Finite Group Databasebeta

← #17005484

Subgroups — #17005484

Order 4352.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538833C211yesmaximal, characteristic
2#14537946C211yesmaximal, characteristic, complemented
3#14537818C211yesmaximal, characteristic, complemented
4#14527676C211yesmaximal, characteristic, complemented
5#14527670C211yesmaximal, characteristic, complemented
6#14527664C211yesmaximal, characteristic, complemented
7#14527650C211yesmaximal, characteristic, complemented
8#14527650C211yesmaximal, characteristic, complemented
9#14527643C211yesmaximal, characteristic, complemented
10C8×#63219C211yesmaximal, characteristic, complemented
11C8×D136C211yesmaximal, characteristic, complemented
12#14527569C211yesmaximal, characteristic, complemented
13#14527245C211yesmaximal, characteristic, complemented
14C2×#11762538C211yesmaximal, characteristic, complemented
15C17×#1450C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18#11763145C411yescharacteristic
19#11763128C411yescharacteristic
20#11763110C411yescharacteristic
21#11763110C411yescharacteristic
22#11763025C411yescharacteristic
23#11763025C411yescharacteristic
24#11762962C411yescharacteristic
25#11762945C411yescharacteristic
26#11762939C2211yescharacteristic, complemented
27C8×Dic34C2211yescharacteristic, complemented
28C4×#63219C2211yescharacteristic
29C4×#63219C2211yescharacteristic
30C4×D136C2211yescharacteristic
31C4×D136C2211yescharacteristic
32#11762888C2211yescharacteristic
33#11762888C2211yescharacteristic
34#11762888C2211yescharacteristic, complemented
35#11762879—21no—
36#11762879—21no—
37#11762877—21no—
38C8×D68C2211yescharacteristic
39C8×D68C2211yescharacteristic
40C8×D68C2211yescharacteristic, complemented
41#11762872—21no—
42#11762869—21no—
43#11762866C2211yescharacteristic
44#11762834—21no—
45C2×C4⋊#3622C2211yescharacteristic
46#11762771—21no—
47C22⋊C8×D17—21no—
48#11762562C2211yescharacteristic, complemented
49#11762562C2211yescharacteristic, complemented
50#11762560C2211yescharacteristic, complemented
51#11762560C2211yescharacteristic, complemented
52#11762541C2211yescharacteristic, complemented
53#11762541C2211yescharacteristic, complemented
54#11762538C2211yescharacteristic
55#11762538C2211yescharacteristic
56#11762538C2211yescharacteristic
57#11762538C2211yescharacteristic
58#11762538C2211yescharacteristic, complemented
59#11762538C2211yescharacteristic, complemented
60C17×#431C2211yescharacteristic
61C17×#431C2211yescharacteristic
62C2×C4×C8×C17C2211yescharacteristic
63C17×#322C2211yescharacteristic, complemented
64C17×#322C2211yescharacteristic, complemented
65C82×C17C2211yescharacteristic, complemented
66C82×C17C2211yescharacteristic, complemented
67C22×D68C2×C411yescharacteristic
68C22×C4×D17—21no—
69C22×C8×C17—21no—
70C2×C42×C17C2311yescharacteristic
71#10587616C2×C411yescharacteristic
72#10587615—21no—
73C4×C22⋊D17—21no—
74C2×#63227—21no—
75C2×C4⋊Dic17C2×C411yescharacteristic
76#10587610C2×C411yescharacteristic
77C22×#3622—21no—
78C2×D136C2×C411yescharacteristic
79C2×D136C2×C411yescharacteristic
