Finite Group Databasebeta

← #16962255

Subgroups — #16962255

Order 4352.

1750 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762704C212yesmaximal, complemented
2C2×#11762703C212yesmaximal
3C2×#11762681C211yesmaximal, characteristic
4C2×#11762667C212yesmaximal
5#14527048C212yesmaximal, complemented
6#14527035C212yesmaximal, complemented
7#14527029C211yesmaximal, characteristic
8#14527015C212yesmaximal, complemented
9C17×#1439C211yesmaximal, characteristic
10C24×Dic17C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63225C2212yes—
13C22×#63225C2212yes—
14C22×#63225C2212yes—
15C22×#63225C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2211yescharacteristic
18C22×C4×Dic17C2212yes—
19#11762704—28no—
20#11762703—28no—
21#11762681C418yescomplemented
22#11762667—28no—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C22×C4⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2212yes—
32C22×C22⋊C4×C17C2211yescharacteristic
33C2×C17×#95C2212yes—
34C2×C17×#95C2211yescharacteristic
35C25×C17C2311yescharacteristic
36C23×C4×C17C2312yes—
37C23×C4×C17C2311yescharacteristic
38C23×C4×C17C2311yescharacteristic
39C23×C4×C17C2312yes—
40C23×Dic17—24no—
41C23×Dic17—24no—
42C23×Dic17—41no—
43C23×Dic17—41no—
44C23×Dic17C2×C414yes—
45C23×Dic17C2312yes—
46C23×Dic17C2312yes—
47C23×Dic17C2312yes—
48C23×Dic17C2312yes—
49C2×C4⋊C4×C17—24no—
50C2×C4⋊C4×C17—41no—
51C2×C22⋊C4×C17—24no—
52C2×C22⋊C4×C17—24no—
53C2×C22⋊C4×C17—41no—
54C2×C22⋊C4×C17—41no—
55C2×C22⋊C4×C17—42no—
56C2×C22⋊C4×C17C2×C414yes—
57C2×C22⋊Dic17—24no—
58C2×C22⋊Dic17—24no—
59C2×C22⋊Dic17—42no—
60C2×C22⋊Dic17C2×C414yes—
61C2×C22⋊Dic17D414yes—
62C2×C22⋊Dic17Q814yes—
63C2×C4⋊Dic17—41no—
64C2×C4⋊Dic17—42no—
65C2×#63225—24no—
66C2×#63225—24no—
67C2×#63225—24no—
68C2×#63225—24no—
69C2×#63225—24no—
70C2×#63225—24no—
71C2×#63225—24no—
72C2×#63225—24no—
73C2×#63225—42no—
74C2×#63225—42no—
75C2×#63225—42no—
76C2×#63225C2×C418yes—
77C2×C4×Dic17—24no—
78C2×C4×Dic17—24no—
79C2×C4×Dic17—42no—
80C17×#95—42no—
81C17×#95—41no—
82#10587502—24no—
83#10587502—24no—
84#10587502—24no—
85#10587502—24no—
86#10587502—41no—
87#10587502C2×C418yes—
88#10587502D418yes—
89C24×C17—22no—
90C24×C17—22no—
91C24×C17—21no—
92C24×C17—21no—
93C24×C17—22no—
94C24×C17—21no—
95C24×C17—21no—
96C24×C17—22no—
97C24×C17C22×C412yes—
98C24×C17C2×D412yes—
99C24×C17C2×Q812yes—
100C24×C17C2411yescharacteristic
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—21no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—21no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17C22×C412yes—
123C22×C4×C17C22×C412yes—
124C22×C4×C17C2×D414yes—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—22no—
130C22×Dic17—22no—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—216no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—44no—
148C22×Dic17—44no—
149C22×Dic17—48no—
150C22×Dic17—44no—
151C22×Dic17C22×C414yes—
152C22×Dic17C22×C414yes—
153C22×Dic17C2×D414yes—
154C22×Dic17C2×D414yes—
155C22×Dic17C2×D414yes—
156C22×Dic17C2×Q814yes—
157C22×Dic17#4114yes—
158C4⋊C4×C17—44no—
159C22⋊C4×C17—44no—
160C22⋊C4×C17—48no—
161C22⋊Dic17—48no—
162C22⋊Dic17C4⋊C4116yescomplemented
163C4⋊Dic17—44no—
164#63225—216no—
165#63225—48no—
166#63225—48no—
167#63225—48no—
168C4×Dic17—48no—
169#14402—171nomaximal, Sylow
170C23×C17—24no—
171C23×C17—22no—
172C23×C17—22no—
173C23×C17—24no—
174C23×C17—22no—
175C23×C17—22no—
176C23×C17—22no—
177C23×C17—22no—
178C23×C17—24no—
179C23×C17—24no—
180C23×C17—24no—
181C23×C17—24no—
182C23×C17—42no—
183C23×C17—42no—
184C23×C17—42no—
185C23×C17—42no—
186C23×C17—41no—
187C23×C17—42no—
188C23×C17—41no—
189C23×C17—41no—
190C23×C17—42no—
191C23×C17—41no—
192C23×C17C2×C4⋊C414yes—
193C23×C17C23×C411yescharacteristic
194C23×C17C22×D411yescharacteristic
195C23×C17C22×D412yes—
