Finite Group Databasebeta

← D17⋊#2905 #17979534

Subgroups — D17⋊#2905 #17979534

Order 4352.

2830 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D17⋊M16C212yesmaximal
2#14545428C214yesmaximal, complemented
3#14545427C218yesmaximal, complemented
4#14545426C214yesmaximal, complemented
5D17⋊#424C218yesmaximal, complemented
6D17⋊#423C214yesmaximal, complemented
7C2×#117×D17C211yesmaximal, characteristic
8C22×#63243C2214yes—
9C2×D17⋊M16—216no—
10C2×D17⋊M16C2214yes—
11C2×D17⋊M16C2214yes—
12C2×D17⋊M16C2214yes—
13C2×D17⋊M16C2214yes—
14C22×#63247C2214yes—
15C22×#63242C2214yes—
16#11763816C22132yescomplemented
17#11763815C22132yescomplemented
18#11763814C2218yescomplemented
19#11763813C2218yescomplemented
20#11763812C22116yescomplemented
21#11763810C22116yescomplemented
22C23×C4×D17C2211yescharacteristic
23C2×#10587612C411yescharacteristic
24C2×#10587578C2212yes—
25C2×#10587558C412yes—
26C2×#10587563C2212yes—
27#117×D17C414yes—
28#117×D17C414yes—
29#117×D17C2214yes—
30#117×D17C2214yes—
31C2×C4⋊C4×D17C412yes—
32C2×C22⋊C4×D17C412yes—
33C2×C42×D17C2212yes—
34C2×C17×#117C411yescharacteristic
35C24×D17C2×C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×Dic17C2311yescharacteristic
38C22×C4×D17C2×C414yes—
39C22×C4×D17C2×C411yescharacteristic
40C22×C4×D17C2×C412yes—
41C22×C4×D17C2×C412yes—
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17D418yes—
44C22×C4×D17Q818yes—
45C22×C4×D17C2311yescharacteristic
46C22×C4×D17C2312yes—
47C22×C4×D17C2312yes—
48C22×C4×D17C2311yescharacteristic
49C2×#63247—216no—
50C2×#63247C2318yes—
51C2×#63247C2318yes—
52C22×#3624C2318yes—
53D17⋊M16—216no—
54D17⋊M16—216no—
55D17⋊M16—216no—
56D17⋊M16—216no—
57C2×#63243—216no—
58C2×#63243C2318yes—
59C2×#63243C2318yes—
60C2×#63242—216no—
61C2×#63242C2318yes—
62C2×#63242C2318yes—
63C17×#117C2×C414yes—
64C17×#117C2×C414yes—
65C2×C4⋊C4×C17C2×C412yes—
66C2×C22⋊C4×C17C2×C412yes—
67C2×C42×C17C2×C412yes—
68C2×C22⋊Dic17C2×C412yes—
69C2×#63227C2×C414yes—
70#10587612C2×C414yes—
71#10587612C2×C414yes—
72C2×C4⋊Dic17C2×C412yes—
73C2×#63225C2×C414yes—
74C2×C4×Dic17C2×C412yes—
75C2×C4×Dic17C2314yes—
76#10587578C2×C418yes—
77#10587578C2318yes—
78C4⋊C4×D17C2×C418yes—
79C4⋊C4×D17C2×C418yes—
80C22⋊C4×D17C2×C418yes—
81C22⋊C4×D17C2×C418yes—
82#10587563C2×C418yes—
83#10587563C2318yes—
84#10587558C2×C418yes—
85#10587558C2×C418yes—
86C42×D17C2×C414yes—
87C42×D17C2×C414yes—
88C42×D17C2314yes—
89C42×D17C2314yes—
90#10587544C23132yescomplemented
91C4⋊#3624C23132yescomplemented
92C24×C17C22×C411yescharacteristic
93C23×D17—44no—
94C23×D17C4⋊C418yes—
95C23×D17C22×C411yescharacteristic
96C23×D17C22×C412yes—
97C23×D17C22×C412yes—
98C23×D17C22×C411yescharacteristic
99C22×C4×C17C4⋊C418yes—
100C22×C4×C17C22×C414yes—
101C22×C4×C17C22×C411yescharacteristic
102C22×C4×C17C22×C411yescharacteristic
103C22×C4×C17C22×C412yes—
