Finite Group Databasebeta

← #17000261

Subgroups — #17000261

Order 4352.

1174 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763288C211yesmaximal, characteristic
2#14537868C212yesmaximal, complemented
3#14527125C211yesmaximal, characteristic, complemented
4#14527123C212yesmaximal, complemented
5#14527116C212yesmaximal, complemented
6#14527115C212yesmaximal, complemented
7#14527103C212yesmaximal, complemented
8#14527095C212yesmaximal, complemented
9C17×#1466C211yesmaximal, characteristic, complemented
10C22×#63254C411yescharacteristic
11#11763288—24no—
12#11763288—24no—
13C2×C4×Dic34C2211yescharacteristic
14C2×#10587573C411yescharacteristic
15C2×D4×Dic17C411yescharacteristic
16C2×C4×C22⋊D17C411yescharacteristic
17C2×C4×C22⋊D17C411yescharacteristic
18C2×#10587567C2211yescharacteristic
19C2×#10587567C2211yescharacteristic
20C2×#10587558C2211yescharacteristic
21C2×#10587563C2211yescharacteristic
22C2×#10587563C2211yescharacteristic
23C22×#63225C411yescharacteristic
24C22×#63225C411yescharacteristic
25C2×C4⋊C4×D17C411yescharacteristic
26#11762938—24no—
27#11762937—24no—
28#11762866C2212yes—
29#11762863C2214yes—
30#11762859C2214yes—
31#11762534C2214yes—
32#11762533C2212yes—
33#11762533C2212yes—
34#11762532C2214yes—
35C2×C4×D4×C17C2211yescharacteristic
36C17×#432C2212yes—
37C17×#323C2212yes—
38C17×#323C2212yes—
39C22×D4×C17C2×C411yescharacteristic
40C23×C4×C17C2×C411yescharacteristic
41C23×C4×C17C2×C411yescharacteristic
42C22×C22⋊D17C2×C411yescharacteristic
43C22×C22⋊D17C2×C411yescharacteristic
44C23×Dic17C2×C411yescharacteristic
45C23×Dic17C2×C411yescharacteristic
46C23×Dic17C2×C411yescharacteristic
47C23×Dic17C2×C411yescharacteristic
48C2×#63254—24no—
49C2×#63254—24no—
50C2×#63254—24no—
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×Dic34C2×C411yescharacteristic
55C4×D4×C17—22no—
56C4×D4×C17—22no—
57C2×C4⋊C4×C17C2×C411yescharacteristic
58C2×C22⋊C4×C17C2311yescharacteristic
59C2×C22⋊C4×C17C2311yescharacteristic
60C2×C42×C17C2311yescharacteristic
61C2×C22⋊Dic17C2×C411yescharacteristic
62C2×C22⋊Dic17C2×C411yescharacteristic
63D4×Dic17—24no—
64C4×C22⋊D17—22no—
65C4×C22⋊D17—22no—
66C4×C22⋊D17—22no—
67C4×C22⋊D17—22no—
68C2×#63227C2×C411yescharacteristic
69C2×#63227C2311yescharacteristic
70C2×C4⋊Dic17C2×C411yescharacteristic
71C2×#63225—22no—
72C2×#63225—22no—
73C2×#63225—22no—
74C2×#63225—22no—
75C2×#63225C2×C411yescharacteristic
76C2×#63225C2×C411yescharacteristic
77C2×#63225C2×C411yescharacteristic
78C2×#63225C2×C411yescharacteristic
79C2×#63225C2×C411yescharacteristic
80C2×#63225C2×C411yescharacteristic
81C2×#63225C2×C411yescharacteristic
82C2×#63225C2311yescharacteristic
83C2×C4×Dic17C2×C411yescharacteristic
84C2×C4×Dic17C2×C411yescharacteristic
85C2×C4×Dic17C2×C411yescharacteristic
86C2×C4×Dic17C2311yescharacteristic
87C2×C4×Dic17C2311yescharacteristic
88C4⋊C4×D17—24no—
89#10587573—24no—
90#10587567—24no—
91#10587567—24no—
92#10587563—24no—
93#10587563—24no—
94#10587558—22no—
95#10587558—22no—
96C4×Dic34D414yes—
97C4×Dic34D414yes—
98C17×C4⋊C8—22no—
