Finite Group Databasebeta

← C47×#9035 #26048733

Subgroups — C47×#9035 #26048733

Order 12032.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2905C211yesmaximal, characteristic, complemented
2C47×#2392C211yesmaximal, characteristic
3C47×#1486C212yesmaximal, complemented
4C47×#1458C211yesmaximal, characteristic, complemented
5C47×#1303C212yesmaximal, complemented
6C22×M16×C47—21no—
7C2×C4×D4×C47—21no—
8C2×C4×D4×C47C2211yescharacteristic
9C2×#117×C47C2211yescharacteristic
10C47×#431C2212yes—
11C47×#424—24no—
12C47×#423—21no—
13C47×#423C2212yes—
14C47×#398C411yescharacteristic
15C47×#397C411yescharacteristic
16C47×#396—21no—
17C47×#394—21no—
18C47×#394C411yescharacteristic
19C47×#392C411yescharacteristic
20C4×C4⋊C4×C47C2211yescharacteristic
21C4×C22⋊C4×C47—21no—
22C47×D4⋊C8—24no—
23C47×#324—21no—
24C47×#323—21no—
25C22×D4×C47—21no—
26C22×D4×C47C2×C411yescharacteristic
27C23×C4×C47—21no—
28C23×C4×C47D411yescharacteristic
29C2×M16×C47—22no—
30C2×M16×C47—22no—
31C2×M16×C47—42no—
32C2×M16×C47—42no—
33C22×C8×C47—22no—
34C4×D4×C47—22no—
35C4×D4×C47—22no—
36C4×D4×C47—42no—
37C4×D4×C47—42no—
38#117×C47—22no—
39#117×C47—22no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47C2×C411yescharacteristic
43C2×C4⋊C4×C47C2×C411yescharacteristic
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47—21no—
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47C2×C411yescharacteristic
51C2×C22⋊C4×C47D411yescharacteristic
52C2×C42×C47—21no—
53C2×C42×C47D411yescharacteristic
54C2×C42×C47C2311yescharacteristic
55C4⋊C8×C47—24no—
56C4⋊C8×C47—22no—
57C4⋊C8×C47—22no—
58C4⋊C8×C47D414yescomplemented
59C22⋊C8×C47—22no—
60C4×C8×C47—22no—
61#95×C47—21no—
62#95×C47—21no—
63#95×C47C2×C411yescharacteristic
64#95×C47C2×C411yescharacteristic
65C24×C47—21no—
66C24×C47C22⋊C411yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—42no—
69C2×D4×C47—42no—
70C2×D4×C47—42no—
71C2×D4×C47—42no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47C22⋊C411yescharacteristic
86C22×C4×C47C22⋊C411yescharacteristic
87C22×C4×C47C22⋊C411yescharacteristic
88C22×C4×C47D812yes—
89C22×C4×C47SD1612yes—
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93M16×C47—44no—
94M16×C47—42no—
95M16×C47—42no—
96C2×C8×C47—24no—
97C2×C8×C47—44no—
98C2×C8×C47—42no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—22no—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—42no—
103C4⋊C4×C47—42no—
104C22⋊C4×C47—22no—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—42no—
107C22⋊C4×C47—42no—
108C22⋊C4×C47—42no—
109C22⋊C4×C47—42no—
110C22⋊C4×C47—42no—
111C42×C47—21no—
112C42×C47—21no—
113C42×C47—41no—
114C42×C47—41no—
115C42×C47C2×D412yes—
116C42×C47#4112yes—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—22no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47—41no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47—41no—
126C23×C47—41no—
127C23×C47—41no—
128C23×C47#10212yes—
129C23×C47C2×C22⋊C411yescharacteristic
130D4×C47—24no—
131D4×C47—42no—
132D4×C47—48no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—81no—
155C2×C4×C47—81no—
156C2×C4×C47—81no—
157C2×C4×C47—81no—
158C2×C4×C47#10212yes—
159C2×C4×C47C4×D412yes—
160C2×C4×C47#12011yescharacteristic
161C2×C4×C47#12112yes—
162C2×C4×C47#12311yescharacteristic
163C2×C4×C47C2×D811yescharacteristic
164C2×C4×C47C2×SD1611yescharacteristic
165C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C47#13711yescharacteristic
167C8×C47—44no—
168C8×C47—82no—
169#9035C4711yesmaximal, characteristic, direct product factor, Sylow
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—22no—
173C22×C47—42no—
174C22×C47—42no—
175C22×C47—42no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—42no—
179C22×C47—81no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47—81no—
183C22×C47—81no—
184C22×C47#38611yescharacteristic
185C22×C47C2×#10211yescharacteristic
186C22×C47#41711yescharacteristic
187C4×C47—22no—
188C4×C47—22no—
189C4×C47—22no—
190C4×C47—42no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—81no—
194C4×C47—81no—
