Finite Group Databasebeta

← #17043835

Subgroups — #17043835

Order 4352.

1066 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D17C211yesmaximal, characteristic
2C2×#11762864C211yesmaximal, characteristic
3#14531189C211yesmaximal, characteristic
4#14529754C211yesmaximal, characteristic, complemented
5#14529753C211yesmaximal, characteristic, complemented
6#14529752C211yesmaximal, characteristic, complemented
7#14529740C212yesmaximal, complemented
8#14529738C212yesmaximal, complemented
9#14528873C212yesmaximal
10#14528869C212yesmaximal
11C17×#1992C211yesmaximal, characteristic, complemented
12C2×#10587556C2211yescharacteristic
13C2×#10587576C2211yescharacteristic
14C2×#10587576C2211yescharacteristic
15C2×#10587575—21no—
16C2×#10587575—21no—
17#125×D17—24no—
18#125×D17C418yescomplemented
19C2×#10587578—21no—
20C2×C4⋊C4×D17—21no—
21C2×C4⋊C4×D17—21no—
22C2×C4⋊C4×D17C2211yescharacteristic
23C2×C4⋊C4×D17C2211yescharacteristic
24C2×C42×D17C2211yescharacteristic
25#11762864—24no—
26C2×#10587485C2212yes—
27C2×#10587491C2212yes—
28C2×#10587474C2211yescharacteristic
29#11762679C2211yescharacteristic
30#11762674—21no—
31#11762666—21no—
32#11762666C2212yes—
33C4⋊C4×Dic17—21no—
34C4⋊C4×Dic17C2212yes—
35#11762572C2212yes—
36#11762572C2212yes—
37#11762571C2212yes—
38#11762571C2212yes—
39#11762571C2212yes—
40#11762571C2212yes—
41C2×C17×#125C2211yescharacteristic
42C2×C17×#97C2211yescharacteristic
43C17×#384C2211yescharacteristic
44C17×#340C2212yes—
45C17×#340C2212yes—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17D411yescharacteristic
49C22×C4×D17D411yescharacteristic
50C22×C4×D17C2311yescharacteristic
51C22×C8×C17C2312yes—
52C17×#125—22no—
53C17×#125C2×C414yes—
54C2×C4⋊C4×C17—21no—
55C2×C4⋊C4×C17—21no—
56C2×C4⋊C4×C17—21no—
57C2×C4⋊C4×C17—21no—
58C2×C4⋊C4×C17C2312yes—
59C2×C4⋊C4×C17C2311yescharacteristic
60C2×C4⋊C4×C17C2311yescharacteristic
61C2×C42×C17C2311yescharacteristic
62C2×#63227—22no—
63C2×C4⋊Dic17—21no—
64C2×C4⋊Dic17—21no—
65C2×C4⋊Dic17—21no—
66C2×C4⋊Dic17—21no—
67C2×C4⋊Dic17C2312yes—
68C2×C4⋊Dic17C2311yescharacteristic
69C2×C4⋊Dic17C2311yescharacteristic
70C2×#63225—21no—
71C2×#63225—21no—
72C2×#63225—21no—
73C2×#63225—21no—
74C2×#63225—21no—
75C2×#63225—21no—
76C2×C4×Dic17—22no—
77C2×C4×Dic17D411yescharacteristic
78C2×C4×Dic17D411yescharacteristic
79C2×C4×Dic17C2311yescharacteristic
80C22×#3622C2312yes—
81#10587578—44no—
82C4⋊C4×D17—28no—
83C4⋊C4×D17—28no—
84C4⋊C4×D17—22no—
85C4⋊C4×D17—22no—
86C4⋊C4×D17C2×C414yes—
87C4⋊C4×D17C2×C414yes—
88#10587576—22no—
89#10587576—22no—
90#10587576C2×C414yes—
91#10587576C2×C414yes—
92#10587575—28no—
93#10587575—28no—
94C42×D17C2×C414yes—
95C42×D17D414yes—
96#10587556—22no—
97#10587556C2×C414yes—
98C17×#97—22no—
99#10587502—22no—
100#10587502—22no—
101#10587491—24no—
102#10587485—24no—
103#10587474—22no—
104C23×D17C2×D411yescharacteristic
