Finite Group Databasebeta

← #17005515

Subgroups — #17005515

Order 4352.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538866C211yesmaximal, characteristic
2#14537940C211yesmaximal, characteristic
3#14537874C211yesmaximal, characteristic, complemented
4#14527680C211yesmaximal, characteristic, complemented
5#14527673C211yesmaximal, characteristic, complemented
6#14527661C211yesmaximal, characteristic, complemented
7#14527654C211yesmaximal, characteristic, complemented
8#14527654C211yesmaximal, characteristic, complemented
9#14527640C211yesmaximal, characteristic, complemented
10#14527590C211yesmaximal, characteristic, complemented
11#14527583C211yesmaximal, characteristic, complemented
12#14527242C211yesmaximal, characteristic
13C2×#11762539C211yesmaximal, characteristic, complemented
14#14527068C211yesmaximal, characteristic, complemented
15C17×#1573C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17C2×C4×Dic34C2211yescharacteristic
18#11763140C411yescharacteristic
19#11763123C411yescharacteristic
20#11763117C411yescharacteristic
21#11763117C411yescharacteristic
22#11763032C411yescharacteristic
23#11763032C411yescharacteristic
24#11762967C411yescharacteristic
25#11762950C411yescharacteristic
26#11762937—21no—
27#11762937—21no—
28#11762936C2211yescharacteristic
29#11762936C2211yescharacteristic
30#11762936C2211yescharacteristic
31#11762933C2211yescharacteristic
32#11762933C2211yescharacteristic
33#11762933C2211yescharacteristic
34C4×Dic68C2211yescharacteristic
35C4×Dic68C2211yescharacteristic
36C4×#63219C2211yescharacteristic
37C4×#63219C2211yescharacteristic
38#11762886C2211yescharacteristic
39#11762880—21no—
40#11762874C2211yescharacteristic
41C8×C22⋊D17—21no—
42#11762869—21no—
43#11762863—21no—
44#11762862C2211yescharacteristic
45#11762859—21no—
46#11762834—21no—
47C2×C4×#3622C2211yescharacteristic
48#11762539C2211yescharacteristic
49#11762539C2211yescharacteristic
50#11762539C2211yescharacteristic
51#11762539C2211yescharacteristic
52#11762539C2211yescharacteristic
53#11762539C2211yescharacteristic
54#11762536C2211yescharacteristic
55#11762536C2211yescharacteristic
56#11762531C2211yescharacteristic
57#11762531C2211yescharacteristic
58C8×#3622C2211yescharacteristic
59C8×#3622C2211yescharacteristic
60C17×#432C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C2×C17×C4⋊C8C2211yescharacteristic
63C17×#335C2211yescharacteristic
64C17×#335C2211yescharacteristic
65C17×#334C2211yescharacteristic
66C17×#334C2211yescharacteristic
67C22×Dic34C2×C411yescharacteristic
68C22×C8×C17—21no—
69C2×C42×C17C2311yescharacteristic
70#10587616C2×C411yescharacteristic
71#10587615—21no—
72C4×C22⋊D17—21no—
73C2×C4⋊Dic17C2×C411yescharacteristic
74#10587610C2×C411yescharacteristic
75C2×#63225—21no—
76C2×C4×Dic17—21no—
77C22×#3622—21no—
78C2×Dic68C2×C411yescharacteristic
79C2×Dic68C2×C411yescharacteristic
80C2×#63219C2×C411yescharacteristic
81C2×#63219C2×C411yescharacteristic
82C2×#63218—21no—
83C2×C8×D17—21no—
84#10587562—21no—
85#10587561C2×C411yescharacteristic
86C4×D68C2311yescharacteristic
87#10587558—21no—
88#10587556C2×C411yescharacteristic
89C4×Dic34—21no—
90C4×Dic34—21no—
91C4×Dic34C2×C411yescharacteristic
92C4×Dic34C2×C411yescharacteristic
93C4×Dic34C2311yescharacteristic
94C4×Dic34C2311yescharacteristic
95C4×Dic34C2311yescharacteristic
96C17×C4⋊C8—21no—
97C17×C4⋊C8C2×C411yescharacteristic
98C17×C4⋊C8C2×C411yescharacteristic
