Finite Group Databasebeta

← #16963503

Subgroups — #16963503

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587621C211yesmaximal, characteristic
2C2×#11762703C212yesmaximal, complemented
3#14527050C212yesmaximal, complemented
4#14527027C212yesmaximal, complemented
5#14527025C211yesmaximal, characteristic
6#14527021C212yesmaximal, complemented
7#14527012C212yesmaximal, complemented
8#14527006C212yesmaximal, complemented
9C17×#1438C211yesmaximal, characteristic
10C24×Dic17C2211yescharacteristic
11C2×#10587621—28no—
12C2×#10587621C418yescomplemented
13C22×#63225C2212yes—
14C22×#63225C2212yes—
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C22⋊Dic17C2212yes—
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C4×Dic17C2212yes—
21#11762703—28no—
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C23×D4×C17C2211yescharacteristic
30C22×C22⋊C4×C17C2212yes—
31C22×C22⋊C4×C17C2212yes—
32C2×C17×#95C2211yescharacteristic
33C2×C17×#95C2211yescharacteristic
34C25×C17C2311yescharacteristic
35C25×C17C2311yescharacteristic
36C22×D4×C17—24no—
37C22×D4×C17—42no—
38C22×D4×C17—41no—
39C22×D4×C17—41no—
40C22×D4×C17C2×C414yes—
41C23×C4×C17C2312yes—
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×Dic17—24no—
45C23×Dic17—42no—
46C23×Dic17—41no—
47C23×Dic17—41no—
48C23×Dic17C2×C414yes—
49C23×Dic17C2312yes—
50C23×Dic17C2312yes—
51C23×Dic17C2312yes—
52C23×Dic17C2312yes—
53C2×C22⋊C4×C17—24no—
54C2×C22⋊C4×C17—24no—
55C2×C22⋊C4×C17—24no—
56C2×C22⋊C4×C17—42no—
57C2×C22⋊C4×C17—42no—
58C2×C22⋊C4×C17—42no—
59C2×C22⋊Dic17—24no—
60C2×C22⋊Dic17—24no—
61C2×C22⋊Dic17—24no—
62C2×C22⋊Dic17—24no—
63C2×C22⋊Dic17—24no—
64C2×C22⋊Dic17—41no—
65C2×C22⋊Dic17—42no—
66C2×C22⋊Dic17—41no—
67C2×C22⋊Dic17—42no—
68C2×C22⋊Dic17C2×C418yes—
69C2×C22⋊Dic17C2×C414yes—
70C2×C22⋊Dic17D418yes—
71#10587621—232no—
72C2×#63225—24no—
73C2×#63225—24no—
74C2×#63225—24no—
75C2×#63225—24no—
76C2×#63225—42no—
77C2×#63225C2×C418yes—
78C2×C4×Dic17—24no—
79C2×C4×Dic17—24no—
80C2×C4×Dic17—42no—
81C17×#95—41no—
82C17×#95—41no—
83#10587502—24no—
84#10587502—24no—
85#10587502—42no—
86#10587502—42no—
87#10587502—42no—
88#10587502—42no—
89#10587502—42no—
90C24×C17—22no—
91C24×C17—22no—
92C24×C17—22no—
93C24×C17—21no—
94C24×C17—21no—
95C24×C17—22no—
96C24×C17—22no—
97C24×C17—22no—
98C24×C17—22no—
99C24×C17—22no—
100C24×C17—21no—
101C24×C17—21no—
102C24×C17—22no—
103C24×C17—22no—
104C24×C17—22no—
105C24×C17C22×C412yes—
106C24×C17C22×C412yes—
107C24×C17C2×D414yes—
108C24×C17C2411yescharacteristic
109C2×D4×C17—28no—
110C2×D4×C17—44no—
111C2×D4×C17—44no—
112C2×D4×C17—48no—
113C2×D4×C17—48no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—22no—
131C22×C4×C17C22×C412yes—
132C22×C4×C17#4114yes—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—28no—
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—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—44no—
158C22×Dic17—44no—
159C22×Dic17—48no—
160C22×Dic17—48no—
161C22×Dic17C22×C414yes—
162C22×Dic17C22×C414yes—
163C22×Dic17C2×D414yes—
164C22×Dic17C2×D414yes—
165C22×Dic17#4114yes—
166C22⋊C4×C17—48no—
167C22⋊C4×C17—48no—
168C22⋊Dic17—216no—
169C22⋊Dic17—44no—
170C22⋊Dic17—48no—
171C22⋊Dic17—44no—
172C22⋊Dic17C22⋊C4116yescomplemented
173#63225—216no—
174#63225—48no—
175C4×Dic17—48no—
176#14506—171nomaximal, Sylow
177C23×C17—24no—
178C23×C17—22no—
179C23×C17—22no—
180C23×C17—24no—
181C23×C17—24no—
182C23×C17—24no—
183C23×C17—24no—
184C23×C17—24no—
185C23×C17—24no—
186C23×C17—24no—
187C23×C17—22no—
188C23×C17—24no—
189C23×C17—22no—
190C23×C17—22no—
191C23×C17—24no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—41no—
197C23×C17—42no—
198C23×C17—41no—
199C23×C17—41no—
200C23×C17—42no—
201C23×C17—41no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17—42no—
