Finite Group Databasebeta

← C4×C47×#324 #26047849

Subgroups — C4×C47×#324 #26047849

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
2C4×C22⋊C8×C47C212yesmaximal
3C2×C47×#324C212yesmaximal
4C47×#1280C212yesmaximal
5C22×C4⋊C4×C47C411yescharacteristic
6C22×C4⋊C4×C47C2211yescharacteristic
7C22×C42×C47C411yescharacteristic
8C22×C42×C47C411yescharacteristic
9C22×C42×C47C2211yescharacteristic
10C2×C22⋊C8×C47C2214yes—
11C2×C4×C8×C47—22no—
12C4×C4⋊C4×C47—22no—
13C4×C4⋊C4×C47—22no—
14C2×#95×C47C411yescharacteristic
15C2×#95×C47C2211yescharacteristic
16C47×#336—22no—
17C47×#324C418yesdirect product factor
18C23×C4×C47C2×C411yescharacteristic
19C23×C4×C47C2×C411yescharacteristic
20C23×C4×C47C2×C411yescharacteristic
21C23×C4×C47C2×C411yescharacteristic
22C23×C4×C47C2×C411yescharacteristic
23C23×C4×C47C2×C411yescharacteristic
24C23×C4×C47C2311yescharacteristic
25C22×C8×C47—24no—
26C2×C4⋊C4×C47—22no—
27C2×C4⋊C4×C47—22no—
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—22no—
30C2×C4⋊C4×C47C814yescomplemented
31C2×C4⋊C4×C47C2×C414yes—
32C2×C42×C47—21no—
33C2×C42×C47—21no—
34C2×C42×C47—22no—
35C2×C42×C47—21no—
36C2×C42×C47—21no—
37C2×C42×C47—42no—
38C2×C42×C47—42no—
39C2×C42×C47C814yescomplemented
40C2×C42×C47D412yes—
41C2×C42×C47D412yes—
42C22⋊C8×C47—24no—
43C22⋊C8×C47C2×C418yes—
44C4×C8×C47—44no—
45#95×C47—22no—
46#95×C47—22no—
47C24×C47C22×C411yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47—21no—
51C22×C4×C47—21no—
52C22×C4×C47—22no—
53C22×C4×C47—22no—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47C4212yes—
71C22×C4×C47C4212yes—
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22⋊C412yes—
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C2×C812yes—
76C22×C4×C47C2×C812yes—
77C22×C4×C47C2×C812yes—
78C22×C4×C47C2×C812yes—
79C22×C4×C47C2×C812yes—
80C22×C4×C47C2×C812yes—
81C22×C4×C47M1612yes—
82C22×C4×C47M1612yes—
83C22×C4×C47C22×C412yes—
84C22×C4×C47C2×D412yes—
85C22×C4×C47#4112yes—
86C2×C8×C47—28no—
87C2×C8×C47—44no—
88C2×C8×C47—44no—
89C4⋊C4×C47—28no—
90C4⋊C4×C47—28no—
91C42×C47—24no—
92C42×C47—24no—
93C42×C47—24no—
94C42×C47—42no—
95C42×C47—42no—
96C42×C47—42no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47C2×C4211yescharacteristic
102C23×C47C2×C22⋊C411yescharacteristic
103C23×C47#11711yescharacteristic
104C23×C47C22×C811yescharacteristic
105C23×C47C22×C811yescharacteristic
106C23×C47C2×M1611yescharacteristic
107C23×C47C2×M1611yescharacteristic
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—22no—
116C2×C4×C47—21no—
117C2×C4×C47—22no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—24no—
121C2×C4×C47—24no—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—42no—
139C2×C4×C47—42no—
140C2×C4×C47—42no—
141C2×C4×C47C4×C814yescomplemented
142C2×C4×C47C22⋊C812yes—
143C2×C4×C47C22⋊C814yes—
144C2×C4×C47C22⋊C812yes—
145C2×C4×C47#9912yes—
146C2×C4×C47#10112yes—
147C2×C4×C47C4×D414yes—
148C8×C47—48no—
149C4×#324C4711yesmaximal, characteristic, direct product factor, Sylow
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47C4×C22⋊C411yescharacteristic
163C22×C47C2×C4×C811yescharacteristic
164C22×C47C4×M1611yescharacteristic
165C22×C47C2×C22⋊C811yescharacteristic
166C22×C47C2×C22⋊C811yescharacteristic
167C22×C47C2×#9911yescharacteristic
168C22×C47#41011yescharacteristic
169C22×C47C2×#10111yescharacteristic
170C22×C47#41311yescharacteristic
171C22×C47#43111yescharacteristic
172C22×C47#43111yescharacteristic
173C4×C47—22no—
174C4×C47—24no—
175C4×C47—24no—
176C4×C47—24no—
177C4×C47—42no—
178C4×C47—42no—
179C4×C47—42no—
180C4×C47#32414yesdirect product factor
181C2×C4×C4⋊C4C2×C4711yescharacteristic
182C4×C22⋊C8C2×C4712yes—
183C2×#324C2×C4712yes—
184#1280C2×C4712yes—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—21no—
189C2×C47C2×#32411yescharacteristic
190C2×C47#145811yescharacteristic
191C2×C47#145911yescharacteristic
192C2×C47#146111yescharacteristic
