Finite Group Databasebeta

← D47×#2159 #26369308

Subgroups — D47×#2159 #26369308

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C211yesmaximal, characteristic
2#427×D47C211yesmaximal, characteristic
3C2×#107×D47C211yesmaximal, characteristic
4#20245177C211yesmaximal, characteristic, complemented
5#20245176C211yesmaximal, characteristic, complemented
6#20245175C212yesmaximal, complemented
7#20245174C211yesmaximal, characteristic, complemented
8#20245173C212yesmaximal, complemented
9#367×D47C212yesmaximal, complemented
10#366×D47C212yesmaximal, complemented
11C47×#2159C211yesmaximal, characteristic, complemented
12C22×C8×D47C2211yescharacteristic
13#117×D47—21no—
14C2×C4⋊C4×D47—21no—
15C2×#13093964C2211yescharacteristic
16C2×#13093963C2212yes—
17M32×D47C418yescomplemented
18C2×C16×D47C2212yes—
19#15689161C2211yescharacteristic
20#15689160C2211yescharacteristic
21#15689160C2211yescharacteristic
22#15689159—21no—
23#15689158—21no—
24C2×#13093958C2211yescharacteristic
25C2×#13093957—21no—
26#107×D47—21no—
27#107×D47—21no—
28#107×D47C2212yes—
29#107×D47C2212yes—
30#107×D47C2211yescharacteristic
31#107×D47C2211yescharacteristic
32#106×D47—21no—
33#15688951C2212yescomplemented
34#15688950C2212yescomplemented
35#15688950C2212yescomplemented
36#15688949C2212yescomplemented
37#15688948C2212yescomplemented
38#15688948C2212yescomplemented
39C2×M32×C47C2211yescharacteristic
40C47×#427C2211yescharacteristic
41C2×#107×C47C2211yescharacteristic
42C47×#367C2212yescomplemented
43C47×#366C2212yescomplemented
44C22×C4×D47—41no—
45C22×C4×D47D411yescharacteristic
46C22×C47⋊C8D411yescharacteristic
47C2×C8×D47C2×C414yes—
48C2×C8×D47D411yescharacteristic
49C2×C8×D47D411yescharacteristic
50C2×C8×D47Q814yes—
51C2×C8×D47C2311yescharacteristic
52C2×C8×D47C2311yescharacteristic
53#13093983—21no—
54#13093982—21no—
55#13093982—21no—
56#13093981—41no—
57#13093980—41no—
58C2×C4⋊Dic47—21no—
59C2×Dic47⋊C4—41no—
60C4⋊C4×D47—22no—
61C4⋊C4×D47—22no—
62C4⋊C4×D47—21no—
63C4⋊C4×D47—21no—
64C4⋊C4×D47—41no—
65C4⋊C4×D47—41no—
66C22⋊C4×D47—41no—
67C42×D47—41no—
68#13093964C2×C414yescomplemented
69#13093963C2×C418yescomplemented
70C2×C47⋊C16C2312yes—
71C16×D47C2×C418yescomplemented
72#13093958—21no—
73#13093958C2312yes—
74#13093958C2311yescharacteristic
75#13093958C2311yescharacteristic
76#13093957—22no—
77#13093957—22no—
78#13093957—21no—
79#13093957—21no—
80#13093956—21no—
81#13093955—21no—
82#13093955—21no—
83C22×C8×C47C2311yescharacteristic
84#117×C47—21no—
85C2×C4⋊C4×C47—21no—
86M32×C47C2×C414yescomplemented
87C2×C16×C47C2312yes—
88#107×C47—21no—
89#107×C47C2311yescharacteristic
90#107×C47C2312yes—
91#107×C47C2311yescharacteristic
92#106×C47—21no—
93C23×D47D811yescharacteristic
94C22×C4×C47—41no—
95C22×C4×C47C2×D411yescharacteristic
96C22×Dic47—41no—
97C22×Dic47D811yescharacteristic
98C2×C4×D47—41no—
99C2×C4×D47—41no—
100C2×C4×D47—42no—
101C2×C4×D47—42no—
102C2×C4×D47—84no—
103C2×C4×D47C4⋊C414yes—
104C2×C4×D47D811yescharacteristic
105C2×C4×D47D811yescharacteristic
106C2×C4×D47Q1614yes—
107C2×C4×D47C2×D411yescharacteristic
108C2×C4×D47C2×D411yescharacteristic
109C2×C8×C47C22×C412yes—
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2×Q812yes—
112C2×C8×C47C2411yescharacteristic
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—22no—
116C4⋊C4×C47—41no—
117C22⋊C4×C47—41no—
118C42×C47—41no—
119C22⋊Dic47—41no—
120(C2×D47)⋊C4—41no—
121(C2×D47)⋊C4—41no—
122C4⋊Dic47—21no—
123C4⋊Dic47—21no—
124C4⋊Dic47—22no—
125C4⋊Dic47—41no—
126Dic47⋊C4—42no—
127Dic47⋊C4—42no—