80C2×#63219C2×C411yescharacteristic
81C2×#63219C2×C411yescharacteristic
82C2×#63218—21no—
83C2×#63218—21no—
84C2×#63218—21no—
85C2×C8×D17—21no—
86C2×C8×D17—21no—
87C2×C8×D17—21no—
88#10587562—21no—
89#10587561C2×C411yescharacteristic
90C4×D68—21no—
91C4×D68—21no—
92C4×D68C2×C411yescharacteristic
93C4×D68C2×C411yescharacteristic
94C4×D68C2311yescharacteristic
95C4×D68C2311yescharacteristic
96C4×D68C2311yescharacteristic
97#10587558—21no—
98#10587556C2×C411yescharacteristic
99C4×Dic34C2311yescharacteristic
100C17×C4⋊C8C2×C411yescharacteristic
101C17×C4⋊C8C2×C411yescharacteristic
102C17×C4⋊C8D411yescharacteristic
103C17×C4⋊C8D411yescharacteristic
104C17×C22⋊C8C2×C411yescharacteristic
105C17×C22⋊C8C2×C411yescharacteristic
106C17×C22⋊C8D411yescharacteristic
107C17×C22⋊C8D411yescharacteristic
108C4×C8×C17—21no—
109C4×C8×C17C2311yescharacteristic
110C4×C8×C17C2311yescharacteristic
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C4×C8×C17C2311yescharacteristic
114C4×C8×C17C2311yescharacteristic
115C22⋊#3622—21no—
116#10587492C2×C411yescharacteristic
117#10587492C2×C411yescharacteristic
118#10587492C2×C411yescharacteristic
119#10587492C2×C411yescharacteristic
120#10587492C2×C411yescharacteristic
121#10587492C2×C411yescharacteristic
122#10587491—21no—
123#10587491—21no—
124#10587491—21no—
125#10587491—21no—
126#10587491—21no—
127#10587491—21no—
128#10587489C2×C411yescharacteristic
129#10587489C2×C411yescharacteristic
130#10587488C2×C411yescharacteristic
131#10587488C2×C411yescharacteristic
132#10587487C2×C411yescharacteristic
133#10587487C2×C411yescharacteristic
134#10587486—21no—
135#10587485—21no—
136#10587485—21no—
137C8×Dic17—21no—
138C4⋊#3622—21no—
139C4⋊#3622C2311yescharacteristic
140C4⋊#3622C2311yescharacteristic
141C4⋊#3622C2311yescharacteristic
142C4⋊#3622C2311yescharacteristic
143#10587474—21no—
144C23×D17—21no—
145C22×C4×C17C22×C411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17#4111yescharacteristic
148C2×C22⋊D17—21no—
149C22×Dic17—21no—
150C2×D68—22no—
151C2×D68—21no—
152C2×D68—41no—
153C2×D68C22×C411yescharacteristic
154C2×D68C22×C411yescharacteristic
155C2×D68C22×C411yescharacteristic
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—21no—
159C2×C4×D17—21no—
160C2×C4×D17—21no—
161C2×C4×D17—81no—
162C2×C4×D17—81no—
163C2×Dic34C22×C411yescharacteristic
164C2×C8×C17—24no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17C22×C411yescharacteristic
168C2×C8×C17C22×C411yescharacteristic
169C2×C8×C17C22×C411yescharacteristic
170C2×C8×C17C22×C411yescharacteristic
171C2×C8×C17C2×D411yescharacteristic
172C2×C8×C17C2×D411yescharacteristic
173C2×C8×C17C2×D411yescharacteristic
174C2×C8×C17C2×D411yescharacteristic
175C42×C17C22×C411yescharacteristic
176C42×C17C2×D411yescharacteristic
177C42×C17#4111yescharacteristic
178C42×C17C2411yescharacteristic
179C22⋊Dic17—21no—
180#63227—21no—
181#63227—21no—
182#63227—21no—
183#63227—21no—
184#63227—21no—
185#63227—21no—
186#63227—21no—
187#63227—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17C22×C411yescharacteristic
190C4⋊Dic17C22×C411yescharacteristic
