Finite Group Databasebeta

← #17046569

Subgroups — #17046569

Order 4352.

732 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
1C2×#11763110C211yesmaximal, characteristic
2#14531523C211yesmaximal, characteristic, complemented
3#14531422C211yesmaximal, characteristic
4#14529741C211yesmaximal, characteristic, complemented
5#14529525C211yesmaximal, characteristic, complemented
6#14529515C211yesmaximal, characteristic, complemented
7#14529479C211yesmaximal, characteristic
8#14529465C211yesmaximal, characteristic
9#14529403C211yesmaximal, characteristic
10#14529403C211yesmaximal, characteristic
11#14529375C211yesmaximal, characteristic, complemented
12#14529361C211yesmaximal, characteristic, complemented
13#14528781C211yesmaximal, characteristic
14#14528643C211yesmaximal, characteristic, complemented
15C17×#1947C211yesmaximal, characteristic, complemented
16C2×#10587556C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18#11763110C418yescomplemented
19C2×#10587489C2211yescharacteristic
20C2×#10587488C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587492C2211yescharacteristic
23C2×#10587492C2211yescharacteristic
24C2×#10587480C2211yescharacteristic
25C2×#10587480C2211yescharacteristic
26C2×#10587486C2211yescharacteristic
27C2×C8×Dic17C2211yescharacteristic
28#11762710C2211yescharacteristic
29#11762710C2211yescharacteristic
30#11762705C2211yescharacteristic
31#11762705C2211yescharacteristic
32#11762705C2211yescharacteristic
33#11762705C2211yescharacteristic
34#11762704—21no—
35#11762704—21no—
36#11762700—21no—
37#11762700—21no—
38#11762690—21no—
39#11762690—21no—
40#11762671—21no—
41#11762668—21no—
42C4⋊C4×Dic17C2211yescharacteristic
43C4⋊C4×Dic17C2211yescharacteristic
44#11762655C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53C2×C17×#107C2211yescharacteristic
54C2×C17×#107C2211yescharacteristic
55C2×C17×C4⋊C8C2211yescharacteristic
56C17×#384C2211yescharacteristic
57C4×C4⋊C4×C17C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C22×D68C2311yescharacteristic
61C22×C4×D17—21no—
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17C2311yescharacteristic
67C2×C4⋊C4×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2311yescharacteristic
69C2×C4⋊C4×C17C2311yescharacteristic
70C2×C42×C17—21no—
71C2×C42×C17C2311yescharacteristic
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227—21no—
75C2×#63227—21no—
76C2×#63227—21no—
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×#63225—21no—
81C2×#63225—21no—
82C2×#63225—21no—
83C2×#63225—21no—
84C2×#63225—21no—
85C2×#63225—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17—21no—
88C2×C4×Dic17C2311yescharacteristic
89C2×C4×Dic17C2311yescharacteristic
90C22×#3622C2311yescharacteristic
91C22×#3622C2311yescharacteristic
92C4×D68—22no—
93C4×D68C2×C414yes—
94#10587556—22no—
95#10587556C2×C414yes—
96C17×#107—41no—
97C17×#107—41no—
98C17×C4⋊C8C2×C414yes—
99C17×#95—21no—
100#10587502—21no—
101#10587502—21no—
102#10587502—21no—
103#10587502—21no—
104#10587502—21no—
105#10587502—21no—
106#10587502D411yescharacteristic
107#10587502D411yescharacteristic
108#10587502D411yescharacteristic