195C4×C47#44711yescharacteristic
196C4×C47#44811yescharacteristic
197C4×C47#48011yescharacteristic
198C4×C47#48111yescharacteristic
199#2905C2×C4711yescharacteristic, complemented
200#2392C2×C4711yescharacteristic
201#1486C2×C4712yescomplemented
202#1458C2×C4711yescharacteristic, complemented
203#1303C2×C4712yescomplemented
204C2×C47—21no—
205C2×C47—21no—
206C2×C47—42no—
207C2×C47—82no—
208C2×C47#187411yescharacteristic
209C2×C47#188411yescharacteristic
210C2×C47#189111yescharacteristic
211C22×M16—21no—
212C2×C4×D4—21no—
213C2×C4×D4C22×C4711yescharacteristic
214C2×#117C22×C4711yescharacteristic
215#431C22×C4712yes—
216#424—24no—
217#423—21no—
218#423C22×C4712yes—
219#398C4×C4711yescharacteristic
220#397C4×C4711yescharacteristic
221#396—21no—
222#394—21no—
223#394C4×C4711yescharacteristic
224#392C4×C4711yescharacteristic
225C4×C4⋊C4C22×C4711yescharacteristic
226C4×C22⋊C4—21no—
227D4⋊C8—24no—
228#324—21no—
229#323—21no—
230C47#903511yescharacteristic, direct product factor, Sylow
231C22×D4—21no—
232C22×D4C2×C4×C4711yescharacteristic
233C23×C4—21no—
234C23×C4D4×C4711yescharacteristic
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—42no—
238C2×M16—42no—
239C22×C8—22no—
240C4×D4—22no—
241C4×D4—22no—
242C4×D4—42no—
243C4×D4—42no—
244#117—22no—
245#117—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×C4×C4711yescharacteristic
249C2×C4⋊C4C2×C4×C4711yescharacteristic
250C2×C4⋊C4D4×C4711yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4C2×C4×C4711yescharacteristic
257C2×C22⋊C4D4×C4711yescharacteristic
258C2×C42—21no—
259C2×C42D4×C4711yescharacteristic
260C2×C42C23×C4711yescharacteristic
261C4⋊C8—24no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8D4×C4714yescomplemented
265C22⋊C8—22no—
266C4×C8—22no—
267#95—21no—
268#95—21no—
269#95C2×C4×C4711yescharacteristic
270#95C2×C4×C4711yescharacteristic
271C24—21no—
272C24C22⋊C4×C4711yescharacteristic
273C2×D4—22no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C22⋊C4×C4711yescharacteristic
292C22×C4C22⋊C4×C4711yescharacteristic
293C22×C4C22⋊C4×C4711yescharacteristic
294C22×C4D8×C4712yes—
295C22×C4SD16×C4712yes—
296C22×C4C22×C4×C4711yescharacteristic
297C22×C4C2×D4×C4711yescharacteristic
298C22×C4C2×D4×C4711yescharacteristic
299M16—44no—
300M16—42no—
301M16—42no—
302C2×C8—24no—
303C2×C8—44no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—41no—
321C42C2×D4×C4712yes—
322C42#41×C4712yes—
323C23—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#102×C4712yes—
335C23C2×C22⋊C4×C4711yescharacteristic
336D4—24no—
337D4—42no—
338D4—48no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4#102×C4712yes—
365C2×C4C4×D4×C4712yes—
366C2×C4#120×C4711yescharacteristic
367C2×C4#121×C4712yes—
368C2×C4#123×C4711yescharacteristic
369C2×C4C2×D8×C4711yescharacteristic
370C2×C4C2×SD16×C4711yescharacteristic
371C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
372C2×C4#137×C4711yescharacteristic
373C8—44no—
374C8—82no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C47×#38611yescharacteristic
390C22C2×#102×C4711yescharacteristic
391C22C47×#41711yescharacteristic
392C4—22no—
393C4—22no—
394C4—22no—
395C4—42no—
396C4—41no—
397C4—41no—
398C4—81no—
399C4—81no—
400C4C47×#44711yescharacteristic
401C4C47×#44811yescharacteristic
402C4C47×#48011yescharacteristic
403C4C47×#48111yescharacteristic
404C2—21no—
405C2—21no—
406C2—42no—
407C2—82no—
408C2C47×#187411yescharacteristic
409C2C47×#188411yescharacteristic
410C2C47×#189111yescharacteristic
subgroupG/H
centerC2×C4×C47#120
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#386
prime radicalC47×#392C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2905C2semidirect
3. C47×#1486C2semidirect
4. C47×#1458C2semidirect
5. C47×#1303C2semidirect
58. C4⋊C8×C47D4semidirect
169. #9035C47direct (N × H)
199. #2905C2×C47semidirect
201. #1486C2×C47semidirect
202. #1458C2×C47semidirect
203. #1303C2×C47semidirect
230. C47#9035direct (N × H)
264. C4⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#29052
C47×#23922
C47×#14862
C47×#14582
C47×#13032
#903547