Finite Group Databasebeta

← #17044591

Subgroups — #17044591

Order 4352.

1266 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D17C211yesmaximal, characteristic
2C2×#11762666C211yesmaximal, characteristic
3D17×#380C211yesmaximal, characteristic
4#14528974C211yesmaximal, characteristic, complemented
5#14528973C212yesmaximal, complemented
6#14528972C211yesmaximal, characteristic, complemented
7#14528971C211yesmaximal, characteristic, complemented
8#14528970C212yesmaximal, complemented
9#14528812C212yesmaximal, complemented
10#14528810C212yesmaximal, complemented
11C17×#1852C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C22×C8×D17C2212yes—
14C22×C4⋊Dic17C2211yescharacteristic
15C2×C4⋊C4×D17C2211yescharacteristic
16C2×C4⋊C4×D17C2211yescharacteristic
17C22×#63227—21no—
18C2×C22⋊C4×D17—21no—
19C2×#10587489C2212yescomplemented
20C2×#10587478C2212yescomplemented
21C2×#10587478C2212yescomplemented
22C2×C22⋊#3622C2211yescharacteristic
23C2×#10587491C2212yes—
24C22⋊C8×D17C418yescomplemented
25#11762669C2211yescharacteristic
26#11762668—21no—
27#11762667—21no—
28#11762666—21no—
29#11762666—21no—
30#11762666C2211yescharacteristic
31#11762666C2212yes—
32#11762666C2211yescharacteristic
33#11762666C2212yes—
34C2×#10587502—21no—
35#95×D17—21no—
36#11762572C2212yescomplemented
37#11762571C2212yescomplemented
38#11762571C2212yescomplemented
39C22×C4⋊C4×C17C2211yescharacteristic
40C2×C17×#107C2212yescomplemented
41C2×C17×C22⋊C8C2211yescharacteristic
42C17×#380C2211yescharacteristic
43C17×#340C2212yescomplemented
44C24×D17D411yescharacteristic
45C23×C4×C17—21no—
46C23×C4×C17C2311yescharacteristic
47C23×Dic17—21no—
48C23×Dic17D411yescharacteristic
49C22×C4×D17—21no—
50C22×C4×D17—21no—
51C22×C4×D17—42no—
52C22×C4×D17—42no—
53C22×C4×D17C2×C414yes—
54C22×C4×D17D411yescharacteristic
55C22×C4×D17D411yescharacteristic
56C22×C4×D17Q814yes—
57C22×C4×D17C2311yescharacteristic
58C22×C4×D17C2311yescharacteristic
59C22×C8×C17C2312yes—
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17—42no—
62C2×C4⋊C4×C17C2312yes—
63C2×C4⋊C4×C17C2311yescharacteristic
64C2×C4⋊C4×C17C2311yescharacteristic
65C2×C22⋊C4×C17—21no—
66C2×C22⋊Dic17—21no—
67C2×#63227—21no—
68C2×#63227—21no—
69C2×#63227—22no—
70C2×#63227—22no—
71C2×#63227—44no—
72C2×C4⋊Dic17—21no—
73C2×C4⋊Dic17—42no—
74C2×C4⋊Dic17C2311yescharacteristic
75C2×C4⋊Dic17C2311yescharacteristic
76C2×C4⋊Dic17C2312yes—
77C2×#63225—21no—
78C2×#63225—21no—
79C22×#3622C2312yes—
80C2×C8×D17—42no—
81C2×C8×D17—42no—
82C2×C8×D17C2×C418yescomplemented
83C4⋊C4×D17—42no—
84C4⋊C4×D17—42no—
85C22⋊C4×D17—44no—
86C17×#107—42no—
87C17×C22⋊C8C2×C414yescomplemented
88C17×#95—21no—
89#10587502—21no—
90#10587502—21no—
91#10587502—21no—
