Finite Group Databasebeta

← C47×#14322 #26054020

Subgroups — C47×#14322 #26054020

Order 12032.

1590 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#399C211yesmaximal, characteristic
2C2×C47×#389C213yesmaximal, complemented
3C2×C47×#388C213yesmaximal
4C47×#1445C213yesmaximal, complemented
5C47×#1444C211yesmaximal, characteristic, complemented
6C47×#1439C213yesmaximal
7C4×#95×C47C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C47C2213yes—
9C22×C4⋊C4×C47C2213yes—
10C22×C4⋊C4×C47C2213yes—
11C22×C22⋊C4×C47C2211yescharacteristic
12C22×C22⋊C4×C47C2213yes—
13C22×C22⋊C4×C47C2213yes—
14C22×C42×C47C2213yes—
15C47×#399C418yescomplemented
16C47×#389—212no—
17C47×#388—212no—
18C2×#95×C47C2213yes—
19C2×#95×C47C2213yes—
20C2×#95×C47C2216yes—
21C2×#95×C47C2213yes—
22C2×#95×C47C2211yescharacteristic
23C25×C47C2311yescharacteristic
24C23×C4×C47C2313yes—
25C23×C4×C47C2311yescharacteristic
26C23×C4×C47C2313yes—
27C23×C4×C47C2313yes—
28C23×C4×C47C2313yes—
29C23×C4×C47C2311yescharacteristic
30C2×C4⋊C4×C47—26no—
31C2×C4⋊C4×C47—26no—
32C2×C4⋊C4×C47—26no—
33C2×C4⋊C4×C47—26no—
34C2×C4⋊C4×C47—212no—
35C2×C4⋊C4×C47—46no—
36C2×C4⋊C4×C47C2×C4112yes—
37C2×C22⋊C4×C47—26no—
38C2×C22⋊C4×C47—26no—
39C2×C22⋊C4×C47—26no—
40C2×C22⋊C4×C47—26no—
41C2×C22⋊C4×C47—46no—
42C2×C22⋊C4×C47C2×C4112yes—
43C2×C42×C47—46no—
44C2×C42×C47D4112yes—
45#95×C47—26no—
46#95×C47—26no—
47#95×C47—212no—
48#95×C47—26no—
49#95×C47C2×C414yes—
50C24×C47—23no—
51C24×C47—23no—
52C24×C47—23no—
53C24×C47—21no—
54C24×C47—21no—
55C24×C47—23no—
56C24×C47C22×C412yes—
57C24×C47C2411yescharacteristic
58C22×C4×C47—23no—
59C22×C4×C47—26no—
60C22×C4×C47—26no—
61C22×C4×C47—21no—
62C22×C4×C47—23no—
63C22×C4×C47—26no—
64C22×C4×C47—23no—
65C22×C4×C47—26no—
66C22×C4×C47—26no—
67C22×C4×C47—26no—
68C22×C4×C47—23no—
69C22×C4×C47—23no—
70C22×C4×C47—23no—
71C22×C4×C47—23no—
72C22×C4×C47—26no—
73C22×C4×C47—26no—
74C22×C4×C47—23no—
75C22×C4×C47—21no—
76C22×C4×C47—23no—
77C22×C4×C47—23no—
78C22×C4×C47C22×C416yes—
79C22×C4×C47C22×C416yes—
80C22×C4×C47C2×D416yes—
81C22×C4×C47C2×D416yes—
82C22×C4×C47C2×D416yes—
83C22×C4×C47#4116yes—
84C4⋊C4×C47—224no—
85C4⋊C4×C47—412no—
86C4⋊C4×C47—412no—
87C22⋊C4×C47—224no—
88C22⋊C4×C47—412no—
89C22⋊C4×C47—44no—
90C42×C47—412no—
91C23×C47—26no—
92C23×C47—22no—
93C23×C47—26no—
94C23×C47—41no—
95C23×C47—43no—
96C23×C47—43no—
97C23×C47—43no—
98C23×C47—43no—
99C23×C47—43no—
100C23×C47—46no—
101C23×C47—43no—
102C23×C47—43no—
103C23×C47C23×C411yescharacteristic
104C23×C47C22×D413yes—
105C23×C47C2×#4113yes—
106C23×C47H(5,𝔽2)13yes—
107C23×C472−1+411yescharacteristic
108C23×C472−1+411yescharacteristic
109C23×C472−1+413yes—
110C2×C4×C47—212no—
