Finite Group Databasebeta

← #17005465

Subgroups — #17005465

Order 4352.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538855C211yesmaximal, characteristic
2#14537731C211yesmaximal, characteristic, complemented
3#14527686C211yesmaximal, characteristic, complemented
4#14527672C211yesmaximal, characteristic, complemented
5#14527660C211yesmaximal, characteristic, complemented
6#14527655C211yesmaximal, characteristic, complemented
7#14527634C211yesmaximal, characteristic, complemented
8#14527625C211yesmaximal, characteristic, complemented
9#14527601C211yesmaximal, characteristic, complemented
10C8×#63231C211yesmaximal, characteristic, complemented
11#14527570C211yesmaximal, characteristic, complemented
12#14527256C211yesmaximal, characteristic, complemented
13#14527171C211yesmaximal, characteristic
14#14527081C211yesmaximal, characteristic, complemented
15C17×#2971C211yesmaximal, characteristic
16#11763366C2211yescharacteristic
17#11763150C411yescharacteristic
18#11763150C411yescharacteristic
19#11763094C411yescharacteristic
20#11763089C411yescharacteristic
21#11763019C411yescharacteristic
22#11763014C411yescharacteristic
23#11762971C411yescharacteristic
24#11762971C411yescharacteristic
25#11762939C2211yescharacteristic
26#11762939C2211yescharacteristic
27#11762937—21no—
28#11762937—21no—
29C8×Dic34C2211yescharacteristic
30C8×Dic34C2211yescharacteristic
31C4×#63231C2211yescharacteristic
32C4×#63231C2211yescharacteristic
33C4×#63229C2211yescharacteristic
34C4×#63229C2211yescharacteristic
35#11762862C2211yescharacteristic
36#11762862C2211yescharacteristic
37#11762837—21no—
38C2×C4⋊#3622C2211yescharacteristic
39#11762767—21no—
40#11762561C2211yescharacteristic
41#11762561C2211yescharacteristic
42#11762559C2211yescharacteristic
43#11762559C2211yescharacteristic
44Q8⋊#3622C2211yescharacteristic
45Q8⋊#3622C2211yescharacteristic
46#11762539C2211yescharacteristic
47#11762539C2211yescharacteristic
48#11762539C2211yescharacteristic
49#11762539C2211yescharacteristic
50D4⋊#3622C2211yescharacteristic
51D4⋊#3622C2211yescharacteristic
52#11762531C2211yescharacteristic
53#11762531C2211yescharacteristic
54#11762530C2211yescharacteristic
55C8×#3622C2211yescharacteristic
56C4×#41×C17C2211yescharacteristic
57C8×Q8×C17C2211yescharacteristic
58C8×Q8×C17C2211yescharacteristic
59C17×#436—21no—
60C17×#436—21no—
61C17×#436C2211yescharacteristic
62C17×#436C2211yescharacteristic
63C17×#432—21no—
64C17×#432C2211yescharacteristic
65C4×M16×C17—21no—
66C4×M16×C17C2211yescharacteristic
67C2×#41×C17C2×C411yescharacteristic
68C2×M16×C17—21no—
69C2×M16×C17—21no—
70C2×M16×C17D411yescharacteristic
71C2×M16×C17D411yescharacteristic
72C4×Q8×C17C2×C411yescharacteristic
73C4×Q8×C17C2311yescharacteristic
74C4×D4×C17—21no—
75C4×D4×C17—21no—
76C4×D4×C17C2×C411yescharacteristic
77C4×D4×C17C2311yescharacteristic
78C17×#117—21no—
79C17×#117C2×C411yescharacteristic
80C2×C42×C17—21no—
81C2×C42×C17C2311yescharacteristic
82C2×#63231C2×C411yescharacteristic
83C2×#63231C2×C411yescharacteristic
84C2×#63229C2×C411yescharacteristic
85C2×#63229C2×C411yescharacteristic
86#10587612—21no—
87#10587610—21no—
88#10587610C2×C411yescharacteristic
89#10587610C2×C411yescharacteristic
90C22×#3622—21no—
91#10587556—21no—
92#10587555C2×C411yescharacteristic
93#10587555C2×C411yescharacteristic
94C4×Dic34—21no—
95C4×Dic34C2311yescharacteristic
96C4×Dic34C2311yescharacteristic
