Finite Group Databasebeta

← C2×D17×#398 #17200534

Subgroups — C2×D17×#398 #17200534

Order 4352.

4158 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D17C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic
3C22×C4⋊C4×D17C212yesmaximal
4C2×#11762743C212yesmaximal, complemented
5C2×#11762742C212yesmaximal, complemented
6C2×#11762741C211yesmaximal, characteristic, complemented
7C2×#11762740C211yesmaximal, characteristic, complemented
8C2×#11762739C211yesmaximal, characteristic, complemented
9D17×#398C2116yesmaximal, direct product factor
10C2×#95×D17C211yesmaximal, characteristic
11C2×#95×D17C212yesmaximal
12C2×C17×#398C211yesmaximal, characteristic, complemented
13C23×C4×D17C2211yescharacteristic
14C23×C4×D17C2212yes—
15C23×C4×D17C2211yescharacteristic
16C23×C4×D17C2211yescharacteristic
17C23×C4×D17C2212yes—
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2212yes—
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2212yes—
22C22×#63225C2211yescharacteristic
23C22×#63225C2212yes—
24C22×#63225C2212yes—
25C22×#63225C2211yescharacteristic
26C2×C4⋊C4×D17—28no—
27C2×C4⋊C4×D17—216no—
28C2×C4⋊C4×D17—28no—
29C2×C4⋊C4×D17C2218yes—
30C2×C4⋊C4×D17C22116yes—
31C2×C4⋊C4×D17C2218yes—
32#11762743C22116yescomplemented
33#11762742C22116yescomplemented
34#11762741C2218yescomplemented
35#11762740C2218yescomplemented
36#11762739C2218yescomplemented
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2212yes—
39C2×#10587502C2212yes—
40C2×#10587502C2212yes—
41C2×#10587502C2212yes—
42#95×D17C22116yes—
43#95×D17C2218yes—
44C22×C4⋊C4×C17C2211yescharacteristic
45C22×C4⋊C4×C17C2211yescharacteristic
46C22×C4⋊C4×C17C2212yes—
47C17×#398C2218yescomplemented
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2212yes—
50C24×D17C2311yescharacteristic
51C23×C4×C17C2312yes—
52C23×C4×C17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2312yes—
56C23×Dic17C2312yes—
57C23×Dic17C2311yescharacteristic
58C23×Dic17C2311yescharacteristic
59C23×Dic17C2311yescharacteristic
60C23×Dic17C2312yes—
61C22×C4×D17—24no—
62C22×C4×D17—28no—
63C22×C4×D17—24no—
64C22×C4×D17—28no—
65C22×C4×D17—28no—
66C22×C4×D17—28no—
67C22×C4×D17—28no—
68C22×C4×D17—24no—
69C22×C4×D17—28no—
70C22×C4×D17—28no—
71C22×C4×D17D418yes—
72C22×C4×D17D418yes—
73C22×C4×D17Q8116yes—
74C22×C4×D17C2318yes—
75C22×C4×D17C2314yes—
76C22×C4×D17C2314yes—
77C22×C4×D17C2314yes—
78C22×C4×D17C2318yes—
79C2×C4⋊C4×C17—28no—
80C2×C4⋊C4×C17—24no—
81C2×C4⋊C4×C17—24no—
82C2×C4⋊C4×C17C2314yes—
83C2×C4⋊C4×C17C2314yes—