92#10587502—22no—
93#10587502—22no—
94C22⋊#3622C2×C414yescomplemented
95#10587491C2×C418yescomplemented
96#10587489—42no—
97#10587478—42no—
98#10587478—42no—
99C24×C17C2×D411yescharacteristic
100C23×D17—41no—
101C23×D17—41no—
102C23×D17—41no—
103C23×D17—41no—
104C23×D17C4⋊C414yes—
105C23×D17D814yes—
106C23×D17Q1614yes—
107C23×D17C2×D411yescharacteristic
108C23×D17C2×D411yescharacteristic
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—22no—
114C22×C4×C17—42no—
115C22×C4×C17—42no—
116C22×C4×C17—42no—
117C22×C4×C17C22×C412yes—
118C22×C4×C17C2×D411yescharacteristic
119C22×C4×C17C2×Q812yes—
120C22×C4×C17C2411yescharacteristic
121C22×Dic17—21no—
122C22×Dic17—21no—
123C22×Dic17—22no—
124C22×Dic17—41no—
125C22×Dic17—41no—
126C22×Dic17—42no—
127C22×Dic17—42no—
128C22×Dic17—42no—
129C22×Dic17C4⋊C414yes—
130C22×Dic17C2×D411yescharacteristic
131C22×Dic17C2×D411yescharacteristic
132C2×C4×D17—22no—
133C2×C4×D17—22no—
134C2×C4×D17—22no—
135C2×C4×D17—22no—
136C2×C4×D17—48no—
137C2×C4×D17—48no—
138C2×C4×D17—41no—
139C2×C4×D17—41no—
140C2×C4×D17—41no—
141C2×C4×D17—41no—
142C2×C4×D17—42no—
143C2×C4×D17—42no—
144C2×C4×D17—42no—
145C2×C4×D17—42no—
146C2×C4×D17—42no—
147C2×C4×D17—42no—
148C2×C4×D17C4⋊C414yes—
149C2×C4×D17C4⋊C414yes—
150C2×C4×D17C22×C412yes—
151C2×C4×D17C22×C412yes—
152C2×C4×D17C2×Q812yes—
153C2×C4×D17C2×Q812yes—
154C2×C8×C17—22no—
155C2×C8×C17—22no—
156C2×C8×C17C22×C414yes—
157C4⋊C4×C17—22no—
158C4⋊C4×C17—22no—
159C4⋊C4×C17—22no—
160C4⋊C4×C17—22no—
161C4⋊C4×C17—42no—
162C22⋊C4×C17—42no—
163C22⋊Dic17—42no—
164#63227—42no—
165#63227—42no—
166#63227—44no—
167#63227—44no—
168C4⋊Dic17—22no—
169C4⋊Dic17—22no—
170C4⋊Dic17—22no—
171C4⋊Dic17—22no—
172C4⋊Dic17—42no—
173#63225—42no—
174#63225—42no—
175C2×#3622—22no—
176C2×#3622—22no—
177C2×#3622C22×C414yes—
178C8×D17—48no—
179#21940—171nomaximal, Sylow
180C23×C17—21no—
181C23×C17—21no—
182C23×C17—21no—
183C23×C17—21no—
184C23×C17C2×C4⋊C412yes—
185C23×C17C2×D812yes—
186C23×C17C2×Q1612yes—
187C23×C17C22×D411yescharacteristic
188C22×D17—21no—
189C22×D17—21no—
190C22×D17—21no—
191C22×D17—21no—
192C22×D17—21no—
193C22×D17—21no—
194C22×D17—21no—
195C22×D17—21no—
196C22×D17—44no—
197C22×D17—44no—
198C22×D17—44no—
199C22×D17—44no—
200C22×D17—44no—
201C22×D17—44no—
202C22×D17#107116yescomplemented
203C22×D17C2×C4⋊C412yes—
204C22×D17C2×C4⋊C412yes—
205C22×D17C2×D812yes—
206C22×D17C2×D812yes—
207C22×D17C2×Q1612yes—
208C22×D17C2×Q1612yes—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—24no—
212C2×C4×C17—24no—
213C2×C4×C17—42no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—42no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—42no—
222C2×C4×C17—84no—
223C2×C4×C17C2×C4⋊C412yes—
