Finite Group Databasebeta

← C47×#13028 #26052726

Subgroups — C47×#13028 #26052726

Order 12032.

476 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#510C211yesmaximal, characteristic
2C2×C47×#443C211yesmaximal, characteristic
3C2×C47×#362C211yesmaximal, characteristic, complemented
4C47×#2139C211yesmaximal, characteristic
5C47×#1969C211yesmaximal, characteristic, complemented
6C47×#1387C211yesmaximal, characteristic, complemented
7C47×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C22×Q16×C47C2211yescharacteristic
10C2×#131×C47—21no—
11C47×#510—22no—
12C47×#510C414yescomplemented
13C2×Q32×C47—21no—
14C2×SD32×C47—21no—
15C2×M32×C47C2211yescharacteristic
16C2×M32×C47C2211yescharacteristic
17C47×#443—22no—
18C47×#443—22no—
19C2×#108×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#104×C47—21no—
22C2×#103×C47—21no—
23C2×C4×C8×C47C2211yescharacteristic
24C47×#391—21no—
25C47×#362—22no—
26C47×#358—21no—
27C47×#357—21no—
28C2×#41×C47—21no—
29C22×Q8×C47—21no—
30#135×C47—21no—
31#135×C47—21no—
32#135×C47C2×C412yes—
33#135×C47D412yes—
34C2×Q16×C47—21no—
35C2×Q16×C47—21no—
36C2×Q16×C47—21no—
37C2×Q16×C47—21no—
38C2×Q16×C47—21no—
39C2×Q16×C47C2×C412yes—
40C2×Q16×C47D411yescharacteristic
41C2×SD16×C47—21no—
42C2×D8×C47D411yescharacteristic
43#131×C47—24no—
44#131×C47—42no—
45C2×M16×C47—21no—
46C2×M16×C47—41no—
47C22×C8×C47—41no—
48C22×C8×C47D411yescharacteristic
49C22×C8×C47C2311yescharacteristic
50C2×C4⋊C4×C47—21no—
51C2×C42×C47D411yescharacteristic
52Q32×C47—24no—
53SD32×C47—24no—
54M32×C47—21no—
55M32×C47—21no—
56M32×C47—21no—
57M32×C47C2×C412yes—
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60#108×C47—21no—
61#108×C47D412yes—
62#107×C47—21no—
63#107×C47—21no—
64#104×C47—24no—
65#103×C47—41no—
66#103×C47—41no—
67C4×C8×C47—21no—
68C4×C8×C47—21no—
69#95×C47—42no—
70#41×C47—22no—
71#41×C47—22no—
72#41×C47—41no—
73#41×C47—41no—
74C2×Q8×C47—22no—
75C2×Q8×C47—21no—
76C2×Q8×C47—41no—
77C2×Q8×C47—41no—
78C2×Q8×C47—41no—
79C2×Q8×C47—41no—
80C2×Q8×C47—41no—
81C2×D4×C47—21no—
82C2×D4×C47—41no—
83C22×C4×C47—21no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47C2×D411yescharacteristic
88Q16×C47—22no—
89Q16×C47—22no—
90Q16×C47—21no—
91Q16×C47—41no—
92Q16×C47—41no—
93Q16×C47C22⋊C412yes—
94SD16×C47—22no—
95SD16×C47—22no—
96D8×C47—21no—
97D8×C47C22⋊C412yes—
98M16×C47—22no—
99M16×C47—44no—
100M16×C47—41no—
101C2×C8×C47—21no—
102C2×C8×C47—21no—
103C2×C8×C47—44no—
104C2×C8×C47—41no—
105C2×C8×C47D811yescharacteristic
106C2×C8×C47D811yescharacteristic
107C2×C8×C47C22×C411yescharacteristic
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47#4111yescharacteristic
112C2×C8×C47#4111yescharacteristic
113C4⋊C4×C47—41no—
114C4⋊C4×C47—41no—
115C42×C47—21no—
116C42×C47—21no—
117C16×C47—22no—
118C16×C47—41no—
119C23×C47—41no—
120C23×C47AGL(1,ℤ/8)11yescharacteristic
121Q8×C47—22no—
122Q8×C47—41no—
123Q8×C47—42no—
124Q8×C47—42no—
125Q8×C47—81no—
126Q8×C47—81no—
127D4×C47—22no—
128D4×C47—42no—
129D4×C47—42no—
130D4×C47—41no—
131C2×C4×C47—22no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—81no—
139C2×C4×C47—81no—
140C2×C4×C47—82no—
141C2×C4×C47—81no—
142C2×C4×C47C4×D411yescharacteristic
143C2×C4×C47#12011yescharacteristic
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47C2×D811yescharacteristic
146C2×C4×C47#13511yescharacteristic
147C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
148C8×C47—21no—
149C8×C47—21no—
150C8×C47—42no—
151C8×C47C2×C22⋊C411yescharacteristic
152C8×C47C4×D411yescharacteristic
153C8×C47#12111yescharacteristic
154C8×C47#12311yescharacteristic
155#13028C4711yesmaximal, characteristic, direct product factor, Sylow
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—42no—
159C22×C47—81no—
160C22×C47—81no—
161C22×C47#44211yescharacteristic
162C22×C47#44911yescharacteristic
163C22×C47#45911yescharacteristic
164C4×C47—42no—
165C4×C47—42no—
166C4×C47—82no—
167C4×C47—161no—
168C4×C47#38611yescharacteristic
169C4×C47C4×D811yescharacteristic
170C4×C47#44711yescharacteristic
171C4×C47#46311yescharacteristic
