Finite Group Databasebeta

← #16924454

Subgroups — #16924454

Order 4352.

1090 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17×#407C211yesmaximal, characteristic
2#14531165C211yesmaximal, characteristic
3C4×C22⋊C4×D17C211yesmaximal, characteristic
4#14526670C211yesmaximal, characteristic, complemented
5#14526670C211yesmaximal, characteristic, complemented
6#14526669C211yesmaximal, characteristic, complemented
7C17×#1297C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C2×M16×D17C412yescomplemented
10C2×#10587558—21no—
11C2×C22⋊C4×D17—21no—
12C2×C42×D17—21no—
13#11762773C2211yescharacteristic
14#11762772C412yescomplemented
15#11762771—21no—
16#11762771—21no—
17C22⋊C8×D17—21no—
18C22⋊C8×D17—21no—
19#11762671C412yescomplemented
20#11762668C412yescomplemented
21#11762667—21no—
22#11762664—21no—
23C22⋊C4×Dic17—21no—
24C4×#63227—21no—
25C4×#63227—21no—
26C4×C22⋊Dic17C2211yescharacteristic
27C4×C22⋊Dic17C2211yescharacteristic
28#11762656C412yescomplemented
29#95×D17C412yescomplemented
30C17×#407C2211yescharacteristic
31C4×C22⋊C4×C17C2211yescharacteristic
32C4×C22⋊C4×C17C2211yescharacteristic
33C24×D17D411yescharacteristic
34C23×C4×C17C2311yescharacteristic
35C23×Dic17D411yescharacteristic
36C22×C4×D17—22no—
37C22×C4×D17—44no—
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17C2×C411yescharacteristic
40C22×C4×D17C2×C411yescharacteristic
41C22×C4×D17C2×C411yescharacteristic
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17C2×C411yescharacteristic
44C22×C4×D17D411yescharacteristic
45C22×C4×D17D411yescharacteristic
46C22×C4×D17D411yescharacteristic
47C22×C4×D17D411yescharacteristic
48C22×C4×D17Q811yescharacteristic
49C22×C4×D17Q811yescharacteristic
50C2×M16×C17C2×C412yescomplemented
51C2×C22⋊C4×C17—21no—
52C2×C22⋊C4×C17—21no—
53C2×C42×C17—21no—
54C2×C42×C17—21no—
55C2×C22⋊Dic17—21no—
56C2×C22⋊Dic17—21no—
57C2×#63227—22no—
58C2×#63227—22no—
59C2×#63227—22no—
60C2×#63225—22no—
61C2×C4×Dic17—21no—
62C2×C4×Dic17—21no—
63C2×C4×Dic17—22no—
64C2×#63223C2×C412yescomplemented
65M16×D17—44no—
66C2×#63218—22no—
67C2×C8×D17—22no—
68C22⋊C4×D17—28no—
69#10587558—44no—
70C42×D17—44no—
71C17×C22⋊C8—21no—
72C17×C22⋊C8—21no—
73C17×#95C2×C412yes—
74C17×#95C2×C412yescomplemented
75#10587502—22no—
76#10587502—22no—
77#10587502C2×C412yes—
78#10587502C2×C412yescomplemented
79C22⋊#3622—21no—
80C22⋊#3622—21no—
81#10587491—22no—
82#10587491—22no—
83C24×C17C2×D411yescharacteristic
84C23×D17—24no—
85C23×D17—42no—
86C23×D17—42no—
87C23×D17C22⋊C411yescharacteristic
88C23×D17C22⋊C411yescharacteristic
89C23×D17C22⋊C411yescharacteristic
90C23×D17C22⋊C411yescharacteristic
91C23×D17C4⋊C411yescharacteristic
92C23×D17C4⋊C411yescharacteristic
93C22×C4×C17—22no—
94C22×C4×C17—22no—
95C22×C4×C17—42no—
96C22×C4×C17C22×C411yescharacteristic
97C22×C4×C17C22×C411yescharacteristic
98C22×C4×C17C22×C411yescharacteristic
99C22×C4×C17C2×D411yescharacteristic
100C22×C4×C17C2×D411yescharacteristic
101C22×C4×C17C2×Q811yescharacteristic
102C22×Dic17—22no—
103C22×Dic17—22no—
104C22×Dic17—42no—
105C22×Dic17C22⋊C411yescharacteristic
106C22×Dic17C22⋊C411yescharacteristic
107C22×Dic17C22⋊C411yescharacteristic