191C4⋊Dic17C22×C411yescharacteristic
192C4⋊Dic17C22×C411yescharacteristic
193#63225—21no—
194#63225—21no—
195#63225—21no—
196#63225—21no—
197C4×Dic17—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—81no—
203D136—22no—
204D136—41no—
205#63219—22no—
206#63219—41no—
207#63218—81no—
208#63218—81no—
209#63218—81no—
210C8×D17—81no—
211C8×D17—81no—
212C8×D17—81no—
213#18014—171nomaximal, Sylow
214C23×C17C4×D411yescharacteristic
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17—42no—
219C22×D17—42no—
220C22×D17—81no—
221C2×C4×C17—22no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17C4×D411yescharacteristic
227C2×C4×C17C4×D411yescharacteristic
228C2×C4×C17C4×D411yescharacteristic
229C2×C4×C17C23×C411yescharacteristic
230C2×C4×C17C22×D411yescharacteristic
231C2×C4×C17C2×#4111yescharacteristic
232C22⋊D17—42no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—21no—
238C2×Dic17—81no—
239D68—21no—
240D68—21no—
241D68—21no—
242D68—21no—
243D68—21no—
244D68—42no—
245D68#13112yes—
246C4×D17—41no—
247C4×D17—41no—
248C4×D17—41no—
249C4×D17—41no—
250C4×D17—41no—
251C4×D17—41no—
252C4×D17—81no—
253C4×D17—81no—
254Dic34—21no—
255Dic34—21no—
256C8×C17—22no—
257C8×C17—22no—
258C8×C17—21no—
259C8×C17—21no—
260C8×C17—21no—
261C8×C17—21no—
262C8×C17—21no—
263C8×C17—21no—
264C8×C17—21no—
265C8×C17—21no—
266#3622—41no—
267#3622—41no—
268#3622—41no—
269#3622—41no—
270#3105—171no—
271#2994—171no—
272#2974—171no—
273#1590—171no—
274#1589—171no—
275#1588—171no—
276#1586—171no—
277#1586—171no—
278#1585—171no—
279C8×SD16—171no—
280C8×D8—171no—
281#1573—171no—
282#1494—171no—
283C2×D4⋊C8—171no—
284#1450D1711yescharacteristic, complemented
285C22×C17—21no—
286C22×C17—21no—
287C22×C17#44312yes—
288C22×C17C2×C4×D411yescharacteristic
289C2×D17—22no—
290C2×D17—41no—
291C2×D17—41no—
292C2×D17—41no—
293C2×D17—41no—
294C2×D17—41no—
295C2×D17—41no—
296C2×D17—41no—
297C2×D17—41no—
298C2×D17—84no—
299C4×C17—21no—
300C4×C17—21no—
301C4×C17—21no—
302C4×C17—21no—
303C4×C17C2×#13111yescharacteristic
304C4×C17#56811yescharacteristic
305C4×C17#57611yescharacteristic
306C4×C17#57711yescharacteristic
307Dic17—41no—
308Dic17—41no—
309Dic17—41no—
310Dic17—41no—
311Dic17—41no—
312#529—171no—
313C2×C4×D4—171no—
314#484—171no—
315#481—171no—
316#478—171no—
317#478—171no—
318#463—171no—
319#463—171no—
320#450—171no—
321#447—171no—
322#446—171no—
323C8×Q8—171no—
324C4×SD16—171no—
325C4×SD16—171no—
326C4×D8—171no—
327C4×D8—171no—
328#436—171no—
329#436—171no—
330#436—171no—
331#435—341no—
332#435—341no—
333#435—341no—
334C8×D4—171no—
335C8×D4—171no—
336C8×D4—171no—
337C8×D4—341no—
338#433—341no—
339#432—171no—
340#431C2×D1711yescharacteristic
341#431C2×D1711yescharacteristic
342#424—341no—
343C2×C4⋊C8—171no—
344#407—341no—
345C2×C22⋊C8—341no—
346C2×C4×C8C2×D1711yescharacteristic
347#335—171no—
348#335—171no—
349#334—171no—
350#334—171no—
351Q8⋊C8—171no—
352Q8⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8—171no—
356D4⋊C8—171no—
357D4⋊C8—171no—
358D4⋊C8—171no—
359#322C2×D1711yescharacteristic, complemented
