Finite Group Databasebeta

← C47×#13809 #26053507

Subgroups — C47×#13809 #26053507

Order 12032.

2154 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊C4×C47C213yesmaximal
2C2×C47×#376C211yesmaximal, characteristic, complemented
3C22×#95×C47C211yesmaximal, characteristic
4C47×#1434C213yesmaximal, complemented
5C47×#1434C213yesmaximal, complemented
6C47×C22⋊#95C213yesmaximal
7C4×#95×C47C211yesmaximal, characteristic, complemented
8C24×C4×C47C2213yes—
9C22×C22⋊C4×C47C2213yes—
10C22×C22⋊C4×C47C2211yescharacteristic
11C22×C42×C47C2213yes—
12C22×C42×C47C2213yes—
13C4×C22⋊C4×C47C4124yescomplemented
14C47×#376—24no—
15C2×#95×C47—24no—
16C2×#95×C47C2213yes—
17C2×#95×C47C2213yes—
18C2×#95×C47C2213yes—
19C2×#95×C47C2216yes—
20C2×#95×C47C2213yes—
21C2×#95×C47C2213yes—
22C2×#95×C47C2211yescharacteristic
23C25×C47C2311yescharacteristic
24C23×C4×C47—212no—
25C23×C4×C47—26no—
26C23×C4×C47—26no—
27C23×C4×C47—46no—
28C23×C4×C47C2×C4112yes—
29C23×C4×C47C2313yes—
30C23×C4×C47C2313yes—
31C23×C4×C47C2313yes—
32C23×C4×C47C2311yescharacteristic
33C23×C4×C47C2311yescharacteristic
34C23×C4×C47C2313yes—
35C2×C22⋊C4×C47—26no—
36C2×C22⋊C4×C47—26no—
37C2×C22⋊C4×C47C2×C4112yes—
38C2×C22⋊C4×C47C2×C4112yes—
39C2×C42×C47—26no—
40C2×C42×C47—26no—
41C2×C42×C47—46no—
42C2×C42×C47C2×C4112yescomplemented
43C2×C42×C47C2×C4112yescomplemented
44#95×C47—26no—
45#95×C47—26no—
46#95×C47—26no—
47#95×C47—46no—
48#95×C47C2×C4112yescomplemented
49#95×C47C2×C4112yescomplemented
50#95×C47D414yes—
51C24×C47—21no—
52C24×C47—23no—
53C24×C47—23no—
54C24×C47—21no—
55C24×C47C22×C416yes—
56C24×C47#4112yes—
57C24×C47#4116yes—
58C24×C47C2411yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47—23no—
61C22×C4×C47—26no—
62C22×C4×C47—23no—
63C22×C4×C47—26no—
64C22×C4×C47—21no—
65C22×C4×C47—224no—
66C22×C4×C47—23no—
67C22×C4×C47—23no—
68C22×C4×C47—23no—
69C22×C4×C47—23no—
70C22×C4×C47—23no—
71C22×C4×C47—23no—
72C22×C4×C47—23no—
73C22×C4×C47—26no—
74C22×C4×C47—23no—
75C22×C4×C47—26no—
76C22×C4×C47—26no—
77C22×C4×C47—26no—
78C22×C4×C47—23no—
79C22×C4×C47—23no—
80C22×C4×C47—224no—
81C22×C4×C47—412no—
82C22×C4×C47—424no—
83C22×C4×C47—424no—
84C22×C4×C47C22×C416yes—
85C22×C4×C47C22×C416yes—
86C22×C4×C47C22×C416yes—
87C22×C4×C47C22×C416yes—
88C22×C4×C47C22×C416yes—
89C22×C4×C47C22×C416yes—
90C22×C4×C47C2×D416yes—
91C22×C4×C47#4116yes—
92C22⋊C4×C47—224no—
93C22⋊C4×C47C42116yes—
94C42×C47—224no—
95C42×C47—412no—
96C23×C47—26no—
97C23×C47—26no—
98C23×C47—26no—
99C23×C47—26no—
100C23×C47—26no—
101C23×C47—22no—
102C23×C47—212no—
103C23×C47—26no—
104C23×C47—26no—
105C23×C47C2×C4214yes—
106C23×C47#117112yes—
107C23×C47#117112yes—
108C23×C47C23×C413yes—
109C23×C47C22×D411yescharacteristic
110C23×C47C2×#4113yes—
111C23×C47C2×#4111yescharacteristic
112C23×C47C2×#4113yes—
113C23×C47H(5,𝔽2)13yes—
114C23×C472−1+411yescharacteristic
115C2×C4×C47—26no—
116C2×C4×C47—26no—
117C2×C4×C47—26no—
118C2×C4×C47—26no—
