Finite Group Databasebeta

← C2×#15689289 #20252710

Subgroups — C2×#15689289 #20252710

Order 6016.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094070C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3C2×#13094020C211yesmaximal, characteristic, complemented
4#15689289C218yesmaximal, direct product factor
5C2×#13093951C211yesmaximal, characteristic, complemented
6C2×#13093950C211yesmaximal, characteristic, complemented
7C2×#13093940C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
9#13094070—22no—
10#13094070—22no—
11#13094070—22no—
12#13094070C2214yescomplemented
13C2×#10625354—21no—
14C2×#10625350—21no—
15C2×#10625350C2211yescharacteristic
16C22×D188—21no—
17C22×D188C2211yescharacteristic
18C22×C22⋊D47—22no—
19C2×D4×D47—22no—
20C2×D4×D47—21no—
21#13094050—22no—
22#13094050C2214yescomplemented
23C2×#10625335—21no—
24C2×#10625334—21no—
25C2×#10625329C2211yescharacteristic, complemented
26#13094020—22no—
27#13094020C2214yescomplemented
28C2×C4×Dic47C2211yescharacteristic, complemented
29#13093951C2214yescomplemented
30#13093950C2214yescomplemented
31#13093940C2214yescomplemented
32C2×#41×C47C2211yescharacteristic
33C22×D4×C47C2211yescharacteristic, complemented
34AGL(1,ℤ/8)×C47—22no—
35AGL(1,ℤ/8)×C47C2214yescomplemented
36C2×SD16×C47—21no—
37C2×D8×C47—21no—
38C2×M16×C47C2211yescharacteristic, complemented
39C24×C47—21no—
40C23×D47—22no—
41C23×D47D412yes—
42#41×C47—21no—
43#41×C47—21no—
44#41×C47D412yescomplemented
45#41×C47C2312yes—
46C2×Q8×C47D411yescharacteristic, complemented
47C2×D4×C47—21no—
48C2×D4×C47—21no—
49C2×D4×C47—21no—
50C2×D4×C47—21no—
51C2×D4×C47—21no—
52C2×D4×C47—21no—
53C2×D4×C47D411yescharacteristic, complemented
54C2×D4×C47C2312yescomplemented
55C22×C4×C47—21no—
56C22×C4×C47C2311yescharacteristic
57C2×C22⋊D47—22no—
58C2×C22⋊D47—21no—
59C2×C22⋊D47—28no—
60C2×C22⋊D47—48no—
61C22×Dic47—21no—
62#10625354—24no—
63#10625354—24no—
64D4×D47—28no—
65D4×D47—24no—
66D4×D47—28no—
67D4×D47—24no—
68#10625350—24no—
69#10625350—21no—
70#10625350—21no—
71#10625350—24no—
72#10625350D412yescomplemented
73#10625350C2312yes—
74C2×D188—22no—
75C2×D188—24no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—24no—
81C2×D188D412yes—
82C2×D188D411yescharacteristic, complemented
83C2×D188C2312yes—
84C2×C4×D47—22no—
85C2×C4×D47—21no—
86C2×Dic94D411yescharacteristic, complemented
87SD16×C47—24no—
88D8×C47—24no—
89M16×C47—21no—
90M16×C47C2312yescomplemented
91C2×C8×C47—21no—
92#10625335—24no—
93#10625334—24no—
94C4×Dic47—21no—
95C4×Dic47C2312yescomplemented
96#10625329—21no—
97#10625329C2312yescomplemented
98C2×C47⋊C8—21no—
99C23×C47—21no—
100C23×C47—22no—
101C23×C47—44no—
102C23×C47—41no—
103C23×C47—41no—
104C23×C47C2×D411yescharacteristic
105C22×D47—22no—
106C22×D47—21no—
107C22×D47—28no—
108C22×D47—22no—
109C22×D47—44no—
110C22×D47—84no—
111C22×D47C2×D414yes—
112Q8×C47—21no—
113Q8×C47C2×D412yescomplemented
114D4×C47—22no—
115D4×C47—22no—
116D4×C47—21no—
117D4×C47—22no—
118D4×C47—22no—
119D4×C47—41no—
