Finite Group Databasebeta

← C2×#14541932 #17940844

Subgroups — C2×#14541932 #17940844

Order 4352.

2074 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763626C211yesmaximal, characteristic, complemented
2C2×#11763614C211yesmaximal, characteristic, complemented
3#14541932C2116yesmaximal, direct product factor
4C2×#11763252C213yesmaximal, complemented
5C2×#11763247C213yesmaximal, complemented
6C2×#11763241C213yesmaximal, complemented
7C22×#10587471C213yesmaximal, complemented
8C2×C17×#504C211yesmaximal, characteristic, complemented
9C2×#10587697—21no—
10C2×#10587696—21no—
11#11763626—24no—
12#11763626C2218yescomplemented
13#11763614—24no—
14#11763614C2218yescomplemented
15C2×#10587595—23no—
16C2×#10587594—23no—
17C2×#10587590C2213yes—
18C2×#10587590C2213yescomplemented
19C22×Dic68C2213yescomplemented
20C22×D136C2213yes—
21#11763252C22124yescomplemented
22#11763247C22124yescomplemented
23#11763241C22124yescomplemented
24C2×Dic136C2213yescomplemented
25C2×#10587471C2213yescomplemented
26C2×#10587471C2216yescomplemented
27C2×#10587471C2211yescharacteristic, complemented
28C2×#10587471C22124yescomplemented
29C2×D272C2213yescomplemented
30C2×C17×#131C2211yescharacteristic
31C17×#504C2218yescomplemented
32C2×C17×M32C2213yescomplemented
33C22×C16×C17C2213yescomplemented
34C2×#41×C17D411yescharacteristic
35#10587697—28no—
36#10587697—44no—
37#10587696—28no—
38#10587696—44no—
39C2×#63256—41no—
40C2×Q8×D17—41no—
41C2×#63254—43no—
42C2×D4×D17—43no—
43C2×#63252—23no—
44C2×#63252—23no—
45C22×D68—23no—
46C22×Dic34—23no—
47C17×#131D414yes—
48C17×#131C2314yes—
49C2×M16×C17D413yes—
50C22×C8×C17C2313yes—
51#10587595—224no—
52#10587594—224no—
53C2×Dic68—23no—
54C2×Dic68—26no—
55C2×Dic68C2313yes—
56C2×Dic68C2311yescharacteristic
57C2×Dic68C23112yescomplemented
58#10587590—26no—
59#10587590—26no—
60#10587590C23112yes—
61#10587590C23112yescomplemented
62C2×D136—23no—
63C2×D136—26no—
64C2×D136C2311yescharacteristic
65C2×D136C2313yes—
66C2×D136C23112yes—
67C2×#63219—23no—
68C2×#63219—23no—
69C17×M32C23112yescomplemented
70C2×C16×C17C2311yescharacteristic
71C2×C16×C17C2313yes—
72C2×C16×C17C23112yescomplemented
73Dic136C23112yescomplemented
74#10587471C23112yescomplemented
75#10587471C23124yescomplemented
76#10587471C2314yescomplemented
77D272C23112yescomplemented
78C23×D17—43no—
79#41×C17D814yes—
80#41×C17C2×D414yes—
81C2×Q8×C17D811yescharacteristic
82C2×D4×C17D813yes—
83C22×C4×C17C2×D413yes—
84C2×C22⋊D17—43no—
85C2×C22⋊D17—43no—
86C22×Dic17—43no—
87#63256—48no—
88Q8×D17—48no—
89#63254—424no—
90D4×D17—424no—
91#63252—212no—
92#63252—212no—
93#63252—46no—
94#63252—46no—
95C2×D68—23no—
96C2×D68—212no—
97C2×D68—21no—
98C2×D68—43no—
99C2×D68—46no—
100C2×C4×D17—43no—
101C2×C4×D17—43no—
102C2×Dic34—23no—
103C2×Dic34—212no—
104C2×Dic34—21no—
105C2×Dic34—43no—
106C2×Dic34—46no—
107M16×C17C2×D4112yes—
108C2×C8×C17C2×D413yes—
109C2×C8×C17C2×D416yes—
110C2×C8×C17C2411yescharacteristic
111C2×C8×C17C2416yes—
112Dic68—21no—
113Dic68—23no—
114Dic68—212no—
115Dic68C2416yes—
