Finite Group Databasebeta

← C47×#12940 #26052638

Subgroups — C47×#12940 #26052638

Order 12032.

424 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2948C211yesmaximal, characteristic
2C47×#2159C211yesmaximal, characteristic, complemented
3C2×C47×#361C211yesmaximal, characteristic
4C2×C47×#357C211yesmaximal, characteristic
5C47×#1952C211yesmaximal, characteristic, complemented
6C47×#1382C211yesmaximal, characteristic, complemented
7C47×#1379C211yesmaximal, characteristic, complemented
8C22×D8×C47C2211yescharacteristic
9C47×#518—21no—
10C2×M32×C47C2211yescharacteristic
11C22×C16×C47C2211yescharacteristic
12C47×#442—22no—
13C4×D8×C47—21no—
14C4×D8×C47—21no—
15C2×#108×C47C2211yescharacteristic
16C47×#428—21no—
17C47×#427C2211yescharacteristic
18C2×#107×C47C2211yescharacteristic
19C47×#418—21no—
20C47×#405C2211yescharacteristic
21C47×#367—21no—
22C47×#366—21no—
23C47×#361C414yescomplemented
24C47×#357—22no—
25C47×#343—21no—
26C22×D4×C47—21no—
27C2×D8×C47—21no—
28C2×D8×C47—21no—
29C2×D8×C47—21no—
30C2×D8×C47C2×C412yes—
31C2×D8×C47D412yes—
32C2×D8×C47Q812yes—
33C2×M16×C47—21no—
34C2×M16×C47D411yescharacteristic
35C22×C8×C47C2311yescharacteristic
36C4×D4×C47—22no—
37C4×D4×C47—22no—
38C4×D4×C47—41no—
39C4×D4×C47—41no—
40#117×C47—21no—
41#117×C47D411yescharacteristic
42C2×C4⋊C4×C47—21no—
43C2×C22⋊C4×C47—42no—
44M32×C47—21no—
45M32×C47C2×C412yescomplemented
46C2×C16×C47—21no—
47C2×C16×C47—21no—
48C2×C16×C47—21no—
49C2×C16×C47—21no—
50#108×C47—21no—
51#108×C47C2×C412yescomplemented
52#107×C47—21no—
53#107×C47—21no—
54#107×C47—41no—
55#107×C47D411yescharacteristic
56#107×C47D411yescharacteristic
57#106×C47—21no—
58#106×C47—41no—
59#102×C47—22no—
60#102×C47—22no—
61#97×C47—21no—
62C4×C8×C47—21no—
63C24×C47—41no—
64C2×D4×C47—22no—
65C2×D4×C47—22no—
66C2×D4×C47—22no—
67C2×D4×C47—41no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C22×C4×C47—42no—
71C22×C4×C47—42no—
72C22×C4×C47—41no—
73C22×C4×C47C2×D411yescharacteristic
74D8×C47—22no—
75D8×C47—22no—
76D8×C47—22no—
77D8×C47C4⋊C414yes—
78M16×C47—22no—
79M16×C47—21no—
80M16×C47—21no—
81M16×C47—41no—
82C2×C8×C47—21no—
83C2×C8×C47—41no—
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—21no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47D811yescharacteristic
95C4⋊C4×C47D811yescharacteristic
96C22⋊C4×C47—21no—
97C22⋊C4×C47—42no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—41no—
100C42×C47—21no—
101C42×C47—41no—
102C16×C47—22no—
103C16×C47—41no—
104C23×C47—42no—
105C23×C47—42no—
106C23×C47—42no—
107C23×C47—161no—
108C23×C47—161no—
109C23×C47AGL(1,ℤ/8)11yescharacteristic
110D4×C47—24no—
111D4×C47—42no—
112D4×C47—42no—
113D4×C47—42no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—81no—
119C2×C4×C47—162no—
120C2×C4×C47—162no—
121C2×C4×C47—161no—
122C2×C4×C47C4×D411yescharacteristic
123C2×C4×C47#12011yescharacteristic
124C2×C4×C47C22⋊Q811yescharacteristic
125C2×C4×C47C2×D811yescharacteristic
126C2×C4×C47#13511yescharacteristic
127C2×C4×C47#13711yescharacteristic
128C8×C47—42no—
129C8×C47—41no—
130C8×C47C2×C4⋊C411yescharacteristic
131C8×C47C4×D411yescharacteristic
132C8×C47C22⋊Q811yescharacteristic
133C8×C47#12311yescharacteristic
134#12940C4711yesmaximal, characteristic, direct product factor, Sylow
135C22×C47—21no—
136C22×C47—21no—
137C22×C47—44no—
138C22×C47—82no—
139C22×C47—82no—
140C22×C47—162no—
141C22×C47—162no—
142C22×C47#44011yescharacteristic
143C22×C47#44711yescharacteristic
144C22×C47#47811yescharacteristic
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—81no—
148C4×C47—81no—
149C4×C47—161no—
150C4×C47#38511yescharacteristic
151C4×C47C4×D811yescharacteristic
152C4×C47#45211yescharacteristic
153C4×C47#47411yescharacteristic
154#2948C2×C4711yescharacteristic
155#2159C2×C4711yescharacteristic, complemented
156C2×#361C2×C4711yescharacteristic
157C2×#357C2×C4711yescharacteristic
158#1952C2×C4711yescharacteristic, complemented
159#1382C2×C4711yescharacteristic, complemented
