Finite Group Databasebeta

← C47×#13151 #26052849

Subgroups — C47×#13151 #26052849

Order 12032.

332 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#359C211yesmaximal, characteristic
2C47×#2138C211yesmaximal, characteristic
3C2×C4×C16×C47C211yesmaximal, characteristic, complemented
4C47×#1974C211yesmaximal, characteristic
5C47×#1945C211yesmaximal, characteristic, complemented
6C47×#1382C211yesmaximal, characteristic, complemented
7C47×#1381C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C22×C16×C47C2211yescharacteristic
10C22×C16×C47C2211yescharacteristic
11C2×#108×C47C2211yescharacteristic
12C2×#108×C47C2211yescharacteristic
13C47×#427C2211yescharacteristic
14C47×#424—21no—
15C2×#104×C47—21no—
16C47×#408—21no—
17C2×C4×C8×C47C2211yescharacteristic
18C47×#359—22no—
19C47×#358C412yescomplemented
20C47×#357C412yescomplemented
21C4×C16×C47—22no—
22C47×#339—21no—
23C2×#41×C47—21no—
24#135×C47—21no—
25#135×C47—21no—
26#135×C47—21no—
27#135×C47—21no—
28C2×Q16×C47C2×C411yescharacteristic
29C2×SD16×C47—21no—
30C2×D8×C47C2×C411yescharacteristic
31C2×M16×C47—21no—
32C2×M16×C47—21no—
33C22×C8×C47D411yescharacteristic
34C22×C8×C47C2311yescharacteristic
35#117×C47—21no—
36C2×C42×C47D411yescharacteristic
37C2×C16×C47—21no—
38C2×C16×C47—21no—
39C2×C16×C47—21no—
40C2×C16×C47—21no—
41C2×C16×C47C2×C412yes—
42C2×C16×C47D412yes—
43#108×C47—21no—
44#108×C47—21no—
45#108×C47—21no—
46#108×C47—21no—
47#107×C47C2×C412yes—
48#106×C47—21no—
49C4⋊C8×C47—42no—
50#104×C47—42no—
51C22⋊C8×C47—42no—
52C4×C8×C47—21no—
53C4×C8×C47—21no—
54#41×C47—41no—
55#41×C47—41no—
56#41×C47—41no—
57#41×C47—41no—
58C2×Q8×C47—21no—
59C2×D4×C47—21no—
60C2×D4×C47—41no—
61C22×C4×C47—21no—
62C22×C4×C47—41no—
63C22×C4×C47C2×D411yescharacteristic
64Q16×C47—21no—
65Q16×C47—21no—
66SD16×C47—41no—
67SD16×C47—41no—
68D8×C47—21no—
69D8×C47—21no—
70M16×C47—41no—
71M16×C47—41no—
72M16×C47—41no—
73M16×C47—41no—
74C2×C8×C47—21no—
75C2×C8×C47—21no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C2×C8×C47D812yes—
79C2×C8×C47C22×C411yescharacteristic
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C2×C8×C47#4111yescharacteristic
85C4⋊C4×C47—22no—
86C22⋊C4×C47—41no—
87C42×C47—21no—
88C42×C47—41no—
89C42×C47SD1612yes—
90C16×C47—22no—
91C16×C47—22no—
92C23×C47—41no—
93C23×C47#13511yescharacteristic
94Q8×C47—41no—
95Q8×C47—41no—
96D4×C47—41no—
97D4×C47—41no—
98D4×C47—81no—
99D4×C47—81no—
100C2×C4×C47—24no—
101C2×C4×C47—22no—
102C2×C4×C47—42no—
103C2×C4×C47—41no—
104C2×C4×C47—81no—
105C2×C4×C47—81no—
106C2×C4×C47C4×D411yescharacteristic
107C2×C4×C47#12111yescharacteristic
108C2×C4×C47#12411yescharacteristic
109C2×C4×C47C2×D811yescharacteristic
110C2×C4×C47C2×SD1611yescharacteristic
111C2×C4×C47#13511yescharacteristic
112C8×C47—22no—
113C8×C47—81no—
114C8×C47—81no—
115C8×C47#11711yescharacteristic
116C8×C47C4×D411yescharacteristic
117C8×C47#12311yescharacteristic
118C8×C47#12611yescharacteristic
119#13151C4711yesmaximal, characteristic, direct product factor, Sylow
120C22×C47—22no—
121C22×C47—82no—
122C22×C47—81no—
123C22×C47C4×D811yescharacteristic
124C22×C47#46511yescharacteristic
125C22×C47#48811yescharacteristic
126C4×C47—24no—
127C4×C47—82no—
128C4×C47—81no—
129C4×C47#38811yescharacteristic
130C4×C47C4×SD1611yescharacteristic
131C4×C47#46611yescharacteristic
132C4×C47#48611yescharacteristic
133C2×#359C2×C4711yescharacteristic
134#2138C2×C4711yescharacteristic
135C2×C4×C16C2×C4711yescharacteristic, complemented
136#1974C2×C4711yescharacteristic
137#1945C2×C4711yescharacteristic, complemented
138#1382C2×C4711yescharacteristic, complemented