104C22×C4×C17C22×C412yes—
105C22×Dic17C22×C414yes—
106C22×Dic17C22×C412yes—
107C22×Dic17C22×C411yescharacteristic
108C22×Dic17C2×D414yes—
109C22×Dic17C2×Q814yes—
110C22×Dic17C2412yes—
111C22×Dic17C2411yescharacteristic
112C2×C4×D17—48no—
113C2×C4×D17C4⋊C418yes—
114C2×C4×D17C4⋊C4116yes—
115C2×C4×D17C4⋊C4116yes—
116C2×C4×D17C4⋊C418yes—
117C2×C4×D17C22×C418yes—
118C2×C4×D17C22×C418yes—
119C2×C4×D17C22×C411yescharacteristic
120C2×C4×D17C22×C411yescharacteristic
121C2×C4×D17C22×C412yes—
122C2×C4×D17C22×C412yes—
123C2×C4×D17C22×C412yes—
124C2×C4×D17C22×C412yes—
125C2×C4×D17C22×C412yes—
126C2×C4×D17C2×D418yes—
127C2×C4×D17C2×D418yes—
128C2×C4×D17C2×D414yes—
129C2×C4×D17C2×D414yes—
130C2×C4×D17C2×Q814yes—
131C2×C4×D17C2×Q818yes—
132C2×C4×D17C2×Q818yes—
133C2×C4×D17C2×Q814yes—
134C2×C4×D17C2411yescharacteristic
135C2×C4×D17C2412yes—
136C2×C4×D17C2411yescharacteristic
137#63247—216no—
138#63247—216no—
139C2×#3624—216no—
140C2×#3624C24116yes—
141#63243—216no—
142#63243—216no—
143#63242—216no—
144#63242—216no—
145C4⋊C4×C17C22×C418yes—
146C22⋊C4×C17C22×C418yes—
147C42×C17C22×C414yes—
148C42×C17C22×C414yes—
149C22⋊Dic17C22×C418yes—
150#63227C22×C4116yes—
151C4⋊Dic17C22×C418yes—
152#63225C22×C4116yes—
153C4×Dic17C22×C418yes—
154C4×Dic17C22×C414yes—
155C4×Dic17C22×C414yes—
156C4×Dic17C2418yes—
157C2×#2905—171nomaximal, Sylow
158C23×C17—42no—
159C23×C17C2×C4⋊C414yes—
160C23×C17C23×C412yes—
161C23×C17C23×C411yescharacteristic
162C22×D17—24no—
163C22×D17—28no—
164C22×D17—416no—
165C22×D17—44no—
166C22×D17—42no—
167C22×D17C2×C4⋊C418yes—
168C22×D17C2×C4⋊C414yes—
169C22×D17C2×C4⋊C418yes—
170C22×D17C2×C4⋊C414yes—
171C22×D17C23×C411yescharacteristic
172C22×D17C23×C412yes—
173C22×D17C23×C411yescharacteristic
174C2×C4×C17—44no—
175C2×C4×C17C2×C4⋊C418yes—
176C2×C4×C17C2×C4⋊C418yes—
177C2×C4×C17C2×C4⋊C414yes—
178C2×C4×C17C2×C4⋊C414yes—
179C2×C4×C17C23×C418yes—
180C2×C4×C17C23×C411yescharacteristic
181C2×C4×C17C23×C412yes—
182C2×C4×C17C23×C411yescharacteristic
183C2×Dic17—44no—
184C2×Dic17C2×C4⋊C418yes—
185C2×Dic17C2×C4⋊C414yes—
186C2×Dic17C23×C418yes—
187C2×Dic17C23×C411yescharacteristic
188C2×Dic17C23×C412yes—
189C2×Dic17C22×D414yes—
190C2×Dic17C22×D412yes—
191C2×Dic17C22×Q814yes—
192C2×Dic17C22×Q812yes—
193C2×Dic17C2511yescharacteristic
194C4×D17—216no—
195C4×D17—48no—
196C4×D17C2×C4⋊C414yes—
197C4×D17C2×C4⋊C418yes—
198C4×D17C2×C4⋊C418yes—
199C4×D17C2×C4⋊C418yes—
200C4×D17C2×C4⋊C418yes—
201C4×D17C2×C4⋊C414yes—
202C4×D17C2×C4⋊C418yes—
203C4×D17C22×D412yes—
204C4×D17C22×D414yes—
205C4×D17C22×D412yes—
206C4×D17C22×Q814yes—
207C4×D17C22×Q812yes—
208C4×D17C22×Q812yes—
209#3624—216no—
210C23×M16—172no—
211C22×#117—171no—
212#2905—174no—
213#2905—178no—
214#2905—174no—
215C2×#424—178no—
216C2×#423—174no—
217C22×C17—22no—
218C22×C17—24no—
219C22×C17—44no—
220C22×C17C22×C4⋊C414yes—