97C17×C4⋊C8—21no—
98C17×C4⋊C8—21no—
99C17×C4⋊C8C2311yescharacteristic
100C17×C4⋊C8C2311yescharacteristic
101C17×C22⋊C8—21no—
102C17×C22⋊C8—21no—
103C17×C22⋊C8—21no—
104C17×#97—21no—
105C17×#97D411yescharacteristic
106C17×#97D411yescharacteristic
107C4×C8×C17—21no—
108C4×C8×C17—21no—
109C4×C8×C17C2311yescharacteristic
110C4×C8×C17C2311yescharacteristic
111#10587506C2×C411yescharacteristic
112#10587506C2×C411yescharacteristic
113#10587503C2×C411yescharacteristic
114#10587503C2×C411yescharacteristic
115C22⋊#3622—21no—
116C22⋊#3622C2×C411yescharacteristic
117C22⋊#3622C2×C411yescharacteristic
118#10587486—21no—
119#10587486—21no—
120#10587485—21no—
121#10587485—21no—
122#10587485—21no—
123#10587485—21no—
124C8×Dic17—21no—
125C8×Dic17—21no—
126#10587481C2×C411yescharacteristic
127#10587481C2×C411yescharacteristic
128#10587481C2×C411yescharacteristic
129#10587481C2×C411yescharacteristic
130#10587479C2×C411yescharacteristic
131#10587479C2×C411yescharacteristic
132#10587478C2×C411yescharacteristic
133#10587478C2×C411yescharacteristic
134C4⋊#3622—21no—
135C4⋊#3622—21no—
136C4⋊#3622C2×C411yescharacteristic
137C4⋊#3622C2×C411yescharacteristic
138C4⋊#3622C2311yescharacteristic
139C4⋊#3622C2311yescharacteristic
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144#41×C17—22no—
145#41×C17—41no—
146C2×Q8×C17C22×C411yescharacteristic
147C2×D4×C17—21no—
148C2×D4×C17C22×C411yescharacteristic
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17C22×C411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17#4111yescharacteristic
155C2×Dic34—21no—
156C2×Dic34C22×C411yescharacteristic
157C2×Dic34C22×C411yescharacteristic
158M16×C17—22no—
159M16×C17—41no—
160M16×C17—42no—
161M16×C17—42no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17C2×D411yescharacteristic
165C2×C8×C17C2×D411yescharacteristic
166C2×C8×C17C2×D411yescharacteristic
167C2×C8×C17C2×D411yescharacteristic
168C4⋊C4×C17—21no—
169C4⋊C4×C17—21no—
170C4⋊C4×C17C22×C411yescharacteristic
171C4⋊C4×C17C22×C411yescharacteristic
172C22⋊C4×C17—21no—
173C22⋊C4×C17—21no—
174C22⋊C4×C17—21no—
175C42×C17—21no—
176C42×C17—21no—
177C42×C17—21no—
178C42×C17C22×C411yescharacteristic
179C42×C17C2×D411yescharacteristic
180C42×C17#4111yescharacteristic
181C42×C17C2411yescharacteristic
182C22⋊Dic17—21no—
183C22⋊Dic17—21no—
184#63231—22no—
185#63231—22no—
186#63229—41no—
187#63229—41no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17C22×C411yescharacteristic
192C4⋊Dic17C22×C411yescharacteristic
193#63225—21no—
194#63225—21no—
195#63225—21no—
196#63225—21no—
197C4×Dic17—21no—
198C4×Dic17—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—42no—
204C2×#3622C22×C411yescharacteristic
205C2×#3622C22×C411yescharacteristic
206C2×#3622C22×C411yescharacteristic
207C2×#3622C22×C411yescharacteristic
208#18013—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17C4×D411yescharacteristic
211Q8×C17—21no—
212Q8×C17#13112yes—
213D4×C17—21no—
214D4×C17—21no—
215D4×C17—42no—
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—41no—
224C2×C4×C17—42no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—81no—
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C4×D411yescharacteristic
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C23×C411yescharacteristic
232C2×C4×C17C22×D411yescharacteristic
233C2×C4×C17C2×#4111yescharacteristic
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238Dic34—21no—
