Finite Group Databasebeta

← #17046579

Subgroups — #17046579

Order 4352.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763087C211yesmaximal, characteristic
2#14531531C211yesmaximal, characteristic, complemented
3#14531421C211yesmaximal, characteristic
4#14529730C211yesmaximal, characteristic, complemented
5#14529555C211yesmaximal, characteristic, complemented
6#14529519C211yesmaximal, characteristic, complemented
7#14529517C211yesmaximal, characteristic, complemented
8#14529484C211yesmaximal, characteristic
9#14529414C211yesmaximal, characteristic
10#14529406C211yesmaximal, characteristic
11#14529374C211yesmaximal, characteristic, complemented
12#14529354C211yesmaximal, characteristic, complemented
13#14528792C211yesmaximal, characteristic
14#14528642C211yesmaximal, characteristic, complemented
15C17×#1934C211yesmaximal, characteristic
16C2×#10587574C2211yescharacteristic
17C2×D4×Dic17C2211yescharacteristic
18#11763087C418yescomplemented
19C2×#10587489C2211yescharacteristic
20C2×#10587489C2211yescharacteristic
21C2×#10587478C2211yescharacteristic
22C2×#10587479C2211yescharacteristic
23C2×#10587485C2211yescharacteristic
24C2×#10587485C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587474C2211yescharacteristic
28#11762714—21no—
29#11762713—21no—
30#11762712C2211yescharacteristic
31#11762707C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762705C2211yescharacteristic
34#11762703—21no—
35#11762697—21no—
36#11762691—21no—
37#11762690—21no—
38#11762674C2211yescharacteristic
39#11762670—21no—
40#11762667—21no—
41C4⋊C4×Dic17C2211yescharacteristic
42C4⋊C4×Dic17C2211yescharacteristic
43C4⋊C4×Dic17C2211yescharacteristic
44#11762655C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53C2×C17×#102C2211yescharacteristic
54C2×C17×#102C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C17×#390C2211yescharacteristic
57C17×#389C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C22×D4×C17C2311yescharacteristic
61C23×Dic17—21no—
62C22×Dic34—21no—
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17C2311yescharacteristic
67C2×C4⋊C4×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2311yescharacteristic
69C2×C22⋊C4×C17—21no—
70C2×C22⋊C4×C17—21no—
71C2×C42×C17C2311yescharacteristic
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75D4×Dic17—22no—
76D4×Dic17C2×C414yes—
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×#63225—21no—
82C2×#63225—21no—
83C2×#63225—21no—
84C2×#63225—21no—
85C2×C4×Dic17—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17—21no—
88C2×C4×Dic17C2311yescharacteristic
89C2×C4×Dic17C2311yescharacteristic
90C22×#3622C2311yescharacteristic
91C22×#3622C2311yescharacteristic
92#10587574—22no—
93#10587574C2×C414yes—
94C17×#102—41no—
95C17×#102C2×C414yes—
96C4×C8×C17—41no—
97C17×#95—21no—
98#10587503—41no—
99#10587503C2×C414yes—
100#10587502—21no—
101#10587502—21no—
102#10587502—21no—
103#10587502—21no—
104#10587502—21no—
105#10587502—21no—
106#10587502—21no—
107#10587502—21no—
108#10587502D411yescharacteristic
109#10587502D411yescharacteristic
110#10587502D411yescharacteristic
111#10587502D411yescharacteristic
112#10587489—41no—
113#10587489C2×C414yes—
114#10587485—22no—
115#10587485C2×C414yes—
116#10587479—41no—
117#10587478C2×C414yes—
118#10587474—41no—
119C24×C17—21no—
120C2×D4×C17—21no—
121C2×D4×C17—21no—
122C2×D4×C17—21no—
123C2×D4×C17—21no—
124C2×D4×C17—21no—
125C2×D4×C17C22×C412yes—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2411yescharacteristic
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—24no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—81no—
138C22×Dic17—81no—
139C22×Dic17C2×D411yescharacteristic
140C22×Dic17C2×D411yescharacteristic
141C22×Dic17C2×D411yescharacteristic
142C22×Dic17C2×D411yescharacteristic
143C2×Dic34—24no—
144C2×Dic34—81no—
145C2×Dic34—81no—
146C2×C8×C17—21no—
147C2×C8×C17—21no—
148C2×C8×C17—21no—
149C2×C8×C17—21no—
150C2×C8×C17—21no—
151C2×C8×C17C22×C412yes—
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×C17C22×C412yes—