196C23×C17C22×Q811yescharacteristic
197C23×C17C2×#4112yes—
198C23×C17H(5,𝔽2)11yescharacteristic
199C23×C17H(5,𝔽2)11yescharacteristic
200C23×C17H(5,𝔽2)12yes—
201C23×C172−1+411yescharacteristic
202C23×C172−1+411yescharacteristic
203C23×C172−1+412yes—
204C2×C4×C17—24no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—24no—
208C2×C4×C17—24no—
209C2×C4×C17—24no—
210C2×C4×C17—24no—
211C2×C4×C17—42no—
212C2×C4×C17—42no—
213C2×C4×C17—41no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17—41no—
217C2×C4×C17—42no—
218C2×C4×C17—41no—
219C2×C4×C17—42no—
220C2×C4×C17—41no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×Dic17—24no—
229C2×Dic17—24no—
230C2×Dic17—24no—
231C2×Dic17—24no—
232C2×Dic17—24no—
233C2×Dic17—24no—
234C2×Dic17—24no—
235C2×Dic17—24no—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—24no—
239C2×Dic17—24no—
240C2×Dic17—24no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—416no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17C2×C4⋊C418yes—
256C2×Dic17C4×D418yes—
257C2×#389—172no—
258C2×#388—172no—
259C2×#385—171no—
260C2×#380—172no—
261#1444—172no—
262#1441—172no—
263#1439—171no—
264#1439D1711yescharacteristic
265#1436—172no—
266C22×C17—24no—
267C22×C17—28no—
268C22×C17—44no—
269C22×C17—42no—
270C22×C17—42no—
271C22×C17—44no—
272C22×C17—42no—
273C22×C17—42no—
274C22×C17—44no—
275C22×C17—42no—
276C22×C17—42no—
277C22×C17C22×C4⋊C411yescharacteristic
278C22×C17C2×C4×D412yes—
279C22×C17#51811yescharacteristic
280C22×C17#51911yescharacteristic
281C22×C17#52012yes—
282C22×C17#53612yes—
283C22×C17#53711yescharacteristic
284C22×C17#53711yescharacteristic
285C22×C17#53712yes—
286C22×C17#54112yes—
287C22×C17#54212yes—
288C22×C17#54411yescharacteristic
289C22×C17#54411yescharacteristic
290C22×C17D4212yes—
291C22×C17D4211yescharacteristic
292C22×C17#54612yes—
293C22×C17#54712yes—
294C22×C17D4×Q812yes—
295C22×C17#55111yescharacteristic
296C22×C17#55412yes—
297C22×C17#56011yescharacteristic
298C22×C17#56212yes—
299C22×C17#56311yescharacteristic
300C4×C17—42no—
301C4×C17—42no—
302C4×C17—44no—
303C4×C17—82no—
304Dic17—28no—
305Dic17—28no—
306Dic17—44no—
307Dic17—82no—
308C24×C4—171no—
309C22×C4⋊C4—172no—
310C22×C4⋊C4—172no—
311C22×C4⋊C4—172no—
312C22×C4⋊C4—172no—
313C22×C4⋊C4—171no—
314C22×C4⋊C4C2×D1711yescharacteristic
315C22×C22⋊C4—171no—
316C22×C22⋊C4—172no—
317C22×C22⋊C4C2×D1712yes—
318C22×C22⋊C4C2×D1711yescharacteristic
319C22×C42—172no—
320#389—348no—
321#388—348no—
322#385—178no—
323#380—348no—
324C2×#95—172no—
325C2×#95—172no—
326C2×#95—172no—
327C2×#95—172no—
328C2×#95—172no—
329C2×#95—172no—
330C2×#95—171no—
331C2×#95C2×D1712yes—
332C2×#95C2×D1711yescharacteristic
333C2×C17—44no—
334C2×C17#231611yescharacteristic
335C2×C17#232312yes—
336C2×C17D4×C4⋊C412yes—
337C2×C17#235811yescharacteristic
338C2×C17#237611yescharacteristic
339C2×C17#267212yes—
340C2×C17#267511yescharacteristic
341C2×C17#267711yescharacteristic
342C2×C17#270412yes—
343C2×C17#272211yescharacteristic
344C2×C17#274211yescharacteristic
345C25C22×D1711yescharacteristic
346C23×C4—172no—
347C23×C4—172no—
348C23×C4—172no—
349C23×C4—174no—
350C23×C4—172no—
351C23×C4—344no—
352C23×C4—344no—
353C23×C4—681no—
354C23×C4—681no—
355C23×C4C22×D1712yes—
356C23×C4C22×D1711yescharacteristic
357C23×C4C22×D1711yescharacteristic
358C23×C4C22×D1712yes—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—178no—
362C2×C4⋊C4—344no—
363C2×C4⋊C4—344no—
364C2×C4⋊C4—344no—
365C2×C4⋊C4—344no—
366C2×C4⋊C4—344no—
367C2×C4⋊C4—344no—
368C2×C4⋊C4—344no—
369C2×C4⋊C4—344no—
370C2×C4⋊C4—682no—
371C2×C4⋊C4—682no—
372C2×C4⋊C4—682no—
373C2×C4⋊C4—682no—
374C2×C4⋊C4—681no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—174no—
381C2×C22⋊C4—174no—
382C2×C22⋊C4—174no—
383C2×C22⋊C4—344no—
384C2×C22⋊C4—344no—
385C2×C22⋊C4—682no—
