Finite Group Databasebeta

← C47×#13259 #26052957

Subgroups — C47×#13259 #26052957

Order 12032.

472 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3147C211yesmaximal, characteristic
2C2×C47×#364C211yesmaximal, characteristic, complemented
3C47×#2145C212yesmaximal, complemented
4C47×#2143C212yesmaximal, complemented
5C47×#1772C211yesmaximal, characteristic, complemented
6C2×#135×C47—21no—
7C2×#135×C47C2212yes—
8C47×#532—21no—
9C2×M32×C47C2212yes—
10C47×#495—21no—
11C47×#495C412yescomplemented
12C47×#494C411yescharacteristic, complemented
13C47×#493C411yescharacteristic, complemented
14C47×#492—21no—
15C2×#108×C47C2211yescharacteristic
16C47×#427C2211yescharacteristic
17C47×#405—21no—
18C2×C4×C8×C47C2211yescharacteristic
19C47×#364—21no—
20C47×#364—21no—
21C47×#360—24no—
22C47×#359—24no—
23C47×#339—21no—
24C2×#41×C47—22no—
25#135×C47—22no—
26#135×C47—22no—
27#135×C47—22no—
28#135×C47—22no—
29#135×C47—41no—
30#135×C47—41no—
31#135×C47—41no—
32#135×C47—41no—
33C2×Q16×C47—21no—
34C2×Q16×C47C2×C412yes—
35C2×SD16×C47—22no—
36C2×SD16×C47—22no—
37C2×D8×C47—21no—
38C2×D8×C47C2×C412yes—
39C2×M16×C47—21no—
40C22×C8×C47D411yescharacteristic
41C22×C8×C47C2311yescharacteristic
42C4⋊Q8×C47—21no—
43#127×C47—21no—
44#124×C47—22no—
45#121×C47—42no—
46C4×D4×C47—42no—
47#117×C47—21no—
48C2×C42×C47D411yescharacteristic
49M32×C47—22no—
50M32×C47—22no—
51C2×C16×C47—22no—
52#108×C47—21no—
53#108×C47D412yescomplemented
54#107×C47—21no—
55#106×C47D412yescomplemented
56#97×C47—41no—
57C4×C8×C47—41no—
58C4×C8×C47C2×C411yescharacteristic
59C4×C8×C47C2×C411yescharacteristic
60C4×C8×C47D411yescharacteristic
61C4×C8×C47D411yescharacteristic
62#41×C47—42no—
63#41×C47—42no—
64#41×C47—42no—
65#41×C47—42no—
66C2×Q8×C47—22no—
67C2×D4×C47—22no—
68C2×D4×C47—42no—
69C2×D4×C47—42no—
70C22×C4×C47—21no—
71C22×C4×C47—42no—
72C22×C4×C47C2×D411yescharacteristic
73Q16×C47—22no—
74Q16×C47—22no—
75Q16×C47—41no—
76Q16×C47—41no—
77SD16×C47—42no—
78SD16×C47—42no—
79SD16×C47—42no—
80SD16×C47—42no—
81D8×C47—22no—
82D8×C47—22no—
83D8×C47—41no—
84D8×C47—41no—
85M16×C47—22no—
86M16×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47C22⋊C411yescharacteristic
89C2×C8×C47C22⋊C411yescharacteristic
90C2×C8×C47D811yescharacteristic
91C2×C8×C47D811yescharacteristic
92C2×C8×C47SD1611yescharacteristic
93C2×C8×C47SD1611yescharacteristic
94C2×C8×C47C22×C411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C2×C8×C47#4111yescharacteristic
100C4⋊C4×C47—22no—
101C4⋊C4×C47—42no—
102C22⋊C4×C47—44no—
103C22⋊C4×C47—41no—
104C42×C47—21no—
105C42×C47—41no—
106C42×C47C22⋊C411yescharacteristic
107C42×C47C22⋊C411yescharacteristic
108C16×C47—42no—
109C23×C47—42no—
110C23×C47AGL(1,ℤ/8)11yescharacteristic
111Q8×C47—42no—
112Q8×C47—42no—
113D4×C47—42no—
114D4×C47—42no—
115D4×C47—84no—
116D4×C47—82no—