224C2×C4×C17C23×C411yescharacteristic
225C2×C4×C17C22×Q811yescharacteristic
226C2×C4×C17H(5,𝔽2)12yes—
227C2×C4×C17H(5,𝔽2)12yes—
228C2×Dic17—21no—
229C2×Dic17—21no—
230C2×Dic17—21no—
231C2×Dic17—21no—
232C2×Dic17—44no—
233C2×Dic17—41no—
234C2×Dic17—41no—
235C2×Dic17—42no—
236C2×Dic17—41no—
237C2×Dic17—41no—
238C2×Dic17—42no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17—42no—
242C2×Dic17—84no—
243C2×Dic17C2×C4⋊C412yes—
244C2×Dic17C2×C4⋊C412yes—
245C4×D17—24no—
246C4×D17—24no—
247C4×D17—24no—
248C4×D17—24no—
249C4×D17—44no—
250C4×D17—44no—
251C4×D17—84no—
252C4×D17—84no—
253C8×C17—24no—
254#3622—24no—
255C22×C22⋊C8—171no—
256C2×#380—171no—
257C2×#380—171no—
258#1852—172no—
259#1852—171no—
260#1852—171no—
261#1852—172no—
262#1852—171no—
263#1852D1711yescharacteristic, complemented
264#1808—172no—
265#1808—172no—
266C22×C17—22no—
267C22×C17—22no—
268C22×C17—22no—
269C22×C17—22no—
270C22×C17—22no—
271C22×C17—22no—
272C22×C17C2×#10714yes—
273C22×C17C22×C4⋊C411yescharacteristic
274C22×C17#53411yescharacteristic
275C22×C17#53411yescharacteristic
276C22×C17C22×D811yescharacteristic
277C22×C17C22×Q1611yescharacteristic
278C22×C17#57511yescharacteristic
279C22×C17#57511yescharacteristic
280C2×D17—22no—
281C2×D17—22no—
282C2×D17—22no—
283C2×D17—22no—
284C2×D17—22no—
285C2×D17—22no—
286C2×D17—22no—
287C2×D17—22no—
288C2×D17—22no—
289C2×D17—22no—
290C2×D17—22no—
291C2×D17—22no—
292C2×D17—416no—
293C2×D17C2×#10714yes—
294C2×D17C2×#10714yes—
295C4×C17—22no—
296C4×C17—81no—
297C4×C17—81no—
298C4×C17—82no—
299C4×C17#51812yes—
300C4×C17#54312yes—
301Dic17—22no—
302Dic17—22no—
303Dic17—81no—
304Dic17—81no—
305Dic17—82no—
306C24×C4—171no—
307C23×C8—172no—
308C22×C4⋊C4—171no—
309C22×C4⋊C4—171no—
310C22×C4⋊C4—171no—
311C22×C4⋊C4C2×D1711yescharacteristic
312C22×C22⋊C4—341no—
313C22×C22⋊C4—341no—
314C2×#107—172no—
315C2×#107—172no—
316C2×#107—172no—
317C2×#107C2×D1712yescomplemented
318C2×C22⋊C8—171no—
319C2×C22⋊C8—172no—
320C2×C22⋊C8—178no—
321C2×C22⋊C8C2×D1711yescharacteristic
322#380—171no—
323#380—171no—
324#380—171no—
325#380—172no—
326#380—172no—
327#380—341no—
328#380—341no—
329#380—341no—
330#380—341no—
331#380C2×D1711yescharacteristic
332C2×#95—341no—
333C2×#95—341no—
334#340—172no—
335#340—172no—
336#340—172no—
337#340C2×D1712yescomplemented
338C2×C17—24no—
339C2×C17#231511yescharacteristic
340C2×C17C22×#10711yescharacteristic
341C2×C17#291111yescharacteristic
342C2×C17#318611yescharacteristic
343C2×C17#318611yescharacteristic
344C2×C17#318911yescharacteristic
345C2×C17#318911yescharacteristic
346D17—24no—
347D17—24no—
348C25—171no—
349C23×C4—21no—
350C23×C4—171no—
351C23×C4—171no—
352C23×C4—171no—
353C23×C4—174no—
354C23×C4—171no—
355C23×C4—171no—