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—22no—
108C22×C4×C17C2×D411yescharacteristic
109C22×C4×C17C2×D411yescharacteristic
110C22×C4×C17C2411yescharacteristic
111C22×Dic17—21no—
112C22×Dic17—21no—
113C22×Dic17—22no—
114C22×Dic17C2×D411yescharacteristic
115C22×Dic17C2×D411yescharacteristic
116C22×Dic17C2×D411yescharacteristic
117C2×C4×D17—22no—
118C2×C4×D17—22no—
119C2×C4×D17—22no—
120C2×C4×D17—22no—
121C2×C4×D17—24no—
122C2×C4×D17—24no—
123C2×C4×D17—41no—
124C2×C4×D17—41no—
125C2×C4×D17—42no—
126C2×C4×D17—42no—
127C2×C4×D17—42no—
128C2×C4×D17—42no—
129C2×C4×D17C22⋊C414yes—
130C2×C4×D17C22⋊C414yes—
131C2×C4×D17C22×C412yes—
132C2×C4×D17C2×D412yes—
133C2×C8×C17—22no—
134C2×C8×C17—22no—
135C2×C8×C17—22no—
136C4⋊C4×C17—24no—
137C4⋊C4×C17—24no—
138C4⋊C4×C17—21no—
139C4⋊C4×C17—21no—
140C4⋊C4×C17—24no—
141C4⋊C4×C17—42no—
142C4⋊C4×C17—42no—
143C4⋊C4×C17C22×C412yes—
144C4⋊C4×C17C22×C412yes—
145C42×C17C22×C412yes—
146C42×C17C2×D412yes—
147#63227—44no—
148C4⋊Dic17—21no—
149C4⋊Dic17—21no—
150C4⋊Dic17—24no—
151C4⋊Dic17—24no—
152C4⋊Dic17—24no—
153C4⋊Dic17—42no—
154C4⋊Dic17—42no—
155C4⋊Dic17C22×C412yes—
156C4⋊Dic17C22×C412yes—
157#63225—24no—
158#63225—24no—
159#63225—24no—
160#63225—24no—
161#63225—24no—
162#63225—24no—
163C4×Dic17—44no—
164C4×Dic17C22⋊C414yes—
165C4×Dic17C22⋊C414yes—
166C4×Dic17C22×C412yes—
167C4×Dic17C2×D412yes—
168C2×#3622—22no—
169C2×#3622—22no—
170C2×#3622—22no—
171#21838—171nomaximal, Sylow
172C23×C17C22×D411yescharacteristic
173C22×D17—21no—
174C22×D17—21no—
175C22×D17—21no—
176C22×D17—21no—
177C22×D17C2×C22⋊C412yes—
178C22×D17AGL(1,ℤ/8)12yes—
179C22×D17#13712yes—
180C2×C4×C17—21no—
181C2×C4×C17—21no—
182C2×C4×C17—21no—
183C2×C4×C17—21no—
184C2×C4×C17—22no—
185C2×C4×C17—22no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—42no—
191C2×C4×C17—42no—
192C2×C4×C17—42no—
193C2×C4×C17C2×C22⋊C412yes—
194C2×C4×C17C2×C22⋊C412yes—
195C2×C4×C17C23×C411yescharacteristic
196C2×C4×C17C22×D411yescharacteristic
197C2×C4×C172−1+412yes—
198C2×C4×C172−1+412yes—
199C2×Dic17—21no—
200C2×Dic17—21no—
201C2×Dic17—21no—
202C2×Dic17—21no—
203C2×Dic17—21no—
204C2×Dic17—21no—
205C2×Dic17—22no—
206C2×Dic17—22no—
207C2×Dic17—41no—
208C2×Dic17—41no—
209C2×Dic17—41no—
210C2×Dic17—41no—
211C2×Dic17—42no—
212C2×Dic17—42no—
213C2×Dic17—42no—
214C2×Dic17C2×C22⋊C412yes—
215C2×Dic17C2×C22⋊C412yes—
216C2×Dic17C2×C22⋊C412yes—
217C4×D17—28no—
218C4×D17—24no—
219C4×D17—24no—
220C4×D17—44no—
221C4×D17—48no—
222C4×D17—48no—
223C8×C17—42no—
224#3622—42no—
225C22×#125—171no—
226C2×#432—171no—
227#2285—171no—
228#1992—171no—
229#1992—171no—
230#1992—171no—
231#1992D1711yescharacteristic, complemented
232#1989—172no—
233#1989—172no—
234#1824—172no—
235#1823—172no—
236C22×C17C22×C22⋊C411yescharacteristic
237C22×C17#53611yescharacteristic
238C22×C17#53611yescharacteristic