111C2×C4×C47—26no—
112C2×C4×C47—26no—
113C2×C4×C47—26no—
114C2×C4×C47—26no—
115C2×C4×C47—212no—
116C2×C4×C47—26no—
117C2×C4×C47—212no—
118C2×C4×C47—26no—
119C2×C4×C47—26no—
120C2×C4×C47—26no—
121C2×C4×C47—43no—
122C2×C4×C47—43no—
123C2×C4×C47—46no—
124C2×C4×C47—46no—
125C2×C4×C47—46no—
126C2×C4×C47—41no—
127C2×C4×C47—43no—
128C2×C4×C47—43no—
129C2×C4×C47—46no—
130C2×C4×C47—43no—
131C2×C4×C47—43no—
132C2×C4×C47—43no—
133C2×C4×C47—46no—
134C2×C4×C47C4×D4112yes—
135C2×C4×C47#12714yes—
136#14322C4711yesmaximal, characteristic, direct product factor, Sylow
137C22×C47—42no—
138C22×C47—46no—
139C22×C47—46no—
140C22×C47—81no—
141C22×C47—81no—
142C22×C47—83no—
143C22×C47—83no—
144C22×C47C2×C4×D413yes—
145C22×C47#51911yescharacteristic
146C22×C47#52013yes—
147C22×C47C2×#12711yescharacteristic
148C22×C47#53213yes—
149C22×C47#53413yes—
150C22×C47#53613yes—
151C22×C47#53613yes—
152C22×C47#53713yes—
153C22×C47#53916yes—
154C22×C47#54113yes—
155C22×C47#54213yes—
156C4×C47—212no—
157C4×C47—24no—
158C4×C47—46no—
159C4×C47—46no—
160C4×C47—83no—
161C4×C47—81no—
162C2×#399C2×C4711yescharacteristic
163C2×#389C2×C4713yescomplemented
164C2×#388C2×C4713yes—
165#1445C2×C4713yescomplemented
166#1444C2×C4711yescharacteristic, complemented
167#1439C2×C4713yes—
168C4×#95C2×C4711yescharacteristic, complemented
169C2×C47—82no—
170C2×C47C4×#12711yescharacteristic
171C2×C47#232213yes—
172C2×C47#232313yes—
173C2×C47#265611yescharacteristic
174C2×C47#265811yescharacteristic
175C2×C47#266313yes—
176C2×C47#266413yes—
177C22×C4⋊C4C22×C4713yes—
178C22×C4⋊C4C22×C4713yes—
179C22×C4⋊C4C22×C4713yes—
180C22×C22⋊C4C22×C4711yescharacteristic
181C22×C22⋊C4C22×C4713yes—
182C22×C22⋊C4C22×C4713yes—
183C22×C42C22×C4713yes—
184#399C4×C4718yescomplemented
185#389—212no—
186#388—212no—
187C2×#95C22×C4713yes—
188C2×#95C22×C4716yes—
189C2×#95C22×C4713yes—
190C2×#95C22×C4713yes—
191C2×#95C22×C4711yescharacteristic
192C47#1432211yescharacteristic, direct product factor, Sylow
193C25C23×C4711yescharacteristic
194C23×C4C23×C4713yes—
195C23×C4C23×C4711yescharacteristic
196C23×C4C23×C4713yes—
197C23×C4C23×C4713yes—
198C23×C4C23×C4713yes—
199C23×C4C23×C4711yescharacteristic
200C2×C4⋊C4—26no—
201C2×C4⋊C4—26no—
202C2×C4⋊C4—26no—
203C2×C4⋊C4—26no—
204C2×C4⋊C4—212no—
205C2×C4⋊C4—46no—
206C2×C4⋊C4C2×C4×C47112yes—
207C2×C22⋊C4—26no—
208C2×C22⋊C4—26no—
209C2×C22⋊C4—26no—
210C2×C22⋊C4—26no—
211C2×C22⋊C4—46no—
212C2×C22⋊C4C2×C4×C47112yes—
213C2×C42—46no—
214C2×C42D4×C47112yes—
215#95—26no—
216#95—26no—
217#95—212no—
218#95—26no—
219#95C2×C4×C4714yes—
220C24—23no—
221C24—23no—
222C24—23no—
223C24—21no—
224C24—21no—
225C24—23no—
226C24C22×C4×C4712yes—