109#10587502D411yescharacteristic
110#10587492C2×C414yes—
111#10587492C2×C414yes—
112#10587489C2×C414yes—
113#10587488C2×C414yes—
114#10587486—41no—
115C8×Dic17—41no—
116#10587480—41no—
117#10587480—41no—
118C4⋊#3622—22no—
119C23×D17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2411yescharacteristic
127C22×Dic17—21no—
128C22×Dic17—21no—
129C22×Dic17—21no—
130C22×Dic17C2×D411yescharacteristic
131C22×Dic17C2×D411yescharacteristic
132C22×Dic17C2×D411yescharacteristic
133C22×Dic17C2×D411yescharacteristic
134C2×D68—21no—
135C2×D68—21no—
136C2×D68—21no—
137C2×D68—21no—
138C2×D68—21no—
139C2×D68C22×C412yes—
140C2×C4×D17—24no—
141C2×C4×D17—81no—
142C2×C4×D17—81no—
143C2×C8×C17—21no—
144C2×C8×C17—21no—
145C2×C8×C17—21no—
146C2×C8×C17—21no—
147C2×C8×C17C22×C412yes—
148C2×C8×C17C22×C412yes—
149C4⋊C4×C17—21no—
150C4⋊C4×C17—21no—
151C4⋊C4×C17—21no—
152C4⋊C4×C17—21no—
153C4⋊C4×C17—21no—
154C4⋊C4×C17—21no—
155C4⋊C4×C17—21no—
156C4⋊C4×C17—21no—
157C4⋊C4×C17—81no—
158C4⋊C4×C17—81no—
159C42×C17—81no—
160C42×C17C22×C412yes—
161C42×C17#4112yes—
162#63227—24no—
163#63227—81no—
164#63227—81no—
165#63227—81no—
166#63227—81no—
167C4⋊Dic17—21no—
168C4⋊Dic17—21no—
169C4⋊Dic17—21no—
170C4⋊Dic17C22×C412yes—
171C4⋊Dic17C22×C412yes—
172C4⋊Dic17C22×C412yes—
173#63225—24no—
174#63225—24no—
175#63225—81no—
176#63225—81no—
177#63225—81no—
178#63225—81no—
179C4×Dic17—21no—
180C4×Dic17—21no—
181C4×Dic17—21no—
182C4×Dic17—21no—
183C4×Dic17—81no—
184C4×Dic17—81no—
185C2×#3622—21no—
186C2×#3622—21no—
187C2×#3622—21no—
188C2×#3622—21no—
189C2×#3622—21no—
190C2×#3622—21no—
191#22126—171nomaximal, Sylow
192C23×C17C22×D411yescharacteristic
193C22×D17—22no—
194C22×D17—41no—
195C22×D17—41no—
196C22×D17—41no—
197C22×D17—41no—
198C22×D17—41no—
199C22×D17—41no—
200C2×C4×C17—21no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17—21no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—41no—
208C2×C4×C17—41no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17C4×D412yes—
217C2×C4×C17C4×D412yes—
218C2×C4×C17C23×C411yescharacteristic
219C2×C4×C17C2×#4111yescharacteristic
220C2×C4×C17H(5,𝔽2)11yescharacteristic
221C2×C4×C172−1+411yescharacteristic
222C2×C4×C172−1+411yescharacteristic
223C2×C4×C172−1+411yescharacteristic
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—21no—
230C2×Dic17—21no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17—41no—
244C2×Dic17—41no—
245D68—22no—
246D68—22no—
247D68—41no—
248D68—41no—
249C4×D17—84no—
250C8×C17—22no—
251C8×C17—22no—
252#3622—41no—
253#3622—41no—
254C2×#478—171no—
255#2330—171no—
256#2319—171no—
257#1989—171no—
258#1947D1711yescharacteristic, complemented
259#1944—171no—
260#1942—171no—
261#1936—171no—
262#1934—171no—
263#1925—171no—
264#1925—171no—
265#1921—171no—
266#1919—171no—
267#1802—171no—
268#1768—171no—
269C22×C17C2×C4×D411yescharacteristic
270C22×C17#53611yescharacteristic
271C22×C17#53711yescharacteristic
272C22×C17#57611yescharacteristic
273C22×C17#57611yescharacteristic
274C22×C17#57711yescharacteristic
275C22×C17#57811yescharacteristic
276C2×D17—42no—
277C2×D17—42no—
278C2×D17—42no—
279C2×D17—81no—
280C2×D17—81no—
