Finite Group Databasebeta

← C47×#9893 #26049591

Subgroups — C47×#9893 #26049591

Order 12032.

388 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2864C211yesmaximal, characteristic
2C47×#1767C211yesmaximal, characteristic
3C47×#1745C211yesmaximal, characteristic
4C47×#1295C212yesmaximal
5C47×#1295C212yesmaximal
6C2×C4⋊C8×C47—21no—
7C2×#97×C47C2212yes—
8C2×#97×C47C2212yes—
9C47×#389C411yescharacteristic
10C47×#389C411yescharacteristic
11C47×#389C411yescharacteristic
12C47×#389C411yescharacteristic
13C47×#387—21no—
14C47×#387—21no—
15C47×#387—21no—
16C47×#387—21no—
17C47×#382C2211yescharacteristic
18C47×#382C2211yescharacteristic
19C43×C47C2211yescharacteristic
20C47×#336—21no—
21C47×#336—21no—
22C47×#336—21no—
23C22×C8×C47—22no—
24C22×C8×C47—22no—
25C2×C4⋊C4×C47—21no—
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47—21no—
28C2×C4⋊C4×C47—21no—
29C2×C4⋊C4×C47C2×C411yescharacteristic
30C2×C4⋊C4×C47C2×C411yescharacteristic
31C2×C4⋊C4×C47C2×C411yescharacteristic
32C2×C4⋊C4×C47C2×C411yescharacteristic
33C2×C42×C47C2×C411yescharacteristic
34C2×C42×C47C2×C411yescharacteristic
35C2×C42×C47D411yescharacteristic
36C2×C42×C47D411yescharacteristic
37C2×C42×C47D411yescharacteristic
38C2×C42×C47D411yescharacteristic
39C2×C42×C47C2311yescharacteristic
40C4⋊C8×C47—24no—
41#97×C47—22no—
42#97×C47—24no—
43#97×C47Q814yes—
44#95×C47—21no—
45#95×C47—21no—
46#95×C47—21no—
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22×C411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×C4×C47C2×D411yescharacteristic
63C2×C8×C47—24no—
64C2×C8×C47—24no—
65C2×C8×C47—42no—
66C2×C8×C47—42no—
67C2×C8×C47—42no—
68C2×C8×C47—42no—
69C4⋊C4×C47—42no—
70C4⋊C4×C47—42no—
71C4⋊C4×C47—42no—
72C4⋊C4×C47—41no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—42no—
77C42×C47—22no—
78C42×C47—41no—
79C42×C47—41no—
80C42×C47—41no—
81C42×C47—41no—
82C42×C47—41no—
83C42×C47C2×Q812yes—
84C42×C47#4112yes—
85C23×C47C2×C22⋊C411yescharacteristic
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47#10412yes—
116C2×C4×C47C4×Q812yes—
117C2×C4×C47C22⋊Q812yes—
118C2×C4×C47#12411yescharacteristic
119C2×C4×C47C4⋊Q811yescharacteristic
120C8×C47—44no—
121C8×C47—44no—
122#9893C4711yesmaximal, characteristic, direct product factor, Sylow
123C22×C47#39111yescharacteristic
124C22×C47#41311yescharacteristic
125C22×C47#41311yescharacteristic
126C22×C47C2×#10411yescharacteristic
127C22×C47#42111yescharacteristic
128C22×C47#42111yescharacteristic
129C22×C47#42111yescharacteristic
130C4×C47—21no—
131C4×C47—21no—
132C4×C47—22no—
133C4×C47—22no—
134C4×C47—22no—
135C4×C47—41no—
136C4×C47—41no—
137C4×C47—41no—
138C4×C47—81no—
139C4×C47—81no—
140C4×C47—81no—
141C4×C47—81no—
142#2864C2×C4711yescharacteristic
143#1767C2×C4711yescharacteristic
144#1745C2×C4711yescharacteristic
145#1295C2×C4712yes—
146#1295C2×C4712yes—
147C2×C47#152911yescharacteristic
148C2×C47#153211yescharacteristic
149C2×C47#153511yescharacteristic
150C2×C47#153511yescharacteristic
151C2×C47#198611yescharacteristic
152C2×C47#199511yescharacteristic
153C2×C47#199811yescharacteristic
154C2×C4⋊C8—21no—
155C2×#97C22×C4712yes—
156C2×#97C22×C4712yes—
157#389C4×C4711yescharacteristic
158#389C4×C4711yescharacteristic
159#389C4×C4711yescharacteristic
160#389C4×C4711yescharacteristic
161#387—21no—
162#387—21no—
163#387—21no—
164#387—21no—
165#382C22×C4711yescharacteristic
166#382C22×C4711yescharacteristic
167C43C22×C4711yescharacteristic
168#336—21no—
169#336—21no—
170#336—21no—
171C47#989311yescharacteristic, direct product factor, Sylow
172C22×C8—22no—
173C22×C8—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×C4×C4711yescharacteristic
179C2×C4⋊C4C2×C4×C4711yescharacteristic
180C2×C4⋊C4C2×C4×C4711yescharacteristic
181C2×C4⋊C4C2×C4×C4711yescharacteristic
182C2×C42C2×C4×C4711yescharacteristic
183C2×C42C2×C4×C4711yescharacteristic
184C2×C42D4×C4711yescharacteristic
185C2×C42D4×C4711yescharacteristic
186C2×C42D4×C4711yescharacteristic
187C2×C42D4×C4711yescharacteristic
188C2×C42C23×C4711yescharacteristic
189C4⋊C8—24no—
190#97—22no—
191#97—24no—
192#97Q8×C4714yes—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4C22⋊C4×C4711yescharacteristic
206C22×C4C22⋊C4×C4711yescharacteristic
207C22×C4C22⋊C4×C4711yescharacteristic
208C22×C4C22⋊C4×C4711yescharacteristic
209C22×C4C22×C4×C4711yescharacteristic
210C22×C4C2×D4×C4711yescharacteristic
211C22×C4C2×D4×C4711yescharacteristic
212C2×C8—24no—
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C42—22no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42C2×Q8×C4712yes—
233C42#41×C4712yes—
234C23C2×C22⋊C4×C4711yescharacteristic
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4#104×C4712yes—
265C2×C4C4×Q8×C4712yes—
266C2×C4C22⋊Q8×C4712yes—
267C2×C4#124×C4711yescharacteristic
268C2×C4C4⋊Q8×C4711yescharacteristic
269C8—44no—
270C8—44no—
271C22C47×#39111yescharacteristic
272C22C47×#41311yescharacteristic
273C22C47×#41311yescharacteristic
274C22C2×#104×C4711yescharacteristic
275C22C47×#42111yescharacteristic
276C22C47×#42111yescharacteristic
277C22C47×#42111yescharacteristic
278C4—22no—
279C4—21no—
280C4—21no—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—81no—
289C4—81no—
290C2C47×#152911yescharacteristic
291C2C47×#153211yescharacteristic
292C2C47×#153511yescharacteristic
293C2C47×#153511yescharacteristic
294C2C47×#198611yescharacteristic
295C2C47×#199511yescharacteristic
296C2C47×#199811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C47C2×C22⋊C4
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C42C23×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C43×C47 ◁ G

Complements

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

NH ≅ G/Ntype
122. #9893C47direct (N × H)
171. C47#9893direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28642
C47×#17672
C47×#17452
C47×#12952
#989347