Finite Group Databasebeta

← C2×#14529964 #17061770

Subgroups — C2×#14529964 #17061770

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×#10587624C211yesmaximal, characteristic
2C22×#10587478C211yesmaximal, characteristic, complemented
3C22×#10587503C211yesmaximal, characteristic, complemented
4C22×#10587491C211yesmaximal, characteristic, complemented
5C2×#11762666C211yesmaximal, characteristic, complemented
6#14529964C218yesmaximal, direct product factor
7C2×#11762572C211yesmaximal, characteristic, complemented
8C22×C17×#102C211yesmaximal, characteristic, complemented
9C23×C22⋊D17—21no—
10C23×C4×D17C2211yescharacteristic
11C23×#3622C2211yescharacteristic
12C2×#10587624—24no—
13C2×#10587624—24no—
14C2×#10587624—22no—
15C2×#10587624C2214yes—
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17—21no—
19C22×#63227—21no—
20C2×#10587478—24no—
21C2×#10587478C2214yescomplemented
22C2×#10587503—24no—
23C2×#10587503C2214yescomplemented
24C2×#10587491—24no—
25C2×#10587491C2214yescomplemented
26#11762666—22no—
27#11762666C2214yescomplemented
28C2×#10587502—21no—
29#11762572C2214yescomplemented
30C23×D4×C17C2211yescharacteristic
31C23×C8×C17C2211yescharacteristic
32C22×C4⋊C4×C17C2211yescharacteristic
33C2×C17×#102—24no—
34C2×C17×#102C2214yescomplemented
35C25×C17—21no—
36C24×D17D411yescharacteristic
37C22×D4×C17—22no—
38C22×D4×C17—21no—
39C22×D4×C17—22no—
40C22×D4×C17—22no—
41C22×D4×C17—22no—
42C22×D4×C17—22no—
43C22×D4×C17D414yes—
44C22×D4×C17C2312yes—
45C23×C4×C17—21no—
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×Dic17D411yescharacteristic
54C22×C4×D17—22no—
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17—22no—
58C22×C4×D17—22no—
59C22×C4×D17—22no—
60C22×C4×D17D412yes—
61C22×C4×D17C2312yes—
62C22×C8×C17—22no—
63C22×C8×C17—22no—
64C22×C8×C17—22no—
65C22×C8×C17C2312yes—
66C2×C4⋊C4×C17—22no—
67C2×C4⋊C4×C17—22no—
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17C2312yes—
70C2×C22⋊Dic17—28no—
71C2×C22⋊Dic17—24no—
72#10587624—216no—
73#10587624—28no—
74#10587624—28no—
75C2×#63227—24no—
76C2×#63227—44no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17D414yes—
83C2×C4⋊Dic17C2312yes—
84C2×C4⋊Dic17C2312yes—
85C22×#3622—22no—
86C22×#3622—22no—
87C22×#3622D414yescomplemented
88C22×#3622C2312yes—
89C17×#102—28no—
90#10587503—28no—
91#10587502—24no—
92#10587491—28no—
93#10587478—28no—
94C24×C17—24no—
95C24×C17—22no—
96C24×C17—42no—
97C24×C17—42no—
98C24×C17—42no—
99C24×C17—42no—
100C24×C17—42no—
101C24×C17—42no—
102C24×C17C2×D411yescharacteristic
103C23×D17—22no—
104C23×D17—22no—
105C23×D17—22no—
106C23×D17—22no—
107C23×D17—22no—
108C23×D17—22no—
109C23×D17D814yes—
110C23×D17C2×D412yes—
111C2×D4×C17—24no—
112C2×D4×C17—28no—
113C2×D4×C17—28no—
114C2×D4×C17—22no—
115C2×D4×C17—22no—
116C2×D4×C17—22no—
117C2×D4×C17—22no—
118C2×D4×C17—22no—
119C2×D4×C17—44no—
120C2×D4×C17—42no—
121C2×D4×C17—42no—
122C2×D4×C17—44no—
123C2×D4×C17C2×D414yes—
124C22×C4×C17—22no—
125C22×C4×C17—42no—
126C22×C4×C17—42no—
127C22×C4×C17—42no—
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—22no—