99C17×C4⋊C8C2311yescharacteristic
100C17×C4⋊C8C2311yescharacteristic
101C17×C4⋊C8C2311yescharacteristic
102C17×C4⋊C8C2311yescharacteristic
103C17×C22⋊C8—21no—
104C17×C22⋊C8C2×C411yescharacteristic
105C17×C22⋊C8C2×C411yescharacteristic
106C17×#97—21no—
107C4×C8×C17C2311yescharacteristic
108C4×C8×C17C2311yescharacteristic
109C22⋊#3622D411yescharacteristic
110C22⋊#3622D411yescharacteristic
111#10587492C2×C411yescharacteristic
112#10587492C2×C411yescharacteristic
113#10587491—21no—
114#10587491—21no—
115#10587489C2×C411yescharacteristic
116#10587489C2×C411yescharacteristic
117#10587488C2×C411yescharacteristic
118#10587488C2×C411yescharacteristic
119#10587487C2×C411yescharacteristic
120#10587487C2×C411yescharacteristic
121#10587487C2×C411yescharacteristic
122#10587487C2×C411yescharacteristic
123#10587487C2×C411yescharacteristic
124#10587487C2×C411yescharacteristic
125#10587486—21no—
126#10587486—21no—
127#10587486—21no—
128#10587485—21no—
129#10587485—21no—
130#10587485—21no—
131#10587485—21no—
132#10587485—21no—
133#10587485—21no—
134C8×Dic17—21no—
135C8×Dic17—21no—
136C8×Dic17—21no—
137C4⋊#3622D411yescharacteristic
138C4⋊#3622D411yescharacteristic
139C4×#3622—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17#4111yescharacteristic
147C2×C22⋊D17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C2×D68C22×C411yescharacteristic
151C2×C4×D17—21no—
152C2×Dic34—22no—
153C2×Dic34—21no—
154C2×Dic34—41no—
155C2×Dic34C22×C411yescharacteristic
156C2×Dic34C22×C411yescharacteristic
157C2×Dic34C22×C411yescharacteristic
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—81no—
163C2×C8×C17C22×C411yescharacteristic
164C2×C8×C17C22×C411yescharacteristic
165C2×C8×C17C22×C411yescharacteristic
166C2×C8×C17C22×C411yescharacteristic
167C42×C17C22×C411yescharacteristic
168C42×C17C2×D411yescharacteristic
169C42×C17#4111yescharacteristic
170C42×C17C2411yescharacteristic
171C22⋊Dic17—21no—
172#63227—21no—
173#63227—21no—
174#63227—21no—
175#63227—21no—
176C4⋊Dic17—21no—
177C4⋊Dic17C22×C411yescharacteristic
178C4⋊Dic17C22×C411yescharacteristic
179C4⋊Dic17C22×C411yescharacteristic
180C4⋊Dic17C22×C411yescharacteristic
181#63225—21no—
182#63225—21no—
183#63225—21no—
184#63225—21no—
185#63225—21no—
186#63225—21no—
187#63225—21no—
188#63225—21no—
189C4×Dic17—21no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
193C4×Dic17—21no—
194C2×#3622—24no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622C2×D411yescharacteristic
198C2×#3622C2×D411yescharacteristic
199C2×#3622C2×D411yescharacteristic
200C2×#3622C2×D411yescharacteristic
201Dic68—22no—
202Dic68—41no—
203#63219—22no—
204#63219—41no—
205#63218—81no—
206C8×D17—81no—
207#18017—171nomaximal, Sylow
208C23×C17C4×D411yescharacteristic
209C22×D17—21no—
210C2×C4×C17—22no—
211C2×C4×C17—21no—
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17C4×D411yescharacteristic
216C2×C4×C17C4×D411yescharacteristic
217C2×C4×C17C4×D411yescharacteristic
218C2×C4×C17C23×C411yescharacteristic
219C2×C4×C17C22×D411yescharacteristic
220C2×C4×C17C2×#4111yescharacteristic
221C22⋊D17—42no—
222C2×Dic17—21no—
223C2×Dic17—21no—
224C2×Dic17—21no—
225C2×Dic17—21no—
226C2×Dic17—21no—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—42no—
230C2×Dic17—42no—
231D68—21no—
232D68—21no—
233C4×D17—41no—
234C4×D17—41no—
235Dic34—21no—
236Dic34—21no—
237Dic34—21no—
238Dic34—21no—
239Dic34—21no—
240Dic34—42no—
