Finite Group Databasebeta

← C47×#9446 #26049144

Subgroups — C47×#9446 #26049144

Order 12032.

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic, complemented
2C47×#2500C211yesmaximal, characteristic
3C47×#1820C211yesmaximal, characteristic, complemented
4C47×#1510C212yesmaximal
5C47×#1284C212yesmaximal, complemented
6C2×#121×C47C2211yescharacteristic
7C2×#117×C47C2211yescharacteristic
8C47×#433—24no—
9C47×#423—21no—
10C47×#407C2212yes—
11C4×M16×C47—21no—
12C47×#394—21no—
13C47×#394—21no—
14C47×#390C411yescharacteristic, complemented
15C47×#390C411yescharacteristic, complemented
16C47×#388—21no—
17C47×#388—21no—
18C47×#384C411yescharacteristic, complemented
19C47×#382C411yescharacteristic, complemented
20C47×#381C2212yes—
21C4×C22⋊C4×C47C2211yescharacteristic
22C47×#342—21no—
23C47×#342—21no—
24C47×#327—24no—
25C22×D4×C47—21no—
26C22×D4×C47C2×C411yescharacteristic
27C23×C4×C47C2311yescharacteristic
28C2×M16×C47—22no—
29#121×C47—22no—
30#121×C47—22no—
31#117×C47—22no—
32#117×C47—22no—
33C2×C4⋊C4×C47—21no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47C2×C411yescharacteristic
36C2×C4⋊C4×C47C2×C411yescharacteristic
37C2×C4⋊C4×C47C2×C411yescharacteristic
38C2×C22⋊C4×C47—21no—
39C2×C22⋊C4×C47—21no—
40C2×C22⋊C4×C47—21no—
41C2×C22⋊C4×C47—21no—
42C2×C22⋊C4×C47—22no—
43C2×C22⋊C4×C47—21no—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47D411yescharacteristic
46C2×C22⋊C4×C47D411yescharacteristic
47C2×C42×C47C2×C411yescharacteristic
48C2×C42×C47C2×C411yescharacteristic
49C2×C42×C47D411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C4⋊C8×C47—24no—
52C22⋊C8×C47—22no—
53C22⋊C8×C47D414yes—
54#97×C47—22no—
55C4×C8×C47—22no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—22no—
60#95×C47—22no—
61C24×C47—21no—
62C24×C47C2×D411yescharacteristic
63C2×D4×C47—22no—
64C2×D4×C47—41no—
65C2×D4×C47—41no—
66C2×D4×C47—42no—
67C2×D4×C47—81no—
68C2×D4×C47—81no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—42no—
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C22⋊C411yescharacteristic
78C22×C4×C47C22⋊C411yescharacteristic
79C22×C4×C47C22×C411yescharacteristic
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D412yes—
82C22×C4×C47#4112yes—
83M16×C47—42no—
84M16×C47—42no—
85C2×C8×C47—24no—
86C4⋊C4×C47—22no—
87C4⋊C4×C47—22no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—81no—
90C4⋊C4×C47—81no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47—22no—
93C22⋊C4×C47—42no—
94C22⋊C4×C47—42no—
95C22⋊C4×C47—42no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—42no—
100C22⋊C4×C47—81no—
101C22⋊C4×C47—81no—
102C42×C47—21no—
103C42×C47—21no—
104C42×C47—21no—
105C42×C47—21no—
106C42×C47—41no—
107C42×C47—41no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—41no—
111C23×C47—41no—
112C23×C47—41no—
113C23×C47—41no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47—41no—
119C23×C47C2×C22⋊C411yescharacteristic
120C23×C47#12112yes—
121D4×C47—82no—
122D4×C47—84no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—22no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
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—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—82no—
147C2×C4×C47—82no—
148C2×C4×C47—82no—
149C2×C4×C47C4×D412yes—
150C2×C4×C47#12011yescharacteristic
151C2×C4×C47#12311yescharacteristic
152C8×C47—44no—
153#9446C4711yesmaximal, characteristic, direct product factor, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—22no—
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—81no—
160C22×C47—81no—
161C22×C47—81no—
162C22×C47—81no—
163C22×C47—81no—
164C22×C47—81no—
165C22×C47—81no—
166C22×C47—81no—
167C22×C47—81no—
168C22×C47#38611yescharacteristic