120D4×C47—41no—
121D4×C47C2×D412yescomplemented
122C2×C4×C47—21no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—28no—
132C22⋊D47—22no—
133C22⋊D47—22no—
134C22⋊D47—416no—
135C2×Dic47—24no—
136C2×Dic47—21no—
137C2×Dic47—22no—
138D188—28no—
139D188—22no—
140D188—21no—
141D188—22no—
142D188—22no—
143D188—22no—
144D188C2×D412yescomplemented
145C4×D47—28no—
146C4×D47—22no—
147C4×D47—22no—
148Dic94—21no—
149Dic94C2×D412yescomplemented
150C8×C47—22no—
151C47⋊C8—22no—
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—44no—
155C22×C47—42no—
156C22×C47—42no—
157C22×C47—82no—
158C22×C47—82no—
159C22×C47#12011yescharacteristic
160C22×C47#12011yescharacteristic
161C22×C47C22×D411yescharacteristic
162C2×D47—24no—
163C2×D47—22no—
164C2×D47—44no—
165C2×D47—42no—
166C2×D47—44no—
167C2×D47—82no—
168C2×D47—88no—
169C4×C47—22no—
170C4×C47#12011yescharacteristic
171C4×C47#12011yescharacteristic
172C4×C47C22×D411yescharacteristic
173C4×C47C22×D411yescharacteristic
174Dic47—24no—
175Dic47—22no—
176C2×#453—471nomaximal, Sylow
177C2×C47—21no—
178C2×C47—21no—
179C2×C47—42no—
180C2×C47—82no—
181C2×C47#45312yescomplemented
182C2×C47C2×#12011yescharacteristic
183D47—44no—
184D47—42no—
185C2×H(5,𝔽2)—471no—
186C2×AGL(1,ℤ/8)—471no—
187C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
188C2×#127—471no—
189#453—478no—
190C2×#104—471no—
191C2×#104—471no—
192C2×#100—471no—
193C47C2×#45311yescharacteristic, complemented, Sylow
194H(5,𝔽2)—474no—
195H(5,𝔽2)—942no—
196H(5,𝔽2)—942no—
197H(5,𝔽2)—942no—
198C2×#41—471no—
199C2×#41—941no—
200C2×#41—941no—
201C2×#41C2×D4711yescharacteristic
202C22×D4—471no—
203C22×D4—941no—
204C22×D4—942no—
205C22×D4—941no—
206C22×D4—942no—
207C22×D4C2×D4711yescharacteristic, complemented
208AGL(1,ℤ/8)—22no—
209AGL(1,ℤ/8)—474no—
210AGL(1,ℤ/8)—942no—
211AGL(1,ℤ/8)C2×D4714yescomplemented
212C2×SD16—21no—
213C2×SD16—941no—
214C2×D8—21no—
215C2×D8—941no—
216C2×M16—471no—
217C2×M16C2×D4711yescharacteristic, complemented
218#127—474no—
219#127—942no—
220C2×C42—471no—
221#104—474no—
222#104—474no—
223#100—474no—
224C24—21no—
225C24—472no—
226C24—942no—
227#41—21no—
228#41—21no—
229#41—472no—
230#41—472no—
231#41—944no—
232#41—944no—
233#41—944no—
234#41—944no—
235#41—941no—
236#41—941no—
237#41C22⋊D4712yescomplemented
238#41C22×D4712yes—
239C2×Q8—471no—
240C2×Q8C22⋊D4711yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—471no—
248C2×D4—472no—
249C2×D4—472no—
250C2×D4—944no—
251C2×D4—942no—
252C2×D4—944no—
253C2×D4—948no—
254C2×D4—948no—
255C2×D4—944no—
256C2×D4—942no—
257C2×D4—941no—
258C2×D4—944no—
259C2×D4—948no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—1888no—
265C2×D4C22⋊D4711yescharacteristic, complemented
266C2×D4C22×D4712yescomplemented
267C22×C4—21no—
268C22×C4—942no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4C22×D4711yescharacteristic
272SD16—24no—
273SD16—944no—
274D8—24no—
275D8—944no—
276M16—21no—
277M16—472no—
278M16—941no—
279M16C22×D4712yescomplemented
280C2×C8—21no—
281C2×C8—941no—