99C17×C22⋊C8C2314yes—
100C17×#97—22no—
101C22⋊#3622C2314yes—
102#10587486—24no—
103#10587485—24no—
104#10587485—24no—
105C8×Dic17—24no—
106C4⋊#3622—22no—
107#10587474—22no—
108C24×C17C22×C411yescharacteristic
109C24×C17C22×C411yescharacteristic
110C23×D17C22×C411yescharacteristic
111C2×D4×C17—22no—
112C2×D4×C17—22no—
113C2×D4×C17—22no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—81no—
119C22×C4×C17—81no—
120C22×C4×C17C22×C411yescharacteristic
121C22×C4×C17C22×C411yescharacteristic
122C22×C4×C17C22×C411yescharacteristic
123C22×C4×C17C22×C411yescharacteristic
124C22×C4×C17C2411yescharacteristic
125C2×C22⋊D17—22no—
126C2×C22⋊D17—22no—
127C2×C22⋊D17—22no—
128C2×C22⋊D17—22no—
129C2×C22⋊D17—22no—
130C2×C22⋊D17M1614yes—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—81no—
139C22×Dic17—81no—
140C22×Dic17M1614yes—
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C411yescharacteristic
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C411yescharacteristic
147C22×Dic17C22×C411yescharacteristic
148#63254—232no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—22no—
153C2×C4×D17—22no—
154C2×C4×D17—81no—
155C2×C4×D17—81no—
156C2×Dic34—22no—
157C2×Dic34—22no—
158C2×Dic34C22⋊C414yes—
159C2×C8×C17—24no—
160C4⋊C4×C17—22no—
161C22⋊C4×C17—22no—
162C22⋊C4×C17—22no—
163C42×C17C2×D412yes—
164C42×C17C2×D412yes—
165C22⋊Dic17—22no—
166C22⋊Dic17—22no—
167#63227—21no—
168#63227—21no—
169#63227—22no—
170C4⋊Dic17C22⋊C414yes—
171#63225—21no—
172#63225—21no—
173#63225—22no—
174#63225—22no—
175#63225—22no—
176#63225—22no—
177#63225—22no—
178#63225C22⋊C412yes—
179#63225C22⋊C412yes—
180#63225C22⋊C412yes—
181#63225C22⋊C412yes—
182C4×Dic17—22no—
183C4×Dic17—22no—
184C4×Dic17—22no—
185C4×Dic17C2×D414yes—
186C4×Dic17C2×D414yes—
187C2×#3622—24no—
188#17372—171nomaximal, Sylow
189C23×C17—21no—
190C23×C17—21no—
191C23×C17—21no—
192C23×C17—21no—
193C23×C17—41no—
194C23×C17—41no—
195C23×C17—41no—
196C23×C17—41no—
197C23×C17C2×M1612yes—
198C23×C17C2×M1612yes—
199C23×C17C23×C411yescharacteristic
200C22×D17—21no—
201C22×D17—21no—
202C22×D17—41no—
203C22×D17—41no—
204C22×D17C2×M1612yes—
205D4×C17—28no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—81no—
215C2×C4×C17—81no—
216C2×C4×C17—81no—
217C2×C4×C17—81no—
218C2×C4×C17C2×C22⋊C412yes—
219C2×C4×C17C2×C22⋊C411yescharacteristic
220C2×C4×C17C2×C22⋊C411yescharacteristic
221C2×C4×C17C22×D412yes—
222C22⋊D17—28no—
223C22⋊D17—28no—
224C2×Dic17—28no—
225C2×Dic17—21no—
226C2×Dic17—21no—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—28no—
230C2×Dic17—21no—
231C2×Dic17—21no—
232C2×Dic17—41no—
233C2×Dic17—41no—
234C2×Dic17—41no—
235C2×Dic17—41no—
236C2×Dic17—82no—
237C2×Dic17—82no—
238C2×Dic17C2×C22⋊C412yes—
239C2×Dic17C2×C22⋊C412yes—
240C2×Dic17C2×C22⋊C412yes—
241C2×Dic17C2×C22⋊C412yes—
242C2×Dic17C2×M1612yes—
243C2×Dic17C2×M1612yes—
244C2×Dic17C2×M1612yes—
245C4×D17—28no—
246C4×D17—82no—
247C4×D17—82no—
248Dic34—28no—
249C8×C17—44no—
250#3622—44no—
251C2×#520—171no—
252#2983—172no—
253#1466—172no—
254#1466—171no—
