Finite Group Databasebeta

← C2×#14521865 #16860477

Subgroups — C2×#14521865 #16860477

Order 3968.

1408 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758564C211yesmaximal, characteristic, complemented
2C2×#11758567C211yesmaximal, characteristic, complemented
3#14521865C2116yesmaximal, direct product factor
4C2×#11758486C211yesmaximal, characteristic, complemented
5C2×#11758495C212yesmaximal, complemented
6C2×#11758492C212yesmaximal, complemented
7C2×#11758493C212yesmaximal, complemented
8C2×#11758527C211yesmaximal, characteristic, complemented
9C22×#92482C211yesmaximal, characteristic, complemented
10C2×Q16×D31C212yesmaximal, complemented
11C2×#11758484C211yesmaximal, characteristic, complemented
12C2×C31×#137C211yesmaximal, characteristic, complemented
13C2×#41×C31C2211yescharacteristic
14C22×Q8×C31C2211yescharacteristic
15#11758567—24no—
16#11758567C2218yescomplemented
17#11758564—24no—
18#11758564C2218yescomplemented
19C2×#92499—21no—
20C2×#92499C2212yes—
21C2×Q8×D31—21no—
22C2×Q8×D31C2212yes—
23C2×Q8×D31C2212yes—
24C2×#92497—22no—
25C2×#92497C2212yes—
26C2×#92495—22no—
27C2×#92495—21no—
28C2×#92495C2211yescharacteristic
29C2×#92495C2211yescharacteristic
30C22×Dic62—21no—
31C22×Dic62C2211yescharacteristic
32C31×#137C2218yescomplemented
33C2×Q16×C31C2212yes—
34C2×SD16×C31C2212yes—
35C2×M16×C31C2211yescharacteristic
36#11758527C2218yescomplemented
37C2×#92482C2211yescharacteristic
38C2×#92482C2212yes—
39C2×#92482C2212yes—
40C2×#92482C2218yescomplemented
41C2×#92481C2211yescharacteristic
42C2×#92480C2211yescharacteristic
43C2×#92479C2211yescharacteristic
44C22×C31⋊C8C2211yescharacteristic
45#11758495C22116yescomplemented
46Q16×D31C22116yescomplemented
47#11758493C22116yescomplemented
48#11758492C22116yescomplemented
49#11758486C2218yescomplemented
50#11758484C2218yescomplemented
51C2×Dic124C2212yes—
52C2×#92470C2212yes—
53C2×#92469C2212yes—
54C2×C8×D31C2212yes—
55#41×C31—22no—
56#41×C31C2314yes—
57C2×Q8×C31—21no—
58C2×Q8×C31—22no—
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2312yes—
61C2×Q8×C31C2314yes—
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—22no—
69C2×C22⋊D31D412yes—
70C22×Dic31—21no—
71C22×Dic31—22no—
72#92499—28no—
73#92499—24no—
74#92499C2318yes—
75Q8×D31—24no—
76Q8×D31—24no—
77Q8×D31—28no—
78Q8×D31C2318yes—
79Q8×D31C2318yes—
80#92497—216no—
81#92497—24no—
82#92497C2318yes—
83#92495—22no—
84#92495—216no—
85#92495—28no—
86#92495D414yes—
87#92495C2314yes—
88#92495C2314yes—
89C2×D124—22no—
90C2×D124D411yescharacteristic
91C2×D124C2311yescharacteristic
92C2×C4×D31—22no—
93C2×C4×D31—22no—
94C2×C4×D31—21no—
95C2×C4×D31—22no—
96C2×C4×D31C2312yes—
97C2×Dic62—21no—
98C2×Dic62—22no—
99C2×Dic62—22no—
100C2×Dic62—22no—
101C2×Dic62—28no—
102C2×Dic62D411yescharacteristic
103C2×Dic62C2312yes—
104C2×Dic62C2311yescharacteristic
105C2×Dic62C2314yes—
106Q16×C31C2318yes—
107SD16×C31C2318yes—
108M16×C31C2314yes—
109C2×C8×C31C2312yes—
110#92482C2318yes—
111#92482C2318yes—
112#92482C2314yes—
113#92481C2314yes—
114#92480C2314yes—
115#92479C2314yes—
116C2×C31⋊C8C2311yescharacteristic
