Finite Group Databasebeta

← D17⋊#2987 #17980212

Subgroups — D17⋊#2987 #17980212

Order 4352.

1706 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545698C214yesmaximal, complemented
2#14545697C214yesmaximal, complemented
3#14545696C218yesmaximal, complemented
4D17⋊#446C218yesmaximal, complemented
5D17⋊#433C214yesmaximal
6D17⋊#432C212yesmaximal
7D17×#533C211yesmaximal, characteristic
8#11763861C22116yescomplemented
9#11763861C22116yescomplemented
10#11763860C22116yescomplemented
11#11763859C22116yescomplemented
12#11763834C22116yes—
13#11763833C22116yes—
14#11763832C2214yes—
15#11763831C2214yes—
16#11763830C2214yes—
17#11763829C2214yes—
18#11763810C2214yes—
19#11763810C2218yes—
20#11763777C2214yes—
21#11763768C2214yes—
22#11763768C2214yes—
23C4×#63242C2214yes—
24#11763366C411yescharacteristic
25#11763365C2212yes—
26#11763364C2212yes—
27#11763363C414yes—
28#11763362C412yes—
29#11763361C2214yes—
30C4⋊Q8×D17C412yes—
31#125×D17C412yes—
32C22⋊Q8×D17C414yes—
33C4×Q8×D17C2214yes—
34#117×D17C2212yes—
35C2×C42×D17C2211yescharacteristic
36C17×#533C411yescharacteristic
37C2×Q8×D17C2×C414yes—
38C22×C4×D17C2×C412yes—
39C22×C4×D17C2311yescharacteristic
40C2×#63242C2318yes—
41C17×C4⋊Q8C2×C412yes—
42C17×#125C2×C412yes—
43C17×C22⋊Q8C2×C414yes—
44C4×Q8×C17C2×C414yes—
45C17×#117C2×C412yes—
46C2×C42×C17C2×C411yescharacteristic
47#10587632C2×C414yes—
48Q8×Dic17C2314yes—
49#10587630C2×C414yes—
50#10587612C2×C412yes—
51#10587610C2×C414yes—
52C2×C4×Dic17C2×C411yescharacteristic
53C2×C4×Dic17C2312yes—
54#10587583C2×C414yes—
55#10587582C2×C418yes—
56#10587578C2314yes—
57C4⋊C4×D17C2×C414yes—
58C4⋊C4×D17C2×C418yes—
59C4⋊C4×D17C2×C414yes—
60#10587576C2×C414yes—
61#10587575C2×C418yes—
62#10587574C2×C414yes—
63#10587574C2×C414yes—
64#10587573C2318yes—
65#10587573C2314yes—
66C22⋊C4×D17C2×C414yes—
67#10587564C2×C418yes—
68#10587563C2314yes—
69#10587558C2×C414yes—
70C42×D17C2×C411yescharacteristic
71C42×D17C2×C411yescharacteristic
72C42×D17C2×C412yes—
73C42×D17C2312yes—
74C42×D17C2311yescharacteristic
75C42×D17C2311yescharacteristic
76C42×D17C2314yes—
77#10587556C2×C412yes—
78#10587555C2×C412yes—
79C4×Dic34C2×C418yes—
80C4×Dic34C2×C414yes—
81C22⋊#3624C2318yes—
82#10587544C2318yes—
83#10587544C23116yes—
84#10587543C2318yes—
85#10587542C2318yes—
86#10587542C2318yes—
87#10587542C23116yes—
88C4⋊#3624C2318yes—
89C4⋊#3624C23116yes—
90C4×#3624C23116yes—
91C23×D17C22×C411yescharacteristic
92C2×Q8×C17C22×C414yes—
93C22×C4×C17C22×C411yescharacteristic
94C22×C4×C17C22×C412yes—
95C22×Dic17C22×C412yes—
96C22×Dic17C2411yescharacteristic
97Q8×D17—48no—
98C2×C4×D17—24no—
99C2×C4×D17—44no—
100C2×C4×D17C22×C412yes—
101C2×C4×D17C22×C412yes—
102C2×C4×D17C22×C411yescharacteristic
103C2×C4×D17C22×C411yescharacteristic
104C2×C4×D17C22×C418yes—
105C2×C4×D17C22×C412yes—
106C2×C4×D17C22×C412yes—
107C2×C4×D17C2411yescharacteristic
108C2×C4×D17C2411yescharacteristic
109C2×Dic34C22×C414yes—
110C2×Dic34C22×C418yes—
111C2×#3624C24116yes—
112#63242—216no—