239C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
240C22×C17C2×#13711yescharacteristic
241C22×C17#57511yescharacteristic
242C22×C17#57511yescharacteristic
243C2×D17—22no—
244C2×D17—22no—
245C2×D17—22no—
246C2×D17—22no—
247C2×D17—22no—
248C2×D17—22no—
249C2×D17#41714yes—
250C4×C17—22no—
251C4×C17—22no—
252C4×C17—42no—
253C4×C17—42no—
254C4×C17—82no—
255C4×C17#51912yes—
256C4×C17#53612yes—
257Dic17—22no—
258Dic17—22no—
259Dic17—22no—
260Dic17—42no—
261Dic17—42no—
262Dic17—82no—
263C2×#125—178no—
264C2×#125—171no—
265C2×#125—171no—
266C2×#125—171no—
267C2×#125—341no—
268C2×#125—341no—
269C2×#125—344no—
270C2×#125C2×D1711yescharacteristic
271C2×#117—341no—
272C22×C4⋊C4—171no—
273C22×C4⋊C4—171no—
274C22×C4⋊C4—341no—
275C22×C4⋊C4—341no—
276C22×C42—171no—
277#432—344no—
278C2×C4⋊C8—172no—
279C2×C22⋊C8—172no—
280C2×#97—171no—
281C2×#97C2×D1711yescharacteristic
282#384—171no—
283#384C2×D1711yescharacteristic
284#382—341no—
285#380—172no—
286#380—341no—
287C4×C4⋊C4—172no—
288C4×C4⋊C4—341no—
289#340—172no—
290#340—172no—
291#340—172no—
292#340—172no—
293#340—172no—
294#340—172no—
295#340C2×D1712yes—
296#340C2×D1712yes—
297C2×C17#231011yescharacteristic
298C2×C17C2×#41711yescharacteristic
299C2×C17#289611yescharacteristic
300C2×C17#323411yescharacteristic
301C2×C17#323411yescharacteristic
302C2×C17#323611yescharacteristic
303C2×C17#323611yescharacteristic
304D17—24no—
305C23×C4—171no—
306C23×C4—171no—
307C23×C4—171no—
308C23×C4—341no—
309C23×C4—341no—
310C22×C8—172no—
311C22×C8C22×D1712yes—
312#125—22no—
313#125—174no—
314#125—174no—
315#125—174no—
316#125—348no—
317#125—348no—
318#125—342no—
319#125—342no—
320#125—342no—
321#125C4×D1714yes—
322#117—684no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—171no—
328C2×C4⋊C4—171no—
329C2×C4⋊C4—174no—
330C2×C4⋊C4—174no—
331C2×C4⋊C4—172no—
332C2×C4⋊C4—342no—
333C2×C4⋊C4—342no—
334C2×C4⋊C4—348no—
335C2×C4⋊C4—348no—
336C2×C4⋊C4—341no—
337C2×C4⋊C4—341no—
338C2×C4⋊C4—341no—
339C2×C4⋊C4—341no—
340C2×C4⋊C4—341no—
341C2×C4⋊C4—341no—
342C2×C4⋊C4—341no—
343C2×C4⋊C4—341no—
344C2×C4⋊C4—341no—
345C2×C4⋊C4—341no—
346C2×C4⋊C4C22×D1712yes—
347C2×C4⋊C4C22×D1711yescharacteristic
348C2×C4⋊C4C22×D1711yescharacteristic
349C2×C22⋊C4—342no—
350C2×C42—171no—
351C2×C42—171no—
352C2×C42—171no—
353C2×C42—174no—
354C2×C42—174no—
355C2×C42—342no—
356C2×C42C22×D1711yescharacteristic
357C4⋊C8—344no—
358C22⋊C8—344no—
359#97—22no—
360#97—342no—
361#95—342no—
362#95—342no—
363C17#2183811yescharacteristic, complemented, Sylow
364C24—171no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—171no—
369C22×C4—171no—
370C22×C4—171no—
371C22×C4—172no—
372C22×C4—172no—
373C22×C4—174no—
374C22×C4—174no—
375C22×C4—342no—
376C22×C4—342no—
377C22×C4—344no—
378C22×C4—344no—
379C22×C4—342no—
380C22×C4—342no—
381C22×C4—341no—
382C22×C4—341no—
383C22×C4—342no—
384C22×C4—681no—
385C22×C4—681no—
