Finite Group Databasebeta

← #16923994

Subgroups — #16923994

Order 4352.

1058 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762771C211yesmaximal, characteristic
2C2×#11762771C211yesmaximal, characteristic
3C4×C22⋊C4×D17C211yesmaximal, characteristic
4#14526632C211yesmaximal, characteristic, complemented
5#14526631C211yesmaximal, characteristic, complemented
6#14526630C211yesmaximal, characteristic, complemented
7C17×#1282C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63218—21no—
10C22×#63218C412yescomplemented
11C2×C22⋊C4×D17C412yes—
12C2×C42×D17—21no—
13#11762771—21no—
14#11762771—21no—
15#11762771—21no—
16#11762771—21no—
17#11762771—21no—
18#11762771—21no—
19#11762771C412yescomplemented
20#11762771C412yescomplemented
21C2×C22⋊#3622C2211yescharacteristic
22C2×C22⋊#3622C2211yescharacteristic
23C2×#10587491—21no—
24C2×#10587491C412yescomplemented
25C22⋊C4×Dic17C412yes—
26C4×#63227—21no—
27C4×C22⋊Dic17C2211yescharacteristic
28#11762656—21no—
29#95×D17—21no—
30C2×C17×C22⋊C8C2211yescharacteristic
31C2×C17×C22⋊C8C2211yescharacteristic
32C4×C22⋊C4×C17C2211yescharacteristic
33C24×D17C2×C411yescharacteristic
34C23×C4×C17C2311yescharacteristic
35C23×Dic17C2×C411yescharacteristic
36C22×C4×D17—22no—
37C22×C4×D17—44no—
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17C2×C411yescharacteristic
40C22×C4×D17C2×C411yescharacteristic
41C22×C4×D17C2×C411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17D411yescharacteristic
44C22×C4×D17D411yescharacteristic
45C22×C4×D17D411yescharacteristic
46C22×C4×D17D411yescharacteristic
47C22×C4×D17D411yescharacteristic
48C22×C4×D17Q811yescharacteristic
49C22×C4×D17Q811yescharacteristic
50C22×C8×C17—21no—
51C22×C8×C17C2×C412yescomplemented
52C2×C22⋊C4×C17C2×C412yes—
53C2×C42×C17—21no—
54C2×C22⋊Dic17C2×C412yes—
55C2×#63227—22no—
56C2×C4×Dic17—21no—
57C2×C4×Dic17—22no—
58C22×#3622—21no—
59C22×#3622C2×C412yescomplemented
60C2×#63218—22no—
61C2×#63218—22no—
62C2×#63218—22no—
63C2×#63218—22no—
64C2×#63218—44no—
65C2×#63218—44no—
66C22⋊C4×D17—24no—
67C22⋊C4×D17—24no—
68C42×D17—44no—
69C17×C22⋊C8—21no—
70C17×C22⋊C8—21no—
71C17×C22⋊C8—21no—
72C17×C22⋊C8C2×C412yescomplemented
73C17×#95—21no—
74#10587502—21no—
75#10587502—22no—
76C22⋊#3622—21no—
77C22⋊#3622—21no—
78C22⋊#3622—21no—
79C22⋊#3622C2×C412yescomplemented
80#10587491—22no—
81#10587491—22no—
82#10587491—22no—
83#10587491—22no—
84C24×C17C22×C411yescharacteristic
85C23×D17—22no—
86C23×D17—22no—
87C23×D17—42no—
88C23×D17—42no—
89C23×D17C4211yescharacteristic
90C23×D17C4211yescharacteristic
91C23×D17C22⋊C411yescharacteristic
92C23×D17C22⋊C411yescharacteristic
93C23×D17C4⋊C411yescharacteristic
94C23×D17C4⋊C411yescharacteristic
95C22×C4×C17—22no—
96C22×C4×C17—42no—
97C22×C4×C17C22×C411yescharacteristic
98C22×C4×C17C22×C411yescharacteristic
99C22×C4×C17C2×D411yescharacteristic
100C22×C4×C17C2×D411yescharacteristic
101C22×C4×C17C2×D411yescharacteristic
102C22×C4×C17C2×Q811yescharacteristic
103C22×Dic17—22no—
104C22×Dic17—42no—
105C22×Dic17C4211yescharacteristic
106C22×Dic17C4211yescharacteristic
107C22×Dic17C22⋊C411yescharacteristic
108C22×Dic17C22⋊C411yescharacteristic
109C22×Dic17C4⋊C411yescharacteristic