239Dic34—21no—
240Dic34—21no—
241Dic34—21no—
242Dic34—81no—
243C8×C17—21no—
244C8×C17—21no—
245C8×C17—21no—
246C8×C17—41no—
247C8×C17—41no—
248C8×C17#13712yes—
249#3622—21no—
250#3622—21no—
251#3622—21no—
252#3622—21no—
253#3622—41no—
254#3622—41no—
255#3622—41no—
256#3622—41no—
257#3107—171no—
258#2971D1711yescharacteristic
259#2962—171no—
260#1592—171no—
261#1590—171no—
262#1588—171no—
263#1587—171no—
264#1584—171no—
265#1583—171no—
266#1579—171no—
267C8×Q16—171no—
268#1573—171no—
269#1497—171no—
270#1477—171no—
271#1453—171no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—41no—
276C22×C17—41no—
277C22×C17—41no—
278C22×C17C2×C4×D411yescharacteristic
279C4×C17—21no—
280C4×C17—22no—
281C4×C17—21no—
282C4×C17—21no—
283C4×C17—21no—
284C4×C17—41no—
285C4×C17—41no—
286C4×C17C2×#13111yescharacteristic
287C4×C17#56811yescharacteristic
288C4×C17C2×#13711yescharacteristic
289C4×C17#57511yescharacteristic
290Dic17—41no—
291Dic17—41no—
292Dic17—41no—
293Dic17—41no—
294#533—171no—
295C4×#41C2×D1711yescharacteristic
296#485—171no—
297#485—171no—
298#475—171no—
299#474—171no—
300#462—171no—
301#461—171no—
302#452—171no—
303#452—171no—
304#446—171no—
305#446—171no—
306#446—341no—
307#446—341no—
308C8×Q8—171no—
309C8×Q8—171no—
310C8×Q8C2×D1711yescharacteristic
311C8×Q8C2×D1711yescharacteristic
312C4×Q16—171no—
313C4×Q16—171no—
314C4×SD16—171no—
315C4×SD16—171no—
316#436—21no—
317#436—21no—
318#436C2×D1711yescharacteristic
319#436C2×D1711yescharacteristic
320#432—21no—
321#432C2×D1711yescharacteristic
322#431—171no—
323#431—171no—
324#424—341no—
325C2×C4⋊C8—171no—
326#405—341no—
327C4×M16—21no—
328C4×M16C2×D1711yescharacteristic
329#335—171no—
330#335—171no—
331#334—171no—
332#334—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336Q8⋊C8—171no—
337Q8⋊C8—171no—
338Q8⋊C8—171no—
339D4⋊C8—171no—
340D4⋊C8—171no—
341#322—171no—
342#322—171no—
343#322—171no—
344C82—171no—
345C2×C17—41no—
346C2×C17—81no—
347C2×C17#293311yescharacteristic
348C2×C17C4×#13711yescharacteristic
349C2×C17#295711yescharacteristic
350C2×#41C4×D1711yescharacteristic
351C2×Q16—171no—
352C2×Q16—171no—
353C2×SD16—171no—
354C2×SD16—171no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16C22⋊D1711yescharacteristic
358C2×M16C22⋊D1711yescharacteristic
359C22×C8—341no—
360C4⋊Q8—171no—
361C4⋊Q8—171no—
362#125—341no—
363C22⋊Q8—171no—
364C22⋊Q8—171no—
365C22⋊Q8—341no—
366C4×Q8—171no—
367C4×Q8—171no—
368C4×Q8—341no—
369C4×Q8C4×D1711yescharacteristic
370C4×Q8C22×D1711yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C4×D1711yescharacteristic
374C4×D4C22×D1711yescharacteristic
375#117—21no—
376#117—341no—
377#117C4×D1711yescharacteristic
378C2×C42—21no—
379C2×C42C22×D1711yescharacteristic
380#107—171no—
381#107—171no—
382#106—171no—
383#106—171no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—171no—
387C4⋊C8—171no—
388C4⋊C8—171no—
389C4⋊C8—171no—
390C4⋊C8—341no—
391C4⋊C8—341no—
392C4⋊C8—341no—
393C4⋊C8—341no—
394C4⋊C8—341no—
395C4⋊C8—341no—
396C4⋊C8C22×D1711yescharacteristic
397C4⋊C8C22×D1711yescharacteristic
398#103—171no—
399#103—171no—
400#103—171no—
401#103—171no—
402#103—171no—
403#103—171no—
404#102—171no—
405#102—171no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—171no—
410C22⋊C8—171no—
411C22⋊C8—341no—
412#97—21no—
413#97—341no—
414#97—341no—
415#97C22⋊D1711yescharacteristic
416#97C22⋊D1711yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—171no—
