Finite Group Databasebeta

← D17⋊#1571 #17966384

Subgroups — D17⋊#1571 #17966384

Order 4352.

770 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17⋊#423C211yesmaximal, characteristic
2C2×#11763810C211yesmaximal, characteristic
3#14544354C214yesmaximal, complemented
4#14544353C214yesmaximal, complemented
5#14544329C214yesmaximal, complemented
6D17×#431C211yesmaximal, characteristic
7C2×D17⋊M16—21no—
8C22×#63242—21no—
9#11763814—21no—
10#11763813C2212yes—
11#11763812—21no—
12#11763812C2212yes—
13C2×#10587544—21no—
14#11763810—21no—
15#11763810—21no—
16#11763810—21no—
17#11763810C2212yes—
18#11763810C2212yes—
19#11763810C2212yes—
20C2×C4⋊#3624C2212yes—
21#11763673C2218yescomplemented
22#11763672C2218yescomplemented
23C2×C42×D17C2211yescharacteristic
24#11762862C411yescharacteristic
25#11762861C2212yes—
26#11762860C412yes—
27#11762859C2212yes—
28C4⋊C8×D17C412yes—
29C22⋊C8×D17C412yes—
30C4×C8×D17C2212yes—
31C17×#431C411yescharacteristic
32C22×C4×D17C2×C411yescharacteristic
33C22×C4×D17D411yescharacteristic
34C22×C4×D17Q811yescharacteristic
35C2×#63247—22no—
36C22×#3624—22no—
37D17⋊M16—44no—
38C2×#63243—22no—
39C2×#63242—22no—
40C2×#63242—22no—
41C2×#63242—22no—
42C2×#63242—44no—
43C2×C42×C17C2×C411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17Q811yescharacteristic
46C2×C4×Dic17C2311yescharacteristic
47C2×C8×D17C2×C414yes—
48C42×D17C2×C411yescharacteristic
49C42×D17C2×C411yescharacteristic
50C42×D17D411yescharacteristic
51C42×D17D411yescharacteristic
52C42×D17Q811yescharacteristic
53C42×D17Q811yescharacteristic
54C42×D17C2311yescharacteristic
55C42×D17C2311yescharacteristic
56#10587544—22no—
57#10587544—22no—
58#10587544—22no—
59#10587544—22no—
60C4⋊#3624—22no—
61C4⋊#3624—22no—
62C4⋊#3624C2314yes—
63C4⋊#3624C2314yes—
64C17×C4⋊C8C2×C412yes—
65C17×C22⋊C8C2×C412yes—
66C4×C8×C17C2×C412yes—
67C22⋊#3622C2×C412yes—
68#10587491C2×C414yes—
69#10587485C2×C414yes—
70C8×Dic17C2314yes—
71C4⋊#3622C2×C412yes—
72C4×#3622C2×C412yes—
73C23×D17C4⋊C411yescharacteristic
74C22×C4×C17C4⋊C411yescharacteristic
75C22×C4×C17C4⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×Dic17C4⋊C411yescharacteristic
78C22×Dic17C2×D411yescharacteristic
79C22×Dic17C2×Q811yescharacteristic
80C2×C4×D17—24no—
81C2×C4×D17—42no—
82C2×C4×D17C4⋊C411yescharacteristic
83C2×C4×D17C4⋊C411yescharacteristic
84C2×C4×D17C4⋊C411yescharacteristic
85C2×C4×D17C4⋊C411yescharacteristic
86C2×C4×D17C4⋊C411yescharacteristic
87C2×C4×D17C4⋊C411yescharacteristic
88C2×C4×D17D814yes—
89C2×C4×D17Q1614yes—
90C2×C4×D17C22×C411yescharacteristic
91C2×C4×D17C22×C411yescharacteristic
92C2×C4×D17C2×D411yescharacteristic
93C2×C4×D17C2×D411yescharacteristic
94C2×C4×D17C2×Q811yescharacteristic
95C2×C4×D17C2×Q811yescharacteristic
96#63247—44no—
97C2×#3624—24no—
98C2×#3624—24no—
99C2×#3624—44no—
100#63243—44no—
101#63242—44no—
102#63242—44no—
103#63242—44no—
104C2×C8×C17C22×C414yes—
105C42×C17C4⋊C411yescharacteristic
106C42×C17C4⋊C411yescharacteristic
107C42×C17C22×C411yescharacteristic
108C42×C17C22×C411yescharacteristic
109C4×Dic17C4⋊C411yescharacteristic
110C4×Dic17C4⋊C411yescharacteristic
111C4×Dic17C4⋊C411yescharacteristic