169C22×C47#41011yescharacteristic
170C22×C47#41011yescharacteristic
171C4×C47—21no—
172C4×C47—22no—
173C4×C47—21no—
174C4×C47—42no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—81no—
180C4×C47—81no—
181C4×C47—162no—
182#2921C2×C4711yescharacteristic, complemented
183#2500C2×C4711yescharacteristic
184#1820C2×C4711yescharacteristic, complemented
185#1510C2×C4712yes—
186#1284C2×C4712yescomplemented
187C2×C47—21no—
188C2×C47—21no—
189C2×C47—42no—
190C2×C47—161no—
191C2×C47#188411yescharacteristic
192C2×C47#189911yescharacteristic
193C2×C47#191011yescharacteristic
194C2×#121C22×C4711yescharacteristic
195C2×#117C22×C4711yescharacteristic
196#433—24no—
197#423—21no—
198#407C22×C4712yes—
199C4×M16—21no—
200#394—21no—
201#394—21no—
202#390C4×C4711yescharacteristic, complemented
203#390C4×C4711yescharacteristic, complemented
204#388—21no—
205#388—21no—
206#384C4×C4711yescharacteristic, complemented
207#382C4×C4711yescharacteristic, complemented
208#381C22×C4712yes—
209C4×C22⋊C4C22×C4711yescharacteristic
210#342—21no—
211#342—21no—
212#327—24no—
213C47#944611yescharacteristic, direct product factor, Sylow
214C22×D4—21no—
215C22×D4C2×C4×C4711yescharacteristic
216C23×C4C23×C4711yescharacteristic
217C2×M16—22no—
218#121—22no—
219#121—22no—
220#117—22no—
221#117—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×C4×C4711yescharacteristic
225C2×C4⋊C4C2×C4×C4711yescharacteristic
226C2×C4⋊C4C2×C4×C4711yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4D4×C4711yescharacteristic
235C2×C22⋊C4D4×C4711yescharacteristic
236C2×C42C2×C4×C4711yescharacteristic
237C2×C42C2×C4×C4711yescharacteristic
238C2×C42D4×C4711yescharacteristic
239C2×C42D4×C4711yescharacteristic
240C4⋊C8—24no—
241C22⋊C8—22no—
242C22⋊C8D4×C4714yes—
243#97—22no—
244C4×C8—22no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—22no—
249#95—22no—
250C24—21no—
251C24C2×D4×C4711yescharacteristic
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—81no—
257C2×D4—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4C22⋊C4×C4711yescharacteristic
265C22×C4C22⋊C4×C4711yescharacteristic
266C22×C4C22⋊C4×C4711yescharacteristic
267C22×C4C22⋊C4×C4711yescharacteristic
268C22×C4C22×C4×C4711yescharacteristic
269C22×C4C2×D4×C4711yescharacteristic
270C22×C4C2×D4×C4712yes—
271C22×C4#41×C4712yes—
272M16—42no—
273M16—42no—
274C2×C8—24no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—41no—
296C42—41no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23C2×C22⋊C4×C4711yescharacteristic
309C23#121×C4712yes—
310D4—82no—
311D4—84no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4C4×D4×C4712yes—
339C2×C4#120×C4711yescharacteristic
340C2×C4#123×C4711yescharacteristic
341C8—44no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C47×#38611yescharacteristic
357C22C47×#41011yescharacteristic
358C22C47×#41011yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—42no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—162no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2C47×#188411yescharacteristic
375C2C47×#189911yescharacteristic
376C2C47×#191011yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC2×#121×C47C22
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
1. C47×#2921C2semidirect
3. C47×#1820C2semidirect
5. C47×#1284C2semidirect
14. C47×#390C4semidirect
15. C47×#390C4semidirect
18. C47×#384C4semidirect
19. C47×#382C4semidirect
153. #9446C47direct (N × H)
182. #2921C2×C47semidirect
184. #1820C2×C47semidirect
186. #1284C2×C47semidirect
202. #390C4×C47semidirect
203. #390C4×C47semidirect
206. #384C4×C47semidirect
207. #382C4×C47semidirect
213. C47#9446direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29212
C47×#25002
C47×#18202
C47×#15102
C47×#12842
#944647