205C23×C17—42no—
206C23×C17—42no—
207C23×C17—42no—
208C23×C17—42no—
209C23×C17—42no—
210C23×C17—42no—
211C23×C17—42no—
212C23×C17—41no—
213C23×C17—42no—
214C23×C17—41no—
215C23×C17—41no—
216C23×C17—42no—
217C23×C17—41no—
218C23×C17C2×C22⋊C414yes—
219C23×C17C23×C411yescharacteristic
220C23×C17C22×D412yes—
221C23×C17C2×#4112yes—
222C23×C17C2×#4112yes—
223C23×C17H(5,𝔽2)12yes—
224C23×C17H(5,𝔽2)11yescharacteristic
225C23×C17H(5,𝔽2)11yescharacteristic
226C23×C17H(5,𝔽2)12yes—
227C23×C172−1+412yes—
228D4×C17—416no—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—24no—
233C2×C4×C17—24no—
234C2×C4×C17—24no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—42no—
240C2×C4×C17—42no—
241C2×C4×C17—42no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—42no—
245C2×C4×C17—42no—
246C2×C4×C17—42no—
247C2×C4×C17—42no—
248C2×Dic17—24no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—24no—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—24no—
255C2×Dic17—24no—
256C2×Dic17—24no—
257C2×Dic17—24no—
258C2×Dic17—24no—
259C2×Dic17—24no—
260C2×Dic17—416no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—42no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—42no—
275C2×Dic17—42no—
276C2×Dic17C2×C22⋊C418yes—
277C22×#123—171no—
278C2×#388—172no—
279#1445—172no—
280#1439—172no—
281#1438—171no—
282#1438D1711yescharacteristic
283#1437—172no—
284C4⋊#95—172no—
285C22⋊#95—172no—
286C22×C17—24no—
287C22×C17—28no—
288C22×C17—44no—
289C22×C17—42no—
290C22×C17—42no—
291C22×C17—44no—
292C22×C17—44no—
293C22×C17—44no—
294C22×C17—44no—
295C22×C17—42no—
296C22×C17—44no—
297C22×C17—44no—
298C22×C17—42no—
299C22×C17—42no—
300C22×C17—82no—
301C22×C17—82no—
302C22×C17—82no—
303C22×C17—82no—
304C22×C17C22×C22⋊C411yescharacteristic
305C22×C17C4×#4112yes—
306C22×C17#51811yescharacteristic
307C22×C17#51811yescharacteristic
308C22×C17#52012yes—
309C22×C17#53512yes—
310C22×C17#53512yes—
311C22×C17#53812yes—
312C22×C17#53912yes—
313C22×C17#54012yes—
314C22×C17#54212yes—
315C22×C17#54612yes—
316C22×C17#54612yes—
317C22×C17#54712yes—
318C22×C17#54712yes—
319C22×C17#55111yescharacteristic
320C22×C17#55312yes—
321C22×C17#55911yescharacteristic
322C22×C17#56011yescharacteristic
323C22×C17#56212yes—
324C22×C17#56311yescharacteristic
325C4×C17—42no—
326C4×C17—44no—
327C4×C17—82no—
328Dic17—28no—
329Dic17—44no—
330Dic17—44no—
331Dic17—82no—
332C23×D4C2×D1711yescharacteristic
333C24×C4—171no—
334C2×#123—178no—
335C2×#123—348no—
336C22×C4⋊C4—172no—
337C22×C4⋊C4—172no—
338C22×C22⋊C4—171no—
339C22×C22⋊C4—172no—
340C22×C22⋊C4—172no—
341C22×C22⋊C4—171no—
342C22×C22⋊C4—171no—
343C22×C22⋊C4C2×D1712yes—
344C22×C22⋊C4C2×D1712yes—
345C22×C42—172no—
346#388—348no—
347C2×#95—172no—
348C2×#95—172no—
349C2×#95—172no—
350C2×#95—172no—
351C2×#95—172no—
352C2×#95—172no—
353C2×#95—172no—
354C2×#95C2×D1711yescharacteristic
355C2×#95C2×D1711yescharacteristic
356C2×C17—44no—
357C2×C17—82no—
358C2×C17#230911yescharacteristic
359C2×C17#233512yes—
360C2×C17#233912yes—
361C2×C17#237411yescharacteristic
362C2×C17#237611yescharacteristic
363C2×C17#270312yes—
364C2×C17#270612yes—
365C2×C17#271012yes—
366C2×C17#271812yes—
367C25C22×D1711yescharacteristic
368C25C22×D1711yescharacteristic
369C22×D4—24no—
370C22×D4—41no—
371C22×D4—41no—
372C22×D4—42no—
373C22×D4C4×D1714yes—
374C23×C4—172no—
375C23×C4—172no—
376C23×C4—172no—
377C23×C4—174no—
378C23×C4—172no—
379C23×C4—344no—
380C23×C4—681no—
381C23×C4—681no—
382C23×C4—682no—
383C23×C4C22×D1712yes—
384C23×C4C22×D1711yescharacteristic
385C23×C4C22×D1712yes—
386#123—3432no—
387C2×C4⋊C4—178no—
388C2×C4⋊C4—344no—
389C2×C4⋊C4—344no—
390C2×C4⋊C4—344no—
391C2×C4⋊C4—344no—
392C2×C4⋊C4—682no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—174no—
