Finite Group Databasebeta

← C47×#9214 #26048912

Subgroups — C47×#9214 #26048912

Order 12032.

428 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3107C211yesmaximal, characteristic
2C47×#2922C211yesmaximal, characteristic
3C47×#1526C211yesmaximal, characteristic, complemented
4C47×#1493C211yesmaximal, characteristic, complemented
5C47×#1489C211yesmaximal, characteristic
6C47×#1299C211yesmaximal, characteristic, complemented
7C47×#1278C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C4×#41×C47C2211yescharacteristic
10C47×#485—21no—
11C47×#475C411yescharacteristic
12C47×#474C411yescharacteristic
13C47×#462C411yescharacteristic
14C47×#461C411yescharacteristic
15C47×#452—21no—
16C4×Q16×C47—21no—
17C4×SD16×C47—21no—
18C47×#433—22no—
19C47×#431—22no—
20C47×#431C2211yescharacteristic
21C47×#424—21no—
22C47×#423C2211yescharacteristic
23C47×#408—21no—
24C4×M16×C47C2211yescharacteristic
25C4×M16×C47C2211yescharacteristic
26C2×C4×C8×C47C2211yescharacteristic
27C47×#330—22no—
28C47×Q8⋊C8—22no—
29C47×Q8⋊C8—21no—
30C47×D4⋊C8—21no—
31C2×#41×C47D411yescharacteristic
32C2×Q16×C47—21no—
33C2×SD16×C47—21no—
34C2×M16×C47—21no—
35C2×M16×C47—21no—
36C2×M16×C47—21no—
37C22×C8×C47—21no—
38C4⋊Q8×C47C2×C411yescharacteristic
39C4⋊Q8×C47C2×C411yescharacteristic
40#125×C47—21no—
41C22⋊Q8×C47—21no—
42C22⋊Q8×C47—21no—
43C4×Q8×C47—21no—
44C4×Q8×C47—21no—
45C4×Q8×C47C2×C411yescharacteristic
46C4×Q8×C47D411yescharacteristic
47C4×D4×C47—21no—
48C4×D4×C47—21no—
49C4×D4×C47C2×C411yescharacteristic
50C4×D4×C47D411yescharacteristic
51#117×C47—21no—
52#117×C47—21no—
53#117×C47D411yescharacteristic
54C2×C42×C47—21no—
55C2×C42×C47C2311yescharacteristic
56#107×C47—21no—
57#106×C47—21no—
58C4⋊C8×C47—24no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47C2×C411yescharacteristic
62C4⋊C8×C47C2×C411yescharacteristic
63#103×C47—21no—
64#103×C47—21no—
65#103×C47—21no—
66#102×C47—21no—
67C22⋊C8×C47—24no—
68C22⋊C8×C47—21no—
69#97×C47—21no—
70#97×C47D412yes—
71C4×C8×C47—21no—
72C4×C8×C47—21no—
73C4×C8×C47—21no—
74C4×C8×C47—21no—
75C4×C8×C47D412yes—
76#41×C47—41no—
77#41×C47—41no—
78C2×Q8×C47—21no—
79C2×Q8×C47—21no—
80C2×Q8×C47C22⋊C411yescharacteristic
81C2×D4×C47—21no—
82C2×D4×C47C22⋊C411yescharacteristic
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47#4111yescharacteristic
88C22×C4×C47#4111yescharacteristic
89Q16×C47—42no—
90SD16×C47—42no—
91M16×C47—22no—
92M16×C47—41no—
93M16×C47—41no—
94M16×C47—41no—
95M16×C47—81no—
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—22no—
99C2×C8×C47—22no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C2×C8×C47—41no—
103C2×C8×C47—41no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—21no—
110C4⋊C4×C47—41no—
111C4⋊C4×C47—41no—
112C4⋊C4×C47C22⋊C411yescharacteristic
113C4⋊C4×C47C22⋊C411yescharacteristic
114C22⋊C4×C47—21no—
115C22⋊C4×C47—21no—
116C22⋊C4×C47—21no—
117C22⋊C4×C47—41no—
118C42×C47—21no—
119C42×C47—21no—
120C42×C47—21no—
121C42×C47—41no—
122C42×C47C22×C411yescharacteristic
123C42×C47C2×D411yescharacteristic
124C42×C47C2×D411yescharacteristic
125C42×C47C2×D411yescharacteristic
126C23×C47—21no—
127C23×C47#12311yescharacteristic
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—41no—
131Q8×C47—41no—
132Q8×C47—41no—
133Q8×C47—41no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—42no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—42no—
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×C47C2×C22⋊C411yescharacteristic
154C2×C4×C47C4×D411yescharacteristic
155C2×C4×C47C4×D411yescharacteristic
156C2×C4×C47#12011yescharacteristic
157C2×C4×C47#12111yescharacteristic
158C2×C4×C47#12111yescharacteristic
159C8×C47—42no—
160C8×C47—42no—
161C8×C47—42no—
162C8×C47—41no—
163C8×C47—41no—
164C8×C47—81no—
165#9214C4711yesmaximal, characteristic, direct product factor, Sylow
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47#38611yescharacteristic
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—81no—
180C4×C47—81no—
181C4×C47#42111yescharacteristic
182C4×C47#42111yescharacteristic
183C4×C47#44311yescharacteristic
184C4×C47#44411yescharacteristic
185C4×C47#47111yescharacteristic
186C4×C47#47311yescharacteristic