159C22⋊C4×C17—81no—
160C22⋊C4×C17—81no—
161C42×C17—21no—
162C42×C17—21no—
163C22⋊Dic17—24no—
164C22⋊Dic17—81no—
165C22⋊Dic17—81no—
166C4⋊Dic17—21no—
167C4⋊Dic17—21no—
168C4⋊Dic17—21no—
169C4⋊Dic17—21no—
170C4⋊Dic17—21no—
171C4⋊Dic17—21no—
172C4⋊Dic17C22×C412yes—
173C4⋊Dic17C22×C412yes—
174#63225—24no—
175#63225—81no—
176#63225—81no—
177#63225—81no—
178C4×Dic17—21no—
179C4×Dic17—21no—
180C4×Dic17—81no—
181C4×Dic17—81no—
182C4×Dic17—81no—
183C4×Dic17C22×C412yes—
184C4×Dic17#4112yes—
185C2×#3622—21no—
186C2×#3622—21no—
187C2×#3622—21no—
188C2×#3622—21no—
189C2×#3622—21no—
190C2×#3622C22×C412yes—
191#22127—171nomaximal, Sylow
192C23×C17—22no—
193C23×C17—41no—
194C23×C17—41no—
195C23×C17—41no—
196C23×C17—41no—
197C23×C17—41no—
198C23×C17—41no—
199C23×C17C22×D411yescharacteristic
200D4×C17—22no—
201D4×C17—22no—
202D4×C17—41no—
203D4×C17—41no—
204C2×C4×C17—22no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17C23×C411yescharacteristic
220C2×C4×C17C2×#4111yescharacteristic
221C2×C4×C17H(5,𝔽2)11yescharacteristic
222C2×C4×C172−1+411yescharacteristic
223C2×C4×C172−1+411yescharacteristic
224C2×C4×C172−1+411yescharacteristic
225C2×Dic17—21no—
226C2×Dic17—21no—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—22no—
230C2×Dic17—22no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—41no—
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—84no—
248C2×Dic17C4×D412yes—
249C2×Dic17C4×D412yes—
250Dic34—84no—
251C8×C17—22no—
252C8×C17—41no—
253#3622—22no—
254#3622—41no—
255C2×#474—171no—
256#2331—171no—
257#2319—171no—
258#1987—171no—
259#1949—171no—
260#1943—171no—
261#1942—171no—
262#1936—171no—
263#1934D1711yescharacteristic
264#1926—171no—
265#1925—171no—
266#1921—171no—
267#1918—171no—
268#1804—171no—
269#1768—171no—
270C22×C17—42no—
271C22×C17—42no—
272C22×C17—42no—
273C22×C17—81no—
274C22×C17—81no—
275C22×C17—81no—
276C22×C17—81no—
277C22×C17C2×C4×D411yescharacteristic
278C22×C17#53611yescharacteristic
279C22×C17#53711yescharacteristic
280C22×C17#57611yescharacteristic
281C22×C17#57611yescharacteristic
282C22×C17#57711yescharacteristic
283C22×C17#57811yescharacteristic
284C4×C17—42no—
285C4×C17—41no—
286C4×C17—41no—
287C4×C17—81no—
288C4×C17—81no—
289C4×C17#51911yescharacteristic
290C4×C17#52011yescharacteristic
291C4×C17#54111yescharacteristic
292C4×C17#54211yescharacteristic
293Dic17—22no—
294Dic17—22no—
295Dic17—42no—
296Dic17—42no—
297Dic17—41no—
298Dic17—41no—
299Dic17—81no—
300Dic17—81no—
301C2×C4⋊Q8—171no—
302C2×C4×D4—171no—
303#474—178no—
304C2×#107—171no—
305C2×#107—171no—
306C2×#107—171no—
307C2×#106—171no—
308C2×C4⋊C8—171no—
309C2×C4⋊C8—171no—
310C2×#102—171no—
311C2×#102—171no—
312C2×#102C2×D1711yescharacteristic
313C2×#102C2×D1711yescharacteristic
314C2×#97—171no—
315C2×C4×C8C2×D1711yescharacteristic
316#391—341no—
317#391—341no—
318#390—171no—
319#390C2×D1711yescharacteristic
320#389—171no—
321#389—171no—
322#389—171no—
323#389C2×D1711yescharacteristic
324#388—341no—
325#388—341no—
326#387—341no—
327#387—341no—
328#382—171no—
329#381—341no—
330#380—341no—
331C4×C4⋊C4—171no—
332C4×C4⋊C4—171no—
333C4×C4⋊C4—171no—
334#376—171no—
335#340—171no—
336#340—171no—
337#340—171no—
338#340—171no—
339#340—171no—
340#340—171no—
341#340C2×D1711yescharacteristic
342#340C2×D1711yescharacteristic
343#336—171no—
344#336—171no—
345C2×C17—82no—
346C2×C17#232311yescharacteristic
347C2×C17#294711yescharacteristic
348C2×C17#294811yescharacteristic
349C2×C17#324111yescharacteristic
350C2×C17#324311yescharacteristic
351C2×C17#325711yescharacteristic
352C2×C17#326211yescharacteristic
353C22×Q8—341no—
354C22×D4C22×D1711yescharacteristic
355C23×C4—341no—
356C22×C8—171no—
357C22×C8—171no—
358C22×C8C22×D1711yescharacteristic
359C22×C8C22×D1711yescharacteristic
360C4⋊Q8—174no—
361C4⋊Q8—342no—
362C4×D4—174no—
363C4×D4—342no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—171no—
366C2×C4⋊C4—171no—
367C2×C4⋊C4—171no—
368C2×C4⋊C4—171no—
