Finite Group Databasebeta

← C47×#7654 #26047352

Subgroups — C47×#7654 #26047352

Order 12032.

580 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2854C211yesmaximal, characteristic
2C47×#1817C211yesmaximal, characteristic, complemented
3C2×C47×#336C211yesmaximal, characteristic, complemented
4C47×#1271C212yesmaximal, complemented
5C47×#1270C212yesmaximal, complemented
6C23×C8×C47—21no—
7C2×#123×C47—21no—
8C2×#121×C47C411yescharacteristic
9C22×C42×C47C2211yescharacteristic
10C2×C22⋊C8×C47—21no—
11C47×#390C411yescharacteristic
12C47×#390C2211yescharacteristic
13C47×#389C411yescharacteristic
14C47×#389C2211yescharacteristic
15C47×#388—21no—
16C47×#388—21no—
17C47×#386—21no—
18C47×#380C411yescharacteristic
19C47×#336—21no—
20C47×#336—21no—
21C47×#336C2212yes—
22C47×#336C2212yes—
23C22×D4×C47—21no—
24C22×D4×C47C2×C411yescharacteristic
25C23×C4×C47C2×C411yescharacteristic
26C23×C4×C47D411yescharacteristic
27C23×C4×C47D411yescharacteristic
28C22×C8×C47—24no—
29C22×C8×C47—22no—
30C22×C8×C47—22no—
31C22×C8×C47—42no—
32C22×C8×C47—42no—
33#123×C47—42no—
34#123×C47—42no—
35#121×C47—42no—
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47C2×C411yescharacteristic
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47C2×C411yescharacteristic
41C2×C22⋊C4×C47—21no—
42C2×C22⋊C4×C47—21no—
43C2×C22⋊C4×C47—21no—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47—21no—
47C2×C42×C47—42no—
48C2×C42×C47C2×C411yescharacteristic
49C2×C42×C47D411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47C2311yescharacteristic
52C22⋊C8×C47—42no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56C24×C47—21no—
57C24×C47C22⋊C411yescharacteristic
58C2×D4×C47—22no—
59C2×D4×C47—41no—
60C2×D4×C47—41no—
61C2×D4×C47—42no—
62C2×D4×C47—42no—
63C2×D4×C47—42no—
64C22×C4×C47—22no—
65C22×C4×C47—22no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C22⋊C411yescharacteristic
78C22×C4×C47D812yes—
79C22×C4×C47SD1612yes—
80C22×C4×C47C22×C411yescharacteristic
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C2×C8×C47—24no—
84C2×C8×C47—48no—
85C2×C8×C47—42no—
86C2×C8×C47—42no—
87C2×C8×C47—42no—
88C2×C8×C47—42no—
89C2×C8×C47—42no—
90C4⋊C4×C47—22no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—42no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C22⋊C4×C47—42no—
97C22⋊C4×C47—42no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—42no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—41no—
102C22⋊C4×C47—42no—
103C42×C47—41no—
104C42×C47—41no—
105C42×C47—41no—
106C42×C47—41no—
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×C47—41no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47#9912yes—
119C23×C47#10212yes—
120C23×C47#10412yes—
121C23×C47C2×C22⋊C411yescharacteristic
122D4×C47—82no—
123D4×C47—84no—
124C2×C4×C47—24no—
125C2×C4×C47—24no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—44no—
141C2×C4×C47—44no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47#10212yes—
152C2×C4×C47#13112yes—
153C2×C4×C47C2×D811yescharacteristic
154C2×C4×C47C2×SD1611yescharacteristic
155C2×C4×C47#13512yes—
156C8×C47—44no—
157C8×C47—82no—
158#7654C4711yesmaximal, characteristic, direct product factor, Sylow
159C22×C47—22no—
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—81no—
166C22×C47—81no—
167C22×C47—81no—
168C22×C47—81no—
169C22×C47—81no—
170C22×C47—81no—
171C22×C47—81no—
172C22×C47#32714yes—
173C22×C47#40811yescharacteristic
174C22×C47C2×#9911yescharacteristic
175C22×C47#41311yescharacteristic
176C22×C47C2×#10211yescharacteristic
177C22×C47#41611yescharacteristic
178C22×C47C2×#10411yescharacteristic
179C22×C47#42111yescharacteristic
180C4×C47—22no—
181C4×C47—21no—
182C4×C47—22no—
183C4×C47—21no—
184C4×C47—22no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—81no—
