Finite Group Databasebeta

← C2×#15689292 #20252713

Subgroups — C2×#15689292 #20252713

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×#13094052C211yesmaximal, characteristic, complemented
3C2×#13094049C211yesmaximal, characteristic, complemented
4C2×#13094021C211yesmaximal, characteristic, complemented
5#15689292C218yesmaximal, direct product factor
6C2×#13093952C211yesmaximal, characteristic, complemented
7C2×#13093940C211yesmaximal, characteristic, complemented
8C2×#104×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×D188—22no—
18C22×D188C2211yescharacteristic
19C22×D188C2211yescharacteristic, complemented
20C2×D4×D47—22no—
21C2×D4×D47—21no—
22#13094052—22no—
23#13094052C2214yescomplemented
24#13094049—22no—
25#13094049C2214yescomplemented
26C2×#10625325—21no—
27C2×#10625336—21no—
28C2×D376—21no—
29C2×#10625334—21no—
30C2×#10625329C2211yescharacteristic, complemented
31#13094021—22no—
32#13094021C2214yescomplemented
33#13093952C2214yescomplemented
34#13093940C2214yescomplemented
35C2×#41×C47C2211yescharacteristic
36C2×M16×C47C2211yescharacteristic, complemented
37C2×C42×C47C2211yescharacteristic, complemented
38#104×C47C2214yescomplemented
39C23×D47—22no—
40C23×D47—21no—
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×C47D411yescharacteristic, complemented
49C22×C4×C47—21no—
50C22×C4×C47—21no—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—22no—
53C2×C22⋊D47—21no—
54#10625354—24no—
55#10625354—24no—
56D4×D47—28no—
57D4×D47—24no—
58D4×D47—28no—
59D4×D47—24no—
60#10625350—24no—
61#10625350—21no—
62#10625350—21no—
63#10625350—24no—
64#10625350D412yescomplemented
65#10625350C2312yes—
66C2×D188—22no—
67C2×D188—24no—
68C2×D188—21no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—24no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—28no—
78C2×D188—21no—
79C2×D188—48no—
80C2×D188D412yes—
81C2×D188D411yescharacteristic, complemented
82C2×D188C2312yes—
83C2×D188C2312yescomplemented
84C2×C4×D47—22no—
85C2×C4×D47—21no—
86C2×Dic94D411yescharacteristic, complemented
87M16×C47—21no—
88M16×C47C2312yescomplemented
89C2×C8×C47—21no—
90C42×C47—21no—
91C42×C47C2312yescomplemented
92#10625336—24no—
93#10625334—24no—
94#10625329—21no—
95#10625329C2312yescomplemented
96C2×C47⋊C8—21no—
97D376—24no—
98#10625325—24no—
99C23×C47—21no—
100C23×C47C2×D411yescharacteristic
101C22×D47—22no—
102C22×D47—21no—
103C22×D47—28no—
104C22×D47—22no—
105C22×D47—22no—
106C22×D47—44no—
107C22×D47—44no—
108C22×D47—41no—
109C22×D47—41no—
110C22×D47—84no—
111C22×D47C2×D414yes—
112Q8×C47—21no—
113Q8×C47C2×D412yescomplemented
114D4×C47—22no—
115D4×C47—22no—
116D4×C47—21no—
117D4×C47C2×D412yescomplemented
118C2×C4×C47—24no—
119C2×C4×C47—21no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—28no—
130C22⋊D47—22no—
131C22⋊D47—22no—
132C2×Dic47—21no—
133D188—28no—
134D188—22no—
135D188—21no—
136D188—22no—
137D188—22no—
138D188—22no—
139D188—22no—
140D188—22no—
141D188—416no—
142D188—41no—
143D188—41no—
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—42no—
155C22×C47#12011yescharacteristic
156C22×C47#12011yescharacteristic
157C22×C47C22×D411yescharacteristic
158C2×D47—24no—
159C2×D47—22no—
160C2×D47—44no—
161C2×D47—42no—
162C2×D47—44no—
163C2×D47—44no—
164C2×D47—42no—
165C2×D47—82no—
166C2×D47—88no—
167C2×D47—82no—
168C2×D47—82no—
169C4×C47—24no—
170C4×C47—22no—
171C4×C47#12011yescharacteristic
172C4×C47#12011yescharacteristic
173C4×C47C22×D411yescharacteristic
174C4×C47C22×D411yescharacteristic
175Dic47—22no—
176C2×#453—471nomaximal, Sylow
177C2×C47—21no—
178C2×C47—21no—
179C2×C47—42no—
180C2×C47#45312yescomplemented
181C2×C47C2×#12011yescharacteristic
182D47—44no—
183D47—42no—
184D47—82no—
185C2×H(5,𝔽2)—471no—
186C2×AGL(1,ℤ/8)—471no—
187C2×AGL(1,ℤ/8)—471no—
188C2×#127—471no—
189#453—478no—
190C2×#104—471no—
191C2×#104D4711yescharacteristic, complemented
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—471no—
204C22×D4—941no—
205C22×D4—942no—
206C22×D4—942no—
207C22×D4—941no—
208AGL(1,ℤ/8)—474no—
