Finite Group Databasebeta

← C47×#8698 #26048396

Subgroups — C47×#8698 #26048396

Order 12032.

1158 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#95×C47C211yesmaximal, characteristic
2C47×#1779C212yesmaximal
3C47×#1280C214yesmaximal, complemented
4C24×C4×C47C411yescharacteristic
5C24×C4×C47C411yescharacteristic
6C24×C4×C47C2211yescharacteristic
7C2×C22⋊C8×C47—22no—
8C2×C22⋊C8×C47—22no—
9C2×C22⋊C8×C47C2214yes—
10C2×#95×C47—22no—
11C2×#95×C47—22no—
12C2×#95×C47C412yes—
13C2×#95×C47C2212yes—
14C25×C47C2×C411yescharacteristic
15C23×C4×C47—21no—
16C23×C4×C47—21no—
17C23×C4×C47—21no—
18C23×C4×C47—21no—
19C23×C4×C47—22no—
20C23×C4×C47—24no—
21C23×C4×C47—24no—
22C23×C4×C47—42no—
23C23×C4×C47—42no—
24C23×C4×C47—42no—
25C23×C4×C47—42no—
26C23×C4×C47—42no—
27C23×C4×C47—42no—
28C23×C4×C47C814yescomplemented
29C23×C4×C47C2×C411yescharacteristic
30C23×C4×C47C2×C412yes—
31C23×C4×C47C2×C412yes—
32C23×C4×C47D412yes—
33C23×C4×C47D412yes—
34C23×C4×C47C2311yescharacteristic
35C22×C8×C47—24no—
36C22⋊C8×C47—28no—
37C22⋊C8×C47—44no—
38C22⋊C8×C47—44no—
39#95×C47—24no—
40#95×C47—24no—
41C24×C47—22no—
42C24×C47—22no—
43C24×C47—22no—
44C24×C47—22no—
45C24×C47—22no—
46C24×C47—22no—
47C24×C47C22⋊C411yescharacteristic
48C24×C47C22⋊C411yescharacteristic
49C24×C47C2×C812yes—
50C24×C47M1612yes—
51C24×C47C22×C411yescharacteristic
52C22×C4×C47—24no—
53C22×C4×C47—24no—
54C22×C4×C47—24no—
55C22×C4×C47—24no—
56C22×C4×C47—24no—
57C22×C4×C47—24no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47—24no—
64C22×C4×C47—24no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47—42no—
68C22×C4×C47—42no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47—416no—
72C22×C4×C47—416no—
73C22×C4×C47—48no—
74C22×C4×C47—42no—
75C22×C4×C47—42no—
76C22×C4×C47—42no—
77C22×C4×C47—42no—
78C22×C4×C47—42no—
79C22×C4×C47—42no—
80C22×C4×C47—42no—
81C22×C4×C47—42no—
82C22×C4×C47—48no—
83C22×C4×C47—42no—
84C22×C4×C47—42no—
85C22×C4×C47—42no—
86C22×C4×C47—42no—
87C22×C4×C47C22⋊C412yes—
88C22×C4×C47C2×C814yes—
89C22×C4×C47M1614yes—
90C22×C4×C47C2×D412yes—
91C22×C4×C47#4114yes—
92C2×C8×C47—44no—
93C2×C8×C47—44no—
94C2×C8×C47—44no—
95C23×C47—28no—
96C23×C47—28no—
97C23×C47—28no—
98C23×C47—28no—
99C23×C47—24no—
100C23×C47—24no—
101C23×C47—24no—
102C23×C47—24no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—24no—
116C23×C47—24no—
117C23×C47C22⋊C812yes—
118C23×C47C22⋊C812yes—
119C23×C47#9912yes—
120C23×C47#9912yes—
121C23×C47#10012yes—
122C23×C47#10112yes—
123C23×C47C2×C22⋊C411yescharacteristic
124C23×C47#11712yes—
125C23×C47C22×C811yescharacteristic
126C23×C47C2×M1611yescharacteristic
127C23×C47C2×M1612yes—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—24no—
132C2×C4×C47—24no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47—44no—
136C2×C4×C47—48no—
137C2×C4×C47—48no—
138C2×C4×C47—44no—
139C2×C4×C47—48no—
140C2×C4×C47—44no—
141C2×C4×C47—48no—
142C2×C4×C47—48no—
143C2×C4×C47—44no—
144C2×C4×C47—48no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—42no—
148C2×C4×C47—42no—
149C2×C4×C47—44no—
150C2×C4×C47—44no—
151C2×C4×C47#12314yes—
152C8×C47—84no—
153#8698C4711yesmaximal, characteristic, direct product factor, Sylow
154C22×C47—216no—
155C22×C47—216no—
156C22×C47—22no—
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—22no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47#32314yes—
177C22×C47#32414yes—
178C22×C47#38111yescharacteristic
179C22×C47C2×C22⋊C811yescharacteristic
180C22×C47#40711yescharacteristic
181C22×C47C2×#9911yescharacteristic
182C22×C47C2×#9911yescharacteristic
183C22×C47C2×#10011yescharacteristic
184C22×C47C2×#10111yescharacteristic
185C22×C47#43112yes—
186C22×C47#43212yes—
187C4×C47—24no—
188C4×C47—42no—
