Finite Group Databasebeta

← #17093401

Subgroups — #17093401

Order 4352.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534018C211yesmaximal, characteristic, complemented
2#14531755C211yesmaximal, characteristic
3#14530316C211yesmaximal, characteristic
4#14530304C211yesmaximal, characteristic
5#14530171C211yesmaximal, characteristic
6#14530171C211yesmaximal, characteristic
7#14529554C211yesmaximal, characteristic, complemented
8#14529554C211yesmaximal, characteristic, complemented
9#14529543C211yesmaximal, characteristic, complemented
10#14529370C211yesmaximal, characteristic, complemented
11#14529363C211yesmaximal, characteristic, complemented
12#14528948C211yesmaximal, characteristic, complemented
13#14528795C211yesmaximal, characteristic
14C4×#10587492C211yesmaximal, characteristic
15C17×#1939C211yesmaximal, characteristic, complemented
16C2×C4×D68C2211yescharacteristic
17C2×#10587489C2211yescharacteristic
18C2×#10587489C2211yescharacteristic
19C2×#10587489C2211yescharacteristic
20C2×#10587488C2211yescharacteristic
21C2×#10587488C2211yescharacteristic
22C2×#10587488C2211yescharacteristic
23C2×#10587492C2211yescharacteristic
24C2×#10587492C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587492C2211yescharacteristic
27#11762748—21no—
28#11762742—21no—
29#11762711C2211yescharacteristic
30#11762711C2211yescharacteristic
31#11762707C2211yescharacteristic
32#11762707C2211yescharacteristic
33#11762699—21no—
34#11762699—21no—
35#11762696—21no—
36#11762692—21no—
37#11762679C2211yescharacteristic
38#11762675C2211yescharacteristic
39#11762675C2211yescharacteristic
40#11762675C2211yescharacteristic
41#11762671—21no—
42C4×C4⋊Dic17C2211yescharacteristic
43C4×C4⋊Dic17C2211yescharacteristic
44C4×C4⋊Dic17C2211yescharacteristic
45#11762656—21no—
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52C2×C17×C4⋊C8C2211yescharacteristic
53C2×C17×C4⋊C8C2211yescharacteristic
54C2×C17×C4⋊C8C2211yescharacteristic
55C2×C4×C8×C17C2211yescharacteristic
56C4×C4⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C22×D68C2311yescharacteristic
60C22×C4×D17—21no—
61C22×C8×C17C2311yescharacteristic
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C2×C4⋊C4×C17D411yescharacteristic
66C2×C4⋊C4×C17D411yescharacteristic
67C2×C42×C17C2311yescharacteristic
68C2×C42×C17C2311yescharacteristic
69C2×C42×C17C2311yescharacteristic
70C2×#63227—21no—
71C2×#63227—21no—
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227—21no—
75C2×C4⋊Dic17—21no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2311yescharacteristic
79C2×C4⋊Dic17C2311yescharacteristic
80C2×C4⋊Dic17C2311yescharacteristic
81C2×C4⋊Dic17C2311yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×C4⋊Dic17C2311yescharacteristic
84C2×#63225—21no—
85C2×#63225—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17—21no—
88C2×C4×Dic17—21no—
89C4×D68—22no—
90C4×D68Q814yes—
91C17×C4⋊C8—22no—
92C17×C4⋊C8—22no—
93C17×C4⋊C8—22no—
94C4×C8×C17—22no—
95C17×#95D411yescharacteristic
96C17×#95D411yescharacteristic
97#10587502—21no—
98#10587502—21no—
99#10587502—21no—
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#10587492—22no—
109#10587492—22no—
110#10587492—41no—
111#10587492—41no—
112#10587489—41no—
113#10587489—41no—
114#10587489—41no—
115#10587488—22no—
116#10587488—22no—
117#10587488—41no—
118C23×D17—21no—
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2411yescharacteristic
126C22×Dic17—21no—
127C22×Dic17—21no—
128C22×Dic17—21no—
129C22×Dic17—21no—
130C22×Dic17—21no—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C2×D68—21no—
134C2×D68—21no—
135C2×D68—21no—
136C2×D68—21no—
137C2×D68—21no—
138C2×D68C2×Q812yes—
139C2×C4×D17—24no—
140C2×C4×D17—81no—
141C2×C4×D17—81no—
142C2×C8×C17—21no—
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#4112yes—
153C2×C8×C17#4112yes—
154C4⋊C4×C17—22no—
155C4⋊C4×C17—41no—
156C42×C17—21no—
157C42×C17—21no—
158C42×C17—21no—
159C42×C17—21no—
160C42×C17C2×Q812yes—
161C42×C17#4112yes—