172C2×#510C2×C4711yescharacteristic
173C2×#443C2×C4711yescharacteristic
174C2×#362C2×C4711yescharacteristic, complemented
175#2139C2×C4711yescharacteristic
176#1969C2×C4711yescharacteristic, complemented
177#1387C2×C4711yescharacteristic, complemented
178#1376C2×C4711yescharacteristic, complemented
179C2×C47—21no—
180C2×C47—21no—
181C2×C47—82no—
182C2×C47#187911yescharacteristic
183C2×C47#221211yescharacteristic
184C2×C47#221411yescharacteristic
185C2×#135C22×C4711yescharacteristic
186C22×Q16C22×C4711yescharacteristic
187C2×#131—21no—
188#510—22no—
189#510C4×C4714yescomplemented
190C2×Q32—21no—
191C2×SD32—21no—
192C2×M32C22×C4711yescharacteristic
193C2×M32C22×C4711yescharacteristic
194#443—22no—
195#443—22no—
196C2×#108C22×C4711yescharacteristic
197C2×#107C22×C4711yescharacteristic
198C2×#104—21no—
199C2×#103—21no—
200C2×C4×C8C22×C4711yescharacteristic
201#391—21no—
202#362—22no—
203#358—21no—
204#357—21no—
205C47#1302811yescharacteristic, direct product factor, Sylow
206C2×#41—21no—
207C22×Q8—21no—
208#135—21no—
209#135—21no—
210#135C2×C4×C4712yes—
211#135D4×C4712yes—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16C2×C4×C4712yes—
218C2×Q16D4×C4711yescharacteristic
219C2×SD16—21no—
220C2×D8D4×C4711yescharacteristic
221#131—24no—
222#131—42no—
223C2×M16—21no—
224C2×M16—41no—
225C22×C8—41no—
226C22×C8D4×C4711yescharacteristic
227C22×C8C23×C4711yescharacteristic
228C2×C4⋊C4—21no—
229C2×C42D4×C4711yescharacteristic
230Q32—24no—
231SD32—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32C2×C4×C4712yes—
236C2×C16—21no—
237C2×C16—21no—
238#108—21no—
239#108D4×C4712yes—
240#107—21no—
241#107—21no—
242#104—24no—
243#103—41no—
244#103—41no—
245C4×C8—21no—
246C4×C8—21no—
247#95—42no—
248#41—22no—
249#41—22no—
250#41—41no—
251#41—41no—
252C2×Q8—22no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C4711yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—21no—
269Q16—41no—
270Q16—41no—
271Q16C22⋊C4×C4712yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8C22⋊C4×C4712yes—
276M16—22no—
277M16—44no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8D8×C4711yescharacteristic
284C2×C8D8×C4711yescharacteristic
285C2×C8C22×C4×C4711yescharacteristic
286C2×C8C2×D4×C4711yescharacteristic
287C2×C8C2×D4×C4711yescharacteristic
288C2×C8C2×D4×C4711yescharacteristic
289C2×C8#41×C4711yescharacteristic
290C2×C8#41×C4711yescharacteristic
291C4⋊C4—41no—
292C4⋊C4—41no—
293C42—21no—
294C42—21no—
295C16—22no—
296C16—41no—
297C23—41no—
298C23AGL(1,ℤ/8)×C4711yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—81no—
304Q8—81no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—81no—
320C2×C4C4×D4×C4711yescharacteristic
321C2×C4#120×C4711yescharacteristic
322C2×C4#121×C4711yescharacteristic
323C2×C4C2×D8×C4711yescharacteristic
324C2×C4#135×C4711yescharacteristic
325C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8C2×C22⋊C4×C4711yescharacteristic
330C8C4×D4×C4711yescharacteristic
331C8#121×C4711yescharacteristic
332C8#123×C4711yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22C47×#44211yescharacteristic
339C22C47×#44911yescharacteristic
340C22C47×#45911yescharacteristic
341C4—42no—
342C4—42no—
343C4—82no—
344C4—161no—
345C4C47×#38611yescharacteristic
346C4C4×D8×C4711yescharacteristic
347C4C47×#44711yescharacteristic
348C4C47×#46311yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2C47×#187911yescharacteristic
353C2C47×#221211yescharacteristic
354C2C47×#221411yescharacteristic
subgroupG/H
center, socleC22×C47#459
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×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#362C2semidirect
5. C47×#1969C2semidirect
6. C47×#1387C2semidirect
7. C47×#1376C2semidirect
12. C47×#510C4semidirect
155. #13028C47direct (N × H)
174. C2×#362C2×C47semidirect
176. #1969C2×C47semidirect
177. #1387C2×C47semidirect
178. #1376C2×C47semidirect
189. #510C4×C47semidirect
205. C47#13028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5102
C2×C47×#4432
C2×C47×#3622
C47×#21392
C47×#19692
C47×#13872
C47×#13762
#1302847