Finite Group Databasebeta

← D47×#1271 #26104210

Subgroups — D47×#1271 #26104210

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D47C211yesmaximal, characteristic
2#336×D47C211yesmaximal, characteristic
3#336×D47C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic, complemented
5#20241211C211yesmaximal, characteristic, complemented
6#20241210C211yesmaximal, characteristic, complemented
7C47×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D47—21no—
9C22×C8×D47—21no—
10C2×C4⋊C4×D47—21no—
11C2×C4⋊C4×D47C411yescharacteristic
12C2×C4⋊C4×D47C411yescharacteristic
13C2×C42×D47C2211yescharacteristic
14#15689022C411yescharacteristic
15#15689021C2211yescharacteristic
16#15689020—21no—
17#15689019C411yescharacteristic
18#15689018—21no—
19#95×D47—21no—
20#15688878C2211yescharacteristic
21#15688878C2211yescharacteristic
22#15688877—21no—
23#15688877—21no—
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C4×D47—21no—
28C22×C4×D47—21no—
29C22×C4×D47C2×C411yescharacteristic
30C22×C4×D47D411yescharacteristic
31C22×C4×D47D411yescharacteristic
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C2×C8×D47—24no—
35C2×C8×D47—24no—
36C2×C8×D47—42no—
37C2×C8×D47—42no—
38C2×C8×D47—42no—
39C2×C8×D47—42no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47C2×C411yescharacteristic
42C2×C4⋊Dic47C2×C411yescharacteristic
43C2×Dic47⋊C4—21no—
44C2×Dic47⋊C4—21no—
45C2×Dic47⋊C4—21no—
46C2×Dic47⋊C4—21no—
47C4⋊C4×D47—22no—
48C4⋊C4×D47—42no—
49C4⋊C4×D47—42no—
50C4⋊C4×D47—42no—
51C4⋊C4×D47C814yescomplemented
52C2×C4×Dic47C2×C411yescharacteristic
53C2×C4×Dic47D411yescharacteristic
54C2×C4×Dic47D411yescharacteristic
55C42×D47—42no—
56C47⋊#95—21no—
57C47⋊#95—21no—
58C47⋊#95—21no—
59C22×C8×C47—21no—
60C22×C8×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47C2×C411yescharacteristic
63C2×C4⋊C4×C47C2×C411yescharacteristic
64C2×C42×C47C2311yescharacteristic
65#95×C47—21no—
66C23×D47C22⋊C411yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47C22⋊C411yescharacteristic
75C22×Dic47C22⋊C411yescharacteristic
76C22×Dic47C22⋊C411yescharacteristic
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—22no—
81C2×C4×D47—22no—
82C2×C4×D47—22no—
83C2×C4×D47—24no—
84C2×C4×D47—42no—
85C2×C4×D47—42no—
86C2×C4×D47—42no—
87C2×C4×D47—42no—
88C2×C4×D47—42no—
89C2×C4×D47C2×C812yes—
90C2×C4×D47M1612yes—
91C2×C4×D47D812yes—
92C2×C4×D47SD1612yes—
93C2×C4×D47SD1612yes—
94C2×C4×D47Q1612yes—
95C2×C8×C47—22no—
96C2×C8×C47—22no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C2×C8×C47—41no—
100C2×C8×C47—41no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47C2×C812yescomplemented
106C42×C47—41no—
107C4⋊Dic47—21no—
108C4⋊Dic47—42no—
109C4⋊Dic47—41no—
110C4⋊Dic47C2×C812yescomplemented
111Dic47⋊C4—24no—
112Dic47⋊C4—42no—
113Dic47⋊C4—41no—
114Dic47⋊C4—41no—
115Dic47⋊C4—42no—
116C4×Dic47—41no—
117C4×Dic47—41no—
118C4×Dic47—41no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8—41no—
125C8×D47—48no—
126C8×D47—48no—
127C23×C47C2×C22⋊C411yescharacteristic
128C22×D47C22⋊C812yes—
129C22×D47#9912yes—
130C22×D47#10112yes—
131C22×D47#10212yes—
