Finite Group Databasebeta

← C47×#7791 #26047489

Subgroups — C47×#7791 #26047489

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2683C211yesmaximal, characteristic
2C47×#2099C211yesmaximal, characteristic, complemented
3C47×#2084C211yesmaximal, characteristic, complemented
4C47×#2071C211yesmaximal, characteristic
5C47×#1271C211yesmaximal, characteristic, complemented
6C47×#1271C211yesmaximal, characteristic, complemented
7C47×#1270C211yesmaximal, characteristic
8C2×C22⋊Q8×C47—21no—
9C2×C22⋊Q8×C47—21no—
10C2×#106×C47—21no—
11C2×#102×C47—21no—
12C47×#396—21no—
13C47×#396—21no—
14C47×#395—21no—
15C47×#390C2211yescharacteristic
16C47×#389C2211yescharacteristic
17C47×#389C2211yescharacteristic
18C47×#386—21no—
19C47×#384C2211yescharacteristic
20C47×#340—21no—
21C47×#340—21no—
22C47×#340—21no—
23C47×#340—21no—
24C47×#336C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×Q8×C47—21no—
28C22×D4×C47D411yescharacteristic
29C23×C4×C47—21no—
30C22×C8×C47—21no—
31C22×C8×C47—21no—
32C22×C8×C47—21no—
33C22⋊Q8×C47—42no—
34C22⋊Q8×C47—42no—
35C22⋊Q8×C47—42no—
36C22⋊Q8×C47—42no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C4⋊C4×C47D411yescharacteristic
48C2×C4⋊C4×C47D411yescharacteristic
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—21no—
51C2×C22⋊C4×C47—21no—
52C2×C22⋊C4×C47—21no—
53C2×C22⋊C4×C47—21no—
54C2×C42×C47C2311yescharacteristic
55#106×C47—42no—
56#102×C47—42no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60C24×C47—21no—
61C2×Q8×C47—42no—
62C2×Q8×C47—42no—
63C2×Q8×C47—81no—
64C2×D4×C47—21no—
65C2×D4×C47—41no—
66C2×D4×C47—41no—
67C2×D4×C47SD1612yes—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—42no—
74C22×C4×C47—42no—
75C22×C4×C47—41no—
76C22×C4×C47—81no—
77C22×C4×C47C2×D411yescharacteristic
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C2×C8×C47—22no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47—41no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—42no—
92C4⋊C4×C47—42no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—42no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47D812yes—
106C4⋊C4×C47SD1612yes—
107C22⋊C4×C47—42no—
108C22⋊C4×C47—42no—
109C22⋊C4×C47—41no—
110C22⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—41no—
113C22⋊C4×C47—81no—
114C42×C47—41no—
115C23×C47—22no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47—41no—
119C23×C47—41no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47#12011yescharacteristic
123Q8×C47—84no—
124D4×C47—42no—
125D4×C47—81no—
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—22no—
133C2×C4×C47—22no—
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—41no—
147C2×C4×C47—84no—
148C2×C4×C47—81no—
149C2×C4×C47—81no—
150C2×C4×C47—81no—
151C2×C4×C47C2×D811yescharacteristic
152C2×C4×C47C2×SD1611yescharacteristic
153C2×C4×C47C2×SD1611yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C47#13711yescharacteristic
157C8×C47—42no—
158C8×C47—81no—
159C8×C47—81no—
160#7791C4711yesmaximal, characteristic, direct product factor, Sylow
161C22×C47—42no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—81no—
165C22×C47—81no—
166C22×C47—81no—
167C22×C47—81no—
168C22×C47#44711yescharacteristic
169C22×C47#44811yescharacteristic
170C22×C47#45011yescharacteristic
171C22×C47#45411yescharacteristic
172C22×C47#45511yescharacteristic
173C22×C47#45611yescharacteristic
174C22×C47#45811yescharacteristic
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47—42no—
183C4×C47—81no—
184C4×C47—81no—
185C4×C47—81no—
186C4×C47—161no—
187#2683C2×C4711yescharacteristic
188#2099C2×C4711yescharacteristic, complemented