110C22×Dic17C4⋊C411yescharacteristic
111C2×C4×D17—24no—
112C2×C4×D17—24no—
113C2×C4×D17—24no—
114C2×C4×D17—28no—
115C2×C4×D17—42no—
116C2×C4×D17—42no—
117C2×C4×D17—42no—
118C2×C4×D17—42no—
119C2×C4×D17—42no—
120C2×C4×D17—42no—
121C2×C4×D17—42no—
122C2×C4×D17—42no—
123C2×C4×D17—42no—
124C2×C4×D17—44no—
125C2×C4×D17—44no—
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C22⋊C411yescharacteristic
132C2×C4×D17C22⋊C411yescharacteristic
133C2×C4×D17C22⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C4⋊C411yescharacteristic
137C2×C4×D17C4⋊C411yescharacteristic
138C2×C4×D17C4⋊C411yescharacteristic
139C2×C4×D17C4⋊C411yescharacteristic
140C2×C4×D17C4⋊C411yescharacteristic
141C2×C4×D17C4⋊C411yescharacteristic
142C2×C8×C17—22no—
143C2×C8×C17—22no—
144C2×C8×C17—42no—
145C2×C8×C17—42no—
146C22⋊C4×C17—22no—
147C22⋊C4×C17M1614yescomplemented
148C42×C17—42no—
149C22⋊Dic17—22no—
150C22⋊Dic17M1614yescomplemented
151#63227—28no—
152C4×Dic17—44no—
153C4×Dic17—42no—
154C2×#3622—22no—
155C2×#3622—22no—
156C2×#3622—42no—
157C2×#3622—42no—
158#63218—44no—
159#63218—44no—
160#63218—44no—
161#63218—44no—
162#7929—171nomaximal, Sylow
163C23×C17—41no—
164C23×C17—41no—
165C23×C17C2×C4211yescharacteristic
166C23×C17C2×C22⋊C411yescharacteristic
167C23×C17C2×C4⋊C411yescharacteristic
168C23×C17C2×M1612yes—
169C23×C17C2×M1612yes—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—21no—
174C22×D17—21no—
175C22×D17—21no—
176C22×D17—21no—
177C22×D17—22no—
178C22×D17—22no—
179C22×D17—22no—
180C22×D17—22no—
181C22×D17—22no—
182C22×D17—22no—
183C22×D17—22no—
184C22×D17—41no—
185C22×D17—41no—
186C22×D17—41no—
187C22×D17—41no—
188C22×D17—41no—
189C22×D17—41no—
190C22×D17—48no—
191C22×D17—48no—
192C22×D17#9511yescharacteristic
193C22×D17#9511yescharacteristic
194C22×D17#9511yescharacteristic
195C22×D17#9511yescharacteristic
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—24no—
200C2×C4×C17—41no—
201C2×C4×C17—41no—
202C2×C4×C17—41no—
203C2×C4×C17—42no—
204C2×C4×C17—42no—
205C2×C4×C17C2×C22⋊C411yescharacteristic
206C2×C4×C17C2×C22⋊C411yescharacteristic
207C2×C4×C17C2×C4⋊C411yescharacteristic
208C2×C4×C17C2×C4⋊C411yescharacteristic
209C2×Dic17—22no—
210C2×Dic17—22no—
211C2×Dic17—22no—
212C2×Dic17—24no—
213C2×Dic17—41no—
214C2×Dic17—41no—
215C2×Dic17—41no—
216C2×Dic17—42no—
217C2×Dic17—42no—
218C2×Dic17#9511yescharacteristic
219C2×Dic17#9511yescharacteristic
220C2×Dic17#9511yescharacteristic
221C2×Dic17#9511yescharacteristic
222C4×D17—22no—
223C4×D17—22no—
224C4×D17—22no—
225C4×D17—22no—
226C4×D17—22no—
227C4×D17—22no—
228C4×D17—22no—
229C4×D17—22no—
230C4×D17—22no—
231C4×D17—41no—
232C4×D17—41no—
233C4×D17—41no—
234C4×D17—41no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—416no—
238C4×D17#9914yes—
239C8×C17—42no—
240C8×C17—42no—
241#3622—42no—
242#3622—42no—
243C2×#407—171no—
244C2×#407—171no—
245C2×C4×C22⋊C4—171no—
246#1282—171no—
247#1282—171no—
248#1282—171no—
249#1282D1711yescharacteristic, complemented
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—42no—
257C22×C17—42no—
258C22×C17C2×#9511yescharacteristic
259C22×C17C4×M1611yescharacteristic
260C22×C17C4×M1611yescharacteristic
261C22×C17#40712yes—
262C22×C17#42312yes—