356C23×C4—174no—
357C23×C4—341no—
358C23×C4—341no—
359C23×C4—341no—
360C23×C4—682no—
361C23×C4—682no—
362C23×C4C22×D1711yescharacteristic
363C22×C8—172no—
364C22×C8—178no—
365C22×C8—682no—
366C22×C8—682no—
367C22×C8C22×D1712yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—171no—
371C2×C4⋊C4—172no—
372C2×C4⋊C4—171no—
373C2×C4⋊C4—341no—
374C2×C4⋊C4—341no—
375C2×C4⋊C4—341no—
376C2×C4⋊C4—682no—
377C2×C4⋊C4—682no—
378C2×C4⋊C4—682no—
379C2×C4⋊C4C22×D1711yescharacteristic
380C2×C4⋊C4C22×D1711yescharacteristic
381C2×C4⋊C4C22×D1712yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—341no—
384C2×C22⋊C4—341no—
385C2×C22⋊C4—342no—
386C2×C22⋊C4—342no—
387C2×C22⋊C4—341no—
388C2×C22⋊C4—684no—
389C2×C22⋊C4—684no—
390#107—42no—
391#107—682no—
392#107—682no—
393#107—682no—
394C22⋊C8—174no—
395C22⋊C8—178no—
396C22⋊C8C4×D1714yescomplemented
397#95—21no—
398#95—341no—
399#95—341no—
400#95—342no—
401#95—342no—
402#95—341no—
403C17#2194011yescharacteristic, complemented, Sylow
404C24—171no—
405C24—171no—
406C24—174no—
407C24—174no—
408C24—174no—
409C24—681no—
410C24—681no—
411C24—681no—
412C24—681no—
413C24D4×D1711yescharacteristic
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—171no—
423C22×C4—171no—
424C22×C4—174no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—172no—
428C22×C4—172no—
429C22×C4—174no—
430C22×C4—174no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—341no—
436C22×C4—341no—
437C22×C4—342no—
438C22×C4—688no—
439C22×C4—688no—
440C22×C4—681no—
441C22×C4—681no—
442C22×C4—681no—
443C22×C4—681no—
444C22×C4—682no—
445C22×C4—682no—
446C22×C4—682no—
447C22×C4—682no—
448C22×C4—682no—
449C22×C4—682no—
450C22×C4—681no—
451C22×C4—681no—
452C22×C4—682no—
453C22×C4—682no—
454C22×C4—682no—
455C22×C4C2×C4×D1712yes—
456C22×C4D4×D1711yescharacteristic
457C22×C4Q8×D1712yes—
458C22×C4C23×D1711yescharacteristic
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—174no—
462C2×C8—342no—
463C2×C8—342no—
464C2×C8—688no—
465C2×C8C2×C4×D1714yes—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—42no—
471C4⋊C4—342no—
472C4⋊C4—342no—
473C4⋊C4—342no—
474C4⋊C4—342no—
475C4⋊C4—682no—
476C4⋊C4—682no—
477C4⋊C4—682no—
478C22⋊C4—42no—
479C22⋊C4—682no—
480C22⋊C4—682no—
481C22⋊C4—684no—
482C22⋊C4—684no—
483C22⋊C4—682no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—172no—
489C23—172no—
490C23—172no—
491C23—172no—
492C23—172no—
493C23—172no—
494C23—1716no—
495C23—341no—
496C23—341no—
497C23—341no—
498C23—341no—
499C23—341no—
500C23—341no—
501C23—341no—
502C23—341no—
503C23—684no—
504C23—684no—
505C23—684no—
506C23—684no—
507C23—684no—
508C23—684no—
509C23C4⋊C4×D1712yes—
510C23D8×D1712yes—
511C23Q16×D1712yes—
