Finite Group Databasebeta

← C47×#10288 #26049986

Subgroups — C47×#10288 #26049986

Order 12032.

554 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3226C211yesmaximal, characteristic
2C47×#3206C211yesmaximal, characteristic
3C47×#2862C211yesmaximal, characteristic, complemented
4C47×#1962C211yesmaximal, characteristic
5C47×#1548C211yesmaximal, characteristic, complemented
6C47×#1546C211yesmaximal, characteristic, complemented
7C47×#1276C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C2×C4⋊Q8×C47C2211yescharacteristic
10C2×C4⋊Q8×C47C2211yescharacteristic
11C47×#500—21no—
12C47×#492—21no—
13C47×#487—21no—
14C47×#486—21no—
15C47×#480—22no—
16C47×#474—22no—
17C47×#461—22no—
18C47×#448—22no—
19C47×#431C2211yescharacteristic
20C47×#431C2211yescharacteristic
21C47×#423C2211yescharacteristic
22C2×#104×C47—22no—
23C47×#391—22no—
24C47×#391—22no—
25C47×#382—22no—
26C43×C47C2211yescharacteristic
27C47×#333—22no—
28C47×#332—22no—
29C2×#41×C47—21no—
30C22×Q8×C47—21no—
31C22×Q8×C47D412yes—
32C2×SD16×C47—24no—
33C2×M16×C47—21no—
34C4⋊Q8×C47—21no—
35C4⋊Q8×C47—21no—
36C4⋊Q8×C47—21no—
37C4⋊Q8×C47—21no—
38C4⋊Q8×C47—21no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47—21no—
41C4⋊Q8×C47—21no—
42C4⋊Q8×C47D411yescharacteristic
43#127×C47D411yescharacteristic
44#124×C47—21no—
45#121×C47—21no—
46#121×C47—21no—
47C4×D4×C47—21no—
48C4×D4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47D412yes—
53C2×C42×C47—21no—
54C2×C42×C47—21no—
55C2×C42×C47D412yes—
56C2×C42×C47C2311yescharacteristic
57#107×C47—24no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D412yes—
61C4⋊C8×C47D412yes—
62#104×C47—44no—
63#103×C47—24no—
64#102×C47—24no—
65C22⋊C8×C47—21no—
66C22⋊C8×C47—21no—
67C4×C8×C47—21no—
68C4×C8×C47—21no—
69#95×C47—28no—
70#41×C47—42no—
71#41×C47—42no—
72C2×Q8×C47—22no—
73C2×Q8×C47—21no—
74C2×Q8×C47—22no—
75C2×Q8×C47—44no—
76C2×Q8×C47—41no—
77C2×Q8×C47—41no—
78C2×Q8×C47—42no—
79C2×Q8×C47—42no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—41no—
84C22×C4×C47—22no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—41no—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91SD16×C47—84no—
92M16×C47—42no—
93C2×C8×C47—22no—
94C2×C8×C47—22no—
95C2×C8×C47—41no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—22no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C22⋊C4×C47—41no—
107C22⋊C4×C47—41no—
108C42×C47—24no—
109C42×C47—22no—
110C42×C47—22no—
111C42×C47—42no—
112C42×C47C2×D411yescharacteristic
113C42×C47C2×D411yescharacteristic
114C42×C47C2×D411yescharacteristic
115C42×C47#4111yescharacteristic
116C23×C47—41no—
117C23×C47#12011yescharacteristic
118Q8×C47—44no—
119Q8×C47—42no—
120Q8×C47—82no—
121Q8×C47—82no—
122Q8×C47—81no—
123Q8×C47—81no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—42no—
127D4×C47—82no—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—24no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47—44no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—44no—
138C2×C4×C47—81no—
139C2×C4×C47—81no—
140C2×C4×C47#12011yescharacteristic
141C2×C4×C47#12011yescharacteristic
142C2×C4×C47#12111yescharacteristic
143C2×C4×C47#12111yescharacteristic
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47#12711yescharacteristic
146C2×C4×C47#13512yes—
147C2×C4×C47AGL(1,ℤ/8)12yes—
148C8×C47—42no—
149C8×C47—42no—
150C8×C47—81no—
151#10288C4711yesmaximal, characteristic, direct product factor, Sylow
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—81no—
155C22×C47—81no—
156C22×C47—81no—
157C22×C47#39211yescharacteristic