400C2×C22⋊C4—178no—
401C2×C22⋊C4—178no—
402C2×C22⋊C4—344no—
403C2×C22⋊C4—344no—
404C2×C22⋊C4—344no—
405C2×C22⋊C4—344no—
406C2×C22⋊C4—344no—
407C2×C22⋊C4—681no—
408C2×C22⋊C4—682no—
409C2×C22⋊C4—681no—
410C2×C22⋊C4—682no—
411C2×C42—344no—
412C2×C42—344no—
413C2×C42—682no—
414#95—41no—
415#95—41no—
416#95—344no—
417#95—344no—
418#95—682no—
419#95—682no—
420#95—682no—
421#95—682no—
422#95—682no—
423C17#1450611yescharacteristic, complemented, Sylow
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24C2×C4×D1712yes—
440C24C2×C4×D1712yes—
441C24D4×D1714yes—
442C24C23×D1711yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—174no—
466C22×C4—174no—
467C22×C4—174no—
468C22×C4—174no—
469C22×C4—174no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4—348no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—684no—
495C22×C4—684no—
496C22×C4—688no—
497C22×C4—688no—
498C22×C4C2×C4×D1712yes—
499C22×C4#6325414yes—
500C4⋊C4—3416no—
501C4⋊C4—688no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—1716no—
505C22⋊C4—3416no—
506C22⋊C4—684no—
507C22⋊C4—688no—
508C22⋊C4—684no—
509C42—688no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—41no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23C22⋊C4×D1714yes—
552C23C22×C4×D1711yescharacteristic
553C23C2×D4×D1712yes—
554C23C2×#6325412yes—
555C23#1058769111yescharacteristic
556C23#1058769111yescharacteristic
557C23#1058769112yes—
558C23#1058769112yes—
559C23#41×D1712yes—
560C23#1058769712yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—178no—
582C2×C4—344no—
583C2×C4—344no—
584C2×C4—344no—
585C2×C4—344no—
586C2×C4—344no—
587C2×C4—344no—
588C2×C4—344no—
589C2×C4—344no—
590C2×C4—344no—
591C2×C4—344no—
592C2×C4—344no—
593C2×C4—344no—
594C2×C4—6816no—
595C2×C4—682no—
596C2×C4—682no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—682no—
600C2×C4—682no—
601C2×C4—682no—
602C2×C4—682no—
603C2×C4—682no—
604C2×C4—682no—
605C2×C4—682no—
606C2×C4—682no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4—682no—
610C22—28no—
611C22—24no—
612C22—44no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—44no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C2×C22⋊C4×D1711yescharacteristic
629C22C4×#6325412yes—
630C22#1176328211yescharacteristic
631C22#1176328211yescharacteristic
632C22#1176328812yes—
633C22#1176337412yes—
634C22#1176337412yes—
635C22#1176339412yes—
636C22#1176340212yes—
637C22#1176340912yes—
638C22#1176342612yes—
639C22#1176344612yes—
640C22#1176344812yes—
641C22#1176345712yes—
642C22#1176345912yes—
643C22#1176348911yescharacteristic
644C22#1176350212yes—
645C22#1176354511yescharacteristic
646C22#1176354611yescharacteristic
647C22#1176355412yes—
648C22#1176355911yescharacteristic
649C4—44no—
650C4—42no—
651C4—82no—
652C4—348no—
653C4—684no—
654C4—684no—
655C4—1362no—
656C2—44no—
657C2—82no—
658C2#1453136511yescharacteristic
659C2#1453157512yes—
660C2#1453161012yes—
661C2#1453191911yescharacteristic
662C2#1453193411yescharacteristic
663C2#1453543212yes—
664C2#1453547712yes—
665C2#1453552812yes—
666C2#1453563612yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1438C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenter#1438D17
hypocenterC17#14506
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#11762703C2semidirect
3. #14527050C2semidirect
4. #14527027C2semidirect
6. #14527021C2semidirect
7. #14527012C2semidirect
8. #14527006C2semidirect
12. C2×#10587621C4semidirect
172. C22⋊Dic17C22⋊C4semidirect
423. C17#14506semidirect

Maximal subgroups

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

subgroupindex
C22×#105876212
C2×#117627032
#145270502
#145270272
#145270252
#145270212
#145270122
#145270062
C17×#14382
#1450617