255#1466D1711yescharacteristic, complemented
256#1464—172no—
257#1464—172no—
258#1460—172no—
259#1458—172no—
260C22×C17—21no—
261C22×C17—21no—
262C22×C17—22no—
263C22×C17—22no—
264C22×C17—42no—
265C22×C17—42no—
266C22×C17—42no—
267C22×C17—42no—
268C22×C17—41no—
269C22×C17—41no—
270C22×C17—41no—
271C22×C17—41no—
272C22×C17C22×C22⋊C411yescharacteristic
273C22×C17C22×M1611yescharacteristic
274C22×C17C22×M1611yescharacteristic
275C2×D17—22no—
276C2×D17—42no—
277C2×D17—41no—
278C2×D17—41no—
279C2×D17—42no—
280C4×C17—22no—
281C4×C17—22no—
282C4×C17—21no—
283C4×C17—21no—
284C4×C17—41no—
285C4×C17—41no—
286Dic17—22no—
287Dic17—22no—
288Dic17—22no—
289Dic17—22no—
290Dic17—41no—
291Dic17—41no—
292Dic17#40714yes—
293C22×#41—171no—
294#520—344no—
295#520—344no—
296C2×C4×Q8—171no—
297C2×C4×Q8—171no—
298C2×C4×D4—171no—
299C2×C4×D4—171no—
300C2×C4×D4—171no—
301C2×C4×D4—171no—
302C2×C4×D4—171no—
303C2×C4×D4C2×D1711yescharacteristic
304C2×#117—171no—
305C2×#117—171no—
306C2×#117—171no—
307C22×C4⋊C4—171no—
308C22×C4⋊C4—171no—
309C22×C4⋊C4—171no—
310#446—344no—
311#446—344no—
312#432—172no—
313#432—174no—
314#432C2×D1712yes—
315#431—174no—
316#324—174no—
317#323—172no—
318#323—172no—
319#323—174no—
320#323C2×D1712yes—
321#323C2×D1712yes—
322C2×C17—21no—
323C2×C17—21no—
324C2×C17—42no—
325C2×C17—42no—
326C2×C17C2×#40711yescharacteristic
327C2×C17#288411yescharacteristic
328C2×C17#288811yescharacteristic
329D17—42no—
330C2×#41—344no—
331C2×#41—344no—
332C2×#41—344no—
333C22×Q8—171no—
334C22×D4—171no—
335C22×D4—171no—
336C22×D4C4×D1711yescharacteristic
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—171no—
344C23×C4C4×D1711yescharacteristic
345C23×C4C4×D1711yescharacteristic
346C4×Q8—174no—
347C4×Q8—174no—
348C4×Q8—344no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—344no—
352C4×D4—344no—
353C4×D4—342no—
354C4×D4—342no—
355C4×D4—342no—
356C4×D4—342no—
357C4×D4—344no—
358#117—344no—
359#117—344no—
360#117—342no—
361#117—342no—
362C2×C4⋊C4—171no—
363C2×C4⋊C4—171no—
364C2×C4⋊C4—171no—
365C2×C4⋊C4—171no—
366C2×C4⋊C4—171no—
367C2×C4⋊C4—171no—
368C2×C4⋊C4—171no—
369C2×C4⋊C4—171no—
370C2×C4⋊C4—171no—
371C2×C4⋊C4—344no—
372C2×C4⋊C4—342no—
373C2×C4⋊C4—342no—
374C2×C4⋊C4—342no—
375C2×C4⋊C4—342no—
376C2×C4⋊C4C4×D1711yescharacteristic
377C2×C22⋊C4—171no—
378C2×C22⋊C4—171no—
379C2×C22⋊C4—171no—
380C2×C22⋊C4—171no—
381C2×C22⋊C4C22×D1711yescharacteristic
382C2×C22⋊C4C22×D1711yescharacteristic
383C2×C42—171no—
384C2×C42—171no—
385C2×C42—171no—
386C2×C42—171no—
387C2×C42—171no—
388C2×C42C22×D1711yescharacteristic
389C4⋊C8—22no—
390C4⋊C8—344no—
391C4⋊C8—344no—
392C4⋊C8—342no—
393C22⋊C8—174no—
394C22⋊C8C22×D1714yes—
395#97—22no—
396#97—344no—
397#97—342no—
398C4×C8—344no—
399C17#1737211yescharacteristic, complemented, Sylow
400C24—171no—
401C24C2×C4×D1711yescharacteristic
402C24C2×C4×D1711yescharacteristic
403#41—3432no—
404C2×Q8—174no—
405C2×Q8—342no—
406C2×Q8—342no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—174no—
411C2×D4—342no—
412C2×D4—342no—
413C2×D4—342no—
414C2×D4—342no—