281C2×D17—81no—
282C2×D17—81no—
283C4×C17—22no—
284C4×C17—22no—
285C4×C17—81no—
286C4×C17—81no—
287C4×C17—81no—
288C4×C17—81no—
289C4×C17#51911yescharacteristic
290C4×C17#52011yescharacteristic
291C4×C17#54111yescharacteristic
292C4×C17#54211yescharacteristic
293Dic17—42no—
294Dic17—42no—
295Dic17—42no—
296Dic17—41no—
297Dic17—41no—
298Dic17—41no—
299Dic17—41no—
300C2×#125—171no—
301C2×C4×D4—171no—
302#478—178no—
303C2×#107—171no—
304C2×#107C2×D1711yescharacteristic
305C2×#107C2×D1711yescharacteristic
306C2×#106—171no—
307C2×C4⋊C8—171no—
308C2×C4⋊C8C2×D1711yescharacteristic
309C2×#102—171no—
310C2×#102—171no—
311C2×#102—171no—
312C2×#102—171no—
313C2×#97—171no—
314C2×C4×C8—171no—
315#390—171no—
316#390—171no—
317#389—171no—
318#389—171no—
319#389—171no—
320#389—171no—
321#389—341no—
322#389—341no—
323#388—341no—
324#388—341no—
325#387—341no—
326#387—341no—
327#384C2×D1711yescharacteristic
328#381—341no—
329#380—341no—
330C4×C4⋊C4—171no—
331C4×C4⋊C4—171no—
332C4×C4⋊C4C2×D1711yescharacteristic
333#376—171no—
334#340—171no—
335#340—171no—
336#340—171no—
337#340—171no—
338#340—171no—
339#340—171no—
340#340C2×D1711yescharacteristic
341#340C2×D1711yescharacteristic
342#336—171no—
343#336—171no—
344C2×C17#232311yescharacteristic
345C2×C17#294611yescharacteristic
346C2×C17#295111yescharacteristic
347C2×C17#324111yescharacteristic
348C2×C17#324311yescharacteristic
349C2×C17#325811yescharacteristic
350C2×C17#325911yescharacteristic
351D17—82no—
352C22×D4—171no—
353C23×C4—341no—
354C22×C8—171no—
355C22×C8—171no—
356C22×C8C22×D1711yescharacteristic
357C22×C8C22×D1711yescharacteristic
358#125—174no—
359#125—342no—
360C4×D4—174no—
361C4×D4—342no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—171no—
365C2×C4⋊C4—171no—
366C2×C4⋊C4—171no—
367C2×C4⋊C4—341no—
368C2×C4⋊C4—341no—
369C2×C4⋊C4—341no—
370C2×C4⋊C4—341no—
371C2×C4⋊C4—341no—
372C2×C4⋊C4—341no—
373C2×C4⋊C4C22×D1711yescharacteristic
374C2×C4⋊C4C22×D1711yescharacteristic
375C2×C4⋊C4C22×D1711yescharacteristic
376C2×C4⋊C4C22×D1711yescharacteristic
377C2×C22⋊C4—341no—
378C2×C22⋊C4—341no—
379C2×C22⋊C4—341no—
380C2×C22⋊C4—341no—
381C2×C22⋊C4—341no—
382C2×C42—21no—
383C2×C42—171no—
384C2×C42—171no—
385C2×C42—341no—
386C2×C42—341no—
387C2×C42C22×D1711yescharacteristic
388#107—41no—
389#107—41no—
390#107—174no—
391#106—174no—
392C4⋊C8—342no—
393C4⋊C8C4×D1714yes—
394#102—174no—
395#102—174no—
396#102—681no—
397#102—681no—
398#97—681no—
399C4×C8—681no—
400#95—21no—
401#95—171no—
402#95—171no—
403#95—171no—
404#95—171no—
405#95—341no—
406#95—341no—
407#95—341no—
408#95—341no—
409#95—341no—
410#95—341no—
411C17#2212611yescharacteristic, complemented, Sylow
412C24—341no—
413C2×D4—172no—
414C2×D4—341no—
415C2×D4—341no—
416C2×D4—341no—
417C2×D4—341no—
418C2×D4—341no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—171no—
424C22×C4—171no—
425C22×C4—171no—
426C22×C4—171no—
427C22×C4—341no—
428C22×C4—341no—
429C22×C4—341no—
430C22×C4—344no—
431C22×C4—1361no—
432C22×C4—1361no—
433C22×C4D4×D1711yescharacteristic
434C22×C4D4×D1711yescharacteristic
435C22×C4C23×D1711yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—341no—
