Finite Group Databasebeta

← #17092390

Subgroups — #17092390

Order 4352.

696 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
1#14532508C211yesmaximal, characteristic
2#14531667C211yesmaximal, characteristic
3#14530353C211yesmaximal, characteristic, complemented
4#14530282C211yesmaximal, characteristic, complemented
5#14530282C211yesmaximal, characteristic, complemented
6#14530123C211yesmaximal, characteristic, complemented
7#14529739C211yesmaximal, characteristic, complemented
8#14529554C211yesmaximal, characteristic, complemented
9#14529363C211yesmaximal, characteristic, complemented
10#14529363C211yesmaximal, characteristic, complemented
11#14528979C211yesmaximal, characteristic
12#14528880C211yesmaximal, characteristic
13#14528817C211yesmaximal, characteristic
14#14528504C211yesmaximal, characteristic
15C17×#1851C211yesmaximal, characteristic
16C2×#10587556C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C2×#10587489C2211yescharacteristic
20C2×#10587488C2211yescharacteristic
21C2×#10587488C2211yescharacteristic
22C2×#10587488C2211yescharacteristic
23#11762751—21no—
24#11762743—21no—
25#11762707C2211yescharacteristic
26#11762707C2211yescharacteristic
27#11762707C2211yescharacteristic
28#11762707C2211yescharacteristic
29#11762697—21no—
30#11762697—21no—
31#11762681—21no—
32#11762675C2211yescharacteristic
33#11762673—21no—
34#11762669C2211yescharacteristic
35#11762669C2211yescharacteristic
36#11762667—21no—
37C4×C4⋊Dic17C2211yescharacteristic
38C4×C4⋊Dic17C2211yescharacteristic
39#11762654—21no—
40#11762572C2211yescharacteristic
41#11762572C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52C22×M16×C17C2211yescharacteristic
53C2×C17×C4⋊C8C2211yescharacteristic
54C2×C17×C4⋊C8C2211yescharacteristic
55C2×C17×C22⋊C8C2211yescharacteristic
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×Dic17—21no—
61C2×M16×C17—22no—
62C2×M16×C17—22no—
63C2×M16×C17—41no—
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C2×C22⋊C4×C17D411yescharacteristic
69C2×C22⋊C4×C17D411yescharacteristic
70C2×C42×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75#10587612—22no—
76#10587612Q814yes—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—22no—
79C2×C4⋊Dic17—41no—
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×C4⋊Dic17C2311yescharacteristic
84C2×C4⋊Dic17C2311yescharacteristic
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×C4⋊Dic17C2311yescharacteristic
88C2×#63225—21no—
89C2×#63225—21no—
90C2×#63225—21no—
91C2×#63225—21no—
92C2×#63225—21no—
93C2×#63225—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17—21no—
96C2×C4×Dic17—21no—
97#10587556—22no—
98#10587556—41no—
99C17×C4⋊C8—22no—
100C17×C4⋊C8—41no—
101C17×C22⋊C8—22no—
102C17×#95D411yescharacteristic
103C17×#95D411yescharacteristic
104#10587502—21no—
105#10587502—21no—
106#10587502—21no—
107#10587502—21no—
108#10587502—21no—
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587489—41no—
115#10587488—22no—
116#10587488—22no—
117#10587488—41no—
118C24×C17C2×D411yescharacteristic
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×Q812yes—
129C22×C4×C17#4112yes—
130C22×C4×C17C2411yescharacteristic
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—42no—
140C22×Dic17—42no—
141C22×Dic17—81no—
142M16×C17—44no—
143C2×C8×C17—21no—
144C2×C8×C17—21no—
145C2×C8×C17—21no—
146C2×C8×C17—21no—
147C2×C8×C17—21no—
148C2×C8×C17—21no—
149C2×C8×C17—21no—
150C2×C8×C17—21no—
151C2×C8×C17—21no—
152C2×C8×C17—21no—
153C2×C8×C17—21no—
154C2×C8×C17#4112yes—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C42×C17—21no—
158C42×C17—21no—
159C42×C17—21no—
160C42×C17—21no—
161C22⋊Dic17—24no—
162C22⋊Dic17—42no—
163C22⋊Dic17—81no—
164C4⋊Dic17—21no—
165C4⋊Dic17—21no—
166C4⋊Dic17—21no—
167C4⋊Dic17—21no—
168C4⋊Dic17—21no—
169C4⋊Dic17—21no—
170C4⋊Dic17—21no—
171C4⋊Dic17—21no—
172C4⋊Dic17—21no—
173C4⋊Dic17—21no—
174C4⋊Dic17—21no—