141C22×Dic17—24no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—42no—
147C22×Dic17—42no—
148C22×Dic17—42no—
149C22×Dic17—42no—
150C22×Dic17—42no—
151C22×Dic17C2×D412yes—
152C2×C4×D17—24no—
153C2×C4×D17—24no—
154C2×C4×D17—24no—
155C2×C4×D17—22no—
156C2×C4×D17—22no—
157C2×C4×D17—22no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—44no—
162C2×C4×D17—44no—
163C2×C4×D17—44no—
164C2×C4×D17—44no—
165C2×C8×C17—22no—
166C2×C8×C17—22no—
167C2×C8×C17—22no—
168C2×C8×C17—44no—
169C4⋊C4×C17—22no—
170C4⋊C4×C17—22no—
171C4⋊C4×C17—42no—
172C22⋊Dic17—216no—
173#63227—48no—
174C4⋊Dic17—24no—
175C4⋊Dic17—22no—
176C4⋊Dic17—22no—
177C4⋊Dic17—22no—
178C4⋊Dic17—42no—
179C4⋊Dic17C2×D414yes—
180C2×#3622—28no—
181C2×#3622—22no—
182C2×#3622—22no—
183C2×#3622C2×D414yescomplemented
184C2×#2033—171nomaximal, Sylow
185C23×C17—24no—
186C23×C17—42no—
187C23×C17—42no—
188C23×C17—42no—
189C23×C17—42no—
190C23×C17—42no—
191C23×C17—42no—
192C23×C17—48no—
193C23×C17—48no—
194C23×C17—48no—
195C23×C17—84no—
196C23×C17—84no—
197C23×C17—84no—
198C23×C17—84no—
199C23×C17#12012yes—
200C23×C17#12112yes—
201C23×C17#12312yes—
202C23×C17C2×D812yes—
203C23×C17#13512yes—
204C23×C17AGL(1,ℤ/8)12yes—
205C23×C17#13712yes—
206C23×C17C22×D411yescharacteristic
207C22×D17—22no—
208C22×D17—22no—
209C22×D17—22no—
210C22×D17—22no—
211C22×D17—22no—
212C22×D17—22no—
213C22×D17—28no—
214C22×D17—28no—
215C22×D17—28no—
216C22×D17—44no—
217C22×D17—44no—
218C22×D17—44no—
219C22×D17—44no—
220C22×D17C2×D814yes—
221D4×C17—24no—
222D4×C17—24no—
223D4×C17—42no—
224D4×C17—42no—
225D4×C17—48no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—84no—
230C2×C4×C17#12012yes—
231C2×C4×C17#12114yes—
232C2×C4×C17#12112yes—
233C2×C4×C17#12114yes—
234C2×C4×C17#12312yes—
235C2×C4×C17#12314yes—
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—22no—
245C2×Dic17—24no—
246C2×Dic17—22no—
247C2×Dic17—22no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—44no—
251C2×Dic17—48no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—84no—
256C4×D17—42no—
257C4×D17—42no—
258C4×D17—42no—
259C4×D17—42no—
260C4×D17—48no—
261C8×C17—42no—
262#3622—24no—
263C22×#121—171no—
264C22×#107—171no—
265C22×#102—171no—
266C22×#102D1711yescharacteristic, complemented
267C22×C22⋊C8—171no—
268C2×#380—171no—
269#2033—178no—
270C2×#340—171no—
271C22×C17—44no—
272C22×C17—44no—
273C22×C17—44no—
274C22×C17—82no—
275C22×C17—82no—
276C22×C17—82no—
277C22×C17—82no—
278C22×C17—816no—
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—24no—
294C2×D17—24no—
295C2×D17—24no—
296C2×D17—42no—
297C2×D17—42no—
298C2×D17—42no—
299C2×D17—42no—
300C2×D17—416no—
301C4×C17—82no—
302C4×C17#39414yes—
303C4×C17C2×#12111yescharacteristic
304C4×C17C2×#12111yescharacteristic
305C4×C17C2×#12311yescharacteristic
306C4×C17C2×#12411yescharacteristic
307Dic17—42no—
308Dic17—44no—
309Dic17—82no—
310C23×D4—341no—
311C23×D4C2×D1711yescharacteristic
312C24×C4—171no—
313C23×C8—171no—
314C23×C8C2×D1711yescharacteristic
315C2×#121—174no—
316C2×#121—344no—
317C2×#121—342no—
318C2×#121—344no—
319C22×C4⋊C4—171no—
320C22×C4⋊C4—171no—
