Finite Group Databasebeta

← #17042439

Subgroups — #17042439

Order 4352.

826 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×#11763169C211yesmaximal, characteristic
2#14531532C211yesmaximal, characteristic, complemented
3#14531495C211yesmaximal, characteristic
4#14529745C211yesmaximal, characteristic, complemented
5#14529595C211yesmaximal, characteristic
6#14529481C211yesmaximal, characteristic
7#14529474C211yesmaximal, characteristic, complemented
8#14529467C211yesmaximal, characteristic
9#14529460C211yesmaximal, characteristic, complemented
10#14528918C211yesmaximal, characteristic, complemented
11#14528615C211yesmaximal, characteristic, complemented
12#14528610C211yesmaximal, characteristic
13C4×#10587487C211yesmaximal, characteristic, complemented
14C4×#10587492C211yesmaximal, characteristic
15C17×#1726C211yesmaximal, characteristic, complemented
16C2×#10587555C2211yescharacteristic
17C2×#10587561C2211yescharacteristic
18C2×C4×Dic34C2211yescharacteristic
19C2×C4×D68C2211yescharacteristic
20#11763169C418yescomplemented
21C2×#10587487C2211yescharacteristic
22C2×#10587487C2211yescharacteristic
23C2×#10587487C2211yescharacteristic
24C2×#10587487C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587492C2211yescharacteristic
27C2×#10587492C2211yescharacteristic
28C2×#10587492C2211yescharacteristic
29#11762715C2211yescharacteristic
30#11762713—21no—
31#11762713—21no—
32#11762711C2211yescharacteristic
33#11762707C2211yescharacteristic
34#11762707C2211yescharacteristic
35#11762701—21no—
36#11762701—21no—
37#11762692—21no—
38#11762692—21no—
39#11762683—21no—
40#11762683—21no—
41#11762679C2211yescharacteristic
42#11762675C2211yescharacteristic
43C4×C4⋊Dic17C2211yescharacteristic
44C4×C4⋊Dic17C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53C2×C17×#97C2211yescharacteristic
54C2×C17×#97C2211yescharacteristic
55C2×C17×#97C2211yescharacteristic
56C2×C4×C8×C17C2211yescharacteristic
57C2×C4×C8×C17C2211yescharacteristic
58C2×C4×C8×C17C2211yescharacteristic
59C17×#376C2211yescharacteristic
60C22×D68C2311yescharacteristic
61C22×C4×D17—21no—
62C22×Dic34—21no—
63C22×Dic34C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C2×C42×C17C2311yescharacteristic
69C2×C42×C17C2311yescharacteristic
70C2×C42×C17C2311yescharacteristic
71C2×#63227—21no—
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227—21no—
75C2×#63227—21no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×#63225—21no—
86C2×#63225—21no—
87C2×#63225—21no—
88C2×C4×Dic17—21no—
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91#10587561—22no—
92#10587561C2×C414yes—
93C4×D68—22no—
94C4×D68—22no—
95#10587555—22no—
96#10587555C2×C414yescomplemented
97C4×Dic34—22no—
98C4×Dic34—22no—
99C17×#97—22no—
100C17×#97—22no—
101C17×#97C2×C414yescomplemented
102C4×C8×C17—22no—
103C4×C8×C17—22no—
104C4×C8×C17—22no—
105C17×#95D411yescharacteristic
106C17×#95D411yescharacteristic
107C17×#95D411yescharacteristic
108C17×#95D411yescharacteristic
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502—21no—
115#10587502—21no—
116#10587502—21no—
117#10587492—22no—
118#10587492—22no—
119#10587492C2×C414yes—
120#10587492C2×C414yes—
