Finite Group Databasebeta

← C2×#14541636 #17914737

Subgroups — C2×#14541636 #17914737

Order 4352.

2286 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763474C212yesmaximal, complemented
2#14541636C2116yesmaximal, direct product factor
3C2×#11763213C212yesmaximal, complemented
4C2×#11763088C214yesmaximal, complemented
5C2×#11763086C212yesmaximal, complemented
6C2×C8×Dic34C211yesmaximal, characteristic, complemented
7C2×C4×D136C211yesmaximal, characteristic
8C2×#11762891C212yesmaximal
9C2×C17×#500C211yesmaximal, characteristic, complemented
10C22×Q8×D17—22no—
11C22×D136C2211yescharacteristic
12#11763474—28no—
13#11763474C22116yescomplemented
14C2×#10587574C2214yes—
15C2×#10587582—24no—
16C2×#10587632—22no—
17C2×C4×Dic34C2211yescharacteristic
18C2×C4×D68C2212yes—
19C2×#10587579C2214yes—
20#11763213C22116yescomplemented
21#11763088C22132yescomplemented
22#11763086C22116yescomplemented
23C8×Dic34C2218yescomplemented
24C4×D136C2218yes—
25#11762891C22116yes—
26C2×#10587489C2211yescharacteristic
27C2×#10587478C2214yes—
28C2×C4⋊#3622C2211yescharacteristic
29C2×#10587485C2212yes—
30C2×#10587492C2212yes—
31C2×#10587480C2214yes—
32C2×C8×Dic17C2212yes—
33C2×C17×C4⋊Q8C2212yes—
34C17×#500C2218yescomplemented
35C2×C17×#107C2212yes—
36C2×C17×#107C2212yes—
37C2×C4×C8×C17C2211yescharacteristic
38C22×Q8×C17—22no—
39C2×Q8×D17—216no—
40C2×Q8×D17—416no—
41C22×D68C2312yes—
42C22×C4×D17—22no—
43C22×C4×D17—24no—
44C22×Dic34—24no—
45C22×Dic34D411yescharacteristic
46C22×C8×C17C2311yescharacteristic
47C22×C8×C17C2311yescharacteristic
48C17×C4⋊Q8—24no—
49C17×C4⋊Q8C2318yes—
50C2×C4⋊C4×C17—22no—
51C2×C4⋊C4×C17C2314yes—
52C2×C42×C17C2311yescharacteristic
53#10587632—216no—
54C2×#63227—22no—
55C2×#63227—24no—
56C2×C4⋊Dic17D411yescharacteristic
57C2×C4⋊Dic17C2312yes—
58C2×#63225—24no—
59C2×#63225D412yes—
60C2×C4×Dic17C2312yes—
61C22×#3622C2312yes—
62C2×D136Q818yescomplemented
63C2×D136C2314yes—
64#10587582—232no—
65#10587579—28no—
66#10587579C23116yes—
67#10587574—28no—
68#10587574C23116yes—
69C4×D68—24no—
70C4×D68C2318yes—
71C4×Dic34D414yes—
72C4×Dic34C2314yes—
73C17×#107C2318yes—
74C17×#107C2318yes—
75C4×C8×C17C2314yes—
76#10587492C2318yes—
77#10587489C2314yes—
78#10587485C2318yes—
79C8×Dic17C2318yes—
80#10587480C23116yes—
81#10587478C23116yes—
82C4⋊#3622C2314yes—
83C23×D17—22no—
84C2×Q8×C17—28no—
85C2×Q8×C17—48no—
86C22×C4×C17—24no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2411yescharacteristic
90C22×Dic17—22no—
91C22×Dic17C2×D412yes—
92C22×Dic17C2×D412yes—
93Q8×D17—464no—
94C2×D68—22no—
95C2×D68—24no—
96C2×D68C2×Q818yescomplemented
97C2×D68C2414yes—
98C2×C4×D17—28no—
99C2×C4×D17—216no—
100C2×C4×D17—48no—
101C2×C4×D17—416no—
102C2×Dic34—216no—
103C2×Dic34—416no—
104C2×Dic34D818yescomplemented
105C2×Dic34C2×D414yes—
106C2×C8×C17—22no—
107C2×C8×C17C2×Q814yescomplemented
108C2×C8×C17C2412yes—
109C2×C8×C17C2412yes—
110C4⋊C4×C17—24no—
111C4⋊C4×C17—28no—
112C4⋊C4×C17C2418yes—
113C42×C17C2×D412yes—
114C42×C17C2412yes—
115#63227—28no—
116#63227—216no—
117C4⋊Dic17—22no—
118C4⋊Dic17C2×D414yes—
119C4⋊Dic17C2414yes—
