Finite Group Databasebeta

← C47×#9301 #26048999

Subgroups — C47×#9301 #26048999

Order 12032.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3206C211yesmaximal, characteristic
2C47×#2331C211yesmaximal, characteristic, complemented
3C47×#1963C211yesmaximal, characteristic
4C47×#1548C211yesmaximal, characteristic, complemented
5C47×#1517C211yesmaximal, characteristic
6C47×#1286C211yesmaximal, characteristic, complemented
7C47×#1274C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C2×C4⋊Q8×C47C2211yescharacteristic
10C47×#492C412yescomplemented
11C47×#487C412yescomplemented
12C47×#461—22no—
13C47×#448—22no—
14C47×#431C2211yescharacteristic
15C47×#431C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C2×#104×C47—21no—
18C2×#104×C47—21no—
19C47×#391—22no—
20C47×#389—21no—
21C47×#387—22no—
22C47×#382C2211yescharacteristic
23C4×C4⋊C4×C47—21no—
24C47×#376C2211yescharacteristic
25C47×#333—22no—
26C47×#327—22no—
27C2×#41×C47—21no—
28C22×Q8×C47D412yes—
29C2×SD16×C47—24no—
30C2×M16×C47—21no—
31C4⋊Q8×C47—21no—
32C4⋊Q8×C47—21no—
33C4⋊Q8×C47C2×C411yescharacteristic
34C4⋊Q8×C47C2×C412yes—
35C4⋊Q8×C47D412yes—
36#127×C47C2×C411yescharacteristic
37#124×C47—21no—
38#121×C47—21no—
39#121×C47—21no—
40C4×D4×C47—21no—
41C4×D4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47—22no—
46C2×C42×C47—22no—
47C2×C42×C47D411yescharacteristic
48C2×C42×C47D411yescharacteristic
49C2×C42×C47C2311yescharacteristic
50C4⋊C8×C47—21no—
51C4⋊C8×C47—21no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54#104×C47—42no—
55#104×C47—42no—
56#103×C47—24no—
57C22⋊C8×C47—21no—
58C22⋊C8×C47—21no—
59C4×C8×C47—21no—
60C4×C8×C47C2×C412yes—
61#95×C47—22no—
62#95×C47—22no—
63#95×C47—21no—
64#95×C47—21no—
65#95×C47—21no—
66#95×C47D412yes—
67#41×C47—41no—
68#41×C47—41no—
69#41×C47—41no—
70#41×C47—41no—
71C2×Q8×C47—22no—
72C2×Q8×C47—21no—
73C2×Q8×C47—82no—
74C2×Q8×C47C22⋊C414yes—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C22×C4×C47—21no—
80C22×C4×C47—22no—
81C22×C4×C47—22no—
82C22×C4×C47—21no—
83C22×C4×C47—41no—
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87SD16×C47—84no—
88M16×C47—41no—
89M16×C47—41no—
90C2×C8×C47—22no—
91C2×C8×C47—41no—
92C2×C8×C47—41no—
93C4⋊C4×C47—22no—
94C4⋊C4×C47—22no—
95C4⋊C4×C47—22no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—82no—
102C22⋊C4×C47—41no—
103C22⋊C4×C47—41no—
104C42×C47—21no—
105C42×C47—21no—
106C42×C47—21no—
107C42×C47—82no—
108C42×C47SD1612yescomplemented
109C42×C47C22×C411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47#4111yescharacteristic
112C42×C47#4111yescharacteristic
113C23×C47—41no—
114C23×C47#12011yescharacteristic
115Q8×C47—44no—
116Q8×C47—41no—
117Q8×C47—41no—
118Q8×C47—82no—
119D4×C47—42no—
120D4×C47—41no—
121D4×C47—41no—
122D4×C47—81no—
123D4×C47—81no—
124D4×C47—81no—
125C2×C4×C47—24no—
126C2×C4×C47—22no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—42no—
140C2×C4×C47—81no—
141C2×C4×C47—81no—
142C2×C4×C47C2×C22⋊C411yescharacteristic
143C2×C4×C47C4×D411yescharacteristic
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47#12311yescharacteristic
148C2×C4×C47C2×SD1611yescharacteristic
149C2×C4×C47#13511yescharacteristic
150C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C47#13711yescharacteristic
152C8×C47—42no—
153C8×C47—81no—
154C8×C47—81no—
155#9301C4711yesmaximal, characteristic, direct product factor, Sylow
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—81no—
159C22×C47—81no—
160C22×C47—81no—
161C22×C47#38611yescharacteristic
162C22×C47#44811yescharacteristic
163C22×C47#44911yescharacteristic
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—42no—
169C4×C47—44no—
170C4×C47—82no—
171C4×C47—81no—
172C4×C47—81no—
173C4×C47C4×SD1611yescharacteristic
174C4×C47#44011yescharacteristic
175C4×C47#46011yescharacteristic
176C4×C47#46411yescharacteristic
177#3206C2×C4711yescharacteristic