112C4×Dic17C4⋊C411yescharacteristic
113C4×Dic17C22×C411yescharacteristic
114C4×Dic17C2×D411yescharacteristic
115C4×Dic17C2×D411yescharacteristic
116C4×Dic17C2×D411yescharacteristic
117C4×Dic17C2×Q811yescharacteristic
118C4×Dic17C2×Q811yescharacteristic
119C4×Dic17C2×Q811yescharacteristic
120C4×Dic17C2411yescharacteristic
121C2×#3622C22×C414yes—
122C8×D17—28no—
123C2×#1571—171nomaximal, Sylow
124C23×C17C2×C4⋊C411yescharacteristic
125C22×D17—22no—
126C22×D17—22no—
127C22×D17#10714yes—
128C22×D17C2×C4⋊C411yescharacteristic
129C22×D17C2×C4⋊C411yescharacteristic
130C2×C4×C17—22no—
131C2×C4×C17—41no—
132C2×C4×C17#10714yes—
133C2×C4×C17C2×C4⋊C411yescharacteristic
134C2×C4×C17C2×C4⋊C411yescharacteristic
135C2×C4×C17C2×C4⋊C411yescharacteristic
136C2×C4×C17C2×C4⋊C411yescharacteristic
137C2×C4×C17C2×C4⋊C411yescharacteristic
138C2×C4×C17C23×C411yescharacteristic
139C2×Dic17—22no—
140C2×Dic17—41no—
141C2×Dic17C2×C4⋊C411yescharacteristic
142C2×Dic17C2×C4⋊C411yescharacteristic
143C2×Dic17C2×C4⋊C411yescharacteristic
144C2×Dic17C2×C4⋊C411yescharacteristic
145C2×Dic17C2×D812yes—
146C2×Dic17C2×Q1612yes—
147C2×Dic17C22×D411yescharacteristic
148C2×Dic17C22×Q811yescharacteristic
149C4×D17—22no—
150C4×D17—22no—
151C4×D17—22no—
152C4×D17—22no—
153C4×D17—22no—
154C4×D17—41no—
155C4×D17—41no—
156C4×D17#10714yes—
157C4×D17#10714yes—
158C4×D17#13114yes—
159C4×D17C2×D812yes—
160C4×D17C2×D812yes—
161C4×D17C2×Q1612yes—
162C4×D17C2×Q1612yes—
163#3624—44no—
164#3624—44no—
165C8×C17—24no—
166#3622—24no—
167C2×#431—171no—
168C2×#423—171no—
169C22×C4⋊C8—171no—
170#1571—174no—
171#1571—174no—
172C2×#335—174no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17C2×#10712yes—
176C22×C17C22×C4⋊C411yescharacteristic
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—28no—
180C2×D17#42412yes—
181C2×D17C2×#10712yes—
182C2×D17C2×#10712yes—
183C2×D17#43012yes—
184C4×C17—21no—
185C4×C17—21no—
186C4×C17—21no—
187C4×C17C2×#10712yes—
188C4×C17C2×#10712yes—
189C4×C17C2×#13112yes—
190Dic17—21no—
191Dic17—21no—
192Dic17—21no—
193Dic17#42412yes—
194Dic17C2×#10712yes—
195Dic17C22×D811yescharacteristic
196Dic17C22×Q1611yescharacteristic
197C22×M16—341no—
198C23×C8—341no—
199C22×C42—171no—
200#431—171no—
201#431—172no—
202#431—172no—
203#431—172no—
204#431#59511yescharacteristic
205#423—172no—
206#423—172no—
207#423—341no—
208#423—341no—
209C2×C4⋊C8—172no—
210C2×C4⋊C8—172no—
211C2×C4⋊C8—172no—
212C2×C4⋊C8—172no—
213C2×C4⋊C8—172no—
214C2×C4⋊C8—341no—
215C2×C4⋊C8—341no—
216C2×C4⋊C8—341no—
217C2×C4⋊C8—341no—
218C2×C22⋊C8—172no—
219C2×C4×C8—172no—
220#335—178no—
221#335—178no—
222C2×C17—22no—
223C2×C17C2×#42411yescharacteristic
224C2×C17C22×#10711yescharacteristic
225C2×C17C2×#43011yescharacteristic
226D17—22no—
227D17#157114yescomplemented
228C23×C4—171no—
229C23×C4—171no—
230C23×C4—171no—
231C2×M16—342no—
232C2×M16—342no—
233C2×M16—684no—
234C22×C8—174no—
235C22×C8—342no—
236C22×C8—342no—
237C22×C8—342no—
238C22×C8—342no—
239C22×C8—684no—
240C2×C42—171no—
241C2×C42—171no—
242C2×C42—171no—
243C2×C42—171no—
244C2×C42—171no—
245C2×C42—171no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42C2×#59511yescharacteristic