415C2×D4—342no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4—171no—
423C22×C4—171no—
424C22×C4—171no—
425C22×C4—174no—
426C22×C4—171no—
427C22×C4—171no—
428C22×C4—171no—
429C22×C4—171no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—342no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—342no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—1361no—
443C22×C4—1361no—
444C22×C4—1361no—
445C22×C4—1361no—
446C22×C4C2×C4×D1711yescharacteristic
447C22×C4C2×C4×D1711yescharacteristic
448C22×C4C2×C4×D1711yescharacteristic
449C22×C4C2×C4×D1711yescharacteristic
450C22×C4C23×D1711yescharacteristic
451C2×C8—24no—
452C2×C8—344no—
453C4⋊C4—22no—
454C4⋊C4—172no—
455C4⋊C4—172no—
456C4⋊C4—172no—
457C4⋊C4—172no—
458C4⋊C4—174no—
459C4⋊C4—342no—
460C4⋊C4—342no—
461C4⋊C4—342no—
462C4⋊C4—342no—
463C4⋊C4—342no—
464C4⋊C4—341no—
465C4⋊C4—341no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—342no—
469C22⋊C4—342no—
470C22⋊C4—342no—
471C22⋊C4—341no—
472C22⋊C4—341no—
473C42—174no—
474C42—174no—
475C42—342no—
476C42—342no—
477C42—342no—
478C42D4×D1712yes—
479C42D4×D1712yes—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—172no—
489C23—341no—
490C23—341no—
491C23—681no—
492C23—681no—
493C23M16×D1712yes—
494C23M16×D1712yes—
495C23C22×C4×D1711yescharacteristic
496Q8—348no—
497D4—28no—
498D4—348no—
499D4—348no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—172no—
513C2×C4—172no—
514C2×C4—172no—
515C2×C4—172no—
516C2×C4—172no—
517C2×C4—172no—
518C2×C4—172no—
519C2×C4—348no—
520C2×C4—348no—
521C2×C4—348no—
522C2×C4—341no—
523C2×C4—341no—
524C2×C4—341no—
525C2×C4—341no—
526C2×C4—341no—
527C2×C4—341no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—1362no—
533C2×C4—1362no—
534C2×C4—1362no—
535C2×C4—1362no—
536C2×C4C22⋊C4×D1712yes—
537C2×C4C22⋊C4×D1711yescharacteristic
538C2×C4C22⋊C4×D1711yescharacteristic
539C2×C4C2×D4×D1712yes—
540C8—44no—
541C8—684no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—342no—
555C22—682no—
556C22—682no—
557C22—681no—
558C22—681no—
559C22C2×C22⋊C4×D1711yescharacteristic
560C22C2×M16×D1711yescharacteristic
561C22C2×M16×D1711yescharacteristic
562C4—22no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—174no—
569C4—342no—
570C4—342no—
571C4—342no—
572C4—342no—
573C4—681no—
574C4—681no—
575C2—21no—
576C2—21no—
577C2—42no—
578C2—42no—
579C2—682no—
580C2D17×#40711yescharacteristic
581C2#1453724611yescharacteristic
582C2#1453726011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1466C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#63254C4
cosocleC22×C4×C17C24
hypercenter#1466D17
hypocenterC17#17372
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #14537868C2semidirect
3. #14527125C2semidirect
4. #14527123C2semidirect
5. #14527116C2semidirect
6. #14527115C2semidirect
7. #14527103C2semidirect
8. #14527095C2semidirect
9. C17×#1466C2semidirect
255. #1466D17semidirect
399. C17#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#117632882
#145378682
#145271252
#145271232
#145271162
#145271152
#145271032
#145270952
C17×#14662
#1737217