Finite Group Databasebeta

← C47×#9184 #26048882

Subgroups — C47×#9184 #26048882

Order 12032.

530 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2975C211yesmaximal, characteristic
2C47×#2638C211yesmaximal, characteristic
3C4×#99×C47C211yesmaximal, characteristic
4C47×#1508C212yesmaximal, complemented
5C47×#1284C212yesmaximal, complemented
6C2×C22⋊Q8×C47C2211yescharacteristic
7C2×C4×D4×C47C2211yescharacteristic
8C47×#436—24no—
9C47×#431—21no—
10C2×#99×C47—21no—
11C47×#407—21no—
12C47×#407C2212yes—
13C47×#398C411yescharacteristic, complemented
14C47×#397—21no—
15C47×#397C411yescharacteristic, complemented
16C47×#395C411yescharacteristic, complemented
17C47×#394—21no—
18C47×#393C411yescharacteristic, complemented
19C47×#387—21no—
20C47×#385—21no—
21C47×#381C2211yescharacteristic
22C4×C22⋊C4×C47C2212yes—
23C47×#342—21no—
24C47×#328—24no—
25C22×Q8×C47C2×C411yescharacteristic
26C22×D4×C47D411yescharacteristic
27C23×C4×C47D411yescharacteristic
28C23×C4×C47C2311yescharacteristic
29C2×M16×C47—22no—
30C2×M16×C47—22no—
31C22⋊Q8×C47—22no—
32C22⋊Q8×C47—22no—
33C4×D4×C47—22no—
34C4×D4×C47—22no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47C2×C411yescharacteristic
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C22⋊C4×C47—22no—
41C2×C22⋊C4×C47—21no—
42C2×C22⋊C4×C47—21no—
43C2×C22⋊C4×C47—21no—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47C2×C411yescharacteristic
46C2×C22⋊C4×C47D411yescharacteristic
47C2×C42×C47—22no—
48C2×C42×C47D411yescharacteristic
49C4⋊C8×C47—22no—
50#99×C47—24no—
51C22⋊C8×C47—22no—
52C22⋊C8×C47—22no—
53C22⋊C8×C47D414yes—
54C4×C8×C47—22no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—22no—
61#95×C47C2×C411yescharacteristic
62#95×C47C2×C411yescharacteristic
63C24×C47C22⋊C411yescharacteristic
64C24×C47C2×D411yescharacteristic
65C2×Q8×C47—22no—
66C2×Q8×C47—81no—
67C2×D4×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47—41no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—42no—
77C22×C4×C47—81no—
78C22×C4×C47—81no—
79C22×C4×C47C22⋊C411yescharacteristic
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22⋊C411yescharacteristic
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C2×D412yes—
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47#4112yes—
86M16×C47—82no—
87M16×C47—82no—
88C2×C8×C47—24no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—22no—
91C4⋊C4×C47—42no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—81no—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47—24no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—42no—
100C22⋊C4×C47—42no—
101C22⋊C4×C47—81no—
102C22⋊C4×C47—81no—
103C42×C47—21no—
104C42×C47—21no—
105C42×C47—82no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—41no—
112C23×C47—41no—
113C23×C47—41no—
114C23×C47—41no—
115C23×C47C2×C22⋊C411yescharacteristic
116C23×C47#12112yes—
117Q8×C47—82no—
118D4×C47—44no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—42no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—44no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—81no—
144C2×C4×C47—82no—
145C2×C4×C47—82no—
146C2×C4×C47#10412yes—
147C2×C4×C47C4×D412yes—
148C2×C4×C47#12011yescharacteristic
149C2×C4×C47#12311yescharacteristic
150C8×C47—44no—
151#9184C4711yesmaximal, characteristic, direct product factor, Sylow
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—22no—
155C22×C47—22no—
156C22×C47—22no—
157C22×C47—42no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—81no—
162C22×C47—81no—
163C22×C47—81no—
164C22×C47#38611yescharacteristic
165C22×C47C2×#10411yescharacteristic
166C22×C47#42111yescharacteristic
