Finite Group Databasebeta

← C47×#10912 #26050610

Subgroups — C47×#10912 #26050610

Order 12032.

1266 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#385C211yesmaximal, characteristic
2C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
3C2×C47×#342C212yesmaximal
4C2×C47×#342C212yesmaximal
5C47×C22⋊#95C211yesmaximal, characteristic
6C24×C4×C47C2211yescharacteristic
7C22×C4⋊C4×C47C412yescomplemented
8C22×C22⋊C4×C47C2211yescharacteristic
9C22×C22⋊C4×C47C2212yes—
10C22×C22⋊C4×C47C2211yescharacteristic
11C22×C22⋊C4×C47C2212yes—
12C22×C42×C47—21no—
13C47×#385—21no—
14C47×#385—22no—
15C47×#385—21no—
16C4×C22⋊C4×C47—24no—
17C2×#95×C47—21no—
18C2×#95×C47—22no—
19C2×#95×C47C412yescomplemented
20C47×#342—24no—
21C47×#342C418yescomplemented
22C25×C47C2311yescharacteristic
23C23×C4×C47—22no—
24C23×C4×C47—22no—
25C23×C4×C47—22no—
26C23×C4×C47—22no—
27C23×C4×C47—44no—
28C23×C4×C47C2×C412yes—
29C23×C4×C47C2×C411yescharacteristic
30C23×C4×C47C2×C411yescharacteristic
31C23×C4×C47C2×C412yes—
32C23×C4×C47D411yescharacteristic
33C23×C4×C47D412yes—
34C23×C4×C47D411yescharacteristic
35C2×C4⋊C4×C47—22no—
36C2×C4⋊C4×C47—22no—
37C2×C4⋊C4×C47—44no—
38C2×C22⋊C4×C47—22no—
39C2×C22⋊C4×C47—21no—
40C2×C22⋊C4×C47—21no—
41C2×C22⋊C4×C47—22no—
42C2×C22⋊C4×C47—22no—
43C2×C22⋊C4×C47—22no—
44C2×C22⋊C4×C47—22no—
45C2×C22⋊C4×C47—22no—
46C2×C22⋊C4×C47—22no—
47C2×C22⋊C4×C47—22no—
48C2×C22⋊C4×C47—22no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—21no—
51C2×C22⋊C4×C47—22no—
52C2×C22⋊C4×C47—22no—
53C2×C22⋊C4×C47C2×C414yes—
54C2×C22⋊C4×C47C2×C414yes—
55C2×C22⋊C4×C47C2×C414yes—
56C2×C22⋊C4×C47D414yes—
57C2×C22⋊C4×C47Q814yes—
58C2×C42×C47—24no—
59C2×C42×C47—44no—
60#95×C47—24no—
61#95×C47—22no—
62#95×C47—22no—
63#95×C47—44no—
64C24×C47—42no—
65C24×C47—42no—
66C24×C47C22×C411yescharacteristic
67C24×C47C22×C412yes—
68C24×C47C2×D411yescharacteristic
69C24×C47C2×D411yescharacteristic
70C24×C47C2×D412yes—
71C24×C47C2×Q812yes—
72C24×C47#4112yes—
73C24×C47#4112yes—
74C24×C47#4112yes—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—24no—
78C22×C4×C47—22no—
79C22×C4×C47—22no—
80C22×C4×C47—24no—
81C22×C4×C47—24no—
82C22×C4×C47—24no—
83C22×C4×C47—21no—
84C22×C4×C47—24no—
85C22×C4×C47—24no—
86C22×C4×C47—21no—
87C22×C4×C47—24no—
88C22×C4×C47—24no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—24no—
92C22×C4×C47—22no—
93C22×C4×C47—22no—
94C22×C4×C47—42no—
95C22×C4×C47—42no—
96C22×C4×C47—42no—
97C22×C4×C47—48no—
98C22×C4×C47—48no—
99C22×C4×C47—44no—
100C22×C4×C47—44no—
101C22×C4×C47—42no—
102C22×C4×C47—42no—
103C22×C4×C47—44no—
104C22×C4×C47—44no—
105C22×C4×C47—42no—
106C22×C4×C47—42no—
107C22×C4×C47—42no—
108C22×C4×C47—42no—
109C22×C4×C47C4214yescomplemented
110C22×C4×C47C22⋊C412yes—
111C22×C4×C47C22⋊C412yes—
112C4⋊C4×C47—44no—
113C4⋊C4×C47—44no—
114C22⋊C4×C47—24no—
115C22⋊C4×C47—24no—
116C22⋊C4×C47—24no—
117C22⋊C4×C47—24no—
118C22⋊C4×C47—24no—
119C22⋊C4×C47—24no—
120C22⋊C4×C47—24no—
121C22⋊C4×C47—41no—
122C22⋊C4×C47—42no—
123C22⋊C4×C47—41no—
124C22⋊C4×C47—42no—
125C22⋊C4×C47—42no—
126C22⋊C4×C47C4⋊C418yescomplemented
127C42×C47—48no—
128C23×C47—22no—
129C23×C47—22no—
130C23×C47—22no—
131C23×C47—22no—
132C23×C47—22no—
133C23×C47—22no—
134C23×C47—42no—
135C23×C47—42no—
136C23×C47—44no—
137C23×C47—42no—
138C23×C47—44no—
139C23×C47—42no—
140C23×C47—44no—
141C23×C47—44no—
142C23×C47C2×C4211yescharacteristic