116Dic68C2412yes—
117D136—23no—
118D136—212no—
119D136—21no—
120D136C2412yes—
121D136C2416yes—
122#63219—212no—
123#63219—212no—
124C16×C17C2416yes—
125C16×C17C2412yes—
126C2×#3416—171nomaximal, Sylow
127C23×C17C2×D813yes—
128C22×D17—41no—
129C22×D17—43no—
130C22×D17—412no—
131C22×D17—166no—
132Q8×C17C2×D814yes—
133D4×C17C2×D8112yes—
134C2×C4×C17C2×D813yes—
135C2×C4×C17C2×D816yes—
136C2×C4×C17C22×D411yescharacteristic
137C2×C4×C17C22×D416yes—
138C22⋊D17—412no—
139C22⋊D17—412no—
140C2×Dic17—43no—
141C2×Dic17—412no—
142C2×Dic17—41no—
143D68—26no—
144D68—22no—
145D68—43no—
146D68—412no—
147D68—41no—
148C4×D17—412no—
149C4×D17—412no—
150Dic34—26no—
151Dic34—22no—
152Dic34—43no—
153Dic34—412no—
154Dic34—41no—
155C8×C17C22×D411yescharacteristic
156C8×C17C22×D416yes—
157C8×C17C2511yescharacteristic
158C2×#578—171no—
159C2×#576—171no—
160#3416—1716no—
161C2×#510—173no—
162C2×#509—173no—
163C2×#508—173no—
164C22×SD32—173no—
165C2×#504D1711yescharacteristic, complemented
166C22×C17—26no—
167C22×C17C22×D816yes—
168C22×C17C22×D811yescharacteristic
169C2×D17—42no—
170C2×D17—46no—
171C2×D17—82no—
172C2×D17—86no—
173C2×D17—1612no—
174C4×C17C22×D811yescharacteristic
175C4×C17C22×D816yes—
176C4×C17C23×D411yescharacteristic
177Dic17—46no—
178Dic17—42no—
179C2×2−1+4—341no—
180C2×H(5,𝔽2)—341no—
181#578—178no—
182#578—344no—
183#576—178no—
184#576—344no—
185C2×#137—343no—
186C2×AGL(1,ℤ/8)—343no—
187C2×#135—173no—
188C2×#135—173no—
189C22×Q16—173no—
190C22×D8—173no—
191C2×#131C2×D1711yescharacteristic
192#510—1724no—
193#509—1724no—
194#508—1724no—
195C2×Q32—173no—
196C2×SD32—173no—
197C2×SD32—176no—
198C2×SD32—171no—
199C2×SD32—1724no—
200C2×D16—173no—
201#504C2×D1718yescomplemented
202C2×M32C2×D1713yescomplemented
203C22×C16C2×D1713yescomplemented
204C2×C17—26no—
205C2×C17#341612yescomplemented
206C2×C17C23×D811yescharacteristic
207D17—82no—
208D17—86no—
2092−1+4—348no—
2102−1+4—684no—
211H(5,𝔽2)—348no—
212H(5,𝔽2)—684no—
213C2×#41—343no—
214C2×#41—343no—
215C2×#41—681no—
216C2×#41—683no—
217C2×#41D6811yescharacteristic
218C22×Q8—343no—
219C22×Q8—681no—
220C22×D4—343no—
221C22×D4—683no—
222#137—3424no—
223AGL(1,ℤ/8)—3424no—
224#135—1712no—
225#135—1712no—
226#135—346no—
227#135—346no—
228C2×Q16—173no—
229C2×Q16—1712no—
230C2×Q16—171no—
231C2×Q16—343no—
232C2×Q16—346no—
233C2×SD16—343no—
234C2×SD16—343no—
235C2×D8—173no—
236C2×D8—1712no—
237C2×D8—171no—
238C2×D8—343no—
239C2×D8—346no—
240#131D6814yes—
241#131C22×D1714yes—
242C2×M16D6813yes—
243C22×C8C22×D1713yes—
244Q32—1712no—
245SD32—1712no—
246SD32—1724no—
247SD32—174no—
248D16—1712no—
249M32C22×D17112yescomplemented
250C2×C16C22×D1711yescharacteristic
251C2×C16C22×D1713yes—
252C2×C16C22×D17112yescomplemented
253C17C2×#341611yescharacteristic, complemented, Sylow
254C24—683no—
255#41—3412no—
256#41—3412no—
257#41—688no—
258#41—6824no—
259#41—686no—
260#41—686no—
261#41D13614yes—
262#41C2×D6814yes—
263C2×Q8—341no—
264C2×Q8—343no—
265C2×Q8—3412no—
266C2×Q8—688no—
267C2×Q8—683no—
268C2×Q8—686no—