209AGL(1,ℤ/8)—474no—
210AGL(1,ℤ/8)—942no—
211AGL(1,ℤ/8)—942no—
212C2×SD16—941no—
213C2×SD16—941no—
214C2×D8—941no—
215C2×D8—941no—
216C2×M16—471no—
217C2×M16C2×D4711yescharacteristic, complemented
218#127—474no—
219#127—942no—
220C2×C42C2×D4711yescharacteristic, complemented
221#104—474no—
222#104C2×D4714yescomplemented
223#100—474no—
224C24—472no—
225C24—942no—
226C24—941no—
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#41D18812yescomplemented
238#41C22×D4712yes—
239C2×Q8—471no—
240C2×Q8D18811yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—471no—
243C2×D4—472no—
244C2×D4—472no—
245C2×D4—472no—
246C2×D4—944no—
247C2×D4—942no—
248C2×D4—944no—
249C2×D4—948no—
250C2×D4—948no—
251C2×D4—948no—
252C2×D4—944no—
253C2×D4—942no—
254C2×D4—941no—
255C2×D4—944no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—1888no—
266C2×D4D18811yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—942no—
270C22×C4—941no—
271C22×C4C22×D4711yescharacteristic
272SD16—944no—
273SD16—944no—
274D8—944no—
275D8—944no—
276M16—21no—
277M16—472no—
278M16—941no—
279M16C22×D4712yescomplemented
280C2×C8—21no—
281C2×C8—941no—
282C42—21no—
283C42C22×D4712yescomplemented
284C23—21no—
285C23—474no—
286C23—948no—
287C23—942no—
288C23—941no—
289C23—942no—
290C23—942no—
291C23—3764no—
292C23—1884no—
293C23—1884no—
294C23—1881no—
295C23—1881no—
296C23D4×D4711yescharacteristic
297Q8—21no—
298Q8—472no—
299Q8—941no—
300Q8C2×D18812yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—472no—
305D4—948no—
306D4—948no—
307D4—942no—
308D4—942no—
309D4—941no—
310D4—942no—
311D4—942no—
312D4—942no—
313D4—942no—
314D4—942no—
315D4—942no—
316D4—18816no—
317D4—1881no—
318D4—1881no—
319D4C2×D18812yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—948no—
326C2×C4—941no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4C2×D18811yescharacteristic
330C2×C4C2×D18811yescharacteristic
331C2×C4D4×D4711yescharacteristic
332C2×C4D4×D4711yescharacteristic
333C2×C4D4×D4711yescharacteristic
334C2×C4C23×D4711yescharacteristic
335C8—22no—
336C8—942no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—942no—
341C22—944no—
342C22—3762no—
343C22—3762no—
344C22—3768no—
345C22—3762no—
346C22—1884no—
347C22—1884no—
348C22—1882no—
349C22—1882no—
350C22—1884no—
351C22#1309399411yescharacteristic
352C22#1309399411yescharacteristic
353C22C2×D4×D4711yescharacteristic
354C4—24no—
355C4—22no—
356C4—942no—
357C4#1309399411yescharacteristic
358C4#1309399411yescharacteristic
359C4C2×D4×D4711yescharacteristic
360C4C22×D18811yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—3762no—
365C2—1882no—
366C2—1884no—
367C2#1568929212yesdirect product factor
368C2C2×#1309399411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47C2×#453
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094052C2semidirect
3. C2×#13094049C2semidirect
4. C2×#13094021C2semidirect
5. #15689292C2direct (N × H)
6. C2×#13093952C2semidirect
7. C2×#13093940C2semidirect
8. C2×#104×C47C2semidirect
12. #13094070C22semidirect
19. C22×D188C22semidirect
23. #13094052C22semidirect
25. #13094049C22semidirect
30. C2×#10625329C22semidirect
32. #13094021C22semidirect
33. #13093952C22semidirect
34. #13093940C22semidirect
36. C2×M16×C47C22semidirect
37. C2×C42×C47C22semidirect
38. #104×C47C22semidirect
44. #41×C47D4semidirect
46. C2×Q8×C47D4semidirect
48. C2×D4×C47D4semidirect
64. #10625350D4semidirect
81. C2×D188D4semidirect
83. C2×D188C23semidirect
86. C2×Dic94D4semidirect
88. M16×C47C23semidirect
91. C42×C47C23semidirect
95. #10625329C23semidirect
113. Q8×C47C2×D4semidirect
117. D4×C47C2×D4semidirect
144. D188C2×D4semidirect
149. Dic94C2×D4semidirect
180. C2×C47#453semidirect
191. C2×#104D47semidirect
193. C47C2×#453semidirect
217. C2×M16C2×D47semidirect
220. C2×C42C2×D47semidirect
222. #104C2×D47semidirect
237. #41D188semidirect
240. C2×Q8D188semidirect
266. C2×D4D188semidirect
279. M16C22×D47semidirect
283. C42C22×D47semidirect
300. Q8C2×D188semidirect
319. D4C2×D188semidirect
367. C2#15689292direct (N × H)