221C22×C17C22×C4⋊C412yes—
222C22×C17C24×C411yescharacteristic
223C2×D17—22no—
224C2×D17—24no—
225C2×D17—28no—
226C2×D17—216no—
227C2×D17—48no—
228C2×D17—44no—
229C2×D17C22×C4⋊C414yes—
230C2×D17C22×C4⋊C412yes—
231C2×D17C22×C4⋊C412yes—
232C2×D17#56814yes—
233C4×C17—28no—
234C4×C17C22×C4⋊C414yes—
235C4×C17C22×C4⋊C412yes—
236C4×C17C22×C4⋊C412yes—
237Dic17—28no—
238Dic17C22×C4⋊C412yes—
239Dic17C22×C4⋊C414yes—
240Dic17C23×D411yescharacteristic
241Dic17C23×Q811yescharacteristic
242C24×C4—171no—
243C22×M16—174no—
244C22×M16—174no—
245C22×M16—174no—
246C22×M16—174no—
247C22×M16—174no—
248C22×M16—174no—
249C22×M16—3416no—
250C23×C8—174no—
251C2×#117—171no—
252C2×#117—174no—
253C2×#117—174no—
254C2×#117—174no—
255C2×#117—174no—
256C2×#117—172no—
257C2×#117—172no—
258C2×#117—172no—
259C2×#117#59511yescharacteristic
260C22×C4⋊C4—172no—
261C22×C22⋊C4—172no—
262C22×C42—172no—
263#424—1732no—
264#424—1732no—
265#423—1716no—
266#423—178no—
267#423—178no—
268C2×C4⋊C8—1716no—
269C2×C17—22no—
270C2×C17—24no—
271C2×C17C23×C4⋊C411yescharacteristic
272C2×C17C2×#56812yes—
273D17—22no—
274D17—24no—
275D17#290514yescomplemented
276C25—171no—
277C23×C4—171no—
278C23×C4—178no—
279C23×C4—178no—
280C23×C4—171no—
281C23×C4—171no—
282C23×C4—172no—
283C23×C4—172no—
284C23×C4—172no—
285C23×C4—171no—
286C23×C4—172no—
287C23×C4—171no—
288C23×C4—174no—
289C23×C4C2×#59511yescharacteristic
290C2×M16—178no—
291C2×M16—178no—
292C2×M16—178no—
293C2×M16—178no—
294C2×M16—3416no—
295C2×M16—3416no—
296C2×M16—3416no—
297C2×M16—3416no—
298C2×M16—3416no—
299C2×M16—3416no—
300C22×C8—178no—
301C22×C8—178no—
302C22×C8—178no—
303C22×C8—3416no—
304#117—174no—
305#117—174no—
306#117—178no—
307#117—178no—
308#117—178no—
309#117—178no—
310#117—178no—
311#117—178no—
312#117C2×#59514yes—
313#117C2×#59514yes—
314C2×C4⋊C4—174no—
315C2×C4⋊C4—172no—
316C2×C4⋊C4—178no—
317C2×C4⋊C4—178no—
318C2×C4⋊C4C2×#59512yes—
319C2×C22⋊C4—172no—
320C2×C22⋊C4—174no—
321C2×C22⋊C4—178no—
322C2×C22⋊C4—178no—
323C2×C22⋊C4C2×#59512yes—
324C2×C42—174no—
325C2×C42—172no—
326C2×C42—174no—
327C2×C42—174no—
328C2×C42—174no—
329C2×C42—174no—
330C2×C42C2×#59512yes—
331C4⋊C8—1732no—
332C4⋊C8—1732no—
333C17C2×#290511yescharacteristic, complemented, Sylow
334C24—172no—
335C24—171no—
336C24—178no—
337C24—171no—
338C24—172no—
339C24—684no—
340C24C22×#59511yescharacteristic
341C22×C4—174no—
342C22×C4—174no—
343C22×C4—171no—
344C22×C4—172no—
345C22×C4—171no—
346C22×C4—172no—
347C22×C4—178no—
348C22×C4—1716no—
349C22×C4—178no—
350C22×C4—1716no—
351C22×C4—178no—
352C22×C4—178no—
353C22×C4—174no—
354C22×C4—174no—
355C22×C4—178no—
356C22×C4—174no—
357C22×C4—174no—
358C22×C4—178no—
359C22×C4—171no—
360C22×C4—172no—
361C22×C4—172no—
362C22×C4—172no—
363C22×C4—172no—
364C22×C4—171no—
365C22×C4—172no—
366C22×C4—171no—
367C22×C4—172no—
368C22×C4—171no—