269C2×Q8D13611yescharacteristic
270C2×D4—343no—
271C2×D4—3412no—
272C2×D4—341no—
273C2×D4—683no—
274C2×D4—683no—
275C2×D4—6824no—
276C2×D4—683no—
277C2×D4—686no—
278C2×D4D13613yes—
279C22×C4—683no—
280C22×C4—683no—
281C22×C4—683no—
282C22×C4C2×D6813yes—
283Q16—176no—
284Q16—172no—
285Q16—343no—
286Q16—3412no—
287Q16—341no—
288SD16—3412no—
289SD16—3412no—
290D8—172no—
291D8—176no—
292D8—343no—
293D8—3412no—
294D8—341no—
295M16C2×D68112yes—
296C2×C8C2×D6813yes—
297C2×C8C2×D6816yes—
298C2×C8C23×D1711yescharacteristic
299C2×C8C23×D1716yes—
300C16C23×D1712yes—
301C16C23×D1716yes—
302C23—2726no—
303C23—6812no—
304C23—681no—
305C23—683no—
306C23C2×D13613yes—
307Q8—342no—
308Q8—346no—
309Q8—6812no—
310Q8—683no—
311Q8—681no—
312Q8C2×D13614yes—
313D4—346no—
314D4—342no—
315D4—6812no—
316D4—6812no—
317D4—6812no—
318D4—683no—
319D4—681no—
320D4C2×D136112yes—
321C2×C4—6812no—
322C2×C4—681no—
323C2×C4—683no—
324C2×C4—6812no—
325C2×C4—6812no—
326C2×C4C2×D13616yes—
327C2×C4C2×D13613yes—
328C2×C4C22×D6816yes—
329C2×C4C22×D6811yescharacteristic
330C8C22×D6811yescharacteristic
331C8C22×D6816yes—
332C8C24×D1711yescharacteristic
333C22—26no—
334C22—27212no—
335C22—682no—
336C22—686no—
337C22—1366no—
338C22—1362no—
339C22C22×D13616yes—
340C22C22×D13611yescharacteristic
341C4—682no—
342C4—686no—
343C4C22×D13616yes—
344C4C22×D13611yescharacteristic
345C4C23×D6811yescharacteristic
346C2—26no—
347C2—1366no—
348C2—1362no—
349C2#1454193212yesdirect product factor
350C2C23×D13611yescharacteristic
subgroupG/H
centerC22C22×D136
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC2×C17×#504C2
socleC22×C17C22×D8
hypercenterC2×#504D17
hypocenterC17C2×#3416
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C2×#11763626C2semidirect
2. C2×#11763614C2semidirect
3. #14541932C2direct (N × H)
4. C2×#11763252C2semidirect
5. C2×#11763247C2semidirect
6. C2×#11763241C2semidirect
7. C22×#10587471C2semidirect
8. C2×C17×#504C2semidirect
12. #11763626C22semidirect
14. #11763614C22semidirect
18. C2×#10587590C22semidirect
19. C22×Dic68C22semidirect
21. #11763252C22semidirect
22. #11763247C22semidirect
23. #11763241C22semidirect
24. C2×Dic136C22semidirect
25. C2×#10587471C22semidirect
26. C2×#10587471C22semidirect
27. C2×#10587471C22semidirect
28. C2×#10587471C22semidirect
29. C2×D272C22semidirect
31. C17×#504C22semidirect
32. C2×C17×M32C22semidirect
33. C22×C16×C17C22semidirect
57. C2×Dic68C23semidirect
61. #10587590C23semidirect
69. C17×M32C23semidirect
72. C2×C16×C17C23semidirect
73. Dic136C23semidirect
74. #10587471C23semidirect
75. #10587471C23semidirect
76. #10587471C23semidirect
77. D272C23semidirect
165. C2×#504D17semidirect
201. #504C2×D17semidirect
202. C2×M32C2×D17semidirect
203. C22×C16C2×D17semidirect
205. C2×C17#3416semidirect
249. M32C22×D17semidirect
252. C2×C16C22×D17semidirect
253. C17C2×#3416semidirect
349. C2#14541932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117636262
C2×#117636142
#145419322
C2×#117632522
C2×#117632472
C2×#117632412
C22×#105874712
C2×C17×#5042
C2×#341617