143C23×C47C2×C22⋊C411yescharacteristic
144C23×C47C2×C4⋊C412yes—
145C23×C47#11711yescharacteristic
146C23×C47#11712yes—
147C23×C47C4×D412yes—
148C23×C47C4×D412yes—
149C23×C47C4×D412yes—
150C23×C47C4×D412yes—
151C23×C47C4×Q812yes—
152C23×C47C4×Q812yes—
153C23×C47#12011yescharacteristic
154C23×C47#12112yes—
155C23×C47C22⋊Q812yes—
156C23×C47C22⋊Q812yes—
157C23×C47#12311yescharacteristic
158C23×C47#12312yes—
159C23×C47#12411yescharacteristic
160C23×C47#12512yes—
161C23×C47#12612yes—
162C23×C47C4⋊Q811yescharacteristic
163C2×C4×C47—24no—
164C2×C4×C47—24no—
165C2×C4×C47—22no—
166C2×C4×C47—22no—
167C2×C4×C47—24no—
168C2×C4×C47—28no—
169C2×C4×C47—22no—
170C2×C4×C47—22no—
171C2×C4×C47—22no—
172C2×C4×C47—48no—
173C2×C4×C47—48no—
174C2×C4×C47—44no—
175C2×C4×C47—44no—
176C2×C4×C47—48no—
177C2×C4×C47—48no—
178C2×C4×C47—44no—
179C2×C4×C47—42no—
180C2×C4×C47—42no—
181C2×C4×C47—42no—
182C2×C4×C47—42no—
183C2×C4×C47—44no—
184C2×C4×C47—48no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—44no—
188C2×C4×C47—42no—
189C2×C4×C47—42no—
190C2×C4×C47—82no—
191C2×C4×C47—82no—
192C2×C4×C47—84no—
193C2×C4×C47—82no—
194C2×C4×C47—82no—
195C2×C4×C47#9914yes—
196#10912C4711yesmaximal, characteristic, direct product factor, Sylow
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—21no—
202C22×C47—22no—
203C22×C47—22no—
204C22×C47—21no—
205C22×C47—24no—
206C22×C47—22no—
207C22×C47—24no—
208C22×C47—22no—
209C22×C47—22no—
210C22×C47—22no—
211C22×C47—24no—
212C22×C47—24no—
213C22×C47—42no—
214C22×C47—42no—
215C22×C47—42no—
216C22×C47—42no—
217C22×C47—42no—
218C22×C47—42no—
219C22×C47—42no—
220C22×C47—42no—
221C22×C47C4×C22⋊C411yescharacteristic
222C22×C47C4×C4⋊C412yes—
223C22×C47#38512yes—
224C22×C47#38611yescharacteristic
225C22×C47#38712yes—
226C22×C47#38712yes—
227C22×C47#38812yes—
228C22×C47#38912yes—
229C22×C47#39111yescharacteristic
230C22×C47C2×#9912yes—
231C22×C47#41012yes—
232C4×C47—24no—
233C4×C47—48no—
234C4×C47—42no—
235C4×C47—44no—
236C4×C47—84no—
237C4×C47—81no—
238C4×C47—81no—
239C2×#385C2×C4711yescharacteristic
240C2×C4×C22⋊C4C2×C4711yescharacteristic
241C2×#342C2×C4712yes—
242C2×#342C2×C4712yes—
243C22⋊#95C2×C4711yescharacteristic
244C2×C47—22no—
245C2×C47—22no—
246C2×C47—22no—
247C2×C47—22no—
248C2×C47—22no—
249C2×C47—22no—
250C2×C47#143611yescharacteristic
251C2×C47C4×#9912yes—
252C2×C47#189811yescharacteristic
253C2×C47#189911yescharacteristic
254C2×C47#199612yes—
255C24×C4C22×C4711yescharacteristic
256C22×C4⋊C4C4×C4712yescomplemented
257C22×C22⋊C4C22×C4711yescharacteristic
258C22×C22⋊C4C22×C4712yes—
259C22×C22⋊C4C22×C4711yescharacteristic
260C22×C22⋊C4C22×C4712yes—
261C22×C42—21no—
262#385—21no—
263#385—22no—
264#385—21no—
265C4×C22⋊C4—24no—
266C2×#95—21no—
267C2×#95—22no—
268C2×#95C4×C4712yescomplemented
269#342—24no—
270#342C4×C4718yescomplemented
271C47#1091211yescharacteristic, direct product factor, Sylow
272C25C23×C4711yescharacteristic
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—44no—
278C23×C4C2×C4×C4712yes—
279C23×C4C2×C4×C4711yescharacteristic
280C23×C4C2×C4×C4711yescharacteristic
281C23×C4C2×C4×C4712yes—
282C23×C4D4×C4711yescharacteristic
283C23×C4D4×C4712yes—
284C23×C4D4×C4711yescharacteristic
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—44no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4C2×C4×C4714yes—
304C2×C22⋊C4C2×C4×C4714yes—
305C2×C22⋊C4C2×C4×C4714yes—
