Finite Group Databasebeta

← C2×#14529967 #17061773

Subgroups — C2×#14529967 #17061773

Order 4352.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587616C211yesmaximal, characteristic
2C22×#10587489C211yesmaximal, characteristic, complemented
3C22×#10587492C211yesmaximal, characteristic, complemented
4C22×#10587492C211yesmaximal, characteristic, complemented
5C2×#11762669C211yesmaximal, characteristic, complemented
6#14529967C218yesmaximal, direct product factor
7C2×#11762572C211yesmaximal, characteristic, complemented
8C22×C17×C22⋊C8C211yesmaximal, characteristic, complemented
9C23×D68C2211yescharacteristic
10C23×C22⋊D17—21no—
11C2×#10587616—24no—
12C2×#10587616—22no—
13C2×#10587616—24no—
14C2×#10587616C2214yes—
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17—21no—
19C22×#63227—21no—
20C2×#10587489—24no—
21C2×#10587489C2214yescomplemented
22C2×#10587492—24no—
23C2×#10587492—24no—
24C2×#10587492C2214yescomplemented
25C2×#10587492C2214yescomplemented
26#11762669—22no—
27#11762669C2214yescomplemented
28C2×#10587502—21no—
29#11762572C2214yescomplemented
30C24×C4×C17C2211yescharacteristic
31C23×C8×C17C2211yescharacteristic
32C23×C8×C17C2211yescharacteristic
33C2×C17×C22⋊C8—24no—
34C2×C17×C22⋊C8C2214yescomplemented
35C25×C17D411yescharacteristic
36C24×D17—21no—
37C23×C4×C17—22no—
38C23×C4×C17—22no—
39C23×C4×C17—22no—
40C23×C4×C17—22no—
41C23×C4×C17—22no—
42C23×C4×C17—22no—
43C23×C4×C17D411yescharacteristic
44C23×C4×C17D412yes—
45C23×C4×C17C2312yes—
46C23×C4×C17C2311yescharacteristic
47C22×C22⋊D17—28no—
48C22×C22⋊D17—24no—
49C22×C22⋊D17—44no—
50C22×C22⋊D17—44no—
51C23×Dic17—21no—
52C23×Dic17—21no—
53C23×Dic17—21no—
54C22×D68—22no—
55C22×D68—22no—
56C22×D68—22no—
57C22×D68—22no—
58C22×D68—21no—
59C22×D68—22no—
60C22×D68D414yes—
61C22×D68C2312yes—
62C22×C8×C17—22no—
63C22×C8×C17—22no—
64C22×C8×C17—22no—
65C22×C8×C17—22no—
66C22×C8×C17—22no—
67C22×C8×C17D414yescomplemented
68C22×C8×C17C2312yes—
69C22×C8×C17C2312yes—
70C2×C22⋊Dic17—24no—
71C2×C22⋊Dic17—44no—
72#10587616—216no—
73#10587616—28no—
74#10587616—28no—
75C2×#63227—28no—
76C2×#63227—24no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17D414yes—
86C2×C4⋊Dic17C2312yes—
87C2×C4⋊Dic17C2312yes—
88C2×C4⋊Dic17C2312yes—
89C17×C22⋊C8—28no—
90#10587502—24no—
91#10587492—28no—
92#10587492—28no—
93#10587489—28no—
94C24×C17—22no—
95C24×C17—22no—
96C24×C17—22no—
97C24×C17—22no—
98C24×C17—22no—
99C24×C17—22no—
100C24×C17D814yes—
101C24×C17C2×D412yes—
102C24×C17C2×D411yescharacteristic
103C23×D17—24no—
104C23×D17—22no—
105C23×D17—42no—
106C23×D17—42no—
107C23×D17—42no—
108C23×D17—42no—
109C23×D17—42no—
110C23×D17—42no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—24no—
115C22×C4×C17—24no—
116C22×C4×C17—24no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—44no—
124C22×C4×C17—44no—
125C22×C4×C17—44no—
126C22×C4×C17—44no—
127C22×C4×C17C2×D412yes—
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17C2×D412yes—
130C22×C4×C17C2×D412yes—
131C22×C4×C17C2×D412yes—
132C22×C4×C17#4112yes—
133C22×C4×C17#4112yes—
134C22×C4×C17#4112yes—
135C22×C4×C17C2411yescharacteristic
136C2×C22⋊D17—216no—
137C2×C22⋊D17—48no—
138C2×C22⋊D17—432no—
139C2×C22⋊D17—48no—
140C22×Dic17—24no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—42no—
145C22×Dic17—42no—