119C2×C4×C47—26no—
120C2×C4×C47—26no—
121C2×C4×C47—212no—
122C2×C4×C47—212no—
123C2×C4×C47—26no—
124C2×C4×C47—26no—
125C2×C4×C47—26no—
126C2×C4×C47—26no—
127C2×C4×C47—26no—
128C2×C4×C47—26no—
129C2×C4×C47—26no—
130C2×C4×C47—26no—
131C2×C4×C47—26no—
132C2×C4×C47—448no—
133C2×C4×C47—43no—
134C2×C4×C47—46no—
135C2×C4×C47—43no—
136C2×C4×C47—46no—
137C2×C4×C47—46no—
138C2×C4×C47—43no—
139C2×C4×C47—43no—
140C2×C4×C47—46no—
141C2×C4×C47C2×C4214yes—
142C2×C4×C47C2×C4214yes—
143C2×C4×C47C4×D4112yes—
144#13809C4711yesmaximal, characteristic, direct product factor, Sylow
145C22×C47—212no—
146C22×C47—212no—
147C22×C47—212no—
148C22×C47—212no—
149C22×C47—24no—
150C22×C47—24no—
151C22×C47#37618yescomplemented
152C22×C47C22×C4211yescharacteristic
153C22×C47C2×#11713yes—
154C22×C47C2×#11713yes—
155C22×C47C2×C4×D413yes—
156C22×C47C4×#4113yes—
157C22×C47#51813yes—
158C22×C47#52013yes—
159C22×C47#54613yes—
160C22×C47#54811yescharacteristic
161C22×C47#55116yes—
162C22×C47#55213yes—
163C22×C47#55313yes—
164C4×C47—212no—
165C4×C47—24no—
166C4×C47—24no—
167C4×C47—46no—
168C4×C47—46no—
169C4×C47—46no—
170C2×C4×C22⋊C4C2×C4713yes—
171C2×#376C2×C4711yescharacteristic, complemented
172C22×#95C2×C4711yescharacteristic
173#1434C2×C4713yescomplemented
174#1434C2×C4713yescomplemented
175C22⋊#95C2×C4713yes—
176C4×#95C2×C4711yescharacteristic, complemented
177C2×C47—28no—
178C2×C47C2×#37611yescharacteristic
179C2×C47C42×D411yescharacteristic
180C2×C47#227511yescharacteristic
181C2×C47#234213yes—
182C2×C47#234313yes—
183C2×C47#235213yes—
184C2×C47#235313yes—
185C24×C4C22×C4713yes—
186C22×C22⋊C4C22×C4713yes—
187C22×C22⋊C4C22×C4711yescharacteristic
188C22×C42C22×C4713yes—
189C22×C42C22×C4713yes—
190C4×C22⋊C4C4×C47124yescomplemented
191#376—24no—
192C2×#95—24no—
193C2×#95C22×C4713yes—
194C2×#95C22×C4713yes—
195C2×#95C22×C4713yes—
196C2×#95C22×C4716yes—
197C2×#95C22×C4713yes—
198C2×#95C22×C4713yes—
199C2×#95C22×C4711yescharacteristic
200C47#1380911yescharacteristic, direct product factor, Sylow
201C25C23×C4711yescharacteristic
202C23×C4—212no—
203C23×C4—26no—
204C23×C4—26no—
205C23×C4—46no—
206C23×C4C2×C4×C47112yes—
207C23×C4C23×C4713yes—
208C23×C4C23×C4713yes—
209C23×C4C23×C4713yes—
210C23×C4C23×C4711yescharacteristic
211C23×C4C23×C4711yescharacteristic
212C23×C4C23×C4713yes—
213C2×C22⋊C4—26no—
214C2×C22⋊C4—26no—
215C2×C22⋊C4C2×C4×C47112yes—
216C2×C22⋊C4C2×C4×C47112yes—
217C2×C42—26no—
218C2×C42—26no—
219C2×C42—46no—
220C2×C42C2×C4×C47112yescomplemented
221C2×C42C2×C4×C47112yescomplemented
222#95—26no—
223#95—26no—
224#95—26no—
225#95—46no—
226#95C2×C4×C47112yescomplemented
227#95C2×C4×C47112yescomplemented
228#95D4×C4714yes—
229C24—21no—
230C24—23no—
231C24—23no—
232C24—21no—
233C24C22×C4×C4716yes—
234C24#41×C4712yes—
235C24#41×C4716yes—
236C24C24×C4711yescharacteristic
237C22×C4—21no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—21no—