132C22×D47#10312yes—
133C22×D47#10412yes—
134C22×D47#10412yes—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—22no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47C22×C811yescharacteristic
148C2×C4×C47C2×M1611yescharacteristic
149C2×C4×C47C2×D811yescharacteristic
150C2×C4×C47C2×SD1611yescharacteristic
151C2×C4×C47C2×SD1611yescharacteristic
152C2×C4×C47C2×Q1611yescharacteristic
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—22no—
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—41no—
163C2×Dic47—41no—
164C2×Dic47—41no—
165C2×Dic47C22⋊C812yes—
166C2×Dic47#10212yes—
167C2×Dic47#10312yes—
168C4×D47—24no—
169C4×D47—24no—
170C4×D47—24no—
171C4×D47—24no—
172C4×D47—24no—
173C4×D47—24no—
174C4×D47—48no—
175C4×D47—84no—
176C8×C47—42no—
177C8×C47—42no—
178C47⋊C8—42no—
179C47⋊C8—42no—
180C2×#1271—471nomaximal, Sylow
181C22×C47C2×C22⋊C811yescharacteristic
182C22×C47C2×#9911yescharacteristic
183C22×C47C2×#10111yescharacteristic
184C22×C47C2×#10211yescharacteristic
185C22×C47C2×#10311yescharacteristic
186C22×C47C2×#10411yescharacteristic
187C22×C47C2×#10411yescharacteristic
188C2×D47#32414yes—
189C2×D47D4⋊C814yes—
190C2×D47Q8⋊C814yes—
191C2×D47#32714yes—
192C2×D47#32814yes—
193C2×D47#33014yes—
194C2×D47#33214yes—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—42no—
202C4×C47—81no—
203Dic47—22no—
204Dic47—22no—
205Dic47—22no—
206Dic47—42no—
207Dic47—81no—
208C2×#389—471no—
209C2×#336—471no—
210C2×#336—471no—
211#1271—471no—
212#1271—471no—
213#1271—471no—
214#1271D4711yescharacteristic, direct product factor
215C2×C47C2×#32411yescharacteristic
216C2×C47C2×D4⋊C811yescharacteristic
217C2×C47C2×Q8⋊C811yescharacteristic
218C2×C47C2×#32711yescharacteristic
219C2×C47C2×#32811yescharacteristic
220C2×C47C2×#33011yescharacteristic
221C2×C47C2×#33211yescharacteristic
222D47#127118yesdirect product factor
223C23×C8—941no—
224C23×C8—941no—
225C22×C4⋊C4—471no—
226C22×C4⋊C4—471no—
227C22×C4⋊C4—941no—
228C22×C42—471no—
229#389—471no—
230#389—471no—
231#389—471no—
232#389—941no—
233#389—941no—
234#389C2×D4711yescharacteristic
235C2×#95—941no—
236#336—471no—
237#336—471no—
238#336—941no—
239#336—941no—
240#336C2×D4711yescharacteristic
241#336C2×D4711yescharacteristic
242C47C2×#127111yescharacteristic, complemented, Sylow
243C23×C4—471no—
244C23×C4—471no—
245C23×C4—471no—
246C23×C4—941no—
247C23×C4—941no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—944no—
251C22×C8—944no—
252C22×C8—941no—
253C22×C8—941no—
254C22×C8—1882no—
255C22×C8—1882no—
256C22×C8—1882no—
257C22×C8—1882no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—471no—
260C2×C4⋊C4—474no—
261C2×C4⋊C4—471no—
262C2×C4⋊C4—942no—
263C2×C4⋊C4—941no—
264C2×C4⋊C4—941no—
265C2×C4⋊C4—941no—
266C2×C4⋊C4—941no—
267C2×C4⋊C4—941no—
268C2×C4⋊C4—1882no—
269C2×C4⋊C4—1882no—
270C2×C4⋊C4—1882no—
271C2×C4⋊C4C4×D4711yescharacteristic
272C2×C4⋊C4C4×D4711yescharacteristic
273C2×C42—471no—
274C2×C42—471no—
275C2×C42—471no—
276C2×C42—1882no—
277C2×C42C22×D4711yescharacteristic
278#95—21no—
279#95—941no—
280#95—941no—
281#95—941no—