120#63225—216no—
121#63225C2×D418yes—
122C4×Dic17C2×D414yes—
123C4×Dic17C2414yes—
124C2×#3622—24no—
125C2×#3622C2414yes—
126D136C2×Q8116yescomplemented
127C2×Q8×D8—171nomaximal, Sylow
128C23×C17C22×D411yescharacteristic
129C22×D17—28no—
130C22×D17—24no—
131C22×D17—44no—
132C22×D17—44no—
133Q8×C17—416no—
134C2×C4×C17—22no—
135C2×C4×C17—28no—
136C2×C4×C17—48no—
137C2×C4×C17C2×D814yes—
138C2×C4×C17C22×D412yes—
139C2×C4×C17C22×D411yescharacteristic
140C2×C4×C17C22×D412yes—
141C2×C4×C17C22×Q812yes—
142C2×C4×C172−1+412yes—
143C2×C4×C17C2511yescharacteristic
144C2×Dic17—24no—
145C2×Dic17—24no—
146C2×Dic17—44no—
147C2×Dic17C2×D818yes—
148C2×Dic17C22×D414yes—
149C2×Dic17C22×D414yes—
150D68—28no—
151D68—24no—
152D68C22×Q818yescomplemented
153C4×D17—416no—
154C4×D17—432no—
155Dic34—432no—
156Dic34C2×D8116yescomplemented
157C8×C17—22no—
158C8×C17C22×Q814yescomplemented
159#3622—24no—
160C2×D4×Q8—172no—
161Q8×D8—1716no—
162C2×#500—172no—
163C2×#500D1711yescharacteristic, complemented
164C2×#474—174no—
165C2×#474—172no—
166C2×C8×Q8—171no—
167C2×C4×D8—172no—
168C2×C4×D8—171no—
169C22×C17D4×Q812yes—
170C22×C17C22×D812yes—
171C22×C17#57812yes—
172C22×C17C23×D411yescharacteristic
173C2×D17—28no—
174C2×D17—416no—
175C2×D17—44no—
176C2×D17—44no—
177C4×C17—22no—
178C4×C17—48no—
179C4×C17D4×Q812yes—
180C4×C17C22×D814yes—
181C4×C17C23×Q811yescharacteristic
182C4×C17C2×2−1+411yescharacteristic
183Dic17—24no—
184Dic17—44no—
185Dic17C22×D818yes—
186C23×Q8—342no—
187C22×D8—171no—
188D4×Q8—1716no—
189D4×Q8—348no—
190C2×C4⋊Q8—174no—
191C2×C4⋊Q8C2×D1712yes—
192C2×C22⋊Q8—344no—
193C2×C22⋊Q8—342no—
194C2×C4×Q8—171no—
195C2×C4×D4—174no—
196C2×C4×D4—172no—
197#500—1716no—
198#500C2×D1718yescomplemented
199#474—1716no—
200#474—1732no—
201C8×Q8—178no—
202C4×D8—1716no—
203C4×D8—178no—
204C2×#107—171no—
205C2×#107—174no—
206C2×#107C2×D1712yes—
207C2×#107C2×D1712yes—
208C2×C4⋊C8—172no—
209C2×C4⋊C8—171no—
210C2×#102—172no—
211C2×#102—174no—
212C2×C4×C8—172no—
213C2×C4×C8C2×D1711yescharacteristic
214C2×C17Q8×D814yescomplemented
215C2×C17C2×D4×Q811yescharacteristic
216C2×C17C23×D811yescharacteristic
217C2×C17C2×#57811yescharacteristic
218D17—48no—
219C22×Q8—22no—
220C22×Q8—171no—
221C22×Q8—344no—
222C22×Q8—3416no—
223C22×Q8—6816no—
224C22×D4—172no—
225C23×C4—344no—
226C23×C4—342no—
227C2×D8—178no—
228C2×D8—174no—
229C22×C8—172no—
230C22×C8C22×D1711yescharacteristic
231C22×C8C22×D1711yescharacteristic
232C4⋊Q8—24no—
233C4⋊Q8—1716no—
234C4⋊Q8—348no—
235C4⋊Q8C22×D1718yes—
236C22⋊Q8—3432no—
237C22⋊Q8—3416no—
238C4×Q8—174no—
239C4×Q8—174no—
240C4×D4—1716no—
241C4×D4—178no—
242C4×D4—348no—
243C4×D4—344no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—172no—
246C2×C4⋊C4—171no—
247C2×C4⋊C4—172no—
248C2×C4⋊C4—344no—
249C2×C4⋊C4C22×D1714yes—
250C2×C22⋊C4—344no—
251C2×C22⋊C4—342no—
252C2×C42—172no—
253C2×C42C22×D1711yescharacteristic
254#107—174no—
255#107—1716no—
256#107C22×D1718yes—
257#107C22×D1718yes—
258C4⋊C8—178no—
259C4⋊C8—174no—
260#102—178no—
261#102—1716no—
262C4×C8—178no—
263C4×C8C22×D1714yes—
