Finite Group Databasebeta

← C47×#12829 #26052527

Subgroups — C47×#12829 #26052527

Order 12032.

378 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2957C211yesmaximal, characteristic
2C47×#2151C211yesmaximal, characteristic, complemented
3C47×#2148C211yesmaximal, characteristic
4C47×#2138C211yesmaximal, characteristic
5C47×#1833C211yesmaximal, characteristic, complemented
6C47×#1389C211yesmaximal, characteristic, complemented
7C47×#1381C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C47×#568—21no—
10C2×M32×C47C2211yescharacteristic
11C22×C16×C47C2211yescharacteristic
12C47×#444C414yescomplemented
13C47×#443—22no—
14C2×#108×C47C2211yescharacteristic
15C2×#108×C47C2211yescharacteristic
16C47×#427C2211yescharacteristic
17C47×#421—21no—
18C47×#405C2211yescharacteristic
19C47×C4⋊C16—22no—
20C47×#362—21no—
21C47×#361—21no—
22C47×#358—21no—
23C47×#357—21no—
24C47×#344—21no—
25C47×H(3,ℤ/4)—21no—
26C2×#41×C47—21no—
27#135×C47—21no—
28#135×C47—21no—
29#135×C47C2×C412yes—
30#135×C47Q812yes—
31C2×Q16×C47D411yescharacteristic
32C2×SD16×C47—21no—
33C2×D8×C47D411yescharacteristic
34#131×C47—24no—
35#131×C47—42no—
36C2×M16×C47—21no—
37C2×M16×C47—21no—
38C2×M16×C47—42no—
39C2×M16×C47D411yescharacteristic
40C22×C8×C47C2311yescharacteristic
41#117×C47—21no—
42#117×C47D411yescharacteristic
43M32×C47—21no—
44M32×C47—21no—
45C2×C16×C47—21no—
46C2×C16×C47—21no—
47C2×C16×C47—21no—
48C2×C16×C47—21no—
49#108×C47—21no—
50#108×C47—21no—
51#108×C47—21no—
52#108×C47C2×C412yes—
53#107×C47—21no—
54#106×C47—21no—
55#104×C47—24no—
56#97×C47C2×C412yes—
57C4×C8×C47D412yes—
58#41×C47—22no—
59#41×C47—22no—
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47C2×D411yescharacteristic
67Q16×C47—21no—
68Q16×C47C4⋊C412yes—
69SD16×C47—22no—
70SD16×C47—22no—
71D8×C47—21no—
72D8×C47C4⋊C412yes—
73M16×C47—21no—
74M16×C47—21no—
75M16×C47—22no—
76M16×C47—44no—
77M16×C47—41no—
78M16×C47—41no—
79M16×C47—41no—
80C2×C8×C47—44no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47C22⋊C412yes—
84C2×C8×C47C22×C411yescharacteristic
85C2×C8×C47C2×D411yescharacteristic
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47C2×Q811yescharacteristic
88C2×C8×C47#4111yescharacteristic
89C2×C8×C47#4111yescharacteristic
90C4⋊C4×C47—21no—
91C4⋊C4×C47—41no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47—41no—
94C42×C47—41no—
95C42×C47C22⋊C412yes—
96C16×C47—41no—
97C16×C47—41no—
98C23×C47—41no—
99C23×C47#13511yescharacteristic
100Q8×C47—22no—
101Q8×C47—41no—
102D4×C47—22no—
103D4×C47—42no—
104D4×C47—42no—
105D4×C47—41no—
106C2×C4×C47—22no—
107C2×C4×C47—41no—
108C2×C4×C47—42no—
109C2×C4×C47—42no—
110C2×C4×C47—81no—
111C2×C4×C47C2×C22⋊C411yescharacteristic
112C2×C4×C47#12111yescharacteristic
113C2×C4×C47C22⋊Q811yescharacteristic
114C2×C4×C47#13511yescharacteristic
115C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
117C8×C47—22no—
118C8×C47—42no—
119C8×C47—81no—
120C8×C47C2×C4⋊C411yescharacteristic
121C8×C47#11711yescharacteristic
122C8×C47#12111yescharacteristic
123C8×C47C22⋊Q811yescharacteristic
124#12829C4711yesmaximal, characteristic, direct product factor, Sylow
125C22×C47—41no—
126C22×C47—42no—
127C22×C47—161no—
128C22×C47#41611yescharacteristic
129C22×C47#46311yescharacteristic
130C22×C47#47811yescharacteristic
131C4×C47—42no—
132C4×C47—42no—
133C4×C47—161no—
134C4×C47#38011yescharacteristic
135C4×C47#41811yescharacteristic
136C4×C47#46311yescharacteristic
137C4×C47#47811yescharacteristic
138#2957C2×C4711yescharacteristic
139#2151C2×C4711yescharacteristic, complemented
140#2148C2×C4711yescharacteristic
141#2138C2×C4711yescharacteristic
142#1833C2×C4711yescharacteristic, complemented
143#1389C2×C4711yescharacteristic, complemented
