Finite Group Databasebeta

← #17036730

Subgroups — #17036730

Order 4352.

1218 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762849C211yesmaximal, characteristic, complemented
2C2×#11762808C211yesmaximal, characteristic
3C2×#11762808C211yesmaximal, characteristic
4#14531274C211yesmaximal, characteristic
5#14529425C212yesmaximal, complemented
6#14529418C212yesmaximal, complemented
7#14529411C212yesmaximal, complemented
8#14529404C212yesmaximal, complemented
9#14528503C211yesmaximal, characteristic, complemented
10#14528478C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C17C211yesmaximal, characteristic, complemented
12C22×#63252C2211yescharacteristic
13C22×#63223C2211yescharacteristic
14C22×#63223C2211yescharacteristic
15C2×#10587612C2211yescharacteristic
16#11762849—24no—
17C2×#10587478C2212yes—
18C2×#10587479C2212yes—
19#11762808—24no—
20#11762808C418yescomplemented
21C2×#10587481C2212yes—
22C2×#10587481C2212yes—
23C2×#10587480C2212yes—
24C2×#10587480C2212yes—
25#11762715C2211yescharacteristic
26#11762715C2211yescharacteristic
27#11762711C2211yescharacteristic
28#11762711C2211yescharacteristic
29#11762688—21no—
30#11762688—21no—
31C4×#63227—21no—
32C4×#63227—21no—
33#11762571C2212yes—
34#11762571C2212yes—
35#11762564C2212yes—
36#11762564C2212yes—
37C22×C4⋊C4×C17C2211yescharacteristic
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C42×C17—21no—
40C22×C42×C17C2211yescharacteristic
41C4×C4⋊C4×C17—21no—
42C4×C4⋊C4×C17—21no—
43C4×C4⋊C4×C17C2212yes—
44C4×C4⋊C4×C17C2212yes—
45C2×C17×#95—21no—
46C23×C4×C17—21no—
47C23×C4×C17—21no—
48C23×C4×C17D411yescharacteristic
49C23×C4×C17D411yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C22×C22⋊D17—21no—
52C2×#63252—22no—
53C2×#63252—22no—
54C2×#63252—22no—
55C2×#63252—22no—
56C2×#63252—22no—
57C2×#63252C2×C414yes—
58C22×D68C2311yescharacteristic
59C22×C4×D17—21no—
60C22×Dic34C2311yescharacteristic
61C2×C4⋊C4×C17—21no—
62C2×C4⋊C4×C17—21no—
63C2×C4⋊C4×C17—22no—
64C2×C4⋊C4×C17—22no—
65C2×C4⋊C4×C17C2×C414yes—
66C2×C4⋊C4×C17D414yes—
67C2×C4⋊C4×C17C2312yes—
68C2×C4⋊C4×C17C2312yes—
69C2×C42×C17—22no—
70C2×C42×C17—22no—
71C2×C42×C17—22no—
72C2×C42×C17—22no—
73C2×C42×C17—44no—
74C2×C42×C17D411yescharacteristic
75C2×C42×C17D411yescharacteristic
76C2×C42×C17C2311yescharacteristic
77C2×C42×C17C2311yescharacteristic
78C2×C22⋊Dic17—21no—
79C2×#63227—21no—
80C2×#63227—21no—
81C2×#63227—21no—
82C2×#63227—21no—
83#10587612—22no—
84#10587612—22no—
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4×Dic17—21no—
88C2×#63223—22no—
89C2×#63223—22no—
90C2×#63223—22no—
91C2×#63223—22no—
92C2×#63223—22no—
93C2×#63223C2×C414yes—
94C22×#3622C2312yes—
95C22×#3622C2312yes—
96C17×#95—22no—
97C17×#95—22no—
98#10587502—21no—
99#10587502—21no—
100#10587502—21no—
101#10587502—21no—
102#10587481—24no—
103#10587481C2×C418yescomplemented
104#10587480—24no—
105#10587480C2×C418yescomplemented
106#10587479—24no—
107#10587478—24no—
108C24×C17C2×D411yescharacteristic
109C23×D17—21no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—24no—
114C22×C4×C17—24no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—41no—
119C22×C4×C17—41no—
120C22×C4×C17—42no—
121C22×C4×C17—42no—
122C22×C4×C17—42no—
123C22×C4×C17—42no—
124C22×C4×C17C22×C412yes—
125C22×C4×C17C2×D412yes—