264C17C2×Q8×D811yescharacteristic, complemented, Sylow
265C24—342no—
266C2×Q8—28no—
267C2×Q8—48no—
268C2×Q8—174no—
269C2×Q8—178no—
270C2×Q8—3416no—
271C2×Q8—6816no—
272C2×Q8—6864no—
273C2×D4—178no—
274C2×D4—174no—
275C2×D4—342no—
276C2×D4—344no—
277C22×C4—24no—
278C22×C4—172no—
279C22×C4—172no—
280C22×C4—3416no—
281C22×C4—342no—
282C22×C4—348no—
283C22×C4—6816no—
284C22×C4—688no—
285C22×C4D4×D1711yescharacteristic
286C22×C4D4×D1711yescharacteristic
287C22×C4C23×D1711yescharacteristic
288D8—1716no—
289C2×C8—22no—
290C2×C8—174no—
291C2×C8—344no—
292C2×C8Q8×D1714yescomplemented
293C2×C8C23×D1712yes—
294C2×C8C23×D1712yes—
295C4⋊C4—28no—
296C4⋊C4—24no—
297C4⋊C4—178no—
298C4⋊C4—174no—
299C4⋊C4—174no—
300C4⋊C4—3416no—
301C4⋊C4—342no—
302C4⋊C4C23×D1718yes—
303C22⋊C4—3416no—
304C22⋊C4—348no—
305C42—174no—
306C42—174no—
307C42D4×D1712yes—
308C42C23×D1712yes—
309C23—348no—
310C23—344no—
311C23—684no—
312C23—684no—
313C23C2×D4×D1711yescharacteristic
314Q8—416no—
315Q8—1716no—
316Q8—6832no—
317D4—178no—
318D4—348no—
319D4—344no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—48no—
323C2×C4—178no—
324C2×C4—174no—
325C2×C4—174no—
326C2×C4—344no—
327C2×C4—344no—
328C2×C4—6832no—
329C2×C4—684no—
330C2×C4—6816no—
331C2×C4D8×D1714yes—
332C2×C4C2×D4×D1712yes—
333C2×C4C2×D4×D1711yescharacteristic
334C2×C4C2×D4×D1712yes—
335C2×C4C2×Q8×D1712yes—
336C2×C4#1058769412yes—
337C2×C4C24×D1711yescharacteristic
338C8—22no—
339C8—344no—
340C8C2×Q8×D1714yescomplemented
341C22—348no—
342C22—6816no—
343C22—684no—
344C22—684no—
345C22#1176347412yes—
346C22C2×D8×D1712yes—
347C22#1176362212yes—
348C22C22×D4×D1711yescharacteristic
349C4—22no—
350C4—48no—
351C4—178no—
352C4—344no—
353C4—684no—
354C4#1176347412yes—
355C4C2×D8×D1714yes—
356C4C22×Q8×D1711yescharacteristic
357C4C2×#1058769411yescharacteristic
358C2—688no—
359C2#1454163614yesdirect product factor
360C2C2×#1176347411yescharacteristic
361C2C22×D8×D1711yescharacteristic
362C2C2×#1176362211yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#500C2
socleC23×C17C22×D4
prime radicalC22×D136C22
hypercenterC2×#500D17
hypocenterC17C2×Q8×D8
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#11763474C2semidirect
2. #14541636C2direct (N × H)
3. C2×#11763213C2semidirect
4. C2×#11763088C2semidirect
5. C2×#11763086C2semidirect
6. C2×C8×Dic34C2semidirect
9. C2×C17×#500C2semidirect
13. #11763474C22semidirect
20. #11763213C22semidirect
21. #11763088C22semidirect
22. #11763086C22semidirect
23. C8×Dic34C22semidirect
34. C17×#500C22semidirect
62. C2×D136Q8semidirect
96. C2×D68C2×Q8semidirect
104. C2×Dic34D8semidirect
107. C2×C8×C17C2×Q8semidirect
126. D136C2×Q8semidirect
152. D68C22×Q8semidirect
156. Dic34C2×D8semidirect
158. C8×C17C22×Q8semidirect
163. C2×#500D17semidirect
198. #500C2×D17semidirect
214. C2×C17Q8×D8semidirect
264. C17C2×Q8×D8semidirect
292. C2×C8Q8×D17semidirect
340. C8C2×Q8×D17semidirect
359. C2#14541636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634742
#145416362
C2×#117632132
C2×#117630882
C2×#117630862
C2×C8×Dic342
C2×C4×D1362
C2×#117628912
C2×C17×#5002
C2×Q8×D817