Finite Group Databasebeta

← C47×#8378 #26048076

Subgroups — C47×#8378 #26048076

Order 12032.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#553C211yesmaximal, characteristic
2C47×#1824C212yesmaximal, complemented
3C47×#1799C211yesmaximal, characteristic, complemented
4C47×#1519C212yesmaximal, complemented
5C47×#1459C211yesmaximal, characteristic, complemented
6C47×#553—24no—
7C47×#553—24no—
8C2×#126×C47—21no—
9C2×#125×C47C411yescharacteristic, complemented
10C2×#123×C47—21no—
11C2×#121×C47—21no—
12C2×#121×C47C411yescharacteristic, complemented
13C2×#121×C47C2211yescharacteristic
14C2×C4×D4×C47—21no—
15C2×C4×D4×C47C411yescharacteristic, complemented
16C2×C4×D4×C47C2211yescharacteristic
17C2×#117×C47C411yescharacteristic, complemented
18C22×C4⋊C4×C47C2211yescharacteristic
19C2×#99×C47—21no—
20C2×C22⋊C8×C47C2212yes—
21C47×#380C2212yes—
22C47×#342—21no—
23C47×#340—24no—
24C47×#327—24no—
25C47×#324—21no—
26C47×#323—21no—
27C22×D4×C47—21no—
28C22×D4×C47—21no—
29C22×D4×C47C2×C411yescharacteristic
30C22×D4×C47D411yescharacteristic
31C23×C4×C47—21no—
32C23×C4×C47—21no—
33C23×C4×C47C2×C411yescharacteristic
34C23×C4×C47C2311yescharacteristic
35C22×C8×C47—22no—
36#126×C47—28no—
37#125×C47—22no—
38#125×C47—22no—
39#123×C47—28no—
40#121×C47—28no—
41#121×C47—22no—
42#121×C47—22no—
43#121×C47—22no—
44#121×C47D414yes—
45C4×D4×C47—28no—
46C4×D4×C47—22no—
47C4×D4×C47—22no—
48C4×D4×C47—22no—
49C4×D4×C47—22no—
50#117×C47—22no—
51#117×C47—22no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47—22no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47C2×C411yescharacteristic
58C2×C4⋊C4×C47C2×C411yescharacteristic
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C4⋊C4×C47D411yescharacteristic
61C2×C4⋊C4×C47D414yes—
62C2×C22⋊C4×C47—21no—
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—21no—
65C2×C22⋊C4×C47—21no—
66C2×C22⋊C4×C47—22no—
67C2×C22⋊C4×C47D411yescharacteristic
68C2×C22⋊C4×C47D411yescharacteristic
69C2×C42×C47—21no—
70C2×C42×C47C2×C411yescharacteristic
71#99×C47—42no—
72C22⋊C8×C47—22no—
73C22⋊C8×C47—22no—
74#95×C47—22no—
75C24×C47—21no—
76C24×C47C22⋊C411yescharacteristic
77C24×C47C2×D411yescharacteristic
78C2×D4×C47—22no—
79C2×D4×C47—24no—
80C2×D4×C47—22no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—24no—
84C2×D4×C47—21no—
85C2×D4×C47—42no—
86C2×D4×C47—42no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—82no—
90C2×D4×C47C22⋊C412yes—
91C22×C4×C47—21no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—24no—
95C22×C4×C47—24no—
96C22×C4×C47—21no—
97C22×C4×C47—21no—
98C22×C4×C47—42no—
99C22×C4×C47—42no—
100C22×C4×C47—42no—
101C22×C4×C47—82no—
102C22×C4×C47—82no—
103C22×C4×C47C22⋊C411yescharacteristic
104C22×C4×C47C22⋊C411yescharacteristic
105C22×C4×C47C22⋊C411yescharacteristic
106C22×C4×C47C22×C411yescharacteristic
107C22×C4×C47C2×D412yes—
108C22×C4×C47C2×D412yes—
109C22×C4×C47C2×D411yescharacteristic
110C2×C8×C47—44no—
111C2×C8×C47—42no—
112C4⋊C4×C47—24no—
113C4⋊C4×C47—24no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47—24no—
118C4⋊C4×C47—22no—
119C4⋊C4×C47—44no—
120C4⋊C4×C47C22⋊C412yes—
121C4⋊C4×C47C22⋊C412yes—
122C4⋊C4×C47C22⋊C412yes—
123C22⋊C4×C47—24no—
124C22⋊C4×C47—24no—
125C22⋊C4×C47—24no—
126C22⋊C4×C47—22no—
127C22⋊C4×C47—24no—
128C22⋊C4×C47—22no—