117D4×C47—82no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—82no—
124C2×C4×C47—82no—
125C2×C4×C47C2×C22⋊C411yescharacteristic
126C2×C4×C47#12111yescharacteristic
127C2×C4×C47#12111yescharacteristic
128C2×C4×C47C2×D811yescharacteristic
129C2×C4×C47C2×SD1611yescharacteristic
130C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
131C8×C47—42no—
132C8×C47#10211yescharacteristic
133C8×C47#10211yescharacteristic
134C8×C47#10211yescharacteristic
135C8×C47#10211yescharacteristic
136C8×C47C4×D411yescharacteristic
137C8×C47C4×D411yescharacteristic
138C8×C47#12411yescharacteristic
139C8×C47#12711yescharacteristic
140#13259C4711yesmaximal, characteristic, direct product factor, Sylow
141C22×C47—41no—
142C22×C47—84no—
143C22×C47—82no—
144C22×C47#41811yescharacteristic
145C22×C47#45911yescharacteristic
146C22×C47#46011yescharacteristic
147C4×C47—22no—
148C4×C47—41no—
149C4×C47—82no—
150C4×C47—82no—
151C4×C47#39011yescharacteristic
152C4×C47C2×#10211yescharacteristic
153C4×C47#45911yescharacteristic
154C4×C47#46011yescharacteristic
155#3147C2×C4711yescharacteristic
156C2×#364C2×C4711yescharacteristic, complemented
157#2145C2×C4712yescomplemented
158#2143C2×C4712yescomplemented
159#1772C2×C4711yescharacteristic, complemented
160C2×C47—21no—
161C2×C47—21no—
162C2×C47—21no—
163C2×C47—162no—
164C2×C47#198211yescharacteristic
165C2×#135—21no—
166C2×#135C22×C4712yes—
167#532—21no—
168C2×M32C22×C4712yes—
169#495—21no—
170#495C4×C4712yescomplemented
171#494C4×C4711yescharacteristic, complemented
172#493C4×C4711yescharacteristic, complemented
173#492—21no—
174C2×#108C22×C4711yescharacteristic
175#427C22×C4711yescharacteristic
176#405—21no—
177C2×C4×C8C22×C4711yescharacteristic
178#364—21no—
179#364—21no—
180#360—24no—
181#359—24no—
182#339—21no—
183C47#1325911yescharacteristic, direct product factor, Sylow
184C2×#41—22no—
185#135—22no—
186#135—22no—
187#135—22no—
188#135—22no—
189#135—41no—
190#135—41no—
191#135—41no—
192#135—41no—
193C2×Q16—21no—
194C2×Q16C2×C4×C4712yes—
195C2×SD16—22no—
196C2×SD16—22no—
197C2×D8—21no—
198C2×D8C2×C4×C4712yes—
199C2×M16—21no—
200C22×C8D4×C4711yescharacteristic
201C22×C8C23×C4711yescharacteristic
202C4⋊Q8—21no—
203#127—21no—
204#124—22no—
205#121—42no—
206C4×D4—42no—
207#117—21no—
208C2×C42D4×C4711yescharacteristic
209M32—22no—
210M32—22no—
211C2×C16—22no—
212#108—21no—
213#108D4×C4712yescomplemented
214#107—21no—
215#106D4×C4712yescomplemented
216#97—41no—
217C4×C8—41no—
218C4×C8C2×C4×C4711yescharacteristic
219C4×C8C2×C4×C4711yescharacteristic
220C4×C8D4×C4711yescharacteristic
221C4×C8D4×C4711yescharacteristic
222#41—42no—
223#41—42no—
224#41—42no—
225#41—42no—
226C2×Q8—22no—
227C2×D4—22no—
228C2×D4—42no—
229C2×D4—42no—
230C22×C4—21no—
231C22×C4—42no—
232C22×C4C2×D4×C4711yescharacteristic
233Q16—22no—