162#63227—24no—
163#63227—42no—
164#63227—42no—
165#63227—81no—
166#63227—81no—
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—21no—
178C4⋊Dic17—21no—
179C4⋊Dic17—21no—
180C4⋊Dic17—42no—
181C4⋊Dic17—81no—
182C4⋊Dic17C2×Q812yes—
183#63225—42no—
184#63225—81no—
185C4×Dic17—81no—
186C4×Dic17—81no—
187C4×Dic17—81no—
188#26096—171nomaximal, Sylow
189C23×C17C22×D411yescharacteristic
190C22×D17—22no—
191C22×D17—41no—
192C22×D17—41no—
193C22×D17—41no—
194C22×D17—41no—
195C22×D17—41no—
196C22×D17—41no—
197C2×C4×C17—21no—
198C2×C4×C17—21no—
199C2×C4×C17—21no—
200C2×C4×C17—21no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17—21no—
204C2×C4×C17—21no—
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×C17C22⋊Q812yes—
213C2×C4×C17C22⋊Q812yes—
214C2×C4×C17#13512yes—
215C2×C4×C17C22×Q811yescharacteristic
216C2×C4×C17C2×#4111yescharacteristic
217C2×C4×C17C2×#4111yescharacteristic
218C2×C4×C17C2×#4111yescharacteristic
219C2×C4×C17H(5,𝔽2)11yescharacteristic
220C2×C4×C172−1+411yescharacteristic
221C2×Dic17—22no—
222C2×Dic17—41no—
223C2×Dic17—41no—
224C2×Dic17—41no—
225C2×Dic17—41no—
226C2×Dic17—41no—
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—
242D68—22no—
243D68—22no—
244D68—41no—
245D68—41no—
246C4×D17—84no—
247C8×C17—22no—
248C8×C17—22no—
249C8×C17—41no—
250C8×C17—41no—
251#2570—171no—
252#2357—171no—
253#2094—171no—
254#2092—171no—
255#2067—171no—
256#2067—171no—
257#1949—171no—
258#1949—171no—
259#1947—171no—
260#1939D1711yescharacteristic, complemented
261#1920—171no—
262#1919—171no—
263#1846—171no—
264#1804—171no—
265C4×#102—171no—
266C22×C17C2×C22⋊Q811yescharacteristic
267C22×C17#54711yescharacteristic
268C22×C17#55011yescharacteristic
269C22×C17C2×#13511yescharacteristic
270C22×C17#57511yescharacteristic
271C22×C17#57611yescharacteristic
272C22×C17#57711yescharacteristic
273C2×D17—42no—
274C2×D17—42no—
275C2×D17—42no—
276C2×D17—81no—
277C2×D17—81no—
278C2×D17—81no—
279C2×D17—81no—
280C4×C17—22no—
281C4×C17—22no—
282C4×C17—22no—
283C4×C17—41no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17#53311yescharacteristic
287C4×C17#54411yescharacteristic
288C4×C17#55211yescharacteristic
289C4×C17#55311yescharacteristic
290Dic17—42no—
291Dic17—81no—
292Dic17—81no—
293Dic17—81no—
294Dic17—81no—
295Dic17—81no—
296Dic17—81no—
297C2×C4×D4—171no—
298C2×#107—171no—
299C2×#107—171no—
300C2×#107—171no—
301C2×#106—171no—
302C2×#106—171no—
303C2×#106—171no—
304C2×C4⋊C8C2×D1711yescharacteristic
305C2×C4⋊C8C2×D1711yescharacteristic
306C2×C4⋊C8C2×D1711yescharacteristic
307C2×#102—171no—
308C2×#102—171no—
309C2×#102—171no—
310C2×#102—171no—
311C2×C4×C8C2×D1711yescharacteristic
312#400—341no—
313#398—341no—
314#390—171no—
315#390—171no—
316#389—171no—
317#389—171no—
318#388—341no—
319#388—341no—
320#387—341no—
321#387—341no—
322#384—171no—
323#382—171no—
324#382—171no—
325#382—171no—
326#381—341no—
327C4×C4⋊C4—171no—
328C4×C4⋊C4—171no—
329C4×C4⋊C4—171no—
330C4×C4⋊C4C2×D1711yescharacteristic
331C4×C22⋊C4—341no—
332#340—171no—
333#340—171no—
334#340—171no—
335#340—171no—
336#340—171no—
337#340—171no—
338#336C2×D1711yescharacteristic
339#336C2×D1711yescharacteristic
340C2×C17#244111yescharacteristic
341C2×C17#307611yescharacteristic
342C2×C17#308111yescharacteristic
343C2×C17#333911yescharacteristic
344C2×C17#335111yescharacteristic
345C2×C17#339411yescharacteristic
346C2×C17#340311yescharacteristic
347D17—82no—
348C22×D4—171no—
349C23×C4—341no—
350C22×C8C22×D1711yescharacteristic
351C22×C8C22×D1711yescharacteristic
352C22×C8C22×D1711yescharacteristic
353C22×C8C22×D1711yescharacteristic
354C4×D4—174no—
355C4×D4—342no—
356C2×C4⋊C4—171no—
357C2×C4⋊C4—171no—
358C2×C4⋊C4—171no—
359C2×C4⋊C4—171no—
360C2×C4⋊C4—171no—
361C2×C4⋊C4—171no—
362C2×C4⋊C4—171no—
363C2×C4⋊C4—341no—
364C2×C4⋊C4—341no—
365C2×C4⋊C4—341no—
366C2×C4⋊C4—341no—
367C2×C4⋊C4D6811yescharacteristic
368C2×C4⋊C4D6811yescharacteristic
369C2×C22⋊C4—341no—
370C2×C22⋊C4—341no—
371C2×C22⋊C4—341no—
372C2×C22⋊C4—341no—
