Finite Group Databasebeta

← C47×#9867 #26049565

Subgroups — C47×#9867 #26049565

Order 12032.

460 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C47C211yesmaximal, characteristic
2C47×#1767C211yesmaximal, characteristic
3C4×C4⋊C8×C47C211yesmaximal, characteristic
4C47×#1279C212yesmaximal
5C47×#1279C212yesmaximal
6C2×#125×C47C411yescharacteristic
7C2×C4⋊C8×C47—21no—
8C2×C4⋊C8×C47C2212yes—
9C2×#97×C47—21no—
10C2×C4×C8×C47C2212yes—
11C47×#389C411yescharacteristic
12C47×#389C411yescharacteristic
13C47×#387—21no—
14C47×#387—21no—
15C47×#382C411yescharacteristic
16C4×C4⋊C4×C47—21no—
17C4×C4⋊C4×C47—21no—
18C4×C4⋊C4×C47C2211yescharacteristic
19C4×C4⋊C4×C47C2211yescharacteristic
20C43×C47C2211yescharacteristic
21C47×#336—21no—
22C47×#336—21no—
23C22×C8×C47—22no—
24C22×C8×C47—22no—
25#125×C47—22no—
26#125×C47—22no—
27C2×C4⋊C4×C47—21no—
28C2×C4⋊C4×C47—21no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—21no—
31C2×C4⋊C4×C47C2×C411yescharacteristic
32C2×C4⋊C4×C47C2×C411yescharacteristic
33C2×C4⋊C4×C47C2×C411yescharacteristic
34C2×C4⋊C4×C47C2×C411yescharacteristic
35C2×C42×C47—21no—
36C2×C42×C47—21no—
37C2×C42×C47C2×C411yescharacteristic
38C2×C42×C47C2×C411yescharacteristic
39C2×C42×C47D411yescharacteristic
40C2×C42×C47D411yescharacteristic
41C2×C42×C47D411yescharacteristic
42C2×C42×C47D411yescharacteristic
43C2×C42×C47C2311yescharacteristic
44C4⋊C8×C47—24no—
45C4⋊C8×C47—22no—
46C4⋊C8×C47Q814yes—
47#97×C47—42no—
48C4×C8×C47—24no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22×C411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C2×C8×C47—24no—
67C2×C8×C47—24no—
68C2×C8×C47—42no—
69C2×C8×C47—42no—
70C2×C8×C47—42no—
71C2×C8×C47—42no—
72C4⋊C4×C47—24no—
73C4⋊C4×C47—24no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—22no—
77C4⋊C4×C47—22no—
78C4⋊C4×C47—42no—
79C4⋊C4×C47—42no—
80C4⋊C4×C47M1612yes—
81C4⋊C4×C47M1612yes—
82C42×C47—22no—
83C42×C47—21no—
84C42×C47—21no—
85C42×C47—22no—
86C42×C47—22no—
87C42×C47—21no—
88C42×C47—21no—
89C42×C47—41no—
90C42×C47—42no—
91C42×C47—41no—
92C42×C47—41no—
93C42×C47C2×Q812yes—
94C42×C47#4112yes—
95C23×C47C2×C22⋊C411yescharacteristic
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—22no—
103C2×C4×C47—22no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47#10412yes—
122C2×C4×C47C4×Q812yes—
123C2×C4×C47C22⋊Q812yes—
124C2×C4×C47#12411yescharacteristic
125C2×C4×C47C4⋊Q811yescharacteristic
126C2×C4×C47C2×M1611yescharacteristic
127C2×C4×C47C2×M1611yescharacteristic
128C2×C4×C47#13112yes—
129C2×C4×C47#13512yes—
130C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C47#13711yescharacteristic
132C8×C47—44no—
133C8×C47—44no—
134#9867C4711yesmaximal, characteristic, direct product factor, Sylow
135C22×C47#39111yescharacteristic
136C22×C47#40711yescharacteristic
137C22×C47#40811yescharacteristic
138C22×C47#41611yescharacteristic
139C22×C47#41711yescharacteristic
140C22×C47C2×#10411yescharacteristic
141C22×C47#42111yescharacteristic
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—22no—
145C4×C47—41no—
146C4×C47—42no—
147C4×C47—41no—
148C4×C47—42no—
149C4×C47—41no—
150C4×C47—81no—
151C4×C47—81no—
152C4×C47#44612yes—
153C4×C47#44612yes—
154C4×C47#47812yes—
155C4×C47#47912yes—
156C4×#125C2×C4711yescharacteristic
157#1767C2×C4711yescharacteristic
158C4×C4⋊C8C2×C4711yescharacteristic
159#1279C2×C4712yes—
160#1279C2×C4712yes—
161C2×C47#148811yescharacteristic
162C2×C47#148911yescharacteristic