234Q16—22no—
235Q16—41no—
236Q16—41no—
237SD16—42no—
238SD16—42no—
239SD16—42no—
240SD16—42no—
241D8—22no—
242D8—22no—
243D8—41no—
244D8—41no—
245M16—22no—
246M16—41no—
247C2×C8—41no—
248C2×C8C22⋊C4×C4711yescharacteristic
249C2×C8C22⋊C4×C4711yescharacteristic
250C2×C8D8×C4711yescharacteristic
251C2×C8D8×C4711yescharacteristic
252C2×C8SD16×C4711yescharacteristic
253C2×C8SD16×C4711yescharacteristic
254C2×C8C22×C4×C4711yescharacteristic
255C2×C8C2×D4×C4711yescharacteristic
256C2×C8C2×D4×C4711yescharacteristic
257C2×C8C2×D4×C4711yescharacteristic
258C2×C8#41×C4711yescharacteristic
259C2×C8#41×C4711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—42no—
262C22⋊C4—44no—
263C22⋊C4—41no—
264C42—21no—
265C42—41no—
266C42C22⋊C4×C4711yescharacteristic
267C42C22⋊C4×C4711yescharacteristic
268C16—42no—
269C23—42no—
270C23AGL(1,ℤ/8)×C4711yescharacteristic
271Q8—42no—
272Q8—42no—
273D4—42no—
274D4—42no—
275D4—84no—
276D4—82no—
277D4—82no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4C2×C22⋊C4×C4711yescharacteristic
286C2×C4#121×C4711yescharacteristic
287C2×C4#121×C4711yescharacteristic
288C2×C4C2×D8×C4711yescharacteristic
289C2×C4C2×SD16×C4711yescharacteristic
290C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
291C8—42no—
292C8#102×C4711yescharacteristic
293C8#102×C4711yescharacteristic
294C8#102×C4711yescharacteristic
295C8#102×C4711yescharacteristic
296C8C4×D4×C4711yescharacteristic
297C8C4×D4×C4711yescharacteristic
298C8#124×C4711yescharacteristic
299C8#127×C4711yescharacteristic
300C22—41no—
301C22—84no—
302C22—82no—
303C22C47×#41811yescharacteristic
304C22C47×#45911yescharacteristic
305C22C47×#46011yescharacteristic
306C4—22no—
307C4—41no—
308C4—82no—
309C4—82no—
310C4C47×#39011yescharacteristic
311C4C2×#102×C4711yescharacteristic
312C4C47×#45911yescharacteristic
313C4C47×#46011yescharacteristic
314C2—21no—
315C2—21no—
316C2—21no—
317C2—162no—
318C2C47×#198211yescharacteristic
subgroupG/H
centerC4×C47#459
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
socleC2×C47#1982
prime radicalC47×#3147C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C22×C4×C47 ◁ C2×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#364C2semidirect
3. C47×#2145C2semidirect
4. C47×#2143C2semidirect
5. C47×#1772C2semidirect
11. C47×#495C4semidirect
12. C47×#494C4semidirect
13. C47×#493C4semidirect
53. #108×C47D4semidirect
55. #106×C47D4semidirect
140. #13259C47direct (N × H)
156. C2×#364C2×C47semidirect
157. #2145C2×C47semidirect
158. #2143C2×C47semidirect
159. #1772C2×C47semidirect
170. #495C4×C47semidirect
171. #494C4×C47semidirect
172. #493C4×C47semidirect
183. C47#13259direct (N × H)
213. #108D4×C47semidirect
215. #106D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31472
C2×C47×#3642
C47×#21452
C47×#21432
C47×#17722
#1325947