48no—
210C22⋊C4—48no—
211C42—24no—
212C42—41no—
213C42—41no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—24no—
218C23—48no—
219C23—416no—
220C23—42no—
221C23—42no—
222C23—44no—
223C23—44no—
224C23—88no—
225C23—84no—
226C23—84no—
227C23#100×C4712yes—
228C23#104×C4714yes—
229C23C2×C22⋊C4×C4711yescharacteristic
230D4—44no—
231D4—44no—
232D4—48no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—48no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—84no—
247C2×C4#99×C4712yes—
248C2×C4C2×M16×C4712yes—
249C2×C4AGL(1,ℤ/8)×C4714yes—
250C8—48no—
251C22—24no—
252C22—22no—
253C22—22no—
254C22—24no—
255C22—44no—
256C22—48no—
257C22—816no—
258C22—84no—
259C22—82no—
260C22—82no—
261C22C47×#32914yes—
262C22C47×#40711yescharacteristic
263C22C2×#99×C4711yescharacteristic
264C22C2×#100×C4711yescharacteristic
265C22C47×#41812yes—
266C22C2×#104×C4712yes—
267C4—24no—
268C4—22no—
269C4—22no—
270C4—42no—
271C4—82no—
272C2—24no—
273C2—84no—
274C2C47×#146211yescharacteristic
275C2C47×#149012yes—
276C2C47×#150712yes—
277C2C2×C47×#32911yescharacteristic
278C2C47×#155511yescharacteristic
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC23×D4×C47C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1749C2semidirect
3. C47×#1270C2semidirect
13. C47×#336C22semidirect
111. #7626C47direct (N × H)
134. #1749C2×C47semidirect
135. #1270C2×C47semidirect
152. #336C22×C47semidirect
153. C47#7626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3902
C47×#17492
C47×#12702
#762647