187#3107C2×C4711yescharacteristic
188#2922C2×C4711yescharacteristic
189#1526C2×C4711yescharacteristic, complemented
190#1493C2×C4711yescharacteristic, complemented
191#1489C2×C4711yescharacteristic
192#1299C2×C4711yescharacteristic, complemented
193#1278C2×C4711yescharacteristic, complemented
194C2×C47—41no—
195C2×C47—81no—
196C2×C47#187611yescharacteristic
197C2×C47#189711yescharacteristic
198C2×C47#190811yescharacteristic
199#533C22×C4711yescharacteristic
200C4×#41C22×C4711yescharacteristic
201#485—21no—
202#475C4×C4711yescharacteristic
203#474C4×C4711yescharacteristic
204#462C4×C4711yescharacteristic
205#461C4×C4711yescharacteristic
206#452—21no—
207C4×Q16—21no—
208C4×SD16—21no—
209#433—22no—
210#431—22no—
211#431C22×C4711yescharacteristic
212#424—21no—
213#423C22×C4711yescharacteristic
214#408—21no—
215C4×M16C22×C4711yescharacteristic
216C4×M16C22×C4711yescharacteristic
217C2×C4×C8C22×C4711yescharacteristic
218#330—22no—
219Q8⋊C8—21no—
220Q8⋊C8—22no—
221D4⋊C8—21no—
222C47#921411yescharacteristic, direct product factor, Sylow
223C2×#41D4×C4711yescharacteristic
224C2×Q16—21no—
225C2×SD16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C22×C8—21no—
230C4⋊Q8C2×C4×C4711yescharacteristic
231C4⋊Q8C2×C4×C4711yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8C2×C4×C4711yescharacteristic
238C4×Q8D4×C4711yescharacteristic
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×C4×C4711yescharacteristic
242C4×D4D4×C4711yescharacteristic
243#117—21no—
244#117—21no—
245#117D4×C4711yescharacteristic
246C2×C42—21no—
247C2×C42C23×C4711yescharacteristic
248#107—21no—
249#106—21no—
250C4⋊C8—24no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8C2×C4×C4711yescharacteristic
254C4⋊C8C2×C4×C4711yescharacteristic
255#103—21no—
256#103—21no—
257#103—21no—
258#102—21no—
259C22⋊C8—24no—
260C22⋊C8—21no—
261#97—21no—
262#97D4×C4712yes—
263C4×C8—21no—
264C4×C8—21no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8D4×C4712yes—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8C22⋊C4×C4711yescharacteristic
273C2×D4—21no—
274C2×D4C22⋊C4×C4711yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4C2×D4×C4711yescharacteristic
279C22×C4#41×C4711yescharacteristic
280C22×C4#41×C4711yescharacteristic
281Q16—42no—
282SD16—42no—
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—81no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C22⋊C4×C4711yescharacteristic
305C4⋊C4C22⋊C4×C4711yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—41no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42—41no—
314C42C22×C4×C4711yescharacteristic
315C42C2×D4×C4711yescharacteristic
316C42C2×D4×C4711yescharacteristic
317C42C2×D4×C4711yescharacteristic
318C23—21no—
319C23#123×C4711yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326D4—21no—
327D4—21no—
328D4—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4C2×C22⋊C4×C4711yescharacteristic
346C2×C4C4×D4×C4711yescharacteristic
347C2×C4C4×D4×C4711yescharacteristic
348C2×C4#120×C4711yescharacteristic
349C2×C4#121×C4711yescharacteristic
350C2×C4#121×C4711yescharacteristic
351C8—42no—
352C8—42no—
353C8—42no—
354C8—41no—
355C8—41no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22C47×#38611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4—81no—
372C4C47×#42111yescharacteristic
373C4C47×#42111yescharacteristic
374C4C47×#44311yescharacteristic
375C4C47×#44411yescharacteristic
376C4C47×#47111yescharacteristic
377C4C47×#47311yescharacteristic
378C2—41no—
379C2—81no—
380C2C47×#187611yescharacteristic
381C2C47×#189711yescharacteristic
382C2C47×#190811yescharacteristic
subgroupG/H
centerC2×C4×C47#121
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#386
prime radicalC2×#41×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1526C2semidirect
4. C47×#1493C2semidirect
6. C47×#1299C2semidirect
7. C47×#1278C2semidirect
165. #9214C47direct (N × H)
189. #1526C2×C47semidirect
190. #1493C2×C47semidirect
192. #1299C2×C47semidirect
193. #1278C2×C47semidirect
222. C47#9214direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31072
C47×#29222
C47×#15262
C47×#14932
C47×#14892
C47×#12992
C47×#12782
#921447