243C22×C4—224no—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—26no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—26no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—26no—
256C22×C4—26no—
257C22×C4—23no—
258C22×C4—224no—
259C22×C4—412no—
260C22×C4—424no—
261C22×C4—424no—
262C22×C4C22×C4×C4716yes—
263C22×C4C22×C4×C4716yes—
264C22×C4C22×C4×C4716yes—
265C22×C4C22×C4×C4716yes—
266C22×C4C22×C4×C4716yes—
267C22×C4C22×C4×C4716yes—
268C22×C4C2×D4×C4716yes—
269C22×C4#41×C4716yes—
270C22⋊C4—224no—
271C22⋊C4C42×C47116yes—
272C42—224no—
273C42—412no—
274C23—26no—
275C23—26no—
276C23—26no—
277C23—26no—
278C23—26no—
279C23—22no—
280C23—212no—
281C23—26no—
282C23—26no—
283C23C2×C42×C4714yes—
284C23#117×C47112yes—
285C23#117×C47112yes—
286C23C23×C4×C4713yes—
287C23C22×D4×C4711yescharacteristic
288C23C2×#41×C4713yes—
289C23C2×#41×C4711yescharacteristic
290C23C2×#41×C4713yes—
291C23H(5,𝔽2)×C4713yes—
292C232−1+4×C4711yescharacteristic
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—212no—
300C2×C4—212no—
301C2×C4—26no—
302C2×C4—26no—
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—448no—
311C2×C4—43no—
312C2×C4—46no—
313C2×C4—43no—
314C2×C4—46no—
315C2×C4—46no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—46no—
319C2×C4C2×C42×C4714yes—
320C2×C4C2×C42×C4714yes—
321C2×C4C4×D4×C47112yes—
322C22—24no—
323C22—24no—
324C22—212no—
325C22—212no—
326C22—212no—
327C22—212no—
328C22C47×#37618yescomplemented
329C22C22×C42×C4711yescharacteristic
330C22C2×#117×C4713yes—
331C22C2×#117×C4713yes—
332C22C2×C4×D4×C4713yes—
333C22C4×#41×C4713yes—
334C22C47×#51813yes—
335C22C47×#52013yes—
336C22C47×#54613yes—
337C22C47×#54811yescharacteristic
338C22C47×#55116yes—
339C22C47×#55213yes—
340C22C47×#55313yes—
341C4—24no—
342C4—24no—
343C4—212no—
344C4—46no—
345C4—46no—
346C4—46no—
347C2—28no—
348C2C2×C47×#37611yescharacteristic
349C2C42×D4×C4711yescharacteristic
350C2C47×#227511yescharacteristic
351C2C47×#234213yes—
352C2C47×#234313yes—
353C2C47×#235213yes—
354C2C47×#235313yes—
subgroupG/H
center, socleC24×C47C24
commutatorC22C22×C42×C47
Frattini, cosocleC24C24×C47
prime radicalC25×C47C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#376C2semidirect
4. C47×#1434C2semidirect
5. C47×#1434C2semidirect
7. C4×#95×C47C2semidirect
13. C4×C22⋊C4×C47C4semidirect
42. C2×C42×C47C2×C4semidirect
43. C2×C42×C47C2×C4semidirect
48. #95×C47C2×C4semidirect
49. #95×C47C2×C4semidirect
144. #13809C47direct (N × H)
151. C22×C47#376semidirect
171. C2×#376C2×C47semidirect
173. #1434C2×C47semidirect
174. #1434C2×C47semidirect
176. C4×#95C2×C47semidirect
190. C4×C22⋊C4C4×C47semidirect
200. C47#13809direct (N × H)
220. C2×C42C2×C4×C47semidirect
221. C2×C42C2×C4×C47semidirect
226. #95C2×C4×C47semidirect
227. #95C2×C4×C47semidirect
328. C22C47×#376semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C472
C2×C47×#3762
C22×#95×C472
C47×#14342
C47×C22⋊#952
C4×#95×C472
#1380947