117C2×C31⋊C8C2311yescharacteristic
118C2×C31⋊C8C2314yes—
119Dic124C2318yes—
120#92470C2318yes—
121#92469C2318yes—
122C8×D31C2318yes—
123C23×C31—21no—
124C23×C31C2×D411yescharacteristic
125C22×D31—21no—
126C22×D31C2×D412yes—
127Q8×C31—21no—
128Q8×C31—22no—
129Q8×C31—24no—
130Q8×C31C2412yes—
131Q8×C31C2414yes—
132D4×C31—24no—
133D4×C31—21no—
134D4×C31C2412yes—
135C2×C4×C31—21no—
136C2×C4×C31—22no—
137C2×C4×C31—24no—
138C2×C4×C31—24no—
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2×D412yes—
141C2×C4×C31C2411yescharacteristic
142C2×C4×C31C2412yes—
143C22⋊D31—24no—
144C22⋊D31—28no—
145C22⋊D31C2×D418yes—
146C2×Dic31—21no—
147C2×Dic31—22no—
148C2×Dic31—24no—
149C2×Dic31—28no—
150C2×Dic31C2×D412yes—
151D124—28no—
152D124—21no—
153D124C2×D414yes—
154D124C2412yes—
155C4×D31—28no—
156C4×D31—28no—
157C4×D31—24no—
158C4×D31—28no—
159C4×D31C2×D414yes—
160C4×D31C2414yes—
161Dic62—24no—
162Dic62—22no—
163Dic62—21no—
164Dic62—28no—
165Dic62—28no—
166Dic62C2×D414yes—
167Dic62C2414yes—
168Dic62C2412yes—
169C8×C31C2414yes—
170C31⋊C8C2412yes—
171C31⋊C8C2412yes—
172C2×#578—311nomaximal, Sylow
173C22×C31—22no—
174C22×C31—22no—
175C22×C31—42no—
176C22×C31C22×D412yes—
177C22×C31C22×D411yescharacteristic
178C2×D31—24no—
179C2×D31—22no—
180C2×D31—42no—
181C2×D31C22×D414yes—
182C4×C31—22no—
183C4×C31—24no—
184C4×C31C22×D411yescharacteristic
185C4×C31C22×D412yes—
186C4×C31C2511yescharacteristic
187Dic31—22no—
188Dic31—24no—
189Dic31C22×D414yes—
190C2×2−1+4—311no—
191C2×2−1+4—311no—
192#578—3116no—
193C2×#137—312no—
194C2×#137—312no—
195C2×#137—311no—
196C2×#137D3111yescharacteristic, complemented
197C2×#135—311no—
198C2×#135—312no—
199C22×Q16—311no—
200C22×Q16—312no—
201C2×#131—311no—
202C2×C31—22no—
203C2×C31—42no—
204C2×C31#57812yescomplemented
205C2×C31C23×D411yescharacteristic
206D31—24no—
207D31—42no—
2082−1+4—318no—
2092−1+4—318no—
2102−1+4—624no—
2112−1+4—624no—
212C2×#41—311no—
213C2×#41—312no—
214C2×#41—312no—
215C2×#41—311no—
216C2×#41—622no—
217C2×#41—621no—
218C2×#41—622no—
219C2×#41—621no—
220C2×#41C2×D3111yescharacteristic
221C22×Q8—312no—
222C22×Q8—312no—
223C22×Q8—311no—
224C22×Q8—621no—
225C22×Q8—621no—
226C22×Q8C2×D3111yescharacteristic
227#137—3116no—
228#137—3116no—
229#137—318no—
230#137C2×D3118yescomplemented
231#135—318no—
232#135—3116no—
233C2×Q16—311no—
234C2×Q16—312no—
235C2×Q16—312no—
236C2×Q16—318no—
237C2×Q16—3116no—
238C2×Q16—312no—
239C2×Q16C2×D3112yes—
240C2×SD16—311no—
241C2×SD16—311no—
242C2×SD16—312no—
243C2×SD16C2×D3112yes—
244C2×D8—311no—
245#131—318no—
246C2×M16—312no—
247C2×M16C2×D3111yescharacteristic
248C22×C8—311no—
249C22×C8—312no—
250C31C2×#57811yescharacteristic, complemented, Sylow
251#41—22no—
252#41—314no—
253#41—314no—
254#41—318no—
255#41—318no—
256#41—314no—
257#41—6216no—
258#41—628no—
259#41—624no—
260#41—624no—
261#41—6216no—
262#41—628no—
263#41—622no—
264#41C22×D3114yes—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—311no—
268C2×Q8—318no—
269C2×Q8—318no—
270C2×Q8—312no—
271C2×Q8—311no—
272C2×Q8—314no—
273C2×Q8—622no—
274C2×Q8—622no—
275C2×Q8—628no—
276C2×Q8—624no—
277C2×Q8—624no—
