Finite Group Databasebeta

← C47×#12955 #26052653

Subgroups — C47×#12955 #26052653

Order 12032.

408 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#444C211yesmaximal, characteristic
2C2×C47×#365C211yesmaximal, characteristic, complemented
3C2×C47×#360C211yesmaximal, characteristic
4C47×#2139C211yesmaximal, characteristic
5C47×#1943C211yesmaximal, characteristic, complemented
6C47×#1387C211yesmaximal, characteristic, complemented
7C47×#1375C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C2×#131×C47—21no—
10C2×M32×C47C2211yescharacteristic
11C2×M32×C47C2211yescharacteristic
12C47×#444—22no—
13C47×#444—22no—
14C2×#108×C47C2211yescharacteristic
15C2×#107×C47C2211yescharacteristic
16C2×#106×C47C2211yescharacteristic
17C2×#104×C47—21no—
18C2×#97×C47C2211yescharacteristic
19C47×#389—21no—
20C47×#365—22no—
21C47×#360—22no—
22C47×#358C412yescomplemented
23C47×#357C412yescomplemented
24C47×#340—21no—
25C2×#41×C47—21no—
26#135×C47—21no—
27#135×C47—21no—
28#135×C47D412yes—
29#135×C47Q812yes—
30C2×Q16×C47C2×C411yescharacteristic
31C2×SD16×C47—21no—
32C2×D8×C47C2×C411yescharacteristic
33#131×C47—24no—
34#131×C47—42no—
35C2×M16×C47—21no—
36C2×M16×C47—41no—
37C22×C8×C47—41no—
38C22×C8×C47D411yescharacteristic
39C22×C8×C47C2311yescharacteristic
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—41no—
43C2×C42×C47D411yescharacteristic
44M32×C47—21no—
45M32×C47—21no—
46M32×C47—21no—
47M32×C47—21no—
48C2×C16×C47—21no—
49C2×C16×C47C2×C412yes—
50#108×C47—21no—
51#108×C47D412yes—
52#107×C47—21no—
53#107×C47C2×C412yes—
54#106×C47—21no—
55#106×C47—21no—
56#104×C47—24no—
57#97×C47—21no—
58#97×C47—21no—
59#95×C47—41no—
60#41×C47—22no—
61#41×C47—22no—
62#41×C47—41no—
63#41×C47—41no—
64C2×Q8×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—41no—
67C22×C4×C47—21no—
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47C2×D411yescharacteristic
72Q16×C47—21no—
73Q16×C47C4⋊C412yescomplemented
74SD16×C47—22no—
75SD16×C47—22no—
76D8×C47—21no—
77D8×C47C4⋊C412yescomplemented
78M16×C47—22no—
79M16×C47—44no—
80M16×C47—41no—
81C2×C8×C47—21no—
82C2×C8×C47—21no—
83C2×C8×C47—44no—
84C2×C8×C47—41no—
85C2×C8×C47SD1612yes—
86C2×C8×C47C22×C411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47C2×Q811yescharacteristic
90C2×C8×C47#4111yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C4⋊C4×C47—22no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—82no—
97C42×C47—21no—
98C42×C47—21no—
99C16×C47—22no—
100C16×C47—41no—
101C23×C47—41no—
102C23×C47AGL(1,ℤ/8)11yescharacteristic
103Q8×C47—22no—
104Q8×C47—41no—
105D4×C47—22no—
106D4×C47—42no—
107D4×C47—42no—
108D4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—42no—
111C2×C4×C47—42no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—42no—
115C2×C4×C47—41no—
116C2×C4×C47—81no—
117C2×C4×C47—81no—
118C2×C4×C47—81no—
119C2×C4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47C4×D411yescharacteristic
122C2×C4×C47#12011yescharacteristic
123C2×C4×C47C22⋊Q811yescharacteristic
124C2×C4×C47C2×SD1611yescharacteristic
125C2×C4×C47#13511yescharacteristic
126C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
127C8×C47—22no—
128C8×C47—42no—
129C8×C47C2×C4⋊C411yescharacteristic
130C8×C47C4×D411yescharacteristic
131C8×C47C22⋊Q811yescharacteristic
132C8×C47#12311yescharacteristic
133#12955C4711yesmaximal, characteristic, direct product factor, Sylow
134C22×C47—21no—
135C22×C47—21no—
136C22×C47—42no—
137C22×C47—81no—
138C22×C47—81no—
139C22×C47#44211yescharacteristic
140C22×C47#44911yescharacteristic
141C22×C47#47611yescharacteristic
142C4×C47—42no—
143C4×C47—81no—
144C4×C47—82no—
145C4×C47—161no—
146C4×C47#38511yescharacteristic
147C4×C47C4×SD1611yescharacteristic
148C4×C47#45011yescharacteristic
149C4×C47#47811yescharacteristic
150C2×#444C2×C4711yescharacteristic
151C2×#365C2×C4711yescharacteristic, complemented
152C2×#360C2×C4711yescharacteristic
153#2139C2×C4711yescharacteristic
154#1943C2×C4711yescharacteristic, complemented
155#1387C2×C4711yescharacteristic, complemented