512C23C2×D4×D1711yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—84no—
527C2×C4—172no—
528C2×C4—172no—
529C2×C4—341no—
530C2×C4—341no—
531C2×C4—341no—
532C2×C4—341no—
533C2×C4—344no—
534C2×C4—344no—
535C2×C4—344no—
536C2×C4—344no—
537C2×C4—684no—
538C2×C4—684no—
539C2×C4—684no—
540C2×C4—681no—
541C2×C4—682no—
542C2×C4—681no—
543C2×C4—681no—
544C2×C4—681no—
545C2×C4—682no—
546C2×C4—681no—
547C2×C4—682no—
548C2×C4—681no—
549C2×C4—1364no—
550C2×C4—1364no—
551C2×C4—1364no—
552C2×C4C4⋊C4×D1712yes—
553C2×C4C22×C4×D1711yescharacteristic
554C2×C4#1058769112yes—
555C2×C4C2×Q8×D1711yescharacteristic
556C2×C4#1058769612yes—
557C8—24no—
558C8—344no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—174no—
566C22—174no—
567C22—342no—
568C22—342no—
569C22—342no—
570C22—342no—
571C22—342no—
572C22—342no—
573C22—342no—
574C22—342no—
575C22—342no—
576C22—342no—
577C22—342no—
578C22—342no—
579C22—6816no—
580C22#107×D1714yes—
581C22C2×C4⋊C4×D1711yescharacteristic
582C22#1176336911yescharacteristic
583C22#1176337011yescharacteristic
584C22C2×D8×D1711yescharacteristic
585C22C2×Q16×D1711yescharacteristic
586C22#1176360511yescharacteristic
587C22#1176360811yescharacteristic
588C4—22no—
589C4—82no—
590C4—81no—
591C4—81no—
592C4—342no—
593C4—342no—
594C4—1361no—
595C4—1361no—
596C4—1362no—
597C4#1176328112yes—
598C4#1176343412yes—
599C2—24no—
600C2—344no—
601C2—344no—
602C2#1453139511yescharacteristic
603C2C2×#107×D1711yescharacteristic
604C2#1453737111yescharacteristic
605C2#1453953311yescharacteristic
606C2#1453953411yescharacteristic
607C2#1453955711yescharacteristic
608C2#1453955811yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1852C2
socleC23×C17C22×D4
prime radicalC24×D17D4
cosocleC22×C4×C17C24
hypercenter#1852D17
hypocenterC17#21940
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #14528974C2semidirect
5. #14528973C2semidirect
6. #14528972C2semidirect
7. #14528971C2semidirect
8. #14528970C2semidirect
9. #14528812C2semidirect
10. #14528810C2semidirect
11. C17×#1852C2semidirect
19. C2×#10587489C22semidirect
20. C2×#10587478C22semidirect
21. C2×#10587478C22semidirect
24. C22⋊C8×D17C4semidirect
36. #11762572C22semidirect
37. #11762571C22semidirect
38. #11762571C22semidirect
40. C2×C17×#107C22semidirect
43. C17×#340C22semidirect
82. C2×C8×D17C2×C4semidirect
87. C17×C22⋊C8C2×C4semidirect
94. C22⋊#3622C2×C4semidirect
95. #10587491C2×C4semidirect
202. C22×D17#107semidirect
263. #1852D17semidirect
317. C2×#107C2×D17semidirect
337. #340C2×D17semidirect
396. C22⋊C8C4×D17semidirect
403. C17#21940semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D172
C2×#117626662
D17×#3802
#145289742
#145289732
#145289722
#145289712
#145289702
#145288122
#145288102
C17×#18522
#2194017