321C22×C4⋊C4C2×D1711yescharacteristic
322C22×C22⋊C4—341no—
323C22×C22⋊C4—341no—
324C2×#107—174no—
325C2×#107—344no—
326C2×#102—24no—
327C2×#102—174no—
328C2×#102—344no—
329C2×#102C2×D1714yescomplemented
330C2×C22⋊C8—174no—
331C2×C22⋊C8—344no—
332#380—174no—
333#380—342no—
334C2×#95—341no—
335#340—174no—
336C2×C17—84no—
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—44no—
346C25—21no—
347C25—171no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4—22no—
354C22×D4—344no—
355C22×D4—348no—
356C22×D4—684no—
357C22×D4—684no—
358C22×D4C22⋊D1714yes—
359C22×D4C22×D1712yes—
360C23×C4—21no—
361C23×C4—171no—
362C23×C4—172no—
363C23×C4—172no—
364C23×C4—341no—
365C23×C4—342no—
366C23×C4—342no—
367C23×C4—342no—
368C23×C4—342no—
369C23×C4—342no—
370C23×C4—342no—
371C23×C4—341no—
372C23×C4C22×D1711yescharacteristic
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—174no—
377C22×C8—172no—
378C22×C8—342no—
379C22×C8—342no—
380C22×C8C22×D1712yes—
381#121—348no—
382#121—3416no—
383#121—348no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—174no—
388C2×C4⋊C4—172no—
389C2×C4⋊C4—172no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—342no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4C22×D1712yes—
396C2×C22⋊C4—344no—
397C2×C22⋊C4—348no—
398C2×C22⋊C4—344no—
399C2×C22⋊C4—684no—
400#107—348no—
401#102—28no—
402#102—348no—
403C22⋊C8—348no—
404#95—344no—
405C17C2×#203311yescharacteristic, complemented, Sylow
406C24—22no—
407C24—24no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—172no—
415C24—174no—
416C24—342no—
417C24—342no—
418C24—342no—
419C24—342no—
420C24—342no—
421C24—342no—
422C24D4×D1711yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—28no—
429C2×D4—24no—
430C2×D4—28no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—3416no—
436C2×D4—688no—
437C2×D4—688no—
438C2×D4—6832no—
439C2×D4C2×C22⋊D1714yes—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—172no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—344no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—344no—
457C22×C4—344no—
458C22×C4—344no—
459C22×C4—342no—
460C22×C4—682no—
461C22×C4—682no—
462C22×C4—684no—
463C22×C4—684no—
464C22×C4—684no—
465C22×C4—684no—
466C22×C4—682no—
467C22×C4—682no—
468C22×C4—682no—
469C22×C4#6325212yes—
470C22×C4#6325212yes—
471C22×C4D4×D1712yes—
472C22×C4D4×D1712yes—
473C22×C4D4×D1711yescharacteristic
474C22×C4#6325412yes—
475C22×C4C2×C22⋊D1712yes—
476C22×C4C23×D1711yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—44no—
481C2×C8—174no—
482C2×C8—342no—
483C2×C8—342no—
484C2×C8—348no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—42no—
488C4⋊C4—174no—
489C4⋊C4—342no—
490C4⋊C4—344no—
491C4⋊C4—342no—
492C4⋊C4—342no—
493C4⋊C4—682no—
494C22⋊C4—3416no—
495C22⋊C4—688no—
496C23—24no—
497C23—48no—
498C23—48no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—48no—
506C23—84no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—174no—
511C23—342no—
512C23—348no—
513C23—342no—
514C23—342no—
515C23—342no—
516C23—342no—
517C23—342no—
518C23—348no—
519C23—348no—
520C23—684no—