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×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—341no—
379C2×C22⋊C4—341no—
380C2×C22⋊C4—341no—
381C2×C42—171no—
382C2×C42—171no—
383C2×C42—341no—
384C2×C42—341no—
385C2×C42—341no—
386C2×C42C22×D1711yescharacteristic
387#107—174no—
388#107—174no—
389#107—681no—
390#106—681no—
391C4⋊C8—174no—
392C4⋊C8—342no—
393#102—41no—
394#102—174no—
395#102—681no—
396#102C4×D1714yes—
397#97—681no—
398C4×C8—41no—
399#95—21no—
400#95—171no—
401#95—171no—
402#95—171no—
403#95—171no—
404#95—341no—
405#95—341no—
406#95—341no—
407#95—341no—
408#95—341no—
409#95—341no—
410#95—341no—
411#95—341no—
412C17#2212711yescharacteristic, complemented, Sylow
413C24—21no—
414C2×Q8—344no—
415C2×Q8—1361no—
416C2×Q8—1361no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×C4×D1712yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—171no—
427C22×C4—171no—
428C22×C4—171no—
429C22×C4—171no—
430C22×C4—344no—
431C22×C4—341no—
432C22×C4—341no—
433C22×C4—341no—
434C22×C4—341no—
435C22×C4—1361no—
436C22×C4—1361no—
437C22×C4D4×D1711yescharacteristic
438C22×C4D4×D1711yescharacteristic
439C22×C4C23×D1711yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—172no—
446C2×C8—341no—
447C2×C8—341no—
448C2×C8—341no—
449C2×C8—341no—
450C2×C8—341no—
451C2×C8C2×C4×D1712yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—81no—
458C4⋊C4—172no—
459C4⋊C4—172no—
460C4⋊C4—344no—
461C4⋊C4—341no—
462C4⋊C4—341no—
463C4⋊C4—341no—
464C4⋊C4—341no—
465C4⋊C4—341no—
466C4⋊C4—341no—
467C4⋊C4—1361no—
468C4⋊C4—1361no—
469C4⋊C4—1361no—
470C4⋊C4C2×C4×D1712yes—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—344no—
474C22⋊C4—1361no—
475C22⋊C4—1361no—
476C42—21no—
477C42—21no—
478C42—172no—
479C42—172no—
480C42—341no—
481C42—341no—
482C42—1361no—
483C42—1361no—
484C42—1361no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C2×D4×D1711yescharacteristic
493Q8—1364no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—172no—
514C2×C4—172no—
515C2×C4—341no—
516C2×C4—341no—
517C2×C4—341no—
518C2×C4—341no—
519C2×C4—342no—
520C2×C4—342no—
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—681no—
534C2×C4—681no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—1364no—
538C2×C4C22×C4×D1711yescharacteristic
539C2×C4#1058769111yescharacteristic
540C2×C4#41×D1711yescharacteristic
541C2×C4#1058769711yescharacteristic
542C2×C4#1058769711yescharacteristic
543C2×C4#1058769711yescharacteristic
544C8—22no—
545C8—41no—
546C8—342no—
547C8—681no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C4×D4×D1711yescharacteristic
556C22#1176337911yescharacteristic
557C22#1176338611yescharacteristic
558C22#1176361011yescharacteristic
559C22#1176361111yescharacteristic
560C22#1176361511yescharacteristic
561C22#1176362311yescharacteristic
562C4—42no—
563C4—41no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—342no—
568C4—342no—
569C4—681no—
570C4—682no—
571C4—682no—
572C4—681no—
573C4—1361no—
574C4—1361no—
575C4#1176328611yescharacteristic
576C4#1176328811yescharacteristic
577C4#1176341611yescharacteristic
578C4#1176342711yescharacteristic
579C2—82no—
580C2#1453145911yescharacteristic
581C2#1453762011yescharacteristic
582C2#1453763111yescharacteristic
583C2#1454003011yescharacteristic
584C2#1454006011yescharacteristic
585C2#1454019811yescharacteristic
586C2#1454023911yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1934C2
socleC23×C17C22×D4
prime radicalC22×D4×C17C23
cosocleC22×C4×C17C24
hypercenter#1934D17
hypocenterC17#22127
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #14531531C2semidirect
4. #14529730C2semidirect
5. #14529555C2semidirect
6. #14529519C2semidirect
7. #14529517C2semidirect
11. #14529374C2semidirect
12. #14529354C2semidirect
14. #14528642C2semidirect
18. #11763087C4semidirect
412. C17#22127semidirect

Maximal subgroups

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

subgroupindex
C2×#117630872
#145315312
#145314212
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C17×#19342
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