156#1375C2×C4711yescharacteristic, complemented
157C2×C47—21no—
158C2×C47—21no—
159C2×C47—82no—
160C2×C47#186411yescharacteristic
161C2×C47#218011yescharacteristic
162C2×C47AGL(1,ℤ/16)11yescharacteristic
163C2×#135C22×C4711yescharacteristic
164C2×#131—21no—
165C2×M32C22×C4711yescharacteristic
166C2×M32C22×C4711yescharacteristic
167#444—22no—
168#444—22no—
169C2×#108C22×C4711yescharacteristic
170C2×#107C22×C4711yescharacteristic
171C2×#106C22×C4711yescharacteristic
172C2×#104—21no—
173C2×#97C22×C4711yescharacteristic
174#389—21no—
175#365—22no—
176#360—22no—
177#358C4×C4712yescomplemented
178#357C4×C4712yescomplemented
179#340—21no—
180C47#1295511yescharacteristic, direct product factor, Sylow
181C2×#41—21no—
182#135—21no—
183#135—21no—
184#135D4×C4712yes—
185#135Q8×C4712yes—
186C2×Q16C2×C4×C4711yescharacteristic
187C2×SD16—21no—
188C2×D8C2×C4×C4711yescharacteristic
189#131—24no—
190#131—42no—
191C2×M16—21no—
192C2×M16—41no—
193C22×C8—41no—
194C22×C8D4×C4711yescharacteristic
195C22×C8C23×C4711yescharacteristic
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—41no—
199C2×C42D4×C4711yescharacteristic
200M32—21no—
201M32—21no—
202M32—21no—
203M32—21no—
204C2×C16—21no—
205C2×C16C2×C4×C4712yes—
206#108—21no—
207#108D4×C4712yes—
208#107—21no—
209#107C2×C4×C4712yes—
210#106—21no—
211#106—21no—
212#104—24no—
213#97—21no—
214#97—21no—
215#95—41no—
216#41—22no—
217#41—22no—
218#41—41no—
219#41—41no—
220C2×Q8—21no—
221C2×D4—21no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4C2×D4×C4711yescharacteristic
228Q16—21no—
229Q16C4⋊C4×C4712yescomplemented
230SD16—22no—
231SD16—22no—
232D8—21no—
233D8C4⋊C4×C4712yescomplemented
234M16—22no—
235M16—44no—
236M16—41no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—44no—
240C2×C8—41no—
241C2×C8SD16×C4712yes—
242C2×C8C22×C4×C4711yescharacteristic
243C2×C8C2×D4×C4711yescharacteristic
244C2×C8C2×D4×C4711yescharacteristic
245C2×C8C2×Q8×C4711yescharacteristic
246C2×C8#41×C4711yescharacteristic
247C2×C8#41×C4711yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—82no—
253C42—21no—
254C42—21no—
255C16—22no—
256C16—41no—
257C23—41no—
258C23AGL(1,ℤ/8)×C4711yescharacteristic
259Q8—22no—
260Q8—41no—
261D4—22no—
262D4—42no—
263D4—42no—
264D4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4C4×D4×C4711yescharacteristic
278C2×C4#120×C4711yescharacteristic
279C2×C4C22⋊Q8×C4711yescharacteristic
280C2×C4C2×SD16×C4711yescharacteristic
281C2×C4#135×C4711yescharacteristic
282C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
283C8—22no—
284C8—42no—
285C8C2×C4⋊C4×C4711yescharacteristic
286C8C4×D4×C4711yescharacteristic
287C8C22⋊Q8×C4711yescharacteristic
288C8#123×C4711yescharacteristic
289C22—21no—
290C22—21no—
291C22—42no—
292C22—81no—
293C22—81no—
294C22C47×#44211yescharacteristic
295C22C47×#44911yescharacteristic
296C22C47×#47611yescharacteristic
297C4—42no—
298C4—81no—
299C4—82no—
300C4—161no—
301C4C47×#38511yescharacteristic
302C4C4×SD16×C4711yescharacteristic
303C4C47×#45011yescharacteristic
304C4C47×#47811yescharacteristic
305C2—21no—
306C2—21no—
307C2—82no—
308C2C47×#186411yescharacteristic
309C2C47×#218011yescharacteristic
310C2C47×AGL(1,ℤ/16)11yescharacteristic
subgroupG/H
center, socleC22×C47#442
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
prime radicalC2×#135×C47C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#97×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#365C2semidirect
5. C47×#1943C2semidirect
6. C47×#1387C2semidirect
7. C47×#1375C2semidirect
22. C47×#358C4semidirect
23. C47×#357C4semidirect
73. Q16×C47C4⋊C4semidirect
77. D8×C47C4⋊C4semidirect
133. #12955C47direct (N × H)
151. C2×#365C2×C47semidirect
154. #1943C2×C47semidirect
155. #1387C2×C47semidirect
156. #1375C2×C47semidirect
177. #358C4×C47semidirect
178. #357C4×C47semidirect
180. C47#12955direct (N × H)
229. Q16C4⋊C4×C47semidirect
233. D8C4⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4442
C2×C47×#3652
C2×C47×#3602
C47×#21392
C47×#19432
C47×#13872
C47×#13752
#1295547