282C42—472no—
283C42—941no—
284C23—21no—
285C23—22no—
286C23—44no—
287C23—41no—
288C23—41no—
289C23—474no—
290C23—948no—
291C23—942no—
292C23—941no—
293C23—942no—
294C23—3764no—
295C23—1884no—
296C23D4×D4711yescharacteristic
297Q8—21no—
298Q8—472no—
299Q8—941no—
300Q8C2×C22⋊D4712yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—22no—
305D4—22no—
306D4—41no—
307D4—41no—
308D4—472no—
309D4—948no—
310D4—948no—
311D4—942no—
312D4—942no—
313D4—941no—
314D4—942no—
315D4—942no—
316D4—942no—
317D4—942no—
318D4—18816no—
319D4C2×C22⋊D4712yescomplemented
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—948no—
324C2×C4—944no—
325C2×C4—941no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4D4×D4711yescharacteristic
330C2×C4D4×D4711yescharacteristic
331C2×C4D4×D4711yescharacteristic
332C2×C4C2×C22⋊D4711yescharacteristic
333C2×C4C2×C22⋊D4711yescharacteristic
334C2×C4C23×D4711yescharacteristic
335C8—22no—
336C8—942no—
337C22—22no—
338C22—22no—
339C22—44no—
340C22—42no—
341C22—42no—
342C22—82no—
343C22—82no—
344C22—942no—
345C22—944no—
346C22—3762no—
347C22—3768no—
348C22—1884no—
349C22—1882no—
350C22—1884no—
351C22#1309399211yescharacteristic
352C22#1309399211yescharacteristic
353C22C2×D4×D4711yescharacteristic
354C4—22no—
355C4—944no—
356C4—942no—
357C4#1309399211yescharacteristic
358C4#1309399211yescharacteristic
359C4C2×D4×D4711yescharacteristic
360C4C22×C22⋊D4711yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—82no—
365C2—1882no—
366C2—1884no—
367C2#1568928912yesdirect product factor
368C2C2×#1309399211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47#120
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47C2×#453
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094050C2semidirect
3. C2×#13094020C2semidirect
4. #15689289C2direct (N × H)
5. C2×#13093951C2semidirect
6. C2×#13093950C2semidirect
7. C2×#13093940C2semidirect
8. C2×AGL(1,ℤ/8)×C47C2semidirect
12. #13094070C22semidirect
22. #13094050C22semidirect
25. C2×#10625329C22semidirect
27. #13094020C22semidirect
28. C2×C4×Dic47C22semidirect
29. #13093951C22semidirect
30. #13093950C22semidirect
31. #13093940C22semidirect
33. C22×D4×C47C22semidirect
35. AGL(1,ℤ/8)×C47C22semidirect
38. C2×M16×C47C22semidirect
44. #41×C47D4semidirect
46. C2×Q8×C47D4semidirect
53. C2×D4×C47D4semidirect
54. C2×D4×C47C23semidirect
72. #10625350D4semidirect
82. C2×D188D4semidirect
86. C2×Dic94D4semidirect
90. M16×C47C23semidirect
95. C4×Dic47C23semidirect
97. #10625329C23semidirect
113. Q8×C47C2×D4semidirect
121. D4×C47C2×D4semidirect
144. D188C2×D4semidirect
149. Dic94C2×D4semidirect
181. C2×C47#453semidirect
187. C2×AGL(1,ℤ/8)D47semidirect
193. C47C2×#453semidirect
207. C22×D4C2×D47semidirect
211. AGL(1,ℤ/8)C2×D47semidirect
217. C2×M16C2×D47semidirect
237. #41C22⋊D47semidirect
240. C2×Q8C22⋊D47semidirect
265. C2×D4C22⋊D47semidirect
266. C2×D4C22×D47semidirect
279. M16C22×D47semidirect
300. Q8C2×C22⋊D47semidirect
319. D4C2×C22⋊D47semidirect
367. C2#15689289direct (N × H)