278C2×Q8—628no—
279C2×Q8—621no—
280C2×Q8—622no—
281C2×Q8C22×D3111yescharacteristic
282C2×Q8C22×D3112yes—
283C2×Q8C22×D3114yes—
284C2×D4—21no—
285C2×D4—312no—
286C2×D4—311no—
287C2×D4—311no—
288C2×D4—622no—
289C2×D4—622no—
290C2×D4—621no—
291C2×D4C22×D3111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—312no—
295C22×C4—622no—
296C22×C4—622no—
297C22×C4—622no—
298C22×C4—622no—
299C22×C4—621no—
300C22×C4—621no—
301C22×C4C22×D3111yescharacteristic
302Q16—314no—
303Q16—318no—
304Q16—318no—
305Q16—318no—
306Q16C22×D3118yes—
307SD16—314no—
308SD16—314no—
309SD16—318no—
310SD16C22×D3118yes—
311D8—314no—
312M16—318no—
313M16C22×D3114yes—
314C2×C8—311no—
315C2×C8—311no—
316C2×C8—314no—
317C2×C8—318no—
318C2×C8C22×D3112yes—
319C23—21no—
320C23—312no—
321C23—621no—
322C23D4×D3111yescharacteristic
323Q8—24no—
324Q8—22no—
325Q8—21no—
326Q8—314no—
327Q8—314no—
328Q8—312no—
329Q8—628no—
330Q8—628no—
331Q8—624no—
332Q8—622no—
333Q8—621no—
334Q8C23×D3112yes—
335Q8C23×D3114yes—
336D4—24no—
337D4—21no—
338D4—318no—
339D4—314no—
340D4—312no—
341D4—628no—
342D4—628no—
343D4—624no—
344D4—621no—
345D4C23×D3112yes—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—312no—
351C2×C4—314no—
352C2×C4—314no—
353C2×C4—628no—
354C2×C4—628no—
355C2×C4—628no—
356C2×C4—628no—
357C2×C4—624no—
358C2×C4—621no—
359C2×C4—622no—
360C2×C4—624no—
361C2×C4D4×D3112yes—
362C2×C4D4×D3111yescharacteristic
363C2×C4C23×D3112yes—
364C2×C4C23×D3111yescharacteristic
365C8—312no—
366C8—312no—
367C8C23×D3114yes—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—314no—
372C22—624no—
373C22—622no—
374C22—1242no—
375C22C2×D4×D3112yes—
376C22C2×D4×D3111yescharacteristic
377C4—22no—
378C4—24no—
379C4—314no—
380C4—622no—
381C4—624no—
382C4C2×D4×D3112yes—
383C4C2×D4×D3111yescharacteristic
384C4C24×D3111yescharacteristic
385C2—22no—
386C2—42no—
387C2—624no—
388C2—1242no—
389C2#1452186512yesdirect product factor
390C2C22×D4×D3111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC2×C31×#137C2
socleC22×C31C22×D4
hypercenterC2×#137D31
hypocenterC31C2×#578
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11758564C2semidirect
2. C2×#11758567C2semidirect
3. #14521865C2direct (N × H)
4. C2×#11758486C2semidirect
5. C2×#11758495C2semidirect
6. C2×#11758492C2semidirect
7. C2×#11758493C2semidirect
8. C2×#11758527C2semidirect
9. C22×#92482C2semidirect
10. C2×Q16×D31C2semidirect
11. C2×#11758484C2semidirect
12. C2×C31×#137C2semidirect
16. #11758567C22semidirect
18. #11758564C22semidirect
32. C31×#137C22semidirect
36. #11758527C22semidirect
40. C2×#92482C22semidirect
45. #11758495C22semidirect
46. Q16×D31C22semidirect
47. #11758493C22semidirect
48. #11758492C22semidirect
49. #11758486C22semidirect
50. #11758484C22semidirect
196. C2×#137D31semidirect
204. C2×C31#578semidirect
230. #137C2×D31semidirect
250. C31C2×#578semidirect
389. C2#14521865direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585642
C2×#117585672
#145218652
C2×#117584862
C2×#117584952
C2×#117584922
C2×#117584932
C2×#117585272
C22×#924822
C2×Q16×D312
C2×#117584842
C2×C31×#1372
C2×#57831