227C24C24×C4711yescharacteristic
228C22×C4—23no—
229C22×C4—26no—
230C22×C4—26no—
231C22×C4—21no—
232C22×C4—23no—
233C22×C4—26no—
234C22×C4—26no—
235C22×C4—23no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—23no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—23no—
242C22×C4—26no—
243C22×C4—26no—
244C22×C4—23no—
245C22×C4—21no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4C22×C4×C4716yes—
249C22×C4C22×C4×C4716yes—
250C22×C4C2×D4×C4716yes—
251C22×C4C2×D4×C4716yes—
252C22×C4C2×D4×C4716yes—
253C22×C4#41×C4716yes—
254C4⋊C4—224no—
255C4⋊C4—412no—
256C4⋊C4—412no—
257C22⋊C4—224no—
258C22⋊C4—412no—
259C22⋊C4—44no—
260C42—412no—
261C23—26no—
262C23—22no—
263C23—26no—
264C23—41no—
265C23—43no—
266C23—43no—
267C23—43no—
268C23—43no—
269C23—43no—
270C23—46no—
271C23—43no—
272C23—43no—
273C23C23×C4×C4711yescharacteristic
274C23C22×D4×C4713yes—
275C23C2×#41×C4713yes—
276C23H(5,𝔽2)×C4713yes—
277C232−1+4×C4711yescharacteristic
278C232−1+4×C4711yescharacteristic
279C232−1+4×C4713yes—
280C2×C4—212no—
281C2×C4—26no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—26no—
285C2×C4—212no—
286C2×C4—26no—
287C2×C4—212no—
288C2×C4—26no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—43no—
292C2×C4—43no—
293C2×C4—46no—
294C2×C4—46no—
295C2×C4—46no—
296C2×C4—41no—
297C2×C4—43no—
298C2×C4—43no—
299C2×C4—46no—
300C2×C4—43no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—46no—
304C2×C4C4×D4×C47112yes—
305C2×C4#127×C4714yes—
306C22—42no—
307C22—46no—
308C22—46no—
309C22—81no—
310C22—81no—
311C22—83no—
312C22—83no—
313C22C2×C4×D4×C4713yes—
314C22C47×#51911yescharacteristic
315C22C47×#52013yes—
316C22C2×#127×C4711yescharacteristic
317C22C47×#53213yes—
318C22C47×#53413yes—
319C22C47×#53613yes—
320C22C47×#53613yes—
321C22C47×#53713yes—
322C22C47×#53916yes—
323C22C47×#54113yes—
324C22C47×#54213yes—
325C4—212no—
326C4—24no—
327C4—46no—
328C4—46no—
329C4—83no—
330C4—81no—
331C2—82no—
332C2C4×#127×C4711yescharacteristic
333C2C47×#232213yes—
334C2C47×#232313yes—
335C2C47×#265611yescharacteristic
336C2C47×#265811yescharacteristic
337C2C47×#266313yes—
338C2C47×#266413yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC25×C47C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#389C2semidirect
4. C47×#1445C2semidirect
5. C47×#1444C2semidirect
7. C4×#95×C47C2semidirect
15. C47×#399C4semidirect
136. #14322C47direct (N × H)
163. C2×#389C2×C47semidirect
165. #1445C2×C47semidirect
166. #1444C2×C47semidirect
168. C4×#95C2×C47semidirect
184. #399C4×C47semidirect
192. C47#14322direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3992
C2×C47×#3892
C2×C47×#3882
C47×#14452
C47×#14442
C47×#14392
C4×#95×C472
#1432247