84C2×C4⋊C4×C17C2318yes—
85C2×C4⋊Dic17—24no—
86C2×C4⋊Dic17—24no—
87C2×C4⋊Dic17—28no—
88C2×C4⋊Dic17C2314yes—
89C2×C4⋊Dic17C2318yes—
90C2×C4⋊Dic17C2314yes—
91C2×#63225—28no—
92C2×#63225—24no—
93C2×#63225—24no—
94C2×#63225—28no—
95C2×#63225—28no—
96C2×#63225C2318yes—
97C2×#63225C2314yes—
98C2×#63225C2318yes—
99C2×#63225C2318yes—
100C2×#63225C2314yes—
101C4⋊C4×D17—264no—
102C4⋊C4×D17—232no—
103C4⋊C4×D17—232no—
104C17×#95C2314yes—
105C17×#95C2318yes—
106#10587502C2314yes—
107#10587502C2318yes—
108#10587502C2318yes—
109#10587502C2318yes—
110#10587502C2318yes—
111C24×C17C2411yescharacteristic
112C23×D17C2×D414yes—
113C23×D17C2×D414yes—
114C23×D17C2×Q818yes—
115C23×D17#4114yes—
116C23×D17#4118yes—
117C23×D17C2412yes—
118C22×C4×C17—22no—
119C22×C4×C17—24no—
120C22×C4×C17—22no—
121C22×C4×C17—24no—
122C22×C4×C17—24no—
123C22×C4×C17—24no—
124C22×C4×C17—24no—
125C22×C4×C17—22no—
126C22×C4×C17—24no—
127C22×C4×C17—24no—
128C22×C4×C17C2×D414yes—
129C22×C4×C17C2×D414yes—
130C22×C4×C17C2×Q818yes—
131C22×C4×C17C2412yes—
132C22×C4×C17C2414yes—
133C22×C4×C17C2412yes—
134C22×C4×C17C2412yes—
135C22×C4×C17C2414yes—
136C22×Dic17—22no—
137C22×Dic17—24no—
138C22×Dic17—22no—
139C22×Dic17—24no—
140C22×Dic17—24no—
141C22×Dic17—24no—
142C22×Dic17—24no—
143C22×Dic17—22no—
144C22×Dic17—24no—
145C22×Dic17—24no—
146C22×Dic17C2×D414yes—
147C22×Dic17C2×D414yes—
148C22×Dic17C2×Q818yes—
149C22×Dic17C2412yes—
150C22×Dic17C2414yes—
151C22×Dic17C2412yes—
152C22×Dic17C2412yes—
153C22×Dic17C2414yes—
154C2×C4×D17—232no—
155C2×C4×D17—264no—
156C2×C4×D17—232no—
157C2×C4×D17—28no—
158C2×C4×D17—216no—
159C2×C4×D17—28no—
160C2×C4×D17—216no—
161C2×C4×D17—216no—
162C2×C4×D17—216no—
163C2×C4×D17—216no—
164C2×C4×D17—28no—
165C2×C4×D17—216no—
166C2×C4×D17—216no—
167C2×C4×D17—432no—
168C2×C4×D17—416no—
169C2×C4×D17C2×D4116yes—
170C2×C4×D17C2×D4116yes—
171C2×C4×D17C2×Q8132yes—
172C4⋊C4×C17—216no—
173C4⋊C4×C17—28no—
174C4⋊C4×C17—28no—
175C4⋊Dic17—28no—
176C4⋊Dic17—28no—
177C4⋊Dic17—216no—
178#63225—216no—
179#63225—28no—
180#63225—28no—
181#63225—216no—
182#63225—216no—
183C22×#398—171nomaximal, Sylow
184C23×C17C22×D412yes—
185C23×C17C22×D412yes—
186C23×C17C22×Q814yes—
187C23×C17C2×#4112yes—
188C23×C17C2×#4114yes—
189C23×C17C2511yescharacteristic
190C22×D17#121116yes—
191C22×D17C22⋊Q8132yes—
192C22×D17#123116yes—
193C22×D17#125132yes—
194C22×D17C4⋊Q8116yes—
195C22×D17C22×D414yes—
196C22×D17C22×D414yes—
197C22×D17C22×Q818yes—
198C22×D17C2×#4114yes—
199C22×D17C2×#4118yes—
200C2×C4×C17—28no—
