Finite Group Databasebeta

← #16965167

Subgroups — #16965167

Order 4352.

1486 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14527052C211yesmaximal, characteristic, complemented
2#14527041C212yesmaximal, complemented
3#14527033C212yesmaximal, complemented
4#14527029C212yesmaximal, complemented
5#14527029C212yesmaximal, complemented
6#14527025C212yesmaximal
7#14527021C212yesmaximal, complemented
8#14527016C211yesmaximal, characteristic, complemented
9C2×C17×#394C211yesmaximal, characteristic
10C22×C4⋊Dic17C2212yes—
11C22×C22⋊Dic17C2212yes—
12C22×C22⋊Dic17C2212yes—
13C22×C22⋊Dic17C2212yes—
14C22×C22⋊Dic17C2212yes—
15C22×C4×Dic17C2211yescharacteristic
16C2×#10587502C2212yes—
17C2×#10587502C2212yes—
18C2×#10587502C2211yescharacteristic
19C2×#10587502C2212yes—
20C2×#10587502C2212yes—
21C2×#10587502C2212yes—
22C2×#10587502C2212yes—
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2212yes—
25C2×#10587502C2211yescharacteristic
26C23×D4×C17C2211yescharacteristic
27C22×C4⋊C4×C17C2211yescharacteristic
28C22×C22⋊C4×C17C2212yes—
29C22×C22⋊C4×C17C2212yes—
30C17×#394C418yescomplemented
31C2×C17×#95C2211yescharacteristic
32C25×C17C2312yes—
33C22×D4×C17—42no—
34C22×D4×C17—42no—
35C22×D4×C17—41no—
36C22×D4×C17—41no—
37C22×D4×C17C2×C414yes—
38C23×C4×C17C2311yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×Dic17C2312yes—
43C23×Dic17C2312yes—
44C23×Dic17C2312yes—
45C23×Dic17C2312yes—
46C2×C4⋊C4×C17—41no—
47C2×C4⋊C4×C17—41no—
48C2×C4⋊C4×C17C2×C414yes—
49C2×C22⋊C4×C17—42no—
50C2×C22⋊C4×C17—42no—
51C2×C22⋊C4×C17—42no—
52C2×C22⋊C4×C17—42no—
53C2×C22⋊C4×C17C2×C418yes—
54C2×C22⋊C4×C17C2×C418yes—
55C2×C22⋊Dic17—24no—
56C2×C22⋊Dic17—24no—
57C2×C22⋊Dic17—42no—
58C2×C22⋊Dic17—42no—
59C2×C22⋊Dic17—42no—
60C2×C22⋊Dic17—42no—
61C2×C22⋊Dic17—42no—
62C2×C22⋊Dic17—42no—
63C2×C22⋊Dic17—42no—
64C2×C22⋊Dic17—42no—
65C2×C22⋊Dic17—42no—
66C2×C22⋊Dic17—42no—
67C2×C4⋊Dic17—42no—
68C2×C4⋊Dic17—42no—
69C2×C4⋊Dic17—42no—
70C2×C4×Dic17—42no—
71C2×C4×Dic17—41no—
72C17×#95C2×C414yes—
73#10587502—24no—
74#10587502—42no—
75#10587502—42no—
76#10587502—42no—
77#10587502—42no—
78#10587502—42no—
79#10587502—42no—
80#10587502—41no—
81#10587502—41no—
82#10587502—41no—
83C24×C17—22no—
84C24×C17—22no—
85C24×C17—22no—
86C24×C17—22no—
87C24×C17—22no—
88C24×C17—22no—
89C24×C17—22no—
90C24×C17—22no—
91C24×C17—22no—
92C24×C17—22no—
93C24×C17—22no—
94C24×C17—22no—
95C24×C17—22no—
96C24×C17—22no—
97C24×C17C22×C414yes—
98C24×C17C2411yescharacteristic
99C2×D4×C17—44no—
100C2×D4×C17—48no—
101C2×D4×C17—48no—
102C2×D4×C17—44no—
103C2×D4×C17—44no—
104C22×C4×C17—22no—
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—21no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—22no—
117C22×C4×C17—21no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17C22×C412yes—
123C22×C4×C17C22×C414yes—
124C22×C4×C17C22×C412yes—
125C22×C4×C17C22×C412yes—
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—22no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17#4114yes—
154C4⋊C4×C17—44no—
155C22⋊C4×C17—48no—
156C22⋊C4×C17—48no—
157C22⋊Dic17—48no—
158C22⋊Dic17—48no—
159C22⋊Dic17—48no—
160C22⋊Dic17—48no—
161C4⋊Dic17—48no—
162C4×Dic17—44no—
163#14641—171nomaximal, Sylow
164C23×C17—24no—
165C23×C17—24no—
166C23×C17—24no—
167C23×C17—24no—
168C23×C17—24no—
169C23×C17—24no—
170C23×C17—24no—
171C23×C17—42no—
172C23×C17—42no—
173C23×C17—42no—
174C23×C17—42no—
175C23×C17—42no—
176C23×C17—42no—
177C23×C17—42no—
178C23×C17—42no—
179C23×C17—42no—