282C24—471no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—471no—
286C22×C4—471no—
287C22×C4—471no—
288C22×C4—472no—
289C22×C4—472no—
290C22×C4—472no—
291C22×C4—472no—
292C22×C4—472no—
293C22×C4—472no—
294C22×C4—942no—
295C22×C4—942no—
296C22×C4—942no—
297C22×C4—942no—
298C22×C4—942no—
299C22×C4—942no—
300C22×C4—944no—
301C22×C4—941no—
302C22×C4—941no—
303C22×C4—1882no—
304C22×C4—1882no—
305C22×C4—1882no—
306C22×C4—1882no—
307C22×C4—1882no—
308C22×C4C2×C4×D4711yescharacteristic
309C22×C4D4×D4711yescharacteristic
310C22×C4D4×D4711yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—942no—
318C2×C8—942no—
319C2×C8—1888no—
320C2×C8—1888no—
321C2×C8—1881no—
322C2×C8—1881no—
323C2×C8—1881no—
324C2×C8—1881no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—472no—
330C4⋊C4—944no—
331C4⋊C4—941no—
332C4⋊C4—1881no—
333C4⋊C4—1882no—
334C4⋊C4—1882no—
335C4⋊C4—1882no—
336C4⋊C4—1881no—
337C4⋊C4—1881no—
338C4⋊C4C8×D4712yescomplemented
339C42—41no—
340C42—1881no—
341C42—1881no—
342C42—1881no—
343C23—472no—
344C23—472no—
345C23—472no—
346C23—472no—
347C23—472no—
348C23—472no—
349C23—472no—
350C23C22⋊C4×D4711yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—472no—
364C2×C4—472no—
365C2×C4—472no—
366C2×C4—944no—
367C2×C4—944no—
368C2×C4—944no—
369C2×C4—944no—
370C2×C4—944no—
371C2×C4—944no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—942no—
379C2×C4—3764no—
380C2×C4—1888no—
381C2×C4—1881no—
382C2×C4—1881no—
383C2×C4—1881no—
384C2×C4—1881no—
385C2×C4—1881no—
386C2×C4C2×C8×D4711yescharacteristic
387C2×C4M16×D4711yescharacteristic
388C2×C4D8×D4711yescharacteristic
389C2×C4SD16×D4711yescharacteristic
390C2×C4SD16×D4711yescharacteristic
391C2×C4Q16×D4711yescharacteristic
392C8—42no—
393C8—42no—
394C8—1882no—
395C8—1882no—
396C22—474no—
397C22—474no—
398C22—474no—
399C22—474no—
400C22—474no—
401C22—474no—
402C22—474no—
403C22C22⋊C8×D4711yescharacteristic
404C22#99×D4711yescharacteristic
405C22#101×D4711yescharacteristic
406C22#102×D4711yescharacteristic
407C22#103×D4711yescharacteristic
408C22#104×D4711yescharacteristic
409C22#104×D4711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—942no—
419C4—942no—
420C4—942no—
421C4—3761no—
422C4—1882no—
423C2—478no—
424C2#324×D4711yescharacteristic
425C2D4⋊C8×D4711yescharacteristic
426C2Q8⋊C8×D4711yescharacteristic
427C2#327×D4711yescharacteristic
428C2#328×D4711yescharacteristic
429C2#330×D4711yescharacteristic
430C2#332×D4711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1271C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1271D47
hypocenterC47C2×#1271
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #20241212C2semidirect
5. #20241211C2semidirect
6. #20241210C2semidirect
7. C47×#1271C2semidirect
51. C4⋊C4×D47C8semidirect
105. C4⋊C4×C47C2×C8semidirect
110. C4⋊Dic47C2×C8semidirect
214. #1271D47direct (N × H)
222. D47#1271direct (N × H)
242. C47C2×#1271semidirect
338. C4⋊C4C8×D47semidirect

Maximal subgroups

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

subgroupindex
#389×D472
#336×D472
#202412122
#202412112
#202412102
C47×#12712
C2×#127147