Finite Group Databasebeta

← C47×#8713 #26048411

Subgroups — C47×#8713 #26048411

Order 12032.

940 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#380C211yesmaximal, characteristic
2C47×#1779C211yesmaximal, characteristic
3C47×C22⋊#95C211yesmaximal, characteristic
4C47×#1294C214yesmaximal, complemented
5C24×C4×C47C2211yescharacteristic
6C22×C4⋊C4×C47C411yescharacteristic, complemented
7C22×C4⋊C4×C47C411yescharacteristic, complemented
8C22×C22⋊C4×C47—21no—
9C22×C22⋊C4×C47—21no—
10C2×C22⋊C8×C47—21no—
11C2×C22⋊C8×C47—21no—
12C2×C22⋊C8×C47C2212yes—
13C47×#380—21no—
14C47×#380—21no—
15C47×#380C412yescomplemented
16C47×#380C2212yes—
17C2×#95×C47—21no—
18C2×#95×C47—21no—
19C2×#95×C47C2212yes—
20C25×C47D411yescharacteristic
21C23×C4×C47—24no—
22C23×C4×C47—21no—
23C23×C4×C47—21no—
24C23×C4×C47—22no—
25C23×C4×C47—42no—
26C23×C4×C47—42no—
27C23×C4×C47C2×C411yescharacteristic
28C23×C4×C47C2×C411yescharacteristic
29C23×C4×C47D411yescharacteristic
30C23×C4×C47D411yescharacteristic
31C23×C4×C47D411yescharacteristic
32C23×C4×C47C2311yescharacteristic
33C22×C8×C47—22no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47—42no—
37C2×C4⋊C4×C47—42no—
38C2×C4⋊C4×C47C2×C412yes—
39C2×C4⋊C4×C47C2×C412yes—
40C2×C22⋊C4×C47—24no—
41C2×C22⋊C4×C47—22no—
42C2×C22⋊C4×C47—22no—
43C2×C22⋊C4×C47—42no—
44C2×C22⋊C4×C47—44no—
45C2×C22⋊C4×C47—42no—
46C22⋊C8×C47—24no—
47C22⋊C8×C47—42no—
48C22⋊C8×C47—42no—
49#95×C47—22no—
50#95×C47—22no—
51#95×C47—24no—
52#95×C47—42no—
53C24×C47—22no—
54C24×C47—22no—
55C24×C47—22no—
56C24×C47—22no—
57C24×C47—41no—
58C24×C47—41no—
59C24×C47C22⋊C411yescharacteristic
60C24×C47C22⋊C411yescharacteristic
61C24×C47SD1612yes—
62C24×C47Q1612yes—
63C24×C47C2×D411yescharacteristic
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—22no—
71C22×C4×C47—22no—
72C22×C4×C47—22no—
73C22×C4×C47—22no—
74C22×C4×C47—24no—
75C22×C4×C47—22no—
76C22×C4×C47—22no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—416no—
85C22×C4×C47—42no—
86C22×C4×C47—42no—
87C22×C4×C47—42no—
88C22×C4×C47—42no—
89C22×C4×C47—42no—
90C22×C4×C47—42no—
91C22×C4×C47—42no—
92C22×C4×C47—42no—
93C22×C4×C47—42no—
94C22×C4×C47—42no—
95C22×C4×C47—42no—
96C22×C4×C47—42no—
97C22×C4×C47C22⋊C411yescharacteristic
98C22×C4×C47C22⋊C411yescharacteristic
99C22×C4×C47C22×C411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47#4114yes—
102C2×C8×C47—42no—
103C2×C8×C47—42no—
104C2×C8×C47—42no—
105C4⋊C4×C47—42no—
106C4⋊C4×C47—42no—
107C4⋊C4×C47—42no—
108C4⋊C4×C47—42no—
109C22⋊C4×C47—48no—
110C22⋊C4×C47—44no—
111C22⋊C4×C47—44no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—24no—
121C23×C47—24no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—24no—
129C23×C47—24no—
130C23×C47—42no—
131C23×C47—42no—
132C23×C47—44no—
133C23×C47—44no—
134C23×C47—44no—
135C23×C47—44no—
136C23×C47#9912yes—
137C23×C47#10312yes—
138C23×C47#10312yes—
139C23×C47#10412yes—
140C23×C47C2×C22⋊C411yescharacteristic
141C23×C47#12312yes—
142C23×C47C2×SD1611yescharacteristic
143C23×C47C2×Q1611yescharacteristic
144C23×C47AGL(1,ℤ/8)12yes—
145C2×C4×C47—28no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—44no—
156C2×C4×C47—44no—
157C2×C4×C47—44no—
158C2×C4×C47—44no—
159C2×C4×C47—44no—
160C2×C4×C47—44no—
161C2×C4×C47—44no—
162C2×C4×C47—44no—
163C2×C4×C47—42no—
164C2×C4×C47—42no—
165C2×C4×C47—42no—
166C2×C4×C47—42no—
167C2×C4×C47—42no—
168C2×C4×C47—42no—
169C2×C4×C47—82no—
170C2×C4×C47—82no—
171C2×C4×C47—82no—
172C2×C4×C47—84no—
173C2×C4×C47—84no—
174C2×C4×C47—82no—
175C2×C4×C47#9912yes—
176C2×C4×C47#11712yes—
177C2×C4×C47#12312yes—
178C8×C47—82no—
179#8713C4711yesmaximal, characteristic, direct product factor, Sylow
180C22×C47—22no—
181C22×C47—22no—
182C22×C47—22no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—22no—
188C22×C47—22no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—21no—
192C22×C47—22no—
193C22×C47—21no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—48no—
198C22×C47—48no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47#32814yes—
204C22×C47#38111yescharacteristic
205C22×C47C2×#9911yescharacteristic
206C22×C47C2×#9911yescharacteristic
207C22×C47C2×#10311yescharacteristic
208C22×C47#41811yescharacteristic
209C22×C47C2×#10411yescharacteristic
210C22×C47#42111yescharacteristic
211C22×C47#48112yes—