373C2×C22⋊C4—341no—
374C2×C42—341no—
375C2×C42—341no—
376C2×C42—341no—
377C2×C42C22×D1711yescharacteristic
378C2×C42C22×D1711yescharacteristic
379C2×C42C22×D1711yescharacteristic
380#107—681no—
381#107—681no—
382#107—681no—
383#106—342no—
384#106—342no—
385#106—681no—
386C4⋊C8—22no—
387C4⋊C8—22no—
388C4⋊C8—22no—
389#102—342no—
390#102—342no—
391#102—681no—
392#102—681no—
393C4×C8—22no—
394#95—341no—
395#95—341no—
396#95—341no—
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#95D6811yescharacteristic
406#95D6811yescharacteristic
407C17#2609611yescharacteristic, complemented, Sylow
408C24—341no—
409C2×D4—172no—
410C2×D4—341no—
411C2×D4—341no—
412C2×D4—341no—
413C2×D4—341no—
414C2×D4—341no—
415C22×C4—341no—
416C22×C4—344no—
417C22×C4—341no—
418C22×C4—341no—
419C22×C4—341no—
420C22×C4—341no—
421C22×C4—341no—
422C22×C4—341no—
423C22×C4—1361no—
424C22×C4—1361no—
425C22×C4C2×D6811yescharacteristic
426C22×C4C2×D6811yescharacteristic
427C22×C4C2×D6811yescharacteristic
428C22×C4C2×D6811yescharacteristic
429C22×C4C2×D6811yescharacteristic
430C22×C4C2×D6811yescharacteristic
431C22×C4C23×D1711yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8#6325412yes—
443C2×C8#6325612yes—
444C4⋊C4—22no—
445C4⋊C4—41no—
446C4⋊C4—172no—
447C4⋊C4—341no—
448C4⋊C4—341no—
449C4⋊C4—341no—
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—682no—
461C4⋊C4—682no—
462C4⋊C4—1361no—
463C4⋊C4—1361no—
464C22⋊C4—344no—
465C22⋊C4—682no—
466C22⋊C4—682no—
467C22⋊C4—1361no—
468C22⋊C4—1361no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—1361no—
474C42—1361no—
475C42—1361no—
476C42#6325412yes—
477C42Q8×D1712yes—
478C23—342no—
479C23—681no—
480C23—681no—
481C23—681no—
482C23—681no—
483C23—681no—
484C23—681no—
485C23C22×D6811yescharacteristic
486D4—342no—
487D4—342no—
488D4—681no—
489D4—681no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
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—342no—
506C2×C4—681no—
507C2×C4—681no—
508C2×C4—681no—
509C2×C4—681no—
510C2×C4—681no—
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—1364no—
527C2×C4#1058758312yes—
528C2×C4#1058758312yes—
529C2×C4#1058759012yes—
530C2×C4C2×#6325411yescharacteristic
531C2×C4C2×#6325411yescharacteristic
532C2×C4C2×Q8×D1711yescharacteristic
533C2×C4C2×#6325611yescharacteristic
534C2×C4#1058769611yescharacteristic
535C2×C4#1058769711yescharacteristic
536C8—22no—
537C8—22no—
538C8—41no—
539C8—41no—
540C22—682no—
541C22—682no—
542C22—682no—
543C22—1361no—
544C22—1361no—
545C22—1361no—
546C22—1361no—
547C22C2×#1058758311yescharacteristic
548C22#1176346311yescharacteristic
549C22#1176348111yescharacteristic
550C22C2×#1058759011yescharacteristic
551C22#1176360911yescharacteristic
552C22#1176361411yescharacteristic
553C22#1176362111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—682no—
561C4—1361no—
562C4—1361no—
563C4—1361no—
564C4—1361no—
565C4—1361no—
566C4—1361no—
567C4#1176336411yescharacteristic
568C4#1176343911yescharacteristic
569C4#1176350111yescharacteristic
570C4#1176351111yescharacteristic
571C2—1362no—
572C2#1453249511yescharacteristic
573C2#1453857411yescharacteristic
574C2#1453861611yescharacteristic
575C2#1454118711yescharacteristic
576C2#1454134611yescharacteristic
577C2#1454178211yescharacteristic
578C2#1454187411yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#1939C2
socleC23×C17C22×D4
prime radicalC22×D68C23
hypercenter#1939D17
hypocenterC17#26096
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #14534018C2semidirect
7. #14529554C2semidirect
8. #14529554C2semidirect
9. #14529543C2semidirect
10. #14529370C2semidirect
11. #14529363C2semidirect
12. #14528948C2semidirect
15. C17×#1939C2semidirect
260. #1939D17semidirect
407. C17#26096semidirect

Maximal subgroups

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

subgroupindex
#145340182
#145317552
#145303162
#145303042
#145301712
#145295542
#145295432
#145293702
#145293632
#145289482
#145287952
C4×#105874922
C17×#19392
#2609617