Finite Group Databasebeta

← C47×#13436 #26053134

Subgroups — C47×#13436 #26053134

Order 12032.

438 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3199C211yesmaximal, characteristic
2C47×#2122C212yesmaximal, complemented
3C47×#1910C212yesmaximal, complemented
4C47×#1858C211yesmaximal, characteristic, complemented
5C47×#1391C211yesmaximal, characteristic, complemented
6C47×#568C2211yescharacteristic
7C47×#535C2212yes—
8C47×#482—22no—
9C47×#469—21no—
10C47×#466—21no—
11C47×#447—22no—
12C47×#430—21no—
13C47×#418—22no—
14C47×#413C2211yescharacteristic
15C47×#410C2212yes—
16C47×#408C2211yescharacteristic
17C47×AΣL(1,𝔽16)—24no—
18C47×#341—21no—
19C47×H(3,ℤ/4)—22no—
20C2×#41×C47C2311yescharacteristic
21C22×D4×C47D412yes—
22C2×D8×C47—21no—
23C2×D8×C47—21no—
24#131×C47—42no—
25C2×M16×C47—22no—
26C2×M16×C47—21no—
27C2×M16×C47—21no—
28C2×M16×C47D411yescharacteristic
29C22×C8×C47D411yescharacteristic
30#127×C47—22no—
31#124×C47—22no—
32#121×C47—22no—
33#121×C47—22no—
34#120×C47—22no—
35#120×C47—22no—
36#117×C47—22no—
37#117×C47D412yes—
38#108×C47—42no—
39#107×C47—21no—
40#106×C47—21no—
41#102×C47—22no—
42#102×C47—22no—
43#102×C47—44no—
44#101×C47—21no—
45#100×C47D412yes—
46#99×C47—22no—
47#99×C47—22no—
48C22⋊C8×C47—22no—
49C24×C47—22no—
50#41×C47—41no—
51#41×C47—41no—
52C2×Q8×C47#4111yescharacteristic
53C2×D4×C47—22no—
54C2×D4×C47—22no—
55C2×D4×C47—42no—
56C2×D4×C47—42no—
57C2×D4×C47—42no—
58C2×D4×C47—42no—
59C2×D4×C47C2×D411yescharacteristic
60C2×D4×C47#4112yes—
61C22×C4×C47C2×D411yescharacteristic
62C22×C4×C47C2×D412yes—
63D8×C47—81no—
64D8×C47—81no—
65M16×C47—22no—
66M16×C47—22no—
67M16×C47—41no—
68M16×C47—42no—
69M16×C47—41no—
70M16×C47—41no—
71C2×C8×C47—24no—
72C2×C8×C47—21no—
73C2×C8×C47—21no—
74C2×C8×C47—41no—
75C2×C8×C47—41no—
76C2×C8×C47—41no—
77C4⋊C4×C47—22no—
78C4⋊C4×C47—42no—
79C22⋊C4×C47—22no—
80C22⋊C4×C47—42no—
81C22⋊C4×C47—42no—
82C22⋊C4×C47—42no—
83C42×C47—22no—
84C42×C47—42no—
85C23×C47—42no—
86C23×C47—82no—
87C23×C47—162no—
88C23×C47#12112yes—
89C23×C47#12411yescharacteristic
90Q8×C47—41no—
91D4×C47—41no—
92D4×C47—42no—
93D4×C47—44no—
94D4×C47—42no—
95D4×C47—42no—
96D4×C47—162no—
97D4×C47—162no—
98C2×C4×C47—22no—
99C2×C4×C47—21no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—42no—
103C2×C4×C47—82no—
104C2×C4×C47#12011yescharacteristic
105C2×C4×C47#12111yescharacteristic
106C2×C4×C47#12312yes—
107C8×C47—42no—
108C8×C47—42no—
109C8×C47—41no—
110C8×C47—41no—
111#13436C4711yesmaximal, characteristic, direct product factor, Sylow
112C22×C47—22no—
113C22×C47—21no—
114C22×C47—41no—
115C22×C47—42no—
116C22×C47—82no—
117C22×C47—82no—
118C22×C47—82no—
119C22×C47—164no—
120C22×C47#39411yescharacteristic
121C4×C47—21no—
122C4×C47—22no—
123C4×C47—82no—
124C4×C47—162no—
125C4×C47B(4,𝔽2)11yescharacteristic
126C4×C47#45811yescharacteristic
127#3199C2×C4711yescharacteristic
128#2122C2×C4712yescomplemented