189C4×C47—44no—
190C4×C47—44no—
191C22×#95C2×C4711yescharacteristic
192#1779C2×C4712yes—
193#1280C2×C4714yescomplemented
194C2×C47—24no—
195C2×C47—24no—
196C2×C47—22no—
197C2×C47—22no—
198C2×C47C2×#32311yescharacteristic
199C2×C47C2×#32411yescharacteristic
200C2×C47#146211yescharacteristic
201C2×C47#146311yescharacteristic
202C2×C47#181711yescharacteristic
203C2×C47#181911yescharacteristic
204C2×C47#182111yescharacteristic
205C24×C4C4×C4711yescharacteristic
206C24×C4C4×C4711yescharacteristic
207C24×C4C22×C4711yescharacteristic
208C2×C22⋊C8—22no—
209C2×C22⋊C8—22no—
210C2×C22⋊C8C22×C4714yes—
211C2×#95—22no—
212C2×#95—22no—
213C2×#95C4×C4712yes—
214C2×#95C22×C4712yes—
215C47#869811yescharacteristic, direct product factor, Sylow
216C25C2×C4×C4711yescharacteristic
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4C8×C4714yescomplemented
231C23×C4C2×C4×C4711yescharacteristic
232C23×C4C2×C4×C4712yes—
233C23×C4C2×C4×C4712yes—
234C23×C4D4×C4712yes—
235C23×C4D4×C4712yes—
236C23×C4C23×C4711yescharacteristic
237C22×C8—24no—
238C22⋊C8—28no—
239C22⋊C8—44no—
240C22⋊C8—44no—
241#95—24no—
242#95—24no—
243C24—22no—
244C24—22no—
245C24—22no—
246C24—22no—
247C24—22no—
248C24—22no—
249C24C22⋊C4×C4711yescharacteristic
250C24C22⋊C4×C4711yescharacteristic
251C24C2×C8×C4712yes—
252C24M16×C4712yes—
253C24C22×C4×C4711yescharacteristic
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—416no—
274C22×C4—416no—
275C22×C4—48no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—48no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C22⋊C4×C4712yes—
290C22×C4C2×C8×C4714yes—
291C22×C4M16×C4714yes—
292C22×C4C2×D4×C4712yes—
293C22×C4#41×C4714yes—
294C2×C8—44no—
295C2×C8—44no—
296C2×C8—44no—
297C23—28no—
298C23—28no—
299C23—28no—
300C23—28no—
301C23—24no—
302C23—24no—
303C23—24no—
304C23—24no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—24no—
318C23—24no—
319C23C22⋊C8×C4712yes—
320C23C22⋊C8×C4712yes—
321C23#99×C4712yes—
322C23#99×C4712yes—
323C23#100×C4712yes—
324C23#101×C4712yes—
325C23C2×C22⋊C4×C4711yescharacteristic
326C23#117×C4712yes—
327C23C22×C8×C4711yescharacteristic
328C23C2×M16×C4711yescharacteristic
329C23C2×M16×C4712yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—48no—
339C2×C4—48no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—48no—
343C2×C4—44no—
344C2×C4—48no—
345C2×C4—48no—
346C2×C4—48no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4#123×C4714yes—
354C8—84no—
355C22—216no—
356C22—216no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—21no—
369C22—21no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22C47×#32314yes—
378C22C47×#32414yes—
379C22C47×#38111yescharacteristic
380C22C2×C22⋊C8×C4711yescharacteristic
381C22C47×#40711yescharacteristic
382C22C2×#99×C4711yescharacteristic
383C22C2×#99×C4711yescharacteristic
384C22C2×#100×C4711yescharacteristic
385C22C2×#101×C4711yescharacteristic
386C22C47×#43112yes—
387C22C47×#43212yes—
388C4—24no—
389C4—42no—
390C4—44no—
391C4—44no—
392C2—24no—
393C2—24no—
394C2—22no—
395C2—22no—
396C2C2×C47×#32311yescharacteristic
397C2C2×C47×#32411yescharacteristic
398C2C47×#146211yescharacteristic
399C2C47×#146311yescharacteristic
400C2C47×#181711yescharacteristic
401C2C47×#181911yescharacteristic
402C2C47×#182111yescharacteristic
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC23C22×C8×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC25×C47C2×C4
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
3. C47×#1280C2semidirect
28. C23×C4×C47C8semidirect
153. #8698C47direct (N × H)
193. #1280C2×C47semidirect
215. C47#8698direct (N × H)
230. C23×C4C8×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#95×C472
C47×#17792
C47×#12802
#869847