420C4×C8—171no—
421C4×C8—171no—
422C4×C8—171no—
423C4×C8—341no—
424C4×C8—341no—
425C4×C8C22×D1711yescharacteristic
426C4×C8C22×D1711yescharacteristic
427C17#1801311yescharacteristic, complemented, Sylow
428#41—22no—
429#41—41no—
430C2×Q8—171no—
431C2×Q8—171no—
432C2×Q8—341no—
433C2×Q8C2×C4×D1711yescharacteristic
434C2×D4—21no—
435C2×D4C2×C4×D1711yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4C2×C4×D1711yescharacteristic
440C22×C4#6325211yescharacteristic
441C22×C4C2×C22⋊D1711yescharacteristic
442Q16—342no—
443Q16—342no—
444SD16—681no—
445SD16—681no—
446M16—22no—
447M16—41no—
448M16—42no—
449M16—42no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—171no—
453C2×C8—171no—
454C2×C8—171no—
455C2×C8—171no—
456C2×C8—341no—
457C2×C8—341no—
458C2×C8—341no—
459C2×C8—341no—
460C2×C8—682no—
461C2×C8C2×C22⋊D1711yescharacteristic
462C2×C8C2×C22⋊D1711yescharacteristic
463C2×C8C2×C22⋊D1711yescharacteristic
464C2×C8C2×C22⋊D1711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—171no—
468C4⋊C4—171no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4—341no—
473C4⋊C4—341no—
474C4⋊C4—341no—
475C4⋊C4—341no—
476C4⋊C4C2×C4×D1711yescharacteristic
477C4⋊C4C2×C4×D1711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—341no—
482C22⋊C4—341no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—341no—
487C42—341no—
488C42C2×C4×D1711yescharacteristic
489C42#6325211yescharacteristic
490C42C2×C22⋊D1711yescharacteristic
491C42C23×D1711yescharacteristic
492C23—21no—
493C23C4×C22⋊D1711yescharacteristic
494Q8—21no—
495Q8—341no—
496Q8—341no—
497Q8—341no—
498Q8—341no—
499Q8—1361no—
500Q8#1058759312yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—341no—
517C2×C4—341no—
518C2×C4—341no—
519C2×C4—341no—
520C2×C4C4×C22⋊D1711yescharacteristic
521C2×C4C4×C22⋊D1711yescharacteristic
522C2×C4C4×C22⋊D1711yescharacteristic
523C2×C4C22×C4×D1711yescharacteristic
524C2×C4C2×#6325211yescharacteristic
525C2×C4C22×C22⋊D1711yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—341no—
532C8—341no—
533C8—341no—
534C8—341no—
535C8—681no—
536C8—681no—
537C8—681no—
538C8—681no—
539C8#1058763712yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D1711yescharacteristic
547C4—21no—
548C4—22no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—681no—
555C4—681no—
556C4—681no—
557C4—681no—
558C4C2×#1058759311yescharacteristic
559C4#1176357511yescharacteristic
560C4C2×#1058763711yescharacteristic
561C4#1176360711yescharacteristic
562C2—41no—
563C2—81no—
564C2#1453750911yescharacteristic
565C2C4×#1058763711yescharacteristic
566C2#1453769911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#2971C2
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C2×C4
cosocleC42×C17C24
hypercenter#2971D17
hypocenterC17#18013
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #14537731C2semidirect
3. #14527686C2semidirect
4. #14527672C2semidirect
5. #14527660C2semidirect
6. #14527655C2semidirect
7. #14527634C2semidirect
8. #14527625C2semidirect
9. #14527601C2semidirect
10. C8×#63231C2semidirect
11. #14527570C2semidirect
12. #14527256C2semidirect
14. #14527081C2semidirect
427. C17#18013semidirect

Maximal subgroups

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

subgroupindex
#145388552
#145377312
#145276862
#145276722
#145276602
#145276552
#145276342
#145276252
#145276012
C8×#632312
#145275702
#145272562
#145271712
#145270812
C17×#29712
#1801317