Finite Group Databasebeta

← D17×#2381 #17196955

Subgroups — D17×#2381 #17196955

Order 4352.

2326 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D17C211yesmaximal, characteristic
2#14531965C211yesmaximal, characteristic, complemented
3#14531964C212yesmaximal, complemented
4#14531963C214yesmaximal, complemented
5#14531962C218yesmaximal, complemented
6D17×#391C214yesmaximal
7D17×#387C218yesmaximal
8D17×#383C212yesmaximal
9C17×#2381C211yesmaximal, characteristic, complemented
10C22×Q8×D17C2212yes—
11C2×#10587555C2211yescharacteristic
12C2×#10587574C2214yes—
13C2×#10587630C2212yes—
14C4⋊Q8×D17C4116yescomplemented
15C2×C4⋊C4×D17C2214yes—
16C2×C4⋊C4×D17C2214yes—
17C2×C42×D17C2214yes—
18C2×C42×D17C2211yescharacteristic
19#11762716C2214yes—
20#11762715C2214yes—
21#11762714C2214yes—
22#11762713C2218yes—
23#11762713C2218yes—
24#11762696C2218yes—
25#11762695C2218yes—
26#11762694C2218yes—
27#11762693C2218yes—
28#11762692C2218yes—
29#11762691C2218yes—
30#11762690C2218yes—
31#11762677C2212yes—
32#11762676C2214yes—
33#11762676C2214yes—
34#11762676C2214yes—
35#95×D17C2214yes—
36#95×D17C2214yes—
37#95×D17C2214yes—
38#95×D17C2218yes—
39C2×C17×C4⋊Q8C2211yescharacteristic
40C17×#391C2214yes—
41C17×#387C2218yes—
42C17×#383C2212yes—
43C22×Q8×C17C2312yes—
44C2×Q8×D17—44no—
45C2×Q8×D17—44no—
46C2×Q8×D17C2×C4116yes—
47C22×C4×D17C2318yes—
48C22×C4×D17C2314yes—
49C22×C4×D17C2312yes—
50C22×C4×D17C2311yescharacteristic
51C22×Dic34C2312yes—
52C22×Dic34C2314yes—
53C17×C4⋊Q8C2×C418yescomplemented
54C2×C4⋊C4×C17C2314yes—
55C2×C4⋊C4×C17C2314yes—
56C2×C42×C17C2314yes—
57C2×C42×C17C2311yescharacteristic
58#10587630C2×C4116yescomplemented
59C2×C4⋊Dic17C2314yes—
60C2×C4⋊Dic17C2314yes—
61C2×#63225C2318yes—
62C2×#63225C2318yes—
63C2×C4×Dic17C2318yes—
64C2×C4×Dic17C2314yes—
65C2×C4×Dic17C2311yescharacteristic
66C2×C4×Dic17C2312yes—
67C4⋊C4×D17—48no—
68C4⋊C4×D17C2×C4132yes—
69#10587574C2×C4132yescomplemented
70C42×D17—48no—
71C42×D17C2×C418yes—
72#10587555C2×C418yescomplemented
73C17×#95C2318yes—
74C17×#95C2314yes—
75C17×#95C2314yes—
76C17×#95C2314yes—
77#10587502C2318yes—
78#10587502C2318yes—
79#10587502C2318yes—
80#10587502C2318yes—
81#10587502C2314yes—
82#10587502C2318yes—
83#10587502C2314yes—
84#10587502C2318yes—
85#10587502C2314yes—
86C23×D17C2411yescharacteristic
87C2×Q8×C17—42no—
88C2×Q8×C17—42no—
89C2×Q8×C17C22×C418yes—
90C22×C4×C17C2418yes—
91C22×C4×C17C2411yescharacteristic
92C22×C4×C17C2414yes—
93C22×C4×C17C2412yes—
94C22×Dic17C2418yes—
95C22×Dic17C2411yescharacteristic
96C22×Dic17C2414yes—
97C22×Dic17C2412yes—
98Q8×D17—432no—
99C2×C4×D17—24no—
100C2×C4×D17—28no—
101C2×C4×D17—28no—
102C2×C4×D17—28no—
103C2×C4×D17—216no—
104C2×C4×D17—232no—
105C2×C4×D17C22×C414yes—