201C2×C4×C17—216no—
202C2×C4×C17—28no—
203C2×C4×C17—22no—
204C2×C4×C17—24no—
205C2×C4×C17—22no—
206C2×C4×C17—24no—
207C2×C4×C17—24no—
208C2×C4×C17—24no—
209C2×C4×C17—24no—
210C2×C4×C17—22no—
211C2×C4×C17—24no—
212C2×C4×C17—24no—
213C2×C4×C17—48no—
214C2×C4×C17—44no—
215C2×C4×C17C22×D414yes—
216C2×C4×C17C22×D414yes—
217C2×C4×C17C22×Q818yes—
218C2×Dic17—28no—
219C2×Dic17—216no—
220C2×Dic17—28no—
221C2×Dic17—22no—
222C2×Dic17—24no—
223C2×Dic17—22no—
224C2×Dic17—24no—
225C2×Dic17—24no—
226C2×Dic17—24no—
227C2×Dic17—24no—
228C2×Dic17—22no—
229C2×Dic17—24no—
230C2×Dic17—24no—
231C2×Dic17—48no—
232C2×Dic17—44no—
233C2×Dic17C22×D414yes—
234C2×Dic17C22×D414yes—
235C2×Dic17C22×Q818yes—
236C4×D17—232no—
237C4×D17—264no—
238C4×D17—232no—
239C4×D17—432no—
240C4×D17—416no—
241C23×C4⋊C4—171no—
242C23×C4⋊C4—172no—
243C23×C4⋊C4—171no—
244C2×#398—1716no—
245C2×#398—171no—
246C2×#398—172no—
247C2×#398—171no—
248C2×#398—171no—
249C2×#398—172no—
250C2×#398D1711yescharacteristic, direct product factor
251C22×#95—171no—
252C22×#95—172no—
253C22×C17C2×#12114yes—
254C22×C17C2×C22⋊Q818yes—
255C22×C17C2×#12314yes—
256C22×C17C2×#12518yes—
257C22×C17C2×C4⋊Q814yes—
258C22×C17C23×D411yescharacteristic
259C22×C17C23×D411yescharacteristic
260C22×C17C23×Q812yes—
261C22×C17C22×#4111yescharacteristic
262C22×C17C22×#4112yes—
263C2×D17#398164yesdirect product factor
264C2×D17C2×#12118yes—
265C2×D17C2×C22⋊Q8116yes—
266C2×D17C2×#12318yes—
267C2×D17C2×#125116yes—
268C2×D17C2×C4⋊Q818yes—
269C4×C17—24no—
270C4×C17—28no—
271C4×C17—24no—
272C4×C17—44no—
273C4×C17—42no—
274Dic17—24no—
275Dic17—28no—
276Dic17—24no—
277Dic17—44no—
278Dic17—42no—
279C24×C4—171no—
280C24×C4—171no—
281C24×C4—172no—
282C24×C4—172no—
283C24×C4—171no—
284C22×C4⋊C4—171no—
285C22×C4⋊C4—172no—
286C22×C4⋊C4—172no—
287C22×C4⋊C4—171no—
288C22×C4⋊C4—172no—
289C22×C4⋊C4—172no—
290C22×C4⋊C4—171no—
291C22×C4⋊C4—171no—
292C22×C4⋊C4—178no—
293C22×C4⋊C4—1716no—
294C22×C4⋊C4—178no—
295C22×C4⋊C4—348no—
296C22×C4⋊C4—3416no—
297C22×C4⋊C4—348no—
298C22×C4⋊C4C2×D1711yescharacteristic
299C22×C4⋊C4C2×D1712yes—
300C22×C4⋊C4C2×D1711yescharacteristic
301#398—178no—
302#398—178no—
303#398—1716no—
304#398—178no—
305#398—1716no—
306#398C2×D1718yesdirect product factor
307C2×#95—172no—
308C2×#95—171no—
309C2×#95—172no—
310C2×#95—172no—
311C2×#95—172no—
312C2×#95—178no—
313C2×#95—1716no—
314C2×#95C2×D1712yes—
315C2×#95C2×D1711yescharacteristic
316C2×C17C2×#39818yescomplemented
317C2×C17C22×#12111yescharacteristic