306C2×C22⋊C4D4×C4714yes—
307C2×C22⋊C4Q8×C4714yes—
308C2×C42—24no—
309C2×C42—44no—
310#95—24no—
311#95—22no—
312#95—22no—
313#95—44no—
314C24—42no—
315C24—42no—
316C24C22×C4×C4711yescharacteristic
317C24C22×C4×C4712yes—
318C24C2×D4×C4711yescharacteristic
319C24C2×D4×C4711yescharacteristic
320C24C2×D4×C4712yes—
321C24C2×Q8×C4712yes—
322C24#41×C4712yes—
323C24#41×C4712yes—
324C24#41×C4712yes—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—21no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—48no—
348C22×C4—48no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—44no—
354C22×C4—44no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4C42×C4714yescomplemented
360C22×C4C22⋊C4×C4712yes—
361C22×C4C22⋊C4×C4712yes—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—41no—
372C22⋊C4—42no—
373C22⋊C4—41no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4C4⋊C4×C4718yescomplemented
377C42—48no—
378C23—22no—
379C23—22no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—44no—
387C23—42no—
388C23—44no—
389C23—44no—
390C23—42no—
391C23—44no—
392C23C2×C42×C4711yescharacteristic
393C23C2×C22⋊C4×C4711yescharacteristic
394C23C2×C4⋊C4×C4712yes—
395C23#117×C4711yescharacteristic
396C23#117×C4712yes—
397C23C4×D4×C4712yes—
398C23C4×D4×C4712yes—
399C23C4×D4×C4712yes—
400C23C4×D4×C4712yes—
401C23C4×Q8×C4712yes—
402C23C4×Q8×C4712yes—
403C23#120×C4711yescharacteristic
404C23#121×C4712yes—
405C23C22⋊Q8×C4712yes—
406C23C22⋊Q8×C4712yes—
407C23#123×C4711yescharacteristic
408C23#123×C4712yes—
409C23#124×C4711yescharacteristic
410C23#125×C4712yes—
411C23#126×C4712yes—
412C23C4⋊Q8×C4711yescharacteristic
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—28no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—48no—
423C2×C4—48no—
424C2×C4—44no—
425C2×C4—48no—
426C2×C4—44no—
427C2×C4—48no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—48no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—84no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4#99×C4714yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—21no—
458C22—24no—
459C22—22no—
460C22—24no—
461C22—22no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C4×C22⋊C4×C4711yescharacteristic
471C22C4×C4⋊C4×C4712yes—
472C22C47×#38512yes—
473C22C47×#38611yescharacteristic
474C22C47×#38712yes—
475C22C47×#38712yes—
476C22C47×#38812yes—
477C22C47×#38912yes—
478C22C47×#39111yescharacteristic
479C22C2×#99×C4712yes—
480C22C47×#41012yes—
481C4—24no—
482C4—48no—
483C4—44no—
484C4—42no—
485C4—84no—
486C4—81no—
487C4—81no—
488C2—22no—
489C2—22no—
490C2—22no—
491C2—22no—
492C2—22no—
493C2—22no—
494C2C47×#143611yescharacteristic
495C2C4×#99×C4712yes—
496C2C47×#189811yescharacteristic
497C2C47×#189911yescharacteristic
498C2C47×#199612yes—
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC23C2×C42×C47
Frattini, cosocleC25C23×C47
prime radicalC25×C47C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
7. C22×C4⋊C4×C47C4semidirect
19. C2×#95×C47C4semidirect
21. C47×#342C4semidirect
109. C22×C4×C47C42semidirect
126. C22⋊C4×C47C4⋊C4semidirect
196. #10912C47direct (N × H)
256. C22×C4⋊C4C4×C47semidirect
268. C2×#95C4×C47semidirect
270. #342C4×C47semidirect
271. C47#10912direct (N × H)
359. C22×C4C42×C47semidirect
376. C22⋊C4C4⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3852
C2×C4×C22⋊C4×C472
C2×C47×#3422
C47×C22⋊#952
#1091247