Finite Group Databasebeta

← C47×#12131 #26051829

Subgroups — C47×#12131 #26051829

Order 12032.

398 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C47×#2809C211yesmaximal, characteristic, complemented
2C47×#2007C211yesmaximal, characteristic
3C47×#1616C212yesmaximal
4C47×#1353C212yesmaximal, complemented
5C47×#1319C211yesmaximal, characteristic, complemented
6C2×#137×C47—21no—
7C47×#537C2211yescharacteristic
8C47×#481—22no—
9C2×#104×C47—21no—
10C47×#400C2212yes—
11C47×#398—22no—
12C47×#391—21no—
13C47×#391C2211yescharacteristic
14C47×#389—21no—
15C47×#387—22no—
16C47×#343C2211yescharacteristic
17C47×#327—22no—
18C47×#324C2212yes—
19C2×#41×C47—21no—
20C22×Q8×C47D411yescharacteristic
21#137×C47—42no—
22#137×C47—42no—
23C2×Q16×C47—41no—
24C2×SD16×C47—41no—
25C2×M16×C47—21no—
26C22⋊Q8×C47—41no—
27#121×C47—22no—
28#121×C47—41no—
29C2×C4⋊C4×C47—22no—
30C2×C4⋊C4×C47—21no—
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47D412yes—
34C2×C4⋊C4×C47C2311yescharacteristic
35C2×C42×C47—21no—
36C2×C42×C47D411yescharacteristic
37#106×C47—42no—
38#104×C47—42no—
39#102×C47—42no—
40C22⋊C8×C47—22no—
41#95×C47—22no—
42#95×C47—22no—
43#95×C47—22no—
44#95×C47—22no—
45#95×C47D412yes—
46#41×C47—41no—
47#41×C47—41no—
48#41×C47—41no—
49#41×C47—41no—
50C2×Q8×C47—21no—
51C2×Q8×C47—21no—
52C2×Q8×C47—41no—
53C2×Q8×C47—41no—
54C2×Q8×C47SD1612yes—
55C2×D4×C47—21no—
56C2×D4×C47—22no—
57C2×D4×C47—41no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—41no—
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D412yes—
65Q16×C47—44no—
66SD16×C47—44no—
67M16×C47—22no—
68M16×C47—41no—
69C2×C8×C47—41no—
70C2×C8×C47—42no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—41no—
73C4⋊C4×C47—44no—
74C4⋊C4×C47—42no—
75C4⋊C4×C47—42no—
76C4⋊C4×C47—81no—
77C4⋊C4×C47—81no—
78C22⋊C4×C47—42no—
79C42×C47—41no—
80C42×C47—81no—
81C23×C47—41no—
82C23×C47#12011yescharacteristic
83Q8×C47—42no—
84Q8×C47—41no—
85Q8×C47—41no—
86Q8×C47—81no—
87D4×C47—41no—
88D4×C47—41no—
89D4×C47—82no—
90D4×C47—81no—
91D4×C47—81no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—42no—
107C2×C4×C47—41no—
108C2×C4×C47—42no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47C2×SD1611yescharacteristic
112C2×C4×C47#13711yescharacteristic
113C8×C47—42no—
114C8×C47—82no—
115#12131C4711yesmaximal, characteristic, direct product factor, Sylow
116C22×C47—21no—
117C22×C47—21no—
118C22×C47—81no—
119C22×C47—81no—
120C22×C47—81no—
121C22×C47#44811yescharacteristic
122C22×C47#45311yescharacteristic
123C22×C47B(4,𝔽2)11yescharacteristic
124C4×C47—21no—
125C4×C47—21no—
126C4×C47—42no—
127C4×C47—42no—
128C4×C47—42no—
129C4×C47—82no—
130C4×C47—81no—
131C4×C47—82no—
132#2809C2×C4711yescharacteristic, complemented
133#2007C2×C4711yescharacteristic
134#1616C2×C4712yes—
135#1353C2×C4712yescomplemented
136#1319C2×C4711yescharacteristic, complemented
137C2×C47—21no—
138C2×C47—21no—
139C2×C47—161no—
140C2×C47#159611yescharacteristic
141C2×C47#220111yescharacteristic
142C2×C47#220411yescharacteristic
143C2×#137—21no—
144#537C22×C4711yescharacteristic
145#481—22no—
146C2×#104—21no—
147#400C22×C4712yes—
148#398—22no—
149#391—21no—
150#391C22×C4711yescharacteristic
151#389—21no—
152#387—22no—
153#343C22×C4711yescharacteristic
154#327—22no—
155#324C22×C4712yes—
156C47#1213111yescharacteristic, direct product factor, Sylow
157C2×#41—21no—
158C22×Q8D4×C4711yescharacteristic
159#137—42no—
160#137—42no—
161C2×Q16—41no—
162C2×SD16—41no—
163C2×M16—21no—
164C22⋊Q8—41no—
165#121—22no—
166#121—41no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4D4×C4712yes—
172C2×C4⋊C4C23×C4711yescharacteristic
173C2×C42—21no—
174C2×C42D4×C4711yescharacteristic
175#106—42no—
176#104—42no—
177#102—42no—
178C22⋊C8—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95D4×C4712yes—
184#41—41no—
185#41—41no—
186#41—41no—
187#41—41no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8SD16×C4712yes—
193C2×D4—21no—
194C2×D4—22no—
195C2×D4—41no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—41no—
201C22×C4C2×D4×C4711yescharacteristic
202C22×C4C2×D4×C4712yes—
203Q16—44no—
204SD16—44no—
205M16—22no—
206M16—41no—
207C2×C8—41no—
208C2×C8—42no—
209C4⋊C4—22no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—44no—
213C4⋊C4—42no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C22⋊C4—42no—
217C42—41no—
218C42—81no—
219C23—41no—
220C23#120×C4711yescharacteristic
221Q8—42no—
222Q8—41no—
223Q8—41no—
224Q8—81no—
225D4—41no—
226D4—41no—
227D4—82no—
228D4—81no—
229D4—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4C2×SD16×C4711yescharacteristic
250C2×C4#137×C4711yescharacteristic
251C8—42no—
252C8—82no—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22C47×#44811yescharacteristic
259C22C47×#45311yescharacteristic
260C22C47×B(4,𝔽2)11yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—42no—
266C4—82no—
267C4—81no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2C47×#159611yescharacteristic
273C2C47×#220111yescharacteristic
274C2C47×#220411yescharacteristic
subgroupG/H
center, socleC22×C47B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C47
prime radicalC47×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C47 ◁ C2×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2809C2semidirect
4. C47×#1353C2semidirect
5. C47×#1319C2semidirect
115. #12131C47direct (N × H)
132. #2809C2×C47semidirect
135. #1353C2×C47semidirect
136. #1319C2×C47semidirect
156. C47#12131direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28092
C47×#20072
C47×#16162
C47×#13532
C47×#13192
#1213147