252C4⋊C8—174no—
253C4⋊C8—174no—
254C4⋊C8—174no—
255C4⋊C8—172no—
256C4⋊C8—342no—
257C4⋊C8—342no—
258C4⋊C8—342no—
259C4⋊C8—342no—
260C4⋊C8—342no—
261C4⋊C8—342no—
262C4⋊C8C2×#59512yes—
263C22⋊C8—172no—
264C22⋊C8—174no—
265C22⋊C8C2×#59512yes—
266C4×C8—174no—
267C4×C8—172no—
268C4×C8C2×#59512yes—
269C17C2×#157111yescharacteristic, complemented, Sylow
270C24—171no—
271C22×C4—171no—
272C22×C4—171no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—174no—
278C22×C4—174no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—171no—
284C22×C4—171no—
285C22×C4—171no—
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—344no—
289C22×C4—682no—
290C22×C4C4⋊#59511yescharacteristic
291C22×C4C4⋊#59511yescharacteristic
292C22×C4C22×#59511yescharacteristic
293M16—684no—
294M16—684no—
295C2×C8—174no—
296C2×C8—348no—
297C2×C8—344no—
298C2×C8—344no—
299C2×C8—684no—
300C2×C8—684no—
301C2×C8—684no—
302C2×C8—684no—
303C2×C8C22×#59514yes—
304C42—171no—
305C42—171no—
306C42—171no—
307C42—171no—
308C42—171no—
309C42—171no—
310C42—171no—
311C42—171no—
312C42—171no—
313C42—171no—
314C42—171no—
315C42—171no—
316C42C4⋊#59511yescharacteristic
317C42C4⋊#59511yescharacteristic
318C42C22×#59511yescharacteristic
319C42C22×#59511yescharacteristic
320C23—171no—
321C23—174no—
322C23—171no—
323C23—342no—
324C23—342no—
325C23C2×C4⋊#59511yescharacteristic
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—172no—
329C2×C4—172no—
330C2×C4—171no—
331C2×C4—171no—
332C2×C4—171no—
333C2×C4—172no—
334C2×C4—172no—
335C2×C4—174no—
336C2×C4—174no—
337C2×C4—172no—
338C2×C4—172no—
339C2×C4—174no—
340C2×C4—171no—
341C2×C4—171no—
342C2×C4—171no—
343C2×C4—342no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—342no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4—681no—
352C2×C4#1058753414yes—
353C2×C4C2×C4⋊#59511yescharacteristic
354C2×C4C2×C4⋊#59511yescharacteristic
355C2×C4C2×C4⋊#59511yescharacteristic
356C2×C4C2×C4⋊#59511yescharacteristic
357C2×C4C2×C4⋊#59511yescharacteristic
358C2×C4C23×#59511yescharacteristic
359C8—24no—
360C8—344no—
361C8—684no—
362C8—684no—
363C22—21no—
364C22—21no—
365C22—172no—
366C22—172no—
367C22—172no—
368C22—172no—
369C22—348no—
370C22—341no—
371C22—341no—
372C22C2×#1058753412yes—
373C22C22×C4⋊#59511yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—172no—
378C4—171no—
379C4—171no—
380C4—172no—
381C4—341no—
382C4—341no—
383C4—341no—
384C4C2×#1058753412yes—
385C4C2×#1058753412yes—
386C4D17⋊#13112yes—
387C2—22no—
388C2—174no—
389C2—342no—
390C2D17⋊#42411yescharacteristic
391C2C22×#1058753411yescharacteristic
392C2D17⋊#43011yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#431C4
socleC22×C17C22×C4⋊C4
prime radicalC23×D17C4⋊C4
cosocleC4×Dic17C24
hypercenter#431#595
hypocenterC17C2×#1571
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #14544354C2semidirect
4. #14544353C2semidirect
5. #14544329C2semidirect
21. #11763673C22semidirect
22. #11763672C22semidirect
227. D17#1571semidirect
269. C17C2×#1571semidirect

Maximal subgroups

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

subgroupindex
D17⋊#4232
C2×#117638102
#145443542
#145443532
#145443292
D17×#4312
C2×#157117