441C2×C8—341no—
442C2×C8—341no—
443C2×C8—341no—
444C2×C8—341no—
445C2×C8—341no—
446C2×C8C2×C4×D1712yes—
447C2×C8C2×C4×D1712yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—172no—
459C4⋊C4—172no—
460C4⋊C4—172no—
461C4⋊C4—341no—
462C4⋊C4—341no—
463C4⋊C4—341no—
464C4⋊C4—344no—
465C4⋊C4—344no—
466C4⋊C4—1361no—
467C4⋊C4—1361no—
468C4⋊C4—1361no—
469C4⋊C4—1361no—
470C22⋊C4—344no—
471C22⋊C4—1361no—
472C22⋊C4—1361no—
473C22⋊C4—1361no—
474C22⋊C4—1361no—
475C42—81no—
476C42—341no—
477C42—341no—
478C42—341no—
479C42—341no—
480C42—1361no—
481C42—1361no—
482C42C2×C4×D1712yes—
483C42#6325612yes—
484C23—342no—
485C23—681no—
486C23—681no—
487C23—681no—
488C23—681no—
489C23—681no—
490C23—681no—
491C23C2×D4×D1711yescharacteristic
492D4—342no—
493D4—342no—
494D4—681no—
495D4—681no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—342no—
513C2×C4—342no—
514C2×C4—342no—
515C2×C4—341no—
516C2×C4—341no—
517C2×C4—341no—
518C2×C4—341no—
519C2×C4—341no—
520C2×C4—341no—
521C2×C4—341no—
522C2×C4—341no—
523C2×C4—341no—
524C2×C4—341no—
525C2×C4—341no—
526C2×C4—341no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—1364no—
534C2×C4#1058757912yes—
535C2×C4#1058757912yes—
536C2×C4C22×C4×D1711yescharacteristic
537C2×C4#1058769111yescharacteristic
538C2×C4C2×#6325611yescharacteristic
539C2×C4#1058769411yescharacteristic
540C2×C4#1058769711yescharacteristic
541C2×C4#1058769711yescharacteristic
542C8—22no—
543C8—22no—
544C8—681no—
545C8—681no—
546C22—682no—
547C22—682no—
548C22—682no—
549C22—1361no—
550C22—1361no—
551C22—1361no—
552C22—1361no—
553C22C2×#1058757911yescharacteristic
554C22#1176338211yescharacteristic
555C22#1176338811yescharacteristic
556C22#1176361011yescharacteristic
557C22#1176361311yescharacteristic
558C22#1176361811yescharacteristic
559C22#1176362211yescharacteristic
560C4—22no—
561C4—22no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—681no—
567C4—681no—
568C4—682no—
569C4—682no—
570C4—681no—
571C4—682no—
572C4—681no—
573C4#1176328511yescharacteristic
574C4#1176328811yescharacteristic
575C4#1176342211yescharacteristic
576C4#1176343311yescharacteristic
577C2—1362no—
578C2#1453146411yescharacteristic
579C2#1453761411yescharacteristic
580C2#1453765811yescharacteristic
581C2#1454004411yescharacteristic
582C2#1454007211yescharacteristic
583C2#1454020811yescharacteristic
584C2#1454022111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1947C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenter#1947D17
hypocenterC17#22126
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #14531523C2semidirect
4. #14529741C2semidirect
5. #14529525C2semidirect
6. #14529515C2semidirect
11. #14529375C2semidirect
12. #14529361C2semidirect
14. #14528643C2semidirect
15. C17×#1947C2semidirect
18. #11763110C4semidirect
258. #1947D17semidirect
411. C17#22126semidirect

Maximal subgroups

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

subgroupindex
C2×#117631102
#145315232
#145314222
#145297412
#145295252
#145295152
#145294792
#145294652
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C17×#19472
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