139#1381C2×C4711yescharacteristic, complemented
140C2×C47—21no—
141C2×C47—21no—
142C2×C47—161no—
143C2×C47#193411yescharacteristic
144C2×C47#217812yes—
145C2×#135C22×C4711yescharacteristic
146C22×C16C22×C4711yescharacteristic
147C22×C16C22×C4711yescharacteristic
148C2×#108C22×C4711yescharacteristic
149C2×#108C22×C4711yescharacteristic
150#427C22×C4711yescharacteristic
151#424—21no—
152C2×#104—21no—
153#408—21no—
154C2×C4×C8C22×C4711yescharacteristic
155#359—22no—
156#358C4×C4712yescomplemented
157#357C4×C4712yescomplemented
158C4×C16—22no—
159#339—21no—
160C47#1315111yescharacteristic, direct product factor, Sylow
161C2×#41—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165#135—21no—
166C2×Q16C2×C4×C4711yescharacteristic
167C2×SD16—21no—
168C2×D8C2×C4×C4711yescharacteristic
169C2×M16—21no—
170C2×M16—21no—
171C22×C8D4×C4711yescharacteristic
172C22×C8C23×C4711yescharacteristic
173#117—21no—
174C2×C42D4×C4711yescharacteristic
175C2×C16—21no—
176C2×C16—21no—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16C2×C4×C4712yes—
180C2×C16D4×C4712yes—
181#108—21no—
182#108—21no—
183#108—21no—
184#108—21no—
185#107C2×C4×C4712yes—
186#106—21no—
187C4⋊C8—42no—
188#104—42no—
189C22⋊C8—42no—
190C4×C8—21no—
191C4×C8—21no—
192#41—41no—
193#41—41no—
194#41—41no—
195#41—41no—
196C2×Q8—21no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4C2×D4×C4711yescharacteristic
202Q16—21no—
203Q16—21no—
204SD16—41no—
205SD16—41no—
206D8—21no—
207D8—21no—
208M16—41no—
209M16—41no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8D8×C4712yes—
217C2×C8C22×C4×C4711yescharacteristic
218C2×C8C2×D4×C4711yescharacteristic
219C2×C8#41×C4711yescharacteristic
220C2×C8#41×C4711yescharacteristic
221C2×C8#41×C4711yescharacteristic
222C2×C8#41×C4711yescharacteristic
223C4⋊C4—22no—
224C22⋊C4—41no—
225C42—21no—
226C42—41no—
227C42SD16×C4712yes—
228C16—22no—
229C16—22no—
230C23—41no—
231C23#135×C4711yescharacteristic
232Q8—41no—
233Q8—41no—
234D4—41no—
235D4—41no—
236D4—81no—
237D4—81no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4C4×D4×C4711yescharacteristic
245C2×C4#121×C4711yescharacteristic
246C2×C4#124×C4711yescharacteristic
247C2×C4C2×D8×C4711yescharacteristic
248C2×C4C2×SD16×C4711yescharacteristic
249C2×C4#135×C4711yescharacteristic
250C8—22no—
251C8—81no—
252C8—81no—
253C8#117×C4711yescharacteristic
254C8C4×D4×C4711yescharacteristic
255C8#123×C4711yescharacteristic
256C8#126×C4711yescharacteristic
257C22—22no—
258C22—82no—
259C22—81no—
260C22C4×D8×C4711yescharacteristic
261C22C47×#46511yescharacteristic
262C22C47×#48811yescharacteristic
263C4—24no—
264C4—82no—
265C4—81no—
266C4C47×#38811yescharacteristic
267C4C4×SD16×C4711yescharacteristic
268C4C47×#46611yescharacteristic
269C4C47×#48611yescharacteristic
270C2—21no—
271C2—21no—
272C2—161no—
273C2C47×#193411yescharacteristic
274C2C47×#217812yes—
subgroupG/H
centerC2×C4×C47C2×D8
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
socleC22×C47C4×D8
prime radicalC2×#135×C47C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C22×C8×C47 ◁ C2×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C16×C47C2semidirect
5. C47×#1945C2semidirect
6. C47×#1382C2semidirect
7. C47×#1381C2semidirect
19. C47×#358C4semidirect
20. C47×#357C4semidirect
119. #13151C47direct (N × H)
135. C2×C4×C16C2×C47semidirect
137. #1945C2×C47semidirect
138. #1382C2×C47semidirect
139. #1381C2×C47semidirect
156. #358C4×C47semidirect
157. #357C4×C47semidirect
160. C47#13151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3592
C47×#21382
C2×C4×C16×C472
C47×#19742
C47×#19452
C47×#13822
C47×#13812
#1315147