Finite Group Databasebeta

← C2×D17×#519 #17940906

Subgroups — C2×D17×#519 #17940906

Order 4352.

11230 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D17C211yesmaximal, characteristic
2C2×#11763287C211yesmaximal, characteristic, complemented
3C2×#11763286C216yesmaximal, complemented
4C2×#11763285C218yesmaximal, complemented
5D17×#519C2132yesmaximal, direct product factor
6C2×C4×Q8×D17C218yesmaximal, complemented
7C2×#117×D17C216yesmaximal
8C2×C17×#519C211yesmaximal, characteristic, complemented
9C23×Dic34C2213yes—
10C22×Q8×D17C4132yescomplemented
11C22×Q8×D17C2214yes—
12C22×Q8×D17C22116yes—
13C22×Q8×D17C2214yes—
14C23×C4×D17C2213yes—
15#11763287C22116yescomplemented
16#11763286C22196yescomplemented
17#11763285C221128yescomplemented
18C2×Q8×Dic17C2218yescomplemented
19C2×C4×Dic34C22124yescomplemented
20C2×#10587573C22124yescomplemented
21C4×Q8×D17C221128yescomplemented
22C2×#10587612C2216yes—
23C2×#10587578C22112yes—
24C2×#10587558C22112yes—
25C2×#10587563C22112yes—
26#117×D17C22196yes—
27C2×C4⋊C4×D17C22112yes—
28C2×C22⋊C4×D17C2214yes—
29C2×C42×D17C22112yes—
30C23×Q8×C17C2211yescharacteristic
31C17×#519C22116yescomplemented
32C2×C4×Q8×C17C2218yescomplemented
33C2×C17×#117C2216yes—
34C24×D17C2311yescharacteristic
35C22×Q8×C17C2×C4116yescomplemented
36C22×Q8×C17C2314yes—
37C22×Q8×C17C2318yes—
38C23×C4×C17C2313yes—
39C23×Dic17C2313yes—
40C2×Q8×D17C2×C4164yes—
41C2×Q8×D17C2×C4164yescomplemented
42C2×Q8×D17C2×C41256yescomplemented
43C2×Q8×D17C23132yes—
44C2×Q8×D17C23132yes—
45C22×C4×D17C2×C4148yes—
46C22×C4×D17C2318yes—
47C22×C4×D17C2316yes—
48C22×C4×D17C23124yes—
49C22×C4×D17C2316yes—
50C22×Dic34C2×C4148yescomplemented
51C22×Dic34C23112yes—
52C22×Dic34C23124yes—
53C4×Q8×C17C23164yescomplemented
54C17×#117C23148yes—
55C2×C4⋊C4×C17C23112yes—
56C2×C22⋊C4×C17C2314yes—
57C2×C42×C17C23112yes—
58C2×C22⋊Dic17C2314yes—
59Q8×Dic17C23164yescomplemented
60C2×#63227C2318yes—
61#10587612C23148yes—
62C2×C4⋊Dic17C23112yes—
63C2×#63225C23124yes—
64C2×C4×Dic17C23124yes—
65C2×C4×Dic17C23112yes—
66#10587578C23196yes—
67C4⋊C4×D17C23196yes—
68#10587573C231192yescomplemented
69C22⋊C4×D17C23132yes—
70#10587563C23196yes—
71#10587558C23196yes—
72C42×D17C23196yes—
73C4×Dic34C231192yescomplemented
74C24×C17C2411yescharacteristic
75C23×D17—28no—
76C23×D17C22×C418yes—
77C23×D17C2414yes—
78C23×D17C2411yescharacteristic
79C23×D17C2411yescharacteristic
80C2×Q8×C17C22×C4132yes—
81C2×Q8×C17C22×C4164yescomplemented
82C2×Q8×C17C24116yes—
83C22×C4×C17C22×C4124yes—
84C22×C4×C17C2418yes—
85C22×C4×C17C2416yes—
86C22×C4×C17C24112yes—
87C22×Dic17C22×C4124yes—
88C22×Dic17C2418yes—
89C22×Dic17C24112yes—
90C22×Dic17C2416yes—
91Q8×D17C22×C41256yes—
92Q8×D17C22×C41256yescomplemented
93C2×C4×D17—232no—
94C2×C4×D17C22×C4148yes—
95C2×C4×D17C22×C41192yes—
96C2×C4×D17C22×C4148yes—
97C2×C4×D17C24132yes—
98C2×C4×D17C24124yes—
99C2×C4×D17C24124yes—
100C2×Dic34C22×C4196yes—
101C2×Dic34C22×C41192yescomplemented
102C2×Dic34C24148yes—
103C4⋊C4×C17C24148yes—
104C22⋊C4×C17C24116yes—
105C42×C17C24148yes—