108C22×Dic17C22⋊C411yescharacteristic
109C22×Dic17C4⋊C411yescharacteristic
110C22×Dic17C4⋊C411yescharacteristic
111C2×C4×D17—24no—
112C2×C4×D17—24no—
113C2×C4×D17—24no—
114C2×C4×D17—28no—
115C2×C4×D17—42no—
116C2×C4×D17—42no—
117C2×C4×D17—42no—
118C2×C4×D17—42no—
119C2×C4×D17—42no—
120C2×C4×D17—42no—
121C2×C4×D17—42no—
122C2×C4×D17—42no—
123C2×C4×D17—42no—
124C2×C4×D17—44no—
125C2×C4×D17—44no—
126C2×C4×D17C4211yescharacteristic
127C2×C4×D17C4211yescharacteristic
128C2×C4×D17C4211yescharacteristic
129C2×C4×D17C4211yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C22⋊C411yescharacteristic
132C2×C4×D17C22⋊C411yescharacteristic
133C2×C4×D17C22⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C4⋊C411yescharacteristic
137C2×C4×D17C4⋊C411yescharacteristic
138C2×C4×D17C4⋊C411yescharacteristic
139C2×C4×D17C4⋊C411yescharacteristic
140C2×C4×D17C4⋊C411yescharacteristic
141C2×C4×D17C4⋊C411yescharacteristic
142M16×C17—42no—
143C2×C8×C17—22no—
144C22⋊C4×C17—24no—
145C22⋊C4×C17—42no—
146C42×C17—42no—
147C42×C17—42no—
148C22⋊Dic17—24no—
149C22⋊Dic17—42no—
150#63227—28no—
151#63227—44no—
152#63227—44no—
153#63225—44no—
154C4×Dic17—44no—
155C4×Dic17—42no—
156C4×Dic17—42no—
157#63223—42no—
158C2×#3622—22no—
159#63218—44no—
160C8×D17—44no—
161#8051—171nomaximal, Sylow
162C23×C17—22no—
163C23×C17—22no—
164C23×C17—41no—
165C23×C17C2×C22⋊C411yescharacteristic
166C23×C17C2×C22⋊C411yescharacteristic
167C23×C17C2×C4⋊C411yescharacteristic
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—22no—
176C22×D17—22no—
177C22×D17—22no—
178C22×D17—41no—
179C22×D17—41no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17—41no—
183C22×D17—41no—
184C22×D17—41no—
185C22×D17—416no—
186C22×D17#9511yescharacteristic
187C22×D17#9511yescharacteristic
188C22×D17#9511yescharacteristic
189C22×D17#9511yescharacteristic
190C22×D17#10414yes—
191C2×C4×C17—22no—
192C2×C4×C17—22no—
193C2×C4×C17—22no—
194C2×C4×C17—24no—
195C2×C4×C17—41no—
196C2×C4×C17—41no—
197C2×C4×C17—41no—
198C2×C4×C17—42no—
199C2×C4×C17—42no—
200C2×C4×C17—42no—
201C2×C4×C17—42no—
202C2×C4×C17—42no—
203C2×C4×C17C2×C4211yescharacteristic
204C2×C4×C17C2×C22⋊C411yescharacteristic
205C2×C4×C17C2×C4⋊C411yescharacteristic
206C2×C4×C17C2×C4⋊C411yescharacteristic
207C2×Dic17—22no—
208C2×Dic17—22no—
209C2×Dic17—22no—
210C2×Dic17—24no—
211C2×Dic17—41no—
212C2×Dic17—41no—
213C2×Dic17—41no—
214C2×Dic17—42no—
215C2×Dic17—42no—
216C2×Dic17—42no—
217C2×Dic17—42no—
218C2×Dic17—42no—
219C2×Dic17#9511yescharacteristic
220C2×Dic17#9511yescharacteristic
221C2×Dic17#9511yescharacteristic
222C2×Dic17#9511yescharacteristic
223C4×D17—22no—
224C4×D17—22no—
225C4×D17—22no—
226C4×D17—22no—
227C4×D17—22no—
228C4×D17—22no—
229C4×D17—22no—
230C4×D17—22no—
231C4×D17—22no—
232C4×D17—41no—
233C4×D17—41no—
234C4×D17—41no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—416no—
239C4×D17#9914yes—
240C8×C17—42no—
241#3622—42no—
242C2×#407—171no—
243#2280—171no—
244C2×C4×C22⋊C4—171no—
245#1297—171no—
246#1297—171no—
247#1297—171no—
248#1297D1711yescharacteristic, complemented
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—44no—
257C22×C17C2×#9511yescharacteristic