175C4⋊Dic17—21no—
176C4⋊Dic17—21no—
177C4⋊Dic17—42no—
178C4⋊Dic17C2×Q812yes—
179C4⋊Dic17C2×Q812yes—
180C4⋊Dic17#4112yes—
181#63225—42no—
182#63225—42no—
183#63225—81no—
184#63225—81no—
185#63225—81no—
186#63225—81no—
187C4×Dic17—24no—
188C4×Dic17—42no—
189C4×Dic17—42no—
190#26019—171nomaximal, Sylow
191C23×C17—21no—
192C23×C17—21no—
193C23×C17—21no—
194C23×C17—21no—
195C23×C17—21no—
196C23×C17—21no—
197C23×C17C22⋊Q812yes—
198C23×C17C22×D411yescharacteristic
199C2×C4×C17—21no—
200C2×C4×C17—21no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
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—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17C22⋊Q812yes—
218C2×C4×C17C22×Q811yescharacteristic
219C2×C4×C17C2×#4111yescharacteristic
220C2×C4×C17C2×#4111yescharacteristic
221C2×C4×C17C2×#4111yescharacteristic
222C2×C4×C17H(5,𝔽2)11yescharacteristic
223C2×C4×C172−1+411yescharacteristic
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—41no—
228C2×Dic17—41no—
229C2×Dic17—41no—
230C2×Dic17—41no—
231C2×Dic17—41no—
232C2×Dic17—41no—
233C2×Dic17—41no—
234C2×Dic17—41no—
235C2×Dic17—41no—
236C2×Dic17—41no—
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—41no—
248C2×Dic17—84no—
249C8×C17—22no—
250C8×C17—41no—
251C8×C17—41no—
252C8×C17—41no—
253#2442—171no—
254#2346—171no—
255#2101—171no—
256#2088—171no—
257#2088—171no—
258#2059—171no—
259#1989—171no—
260#1949—171no—
261#1919—171no—
262#1919—171no—
263#1853—171no—
264#1851D1711yescharacteristic
265#1825—171no—
266#1809—171no—
267#1736—171no—
268C22×C17—22no—
269C22×C17—22no—
270C22×C17—22no—
271C22×C17—41no—
272C22×C17—41no—
273C22×C17—41no—
274C22×C17—41no—
275C22×C17C2×C22⋊Q811yescharacteristic
276C22×C17#54611yescharacteristic
277C22×C17#54711yescharacteristic
278C22×C17#57511yescharacteristic
279C22×C17#57511yescharacteristic
280C22×C17#57711yescharacteristic
281C22×C17#57711yescharacteristic
282C4×C17—22no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17—41no—
287C4×C17#53311yescharacteristic
288C4×C17#54411yescharacteristic
289C4×C17#55111yescharacteristic
290C4×C17#55211yescharacteristic
291Dic17—42no—
292Dic17—42no—
293Dic17—42no—
294Dic17—81no—
295Dic17—81no—
296Dic17—81no—
297Dic17—81no—
298Dic17—81no—
299C22×M16C2×D1711yescharacteristic
300C2×#125—171no—
301C2×#117—171no—
302C22×C4⋊C4—171no—
303C2×#107—171no—
304C2×#106—171no—
305C2×#106—171no—
306C2×#106—171no—
307C2×C4⋊C8C2×D1711yescharacteristic
308C2×C4⋊C8C2×D1711yescharacteristic
309C2×C22⋊C8C2×D1711yescharacteristic
310#400—341no—
311#398—341no—
312#389—171no—
313#389—171no—
314#389—171no—
315#389—171no—
316#388—341no—
317#388—341no—
318#385—341no—
319#382—171no—
320#382—341no—
321#380—171no—
322#380—171no—
323#380—341no—
324C4×C4⋊C4—171no—
325C4×C4⋊C4—171no—
326C4×C22⋊C4C2×D1711yescharacteristic
327#376—341no—
328#340—171no—
329#340—171no—
330#340—171no—
331#340—171no—
332#340—171no—
333#340—171no—
334#340—171no—
335#340—171no—
336#340—171no—
337#340—171no—
338#340—171no—
339#340—171no—
340#336C2×D1711yescharacteristic
341#336C2×D1711yescharacteristic
342C2×C17—42no—
343C2×C17#243811yescharacteristic
344C2×C17#308011yescharacteristic
345C2×C17#308411yescharacteristic
346C2×C17#332111yescharacteristic
347C2×C17#332311yescharacteristic
348C2×C17#334811yescharacteristic
349C2×C17#335111yescharacteristic
350C23×C4—341no—
351C23×C4C22×D1711yescharacteristic
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—41no—
355C22×C8C22×D1711yescharacteristic
356C22×C8C22×D1711yescharacteristic
357C22×C8C22×D1711yescharacteristic
358C22×C8C22×D1711yescharacteristic
359#125—342no—
360#125—681no—
361#117—174no—
362#117—342no—
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—342no—
372C2×C4⋊C4—341no—
373C2×C4⋊C4—341no—
374C2×C4⋊C4—341no—
375C2×C4⋊C4—341no—
376C2×C4⋊C4—341no—
377C2×C4⋊C4—341no—
378C2×C4⋊C4—341no—
379C2×C4⋊C4—681no—
380C2×C22⋊C4—341no—
381C2×C22⋊C4—341no—