241Dic34#13112yes—
242C8×C17—21no—
243C8×C17—21no—
244C8×C17—21no—
245C8×C17—21no—
246C8×C17—41no—
247C8×C17—41no—
248C8×C17—41no—
249C8×C17—41no—
250#3622—22no—
251#3622—22no—
252#3622—21no—
253#3622—21no—
254#3622—21no—
255#3622—21no—
256#3108—171no—
257#2994—171no—
258#2984—171no—
259#1591—171no—
260#1590—171no—
261#1588—171no—
262#1587—171no—
263#1587—171no—
264#1585—171no—
265C8×Q16—171no—
266C8×SD16—171no—
267#1573D1711yescharacteristic, complemented
268#1494—171no—
269C2×Q8⋊C8—171no—
270#1450—171no—
271C22×C17—21no—
272C22×C17—21no—
273C22×C17#44312yes—
274C22×C17C2×C4×D411yescharacteristic
275C2×D17—41no—
276C2×D17—41no—
277C2×D17—41no—
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—21no—
282C4×C17C2×#13111yescharacteristic
283C4×C17#56811yescharacteristic
284C4×C17#57711yescharacteristic
285C4×C17#57811yescharacteristic
286Dic17—22no—
287Dic17—41no—
288Dic17—41no—
289Dic17—41no—
290Dic17—41no—
291Dic17—41no—
292Dic17—41no—
293#529—171no—
294C2×C4×Q8—171no—
295#483—171no—
296#480—171no—
297#479—171no—
298#479—171no—
299#464—171no—
300#464—171no—
301#451—171no—
302#448—171no—
303#446—171no—
304#446—171no—
305#446—171no—
306#446—341no—
307#446—341no—
308C8×Q8—171no—
309C8×Q8—171no—
310C8×Q8—171no—
311C4×Q16—171no—
312C4×Q16—171no—
313C4×SD16—171no—
314C4×SD16—171no—
315#436—171no—
316#435—341no—
317C8×D4—171no—
318C8×D4—341no—
319#433—341no—
320#432—341no—
321#432C2×D1711yescharacteristic
322#431—171no—
323#431—341no—
324#431C2×D1711yescharacteristic
325#424—341no—
326C2×C4⋊C8C2×D1711yescharacteristic
327C2×C4×C8—171no—
328#335C2×D1711yescharacteristic
329#335C2×D1711yescharacteristic
330#334C2×D1711yescharacteristic
331#334C2×D1711yescharacteristic
332Q8⋊C8—171no—
333Q8⋊C8—171no—
334Q8⋊C8—171no—
335Q8⋊C8—171no—
336Q8⋊C8—171no—
337Q8⋊C8—171no—
338D4⋊C8—171no—
339D4⋊C8—171no—
340#322—171no—
341#322—171no—
342C82—171no—
343C82—171no—
344C2×C17—22no—
345C2×C17#293311yescharacteristic
346C2×C17#294711yescharacteristic
347C2×C17C2×#44311yescharacteristic
348D17—81no—
349C22×Q8—171no—
350C2×Q16—171no—
351C2×Q16—171no—
352C2×SD16—171no—
353C2×SD16—171no—
354C2×M16—341no—
355C22×C8—21no—
356C22×C8—341no—
357C22×C8—341no—
358#126—341no—
359#125—171no—
360#124—171no—
361#123—341no—
362C22⋊Q8—171no—
363#121—171no—
364C4×Q8—171no—
365C4×Q8—171no—
366C4×Q8—171no—
367C4×Q8—171no—
368C4×Q8—171no—
369C4×Q8—341no—
370C4×Q8—341no—
371C4×D4—171no—
372C4×D4—341no—
373#117—341no—
374C2×C4⋊C4—171no—
375C2×C4⋊C4—341no—
376C2×C42—341no—
377C2×C42C22×D1711yescharacteristic
378#107—171no—
379#107—171no—
380#106—171no—
381#106—171no—
382C4⋊C8—21no—
383C4⋊C8—171no—
384C4⋊C8—171no—
385C4⋊C8—341no—
386C4⋊C8—341no—
387C4⋊C8—341no—
388C4⋊C8—341no—
389C4⋊C8—341no—
390C4⋊C8—341no—
391C4⋊C8C4×D1711yescharacteristic
392C4⋊C8C4×D1711yescharacteristic
393C4⋊C8C22×D1711yescharacteristic
394C4⋊C8C22×D1711yescharacteristic
395C4⋊C8C22×D1711yescharacteristic
396C4⋊C8C22×D1711yescharacteristic
397#103—171no—
398#103—171no—
399#103—171no—
400#103—171no—
401#103—171no—
402#103—171no—
403#102—171no—
404#102—171no—
405C22⋊C8—21no—
406C22⋊C8—171no—
407C22⋊C8—171no—
408C22⋊C8—341no—
409C22⋊C8—341no—
410C22⋊C8C4×D1711yescharacteristic
411C22⋊C8C4×D1711yescharacteristic
412#97—21no—
413#97—341no—
414#97—341no—
415#97—341no—
416C4×C8—171no—
417C4×C8—171no—
418C4×C8—171no—
419C4×C8—171no—
420C4×C8—341no—
421C4×C8—341no—
422C4×C8—341no—