113C4⋊C4×C17C22×C418yes—
114C4⋊C4×C17C22×C414yes—
115C4⋊C4×C17C22×C414yes—
116C22⋊C4×C17C22×C414yes—
117C42×C17C22×C411yescharacteristic
118C42×C17C22×C411yescharacteristic
119C42×C17C22×C412yes—
120C42×C17C22×C414yes—
121C22⋊Dic17C22×C414yes—
122#63227C22×C418yes—
123C4⋊Dic17C22×C414yes—
124C4⋊Dic17C22×C418yes—
125C4⋊Dic17C22×C414yes—
126#63225C22×C418yes—
127#63225C22×C418yes—
128#63225C22×C418yes—
129#63225C22×C418yes—
130C4×Dic17C22×C412yes—
131C4×Dic17C22×C414yes—
132C4×Dic17C22×C412yes—
133C4×Dic17C22×C412yes—
134C4×Dic17C22×C411yescharacteristic
135C4×Dic17C22×C411yescharacteristic
136C4×Dic17C2418yes—
137C4×Dic17C2412yes—
138C4×Dic17C2412yes—
139C2×#2987—171nomaximal, Sylow
140C23×C17C23×C411yescharacteristic
141C22×D17—22no—
142C22×D17—24no—
143C22×D17C23×C411yescharacteristic
144C22×D17C23×C411yescharacteristic
145Q8×C17—44no—
146C2×C4×C17—22no—
147C2×C4×C17—42no—
148C2×C4×C17C23×C412yes—
149C2×C4×C17C23×C411yescharacteristic
150C2×C4×C17C23×C412yes—
151C2×C4×C17C23×C418yes—
152C2×C4×C17C23×C411yescharacteristic
153C2×Dic17—22no—
154C2×Dic17—42no—
155C2×Dic17C23×C418yes—
156C2×Dic17C23×C412yes—
157C2×Dic17C23×C412yes—
158C2×Dic17C23×C411yescharacteristic
159C2×Dic17C2511yescharacteristic
160C4×D17—22no—
161C4×D17—24no—
162C4×D17—24no—
163C4×D17—216no—
164C4×D17—22no—
165C4×D17—22no—
166C4×D17—42no—
167C4×D17—42no—
168C4×D172−1+414yes—
169Dic34—48no—
170Dic34—44no—
171#3624—216no—
172C2×#533—171no—
173#2987—178no—
174#2987—174no—
175#2987—174no—
176C2×#446—178no—
177C2×#433—174no—
178C2×#432—172no—
179C22×C17—21no—
180C22×C17—22no—
181C22×C17C24×C411yescharacteristic
182C2×D17—21no—
183C2×D17—22no—
184C2×D17—44no—
185C2×D17#51912yes—
186C2×D17#56814yes—
187C4×C17—21no—
188C4×C17—22no—
189C4×C17—28no—
190C4×C17—22no—
191C4×C17#51912yes—
192Dic17—21no—
193Dic17—22no—
194Dic17—28no—
195Dic17—22no—
196Dic17C2×2−1+412yes—
197#533—172no—
198#533—172no—
199#533—174no—
200#533—174no—
201#533—172no—
202#533—171no—
203#533#59511yescharacteristic
204C2×C4⋊Q8—172no—
205C2×#125—172no—
206C2×C22⋊Q8—174no—
207C2×C4×Q8—174no—
208C2×#117—172no—
209C22×C42—171no—
210#446—1716no—
211#446—1716no—
212#446—1716no—
213#446—1716no—
214#433—1716no—
215#433—1716no—
216#432—174no—
217#432—174no—
218#432—174no—
219#432—174no—
220C2×C4⋊C8—174no—
221C2×C4⋊C8—178no—
222C2×C22⋊C8—174no—
223C2×#97—174no—
224C2×#97—174no—
225C2×C4×C8—174no—
226C2×C17—41no—
227C2×C17C2×#51911yescharacteristic
228C2×C17C2×#56812yes—
229D17—41no—
230D17#298714yescomplemented
231C22×Q8—174no—
232C23×C4—171no—
233C23×C4—172no—
234C22×C8—178no—
235C4⋊Q8—174no—
236C4⋊Q8—174no—
237C4⋊Q8—174no—
238C4⋊Q8—172no—
239C4⋊Q8C2×#59512yes—
240#125—178no—
241#125—174no—
242#125—172no—
243#125C2×#59512yes—
244C22⋊Q8—174no—
245C22⋊Q8—174no—
246C22⋊Q8—178no—
247C22⋊Q8—174no—
248C22⋊Q8—178no—
249C22⋊Q8C2×#59514yes—
250C4×Q8—174no—
251C4×Q8—174no—
252C4×Q8—178no—
253C4×Q8—178no—
254C4×Q8—174no—
255C4×Q8C2×#59514yes—
256#117—172no—
257#117—174no—
258#117—174no—
259#117—174no—