382C2×C22⋊C4—341no—
383C2×C22⋊C4D6811yescharacteristic
384C2×C22⋊C4D6811yescharacteristic
385C2×C42—341no—
386C2×C42—341no—
387C2×C42—341no—
388C2×C42C22×D1711yescharacteristic
389C2×C42C22×D1711yescharacteristic
390#107—681no—
391#106—342no—
392#106—342no—
393#106—681no—
394C4⋊C8—22no—
395C4⋊C8—41no—
396C22⋊C8—22no—
397#95—341no—
398#95—341no—
399#95—341no—
400#95—341no—
401#95—341no—
402#95—341no—
403#95—341no—
404#95—341no—
405#95—341no—
406#95—341no—
407#95D6811yescharacteristic
408#95D6811yescharacteristic
409C17#2601911yescharacteristic, complemented, Sylow
410C24C2×D6811yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—341no—
416C22×C4—341no—
417C22×C4—341no—
418C22×C4—341no—
419C22×C4—341no—
420C22×C4—341no—
421C22×C4—341no—
422C22×C4—341no—
423C22×C4—682no—
424C22×C4—682no—
425C22×C4—1361no—
426C22×C4C2×D6811yescharacteristic
427C22×C4C2×D6811yescharacteristic
428C22×C4C2×D6811yescharacteristic
429C22×C4C2×D6811yescharacteristic
430C22×C4C2×D6811yescharacteristic
431C22×C4#6325412yes—
432C22×C4Q8×D1712yes—
433C22×C4C23×D1711yescharacteristic
434M16—44no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8#6325412yes—
447C4⋊C4—172no—
448C4⋊C4—172no—
449C4⋊C4—172no—
450C4⋊C4—341no—
451C4⋊C4—341no—
452C4⋊C4—341no—
453C4⋊C4—341no—
454C4⋊C4—341no—
455C4⋊C4—341no—
456C4⋊C4—341no—
457C4⋊C4—341no—
458C4⋊C4—341no—
459C4⋊C4—341no—
460C4⋊C4—341no—
461C4⋊C4—341no—
462C4⋊C4—341no—
463C4⋊C4—682no—
464C4⋊C4—682no—
465C4⋊C4—682no—
466C4⋊C4—1361no—
467C4⋊C4—1361no—
468C4⋊C4—1361no—
469C4⋊C4—1361no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—344no—
473C22⋊C4—682no—
474C22⋊C4—1361no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—344no—
480C42—682no—
481C42—682no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#1058758312yes—
489C23C22×D6811yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—342no—
509C2×C4—342no—
510C2×C4—342no—
511C2×C4—681no—
512C2×C4—681no—
513C2×C4—681no—
514C2×C4—681no—
515C2×C4—681no—
516C2×C4—681no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—681no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—1364no—
533C2×C4#1058758312yes—
534C2×C4C2×#6325411yescharacteristic
535C2×C4C2×#6325411yescharacteristic
536C2×C4#1058769111yescharacteristic
537C2×C4C2×Q8×D1711yescharacteristic
538C2×C4#41×D1711yescharacteristic
539C2×C4#1058769711yescharacteristic
540C8—22no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#1058758311yescharacteristic
552C22#1176345411yescharacteristic
553C22#1176346311yescharacteristic
554C22#1176360911yescharacteristic
555C22#1176360911yescharacteristic
556C22#1176362111yescharacteristic
557C22#1176362111yescharacteristic
558C4—22no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—682no—
564C4—682no—
565C4—682no—
566C4—1361no—
567C4—1361no—
568C4—1361no—
569C4—1361no—
570C4—1361no—
571C4#1176336111yescharacteristic
572C4#1176343811yescharacteristic
573C4#1176349011yescharacteristic
574C4#1176349611yescharacteristic
575C2—42no—
576C2#1453245811yescharacteristic
577C2#1453860711yescharacteristic
578C2#1453864811yescharacteristic
579C2#1454097211yescharacteristic
580C2#1454100211yescharacteristic
581C2#1454130111yescharacteristic
582C2#1454134611yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#1851C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
hypercenter#1851D17
hypocenterC17#26019
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
3. #14530353C2semidirect
4. #14530282C2semidirect
5. #14530282C2semidirect
6. #14530123C2semidirect
7. #14529739C2semidirect
8. #14529554C2semidirect
9. #14529363C2semidirect
10. #14529363C2semidirect
409. C17#26019semidirect

Maximal subgroups

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

subgroupindex
#145325082
#145316672
#145303532
#145302822
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C17×#18512
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