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17#4112yes—
132C22×C4×C17#4112yes—
133C22×C4×C17#4112yes—
134C22×C4×C17#4112yes—
135C22×C4×C17C2411yescharacteristic
136C2×C22⋊D17—24no—
137C2×C22⋊D17—42no—
138C2×C22⋊D17—42no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142#63252—28no—
143#63252—28no—
144#63252—44no—
145#63252—44no—
146C2×D68—21no—
147C2×D68—21no—
148C2×D68—21no—
149C2×D68—21no—
150C2×D68—21no—
151C2×D68C22×C412yes—
152C2×C4×D17—24no—
153C2×C4×D17—42no—
154C2×C4×D17—42no—
155C2×Dic34—21no—
156C2×Dic34—21no—
157C2×Dic34—21no—
158C2×Dic34—21no—
159C2×Dic34—21no—
160C2×Dic34C22×C412yes—
161C4⋊C4×C17—24no—
162C4⋊C4×C17—24no—
163C4⋊C4×C17—22no—
164C4⋊C4×C17—22no—
165C4⋊C4×C17C22×C414yes—
166C4⋊C4×C17C2×D414yes—
167C42×C17—22no—
168C42×C17—22no—
169C42×C17—21no—
170C42×C17—21no—
171C42×C17—21no—
172C42×C17—21no—
173C42×C17—44no—
174C42×C17—44no—
175C22⋊Dic17—42no—
176#63227—42no—
177#63227—42no—
178#63227—42no—
179#63227—42no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4×Dic17—42no—
185#63223—28no—
186#63223—44no—
187C2×#3622—22no—
188C2×#3622—22no—
189C2×#3622—22no—
190C2×#3622—22no—
191C2×#3622—22no—
192C2×#3622C22×C414yes—
193#21059—171nomaximal, Sylow
194C23×C17—21no—
195C23×C17—21no—
196C23×C17—21no—
197C23×C17—21no—
198C23×C17C4×D412yes—
199C23×C17#12112yes—
200C23×C17#12312yes—
201C23×C17C22×D411yescharacteristic
202C22×D17—22no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—41no—
206C22×D17—41no—
207C22×D17—41no—
208C22×D17—41no—
209C2×C4×C17—28no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—24no—
215C2×C4×C17—24no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—44no—
223C2×C4×C17—48no—
224C2×C4×C17—48no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17#11714yes—
230C2×C4×C17C4×D414yes—
231C2×C4×C17C4×D412yes—
232C2×C4×C17#12112yes—
233C2×C4×C17#12312yes—
234C2×C4×C17#12414yes—
235C2×C4×C17#12614yes—
236C2×C4×C17AGL(1,ℤ/8)12yes—
237C2×C4×C17#13712yes—
238C2×C4×C17C23×C411yescharacteristic
239C2×C4×C17C22×D411yescharacteristic
240C2×C4×C17C2×#4111yescharacteristic
241C2×C4×C17C2×#4111yescharacteristic
242C2×C4×C17C2×#4111yescharacteristic
243C2×C4×C17C2×#4111yescharacteristic
244C22⋊D17—48no—
245C2×Dic17—22no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254D68—22no—
255D68—22no—
256D68—41no—
257D68—41no—
258C4×D17—48no—
259Dic34—22no—
260Dic34—22no—
261Dic34—41no—
262Dic34—41no—
263#3622—24no—
264#3622—42no—
265C2×#428—171no—
266C2×#417—171no—
267C2×#417—171no—
268#2297—171no—
269C2×C4×C4⋊C4D1711yescharacteristic, complemented
270#1928—172no—
271#1927—172no—
272#1926—172no—
273#1925—172no—
274#1736—171no—
275#1728—171no—
276C22×C17—22no—
277C22×C17—22no—
278C22×C17—22no—
279C22×C17—22no—
280C22×C17—22no—
281C22×C17—22no—
282C22×C17#38814yes—
283C22×C17C2×C4×D411yescharacteristic
284C22×C17C2×#12111yescharacteristic
285C22×C17C2×#12311yescharacteristic
286C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C17C2×#13711yescharacteristic
288C22×C17#57511yescharacteristic
289C22×C17#57511yescharacteristic
290C2×D17—42no—
291C2×D17—42no—
292C2×D17—42no—
293C2×D17—81no—
294C2×D17—81no—
295C2×D17—81no—
296C2×D17—81no—
297C4×C17—22no—
298C4×C17—22no—
299C4×C17—41no—
300C4×C17—41no—
301C4×C17—44no—
302C4×C17—44no—