386C2×C22⋊C4C4×D1714yes—
387C2×C42—344no—
388C2×C42—344no—
389C2×C42—682no—
390#95—42no—
391#95—41no—
392#95—178no—
393#95—178no—
394#95—344no—
395#95—344no—
396#95—344no—
397#95—344no—
398#95—681no—
399C17#1440211yescharacteristic, complemented, Sylow
400C24—22no—
401C24—22no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—21no—
408C24C2×C4×D1712yes—
409C24D4×D1712yes—
410C24Q8×D1712yes—
411C24C23×D1711yescharacteristic
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—174no—
434C22×C4—174no—
435C22×C4—174no—
436C22×C4—174no—
437C22×C4—174no—
438C22×C4—174no—
439C22×C4—174no—
440C22×C4—3416no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—342no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—684no—
463C22×C4—688no—
464C22×C4—684no—
465C22×C4—684no—
466C22×C4C2×C4×D1712yes—
467C22×C4C2×C4×D1712yes—
468C22×C4D4×D1714yes—
469C4⋊C4—44no—
470C4⋊C4—3416no—
471C4⋊C4—688no—
472C4⋊C4—688no—
473C4⋊C4—688no—
474C4⋊C4—684no—
475C22⋊C4—44no—
476C22⋊C4—48no—
477C22⋊C4—1716no—
478C22⋊C4—688no—
479C42—688no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—22no—
485C23—22no—
486C23—24no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—42no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—41no—
502C23C4⋊C4×D1714yes—
503C23C22×C4×D1711yescharacteristic
504C23C2×D4×D1712yes—
505C23C2×D4×D1711yescharacteristic
506C23#1058769111yescharacteristic
507C23#1058769111yescharacteristic
508C23#1058769112yes—
509C23C2×Q8×D1711yescharacteristic
510C23#41×D1712yes—
511C23#1058769712yes—
512C23#1058769711yescharacteristic
513C23#1058769711yescharacteristic
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—178no—
539C2×C4—178no—
540C2×C4—344no—
541C2×C4—344no—
542C2×C4—344no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—344no—
546C2×C4—344no—
547C2×C4—344no—
548C2×C4—344no—
549C2×C4—344no—
550C2×C4—344no—
551C2×C4—344no—
552C2×C4—344no—
553C2×C4—344no—
554C2×C4—344no—
555C2×C4—6816no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4—682no—
564C2×C4—682no—
565C2×C4—682no—
566C2×C4—682no—
567C22—24no—
568C22—28no—
569C22—42no—
570C22—44no—
571C22—42no—
572C22—44no—
573C22—44no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22C2×C4⋊C4×D1711yescharacteristic
579C22C4×D4×D1712yes—
580C22#1176328211yescharacteristic
581C22#1176328611yescharacteristic
582C22#1176328812yes—
583C22#1176337912yes—
584C22#1176338611yescharacteristic
585C22#1176338612yes—
586C22#1176338611yescharacteristic
587C22#1176341612yes—
588C22#1176342712yes—
589C22#1176343811yescharacteristic
590C22#1176343811yescharacteristic
591C22#1176344112yes—
592C22#1176344111yescharacteristic
593C22#1176345612yes—
594C22#1176345712yes—
595C22#1176347212yes—
596C22#1176348711yescharacteristic
597C22#1176351312yes—
598C22#1176354611yescharacteristic
599C22#1176355412yes—
600C22#1176355911yescharacteristic
601C4—42no—
602C4—44no—
603C4—42no—
604C4—82no—
605C4—348no—
606C4—348no—
607C4—684no—
608C4—1362no—
609C2—44no—
610C2#1453140111yescharacteristic
611C2#1453145912yes—
612C2#1453168212yes—
613C2#1453176711yescharacteristic
614C2#1453193411yescharacteristic
615C2#1453502812yes—
616C2#1453507311yescharacteristic
617C2#1453509311yescharacteristic
618C2#1453543512yes—
619C2#1453568711yescharacteristic
620C2#1453591411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenter#1439D17
hypocenterC17#14402
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#11762704C2semidirect
5. #14527048C2semidirect
6. #14527035C2semidirect
8. #14527015C2semidirect
21. #11762681C4semidirect
162. C22⋊Dic17C4⋊C4semidirect
399. C17#14402semidirect

Maximal subgroups

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

subgroupindex
C2×#117627042
C2×#117627032
C2×#117626812
C2×#117626672
#145270482
#145270352
#145270292
#145270152
C17×#14392
#1440217