193C2×C47C4×C22⋊C811yescharacteristic
194C2×C47C4×#9911yescharacteristic
195C2×C47C4×#10111yescharacteristic
196C22×C4⋊C4C4×C4711yescharacteristic
197C22×C4⋊C4C22×C4711yescharacteristic
198C22×C42C4×C4711yescharacteristic
199C22×C42C4×C4711yescharacteristic
200C22×C42C22×C4711yescharacteristic
201C2×C22⋊C8C22×C4714yes—
202C2×C4×C8—22no—
203C4×C4⋊C4—22no—
204C4×C4⋊C4—22no—
205C2×#95C4×C4711yescharacteristic
206C2×#95C22×C4711yescharacteristic
207#336—22no—
208#324C4×C4718yesdirect product factor
209C47C4×#32411yescharacteristic, direct product factor, Sylow
210C23×C4C2×C4×C4711yescharacteristic
211C23×C4C2×C4×C4711yescharacteristic
212C23×C4C2×C4×C4711yescharacteristic
213C23×C4C2×C4×C4711yescharacteristic
214C23×C4C2×C4×C4711yescharacteristic
215C23×C4C2×C4×C4711yescharacteristic
216C23×C4C23×C4711yescharacteristic
217C22×C8—24no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4C8×C4714yescomplemented
223C2×C4⋊C4C2×C4×C4714yes—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—22no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—42no—
230C2×C42—42no—
231C2×C42C8×C4714yescomplemented
232C2×C42D4×C4712yes—
233C2×C42D4×C4712yes—
234C22⋊C8—24no—
235C22⋊C8C2×C4×C4718yes—
236C4×C8—44no—
237#95—22no—
238#95—22no—
239C24C22×C4×C4711yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C42×C4712yes—
263C22×C4C42×C4712yes—
264C22×C4C22⋊C4×C4712yes—
265C22×C4C22⋊C4×C4711yescharacteristic
266C22×C4C22⋊C4×C4711yescharacteristic
267C22×C4C2×C8×C4712yes—
268C22×C4C2×C8×C4712yes—
269C22×C4C2×C8×C4712yes—
270C22×C4C2×C8×C4712yes—
271C22×C4C2×C8×C4712yes—
272C22×C4C2×C8×C4712yes—
273C22×C4M16×C4712yes—
274C22×C4M16×C4712yes—
275C22×C4C22×C4×C4712yes—
276C22×C4C2×D4×C4712yes—
277C22×C4#41×C4712yes—
278C2×C8—28no—
279C2×C8—44no—
280C2×C8—44no—
281C4⋊C4—28no—
282C4⋊C4—28no—
283C42—24no—
284C42—24no—
285C42—24no—
286C42—42no—
287C42—42no—
288C42—42no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23C2×C42×C4711yescharacteristic
294C23C2×C22⋊C4×C4711yescharacteristic
295C23#117×C4711yescharacteristic
296C23C22×C8×C4711yescharacteristic
297C23C22×C8×C4711yescharacteristic
298C23C2×M16×C4711yescharacteristic
299C23C2×M16×C4711yescharacteristic
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4C4×C8×C4714yescomplemented
334C2×C4C22⋊C8×C4712yes—
335C2×C4C22⋊C8×C4714yes—
336C2×C4C22⋊C8×C4712yes—
337C2×C4#99×C4712yes—
338C2×C4#101×C4712yes—
339C2×C4C4×D4×C4714yes—
340C8—48no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22C4×C22⋊C4×C4711yescharacteristic
354C22C2×C4×C8×C4711yescharacteristic
355C22C4×M16×C4711yescharacteristic
356C22C2×C22⋊C8×C4711yescharacteristic
357C22C2×C22⋊C8×C4711yescharacteristic
358C22C2×#99×C4711yescharacteristic
359C22C47×#41011yescharacteristic
360C22C2×#101×C4711yescharacteristic
361C22C47×#41311yescharacteristic
362C22C47×#43111yescharacteristic
363C22C47×#43111yescharacteristic
364C4—24no—
365C4—22no—
366C4—24no—
367C4—24no—
368C4—42no—
369C4—42no—
370C4—42no—
371C4C47×#32414yesdirect product factor
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2C2×C47×#32411yescharacteristic
377C2C47×#145811yescharacteristic
378C2C47×#145911yescharacteristic
379C2C47×#146111yescharacteristic
380C2C4×C22⋊C8×C4711yescharacteristic
381C2C4×#99×C4711yescharacteristic
382C2C4×#101×C4711yescharacteristic
subgroupG/H
centerC22×C4×C47C22⋊C4
commutatorC22C2×C4×C8×C47
Frattini, cosocleC23×C4C23×C47
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
17. C47×#324C4direct (N × H)
30. C2×C4⋊C4×C47C8semidirect
39. C2×C42×C47C8semidirect
141. C2×C4×C47C4×C8semidirect
149. C4×#324C47direct (N × H)
180. C4×C47#324direct (N × H)
208. #324C4×C47direct (N × H)
209. C47C4×#324direct (N × H)
222. C2×C4⋊C4C8×C47semidirect
231. C2×C42C8×C47semidirect
333. C2×C4C4×C8×C47semidirect
371. C4C47×#324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊C4×C472
C4×C22⋊C8×C472
C2×C47×#3242
C47×#12802
C4×#32447