180C23×C17—42no—
181C23×C17—42no—
182C23×C17—42no—
183C23×C17—42no—
184C23×C17—42no—
185C23×C17—42no—
186C23×C17—42no—
187C23×C17—42no—
188C23×C17—42no—
189C23×C17—42no—
190C23×C17—42no—
191C23×C17—42no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—42no—
197C23×C17—42no—
198C23×C17—42no—
199C23×C17C23×C411yescharacteristic
200C23×C17C2×#4112yes—
201C23×C17H(5,𝔽2)11yescharacteristic
202C23×C17H(5,𝔽2)12yes—
203C23×C17H(5,𝔽2)12yes—
204C23×C17H(5,𝔽2)11yescharacteristic
205C23×C17H(5,𝔽2)12yes—
206C23×C17H(5,𝔽2)12yes—
207C23×C172−1+412yes—
208D4×C17—416no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—24no—
212C2×C4×C17—24no—
213C2×C4×C17—24no—
214C2×C4×C17—22no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—42no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—41no—
224C2×C4×C17—42no—
225C2×C4×C17—41no—
226C2×C4×C17—42no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×Dic17—24no—
232C2×Dic17—24no—
233C2×Dic17—24no—
234C2×Dic17—42no—
235C2×Dic17—42no—
236C2×Dic17—42no—
237C2×Dic17—42no—
238C2×Dic17—42no—
239C2×Dic17—42no—
240C2×Dic17—42no—
241C2×Dic17—42no—
242C2×Dic17—42no—
243C2×Dic17—42no—
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×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×#394D1711yescharacteristic
260#1445—171no—
261#1442—172no—
262#1440—172no—
263#1439—172no—
264#1439—172no—
265#1438—172no—
266#1437—172no—
267#1436—171no—
268C22×C17—44no—
269C22×C17—44no—
270C22×C17—44no—
271C22×C17—44no—
272C22×C17—44no—
273C22×C17—44no—
274C22×C17—44no—
275C22×C17—82no—
276C22×C17—82no—
277C22×C17—82no—
278C22×C17—82no—
279C22×C17—82no—
280C22×C17—82no—
281C22×C17—82no—
282C22×C17—82no—
283C22×C17C4×#4111yescharacteristic
284C22×C17#51811yescharacteristic
285C22×C17#51811yescharacteristic
286C22×C17#51812yes—
287C22×C17#52012yes—
288C22×C17#53812yes—
289C22×C17#53812yes—
290C22×C17#53912yes—
291C22×C17#54012yes—
292C22×C17#54012yes—
293C22×C17#54212yes—
294C22×C17#56012yes—
295C22×C17#56012yes—
296C22×C17#56012yes—
297C22×C17#56011yescharacteristic
298C22×C17H(3,𝔽4)11yescharacteristic
299C22×C17H(3,𝔽4)11yescharacteristic
300C22×C17#56212yes—
301C22×C17#56212yes—
302C22×C17#56212yes—
303C22×C17#56311yescharacteristic
304C4×C17—42no—
305C4×C17—42no—
306C4×C17—42no—
307C4×C17—44no—
308Dic17—44no—
309Dic17—82no—
310Dic17—82no—
311Dic17—82no—
312C23×D4C2×D1711yescharacteristic
313C22×C4⋊C4—172no—
314C22×C4⋊C4C2×D1711yescharacteristic
315C22×C22⋊C4—172no—
316C22×C22⋊C4—172no—
317C22×C22⋊C4—172no—
318C22×C22⋊C4—172no—
319C22×C22⋊C4C2×D1712yes—
320C22×C22⋊C4C2×D1712yes—
321C22×C42—171no—
322#394Dic1718yescomplemented
323C2×#95—172no—
324C2×#95—172no—
325C2×#95—171no—
326C2×#95—172no—
327C2×#95—172no—
328C2×#95—172no—
329C2×#95—172no—
330C2×#95—171no—
331C2×#95—172no—
332C2×#95—171no—
333C2×#95C2×D1711yescharacteristic
334C2×C17—84no—
335C2×C17#233311yescharacteristic
336C2×C17#233512yes—
337C2×C17#237511yescharacteristic
338C2×C17#237712yes—
339C2×C17#237911yescharacteristic
340C2×C17#282412yes—
341C2×C17#282812yes—
342C2×C17#282912yes—
343C2×C17#283712yes—
344C25C22×D1712yes—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4C2×Dic1714yes—
350C23×C4—172no—
351C23×C4—172no—
352C23×C4—172no—
353C23×C4—172no—
354C23×C4C22×D1712yes—
355C23×C4C22×D1711yescharacteristic
356C23×C4C22×D1711yescharacteristic
357C23×C4C22×D1711yescharacteristic
358C2×C4⋊C4—41no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—682no—
361C2×C4⋊C4—682no—