258C22×C17C2×#10412yes—
259C22×C17#42112yes—
260C2×D17—28no—
261C2×D17—21no—
262C2×D17—21no—
263C2×D17—21no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—44no—
271C2×D17—44no—
272C2×D17—44no—
273C2×D17—44no—
274C2×D17—44no—
275C2×D17#33912yes—
276C2×D17#33912yes—
277C2×D17#34212yes—
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—44no—
282C4×C17—82no—
283C4×C17C2×#9912yes—
284Dic17—21no—
285Dic17—21no—
286Dic17—21no—
287Dic17—44no—
288Dic17—82no—
289Dic17#34212yes—
290C24×C4—171no—
291C22×M16—172no—
292C2×#117—341no—
293C22×C22⋊C4—341no—
294C22×C42—341no—
295#407—171no—
296#407—172no—
297#407—341no—
298#407—341no—
299#407C2×D1711yescharacteristic
300C2×C22⋊C8—341no—
301C2×C22⋊C8—341no—
302#381—172no—
303#380—172no—
304#380—341no—
305#379—341no—
306C4×C22⋊C4—171no—
307C4×C22⋊C4—171no—
308C4×C22⋊C4—172no—
309C4×C22⋊C4—341no—
310C4×C22⋊C4—341no—
311C4×C22⋊C4—341no—
312C4×C22⋊C4C2×D1711yescharacteristic
313C4×C22⋊C4C2×D1711yescharacteristic
314C2×#95—172no—
315C2×C17—22no—
316C2×C17—22no—
317C2×C17—41no—
318C2×C17C2×#33911yescharacteristic
319C2×C17#173311yescharacteristic
320C2×C17C2×#34211yescharacteristic
321D17—22no—
322D17—22no—
323D17—22no—
324D17—41no—
325C25—171no—
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—171no—
329C23×C4—171no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—342no—
340C23×C4—684no—
341C23×C4C22×D1711yescharacteristic
342C2×M16—172no—
343C2×M16—342no—
344C2×M16—684no—
345C2×M16C4×D1712yescomplemented
346C22×C8—342no—
347#117—684no—
348C2×C4⋊C4—342no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—348no—
352C2×C22⋊C4—342no—
353C2×C22⋊C4—341no—
354C2×C22⋊C4—342no—
355C2×C22⋊C4—342no—
356C2×C22⋊C4—341no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—342no—
360C2×C42—341no—
361C2×C42—341no—
362C2×C42—684no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—342no—
366C22⋊C8—342no—
367C22⋊C8—341no—
368C22⋊C8—341no—
369#95—172no—
370#95—172no—
371#95—342no—
372#95—342no—
373#95C4×D1712yes—
374#95C4×D1712yescomplemented
375C17#805111yescharacteristic, complemented, Sylow
376C24—171no—
377C24—171no—
378C24—171no—
379C24—171no—
380C24—171no—
381C24—171no—
382C24—344no—
383C24—682no—
384C24—682no—
385C24D4×D1711yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—42no—
389C22×C4—171no—
390C22×C4—171no—
391C22×C4—171no—
392C22×C4—171no—
393C22×C4—171no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—171no—
398C22×C4—171no—
399C22×C4—171no—
400C22×C4—171no—
401C22×C4—171no—
402C22×C4—171no—
403C22×C4—171no—
404C22×C4—171no—
405C22×C4—171no—
406C22×C4—171no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—171no—
411C22×C4—344no—
412C22×C4—344no—
413C22×C4—344no—
414C22×C4—348no—
415C22×C4—342no—
416C22×C4—342no—
417C22×C4—682no—
418C22×C4—682no—
419C22×C4—682no—
420C22×C4—682no—
421C22×C4—682no—
422C22×C4—682no—
423C22×C4—682no—
424C22×C4—682no—
425C22×C4—682no—
426C22×C4—684no—
427C22×C4—684no—
428C22×C4—682no—
429C22×C4C2×C4×D1711yescharacteristic
430C22×C4C2×C4×D1711yescharacteristic
431C22×C4C2×C4×D1711yescharacteristic
432C22×C4D4×D1711yescharacteristic
433C22×C4D4×D1711yescharacteristic