318C2×C17C22×C22⋊Q812yes—
319C2×C17C22×#12311yescharacteristic
320C2×C17C22×#12512yes—
321C2×C17C22×C4⋊Q811yescharacteristic
322D17C2×#398116yesdirect product factor
323C25—171no—
324C23×C4—171no—
325C23×C4—171no—
326C23×C4—172no—
327C23×C4—178no—
328C23×C4—178no—
329C23×C4—1716no—
330C23×C4—174no—
331C23×C4—174no—
332C23×C4—178no—
333C23×C4—172no—
334C23×C4—171no—
335C23×C4—178no—
336C23×C4—174no—
337C23×C4—344no—
338C23×C4—348no—
339C23×C4—344no—
340C23×C4—348no—
341C23×C4—348no—
342C23×C4—348no—
343C23×C4—348no—
344C23×C4—344no—
345C23×C4—348no—
346C23×C4—348no—
347C23×C4C22×D1712yes—
348C23×C4C22×D1711yescharacteristic
349C23×C4C22×D1711yescharacteristic
350C23×C4C22×D1711yescharacteristic
351C23×C4C22×D1712yes—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—178no—
356C2×C4⋊C4—174no—
357C2×C4⋊C4—178no—
358C2×C4⋊C4—178no—
359C2×C4⋊C4—174no—
360C2×C4⋊C4—174no—
361C2×C4⋊C4—178no—
362C2×C4⋊C4—174no—
363C2×C4⋊C4—3432no—
364C2×C4⋊C4—3464no—
365C2×C4⋊C4—3432no—
366C2×C4⋊C4—348no—
367C2×C4⋊C4—344no—
368C2×C4⋊C4—348no—
369C2×C4⋊C4—344no—
370C2×C4⋊C4—348no—
371C2×C4⋊C4—344no—
372C2×C4⋊C4—348no—
373C2×C4⋊C4—344no—
374C2×C4⋊C4C22×D1714yes—
375C2×C4⋊C4C22×D1714yes—
376C2×C4⋊C4C22×D1718yes—
377#95—174no—
378#95—178no—
379#95—178no—
380#95—178no—
381#95—178no—
382#95C22×D1718yes—
383#95C22×D1714yes—
384C17C22×#39811yescharacteristic, complemented, Sylow
385C24—174no—
386C24—174no—
387C24—178no—
388C24—174no—
389C24—178no—
390C24—172no—
391C24C23×D1711yescharacteristic
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—174no—
403C22×C4—174no—
404C22×C4—178no—
405C22×C4—174no—
406C22×C4—172no—
407C22×C4—172no—
408C22×C4—1716no—
409C22×C4—1716no—
410C22×C4—1732no—
411C22×C4—172no—
412C22×C4—174no—
413C22×C4—348no—
414C22×C4—3416no—
415C22×C4—3432no—
416C22×C4—3464no—
417C22×C4—3432no—
418C22×C4—348no—
419C22×C4—3416no—
420C22×C4—3416no—
421C22×C4—3416no—
422C22×C4—3416no—
423C22×C4—348no—
424C22×C4—3416no—
425C22×C4—3416no—
426C22×C4—342no—
427C22×C4—344no—
428C22×C4—342no—
429C22×C4—344no—
430C22×C4—344no—
431C22×C4—344no—
432C22×C4—344no—
433C22×C4—342no—
434C22×C4—344no—
435C22×C4—344no—
436C22×C4—6832no—
437C22×C4—6816no—
438C22×C4D4×D1714yes—
439C22×C4D4×D1714yes—
440C22×C4Q8×D1718yes—
441C22×C4C23×D1712yes—
442C22×C4C23×D1714yes—
443C22×C4C23×D1712yes—
444C22×C4C23×D1712yes—
445C22×C4C23×D1714yes—
446C4⋊C4—28no—
447C4⋊C4—216no—
448C4⋊C4—28no—
449C4⋊C4—3416no—
450C4⋊C4—348no—
451C4⋊C4—3416no—
452C4⋊C4—348no—
453C4⋊C4—3416no—
454C4⋊C4—348no—