178#2331C2×C4711yescharacteristic, complemented
179#1963C2×C4711yescharacteristic
180#1548C2×C4711yescharacteristic, complemented
181#1517C2×C4711yescharacteristic
182#1286C2×C4711yescharacteristic, complemented
183#1274C2×C4711yescharacteristic, complemented
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—161no—
187C2×C47#188011yescharacteristic
188C2×C47#190511yescharacteristic
189C2×C47#191111yescharacteristic
190#532C22×C4711yescharacteristic
191C2×C4⋊Q8C22×C4711yescharacteristic
192#492C4×C4712yescomplemented
193#487C4×C4712yescomplemented
194#461—22no—
195#448—22no—
196#431C22×C4711yescharacteristic
197#431C22×C4711yescharacteristic
198#423C22×C4711yescharacteristic
199C2×#104—21no—
200C2×#104—21no—
201#391—22no—
202#389—21no—
203#387—22no—
204#382C22×C4711yescharacteristic
205C4×C4⋊C4—21no—
206#376C22×C4711yescharacteristic
207#333—22no—
208#327—22no—
209C47#930111yescharacteristic, direct product factor, Sylow
210C2×#41—21no—
211C22×Q8D4×C4712yes—
212C2×SD16—24no—
213C2×M16—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8C2×C4×C4711yescharacteristic
217C4⋊Q8C2×C4×C4712yes—
218C4⋊Q8D4×C4712yes—
219#127C2×C4×C4711yescharacteristic
220#124—21no—
221#121—21no—
222#121—21no—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C42—22no—
230C2×C42D4×C4711yescharacteristic
231C2×C42D4×C4711yescharacteristic
232C2×C42C23×C4711yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#104—42no—
238#104—42no—
239#103—24no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C4×C8—21no—
243C4×C8C2×C4×C4712yes—
244#95—22no—
245#95—22no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95D4×C4712yes—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—22no—
255C2×Q8—21no—
256C2×Q8—82no—
257C2×Q8C22⋊C4×C4714yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4C2×D4×C4711yescharacteristic
268C22×C4C2×D4×C4711yescharacteristic
269C22×C4C2×D4×C4711yescharacteristic
270SD16—84no—
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—82no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—82no—
291C42SD16×C4712yescomplemented
292C42C22×C4×C4711yescharacteristic
293C42C2×D4×C4711yescharacteristic
294C42#41×C4711yescharacteristic
295C42#41×C4711yescharacteristic
296C23—41no—
297C23#120×C4711yescharacteristic
298Q8—44no—
299Q8—41no—
300Q8—41no—
301Q8—82no—
302D4—42no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—81no—
307D4—81no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C2×C22⋊C4×C4711yescharacteristic
326C2×C4C4×D4×C4711yescharacteristic
327C2×C4C4×D4×C4711yescharacteristic
328C2×C4#121×C4711yescharacteristic
329C2×C4#121×C4711yescharacteristic
330C2×C4#123×C4711yescharacteristic
331C2×C4C2×SD16×C4711yescharacteristic
332C2×C4#135×C4711yescharacteristic
333C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
334C2×C4#137×C4711yescharacteristic
335C8—42no—
336C8—81no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C47×#38611yescharacteristic
344C22C47×#44811yescharacteristic
345C22C47×#44911yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C4—81no—
355C4C4×SD16×C4711yescharacteristic
356C4C47×#44011yescharacteristic
357C4C47×#46011yescharacteristic
358C4C47×#46411yescharacteristic
359C2—21no—
360C2—21no—
361C2—161no—
362C2C47×#188011yescharacteristic
363C2C47×#190511yescharacteristic
364C2C47×#191111yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2331C2semidirect
4. C47×#1548C2semidirect
6. C47×#1286C2semidirect
7. C47×#1274C2semidirect
10. C47×#492C4semidirect
11. C47×#487C4semidirect
108. C42×C47SD16semidirect
155. #9301C47direct (N × H)
178. #2331C2×C47semidirect
180. #1548C2×C47semidirect
182. #1286C2×C47semidirect
183. #1274C2×C47semidirect
192. #492C4×C47semidirect
193. #487C4×C47semidirect
209. C47#9301direct (N × H)
291. C42SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#32062
C47×#23312
C47×#19632
C47×#15482
C47×#15172
C47×#12862
C47×#12742
#930147