386C22×C4—682no—
387C22×C4—682no—
388C22×C4—682no—
389C22×C4—682no—
390C22×C4D4×D1711yescharacteristic
391C22×C4D4×D1711yescharacteristic
392C22×C4C23×D1711yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—342no—
397C2×C8—342no—
398C2×C8—342no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—172no—
407C4⋊C4—172no—
408C4⋊C4—344no—
409C4⋊C4—344no—
410C4⋊C4—344no—
411C4⋊C4—344no—
412C4⋊C4—344no—
413C4⋊C4—344no—
414C4⋊C4—341no—
415C4⋊C4—341no—
416C4⋊C4—344no—
417C4⋊C4—344no—
418C4⋊C4—344no—
419C4⋊C4—682no—
420C4⋊C4—682no—
421C4⋊C4C2×C4×D1712yes—
422C4⋊C4C2×C4×D1712yes—
423C22⋊C4—684no—
424C42—172no—
425C42—172no—
426C42—174no—
427C42—174no—
428C42—684no—
429C42C2×C4×D1712yes—
430C42D4×D1712yes—
431C23—172no—
432C23—172no—
433C23—172no—
434C23—341no—
435C23—341no—
436C23—341no—
437C23—341no—
438C23C2×D4×D1711yescharacteristic
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—172no—
453C2×C4—172no—
454C2×C4—172no—
455C2×C4—348no—
456C2×C4—341no—
457C2×C4—341no—
458C2×C4—341no—
459C2×C4—341no—
460C2×C4—341no—
461C2×C4—341no—
462C2×C4—344no—
463C2×C4—344no—
464C2×C4—342no—
465C2×C4—342no—
466C2×C4—684no—
467C2×C4—688no—
468C2×C4—688no—
469C2×C4—681no—
470C2×C4—681no—
471C2×C4—681no—
472C2×C4—681no—
473C2×C4—682no—
474C2×C4—682no—
475C2×C4—682no—
476C2×C4C22⋊C4×D1712yes—
477C2×C4C22⋊C4×D1712yes—
478C2×C4C22×C4×D1711yescharacteristic
479C2×C4C2×D4×D1711yescharacteristic
480C2×C4#1058769412yes—
481C2×C4#1058769712yes—
482C8—42no—
483C8—682no—
484C22—174no—
485C22—342no—
486C22—342no—
487C22—342no—
488C22—342no—
489C22—342no—
490C22—342no—
491C22C2×C22⋊C4×D1711yescharacteristic
492C22#1176337911yescharacteristic
493C22#1176338411yescharacteristic
494C22AGL(1,ℤ/8)×D1711yescharacteristic
495C22#137×D1711yescharacteristic
496C22#1176360511yescharacteristic
497C22#1176360811yescharacteristic
498C4—22no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—342no—
504C4—342no—
505C4—342no—
506C4—682no—
507C4—682no—
508C4—1362no—
509C4#1176328512yes—
510C4#1176338212yes—
511C2—344no—
512C2#1453136711yescharacteristic
513C2D17×#41711yescharacteristic
514C2#1453730011yescharacteristic
515C2#1453996911yescharacteristic
516C2#1453997511yescharacteristic
517C2#1453998511yescharacteristic
518C2#1453999111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1992C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1992D17
hypocenterC17#21838
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
4. #14529754C2semidirect
5. #14529753C2semidirect
6. #14529752C2semidirect
7. #14529740C2semidirect
8. #14529738C2semidirect
11. C17×#1992C2semidirect
18. #125×D17C4semidirect
231. #1992D17semidirect
363. C17#21838semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D172
C2×#117628642
#145311892
#145297542
#145297532
#145297522
#145297402
#145297382
#145288732
#145288692
C17×#19922
#2183817