521C23—684no—
522C23—684no—
523C23—684no—
524C23#1058756912yes—
525C23#1058757012yes—
526C23D8×D1712yes—
527C23#1058759712yes—
528C23#1058760112yes—
529C23#1058760212yes—
530C23#1058762312yes—
531C23C2×D4×D1711yescharacteristic
532D4—24no—
533D4—24no—
534D4—48no—
535D4—42no—
536D4—42no—
537D4—6832no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—342no—
543C2×C4—344no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—684no—
547C2×C4—682no—
548C2×C4—682no—
549C2×C4—688no—
550C2×C4—688no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—1364no—
559C2×C4#1058756912yes—
560C2×C4#1058757012yes—
561C2×C4#1058757014yes—
562C2×C4#1058757114yes—
563C2×C4#1058761514yes—
564C2×C4#1058762312yes—
565C2×C4#1058762514yes—
566C2×C4C2×#6325211yescharacteristic
567C2×C4C2×#6325211yescharacteristic
568C2×C4C2×D4×D1711yescharacteristic
569C2×C4C2×D4×D1711yescharacteristic
570C2×C4C2×#6325411yescharacteristic
571C2×C4C22×C22⋊D1711yescharacteristic
572C8—42no—
573C8—344no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—816no—
582C22—344no—
583C22—344no—
584C22—344no—
585C22—682no—
586C22—682no—
587C22—682no—
588C22—682no—
589C22—6816no—
590C22#1176272414yes—
591C22#1176294114yes—
592C22#1176296814yes—
593C22#1176304414yes—
594C22#1176305414yes—
595C22#1176312114yes—
596C22#1176313214yes—
597C22C2×#1058762311yescharacteristic
598C22C2×#1058757011yescharacteristic
599C22C2×#1058756911yescharacteristic
600C22C2×D8×D1711yescharacteristic
601C22C2×#1058760211yescharacteristic
602C22C2×#1058759711yescharacteristic
603C22C2×#1058760111yescharacteristic
604C4—82no—
605C4—682no—
606C4—684no—
607C4—1362no—
608C4#1176272414yes—
609C4C2×#1058762511yescharacteristic
610C4C2×#1058757011yescharacteristic
611C4C2×#1058761511yescharacteristic
612C4C2×#1058757111yescharacteristic
613C2—84no—
614C2—684no—
615C2#1452996418yesdirect product factor
616C2C2×#1176272411yescharacteristic
617C2C2×#1176294111yescharacteristic
618C2C2×#1176296811yescharacteristic
619C2C2×#1176304411yescharacteristic
620C2C2×#1176305411yescharacteristic
621C2C2×#1176312111yescharacteristic
622C2C2×#1176313211yescharacteristic
subgroupG/H
centerC24D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#102C2
socleC24×C17C2×D4
prime radicalC22×#10587624C2
hypercenterC22×#102D17
hypocenterC17C2×#2033
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#10587478C2semidirect
3. C22×#10587503C2semidirect
4. C22×#10587491C2semidirect
5. C2×#11762666C2semidirect
6. #14529964C2direct (N × H)
7. C2×#11762572C2semidirect
8. C22×C17×#102C2semidirect
21. C2×#10587478C22semidirect
23. C2×#10587503C22semidirect
25. C2×#10587491C22semidirect
27. #11762666C22semidirect
29. #11762572C22semidirect
34. C2×C17×#102C22semidirect
87. C22×#3622D4semidirect
183. C2×#3622C2×D4semidirect
266. C22×#102D17semidirect
329. C2×#102C2×D17semidirect
337. C2×C17#2033semidirect
405. C17C2×#2033semidirect
615. C2#14529964direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876242
C22×#105874782
C22×#105875032
C22×#105874912
C2×#117626662
#145299642
C2×#117625722
C22×C17×#1022
C2×#203317