146C22×Dic17—42no—
147C22×Dic17—42no—
148C22×Dic17—42no—
149C22×Dic17—42no—
150C22×Dic17—42no—
151C22×Dic17—42no—
152C2×D68—28no—
153C2×D68—28no—
154C2×D68—22no—
155C2×D68—22no—
156C2×D68—22no—
157C2×D68—22no—
158C2×D68—24no—
159C2×D68—22no—
160C2×D68—42no—
161C2×D68—44no—
162C2×D68—42no—
163C2×D68—44no—
164C2×D68C2×D414yes—
165C2×C8×C17—28no—
166C2×C8×C17—22no—
167C2×C8×C17—22no—
168C2×C8×C17—22no—
169C2×C8×C17—22no—
170C2×C8×C17—22no—
171C2×C8×C17—44no—
172C2×C8×C17C2×D414yescomplemented
173C22⋊Dic17—48no—
174#63227—216no—
175C4⋊Dic17—24no—
176C4⋊Dic17—22no—
177C4⋊Dic17—22no—
178C4⋊Dic17—22no—
179C4⋊Dic17—22no—
180C4⋊Dic17—22no—
181C4⋊Dic17—42no—
182C4⋊Dic17—42no—
183C4⋊Dic17C2×D414yes—
184C2×#2033—171nomaximal, Sylow
185C23×C17—22no—
186C23×C17—22no—
187C23×C17—22no—
188C23×C17—22no—
189C23×C17—22no—
190C23×C17—22no—
191C23×C17—28no—
192C23×C17—28no—
193C23×C17—28no—
194C23×C17—44no—
195C23×C17—44no—
196C23×C17—44no—
197C23×C17—44no—
198C23×C17#12012yes—
199C23×C17#12112yes—
200C23×C17#12312yes—
201C23×C17C2×D814yes—
202C23×C17C2×D812yes—
203C23×C17#13512yes—
204C23×C17AGL(1,ℤ/8)12yes—
205C23×C17#13712yes—
206C23×C17C22×D411yescharacteristic
207C22×D17—24no—
208C22×D17—42no—
209C22×D17—42no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—42no—
213C22×D17—42no—
214C22×D17—48no—
215C22×D17—48no—
216C22×D17—48no—
217C22×D17—84no—
218C22×D17—84no—
219C22×D17—84no—
220C22×D17—84no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—44no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—48no—
230C2×C4×C17#12012yes—
231C2×C4×C17#12112yes—
232C2×C4×C17#12114yes—
233C2×C4×C17#12114yes—
234C2×C4×C17#12314yes—
235C2×C4×C17#12312yes—
236C2×C4×C17#12414yes—
237C2×C4×C17C22×D411yescharacteristic
238C2×C4×C17C22×D411yescharacteristic
239C2×C4×C17C22×D411yescharacteristic
240C2×C4×C17C2×#4111yescharacteristic
241C2×C4×C17C2×#4111yescharacteristic
242C2×C4×C17C2×#4111yescharacteristic
243C22⋊D17—432no—
244C2×Dic17—24no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—48no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—84no—
255C2×Dic17—84no—
256D68—24no—
257D68—24no—
258D68—42no—
259D68—42no—
260D68—48no—
261C8×C17—24no—
262C8×C17—42no—
263C22×#121—171no—
264C22×#107—171no—
265C22×#102—171no—
266C22×#102—171no—
267C22×C22⋊C8D1711yescharacteristic, complemented
268C2×#380—171no—
269#2033—178no—
270C2×#340—171no—
271C22×C17—24no—
272C22×C17—24no—
273C22×C17—24no—
274C22×C17—42no—
275C22×C17—42no—
276C22×C17—42no—
277C22×C17—42no—
278C22×C17—416no—
279C22×C17#39414yes—
280C22×C17#44714yes—
281C22×C17#45214yes—
282C22×C17#46614yes—
283C22×C17#46814yes—
284C22×C17#48014yes—
285C22×C17#48214yes—
286C22×C17C2×#12011yescharacteristic
287C22×C17C2×#12111yescharacteristic
288C22×C17C2×#12311yescharacteristic
289C22×C17C22×D811yescharacteristic
290C22×C17C2×#13511yescharacteristic
291C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C17C2×#13711yescharacteristic
293C2×D17—44no—
294C2×D17—44no—
295C2×D17—44no—
296C2×D17—82no—
297C2×D17—82no—
298C2×D17—82no—
299C2×D17—82no—
300C2×D17—816no—
301C4×C17—42no—
302C4×C17#39414yes—
303C4×C17C2×#12111yescharacteristic
304C4×C17C2×#12111yescharacteristic
305C4×C17C2×#12311yescharacteristic
306C4×C17C2×#12411yescharacteristic
307Dic17—44no—
308Dic17—82no—
309Dic17—82no—