369C22×C4—174no—
370C22×C4—178no—
371C22×C4—178no—
372C22×C4—688no—
373C22×C4C4⋊#59518yes—
374C22×C4C22×#59514yes—
375C22×C4C22×#59511yescharacteristic
376C22×C4C22×#59512yes—
377C22×C4C22×#59511yescharacteristic
378C22×C4C22×#59512yes—
379M16—3416no—
380M16—3416no—
381M16—3416no—
382M16—3416no—
383C2×C8—1716no—
384C2×C8—3416no—
385C2×C8—3416no—
386C2×C8—3416no—
387C4⋊C4—1716no—
388C4⋊C4—178no—
389C4⋊C4C22×#59518yes—
390C22⋊C4—178no—
391C22⋊C4—1716no—
392C22⋊C4C22×#59518yes—
393C42—178no—
394C42—178no—
395C42—174no—
396C42—174no—
397C42C22×#59514yes—
398C42C22×#59514yes—
399C23—42no—
400C23—171no—
401C23—178no—
402C23—174no—
403C23—172no—
404C23—171no—
405C23—174no—
406C23—178no—
407C23—344no—
408C23—348no—
409C23—682no—
410C23—684no—
411C23—6816no—
412C23C2×C4⋊#59514yes—
413C23C23×#59512yes—
414C23C23×#59511yescharacteristic
415C2×C4—44no—
416C2×C4—174no—
417C2×C4—172no—
418C2×C4—174no—
419C2×C4—178no—
420C2×C4—172no—
421C2×C4—174no—
422C2×C4—171no—
423C2×C4—171no—
424C2×C4—172no—
425C2×C4—172no—
426C2×C4—174no—
427C2×C4—172no—
428C2×C4—178no—
429C2×C4—174no—
430C2×C4—178no—
431C2×C4—178no—
432C2×C4—178no—
433C2×C4—178no—
434C2×C4—174no—
435C2×C4—172no—
436C2×C4—174no—
437C2×C4—172no—
438C2×C4—178no—
439C2×C4—3416no—
440C2×C4—688no—
441C2×C4—684no—
442C2×C4C2×C4⋊#59514yes—
443C2×C4C2×C4⋊#59518yes—
444C2×C4C2×C4⋊#59518yes—
445C2×C4C2×C4⋊#59514yes—
446C2×C4C23×#59518yes—
447C2×C4C23×#59511yescharacteristic
448C2×C4C23×#59512yes—
449C2×C4C23×#59511yescharacteristic
450C8—3416no—
451C22—22no—
452C22—24no—
453C22—44no—
454C22—172no—
455C22—174no—
456C22—174no—
457C22—172no—
458C22—348no—
459C22—3416no—
460C22—342no—
461C22—344no—
462C22—684no—
463C22—688no—
464C22C22×C4⋊#59514yes—
465C22C22×C4⋊#59512yes—
466C22C24×#59511yescharacteristic
467C4—28no—
468C4—171no—
469C4—174no—
470C4—172no—
471C4—171no—
472C4—348no—
473C4C22×C4⋊#59514yes—
474C4C22×C4⋊#59512yes—
475C4C22×C4⋊#59512yes—
476C2—22no—
477C2—24no—
478C2—174no—
479C2—342no—
480C2—344no—
481C2C23×C4⋊#59511yescharacteristic
482C2D17⋊#56812yes—
subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#117C4
prime radicalC24×D17C2×C4
cosocleC2×Dic17C25
hypercenterC2×#117#595
hypocenterC17C2×#2905
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14545428C2semidirect
3. #14545427C2semidirect
4. #14545426C2semidirect
5. D17⋊#424C2semidirect
6. D17⋊#423C2semidirect
16. #11763816C22semidirect
17. #11763815C22semidirect
18. #11763814C22semidirect
19. #11763813C22semidirect
20. #11763812C22semidirect
21. #11763810C22semidirect
90. #10587544C23semidirect
91. C4⋊#3624C23semidirect
275. D17#2905semidirect
333. C17C2×#2905semidirect

Maximal subgroups

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

subgroupindex
C22×D17⋊M162
#145454282
#145454272
#145454262
D17⋊#4242
D17⋊#4232
C2×#117×D172
C2×#290517