434C22×C4Q8×D1711yescharacteristic
435M16—42no—
436M16—684no—
437M16—682no—
438C2×C8—22no—
439C2×C8—342no—
440C2×C8—684no—
441C4⋊C4—684no—
442C22⋊C4—24no—
443C22⋊C4—42no—
444C22⋊C4—348no—
445C22⋊C4—344no—
446C22⋊C4—684no—
447C22⋊C4—684no—
448C22⋊C4—682no—
449C42—42no—
450C42—42no—
451C42—682no—
452C42—682no—
453C42—684no—
454C23—22no—
455C23—22no—
456C23—41no—
457C23—171no—
458C23—171no—
459C23—171no—
460C23—174no—
461C23—171no—
462C23—342no—
463C23—342no—
464C23—342no—
465C23—342no—
466C23—342no—
467C23—342no—
468C23—342no—
469C23—342no—
470C23—342no—
471C23—342no—
472C23—681no—
473C23—681no—
474C23—681no—
475C23—681no—
476C23—681no—
477C23—681no—
478C23—681no—
479C23—6816no—
480C23C22⋊C4×D1711yescharacteristic
481C23C22⋊C4×D1711yescharacteristic
482C23C4⋊C4×D1711yescharacteristic
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—171no—
496C2×C4—174no—
497C2×C4—171no—
498C2×C4—171no—
499C2×C4—171no—
500C2×C4—342no—
501C2×C4—342no—
502C2×C4—342no—
503C2×C4—342no—
504C2×C4—342no—
505C2×C4—342no—
506C2×C4—342no—
507C2×C4—342no—
508C2×C4—342no—
509C2×C4—342no—
510C2×C4—342no—
511C2×C4—342no—
512C2×C4—344no—
513C2×C4—681no—
514C2×C4—681no—
515C2×C4—681no—
516C2×C4—681no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—6816no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—682no—
524C2×C4—682no—
525C2×C4—682no—
526C2×C4—682no—
527C2×C4—682no—
528C2×C4C42×D1711yescharacteristic
529C2×C4C22⋊C4×D1711yescharacteristic
530C2×C4C4⋊C4×D1711yescharacteristic
531C2×C4C4⋊C4×D1711yescharacteristic
532C8—42no—
533C8—682no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—44no—
542C22—172no—
543C22—172no—
544C22—172no—
545C22—348no—
546C22—341no—
547C22—341no—
548C22—341no—
549C22—341no—
550C22—341no—
551C22—341no—
552C22—341no—
553C22—341no—
554C22—341no—
555C22—684no—
556C22—684no—
557C22—684no—
558C22—684no—
559C22—684no—
560C22#95×D1711yescharacteristic
561C22#104×D1712yes—
562C22#1176282412yes—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—44no—
567C4—82no—
568C4—172no—
569C4—341no—
570C4—341no—
571C4—341no—
572C4—684no—
573C4—1362no—
574C4#99×D1712yes—
575C2—22no—
576C2—22no—
577C2—41no—
578C2—342no—
579C2—342no—
580C2—342no—
581C2—681no—
582C2D17×#33911yescharacteristic
583C2#1452849211yescharacteristic
584C2D17×#34211yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC17×#1297C2
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenter#1297D17
hypocenterC17#8051
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
4. #14526670C2semidirect
5. #14526670C2semidirect
6. #14526669C2semidirect
7. C17×#1297C2semidirect
9. C2×M16×D17C4semidirect
14. #11762772C4semidirect
19. #11762671C4semidirect
20. #11762668C4semidirect
28. #11762656C4semidirect
29. #95×D17C4semidirect
50. C2×M16×C17C2×C4semidirect
64. C2×#63223C2×C4semidirect
74. C17×#95C2×C4semidirect
78. #10587502C2×C4semidirect
248. #1297D17semidirect
345. C2×M16C4×D17semidirect
374. #95C4×D17semidirect
375. C17#8051semidirect

Maximal subgroups

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

subgroupindex
D17×#4072
#145311652
C4×C22⋊C4×D172
#145266702
#145266692
C17×#12972
#805117