212C22×C47#48412yes—
213C4×C47—22no—
214C4×C47—22no—
215C4×C47—22no—
216C4×C47—41no—
217C4×C47—84no—
218C4×C47—82no—
219C4×C47—82no—
220C2×#380C2×C4711yescharacteristic
221#1779C2×C4711yescharacteristic
222C22⋊#95C2×C4711yescharacteristic
223#1294C2×C4714yescomplemented
224C2×C47—22no—
225C2×C47—24no—
226C2×C47—22no—
227C2×C47—42no—
228C2×C47C2×#32811yescharacteristic
229C2×C47#150711yescharacteristic
230C2×C47#151011yescharacteristic
231C2×C47#152011yescharacteristic
232C2×C47#181911yescharacteristic
233C2×C47#182411yescharacteristic
234C2×C47#182611yescharacteristic
235C24×C4C22×C4711yescharacteristic
236C22×C4⋊C4C4×C4711yescharacteristic, complemented
237C22×C4⋊C4C4×C4711yescharacteristic, complemented
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C2×C22⋊C8—21no—
241C2×C22⋊C8—21no—
242C2×C22⋊C8C22×C4712yes—
243#380—21no—
244#380—21no—
245#380C4×C4712yescomplemented
246#380C22×C4712yes—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95C22×C4712yes—
250C47#871311yescharacteristic, direct product factor, Sylow
251C25D4×C4711yescharacteristic
252C23×C4—24no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—22no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4C2×C4×C4711yescharacteristic
259C23×C4C2×C4×C4711yescharacteristic
260C23×C4D4×C4711yescharacteristic
261C23×C4D4×C4711yescharacteristic
262C23×C4D4×C4711yescharacteristic
263C23×C4C23×C4711yescharacteristic
264C22×C8—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4C2×C4×C4712yes—
270C2×C4⋊C4C2×C4×C4712yes—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—44no—
276C2×C22⋊C4—42no—
277C22⋊C8—24no—
278C22⋊C8—42no—
279C22⋊C8—42no—
280#95—22no—
281#95—22no—
282#95—24no—
283#95—42no—
284C24—22no—
285C24—22no—
286C24—22no—
287C24—22no—
288C24—41no—
289C24—41no—
290C24C22⋊C4×C4711yescharacteristic
291C24C22⋊C4×C4711yescharacteristic
292C24SD16×C4712yes—
293C24Q16×C4712yes—
294C24C2×D4×C4711yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—416no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C22⋊C4×C4711yescharacteristic
329C22×C4C22⋊C4×C4711yescharacteristic
330C22×C4C22×C4×C4711yescharacteristic
331C22×C4C2×D4×C4711yescharacteristic
332C22×C4#41×C4714yes—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C22⋊C4—48no—
341C22⋊C4—44no—
342C22⋊C4—44no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—24no—
352C23—24no—
353C23—24no—
354C23—24no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—42no—
362C23—42no—
363C23—44no—
364C23—44no—
365C23—44no—
366C23—44no—
367C23#99×C4712yes—
368C23#103×C4712yes—
369C23#103×C4712yes—
370C23#104×C4712yes—
371C23C2×C22⋊C4×C4711yescharacteristic
372C23#123×C4712yes—
373C23C2×SD16×C4711yescharacteristic
374C23C2×Q16×C4711yescharacteristic
375C23AGL(1,ℤ/8)×C4712yes—
376C2×C4—28no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—84no—
404C2×C4—84no—
405C2×C4—82no—
406C2×C4#99×C4712yes—
407C2×C4#117×C4712yes—
408C2×C4#123×C4712yes—
409C8—82no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—22no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—48no—
428C22—48no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22C47×#32814yes—
434C22C47×#38111yescharacteristic
435C22C2×#99×C4711yescharacteristic
436C22C2×#99×C4711yescharacteristic
437C22C2×#103×C4711yescharacteristic
438C22C47×#41811yescharacteristic
439C22C2×#104×C4711yescharacteristic
440C22C47×#42111yescharacteristic
441C22C47×#48112yes—
442C22C47×#48412yes—
443C4—22no—
444C4—22no—
445C4—22no—
446C4—41no—
447C4—84no—
448C4—82no—
449C4—82no—
450C2—22no—
451C2—22no—
452C2—24no—
453C2—42no—
454C2C2×C47×#32811yescharacteristic
455C2C47×#150711yescharacteristic
456C2C47×#151011yescharacteristic
457C2C47×#152011yescharacteristic
458C2C47×#181911yescharacteristic
459C2C47×#182411yescharacteristic
460C2C47×#182611yescharacteristic
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC25×C47D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1294C2semidirect
6. C22×C4⋊C4×C47C4semidirect
7. C22×C4⋊C4×C47C4semidirect
15. C47×#380C4semidirect
179. #8713C47direct (N × H)
223. #1294C2×C47semidirect
236. C22×C4⋊C4C4×C47semidirect
237. C22×C4⋊C4C4×C47semidirect
245. #380C4×C47semidirect
250. C47#8713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3802
C47×#17792
C47×C22⋊#952
C47×#12942
#871347