423C4×C8—341no—
424C4×C8C22×D1711yescharacteristic
425C4×C8C22×D1711yescharacteristic
426C17#1801711yescharacteristic, complemented, Sylow
427C2×Q8—171no—
428C2×Q8—171no—
429C2×Q8—171no—
430C2×Q8—342no—
431C2×Q8—341no—
432C2×Q8—681no—
433C2×D4—171no—
434C2×D4—341no—
435C22×C4—341no—
436C22×C4—341no—
437C22×C4—341no—
438C22×C4C2×C4×D1711yescharacteristic
439C22×C4D4×D1711yescharacteristic
440C22×C4#6325611yescharacteristic
441Q16—342no—
442Q16—681no—
443SD16—342no—
444SD16—681no—
445M16—1361no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—171no—
452C2×C8—171no—
453C2×C8—171no—
454C2×C8—171no—
455C2×C8—344no—
456C2×C8—341no—
457C2×C8—341no—
458C2×C8—1361no—
459C2×C8C2×C4×D1711yescharacteristic
460C2×C8C2×C4×D1711yescharacteristic
461C2×C8C2×C4×D1711yescharacteristic
462C2×C8C2×C4×D1711yescharacteristic
463C4⋊C4—171no—
464C4⋊C4—171no—
465C4⋊C4—171no—
466C4⋊C4—171no—
467C4⋊C4—341no—
468C4⋊C4—341no—
469C4⋊C4—341no—
470C4⋊C4—341no—
471C4⋊C4—341no—
472C4⋊C4—341no—
473C4⋊C4—341no—
474C4⋊C4—341no—
475C4⋊C4—341no—
476C22⋊C4—341no—
477C22⋊C4—341no—
478C22⋊C4—341no—
479C22⋊C4—341no—
480C22⋊C4—341no—
481C42—341no—
482C42—341no—
483C42—341no—
484C42—341no—
485C42—341no—
486C42C2×C4×D1711yescharacteristic
487C42D4×D1711yescharacteristic
488C42#6325611yescharacteristic
489C42C23×D1711yescharacteristic
490C23—341no—
491C23#1058757911yescharacteristic
492Q8—172no—
493Q8—341no—
494Q8—341no—
495Q8—341no—
496Q8—341no—
497Q8—341no—
498Q8—682no—
499D4—341no—
500D4—341no—
501D4—682no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—341no—
508C2×C4—341no—
509C2×C4—341no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—341no—
513C2×C4—341no—
514C2×C4—682no—
515C2×C4—682no—
516C2×C4—681no—
517C2×C4—681no—
518C2×C4#1058757911yescharacteristic
519C2×C4#1058757911yescharacteristic
520C2×C4#1058757911yescharacteristic
521C2×C4C22×C4×D1711yescharacteristic
522C2×C4C2×D4×D1711yescharacteristic
523C2×C4C2×#6325611yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—342no—
533C8—342no—
534C8—341no—
535C8—341no—
536C8—341no—
537C8—341no—
538C22—21no—
539C22—21no—
540C22—681no—
541C22—681no—
542C22—681no—
543C22#1176292512yes—
544C22C2×#1058757911yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—342no—
550C4—681no—
551C4—681no—
552C4—681no—
553C4—681no—
554C4—681no—
555C4—681no—
556C4#131×D1711yescharacteristic
557C4#1176357411yescharacteristic
558C4#1176361911yescharacteristic
559C4#1176362511yescharacteristic
560C2—22no—
561C2—1361no—
562C2#1453750811yescharacteristic
563C2#1453762511yescharacteristic
564C2C2×#1176292511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1573C2
socleC22×C17C2×C4×D4
prime radical#10587616C2×C4
cosocleC42×C17C24
hypercenter#1573D17
hypocenterC17#18017
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #14537874C2semidirect
4. #14527680C2semidirect
5. #14527673C2semidirect
6. #14527661C2semidirect
7. #14527654C2semidirect
8. #14527654C2semidirect
9. #14527640C2semidirect
10. #14527590C2semidirect
11. #14527583C2semidirect
13. C2×#11762539C2semidirect
14. #14527068C2semidirect
15. C17×#1573C2semidirect
267. #1573D17semidirect
426. C17#18017semidirect

Maximal subgroups

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

subgroupindex
#145388662
#145379402
#145378742
#145276802
#145276732
#145276612
#145276542
#145276402
#145275902
#145275832
#145272422
C2×#117625392
#145270682
C17×#15732
#1801717