144#1381C2×C4711yescharacteristic, complemented
145C2×C47—21no—
146C2×C47—21no—
147C2×C47—21no—
148C2×C47—82no—
149C2×C47#180411yescharacteristic
150C2×#135C22×C4711yescharacteristic
151#568—21no—
152C2×M32C22×C4711yescharacteristic
153C22×C16C22×C4711yescharacteristic
154#444C4×C4714yescomplemented
155#443—22no—
156C2×#108C22×C4711yescharacteristic
157C2×#108C22×C4711yescharacteristic
158#427C22×C4711yescharacteristic
159#421—21no—
160#405C22×C4711yescharacteristic
161C4⋊C16—22no—
162#362—21no—
163#361—21no—
164#358—21no—
165#357—21no—
166#344—21no—
167H(3,ℤ/4)—21no—
168C47#1282911yescharacteristic, direct product factor, Sylow
169C2×#41—21no—
170#135—21no—
171#135—21no—
172#135C2×C4×C4712yes—
173#135Q8×C4712yes—
174C2×Q16D4×C4711yescharacteristic
175C2×SD16—21no—
176C2×D8D4×C4711yescharacteristic
177#131—24no—
178#131—42no—
179C2×M16—21no—
180C2×M16—21no—
181C2×M16—42no—
182C2×M16D4×C4711yescharacteristic
183C22×C8C23×C4711yescharacteristic
184#117—21no—
185#117D4×C4711yescharacteristic
186M32—21no—
187M32—21no—
188C2×C16—21no—
189C2×C16—21no—
190C2×C16—21no—
191C2×C16—21no—
192#108—21no—
193#108—21no—
194#108—21no—
195#108C2×C4×C4712yes—
196#107—21no—
197#106—21no—
198#104—24no—
199#97C2×C4×C4712yes—
200C4×C8D4×C4712yes—
201#41—22no—
202#41—22no—
203#41—41no—
204#41—41no—
205C2×Q8—21no—
206C2×D4—21no—
207C2×D4—41no—
208C22×C4—41no—
209C22×C4C2×D4×C4711yescharacteristic
210Q16—21no—
211Q16C4⋊C4×C4712yes—
212SD16—22no—
213SD16—22no—
214D8—21no—
215D8C4⋊C4×C4712yes—
216M16—21no—
217M16—21no—
218M16—22no—
219M16—44no—
220M16—41no—
221M16—41no—
222M16—41no—
223C2×C8—44no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8C22⋊C4×C4712yes—
227C2×C8C22×C4×C4711yescharacteristic
228C2×C8C2×D4×C4711yescharacteristic
229C2×C8C2×D4×C4711yescharacteristic
230C2×C8C2×Q8×C4711yescharacteristic
231C2×C8#41×C4711yescharacteristic
232C2×C8#41×C4711yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—41no—
235C22⋊C4—21no—
236C22⋊C4—41no—
237C42—41no—
238C42C22⋊C4×C4712yes—
239C16—41no—
240C16—41no—
241C23—41no—
242C23#135×C4711yescharacteristic
243Q8—22no—
244Q8—41no—
245D4—22no—
246D4—42no—
247D4—42no—
248D4—41no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4C2×C22⋊C4×C4711yescharacteristic
255C2×C4#121×C4711yescharacteristic
256C2×C4C22⋊Q8×C4711yescharacteristic
257C2×C4#135×C4711yescharacteristic
258C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
259C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
260C8—22no—
261C8—42no—
262C8—81no—
263C8C2×C4⋊C4×C4711yescharacteristic
264C8#117×C4711yescharacteristic
265C8#121×C4711yescharacteristic
266C8C22⋊Q8×C4711yescharacteristic
267C22—41no—
268C22—42no—
269C22—161no—
270C22C47×#41611yescharacteristic
271C22C47×#46311yescharacteristic
272C22C47×#47811yescharacteristic
273C4—42no—
274C4—42no—
275C4—161no—
276C4C47×#38011yescharacteristic
277C4C47×#41811yescharacteristic
278C4C47×#46311yescharacteristic
279C4C47×#47811yescharacteristic
280C2—21no—
281C2—21no—
282C2—21no—
283C2—82no—
284C2C47×#180411yescharacteristic
subgroupG/H
centerC4×C47#418
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
socleC2×C47#1804
prime radicalC2×#135×C47C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2151C2semidirect
5. C47×#1833C2semidirect
6. C47×#1389C2semidirect
7. C47×#1381C2semidirect
12. C47×#444C4semidirect
124. #12829C47direct (N × H)
139. #2151C2×C47semidirect
142. #1833C2×C47semidirect
143. #1389C2×C47semidirect
144. #1381C2×C47semidirect
154. #444C4×C47semidirect
168. C47#12829direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29572
C47×#21512
C47×#21482
C47×#21382
C47×#18332
C47×#13892
C47×#13812
#1282947