360#322C2×D1711yescharacteristic, complemented
361C82C2×D1711yescharacteristic, complemented
362C82C2×D1711yescharacteristic, complemented
363C2×C17—22no—
364C2×C17#293311yescharacteristic
365C2×C17#294611yescharacteristic
366C2×C17C2×#44311yescharacteristic
367D17—42no—
368D17—81no—
369D17—81no—
370C22×D4—171no—
371C23×C4—341no—
372C2×SD16—171no—
373C2×SD16—171no—
374C2×D8—171no—
375C2×D8—171no—
376C2×M16—341no—
377C2×M16—341no—
378C2×M16—341no—
379C22×C8—21no—
380C22×C8—341no—
381C22×C8—341no—
382C22×C8—341no—
383C22×C8—341no—
384#126—341no—
385#125—171no—
386#124—171no—
387#123—341no—
388C22⋊Q8—171no—
389#121—171no—
390C4×Q8—171no—
391C4×D4—171no—
392C4×D4—171no—
393C4×D4—171no—
394C4×D4—171no—
395C4×D4—171no—
396C4×D4—341no—
397C4×D4—341no—
398C4×D4—341no—
399#117—341no—
400C2×C4⋊C4—171no—
401C2×C22⋊C4—341no—
402C2×C42C22×D1711yescharacteristic
403#107—171no—
404#107—171no—
405#106—171no—
406#106—171no—
407C4⋊C8—171no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—171no—
411C4⋊C8—341no—
412C4⋊C8—341no—
413C4⋊C8—341no—
414C4⋊C8C4×D1711yescharacteristic
415C4⋊C8C4×D1711yescharacteristic
416C4⋊C8D6811yescharacteristic
417C4⋊C8D6811yescharacteristic
418#103—171no—
419#103—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423#102—171no—
424#102—171no—
425#102—171no—
426C22⋊C8—341no—
427C22⋊C8—341no—
428C22⋊C8—341no—
429C22⋊C8—341no—
430C22⋊C8—341no—
431C22⋊C8—341no—
432C22⋊C8—341no—
433C22⋊C8C4×D1711yescharacteristic
434C22⋊C8C4×D1711yescharacteristic
435C22⋊C8D6811yescharacteristic
436C22⋊C8D6811yescharacteristic
437#97—341no—
438#97—341no—
439C4×C8—21no—
440C4×C8—341no—
441C4×C8C22×D1711yescharacteristic
442C4×C8C22×D1711yescharacteristic
443C4×C8C22×D1711yescharacteristic
444C4×C8C22×D1711yescharacteristic
445C4×C8C22×D1711yescharacteristic
446C4×C8C22×D1711yescharacteristic
447C17#1801411yescharacteristic, complemented, Sylow
448C24—341no—
449C2×Q8—171no—
450C2×D4—171no—
451C2×D4—171no—
452C2×D4—171no—
453C2×D4—342no—
454C2×D4—341no—
455C2×D4—341no—
456C2×D4—681no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—1361no—
464C22×C4—1361no—
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4C2×D6811yescharacteristic
467C22×C4#6325211yescharacteristic
468SD16—342no—
469SD16—681no—
470D8—342no—
471D8—681no—
472M16—1361no—
473M16—1361no—
474M16—1361no—
475C2×C8—24no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—341no—
479C2×C8—341no—
480C2×C8—341no—
481C2×C8—341no—
482C2×C8—1361no—
483C2×C8—1361no—
484C2×C8—1361no—
485C2×C8—1361no—
486C2×C8C2×C4×D1711yescharacteristic
487C2×C8C2×C4×D1711yescharacteristic
488C2×C8C2×C4×D1711yescharacteristic
489C2×C8C2×C4×D1711yescharacteristic
490C2×C8C2×D6811yescharacteristic
491C2×C8C2×D6811yescharacteristic
492C2×C8C2×D6811yescharacteristic
493C2×C8C2×D6811yescharacteristic
494C4⋊C4—171no—
495C4⋊C4—171no—
496C4⋊C4—171no—
497C4⋊C4—171no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C4⋊C4—341no—
501C4⋊C4—341no—
502C4⋊C4—341no—
503C22⋊C4—341no—
504C22⋊C4—341no—
505C22⋊C4—341no—
506C22⋊C4—341no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C22⋊C4—341no—