263C2×D17—28no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—21no—
271C2×D17—21no—
272C2×D17—21no—
273C2×D17—21no—
274C2×D17—42no—
275C2×D17—42no—
276C2×D17—44no—
277C2×D17—42no—
278C2×D17—42no—
279C2×D17—44no—
280C2×D17—44no—
281C2×D17#34212yes—
282C2×D17#34412yes—
283C4×C17—21no—
284C4×C17—21no—
285C4×C17—21no—
286C4×C17—44no—
287C4×C17C2×#9912yes—
288Dic17—21no—
289Dic17—21no—
290Dic17—21no—
291Dic17—44no—
292Dic17#34212yes—
293C24×C4—171no—
294C22×M16—172no—
295C22×M16—341no—
296C22×C22⋊C4—172no—
297C22×C42—341no—
298#407—172no—
299#407—172no—
300#407—341no—
301#407—341no—
302#407—341no—
303#407—341no—
304#407—341no—
305#407—341no—
306C2×C22⋊C8—171no—
307C2×C22⋊C8—171no—
308C2×C22⋊C8—172no—
309C2×C22⋊C8—341no—
310C2×C22⋊C8C2×D1711yescharacteristic
311C2×C22⋊C8C2×D1711yescharacteristic
312C4×C22⋊C4—171no—
313C4×C22⋊C4—172no—
314C4×C22⋊C4—341no—
315C4×C22⋊C4—341no—
316C4×C22⋊C4C2×D1711yescharacteristic
317C2×#95—341no—
318C2×C17—22no—
319C2×C17—21no—
320C2×C17—21no—
321C2×C17—22no—
322C2×C17#172811yescharacteristic
323C2×C17C2×#34211yescharacteristic
324C2×C17C2×#34411yescharacteristic
325D17—22no—
326D17—22no—
327D17—41no—
328D17—41no—
329C25—171no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—342no—
344C23×C4—684no—
345C23×C4C22×D1711yescharacteristic
346C2×M16—342no—
347C2×M16—342no—
348C2×M16—342no—
349C2×M16—342no—
350C2×M16—684no—
351C2×M16—684no—
352C22×C8—21no—
353C22×C8—172no—
354C22×C8—341no—
355C22×C8C4×D1712yescomplemented
356C2×C22⋊C4—172no—
357C2×C22⋊C4—344no—
358C2×C22⋊C4—342no—
359C2×C22⋊C4—344no—
360C2×C22⋊C4C4×D1712yes—
361C2×C42—21no—
362C2×C42—342no—
363C2×C42—341no—
364C2×C42—684no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—172no—
369C22⋊C8—342no—
370C22⋊C8—342no—
371C22⋊C8—342no—
372C22⋊C8—342no—
373C22⋊C8—341no—
374C22⋊C8—341no—
375C22⋊C8—341no—
376C22⋊C8C4×D1712yescomplemented
377#95—21no—
378#95—342no—
379#95—341no—
380C17#792911yescharacteristic, complemented, Sylow
381C24—171no—
382C24—171no—
383C24—171no—
384C24—171no—
385C24—171no—
386C24—171no—
387C24—342no—
388C24—342no—
389C24—682no—
390C24—682no—
391C24C2×C4×D1711yescharacteristic
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—171no—
398C22×C4—171no—
399C22×C4—171no—
400C22×C4—171no—
401C22×C4—171no—
402C22×C4—171no—
403C22×C4—171no—
404C22×C4—171no—
405C22×C4—171no—
406C22×C4—171no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—171no—
411C22×C4—171no—
412C22×C4—171no—
413C22×C4—171no—
414C22×C4—171no—
415C22×C4—171no—
416C22×C4—344no—
417C22×C4—344no—
418C22×C4—344no—
419C22×C4—348no—
420C22×C4—342no—
421C22×C4—682no—
422C22×C4—682no—
423C22×C4—682no—
424C22×C4—682no—
425C22×C4—682no—
426C22×C4—682no—
427C22×C4—682no—
428C22×C4—682no—
429C22×C4—682no—
430C22×C4—684no—
431C22×C4—684no—
432C22×C4—682no—
433C22×C4C2×C4×D1711yescharacteristic
434C22×C4C2×C4×D1711yescharacteristic
435C22×C4D4×D1711yescharacteristic
436C22×C4D4×D1711yescharacteristic
437C22×C4D4×D1711yescharacteristic
438C22×C4Q8×D1711yescharacteristic
439M16—684no—
440M16—684no—
441M16—684no—
442M16—684no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—42no—
446C2×C8—42no—
447C2×C8—342no—
448C2×C8—342no—