158C22×C47#44912yes—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—44no—
162C4×C47—82no—
163C4×C47—82no—
164C4×C47—81no—
165C4×C47#45512yes—
166C4×C47#45612yes—
167C4×C47#46312yes—
168C4×C47#49511yescharacteristic
169C4×C47#49611yescharacteristic
170#3226C2×C4711yescharacteristic
171#3206C2×C4711yescharacteristic
172#2862C2×C4711yescharacteristic, complemented
173#1962C2×C4711yescharacteristic
174#1548C2×C4711yescharacteristic, complemented
175#1546C2×C4711yescharacteristic, complemented
176#1276C2×C4711yescharacteristic, complemented
177C2×C47—22no—
178C2×C47—161no—
179C2×C47#200411yescharacteristic
180C2×C47#200511yescharacteristic
181C2×C47#201211yescharacteristic
182#532C22×C4711yescharacteristic
183C2×C4⋊Q8C22×C4711yescharacteristic
184C2×C4⋊Q8C22×C4711yescharacteristic
185#500—21no—
186#492—21no—
187#487—21no—
188#486—21no—
189#480—22no—
190#474—22no—
191#461—22no—
192#448—22no—
193#431C22×C4711yescharacteristic
194#431C22×C4711yescharacteristic
195#423C22×C4711yescharacteristic
196C2×#104—22no—
197#391—22no—
198#391—22no—
199#382—22no—
200C43C22×C4711yescharacteristic
201#333—22no—
202#332—22no—
203C47#1028811yescharacteristic, direct product factor, Sylow
204C2×#41—21no—
205C22×Q8—21no—
206C22×Q8D4×C4712yes—
207C2×SD16—24no—
208C2×M16—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C4711yescharacteristic
218#127D4×C4711yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C4712yes—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42D4×C4712yes—
231C2×C42C23×C4711yescharacteristic
232#107—24no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8D4×C4712yes—
236C4⋊C8D4×C4712yes—
237#104—44no—
238#103—24no—
239#102—24no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C4×C8—21no—
243C4×C8—21no—
244#95—28no—
245#41—42no—
246#41—42no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4C2×D4×C4711yescharacteristic
264C22×C4C2×D4×C4711yescharacteristic
265C22×C4C2×D4×C4711yescharacteristic
266SD16—84no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—24no—
284C42—22no—
285C42—22no—
286C42—42no—
287C42C2×D4×C4711yescharacteristic
288C42C2×D4×C4711yescharacteristic
289C42C2×D4×C4711yescharacteristic
290C42#41×C4711yescharacteristic
291C23—41no—
292C23#120×C4711yescharacteristic
293Q8—44no—
294Q8—42no—
295Q8—82no—
296Q8—82no—
297Q8—81no—
298Q8—81no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#120×C4711yescharacteristic
316C2×C4#120×C4711yescharacteristic
317C2×C4#121×C4711yescharacteristic
318C2×C4#121×C4711yescharacteristic
319C2×C4#121×C4711yescharacteristic
320C2×C4#127×C4711yescharacteristic
321C2×C4#135×C4712yes—
322C2×C4AGL(1,ℤ/8)×C4712yes—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C47×#39211yescharacteristic
332C22C47×#44912yes—
333C4—21no—
334C4—21no—
335C4—44no—
336C4—82no—
337C4—81no—
338C4—82no—
339C4C47×#45512yes—
340C4C47×#45612yes—
341C4C47×#46312yes—
342C4C47×#49511yescharacteristic
343C4C47×#49611yescharacteristic
344C2—22no—
345C2—161no—
346C2C47×#200411yescharacteristic
347C2C47×#200511yescharacteristic
348C2C47×#201211yescharacteristic
subgroupG/H
center, socleC22×C47#392
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2862C2semidirect
5. C47×#1548C2semidirect
6. C47×#1546C2semidirect
7. C47×#1276C2semidirect
151. #10288C47direct (N × H)
172. #2862C2×C47semidirect
174. #1548C2×C47semidirect
175. #1546C2×C47semidirect
176. #1276C2×C47semidirect
203. C47#10288direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32262
C47×#32062
C47×#28622
C47×#19622
C47×#15482
C47×#15462
C47×#12762
#1028847