Finite Group Databasebeta

← C47×#9497 #26049195

Subgroups — C47×#9497 #26049195

Order 12032.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2403C211yesmaximal, characteristic
2C47×#2309C211yesmaximal, characteristic, complemented
3C47×#1781C212yesmaximal, complemented
4C47×#1781C211yesmaximal, characteristic, complemented
5C47×#1304C212yesmaximal, complemented
6C23×D4×C47C2211yescharacteristic
7C23×D4×C47C2211yescharacteristic
8C2×#120×C47—21no—
9C2×#120×C47C412yescomplemented
10C2×#117×C47—21no—
11C2×#99×C47—22no—
12C2×#99×C47—24no—
13C47×#392—22no—
14C47×#390—24no—
15C47×#386—21no—
16C47×#386C412yescomplemented
17C47×#379—21no—
18C47×#379C2212yes—
19C47×#379C2211yescharacteristic
20C47×#379C2212yes—
21C25×C47C2×C411yescharacteristic
22C25×C47D411yescharacteristic
23C25×C47C2311yescharacteristic
24C22×D4×C47—21no—
25C22×D4×C47—22no—
26C22×D4×C47—22no—
27C22×D4×C47—22no—
28C22×D4×C47—21no—
29C22×D4×C47—22no—
30C22×D4×C47—22no—
31C22×D4×C47—44no—
32C22×D4×C47—44no—
33C22×D4×C47C2×C412yes—
34C22×D4×C47D412yes—
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47D411yescharacteristic
37#120×C47—44no—
38#120×C47—44no—
39#117×C47—44no—
40C2×C4⋊C4×C47—22no—
41C2×C22⋊C4×C47—22no—
42C2×C22⋊C4×C47—22no—
43C2×C22⋊C4×C47—21no—
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—22no—
50C2×C22⋊C4×C47—21no—
51C2×C22⋊C4×C47—22no—
52C2×C22⋊C4×C47C2×C412yes—
53C2×C22⋊C4×C47D414yescomplemented
54C2×C42×C47—22no—
55#99×C47—48no—
56#99×C47—44no—
57#95×C47—22no—
58C24×C47—21no—
59C24×C47—21no—
60C24×C47—22no—
61C24×C47—21no—
62C24×C47—42no—
63C24×C47—42no—
64C24×C47—42no—
65C24×C47—42no—
66C24×C47—42no—
67C24×C47—42no—
68C24×C47—81no—
69C24×C47—81no—
70C24×C47—81no—
71C24×C47C22⋊C412yes—
72C24×C47C22×C411yescharacteristic
73C24×C47C2×D411yescharacteristic
74C24×C47C2×D411yescharacteristic
75C24×C47C2×D412yes—
76C24×C47#4112yes—
77C2×D4×C47—24no—
78C2×D4×C47—28no—
79C2×D4×C47—24no—
80C2×D4×C47—24no—
81C2×D4×C47—24no—
82C2×D4×C47—24no—
83C2×D4×C47—42no—
84C2×D4×C47—42no—
85C2×D4×C47—44no—
86C2×D4×C47—44no—
87C2×D4×C47—48no—
88C2×D4×C47—42no—
89C2×D4×C47—44no—
90C2×D4×C47—42no—
91C2×D4×C47—44no—
92C2×D4×C47—42no—
93C2×D4×C47—44no—
94C2×D4×C47—41no—
95C2×D4×C47—42no—
96C2×D4×C47—41no—
97C2×D4×C47—44no—
98C2×D4×C47—44no—
99C2×D4×C47—82no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—24no—
103C22×C4×C47—21no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—24no—
107C22×C4×C47—42no—
108C22×C4×C47—42no—
109C22×C4×C47C22⋊C412yes—
110C4⋊C4×C47—44no—
111C22⋊C4×C47—44no—
112C22⋊C4×C47—44no—
113C22⋊C4×C47—42no—
114C22⋊C4×C47—44no—
115C22⋊C4×C47—42no—
116C22⋊C4×C47—44no—
117C22⋊C4×C47—44no—
118C22⋊C4×C47—44no—
119C22⋊C4×C47—82no—
120C22⋊C4×C47—82no—
121C22⋊C4×C47—81no—
122C22⋊C4×C47—82no—
123C22⋊C4×C47—82no—
124C42×C47—44no—
125C23×C47—22no—
126C23×C47—22no—
127C23×C47—22no—
128C23×C47—22no—
129C23×C47—24no—
130C23×C47—22no—
131C23×C47—24no—
132C23×C47—22no—
133C23×C47—22no—
134C23×C47—22no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47—41no—
138C23×C47—42no—
139C23×C47—41no—
140C23×C47—42no—
141C23×C47—41no—
142C23×C47—42no—
143C23×C47—42no—
144C23×C47—42no—
145C23×C47—42no—
146C23×C47—42no—
147C23×C47—42no—
148C23×C47—41no—
149C23×C47—42no—
150C23×C47—42no—
151C23×C47—42no—
152C23×C47—42no—
153C23×C47—41no—
154C23×C47—42no—
155C23×C47—42no—
156C23×C47—81no—
157C23×C47—81no—
158C23×C47—82no—
159C23×C47—82no—
160C23×C47—88no—
161C23×C47—88no—
162C23×C47—88no—
163C23×C47C2×C22⋊C411yescharacteristic
164C23×C47C4×D412yes—
165C23×C47#12011yescharacteristic
166C23×C47#12112yes—
167C23×C47#12311yescharacteristic
168D4×C47—48no—
169D4×C47—48no—
170D4×C47—48no—
171D4×C47—44no—
172D4×C47—44no—
173D4×C47—88no—
174C2×C4×C47—22no—
175C2×C4×C47—22no—
176C2×C4×C47—24no—
177C2×C4×C47—22no—
178C2×C4×C47—22no—