106C22⋊Dic17C24116yes—
107#63227C24132yes—
108C4⋊Dic17C24148yes—
109#63225C24196yes—
110C4×Dic17C24196yes—
111C4×Dic17C24148yes—
112C22×#519—171nomaximal, Sylow
113C23×C17—24no—
114C23×C17C23×C414yes—
115C23×C17C2512yes—
116C23×C17C2511yescharacteristic
117C22×D17—24no—
118C22×D17—232no—
119C22×D17—216no—
120C22×D17C23×C414yes—
121C22×D17C23×C4116yes—
122C22×D17C23×C414yes—
123C22×D172−1+418yes—
124C22×D17C2512yes—
125C22×D17C2512yes—
126Q8×C17C23×C4164yes—
127C2×C4×C17—216no—
128C2×C4×C17C23×C4124yes—
129C2×C4×C17C23×C4148yes—
130C2×C4×C17C25116yes—
131C2×C4×C17C25112yes—
132C2×Dic17—216no—
133C2×Dic17C23×C4124yes—
134C2×Dic17C23×C4148yes—
135C2×Dic17C25116yes—
136C2×Dic17C25112yes—
137C4×D17—264no—
138C4×D17C23×C4196yes—
139C4×D17C23×C4196yes—
140Dic34C23×C41192yes—
141C24×Q8—171no—
142C2×#519—171no—
143C2×#519—1732no—
144C2×#519—178no—
145C2×#519—176no—
146C2×#519D1711yescharacteristic, direct product factor
147C22×C4×Q8—178no—
148C22×#117—176no—
149C22×C17—24no—
150C22×C17—28no—
151C22×C17C24×C414yes—
152C22×C17C24×C412yes—
153C22×C17C2×2−1+414yes—
154C22×C17C2611yescharacteristic
155C2×D17—24no—
156C2×D17—28no—
157C2×D17—232no—
158C2×D17#519116yesdirect product factor
159C2×D17C24×C414yes—
160C2×D17C24×C414yes—
161C2×D17C2×2−1+418yes—
162C4×C17—216no—
163C4×C17C24×C4124yes—
164Dic17—216no—
165Dic17C24×C4124yes—
166C23×Q8—1732no—
167C23×Q8—174no—
168C23×Q8—174no—
169C23×Q8—1716no—
170C23×Q8—173no—
171C23×Q8C2×D1711yescharacteristic
172C24×C4—173no—
173#519—1716no—
174#519—17128no—
175#519—1796no—
176#519C2×D17116yesdirect product factor
177C2×C4×Q8—178no—
178C2×C4×Q8—17128no—
179C2×C4×Q8—1724no—
180C2×C4×Q8—1724no—
181C2×C4×Q8C2×D1718yescomplemented
182C2×#117—176no—
183C2×#117—1796no—
184C2×#117—1712no—
185C2×#117—1712no—
186C2×#117—1712no—
187C2×#117C2×D1716yes—
188C22×C4⋊C4—1712no—
189C22×C22⋊C4—174no—
190C22×C42—1712no—
191C2×C17—24no—
192C2×C17C2×#51914yescomplemented
193C2×C17C25×C411yescharacteristic
194C2×C17C22×2−1+412yes—
195D17—24no—
196D17C2×#51918yesdirect product factor
197C25—171no—
198C22×Q8—1764no—
199C22×Q8—1764no—
200C22×Q8—17256no—
201C22×Q8—1732no—
202C22×Q8—1732no—
203C22×Q8—1748no—
204C22×Q8—1712no—
205C22×Q8—1724no—
206C22×Q8C4×D17116yescomplemented
207C22×Q8C22×D1714yes—
208C22×Q8C22×D1718yes—
209C23×C4—173no—
210C23×C4—1748no—
211C23×C4—176no—
212C23×C4—1724no—
213C23×C4—176no—
214C23×C4—178no—
215C23×C4C22×D1713yes—
216C4×Q8—1764no—
217C4×Q8—17192no—
218C4×Q8—17192no—
219C4×Q8C22×D17164yescomplemented
220#117—1748no—
221#117—1796no—
222#117—1796no—
223#117—1796no—
224#117C22×D17148yes—
225C2×C4⋊C4—1724no—
226C2×C4⋊C4—1712no—
227C2×C4⋊C4—1796no—
228C2×C4⋊C4C22×D17112yes—
229C2×C22⋊C4—174no—
230C2×C22⋊C4—178no—
231C2×C22⋊C4—1732no—
232C2×C22⋊C4C22×D1714yes—
233C2×C42—1724no—
234C2×C42—1712no—
235C2×C42—1796no—
236C2×C42C22×D17112yes—
237C17C22×#51911yescharacteristic, complemented, Sylow
238C24—171no—
239C24—178no—
240C24—174no—
241C24—171no—
242C24—348no—
243C24C23×D1711yescharacteristic
244C2×Q8—17256no—
245C2×Q8—17256no—