303C4×C17#38814yes—
304C4×C17C2×#11711yescharacteristic
305C4×C17C2×C4×D411yescharacteristic
306C4×C17C2×#12411yescharacteristic
307C4×C17C2×#12611yescharacteristic
308Dic17—42no—
309Dic17—81no—
310Dic17—81no—
311C22×#41—171no—
312C22×M16—171no—
313C22×M16—171no—
314C2×#117—171no—
315C22×C4⋊C4C2×D1711yescharacteristic
316C22×C4⋊C4C2×D1711yescharacteristic
317C22×C42—21no—
318C22×C42C2×D1711yescharacteristic
319#428—344no—
320C2×#107—172no—
321C2×#106—172no—
322#417—178no—
323#417—344no—
324C2×#103—172no—
325C2×#103—172no—
326C2×#102—172no—
327C2×#102—172no—
328#391—171no—
329#391—171no—
330#390—171no—
331#390—171no—
332#386—341no—
333#386—341no—
334C4×C4⋊C4—21no—
335C4×C4⋊C4—21no—
336C4×C4⋊C4C2×D1712yes—
337C4×C4⋊C4C2×D1712yes—
338C4×C22⋊C4—341no—
339C4×C22⋊C4—341no—
340C2×#95—21no—
341#340—172no—
342#340—172no—
343#336—172no—
344#336—172no—
345C2×C17—24no—
346C2×C17C2×#38811yescharacteristic
347C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
348C2×C17C4×#13711yescharacteristic
349C2×C17#303611yescharacteristic
350C2×C17#303711yescharacteristic
351C2×C17#309211yescharacteristic
352C2×C17#309311yescharacteristic
353D17—82no—
354C2×#41—174no—
355C2×#41—342no—
356C2×#41—342no—
357C2×#41—342no—
358C2×#41—342no—
359C2×#41—342no—
360C22×Q8—171no—
361C22×D4—171no—
362C22×D4—341no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—341no—
366C23×C4C22⋊D1711yescharacteristic
367C23×C4C22⋊D1711yescharacteristic
368C23×C4C22×D1711yescharacteristic
369C2×M16—174no—
370C2×M16—342no—
371C2×M16—342no—
372C2×M16—342no—
373C2×M16—342no—
374C2×M16—342no—
375C22×C8—172no—
376C22×C8—172no—
377#117—342no—
378#117—342no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4C4×D1714yes—
386C2×C4⋊C4D6814yes—
387C2×C4⋊C4C22×D1712yes—
388C2×C4⋊C4C22×D1712yes—
389C2×C22⋊C4—341no—
390C2×C22⋊C4—341no—
391C2×C22⋊C4—341no—
392C2×C22⋊C4—341no—
393C2×C22⋊C4—341no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—44no—
399C2×C42—341no—
400C2×C42C22⋊D1711yescharacteristic
401C2×C42C22⋊D1711yescharacteristic
402C2×C42C22×D1711yescharacteristic
403C2×C42C22×D1711yescharacteristic
404#107—344no—
405#106—344no—
406#103—178no—
407#103—344no—
408#102—178no—
409#102—344no—
410#95—22no—
411#95—22no—
412#95—341no—
413#95—341no—
414#95—341no—
415#95—341no—
416C17#2105911yescharacteristic, complemented, Sylow
417C24—341no—
418C24C2×C22⋊D1711yescharacteristic
419#41—348no—
420#41—348no—
421#41—684no—
422#41—684no—
423C2×Q8—172no—
424C2×Q8—341no—
425C2×Q8—341no—
426C2×Q8—341no—
427C2×Q8—341no—
428C2×Q8—341no—
429C2×D4—172no—
430C2×D4—344no—
431C2×D4—341no—
432C2×D4—341no—
433C2×D4—341no—
434C2×D4—341no—
435C2×D4—341no—
436C2×D4—682no—
437C2×D4—682no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—341no—
453C22×C4—344no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—682no—
457C22×C4—682no—
458C22×C4C2×C4×D1712yes—
459C22×C4C2×D6812yes—
460C22×C4#6325212yes—
461C22×C4#6325212yes—
462C22×C4#6325212yes—
463C22×C4#6325212yes—
464C22×C4C2×C22⋊D1711yescharacteristic
465C22×C4C2×C22⋊D1711yescharacteristic
466C22×C4C2×C22⋊D1711yescharacteristic
467C22×C4C2×C22⋊D1711yescharacteristic
468C22×C4C2×C22⋊D1711yescharacteristic
469C22×C4C23×D1711yescharacteristic
470M16—348no—
471M16—684no—
472C2×C8—174no—
