Finite Group Databasebeta

← D17×#2645 #17201441

Subgroups — D17×#2645 #17201441

Order 4352.

1830 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534752C213yesmaximal, complemented
2#14534751C212yesmaximal, complemented
3#14534750C213yesmaximal, complemented
4#14534749C211yesmaximal, characteristic, complemented
5#14534748C216yesmaximal, complemented
6D17×#401C212yesmaximal
7D17×#400C216yesmaximal
8D17×#391C213yesmaximal
9D17×#389C213yesmaximal
10D17×#376C211yesmaximal, characteristic
11C17×#2645C211yesmaximal, characteristic, complemented
12C22×Q8×D17C2211yescharacteristic
13C2×C4⋊C4×D17C2213yes—
14C2×C4⋊C4×D17C2216yes—
15C2×C42×D17C2213yes—
16C17⋊#401C2216yes—
17C17⋊#401C2216yes—
18C17⋊#401C2212yes—
19#11762751C2216yes—
20#11762751C2216yes—
21#11762750C2216yes—
22#11762750C2216yes—
23#11762749C2216yes—
24#11762748C2216yes—
25#11762747C2216yes—
26#11762716C2213yes—
27#11762715C2213yes—
28#11762714C2213yes—
29#11762713C2216yes—
30#11762713C2216yes—
31#11762708C2213yes—
32#11762707C2213yes—
33#11762706C2216yes—
34#11762705C2213yes—
35#11762704C2216yes—
36#11762655C2213yes—
37#11762654C2213yes—
38#11762654C2211yescharacteristic
39#95×D17C2213yes—
40#95×D17C2211yescharacteristic
41#95×D17C2216yes—
42#95×D17C2216yes—
43#95×D17C2216yes—
44C17×#401C2212yes—
45C17×#400C2216yes—
46C17×#391C2213yes—
47C17×#389C2213yes—
48C17×#376C2211yescharacteristic
49C22×Q8×C17C2311yescharacteristic
50C2×Q8×D17—212no—
51C22×C4×D17C2313yes—
52C22×C4×D17C2313yes—
53C22×C4×D17C2316yes—
54C22×C4×D17C2312yes—
55C22×C4×D17C2311yescharacteristic
56C22×Dic34C2312yes—
57C22×Dic34C2311yescharacteristic
58C2×C4⋊C4×C17C2313yes—
59C2×C4⋊C4×C17C2316yes—
60C2×C42×C17C2313yes—
61C2×C4⋊Dic17C2313yes—
62C2×C4⋊Dic17C2316yes—
63C2×#63225C2316yes—
64C2×#63225C2316yes—
65C2×#63225C2316yes—
66C2×C4×Dic17C2313yes—
67C2×C4×Dic17C2313yes—
68C2×C4×Dic17C2313yes—
69C4⋊C4×D17—212no—
70C4⋊C4×D17—412no—
71C42×D17—212no—
72C17×#95C2316yes—
73C17×#95C2316yes—
74C17×#95C2316yes—
75C17×#95C2313yes—
76C17×#95C2311yescharacteristic
77#10587502C2316yes—
78#10587502C2316yes—
79#10587502C2316yes—
80#10587502C2316yes—
81#10587502C2316yes—
82#10587502C2316yes—
83#10587502C2316yes—
84#10587502C2316yes—
85#10587502C2316yes—
86#10587502C2313yes—
87#10587502C2313yes—
88#10587502C2313yes—
89#10587502C2313yes—
90C23×D17C2411yescharacteristic
91C2×Q8×C17—26no—
92C22×C4×C17C2412yes—
93C22×C4×C17C2413yes—
94C22×C4×C17C2413yes—
95C22×C4×C17C2416yes—
96C22×C4×C17C2411yescharacteristic
97C22×Dic17C2412yes—
98C22×Dic17C2413yes—
99C22×Dic17C2413yes—
100C22×Dic17C2416yes—
101C22×Dic17C2411yescharacteristic
102Q8×D17—416no—
103C2×C4×D17—212no—
104C2×C4×D17—26no—
105C2×C4×D17—26no—