362C2×C4⋊C4—682no—
363C2×C4⋊C4C2×Dic1714yes—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—344no—
369C2×C22⋊C4—344no—
370C2×C22⋊C4—682no—
371C2×C22⋊C4—682no—
372C2×C22⋊C4—682no—
373C2×C22⋊C4—682no—
374C2×C22⋊C4—682no—
375C2×C22⋊C4—682no—
376C2×C22⋊C4—682no—
377C2×C22⋊C4—682no—
378C2×C22⋊C4—682no—
379C2×C22⋊C4—682no—
380C2×C22⋊C4C2×Dic1718yes—
381C2×C22⋊C4C2×Dic1718yes—
382C2×C42—682no—
383C2×C42—681no—
384#95—344no—
385#95—682no—
386#95—682no—
387#95—682no—
388#95—681no—
389#95—681no—
390#95—681no—
391#95—682no—
392#95—682no—
393#95—682no—
394#95C2×Dic1714yes—
395C17#1464111yescharacteristic, complemented, Sylow
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24C22×Dic1714yes—
411C24C23×D1711yescharacteristic
412C2×D4—44no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—44no—
416C2×D4—44no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—174no—
436C22×C4—342no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—342no—
440C22×C4—342no—
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—342no—
463C22×C4C22×Dic1714yes—
464C22×C4C22×Dic1712yes—
465C22×C4C22×Dic1712yes—
466C22×C4C22×Dic1712yes—
467C4⋊C4—44no—
468C4⋊C4—688no—
469C22⋊C4—48no—
470C22⋊C4—48no—
471C22⋊C4—688no—
472C22⋊C4—688no—
473C22⋊C4—688no—
474C22⋊C4—688no—
475C42—684no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#1058769112yes—
512C23#1058769112yes—
513C23#1058769112yes—
514C23#1058769111yescharacteristic
515C23#1058769111yescharacteristic
516C23#41×D1712yes—
517C23#1058769612yes—
518C23#1058769712yes—
519C23C23×Dic1711yescharacteristic
520D4—416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—344no—
546C2×C4—682no—
547C2×C4—682no—
548C2×C4—682no—
549C2×C4—682no—
550C2×C4—682no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
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—
567C2×C4—682no—
568C2×C4—682no—
569C2×C4—682no—
570C2×C4—682no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#41×Dic1711yescharacteristic
587C22#1176328412yes—
588C22#1176328411yescharacteristic
589C22#1176328411yescharacteristic
590C22#1176329212yes—
591C22#1176339112yes—
592C22#1176339512yes—
593C22#1176340212yes—
594C22#1176340912yes—
595C22#1176341112yes—
596C22#1176342712yes—
597C22#1176354712yes—
598C22#1176354712yes—
599C22#1176354812yes—
600C22#1176354811yescharacteristic
601C22#1176355111yescharacteristic
602C22#1176355211yescharacteristic
603C22#1176355312yes—
604C22#1176355412yes—
605C22#1176355412yes—
606C22#1176355911yescharacteristic
607C4—42no—
608C4—42no—
609C4—44no—
610C4—42no—
611C4—684no—
612C4—1362no—
613C4—1362no—
614C4—1362no—
615C2—84no—
616C2#1453155111yescharacteristic
617C2#1453157812yes—
618C2#1453192511yescharacteristic
619C2#1453194112yes—
620C2#1453195811yescharacteristic
621C2#1453686012yes—
622C2#1453690012yes—
623C2#1453691712yes—
624C2#1453699112yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#394C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#394D17
hypocenterC17#14641
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #14527052C2semidirect
2. #14527041C2semidirect
3. #14527033C2semidirect
4. #14527029C2semidirect
5. #14527029C2semidirect
7. #14527021C2semidirect
8. #14527016C2semidirect
30. C17×#394C4semidirect
322. #394Dic17semidirect
395. C17#14641semidirect

Maximal subgroups

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

subgroupindex
#145270522
#145270412
#145270332
#145270292
#145270252
#145270212
#145270162
C2×C17×#3942
#1464117