106C2×C4×D17C22×C4116yes—
107C2×C4×D17C22×C418yes—
108C2×Dic34—44no—
109C2×Dic34—44no—
110C2×Dic34—42no—
111C2×Dic34—42no—
112C2×Dic34C22×C418yes—
113C2×Dic34C22×C4116yes—
114C4⋊C4×C17—44no—
115C4⋊C4×C17C22×C4116yes—
116C42×C17—44no—
117C42×C17C22×C414yes—
118C4⋊Dic17—44no—
119C4⋊Dic17C22×C4116yes—
120#63225—48no—
121#63225C22×C4132yes—
122C4×Dic17—48no—
123C4×Dic17—44no—
124C4×Dic17C22×C418yes—
125C4×Dic17C22×C414yes—
126C2×#2381—171nomaximal, Sylow
127C23×C17C2511yescharacteristic
128C22×D17C23×C412yes—
129C22×D17H(5,𝔽2)14yes—
130C22×D172−1+418yes—
131Q8×C17—48no—
132C2×C4×C17—24no—
133C2×C4×C17—24no—
134C2×C4×C17—22no—
135C2×C4×C17—24no—
136C2×C4×C17—28no—
137C2×C4×C17—216no—
138C2×C4×C17C23×C414yes—
139C2×C4×C17C23×C412yes—
140C2×C4×C17C23×C418yes—
141C2×Dic17—22no—
142C2×Dic17—24no—
143C2×Dic17—24no—
144C2×Dic17—24no—
145C2×Dic17—28no—
146C2×Dic17—216no—
147C2×Dic17C23×C412yes—
148C2×Dic17C23×C418yes—
149C2×Dic17C23×C414yes—
150C4×D17—232no—
151C4×D17—28no—
152C4×D17—216no—
153C4×D17—432no—
154Dic34—416no—
155Dic34—48no—
156C22×C4⋊Q8—171no—
157#2381—174no—
158#2381—178no—
159#2381—172no—
160#2381—171no—
161#2381D1711yescharacteristic, direct product factor
162C2×#391—174no—
163C2×#387—178no—
164C2×#383—172no—
165C22×C17C24×C411yescharacteristic
166C22×C17C2×H(5,𝔽2)12yes—
167C22×C17C2×2−1+414yes—
168C2×D17#51814yes—
169C2×D17#51918yes—
170C2×D17#563116yes—
171C4×C17—22no—
172C4×C17—28no—
173C4×C17—24no—
174C4×C17—48no—
175Dic17—22no—
176Dic17—28no—
177Dic17—24no—
178Dic17—48no—
179C23×Q8—172no—
180C2×C4⋊Q8—172no—
181C2×C4⋊Q8—1716no—
182C2×C4⋊Q8—174no—
183C2×C4⋊Q8—171no—
184C2×C4⋊Q8C2×D1711yescharacteristic
185C22×C4⋊C4—174no—
186C22×C4⋊C4—174no—
187C22×C42—171no—
188C22×C42—174no—
189#391—174no—
190#391—174no—
191#391—174no—
192#391—178no—
193#391—178no—
194#391C2×D1714yes—
195#387—178no—
196#387—178no—
197#387—178no—
198#387—178no—
199#387—178no—
200#387—178no—
201#387—178no—
202#387C2×D1718yes—
203#383—172no—
204#383—174no—
205#383—174no—
206#383—174no—
207#383C2×D1712yes—
208C2×#95—174no—
209C2×#95—174no—
210C2×#95—174no—
211C2×#95—178no—
212C2×C17C2×#51811yescharacteristic
213C2×C17C2×#51912yes—
214C2×C17C2×#56314yes—
215D17#238118yesdirect product factor
216C22×Q8—1716no—
217C22×Q8—174no—
218C22×Q8—172no—
219C22×Q8—684no—
220C22×Q8—684no—
221C22×Q8C22×D1712yes—
222C23×C4—174no—
223C23×C4—172no—
224C23×C4—171no—
225C23×C4—178no—
226C4⋊Q8—1716no—
227C4⋊Q8—1732no—
228C4⋊Q8—178no—
229C4⋊Q8C4×D1718yescomplemented
230C2×C4⋊C4—178no—
231C2×C4⋊C4—174no—
232C2×C4⋊C4—1732no—
233C2×C4⋊C4—178no—
234C2×C4⋊C4—174no—
235C2×C4⋊C4—688no—
236C2×C4⋊C4C22×D1714yes—
237C2×C4⋊C4C22×D1714yes—
238C2×C42—171no—
239C2×C42—172no—
240C2×C42—178no—