129C22⋊C4×C47—42no—
130C22⋊C4×C47—42no—
131C42×C47—24no—
132C42×C47—21no—
133C42×C47—21no—
134C23×C47—21no—
135C23×C47—22no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—41no—
139C23×C47—41no—
140C23×C47—42no—
141C23×C47—42no—
142C23×C47—41no—
143C23×C47—41no—
144C23×C47—41no—
145C23×C47—41no—
146C23×C47C2×C22⋊C411yescharacteristic
147C23×C47#12012yes—
148C23×C47#13512yes—
149C23×C47AGL(1,ℤ/8)11yescharacteristic
150C23×C47#13711yescharacteristic
151D4×C47—42no—
152D4×C47—42no—
153D4×C47—44no—
154D4×C47—42no—
155D4×C47—44no—
156D4×C47—42no—
157D4×C47—84no—
158C2×C4×C47—24no—
159C2×C4×C47—22no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—22no—
163C2×C4×C47—21no—
164C2×C4×C47—22no—
165C2×C4×C47—22no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—41no—
169C2×C4×C47—42no—
170C2×C4×C47—42no—
171C2×C4×C47—42no—
172C2×C4×C47—42no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—42no—
176C2×C4×C47—41no—
177C2×C4×C47—41no—
178C2×C4×C47—84no—
179C2×C4×C47—84no—
180C2×C4×C47—82no—
181C2×C4×C47—82no—
182C2×C4×C47—82no—
183C2×C4×C47C2×C22⋊C411yescharacteristic
184C2×C4×C47C2×C22⋊C411yescharacteristic
185C2×C4×C47#12012yes—
186C8×C47—82no—
187#8378C4711yesmaximal, characteristic, direct product factor, Sylow
188C22×C47—21no—
189C22×C47—22no—
190C22×C47—21no—
191C22×C47—22no—
192C22×C47—42no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—42no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—42no—
199C22×C47—41no—
200C22×C47—42no—
201C22×C47—81no—
202C22×C47—81no—
203C22×C47—82no—
204C22×C47—82no—
205C22×C47#37911yescharacteristic
206C22×C47#41611yescharacteristic
207C22×C47#41711yescharacteristic
208C22×C47#44912yes—
209C22×C47#45212yes—
210C4×C47—22no—
211C4×C47—21no—
212C4×C47—42no—
213C4×C47—42no—
214C4×C47—41no—
215C4×C47—41no—
216C4×C47—41no—
217C4×C47—42no—
218C4×C47—162no—
219C4×C47#41012yes—
220C2×#553C2×C4711yescharacteristic
221#1824C2×C4712yescomplemented
222#1799C2×C4711yescharacteristic, complemented
223#1519C2×C4712yescomplemented
224#1459C2×C4711yescharacteristic, complemented
225C2×C47—22no—
226C2×C47—21no—
227C2×C47—21no—
228C2×C47—22no—
229C2×C47—81no—
230C2×C47—82no—
231C2×C47#178211yescharacteristic
232C2×C47#178811yescharacteristic
233C2×C47#179511yescharacteristic
234#553—24no—
235#553—24no—
236C2×#126—21no—
237C2×#125C4×C4711yescharacteristic, complemented
238C2×#123—21no—
239C2×#121—21no—
240C2×#121C4×C4711yescharacteristic, complemented
241C2×#121C22×C4711yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4C4×C4711yescharacteristic, complemented
244C2×C4×D4C22×C4711yescharacteristic
245C2×#117C4×C4711yescharacteristic, complemented
246C22×C4⋊C4C22×C4711yescharacteristic
247C2×#99—21no—
248C2×C22⋊C8C22×C4712yes—
249#380C22×C4712yes—
250#342—21no—
251#340—24no—
252#327—24no—
253#324—21no—
254#323—21no—
255C47#837811yescharacteristic, direct product factor, Sylow
256C22×D4—21no—
257C22×D4—21no—
258C22×D4C2×C4×C4711yescharacteristic
259C22×D4D4×C4711yescharacteristic
260C23×C4—21no—
261C23×C4—21no—
262C23×C4C2×C4×C4711yescharacteristic
263C23×C4C23×C4711yescharacteristic
264C22×C8—22no—
265#126—28no—
266#125—22no—
267#125—22no—
268#123—28no—
269#121—28no—
270#121—22no—
271#121—22no—
272#121—22no—
273#121D4×C4714yes—
274C4×D4—28no—
275C4×D4—22no—
276C4×D4—22no—