121#10587487—22no—
122#10587487—22no—
123#10587487C2×C414yescomplemented
124#10587487C2×C414yescomplemented
125C23×D17—21no—
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2×D411yescharacteristic
132C22×C4×C17C2411yescharacteristic
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C2×D68—21no—
141C2×D68—21no—
142C2×D68—21no—
143C2×D68—21no—
144C2×D68—21no—
145C2×D68C22×C412yes—
146C2×C4×D17—42no—
147C2×C4×D17—81no—
148C2×C4×D17—81no—
149C2×Dic34—21no—
150C2×Dic34—21no—
151C2×Dic34—21no—
152C2×Dic34—21no—
153C2×Dic34—21no—
154C2×Dic34—24no—
155C2×Dic34—81no—
156C2×Dic34—81no—
157C2×Dic34C22×C412yes—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17C22×C412yes—
167C2×C8×C17C22×C412yes—
168C2×C8×C17#4112yes—
169C2×C8×C17#4112yes—
170C42×C17—21no—
171C42×C17—21no—
172C42×C17C22×C412yes—
173C42×C17#4112yes—
174C42×C17#4112yes—
175C42×C17#4112yes—
176#63227—24no—
177#63227—24no—
178#63227—42no—
179#63227—81no—
180#63227—81no—
181C4⋊Dic17—24no—
182C4⋊Dic17—21no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17—21no—
192C4⋊Dic17—81no—
193C4⋊Dic17—81no—
194C4⋊Dic17C22×C412yes—
195C4⋊Dic17C22×C412yes—
196#63225—42no—
197#63225—81no—
198#63225—81no—
199C4×Dic17—42no—
200C4×Dic17—81no—
201C4×Dic17—81no—
202#21654—171nomaximal, Sylow
203C23×C17C22×D411yescharacteristic
204C22×D17—22no—
205C22×D17—41no—
206C22×D17—41no—
207C22×D17—41no—
208C22×D17—41no—
209C22×D17—41no—
210C22×D17—41no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
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—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17C4×D412yes—
226C2×C4×C17C4×D412yes—
227C2×C4×C17#12412yes—
228C2×C4×C17#12412yes—
229C2×C4×C17C23×C411yescharacteristic
230C2×C4×C17C2×#4111yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C2×C4×C17C2×#4111yescharacteristic
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17—41no—
244C2×Dic17—41no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256D68—22no—
257D68—22no—
258D68—41no—
259D68—41no—
260C4×D17—84no—
261Dic34—22no—
262Dic34—22no—
263Dic34—41no—
264Dic34—41no—
265Dic34—84no—
266C8×C17—22no—
267C8×C17—22no—
268C8×C17—22no—
269C8×C17—22no—
270C2×#489—171no—
271#2331—171no—
272#2326—171no—
273#1990—171no—
274#1958—171no—
275#1936—171no—
276#1935—171no—
277#1934—171no—
278#1933—171no—
279#1836—171no—
280#1763—171no—
281#1762—171no—
282C4×#103—171no—
283C4×#102—171no—
284#1726D1711yescharacteristic, complemented
285C22×C17C2×C4×D411yescharacteristic
286C22×C17C2×#12411yescharacteristic
287C22×C17#53211yescharacteristic
288C22×C17#57611yescharacteristic
289C22×C17#57711yescharacteristic
290C22×C17#57711yescharacteristic
291C22×C17#57811yescharacteristic
292C2×D17—42no—
293C2×D17—42no—
294C2×D17—42no—
295C2×D17—81no—
296C2×D17—81no—
297C2×D17—81no—
298C2×D17—81no—
299C4×C17—22no—
300C4×C17—22no—
301C4×C17—22no—
302C4×C17—22no—
303C4×C17—41no—
304C4×C17—41no—
305C4×C17C4×#4111yescharacteristic
306C4×C17C4×#4111yescharacteristic
307C4×C17#52911yescharacteristic
308C4×C17#52911yescharacteristic
309Dic17—42no—
310Dic17—42no—
311Dic17—42no—
312Dic17—81no—
313Dic17—81no—
314Dic17—81no—
315Dic17—81no—
316C2×C4⋊Q8—171no—