473C2×C8—342no—
474C2×C8—342no—
475C2×C8—342no—
476C2×C8—342no—
477C2×C8—342no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—341no—
483C4⋊C4—341no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4C2×C4×D1714yes—
487C4⋊C4C2×D6814yes—
488C22⋊C4—682no—
489C22⋊C4—682no—
490C22⋊C4—682no—
491C22⋊C4—682no—
492C22⋊C4—682no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—22no—
498C42—22no—
499C42—44no—
500C42—44no—
501C42—682no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—342no—
507C23—681no—
508C23—681no—
509C23—681no—
510C23—681no—
511C23—681no—
512C23—681no—
513C23C4×C22⋊D1712yes—
514C23#1058761512yes—
515C23#1058761612yes—
516C23C22×C22⋊D1711yescharacteristic
517Q8—342no—
518Q8—342no—
519Q8—681no—
520Q8—681no—
521D4—342no—
522D4—342no—
523D4—688no—
524D4—681no—
525D4—681no—
526C2×C4—28no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—48no—
540C2×C4—48no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—342no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—688no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4#1058755814yes—
557C2×C4C4×D6814yes—
558C2×C4#1058756114yes—
559C2×C4#1058756214yes—
560C2×C4C4×C22⋊D1712yes—
561C2×C4#1058761512yes—
562C2×C4#1058761612yes—
563C2×C4#1058761812yes—
564C2×C4#1058762812yes—
565C2×C4C22×C4×D1711yescharacteristic
566C2×C4C22×D6811yescharacteristic
567C2×C4C2×#6325211yescharacteristic
568C2×C4C2×#6325211yescharacteristic
569C2×C4C2×#6325211yescharacteristic
570C2×C4C2×#6325211yescharacteristic
571C8—344no—
572C8—682no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—682no—
580C22—682no—
581C22—682no—
582C22—1361no—
583C22—1361no—
584C22—1361no—
585C22—1361no—
586C22#1176270014yes—
587C22C2×C4×C22⋊D1711yescharacteristic
588C22C2×#1058761611yescharacteristic
589C22C2×#1058761511yescharacteristic
590C22C2×#1058761811yescharacteristic
591C22C2×#1058762811yescharacteristic
592C22#1176360711yescharacteristic
593C22#1176360711yescharacteristic
594C4—22no—
595C4—22no—
596C4—44no—
597C4—44no—
598C4—41no—
599C4—41no—
600C4—682no—
601C4—1361no—
602C4—1361no—
603C4#1176270014yes—
604C4C2×#1058755811yescharacteristic
605C4C2×C4×D6811yescharacteristic
606C4C2×#1058756111yescharacteristic
607C4C2×#1058756211yescharacteristic
608C2—24no—
609C2—1362no—
610C2C2×#1176270011yescharacteristic
611C2C4×#1058761811yescharacteristic
612C2C4×#1058762811yescharacteristic
613C2#1453824811yescharacteristic
614C2#1453825611yescharacteristic
615C2#1453870711yescharacteristic
616C2#1453871511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×C4⋊C4×C17C2
socleC23×C17C22×D4
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17#21059
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11762849C2semidirect
5. #14529425C2semidirect
6. #14529418C2semidirect
7. #14529411C2semidirect
8. #14529404C2semidirect
9. #14528503C2semidirect
10. #14528478C2semidirect
11. C2×C4×C4⋊C4×C17C2semidirect
20. #11762808C4semidirect
103. #10587481C2×C4semidirect
105. #10587480C2×C4semidirect
269. C2×C4×C4⋊C4D17semidirect
416. C17#21059semidirect

Maximal subgroups

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

subgroupindex
C2×#117628492
C2×#117628082
#145312742
#145294252
#145294182
#145294112
#145294042
#145285032
#145284782
C2×C4×C4⋊C4×C172
#2105917