277C4×D4—22no—
278C4×D4—22no—
279#117—22no—
280#117—22no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4C2×C4×C4711yescharacteristic
287C2×C4⋊C4C2×C4×C4711yescharacteristic
288C2×C4⋊C4C2×C4×C4711yescharacteristic
289C2×C4⋊C4D4×C4711yescharacteristic
290C2×C4⋊C4D4×C4714yes—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4D4×C4711yescharacteristic
297C2×C22⋊C4D4×C4711yescharacteristic
298C2×C42—21no—
299C2×C42C2×C4×C4711yescharacteristic
300#99—42no—
301C22⋊C8—22no—
302C22⋊C8—22no—
303#95—22no—
304C24—21no—
305C24C22⋊C4×C4711yescharacteristic
306C24C2×D4×C4711yescharacteristic
307C2×D4—22no—
308C2×D4—24no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—24no—
313C2×D4—21no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—82no—
319C2×D4C22⋊C4×C4712yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—82no—
331C22×C4—82no—
332C22×C4C22⋊C4×C4711yescharacteristic
333C22×C4C22⋊C4×C4711yescharacteristic
334C22×C4C22⋊C4×C4711yescharacteristic
335C22×C4C22×C4×C4711yescharacteristic
336C22×C4C2×D4×C4712yes—
337C22×C4C2×D4×C4712yes—
338C22×C4C2×D4×C4711yescharacteristic
339C2×C8—44no—
340C2×C8—42no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—44no—
349C4⋊C4C22⋊C4×C4712yes—
350C4⋊C4C22⋊C4×C4712yes—
351C4⋊C4C22⋊C4×C4712yes—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—22no—
356C22⋊C4—24no—
357C22⋊C4—22no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C42—24no—
361C42—21no—
362C42—21no—
363C23—21no—
364C23—22no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23C2×C22⋊C4×C4711yescharacteristic
376C23#120×C4712yes—
377C23#135×C4712yes—
378C23AGL(1,ℤ/8)×C4711yescharacteristic
379C23#137×C4711yescharacteristic
380D4—42no—
381D4—42no—
382D4—44no—
383D4—42no—
384D4—44no—
385D4—42no—
386D4—84no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4C2×C22⋊C4×C4711yescharacteristic
413C2×C4C2×C22⋊C4×C4711yescharacteristic
414C2×C4#120×C4712yes—
415C8—82no—
416C22—21no—
417C22—22no—
418C22—21no—
419C22—22no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—42no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—82no—
432C22—82no—
433C22C47×#37911yescharacteristic
434C22C47×#41611yescharacteristic
435C22C47×#41711yescharacteristic
436C22C47×#44912yes—
437C22C47×#45212yes—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—41no—
446C4—162no—
447C4C47×#41012yes—
448C2—22no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—82no—
453C2—81no—
454C2C47×#178211yescharacteristic
455C2C47×#178811yescharacteristic
456C2C47×#179511yescharacteristic
subgroupG/H
center, socleC22×C47#379
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC2×C47×#553C2
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
2. C47×#1824C2semidirect
3. C47×#1799C2semidirect
4. C47×#1519C2semidirect
5. C47×#1459C2semidirect
9. C2×#125×C47C4semidirect
12. C2×#121×C47C4semidirect
15. C2×C4×D4×C47C4semidirect
17. C2×#117×C47C4semidirect
187. #8378C47direct (N × H)
221. #1824C2×C47semidirect
222. #1799C2×C47semidirect
223. #1519C2×C47semidirect
224. #1459C2×C47semidirect
237. C2×#125C4×C47semidirect
240. C2×#121C4×C47semidirect
243. C2×C4×D4C4×C47semidirect
245. C2×#117C4×C47semidirect
255. C47#8378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5532
C47×#18242
C47×#17992
C47×#15192
C47×#14592
#837847