310C23×D4—171no—
311C23×D4—341no—
312C24×C4C2×D1711yescharacteristic
313C23×C8C2×D1711yescharacteristic
314C23×C8C2×D1711yescharacteristic
315C2×#121—174no—
316C2×#121—344no—
317C2×#121—344no—
318C2×#121—342no—
319C22×C4⋊C4—171no—
320C22×C4⋊C4—171no—
321C22×C4⋊C4—171no—
322C22×C22⋊C4—341no—
323C22×C22⋊C4—341no—
324C2×#107—174no—
325C2×#107—344no—
326C2×#102—174no—
327C2×#102—174no—
328C2×#102—344no—
329C2×#102—344no—
330C2×C22⋊C8—24no—
331C2×C22⋊C8C2×D1714yescomplemented
332#380—174no—
333#380—342no—
334C2×#95—341no—
335#340—174no—
336C2×C17—44no—
337C2×C17#203318yescomplemented
338C2×C17C2×#39411yescharacteristic
339C2×C17C2×#44711yescharacteristic
340C2×C17C2×#45211yescharacteristic
341C2×C17C2×#46611yescharacteristic
342C2×C17C2×#46811yescharacteristic
343C2×C17C2×#48011yescharacteristic
344C2×C17C2×#48211yescharacteristic
345D17—84no—
346C25—341no—
347C25D6811yescharacteristic
348C22×D4—174no—
349C22×D4—172no—
350C22×D4—348no—
351C22×D4—344no—
352C22×D4—341no—
353C22×D4—342no—
354C22×D4—342no—
355C22×D4—342no—
356C22×D4—342no—
357C22×D4—342no—
358C22×D4—684no—
359C22×D4—684no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—341no—
367C23×C4—341no—
368C23×C4—341no—
369C23×C4D6812yes—
370C23×C4D6811yescharacteristic
371C23×C4C22×D1712yes—
372C23×C4C22×D1711yescharacteristic
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8C22⋊D1714yescomplemented
379C22×C8C22×D1712yes—
380C22×C8C22×D1712yes—
381#121—348no—
382#121—348no—
383#121—3416no—
384C2×C4⋊C4—174no—
385C2×C4⋊C4—172no—
386C2×C4⋊C4—172no—
387C2×C4⋊C4—172no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—342no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C22⋊C4—348no—
397C2×C22⋊C4—344no—
398C2×C22⋊C4—344no—
399C2×C22⋊C4—684no—
400#107—348no—
401#102—348no—
402#102—348no—
403C22⋊C8—28no—
404#95—344no—
405C17C2×#203311yescharacteristic, complemented, Sylow
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—342no—
413C24—344no—
414C24—682no—
415C24—682no—
416C24—682no—
417C24—682no—
418C24—682no—
419C24—682no—
420C24D13614yes—
421C24C2×D6812yes—
422C24C2×D6811yescharacteristic
423C2×D4—174no—
424C2×D4—3416no—
425C2×D4—342no—
426C2×D4—342no—
427C2×D4—342no—
428C2×D4—342no—
429C2×D4—342no—
430C2×D4—344no—
431C2×D4—348no—
432C2×D4—348no—
433C2×D4—6832no—
434C2×D4—688no—
435C2×D4—688no—
436C2×D4—684no—
437C2×D4—682no—
438C2×D4—682no—
439C2×D4—684no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—342no—
457C22×C4—344no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—682no—
461C22×C4—682no—
462C22×C4—682no—
463C22×C4—682no—
464C22×C4—682no—
465C22×C4—682no—
466C22×C4—682no—
467C22×C4—682no—
468C22×C4C2×D6812yes—
469C22×C4C2×D6811yescharacteristic
470C22×C4#6325212yes—
471C22×C4D4×D1712yes—
472C22×C4D4×D1712yes—
473C22×C4#6325412yes—
474C22×C4#6325412yes—
475C22×C4C2×C22⋊D1712yes—
476C22×C4C23×D1711yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—28no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—44no—
484C2×C8C2×C22⋊D1714yescomplemented
485C4⋊C4—174no—
486C4⋊C4—342no—
487C4⋊C4—344no—
488C4⋊C4—342no—
489C4⋊C4—342no—
490C4⋊C4—342no—
491C4⋊C4—342no—
492C4⋊C4—682no—
493C4⋊C4—682no—
494C22⋊C4—3416no—
495C22⋊C4—688no—
496C23—28no—
497C23—22no—
498C23—28no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—28no—