163C2×C47#149411yescharacteristic
164C2×C47#149511yescharacteristic
165C2×C47#198511yescharacteristic
166C2×C47#198611yescharacteristic
167C2×C47#198911yescharacteristic
168C2×#125C4×C4711yescharacteristic
169C2×C4⋊C8—21no—
170C2×C4⋊C8C22×C4712yes—
171C2×#97—21no—
172C2×C4×C8C22×C4712yes—
173#389C4×C4711yescharacteristic
174#389C4×C4711yescharacteristic
175#387—21no—
176#387—21no—
177#382C4×C4711yescharacteristic
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4C22×C4711yescharacteristic
181C4×C4⋊C4C22×C4711yescharacteristic
182C43C22×C4711yescharacteristic
183#336—21no—
184#336—21no—
185C47#986711yescharacteristic, direct product factor, Sylow
186C22×C8—22no—
187C22×C8—22no—
188#125—22no—
189#125—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C4711yescharacteristic
195C2×C4⋊C4C2×C4×C4711yescharacteristic
196C2×C4⋊C4C2×C4×C4711yescharacteristic
197C2×C4⋊C4C2×C4×C4711yescharacteristic
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C2×C4×C4711yescharacteristic
201C2×C42C2×C4×C4711yescharacteristic
202C2×C42D4×C4711yescharacteristic
203C2×C42D4×C4711yescharacteristic
204C2×C42D4×C4711yescharacteristic
205C2×C42D4×C4711yescharacteristic
206C2×C42C23×C4711yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—22no—
209C4⋊C8Q8×C4714yes—
210#97—42no—
211C4×C8—24no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C4711yescharacteristic
223C22×C4C22⋊C4×C4711yescharacteristic
224C22×C4C22⋊C4×C4711yescharacteristic
225C22×C4C22⋊C4×C4711yescharacteristic
226C22×C4C22×C4×C4711yescharacteristic
227C22×C4C2×D4×C4711yescharacteristic
228C22×C4C2×D4×C4711yescharacteristic
229C2×C8—24no—
230C2×C8—24no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4M16×C4712yes—
244C4⋊C4M16×C4712yes—
245C42—22no—
246C42—21no—
247C42—21no—
248C42—22no—
249C42—22no—
250C42—21no—
251C42—21no—
252C42—41no—
253C42—42no—
254C42—41no—
255C42—41no—
256C42C2×Q8×C4712yes—
257C42#41×C4712yes—
258C23C2×C22⋊C4×C4711yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4#104×C4712yes—
285C2×C4C4×Q8×C4712yes—
286C2×C4C22⋊Q8×C4712yes—
287C2×C4#124×C4711yescharacteristic
288C2×C4C4⋊Q8×C4711yescharacteristic
289C2×C4C2×M16×C4711yescharacteristic
290C2×C4C2×M16×C4711yescharacteristic
291C2×C4#131×C4712yes—
292C2×C4#135×C4712yes—
293C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
294C2×C4#137×C4711yescharacteristic
295C8—44no—
296C8—44no—
297C22C47×#39111yescharacteristic
298C22C47×#40711yescharacteristic
299C22C47×#40811yescharacteristic
300C22C47×#41611yescharacteristic
301C22C47×#41711yescharacteristic
302C22C2×#104×C4711yescharacteristic
303C22C47×#42111yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—42no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—81no—
314C4C47×#44612yes—
315C4C47×#44612yes—
316C4C47×#47812yes—
317C4C47×#47912yes—
318C2C47×#148811yescharacteristic
319C2C47×#148911yescharacteristic
320C2C47×#149411yescharacteristic
321C2C47×#149511yescharacteristic
322C2C47×#198511yescharacteristic
323C2C47×#198611yescharacteristic
324C2C47×#198911yescharacteristic
subgroupG/H
centerC22×C4×C47C2×D4
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socle, prime radicalC23×C47C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ C43×C47 ◁ G

Complements

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

NH ≅ G/Ntype
134. #9867C47direct (N × H)
185. C47#9867direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#125×C472
C47×#17672
C4×C4⋊C8×C472
C47×#12792
#986747