128Dic47⋊C4—41no—
129Dic47⋊C4—41no—
130C4×Dic47—41no—
131C4×Dic47—41no—
132C4×Dic47—41no—
133C2×C47⋊C8C4⋊C414yes—
134C2×C47⋊C8C2×D411yescharacteristic
135C2×C47⋊C8C2×D411yescharacteristic
136C8×D47C4⋊C414yes—
137C8×D47C4⋊C414yes—
138C8×D47C22×C412yes—
139C8×D47C22×C412yes—
140C8×D47C2×Q812yes—
141C8×D47C2×Q812yes—
142C16×C47C22×C414yescomplemented
143C47⋊C16C22×C414yescomplemented
144C23×C47C2×D811yescharacteristic
145C22×D47—22no—
146C22×D47—22no—
147C22×D47#10714yes—
148C22×D47C2×D811yescharacteristic
149C22×D47C2×D811yescharacteristic
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—42no—
153C2×C4×C47—82no—
154C2×C4×C47C2×C4⋊C412yes—
155C2×C4×C47C2×D811yescharacteristic
156C2×C4×C47C2×Q1612yes—
157C2×C4×C47C22×D411yescharacteristic
158C2×Dic47—41no—
159C2×Dic47—41no—
160C2×Dic47—42no—
161C2×Dic47—82no—
162C2×Dic47#10714yes—
163C2×Dic47C2×D811yescharacteristic
164C2×Dic47C2×D811yescharacteristic
165C4×D47—84no—
166C4×D47—82no—
167C4×D47—84no—
168C4×D47—82no—
169C4×D47#10714yes—
170C4×D47#10714yes—
171C4×D47C2×C4⋊C412yes—
172C4×D47C2×C4⋊C412yes—
173C4×D47C2×Q1612yes—
174C4×D47C2×Q1612yes—
175C8×C47C2×C4⋊C412yes—
176C8×C47C23×C411yescharacteristic
177C8×C47C22×Q811yescharacteristic
178C47⋊C8C2×C4⋊C412yes—
179C47⋊C8C2×C4⋊C412yes—
180C2×#2159—471nomaximal, Sylow
181C22×C47—21no—
182C22×C47—21no—
183C22×C47C2×#10712yes—
184C22×C47C22×D811yescharacteristic
185C2×D47—21no—
186C2×D47—21no—
187C2×D47—28no—
188C2×D47C2×#10712yes—
189C2×D47C2×#10712yes—
190C2×D47#50912yes—
191C2×D47#51012yes—
192C4×C47—82no—
193C4×C47—81no—
194C4×C47—81no—
195C4×C47C2×#10712yes—
196C4×C47C22×C4⋊C411yescharacteristic
197C4×C47C22×Q1611yescharacteristic
198Dic47—82no—
199Dic47—81no—
200Dic47—81no—
201Dic47C2×#10712yes—
202Dic47C2×#10712yes—
203C22×M32—471no—
204C2×#427—471no—
205C22×#107—471no—
206#2159—471no—
207#2159—471no—
208#2159—471no—
209#2159—472no—
210#2159—472no—
211#2159D4711yescharacteristic, direct product factor
212C2×#367—472no—
213C2×#366—472no—
214C2×C47—22no—
215C2×C47C22×#10711yescharacteristic
216C2×C47C2×#50911yescharacteristic
217C2×C47C2×#51011yescharacteristic
218D47—22no—
219D47#215914yesdirect product factor
220C23×C8—471no—
221C2×#117—941no—
222C22×C4⋊C4—941no—
223C2×M32—471no—
224C2×M32—478no—
225C2×M32—472no—
226C2×M32C2×D4711yescharacteristic
227C22×C16—472no—
228#427—471no—
229#427—471no—
230#427—471no—
231#427—941no—
232#427—941no—
233#427C2×D4711yescharacteristic
234C2×#107—471no—
235C2×#107—472no—
236C2×#107—472no—
237C2×#107—471no—
238C2×#107—471no—
239C2×#107—941no—
240C2×#107—941no—
241C2×#107—941no—
242C2×#107C2×D4711yescharacteristic
243C2×#106—941no—
244#367—472no—
245#367—472no—
246#367—472no—
247#367C2×D4712yescomplemented
248#366—472no—
249#366—472no—
250#366—472no—
251#366C2×D4712yescomplemented
252C47C2×#215911yescharacteristic, complemented, Sylow
253C23×C4—471no—
254C23×C4—1881no—
255C22×C8—471no—
256C22×C8—474no—
257C22×C8—471no—
258C22×C8—471no—
259C22×C8—474no—
260C22×C8—471no—
261C22×C8—471no—
262C22×C8C22×D4711yescharacteristic
263#117—21no—
264#117—941no—
265#117—941no—
266#117—941no—
267#117—1881no—
268#117—1881no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—942no—
271C2×C4⋊C4—942no—
272C2×C4⋊C4—941no—
273C2×C4⋊C4—941no—
274C2×C4⋊C4—941no—
275C2×C4⋊C4—1881no—
276C2×C4⋊C4—1881no—
277C2×C4⋊C4—1881no—
278C2×C22⋊C4—1881no—
279C2×C42—1881no—
280M32—474no—
281M32—478no—
282M32C4×D4714yescomplemented
283C2×C16—472no—
284C2×C16—478no—
285C2×C16C22×D4712yes—
286#107—21no—
287#107—471no—
288#107—472no—
289#107—471no—