246C2×Q8—1796no—
247C2×Q8—17192no—
248C2×Q8—1748no—
249C2×Q8C2×C4×D17132yes—
250C2×Q8C2×C4×D17164yescomplemented
251C2×Q8C23×D17116yes—
252C22×C4—1724no—
253C22×C4—1712no—
254C22×C4—176no—
255C22×C4—1748no—
256C22×C4—1748no—
257C22×C4—17192no—
258C22×C4—1724no—
259C22×C4—1724no—
260C22×C4—178no—
261C22×C4—1732no—
262C22×C4—3432no—
263C22×C4C2×C4×D17124yes—
264C22×C4C23×D1718yes—
265C22×C4C23×D17112yes—
266C22×C4C23×D1716yes—
267C4⋊C4—1796no—
268C4⋊C4—1748no—
269C4⋊C4C23×D17148yes—
270C22⋊C4—1716no—
271C22⋊C4—1732no—
272C22⋊C4C23×D17116yes—
273C42—1796no—
274C42—1748no—
275C42C23×D17148yes—
276C23—24no—
277C23—174no—
278C23—178no—
279C23—172no—
280C23—1716no—
281C23—174no—
282C23—172no—
283C23—3432no—
284C23—3416no—
285C23—344no—
286C23C22×C4×D1714yes—
287C23C24×D1712yes—
288C23C24×D1711yescharacteristic
289Q8—17192no—
290Q8C22×C4×D17164yes—
291C2×C4—216no—
292C2×C4—1748no—
293C2×C4—1724no—
294C2×C4—1712no—
295C2×C4—1796no—
296C2×C4—1796no—
297C2×C4—1716no—
298C2×C4—3464no—
299C2×C4—3416no—
300C2×C4C22×C4×D17124yes—
301C2×C4C22×C4×D17148yes—
302C2×C4C24×D17116yes—
303C2×C4C24×D17112yes—
304C22—28no—
305C22—24no—
306C22—1716no—
307C22—174no—
308C22—178no—
309C22—174no—
310C22—3432no—
311C22—348no—
312C22—344no—
313C22C23×C4×D1714yes—
314C22C23×C4×D1712yes—
315C222−1+4×D1714yes—
316C22C25×D1711yescharacteristic
317C4—216no—
318C4—1724no—
319C4—3416no—
320C4C23×C4×D17124yes—
321C2—24no—
322C2—178no—
323C2—344no—
324C2D17×#51914yesdirect product factor
325C2C24×C4×D1711yescharacteristic
326C2C2×2−1+4×D1712yes—
subgroupG/H
centerC23C24×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC2×C17×#519C2
socleC23×C17C25
prime radicalC24×D17C23
cosocleC22×C17C26
hypercenterC2×#519D17
hypocenterC17C22×#519
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#11763287C2semidirect
3. C2×#11763286C2semidirect
4. C2×#11763285C2semidirect
5. D17×#519C2direct (N × H)
6. C2×C4×Q8×D17C2semidirect
8. C2×C17×#519C2semidirect
10. C22×Q8×D17C4semidirect
15. #11763287C22semidirect
16. #11763286C22semidirect
17. #11763285C22semidirect
18. C2×Q8×Dic17C22semidirect
19. C2×C4×Dic34C22semidirect
20. C2×#10587573C22semidirect
21. C4×Q8×D17C22semidirect
31. C17×#519C22semidirect
32. C2×C4×Q8×C17C22semidirect
35. C22×Q8×C17C2×C4semidirect
41. C2×Q8×D17C2×C4semidirect
42. C2×Q8×D17C2×C4semidirect
50. C22×Dic34C2×C4semidirect
53. C4×Q8×C17C23semidirect
59. Q8×Dic17C23semidirect
68. #10587573C23semidirect
73. C4×Dic34C23semidirect
81. C2×Q8×C17C22×C4semidirect
92. Q8×D17C22×C4semidirect
101. C2×Dic34C22×C4semidirect
146. C2×#519D17direct (N × H)
158. C2×D17#519direct (N × H)
176. #519C2×D17direct (N × H)
181. C2×C4×Q8C2×D17semidirect
192. C2×C17C2×#519semidirect
196. D17C2×#519direct (N × H)
206. C22×Q8C4×D17semidirect
219. C4×Q8C22×D17semidirect
237. C17C22×#519semidirect
250. C2×Q8C2×C4×D17semidirect
324. C2D17×#519direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D172
C2×#117632872
C2×#117632862
C2×#117632852
D17×#5192
C2×C4×Q8×D172
C2×#117×D172
C2×C17×#5192
C22×#51917