129#1910C2×C4712yescomplemented
130#1858C2×C4711yescharacteristic, complemented
131#1391C2×C4711yescharacteristic, complemented
132C2×C47—21no—
133C2×C47—42no—
134C2×C47—41no—
135C2×C47—162no—
136C2×C47#204411yescharacteristic
137#568C22×C4711yescharacteristic
138#535C22×C4712yes—
139#482—22no—
140#469—21no—
141#466—21no—
142#447—22no—
143#430—21no—
144#418—22no—
145#413C22×C4711yescharacteristic
146#410C22×C4712yes—
147#408C22×C4711yescharacteristic
148AΣL(1,𝔽16)—24no—
149#341—21no—
150H(3,ℤ/4)—22no—
151C47#1343611yescharacteristic, direct product factor, Sylow
152C2×#41C23×C4711yescharacteristic
153C22×D4D4×C4712yes—
154C2×D8—21no—
155C2×D8—21no—
156#131—42no—
157C2×M16—22no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16D4×C4711yescharacteristic
161C22×C8D4×C4711yescharacteristic
162#127—22no—
163#124—22no—
164#121—22no—
165#121—22no—
166#120—22no—
167#120—22no—
168#117—22no—
169#117D4×C4712yes—
170#108—42no—
171#107—21no—
172#106—21no—
173#102—22no—
174#102—22no—
175#102—44no—
176#101—21no—
177#100D4×C4712yes—
178#99—22no—
179#99—22no—
180C22⋊C8—22no—
181C24—22no—
182#41—41no—
183#41—41no—
184C2×Q8#41×C4711yescharacteristic
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4C2×D4×C4711yescharacteristic
192C2×D4#41×C4712yes—
193C22×C4C2×D4×C4711yescharacteristic
194C22×C4C2×D4×C4712yes—
195D8—81no—
196D8—81no—
197M16—22no—
198M16—22no—
199M16—41no—
200M16—42no—
201M16—41no—
202M16—41no—
203C2×C8—24no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C22⋊C4—22no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C42—22no—
216C42—42no—
217C23—42no—
218C23—82no—
219C23—162no—
220C23#121×C4712yes—
221C23#124×C4711yescharacteristic
222Q8—41no—
223D4—41no—
224D4—42no—
225D4—44no—
226D4—42no—
227D4—42no—
228D4—162no—
229D4—162no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4#120×C4711yescharacteristic
237C2×C4#121×C4711yescharacteristic
238C2×C4#123×C4712yes—
239C8—42no—
240C8—42no—
241C8—41no—
242C8—41no—
243C22—22no—
244C22—21no—
245C22—41no—
246C22—42no—
247C22—82no—
248C22—82no—
249C22—82no—
250C22—164no—
251C22C47×#39411yescharacteristic
252C4—21no—
253C4—22no—
254C4—82no—
255C4—162no—
256C4C47×B(4,𝔽2)11yescharacteristic
257C4C47×#45811yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—162no—
262C2C47×#204411yescharacteristic
subgroupG/H
center, socleC2×C47#2044
commutator, Frattini, cosocleC2×#41C23×C47
prime radicalC47×#3199C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C2×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2122C2semidirect
3. C47×#1910C2semidirect
4. C47×#1858C2semidirect
5. C47×#1391C2semidirect
111. #13436C47direct (N × H)
128. #2122C2×C47semidirect
129. #1910C2×C47semidirect
130. #1858C2×C47semidirect
131. #1391C2×C47semidirect
151. C47#13436direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31992
C47×#21222
C47×#19102
C47×#18582
C47×#13912
#1343647