167C4×C47—22no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—22no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—81no—
174C4×C47—81no—
175C4×C47—84no—
176C4×C47—81no—
177C4×C47—81no—
178#2975C2×C4711yescharacteristic
179#2638C2×C4711yescharacteristic
180C4×#99C2×C4711yescharacteristic
181#1508C2×C4712yescomplemented
182#1284C2×C4712yescomplemented
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—42no—
186C2×C47—81no—
187C2×C47#187111yescharacteristic
188C2×C47#190911yescharacteristic
189C2×C47#191311yescharacteristic
190C2×C22⋊Q8C22×C4711yescharacteristic
191C2×C4×D4C22×C4711yescharacteristic
192#436—24no—
193#431—21no—
194C2×#99—21no—
195#407—21no—
196#407C22×C4712yes—
197#398C4×C4711yescharacteristic, complemented
198#397—21no—
199#397C4×C4711yescharacteristic, complemented
200#395C4×C4711yescharacteristic, complemented
201#394—21no—
202#393C4×C4711yescharacteristic, complemented
203#387—21no—
204#385—21no—
205#381C22×C4711yescharacteristic
206C4×C22⋊C4C22×C4712yes—
207#342—21no—
208#328—24no—
209C47#918411yescharacteristic, direct product factor, Sylow
210C22×Q8C2×C4×C4711yescharacteristic
211C22×D4D4×C4711yescharacteristic
212C23×C4D4×C4711yescharacteristic
213C23×C4C23×C4711yescharacteristic
214C2×M16—22no—
215C2×M16—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C4×D4—22no—
219C4×D4—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×C4×C4711yescharacteristic
224C2×C4⋊C4C2×C4×C4711yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4C2×C4×C4711yescharacteristic
231C2×C22⋊C4D4×C4711yescharacteristic
232C2×C42—22no—
233C2×C42D4×C4711yescharacteristic
234C4⋊C8—22no—
235#99—24no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8D4×C4714yes—
239C4×C8—22no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—22no—
246#95C2×C4×C4711yescharacteristic
247#95C2×C4×C4711yescharacteristic
248C24C22⋊C4×C4711yescharacteristic
249C24C2×D4×C4711yescharacteristic
250C2×Q8—22no—
251C2×Q8—81no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4C22⋊C4×C4711yescharacteristic
265C22×C4C22⋊C4×C4711yescharacteristic
266C22×C4C22⋊C4×C4711yescharacteristic
267C22×C4C22×C4×C4711yescharacteristic
268C22×C4C2×D4×C4712yes—
269C22×C4C2×D4×C4711yescharacteristic
270C22×C4#41×C4712yes—
271M16—82no—
272M16—82no—
273C2×C8—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—24no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C42—21no—
289C42—21no—
290C42—82no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×C22⋊C4×C4711yescharacteristic
301C23#121×C4712yes—
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4#104×C4712yes—
332C2×C4C4×D4×C4712yes—
333C2×C4#120×C4711yescharacteristic
334C2×C4#123×C4711yescharacteristic
335C8—44no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C47×#38611yescharacteristic
349C22C2×#104×C4711yescharacteristic
350C22C47×#42111yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—84no—
360C4—81no—
361C4—81no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2C47×#187111yescharacteristic
367C2C47×#190911yescharacteristic
368C2C47×#191311yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC22×D4×C47D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1508C2semidirect
5. C47×#1284C2semidirect
13. C47×#398C4semidirect
15. C47×#397C4semidirect
16. C47×#395C4semidirect
18. C47×#393C4semidirect
151. #9184C47direct (N × H)
181. #1508C2×C47semidirect
182. #1284C2×C47semidirect
197. #398C4×C47semidirect
199. #397C4×C47semidirect
200. #395C4×C47semidirect
202. #393C4×C47semidirect
209. C47#9184direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29752
C47×#26382
C4×#99×C472
C47×#15082
C47×#12842
#918447