241C2×C42—178no—
242C2×C42—174no—
243C2×C42—688no—
244C2×C42C22×D1714yes—
245C2×C42C22×D1711yescharacteristic
246#95—178no—
247#95—178no—
248#95—174no—
249#95—174no—
250#95—178no—
251#95—174no—
252#95—178no—
253#95—178no—
254#95—178no—
255#95C22×D1714yes—
256#95C22×D1714yes—
257#95C22×D1714yes—
258#95C22×D1718yes—
259C17C2×#238111yescharacteristic, complemented, Sylow
260C24—171no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—1716no—
264C2×Q8—178no—
265C2×Q8—684no—
266C2×Q8—684no—
267C2×Q8—682no—
268C2×Q8—682no—
269C2×Q8—6832no—
270C2×Q8C2×C4×D1718yes—
271C22×C4—172no—
272C22×C4—171no—
273C22×C4—174no—
274C22×C4—178no—
275C22×C4—174no—
276C22×C4—1716no—
277C22×C4—178no—
278C22×C4—348no—
279C22×C4—348no—
280C22×C4—348no—
281C22×C4—344no—
282C22×C4—3416no—
283C22×C4—3432no—
284C22×C4C23×D1718yes—
285C22×C4C23×D1712yes—
286C22×C4C23×D1711yescharacteristic
287C22×C4C23×D1714yes—
288C4⋊C4—44no—
289C4⋊C4—1732no—
290C4⋊C4—1716no—
291C4⋊C4—688no—
292C4⋊C4—684no—
293C4⋊C4C2×C4×D17116yes—
294C42—44no—
295C42—174no—
296C42—178no—
297C42—684no—
298C42—688no—
299C42C2×C4×D1714yes—
300C23—172no—
301C23—174no—
302C23—178no—
303C23C24×D1711yescharacteristic
304Q8—48no—
305Q8—688no—
306Q8—6816no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—216no—
313C2×C4—174no—
314C2×C4—172no—
315C2×C4—178no—
316C2×C4—348no—
317C2×C4—3432no—
318C2×C4—3416no—
319C2×C4—344no—
320C2×C4—344no—
321C2×C4—342no—
322C2×C4—344no—
323C2×C4—348no—
324C2×C4—3416no—
325C2×C4—6832no—
326C2×C4C22×C4×D1714yes—
327C2×C4C22×C4×D1712yes—
328C2×C4C22×C4×D1718yes—
329C22—1716no—
330C22—174no—
331C22—178no—
332C22C23×C4×D1711yescharacteristic
333C22H(5,𝔽2)×D1712yes—
334C222−1+4×D1714yes—
335C4—22no—
336C4—28no—
337C4—24no—
338C4—48no—
339C4—342no—
340C4—348no—
341C4—344no—
342C4—688no—
343C2—178no—
344C2D17×#51811yescharacteristic
345C2D17×#51912yes—
346C2D17×#56314yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2381C2
socle, cosocleC23×C17C25
prime radicalC23×D17C24
hypercenter#2381D17
hypocenterC17C2×#2381
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2381

Complements

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

NH ≅ G/Ntype
2. #14531965C2semidirect
3. #14531964C2semidirect
4. #14531963C2semidirect
5. #14531962C2semidirect
9. C17×#2381C2semidirect
14. C4⋊Q8×D17C4semidirect
53. C17×C4⋊Q8C2×C4semidirect
58. #10587630C2×C4semidirect
69. #10587574C2×C4semidirect
72. #10587555C2×C4semidirect
161. #2381D17direct (N × H)
215. D17#2381direct (N × H)
229. C4⋊Q8C4×D17semidirect
259. C17C2×#2381semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D172
#145319652
#145319642
#145319632
#145319622
D17×#3912
D17×#3872
D17×#3832
C17×#23812
C2×#238117