188C4×C47—81no—
189C4×C47—81no—
190#2854C2×C4711yescharacteristic
191#1817C2×C4711yescharacteristic, complemented
192C2×#336C2×C4711yescharacteristic, complemented
193#1271C2×C4712yescomplemented
194#1270C2×C4712yescomplemented
195C2×C47—24no—
196C2×C47—161no—
197C2×C47#146811yescharacteristic
198C2×C47#148011yescharacteristic
199C2×C47#149411yescharacteristic
200C2×C47C2×#32711yescharacteristic
201C2×C47#151611yescharacteristic
202C2×C47#153211yescharacteristic
203C2×C47#154011yescharacteristic
204C23×C8—21no—
205C2×#123—21no—
206C2×#121C4×C4711yescharacteristic
207C22×C42C22×C4711yescharacteristic
208C2×C22⋊C8—21no—
209#390C4×C4711yescharacteristic
210#390C22×C4711yescharacteristic
211#389C4×C4711yescharacteristic
212#389C22×C4711yescharacteristic
213#388—21no—
214#388—21no—
215#386—21no—
216#380C4×C4711yescharacteristic
217#336—21no—
218#336—21no—
219#336C22×C4712yes—
220#336C22×C4712yes—
221C47#765411yescharacteristic, direct product factor, Sylow
222C22×D4—21no—
223C22×D4C2×C4×C4711yescharacteristic
224C23×C4C2×C4×C4711yescharacteristic
225C23×C4D4×C4711yescharacteristic
226C23×C4D4×C4711yescharacteristic
227C22×C8—24no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—42no—
231C22×C8—42no—
232#123—42no—
233#123—42no—
234#121—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×C4×C4711yescharacteristic
238C2×C4⋊C4C2×C4×C4711yescharacteristic
239C2×C4⋊C4C2×C4×C4711yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—42no—
247C2×C42C2×C4×C4711yescharacteristic
248C2×C42D4×C4711yescharacteristic
249C2×C42D4×C4711yescharacteristic
250C2×C42C23×C4711yescharacteristic
251C22⋊C8—42no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24—21no—
256C24C22⋊C4×C4711yescharacteristic
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—42no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C22⋊C4×C4711yescharacteristic
275C22×C4C22⋊C4×C4711yescharacteristic
276C22×C4C22⋊C4×C4711yescharacteristic
277C22×C4D8×C4712yes—
278C22×C4SD16×C4712yes—
279C22×C4C22×C4×C4711yescharacteristic
280C22×C4C2×D4×C4711yescharacteristic
281C22×C4C2×D4×C4711yescharacteristic
282C2×C8—24no—
283C2×C8—48no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#99×C4712yes—
318C23#102×C4712yes—
319C23#104×C4712yes—
320C23C2×C22⋊C4×C4711yescharacteristic
321D4—82no—
322D4—84no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
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—21no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4#102×C4712yes—
351C2×C4#131×C4712yes—
352C2×C4C2×D8×C4711yescharacteristic
353C2×C4C2×SD16×C4711yescharacteristic
354C2×C4#135×C4712yes—
355C8—44no—
356C8—82no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22C47×#32714yes—
371C22C47×#40811yescharacteristic
372C22C2×#99×C4711yescharacteristic
373C22C47×#41311yescharacteristic
374C22C2×#102×C4711yescharacteristic
375C22C47×#41611yescharacteristic
376C22C2×#104×C4711yescharacteristic
377C22C47×#42111yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C2—24no—
389C2—161no—
390C2C47×#146811yescharacteristic
391C2C47×#148011yescharacteristic
392C2C47×#149411yescharacteristic
393C2C2×C47×#32711yescharacteristic
394C2C47×#151611yescharacteristic
395C2C47×#153211yescharacteristic
396C2C47×#154011yescharacteristic
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC2×#121×C47C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1817C2semidirect
3. C2×C47×#336C2semidirect
4. C47×#1271C2semidirect
5. C47×#1270C2semidirect
158. #7654C47direct (N × H)
191. #1817C2×C47semidirect
192. C2×#336C2×C47semidirect
193. #1271C2×C47semidirect
194. #1270C2×C47semidirect
221. C47#7654direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28542
C47×#18172
C2×C47×#3362
C47×#12712
C47×#12702
#765447