260#117C2×#59512yes—
261C2×C4⋊C4—174no—
262C2×C4⋊C4—178no—
263C2×C4⋊C4—174no—
264C2×C22⋊C4—174no—
265C2×C42—172no—
266C2×C42—171no—
267C2×C42—174no—
268C2×C42—172no—
269C2×C42—171no—
270C2×C42—171no—
271C2×C42—172no—
272C2×C42—171no—
273C2×C42—171no—
274C2×C42C2×#59511yescharacteristic
275C4⋊C8—178no—
276C4⋊C8—1716no—
277C4⋊C8—178no—
278C4⋊C8—1716no—
279C22⋊C8—178no—
280C22⋊C8—178no—
281#97—178no—
282#97—178no—
283#97—1716no—
284C4×C8—1716no—
285C17C2×#298711yescharacteristic, complemented, Sylow
286C24—171no—
287C2×Q8—178no—
288C2×Q8—174no—
289C2×Q8—688no—
290C2×Q8C22×#59514yes—
291C22×C4—171no—
292C22×C4—171no—
293C22×C4—172no—
294C22×C4—171no—
295C22×C4—172no—
296C22×C4—172no—
297C22×C4—178no—
298C22×C4—171no—
299C22×C4—171no—
300C22×C4—172no—
301C22×C4—172no—
302C22×C4—344no—
303C22×C4—684no—
304C22×C4C22×#59511yescharacteristic
305C22×C4C22×#59512yes—
306C2×C8—1716no—
307C2×C8—3416no—
308C4⋊C4—178no—
309C4⋊C4—174no—
310C4⋊C4—178no—
311C4⋊C4—178no—
312C4⋊C4—178no—
313C4⋊C4—178no—
314C4⋊C4—174no—
315C4⋊C4C22×#59514yes—
316C4⋊C4C22×#59518yes—
317C4⋊C4C22×#59514yes—
318C22⋊C4—174no—
319C22⋊C4—178no—
320C22⋊C4C22×#59514yes—
321C42—178no—
322C42—172no—
323C42—172no—
324C42—172no—
325C42—171no—
326C42—172no—
327C42—171no—
328C42—172no—
329C42—174no—
330C42C22×#59511yescharacteristic
331C42C22×#59511yescharacteristic
332C42C22×#59512yes—
333C42C22×#59514yes—
334C23—171no—
335C23—171no—
336C23—342no—
337C23—344no—
338C23C23×#59511yescharacteristic
339Q8—44no—
340Q8—684no—
341Q8—688no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—171no—
345C2×C4—174no—
346C2×C4—171no—
347C2×C4—172no—
348C2×C4—172no—
349C2×C4—178no—
350C2×C4—342no—
351C2×C4—342no—
352C2×C4—344no—
353C2×C4—344no—
354C2×C4—3416no—
355C2×C4—342no—
356C2×C4—342no—
357C2×C4—682no—
358C2×C4—682no—
359C2×C4—682no—
360C2×C4C23×#59511yescharacteristic
361C2×C4C23×#59512yes—
362C2×C4C23×#59512yes—
363C2×C4C23×#59518yes—
364C2×C4C23×#59511yescharacteristic
365C8—3416no—
366C22—21no—
367C22—22no—
368C22—172no—
369C22—174no—
370C22—341no—
371C22—342no—
372C22—684no—
373C22C24×#59511yescharacteristic
374C4—21no—
375C4—22no—
376C4—22no—
377C4—28no—
378C4—172no—
379C4—341no—
380C4—342no—
381C4—342no—
382C4—348no—
383C4#1176387712yes—
384C2—41no—
385C2—174no—
386C2—681no—
387C2C2×#1176387711yescharacteristic
388C2D17⋊#56812yes—
subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC17×#533C4
prime radicalC23×D17C22×C4
cosocleC2×Dic17C25
hypercenter#533#595
hypocenterC17C2×#2987
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #14545698C2semidirect
2. #14545697C2semidirect
3. #14545696C2semidirect
4. D17⋊#446C2semidirect
8. #11763861C22semidirect
9. #11763861C22semidirect
10. #11763860C22semidirect
11. #11763859C22semidirect
230. D17#2987semidirect
285. C17C2×#2987semidirect

Maximal subgroups

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

subgroupindex
#145456982
#145456972
#145456962
D17⋊#4462
D17⋊#4332
D17⋊#4322
D17×#5332
C2×#298717