290#107—942no—
291#107—942no—
292#107—941no—
293#107—941no—
294#107—941no—
295#107C22×D4711yescharacteristic
296#107C22×D4712yes—
297#107C22×D4711yescharacteristic
298#106—21no—
299#106—941no—
300#106—941no—
301#106—941no—
302C24—471no—
303C22×C4—41no—
304C22×C4—471no—
305C22×C4—474no—
306C22×C4—471no—
307C22×C4—471no—
308C22×C4—474no—
309C22×C4—471no—
310C22×C4—471no—
311C22×C4—3764no—
312C22×C4—1881no—
313C22×C4—1881no—
314C22×C4—1882no—
315C22×C4—1882no—
316C22×C4—1881no—
317C22×C4D4×D4711yescharacteristic
318C2×C8—474no—
319C2×C8—471no—
320C2×C8—471no—
321C2×C8—474no—
322C2×C8—474no—
323C2×C8—472no—
324C2×C8—472no—
325C2×C8—472no—
326C2×C8—472no—
327C2×C8C2×C4×D4712yes—
328C2×C8D4×D4711yescharacteristic
329C2×C8Q8×D4712yes—
330C2×C8C23×D4711yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—941no—
336C4⋊C4—941no—
337C4⋊C4—942no—
338C4⋊C4—1882no—
339C4⋊C4—1882no—
340C4⋊C4—1881no—
341C4⋊C4—1881no—
342C4⋊C4—1881no—
343C22⋊C4—41no—
344C22⋊C4—1881no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C42—41no—
348C42—1881no—
349C42—1881no—
350C42—1881no—
351C16—474no—
352C16C2×C4×D4714yescomplemented
353C23—471no—
354C23—471no—
355C23—474no—
356C23—942no—
357C23—942no—
358C23D8×D4711yescharacteristic
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—471no—
364C2×C4—471no—
365C2×C4—474no—
366C2×C4—472no—
367C2×C4—472no—
368C2×C4—472no—
369C2×C4—472no—
370C2×C4—474no—
371C2×C4—474no—
372C2×C4—3764no—
373C2×C4—3762no—
374C2×C4—3762no—
375C2×C4—3764no—
376C2×C4—3762no—
377C2×C4—1881no—
378C2×C4—1881no—
379C2×C4—1882no—
380C2×C4C4⋊C4×D4712yes—
381C2×C4D8×D4711yescharacteristic
382C2×C4Q16×D4712yes—
383C2×C4C2×D4×D4711yescharacteristic
384C8—472no—
385C8—472no—
386C8C4⋊C4×D4712yes—
387C8C22×C4×D4711yescharacteristic
388C8C2×Q8×D4711yescharacteristic
389C22—21no—
390C22—21no—
391C22—472no—
392C22—472no—
393C22—472no—
394C22—472no—
395C22—948no—
396C22—941no—
397C22—941no—
398C22#107×D4712yes—
399C22C2×D8×D4711yescharacteristic
400C4—81no—
401C4—82no—
402C4—81no—
403C4—472no—
404C4—472no—
405C4—3761no—
406C4—3762no—
407C4—3761no—
408C4#107×D4712yes—
409C4C2×C4⋊C4×D4711yescharacteristic
410C4C2×Q16×D4711yescharacteristic
411C2—22no—
412C2—474no—
413C2—942no—
414C2C2×#107×D4711yescharacteristic
415C2#509×D4711yescharacteristic
416C2#510×D4711yescharacteristic
subgroupG/H
centerC22C2×D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2159C2
socleC22×C47C22×D8
prime radicalC23×D47D8
cosocleC2×C8×C47C24
hypercenter#2159D47
hypocenterC47C2×#2159
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
4. #20245177C2semidirect
5. #20245176C2semidirect
6. #20245175C2semidirect
7. #20245174C2semidirect
8. #20245173C2semidirect
9. #367×D47C2semidirect
10. #366×D47C2semidirect
11. C47×#2159C2semidirect
17. M32×D47C4semidirect
33. #15688951C22semidirect
34. #15688950C22semidirect
35. #15688950C22semidirect
36. #15688949C22semidirect
37. #15688948C22semidirect
38. #15688948C22semidirect
42. C47×#367C22semidirect
43. C47×#366C22semidirect
68. #13093964C2×C4semidirect
69. #13093963C2×C4semidirect
71. C16×D47C2×C4semidirect
86. M32×C47C2×C4semidirect
142. C16×C47C22×C4semidirect
143. C47⋊C16C22×C4semidirect
211. #2159D47direct (N × H)
219. D47#2159direct (N × H)
247. #367C2×D47semidirect
251. #366C2×D47semidirect
252. C47C2×#2159semidirect
282. M32C4×D47semidirect
352. C16C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
#427×D472
C2×#107×D472
#202451772
#202451762
#202451752
#202451742
#202451732
#367×D472
#366×D472
C47×#21592
C2×#215947