106C2×C4×D17—212no—
107C2×C4×D17—212no—
108C2×C4×D17—26no—
109C2×C4×D17—212no—
110C2×C4×D17—26no—
111C2×C4×D17—212no—
112C2×C4×D17#41112yes—
113C2×Dic34—26no—
114C2×Dic34—212no—
115C4⋊C4×C17—26no—
116C4⋊C4×C17—46no—
117C42×C17—26no—
118C4⋊Dic17—26no—
119C4⋊Dic17—46no—
120#63225—212no—
121#63225—46no—
122#63225—46no—
123C4×Dic17—26no—
124C4×Dic17—26no—
125C4×Dic17—26no—
126C2×#2645—171nomaximal, Sylow
127C23×C17C2511yescharacteristic
128C22×D17C2×#4116yes—
129C22×D17H(5,𝔽2)12yes—
130C22×D172−1+416yes—
131Q8×C17—44no—
132C2×C4×C17—23no—
133C2×C4×C17—23no—
134C2×C4×C17—26no—
135C2×C4×C17—26no—
136C2×C4×C17—23no—
137C2×C4×C17—26no—
138C2×C4×C17—26no—
139C2×C4×C17—23no—
140C2×C4×C17—26no—
141C2×C4×C17C2×#4116yes—
142C2×Dic17—26no—
143C2×Dic17—23no—
144C2×Dic17—23no—
145C2×Dic17—26no—
146C2×Dic17—26no—
147C2×Dic17—23no—
148C2×Dic17—26no—
149C2×Dic17—23no—
150C2×Dic17—26no—
151C2×Dic17C2×#4116yes—
152C4×D17—48no—
153C4×D17—412no—
154C4×D17—412no—
155C4×D17—424no—
156C4×D17#126116yes—
157Dic34—44no—
158Dic34—48no—
159#2645—172no—
160#2645—176no—
161#2645—173no—
162#2645—173no—
163#2645—171no—
164#2645D1711yescharacteristic, direct product factor
165C2×#401—172no—
166C2×#400—176no—
167C2×#391—173no—
168C2×#389—173no—
169C2×#376—171no—
170C22×C17C22×#4113yes—
171C22×C17C2×H(5,𝔽2)11yescharacteristic
172C22×C17C2×2−1+413yes—
173C2×D17C2×#12614yes—
174C2×D17#541112yes—
175C2×D17#542112yes—
176C4×C17—42no—
177C4×C17—43no—
178C4×C17—43no—
179C4×C17—46no—
180C4×C17C2×#12614yes—
181Dic17—42no—
182Dic17—43no—
183Dic17—43no—
184Dic17—46no—
185Dic17C2×#12614yes—
186C23×Q8—171no—
187C22×C4⋊C4—173no—
188C22×C4⋊C4—176no—
189C22×C42—173no—
190#401—176no—
191#401—176no—
192#401—172no—
193#401C2×D1712yes—
194#400—176no—
195#400—176no—
196#400—176no—
197#400—176no—
198#400—176no—
199#400—176no—
200#400—176no—
201#400C2×D1716yes—
202#391—173no—
203#391—173no—
204#391—173no—
205#391—176no—
206#391—176no—
207#391C2×D1713yes—
208#389—176no—
209#389—173no—
210#389—173no—
211#389—173no—
212#389—176no—
213#389C2×D1713yes—
214#376—173no—
215#376—171no—
216#376—173no—
217#376C2×D1711yescharacteristic
218C2×#95—173no—
219C2×#95—176no—
220C2×#95—176no—
221C2×#95—176no—
222C2×#95—171no—
223C2×C17C22×#12611yescharacteristic
224C2×C17C2×#54113yes—
225C2×C17C2×#54213yes—
226D17#264518yesdirect product factor
227C22×Q8—172no—
228C22×Q8—171no—
229C22×Q8—3412no—
230C22×Q8C22×D1711yescharacteristic
231C23×C4—171no—
232C23×C4—176no—
233C23×C4—173no—
234C23×C4—172no—
235C23×C4—173no—
236C2×C4⋊C4—176no—
237C2×C4⋊C4—173no—
238C2×C4⋊C4—176no—
239C2×C4⋊C4—176no—
240C2×C4⋊C4—176no—
241C2×C4⋊C4—3412no—
242C2×C4⋊C4—6812no—
243C2×C4⋊C4C22×D1713yes—
244C2×C4⋊C4C22×D1716yes—