317C2×#124—171no—
318C2×C4×Q8—171no—
319C2×C4×D4—171no—
320#489—178no—
321C2×#103—171no—
322C2×#103—171no—
323C2×#103—171no—
324C2×#103—171no—
325C2×#102—171no—
326C2×#102—171no—
327C2×#102—171no—
328C2×#102—171no—
329C2×#97C2×D1711yescharacteristic
330C2×#97C2×D1711yescharacteristic
331C2×#97C2×D1711yescharacteristic
332C2×C4×C8C2×D1711yescharacteristic
333C2×C4×C8C2×D1711yescharacteristic
334C2×C4×C8C2×D1711yescharacteristic
335#391—171no—
336#391—341no—
337#391—341no—
338#390—171no—
339#389—171no—
340#389—171no—
341#388—341no—
342#388—341no—
343#387—341no—
344#387—341no—
345#385—341no—
346#385—341no—
347#384—171no—
348#382—171no—
349C4×C4⋊C4—171no—
350C4×C4⋊C4—171no—
351#376C2×D1711yescharacteristic
352#340—171no—
353#340—171no—
354#340—171no—
355#340—171no—
356#340—171no—
357#340—171no—
358#340—171no—
359#340—171no—
360C2×C17C4×#12411yescharacteristic
361C2×C17#294611yescharacteristic
362C2×C17#294711yescharacteristic
363C2×C17#313611yescharacteristic
364C2×C17#313711yescharacteristic
365C2×C17#317311yescharacteristic
366C2×C17#317511yescharacteristic
367D17—82no—
368C22×Q8—171no—
369C22×Q8—341no—
370C22×D4—171no—
371C23×C4—341no—
372C22×C8C22×D1711yescharacteristic
373C22×C8C22×D1711yescharacteristic
374C22×C8C22×D1711yescharacteristic
375C22×C8C22×D1711yescharacteristic
376C4⋊Q8—174no—
377C4⋊Q8—342no—
378#124—174no—
379#124—342no—
380C4×Q8—342no—
381C4×Q8—342no—
382C4×D4—342no—
383C4×D4—342no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—171no—
388C2×C4⋊C4—171no—
389C2×C4⋊C4—171no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4—341no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C22⋊C4—341no—
397C2×C22⋊C4—341no—
398C2×C22⋊C4—341no—
399C2×C22⋊C4—341no—
400C2×C22⋊C4—341no—
401C2×C42—341no—
402C2×C42—341no—
403C2×C42—341no—
404C2×C42C22×D1711yescharacteristic
405C2×C42C22×D1711yescharacteristic
406C2×C42C22×D1711yescharacteristic
407#103—174no—
408#103—174no—
409#103—342no—
410#103—342no—
411#102—174no—
412#102—174no—
413#102—342no—
414#102—342no—
415#97—22no—
416#97—22no—
417#97C4×D1714yescomplemented
418C4×C8—22no—
419C4×C8—22no—
420C4×C8—22no—
421#95—341no—
422#95—341no—
423#95—341no—
424#95—341no—
425#95—341no—
426#95—341no—
427#95—341no—
428#95—341no—
429#95D6811yescharacteristic
430#95D6811yescharacteristic
431#95D6811yescharacteristic
432#95D6811yescharacteristic
433C17#2165411yescharacteristic, complemented, Sylow
434C24—341no—
435C2×Q8—172no—
436C2×Q8—341no—
437C2×Q8—344no—
438C2×Q8—341no—
439C2×Q8—341no—
440C2×Q8—341no—
441C2×Q8—341no—
442C2×Q8—1361no—
443C2×Q8—1361no—
444C2×D4—172no—
445C2×D4—341no—
446C2×D4—341no—
447C2×D4—341no—
448C2×D4—341no—
449C2×D4—341no—
450C22×C4—341no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—341no—
457C22×C4—682no—
458C22×C4—1361no—
459C22×C4—1361no—
460C22×C4C2×D6811yescharacteristic
461C22×C4C2×D6811yescharacteristic
462C22×C4C2×D6811yescharacteristic
463C22×C4C2×D6811yescharacteristic
464C22×C4C2×D6811yescharacteristic
465C22×C4C2×D6811yescharacteristic
466C22×C4C23×D1711yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×C4×D1712yes—
476C2×C8C2×C4×D1712yes—
477C2×C8#6325212yes—
478C2×C8#6325212yes—