189#2084C2×C4711yescharacteristic, complemented
190#2071C2×C4711yescharacteristic
191#1271C2×C4711yescharacteristic, complemented
192#1271C2×C4711yescharacteristic, complemented
193#1270C2×C4711yescharacteristic
194C2×C47—82no—
195C2×C47#160811yescharacteristic
196C2×C47#161011yescharacteristic
197C2×C47#161611yescharacteristic
198C2×C47#162711yescharacteristic
199C2×C47#163911yescharacteristic
200C2×C47#165111yescharacteristic
201C2×C47#166411yescharacteristic
202C2×C22⋊Q8—21no—
203C2×C22⋊Q8—21no—
204C2×#106—21no—
205C2×#102—21no—
206#396—21no—
207#396—21no—
208#395—21no—
209#390C22×C4711yescharacteristic
210#389C22×C4711yescharacteristic
211#389C22×C4711yescharacteristic
212#386—21no—
213#384C22×C4711yescharacteristic
214#340—21no—
215#340—21no—
216#340—21no—
217#340—21no—
218#336C22×C4711yescharacteristic
219#336C22×C4711yescharacteristic
220#336C22×C4711yescharacteristic
221C47#779111yescharacteristic, direct product factor, Sylow
222C22×Q8—21no—
223C22×D4D4×C4711yescharacteristic
224C23×C4—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22⋊Q8—42no—
229C22⋊Q8—42no—
230C22⋊Q8—42no—
231C22⋊Q8—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C4711yescharacteristic
240C2×C4⋊C4D4×C4711yescharacteristic
241C2×C4⋊C4D4×C4711yescharacteristic
242C2×C4⋊C4D4×C4711yescharacteristic
243C2×C4⋊C4D4×C4711yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C42C23×C4711yescharacteristic
250#106—42no—
251#102—42no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24—21no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—81no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4SD16×C4712yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—81no—
272C22×C4C2×D4×C4711yescharacteristic
273C22×C4C2×D4×C4711yescharacteristic
274C22×C4C2×D4×C4711yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4D8×C4712yes—
301C4⋊C4SD16×C4712yes—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C42—41no—
310C23—22no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#120×C4711yescharacteristic
318Q8—84no—
319D4—42no—
320D4—81no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—84no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×D8×C4711yescharacteristic
347C2×C4C2×SD16×C4711yescharacteristic
348C2×C4C2×SD16×C4711yescharacteristic
349C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
350C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
351C2×C4#137×C4711yescharacteristic
352C8—42no—
353C8—81no—
354C8—81no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22C47×#44711yescharacteristic
363C22C47×#44811yescharacteristic
364C22C47×#45011yescharacteristic
365C22C47×#45411yescharacteristic
366C22C47×#45511yescharacteristic
367C22C47×#45611yescharacteristic
368C22C47×#45811yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—161no—
381C2—82no—
382C2C47×#160811yescharacteristic
383C2C47×#161011yescharacteristic
384C2C47×#161611yescharacteristic
385C2C47×#162711yescharacteristic
386C2C47×#163911yescharacteristic
387C2C47×#165111yescharacteristic
388C2C47×#166411yescharacteristic
subgroupG/H
center, socleC23×C47#120
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC22×D4×C47D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2099C2semidirect
3. C47×#2084C2semidirect
5. C47×#1271C2semidirect
6. C47×#1271C2semidirect
160. #7791C47direct (N × H)
188. #2099C2×C47semidirect
189. #2084C2×C47semidirect
191. #1271C2×C47semidirect
192. #1271C2×C47semidirect
221. C47#7791direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26832
C47×#20992
C47×#20842
C47×#20712
C47×#12712
C47×#12702
#779147