179C2×C4×C47—22no—
180C2×C4×C47—24no—
181C2×C4×C47—41no—
182C2×C4×C47—42no—
183C2×C4×C47—41no—
184C2×C4×C47—44no—
185C2×C4×C47—42no—
186C2×C4×C47—44no—
187C2×C4×C47—42no—
188C2×C4×C47—42no—
189C2×C4×C47—44no—
190C2×C4×C47—82no—
191C2×C4×C47—82no—
192C2×C4×C47—82no—
193C2×C4×C47#9914yescomplemented
194#9497C4711yesmaximal, characteristic, direct product factor, Sylow
195C22×C47—21no—
196C22×C47—21no—
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—21no—
202C22×C47—21no—
203C22×C47—22no—
204C22×C47—22no—
205C22×C47—22no—
206C22×C47—22no—
207C22×C47—21no—
208C22×C47—44no—
209C22×C47—44no—
210C22×C47—44no—
211C22×C47—44no—
212C22×C47—42no—
213C22×C47—42no—
214C22×C47—42no—
215C22×C47—42no—
216C22×C47—84no—
217C22×C47—82no—
218C22×C47—82no—
219C22×C47—84no—
220C22×C47—82no—
221C22×C47—84no—
222C22×C47—84no—
223C22×C47—84no—
224C22×C47—84no—
225C22×C47—81no—
226C22×C47—81no—
227C22×C47#38611yescharacteristic
228C22×C47C2×#9912yes—
229C22×C47B(4,𝔽2)12yes—
230C4×C47—24no—
231C4×C47—42no—
232C4×C47—84no—
233C4×C47—82no—
234C4×C47—162no—
235#2403C2×C4711yescharacteristic
236#2309C2×C4711yescharacteristic, complemented
237#1781C2×C4712yescomplemented
238#1781C2×C4711yescharacteristic, complemented
239#1304C2×C4712yescomplemented
240C2×C47—22no—
241C2×C47—22no—
242C2×C47—42no—
243C2×C47—42no—
244C2×C47—41no—
245C2×C47—82no—
246C2×C47—82no—
247C2×C47#188911yescharacteristic
248C2×C47#189811yescharacteristic
249C2×C47#191311yescharacteristic
250C23×D4C22×C4711yescharacteristic
251C23×D4C22×C4711yescharacteristic
252C2×#120—21no—
253C2×#120C4×C4712yescomplemented
254C2×#117—21no—
255C2×#99—22no—
256C2×#99—24no—
257#392—22no—
258#390—24no—
259#386—21no—
260#386C4×C4712yescomplemented
261#379—21no—
262#379C22×C4712yes—
263#379C22×C4711yescharacteristic
264#379C22×C4712yes—
265C47#949711yescharacteristic, direct product factor, Sylow
266C25C2×C4×C4711yescharacteristic
267C25D4×C4711yescharacteristic
268C25C23×C4711yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C4712yes—
279C22×D4D4×C4712yes—
280C23×C4C2×C4×C4711yescharacteristic
281C23×C4D4×C4711yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C4712yes—
298C2×C22⋊C4D4×C4714yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C4712yes—
317C24C22×C4×C4711yescharacteristic
318C24C2×D4×C4711yescharacteristic
319C24C2×D4×C4711yescharacteristic
320C24C2×D4×C4712yes—
321C24#41×C4712yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C4712yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—24no—
374C23—22no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—41no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C4711yescharacteristic
409C23C4×D4×C4712yes—
410C23#120×C4711yescharacteristic
411C23#121×C4712yes—
412C23#123×C4711yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C4714yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22C47×#38611yescharacteristic
472C22C2×#99×C4712yes—
473C22C47×B(4,𝔽2)12yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C47×#188911yescharacteristic
487C2C47×#189811yescharacteristic
488C2C47×#191311yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC24C22×C4×C47
Frattini, cosocleC25C23×C47
prime radicalC47×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2309C2semidirect
3. C47×#1781C2semidirect
4. C47×#1781C2semidirect
5. C47×#1304C2semidirect
9. C2×#120×C47C4semidirect
16. C47×#386C4semidirect
53. C2×C22⋊C4×C47D4semidirect
193. C2×C4×C47#99semidirect
194. #9497C47direct (N × H)
236. #2309C2×C47semidirect
237. #1781C2×C47semidirect
238. #1781C2×C47semidirect
239. #1304C2×C47semidirect
253. C2×#120C4×C47semidirect
260. #386C4×C47semidirect
265. C47#9497direct (N × H)
298. C2×C22⋊C4D4×C47semidirect
438. C2×C4#99×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#24032
C47×#23092
C47×#17812
C47×#13042
#949747