505C23—44no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—344no—
510C23—688no—
511C23—688no—
512C23—688no—
513C23—682no—
514C23—682no—
515C23—682no—
516C23—682no—
517C23—682no—
518C23—682no—
519C23—1364no—
520C23—1364no—
521C23—1364no—
522C23—1364no—
523C23#1058756812yes—
524C23#1058757212yes—
525C23C2×D13614yes—
526C23C2×D13612yes—
527C23#1058759012yes—
528C23#1058759412yes—
529C23#1058759512yes—
530C23#1058761612yes—
531C23C22×D6811yescharacteristic
532D4—344no—
533D4—344no—
534D4—6832no—
535D4—688no—
536D4—682no—
537D4—682no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—344no—
548C2×C4—688no—
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—1364no—
558C2×C4—1364no—
559C2×C4#1058756812yes—
560C2×C4#1058756914yes—
561C2×C4#1058757114yes—
562C2×C4#1058757212yes—
563C2×C4#1058761612yes—
564C2×C4#1058762414yes—
565C2×C4#1058762514yes—
566C2×C4C2×#6325211yescharacteristic
567C2×C4C2×D4×D1711yescharacteristic
568C2×C4C2×D4×D1711yescharacteristic
569C2×C4C2×#6325411yescharacteristic
570C2×C4C2×#6325411yescharacteristic
571C2×C4C22×C22⋊D1711yescharacteristic
572C8—24no—
573C8—42no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—416no—
582C22—684no—
583C22—684no—
584C22—684no—
585C22—1362no—
586C22—1362no—
587C22—1362no—
588C22—1362no—
589C22—13616no—
590C22#1176272514yes—
591C22#1176294514yes—
592C22#1176297314yes—
593C22#1176304514yes—
594C22#1176305514yes—
595C22#1176312314yes—
596C22#1176313414yes—
597C22C2×#1058756811yescharacteristic
598C22C2×#1058761611yescharacteristic
599C22C2×#1058757211yescharacteristic
600C22C22×D13611yescharacteristic
601C22C2×#1058759011yescharacteristic
602C22C2×#1058759411yescharacteristic
603C22C2×#1058759511yescharacteristic
604C4—42no—
605C4—684no—
606C4—1362no—
607C4—1362no—
608C4#1176272514yes—
609C4C2×#1058762411yescharacteristic
610C4C2×#1058762511yescharacteristic
611C4C2×#1058756911yescharacteristic
612C4C2×#1058757111yescharacteristic
613C2—44no—
614C2—1364no—
615C2#1452996718yesdirect product factor
616C2C2×#1176272511yescharacteristic
617C2C2×#1176294511yescharacteristic
618C2C2×#1176297311yescharacteristic
619C2C2×#1176304511yescharacteristic
620C2C2×#1176305511yescharacteristic
621C2C2×#1176312311yescharacteristic
622C2C2×#1176313411yescharacteristic
subgroupG/H
centerC24C2×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×C22⋊C8C2
socleC24×C17C2×D4
prime radicalC22×#10587616C2
hypercenterC22×C22⋊C8D17
hypocenterC17C2×#2033
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#10587489C2semidirect
3. C22×#10587492C2semidirect
4. C22×#10587492C2semidirect
5. C2×#11762669C2semidirect
6. #14529967C2direct (N × H)
7. C2×#11762572C2semidirect
8. C22×C17×C22⋊C8C2semidirect
21. C2×#10587489C22semidirect
24. C2×#10587492C22semidirect
25. C2×#10587492C22semidirect
27. #11762669C22semidirect
29. #11762572C22semidirect
34. C2×C17×C22⋊C8C22semidirect
67. C22×C8×C17D4semidirect
172. C2×C8×C17C2×D4semidirect
267. C22×C22⋊C8D17semidirect
331. C2×C22⋊C8C2×D17semidirect
337. C2×C17#2033semidirect
378. C22×C8C22⋊D17semidirect
405. C17C2×#2033semidirect
484. C2×C8C2×C22⋊D17semidirect
615. C2#14529967direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876162
C22×#105874892
C22×#105874922
C2×#117626692
#145299672
C2×#117625722
C22×C17×C22⋊C82
C2×#203317