510C22⋊C4—341no—
511C22⋊C4—341no—
512C42—341no—
513C42C2×C4×D1711yescharacteristic
514C42C2×D6811yescharacteristic
515C42#6325211yescharacteristic
516C42C23×D1711yescharacteristic
517C23—341no—
518C23—341no—
519C23—341no—
520C23—682no—
521C23—682no—
522C23—1361no—
523C23C4×D6811yescharacteristic
524Q8—341no—
525Q8—341no—
526D4—172no—
527D4—341no—
528D4—341no—
529D4—341no—
530D4—341no—
531D4—341no—
532D4—682no—
533D4—682no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—341no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—681no—
545C2×C4—681no—
546C2×C4—681no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—1361no—
551C2×C4—1361no—
552C2×C4—1361no—
553C2×C4C4×D6811yescharacteristic
554C2×C4C4×D6811yescharacteristic
555C2×C4C4×D6811yescharacteristic
556C2×C4C22×C4×D1711yescharacteristic
557C2×C4C22×D6811yescharacteristic
558C2×C4C2×#6325211yescharacteristic
559C8—22no—
560C8—22no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—681no—
570C8—681no—
571C8—681no—
572C8—681no—
573C22—21no—
574C22—21no—
575C22—342no—
576C22—681no—
577C22—681no—
578C22—681no—
579C22—681no—
580C22—681no—
581C22—681no—
582C22—681no—
583C22—681no—
584C22—1364no—
585C22#1176292712yes—
586C22C2×C4×D6811yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—681no—
592C4—681no—
593C4—681no—
594C4—681no—
595C4—681no—
596C4#131×D1711yescharacteristic
597C4#1176357411yescharacteristic
598C4#1176361411yescharacteristic
599C4#1176362111yescharacteristic
600C2—22no—
601C2—682no—
602C2—1361no—
603C2—1361no—
604C2#1453751211yescharacteristic
605C2#1453761811yescharacteristic
606C2C2×#1176292711yescharacteristic
subgroupG/H
centerC2×C4C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1450C2
socleC22×C17C2×C4×D4
prime radical#11762945C4
cosocleC42×C17C24
hypercenter#1450D17
hypocenterC17#18014
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
2. #14537946C2semidirect
3. #14537818C2semidirect
4. #14527676C2semidirect
5. #14527670C2semidirect
6. #14527664C2semidirect
7. #14527650C2semidirect
8. #14527650C2semidirect
9. #14527643C2semidirect
10. C8×#63219C2semidirect
11. C8×D136C2semidirect
12. #14527569C2semidirect
13. #14527245C2semidirect
14. C2×#11762538C2semidirect
15. C17×#1450C2semidirect
26. #11762939C22semidirect
27. C8×Dic34C22semidirect
34. #11762888C22semidirect
40. C8×D68C22semidirect
48. #11762562C22semidirect
49. #11762562C22semidirect
50. #11762560C22semidirect
51. #11762560C22semidirect
52. #11762541C22semidirect
53. #11762541C22semidirect
58. #11762538C22semidirect
59. #11762538C22semidirect
63. C17×#322C22semidirect
64. C17×#322C22semidirect
65. C82×C17C22semidirect
66. C82×C17C22semidirect
284. #1450D17semidirect
359. #322C2×D17semidirect
360. #322C2×D17semidirect
361. C82C2×D17semidirect
362. C82C2×D17semidirect
447. C17#18014semidirect

Maximal subgroups

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

subgroupindex
#145388332
#145379462
#145378182
#145276762
#145276702
#145276642
#145276502
#145276432
C8×#632192
C8×D1362
#145275692
#145272452
C2×#117625382
C17×#14502
#1801417