449C2×C8—682no—
450C2×C8—682no—
451C22⋊C4—22no—
452C22⋊C4—174no—
453C22⋊C4—348no—
454C22⋊C4—342no—
455C22⋊C4#6321814yescomplemented
456C42—42no—
457C42—682no—
458C42—684no—
459C23—41no—
460C23—41no—
461C23—171no—
462C23—171no—
463C23—171no—
464C23—171no—
465C23—342no—
466C23—342no—
467C23—342no—
468C23—342no—
469C23—342no—
470C23—342no—
471C23—342no—
472C23—341no—
473C23—341no—
474C23—341no—
475C23—341no—
476C23—342no—
477C23—342no—
478C23—342no—
479C23—681no—
480C23—681no—
481C23—681no—
482C23—681no—
483C23—681no—
484C23—681no—
485C23—688no—
486C23—688no—
487C23C42×D1711yescharacteristic
488C23C22⋊C4×D1711yescharacteristic
489C23C4⋊C4×D1711yescharacteristic
490C23C2×#6321812yes—
491C23M16×D1712yes—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—171no—
502C2×C4—174no—
503C2×C4—171no—
504C2×C4—171no—
505C2×C4—171no—
506C2×C4—342no—
507C2×C4—342no—
508C2×C4—342no—
509C2×C4—342no—
510C2×C4—342no—
511C2×C4—342no—
512C2×C4—342no—
513C2×C4—342no—
514C2×C4—342no—
515C2×C4—342no—
516C2×C4—342no—
517C2×C4—342no—
518C2×C4—344no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—6816no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—682no—
530C2×C4—682no—
531C2×C4C22⋊C4×D1711yescharacteristic
532C2×C4C22⋊C4×D1711yescharacteristic
533C2×C4C4⋊C4×D1711yescharacteristic
534C2×C4C4⋊C4×D1711yescharacteristic
535C8—42no—
536C8—42no—
537C8—682no—
538C8—682no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—42no—
546C22—42no—
547C22—172no—
548C22—172no—
549C22—348no—
550C22—341no—
551C22—341no—
552C22—341no—
553C22—341no—
554C22—341no—
555C22—341no—
556C22—341no—
557C22—341no—
558C22—341no—
559C22—341no—
560C22—682no—
561C22—682no—
562C22—682no—
563C22—682no—
564C22—684no—
565C22—684no—
566C22—684no—
567C22#95×D1711yescharacteristic
568C22C4×#6321811yescharacteristic
569C22#1176276111yescharacteristic
570C22#1176277112yes—
571C22#1176283112yes—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—44no—
576C4—172no—
577C4—341no—
578C4—341no—
579C4—341no—
580C4—684no—
581C4#99×D1712yes—
582C2—22no—
583C2—21no—
584C2—21no—
585C2—22no—
586C2—342no—
587C2—342no—
588C2—681no—
589C2—681no—
590C2#1452847611yescharacteristic
591C2D17×#34211yescharacteristic
592C2D17×#34411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC23×C17C2×C42
FrattiniC23×C4C22×D17
FittingC17×#1282C2
socleC22×C17C2×#95
prime radicalC24×D17C2×C4
cosocleC23×C4×C17C23
hypercenter#1282D17
hypocenterC17#7929
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
4. #14526632C2semidirect
5. #14526631C2semidirect
6. #14526630C2semidirect
7. C17×#1282C2semidirect
10. C22×#63218C4semidirect
19. #11762771C4semidirect
20. #11762771C4semidirect
24. C2×#10587491C4semidirect
51. C22×C8×C17C2×C4semidirect
59. C22×#3622C2×C4semidirect
72. C17×C22⋊C8C2×C4semidirect
79. C22⋊#3622C2×C4semidirect
147. C22⋊C4×C17M16semidirect
150. C22⋊Dic17M16semidirect
249. #1282D17semidirect
355. C22×C8C4×D17semidirect
376. C22⋊C8C4×D17semidirect
380. C17#7929semidirect
455. C22⋊C4#63218semidirect

Maximal subgroups

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

subgroupindex
C2×#117627712
C4×C22⋊C4×D172
#145266322
#145266312
#145266302
C17×#12822
#792917