160#1379C2×C4711yescharacteristic, complemented
161C2×C47—21no—
162C2×C47—21no—
163C2×C47—84no—
164C2×C47#186211yescharacteristic
165C2×C47#219211yescharacteristic
166C2×C47#219411yescharacteristic
167C22×D8C22×C4711yescharacteristic
168#518—21no—
169C2×M32C22×C4711yescharacteristic
170C22×C16C22×C4711yescharacteristic
171#442—22no—
172C4×D8—21no—
173C4×D8—21no—
174C2×#108C22×C4711yescharacteristic
175#428—21no—
176#427C22×C4711yescharacteristic
177C2×#107C22×C4711yescharacteristic
178#418—21no—
179#405C22×C4711yescharacteristic
180#367—21no—
181#366—21no—
182#361C4×C4714yescomplemented
183#357—22no—
184#343—21no—
185C47#1294011yescharacteristic, direct product factor, Sylow
186C22×D4—21no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8C2×C4×C4712yes—
191C2×D8D4×C4712yes—
192C2×D8Q8×C4712yes—
193C2×M16—21no—
194C2×M16D4×C4711yescharacteristic
195C22×C8C23×C4711yescharacteristic
196C4×D4—22no—
197C4×D4—22no—
198C4×D4—41no—
199C4×D4—41no—
200#117—21no—
201#117D4×C4711yescharacteristic
202C2×C4⋊C4—21no—
203C2×C22⋊C4—42no—
204M32—21no—
205M32C2×C4×C4712yescomplemented
206C2×C16—21no—
207C2×C16—21no—
208C2×C16—21no—
209C2×C16—21no—
210#108—21no—
211#108C2×C4×C4712yescomplemented
212#107—21no—
213#107—21no—
214#107—41no—
215#107D4×C4711yescharacteristic
216#107D4×C4711yescharacteristic
217#106—21no—
218#106—41no—
219#102—22no—
220#102—22no—
221#97—21no—
222C4×C8—21no—
223C24—41no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4C2×D4×C4711yescharacteristic
234D8—22no—
235D8—22no—
236D8—22no—
237D8C4⋊C4×C4714yes—
238M16—22no—
239M16—21no—
240M16—21no—
241M16—41no—
242C2×C8—21no—
243C2×C8—41no—
244C2×C8C22×C4×C4711yescharacteristic
245C2×C8C2×D4×C4711yescharacteristic
246C2×C8C2×D4×C4711yescharacteristic
247C2×C8C2×Q8×C4711yescharacteristic
248C2×C8#41×C4711yescharacteristic
249C2×C8#41×C4711yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4D8×C4711yescharacteristic
255C4⋊C4D8×C4711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—41no—
260C42—21no—
261C42—41no—
262C16—22no—
263C16—41no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—161no—
268C23—161no—
269C23AGL(1,ℤ/8)×C4711yescharacteristic
270D4—24no—
271D4—42no—
272D4—42no—
273D4—42no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—162no—
280C2×C4—162no—
281C2×C4—161no—
282C2×C4C4×D4×C4711yescharacteristic
283C2×C4#120×C4711yescharacteristic
284C2×C4C22⋊Q8×C4711yescharacteristic
285C2×C4C2×D8×C4711yescharacteristic
286C2×C4#135×C4711yescharacteristic
287C2×C4#137×C4711yescharacteristic
288C8—41no—
289C8—42no—
290C8C2×C4⋊C4×C4711yescharacteristic
291C8C4×D4×C4711yescharacteristic
292C8C22⋊Q8×C4711yescharacteristic
293C8#123×C4711yescharacteristic
294C22—21no—
295C22—21no—
296C22—44no—
297C22—82no—
298C22—82no—
299C22—162no—
300C22—162no—
301C22C47×#44011yescharacteristic
302C22C47×#44711yescharacteristic
303C22C47×#47811yescharacteristic
304C4—41no—
305C4—41no—
306C4—81no—
307C4—81no—
308C4—161no—
309C4C47×#38511yescharacteristic
310C4C4×D8×C4711yescharacteristic
311C4C47×#45211yescharacteristic
312C4C47×#47411yescharacteristic
313C2—21no—
314C2—21no—
315C2—84no—
316C2C47×#186211yescharacteristic
317C2C47×#219211yescharacteristic
318C2C47×#219411yescharacteristic
subgroupG/H
center, socleC22×C47#447
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
prime radicalC22×D8×C47C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2159C2semidirect
5. C47×#1952C2semidirect
6. C47×#1382C2semidirect
7. C47×#1379C2semidirect
23. C47×#361C4semidirect
45. M32×C47C2×C4semidirect
51. #108×C47C2×C4semidirect
134. #12940C47direct (N × H)
155. #2159C2×C47semidirect
158. #1952C2×C47semidirect
159. #1382C2×C47semidirect
160. #1379C2×C47semidirect
182. #361C4×C47semidirect
185. C47#12940direct (N × H)
205. M32C2×C4×C47semidirect
211. #108C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#29482
C47×#21592
C2×C47×#3612
C2×C47×#3572
C47×#19522
C47×#13822
C47×#13792
#1294047