479C4⋊C4—172no—
480C4⋊C4—172no—
481C4⋊C4—341no—
482C4⋊C4—341no—
483C4⋊C4—344no—
484C4⋊C4—341no—
485C4⋊C4—341no—
486C4⋊C4—341no—
487C4⋊C4—341no—
488C4⋊C4—341no—
489C4⋊C4—341no—
490C4⋊C4—341no—
491C4⋊C4—341no—
492C4⋊C4—682no—
493C4⋊C4—1361no—
494C4⋊C4—1361no—
495C4⋊C4—1361no—
496C4⋊C4—1361no—
497C22⋊C4—344no—
498C22⋊C4—344no—
499C22⋊C4—682no—
500C22⋊C4—1361no—
501C22⋊C4—1361no—
502C42—21no—
503C42—21no—
504C42—682no—
505C42—1361no—
506C42—1361no—
507C42C2×C4×D1712yes—
508C42#6325212yes—
509C42#6325212yes—
510C42#6325212yes—
511C23—342no—
512C23—681no—
513C23—681no—
514C23—681no—
515C23—681no—
516C23—681no—
517C23—681no—
518C23C22×D6811yescharacteristic
519Q8—342no—
520Q8—342no—
521Q8—681no—
522Q8—681no—
523Q8—1364no—
524D4—342no—
525D4—342no—
526D4—681no—
527D4—681no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—342no—
543C2×C4—342no—
544C2×C4—342no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—681no—
557C2×C4—681no—
558C2×C4—681no—
559C2×C4—681no—
560C2×C4—681no—
561C2×C4—681no—
562C2×C4—681no—
563C2×C4—1364no—
564C2×C4C4×D6812yes—
565C2×C4C4×D6812yes—
566C2×C4#1058756112yes—
567C2×C4#1058756112yes—
568C2×C4C22×C4×D1711yescharacteristic
569C2×C4C2×#6325211yescharacteristic
570C2×C4C2×#6325211yescharacteristic
571C2×C4C2×#6325211yescharacteristic
572C2×C4C2×#6325211yescharacteristic
573C2×C4C2×#6325211yescharacteristic
574C8—22no—
575C8—22no—
576C8—22no—
577C8—22no—
578C22—682no—
579C22—682no—
580C22—682no—
581C22—1361no—
582C22—1361no—
583C22—1361no—
584C22—1361no—
585C22C2×C4×D6811yescharacteristic
586C22C2×#1058756111yescharacteristic
587C22#1176335911yescharacteristic
588C22#1176361411yescharacteristic
589C22#1176362111yescharacteristic
590C22#1176362111yescharacteristic
591C22#1176362611yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—682no—
599C4—682no—
600C4—682no—
601C4—1361no—
602C4—1361no—
603C4—1361no—
604C4—1361no—
605C4C4×#6325211yescharacteristic
606C4C4×#6325211yescharacteristic
607C4#1176334311yescharacteristic
608C4#1176334311yescharacteristic
609C2—1362no—
610C2C4×#1058756111yescharacteristic
611C2#1453761811yescharacteristic
612C2#1453762911yescharacteristic
613C2#1453914011yescharacteristic
614C2#1453915111yescharacteristic
615C2#1453940111yescharacteristic
616C2#1453942311yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1726C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenter#1726D17
hypocenterC17#21654
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #14531532C2semidirect
4. #14529745C2semidirect
7. #14529474C2semidirect
9. #14529460C2semidirect
10. #14528918C2semidirect
11. #14528615C2semidirect
13. C4×#10587487C2semidirect
15. C17×#1726C2semidirect
20. #11763169C4semidirect
96. #10587555C2×C4semidirect
101. C17×#97C2×C4semidirect
123. #10587487C2×C4semidirect
124. #10587487C2×C4semidirect
284. #1726D17semidirect
417. #97C4×D17semidirect
433. C17#21654semidirect

Maximal subgroups

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

subgroupindex
C2×#117631692
#145315322
#145314952
#145297452
#145295952
#145294812
#145294742
#145294672
#145294602
#145289182
#145286152
#145286102
C4×#105874872
C4×#105874922
C17×#17262
#2165417