245C2×C42—173no—
246C2×C42—173no—
247C2×C42—173no—
248C2×C42—3412no—
249C2×C42C22×D1713yes—
250#95—173no—
251#95—173no—
252#95—173no—
253#95—173no—
254#95—176no—
255#95—176no—
256#95—176no—
257#95—176no—
258#95—176no—
259#95—176no—
260#95—176no—
261#95—176no—
262#95—176no—
263#95C22×D1713yes—
264#95C22×D1711yescharacteristic
265#95C22×D1716yes—
266#95C22×D1716yes—
267#95C22×D1716yes—
268C17C2×#264511yescharacteristic, complemented, Sylow
269C24—171no—
270C2×Q8—26no—
271C2×Q8—3412no—
272C2×Q8—346no—
273C2×Q8—6816no—
274C22×C4—171no—
275C22×C4—1712no—
276C22×C4—173no—
277C22×C4—172no—
278C22×C4—173no—
279C22×C4—176no—
280C22×C4—346no—
281C22×C4—346no—
282C22×C4—3412no—
283C22×C4—3412no—
284C22×C4—346no—
285C22×C4—3412no—
286C22×C4—346no—
287C22×C4—3412no—
288C22×C4—3412no—
289C22×C4C23×D1713yes—
290C22×C4C23×D1712yes—
291C22×C4C23×D1713yes—
292C22×C4C23×D1716yes—
293C22×C4C23×D1711yescharacteristic
294C4⋊C4—26no—
295C4⋊C4—46no—
296C4⋊C4—3412no—
297C4⋊C4—346no—
298C4⋊C4—686no—
299C4⋊C4—686no—
300C4⋊C4—686no—
301C42—26no—
302C42—346no—
303C42—346no—
304C42—346no—
305C23—176no—
306C23—172no—
307C23—176no—
308C23C24×D1711yescharacteristic
309Q8—44no—
310Q8—688no—
311Q8—684no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—23no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—23no—
320C2×C4—26no—
321C2×C4—176no—
322C2×C4—1716no—
323C2×C4—343no—
324C2×C4—343no—
325C2×C4—346no—
326C2×C4—346no—
327C2×C4—346no—
328C2×C4—343no—
329C2×C4—346no—
330C2×C4—343no—
331C2×C4—346no—
332C2×C4—688no—
333C2×C4—6812no—
334C2×C4—6812no—
335C2×C4—6824no—
336C2×C4#41×D1716yes—
337C22—1712no—
338C22—1712no—
339C22—174no—
340C22C2×#41×D1713yes—
341C22H(5,𝔽2)×D1711yescharacteristic
342C222−1+4×D1713yes—
343C4—43no—
344C4—43no—
345C4—46no—
346C4—42no—
347C4—174no—
348C4—683no—
349C4—683no—
350C4—686no—
351C4—682no—
352C4#126×D1714yes—
353C2—178no—
354C2C2×#126×D1711yescharacteristic
355C2D17×#54113yes—
356C2D17×#54213yes—
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2645C2
prime radicalC23×D17C24
hypercenter#2645D17
hypocenterC17C2×#2645
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2645

Complements

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

NH ≅ G/Ntype
1. #14534752C2semidirect
2. #14534751C2semidirect
3. #14534750C2semidirect
4. #14534749C2semidirect
5. #14534748C2semidirect
11. C17×#2645C2semidirect
164. #2645D17direct (N × H)
226. D17#2645direct (N × H)
268. C17C2×#2645semidirect

Maximal subgroups

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

subgroupindex
#145347522
#145347512
#145347502
#145347492
#145347482
D17×#4012
D17×#4002
D17×#3912
D17×#3892
D17×#3762
C17×#26452
C2×#264517