455C4⋊C4—3416no—
456C4⋊C4—348no—
457C23—1716no—
458C23—1732no—
459C23—1716no—
460C23—1732no—
461C23—1716no—
462C23—174no—
463C23—174no—
464C23—178no—
465C23—174no—
466C23—178no—
467C23C2×D4×D1712yes—
468C23C2×D4×D1712yes—
469C23C2×Q8×D1714yes—
470C23#41×D1712yes—
471C23#41×D1714yes—
472C23C24×D1711yescharacteristic
473C2×C4—28no—
474C2×C4—216no—
475C2×C4—28no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—48no—
487C2×C4—44no—
488C2×C4—174no—
489C2×C4—174no—
490C2×C4—178no—
491C2×C4—3432no—
492C2×C4—3464no—
493C2×C4—3432no—
494C2×C4—348no—
495C2×C4—3416no—
496C2×C4—348no—
497C2×C4—342no—
498C2×C4—344no—
499C2×C4—342no—
500C2×C4—344no—
501C2×C4—344no—
502C2×C4—344no—
503C2×C4—344no—
504C2×C4—342no—
505C2×C4—344no—
506C2×C4—344no—
507C2×C4—6832no—
508C2×C4—6816no—
509C2×C4—688no—
510C2×C4—684no—
511C2×C4C2×D4×D1714yes—
512C2×C4C2×D4×D1714yes—
513C2×C4C2×Q8×D1718yes—
514C22—1764no—
515C22—178no—
516C22—1716no—
517C22—178no—
518C22—1716no—
519C22—178no—
520C22#121×D1714yes—
521C22C22⋊Q8×D1718yes—
522C22#123×D1714yes—
523C22#125×D1718yes—
524C22C4⋊Q8×D1714yes—
525C22C22×D4×D1711yescharacteristic
526C22C22×D4×D1711yescharacteristic
527C22C22×Q8×D1712yes—
528C22C2×#41×D1711yescharacteristic
529C22C2×#41×D1712yes—
530C4—24no—
531C4—28no—
532C4—24no—
533C4—44no—
534C4—42no—
535C4—344no—
536C4—348no—
537C4—344no—
538C4—684no—
539C4—682no—
540C2—1716no—
541C2D17×#39818yesdirect product factor
542C2C2×#121×D1711yescharacteristic
543C2C2×C22⋊Q8×D1712yes—
544C2C2×#123×D1711yescharacteristic
545C2C2×#125×D1712yes—
546C2C2×C4⋊Q8×D1711yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#398C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#398D17
hypocenterC17C22×#398
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
4. C2×#11762743C2semidirect
5. C2×#11762742C2semidirect
6. C2×#11762741C2semidirect
7. C2×#11762740C2semidirect
8. C2×#11762739C2semidirect
9. D17×#398C2direct (N × H)
12. C2×C17×#398C2semidirect
32. #11762743C22semidirect
33. #11762742C22semidirect
34. #11762741C22semidirect
35. #11762740C22semidirect
36. #11762739C22semidirect
47. C17×#398C22semidirect
250. C2×#398D17direct (N × H)
263. C2×D17#398direct (N × H)
306. #398C2×D17direct (N × H)
316. C2×C17C2×#398semidirect
322. D17C2×#398direct (N × H)
384. C17C22×#398semidirect
541. C2D17×#398direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D172
C2×#117627432
C2×#117627422
C2×#117627412
C2×#117627402
C2×#117627392
D17×#3982
C2×#95×D172
C2×C17×#3982
C22×#39817