Finite Group Databasebeta

← C2×#14529103 #17035533

Subgroups — C2×#14529103 #17035533

Order 4352.

2310 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587624C211yesmaximal, characteristic
2C22×#10587578C211yesmaximal, characteristic, complemented
3C22×#10587503C211yesmaximal, characteristic, complemented
4C22×#10587491C211yesmaximal, characteristic, complemented
5#14529103C218yesmaximal, direct product factor
6C2×#11762572C211yesmaximal, characteristic, complemented
7C2×#11762571C211yesmaximal, characteristic, complemented
8C22×C17×#102C211yesmaximal, characteristic, complemented
9C23×C22⋊D17—21no—
10C23×C4×D17C2211yescharacteristic
11C23×#3622C2211yescharacteristic
12C2×#10587624—22no—
13C2×#10587624—24no—
14C2×#10587624C418yescomplemented
15C2×#10587624C2214yes—
16C2×#10587578—24no—
17C2×#10587578—24no—
18C2×#10587578—22no—
19C2×#10587578C2214yescomplemented
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17—21no—
23C22×#63227—21no—
24C22×C4×Dic17—21no—
25C2×#10587503—24no—
26C2×#10587503C2214yescomplemented
27C2×#10587491—24no—
28C2×#10587491C2214yescomplemented
29#11762572C2214yescomplemented
30#11762571C2214yescomplemented
31C23×D4×C17C2211yescharacteristic
32C23×C8×C17C2211yescharacteristic
33C22×C4⋊C4×C17C2211yescharacteristic
34C2×C17×#102—24no—
35C2×C17×#102C2214yescomplemented
36C25×C17—21no—
37C24×D17D411yescharacteristic
38C22×D4×C17—22no—
39C22×D4×C17—22no—
40C22×D4×C17—21no—
41C22×D4×C17—22no—
42C22×D4×C17—22no—
43C22×D4×C17—22no—
44C22×D4×C17C2×C414yes—
45C22×D4×C17C2312yes—
46C23×C4×C17—21no—
47C23×C4×C17C2311yescharacteristic
48C22×C22⋊D17—28no—
49C22×C22⋊D17—24no—
50C22×C22⋊D17—44no—
51C22×C22⋊D17—44no—
52C23×Dic17—21no—
53C23×Dic17—21no—
54C23×Dic17D411yescharacteristic
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17—22no—
58C22×C4×D17—22no—
59C22×C4×D17C2×C414yes—
60C22×C4×D17D412yes—
61C22×C4×D17D414yes—
62C22×C4×D17C2312yes—
63C22×C8×C17—22no—
64C22×C8×C17—22no—
65C22×C8×C17—22no—
66C22×C8×C17C2312yes—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17—22no—
69C2×C4⋊C4×C17D414yescomplemented
70C2×C4⋊C4×C17C2312yes—
71C2×C22⋊Dic17—28no—
72C2×C22⋊Dic17—24no—
73#10587624—216no—
74#10587624—28no—
75#10587624C2×C4116yescomplemented
76C2×#63227—28no—
77C2×#63227—24no—
78C2×C4⋊Dic17—22no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17C2×C414yes—
83C2×C4⋊Dic17D414yescomplemented
84C2×C4⋊Dic17C2312yes—
85C2×C4⋊Dic17C2312yes—
86C2×C4×Dic17—28no—
87C2×C4×Dic17—24no—
88C22×#3622—22no—
89C22×#3622—22no—
90C22×#3622—22no—
91C22×#3622C2312yes—
92#10587578—216no—
93#10587578—28no—
94#10587578—28no—
95C17×#102—28no—
96#10587503—28no—
97#10587491—28no—
98C24×C17—24no—
99C24×C17—22no—
100C24×C17—42no—
101C24×C17—42no—
102C24×C17—42no—
103C24×C17—42no—
104C24×C17—42no—
105C24×C17—42no—
106C24×C17C2×D411yescharacteristic
107C23×D17—22no—
108C23×D17—22no—
109C23×D17—22no—
110C23×D17—22no—
111C23×D17—22no—
112C23×D17—22no—
113C23×D17C22⋊C414yes—
114C23×D17C2×D412yes—
115C2×D4×C17—24no—
116C2×D4×C17—28no—
117C2×D4×C17—28no—
118C2×D4×C17—22no—
119C2×D4×C17—22no—
120C2×D4×C17—22no—
121C2×D4×C17—22no—
122C2×D4×C17—22no—
123C2×D4×C17—42no—
124C2×D4×C17—44no—
125C2×D4×C17—44no—
126C2×D4×C17—42no—
127C2×D4×C17C22×C414yes—
128C22×C4×C17—24no—
129C22×C4×C17—22no—
130C22×C4×C17—42no—
131C22×C4×C17—42no—
132C22×C4×C17C22×C412yes—
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2×D412yes—
135C22×C4×C17C2×D412yes—
136C22×C4×C17C2×D412yes—
137C22×C4×C17#4112yes—
138C22×C4×C17#4112yes—
139C22×C4×C17C2411yescharacteristic
140C2×C22⋊D17—216no—
141C2×C22⋊D17—48no—
142C2×C22⋊D17—48no—
143C2×C22⋊D17—432no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—24no—
147C22×Dic17—24no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—42no—
151C22×Dic17—42no—
152C22×Dic17—42no—
153C22×Dic17—42no—
154C22×Dic17C22⋊C414yes—
155C22×Dic17C2×D412yes—
156C2×C4×D17—28no—
157C2×C4×D17—28no—
158C2×C4×D17—24no—
159C2×C4×D17—28no—
160C2×C4×D17—28no—
161C2×C4×D17—24no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17C22⋊C418yes—
167C2×C4×D17C22×C414yes—
168C2×C4×D17C2×D414yes—
169C2×C8×C17—22no—
170C2×C8×C17—22no—
171C2×C8×C17—22no—
172C2×C8×C17—44no—
173C4⋊C4×C17—24no—
174C4⋊C4×C17—22no—
175C4⋊C4×C17C2×D414yescomplemented
176C22⋊Dic17—216no—
177#63227—216no—
178C4⋊Dic17—24no—
179C4⋊Dic17—24no—
180C4⋊Dic17—22no—
181C4⋊Dic17—22no—
182C4⋊Dic17C22×C414yes—
183C4⋊Dic17C2×D414yescomplemented
184C4×Dic17—216no—
185C2×#3622—22no—
186C2×#3622—22no—
187C2×#3622—22no—
188C2×#3622—44no—
189C2×#1875—171nomaximal, Sylow
190C23×C17—24no—
191C23×C17—42no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—42no—
197C23×C17—48no—
198C23×C17—48no—
199C23×C17—48no—
200C23×C17—84no—
201C23×C17—84no—
202C23×C17—84no—
203C23×C17—84no—
204C23×C17C2×C22⋊C412yes—
205C23×C17#12012yes—
206C23×C17#12312yes—
207C23×C17#13512yes—
208C23×C17#13512yes—
209C23×C17AGL(1,ℤ/8)12yes—
210C23×C17AGL(1,ℤ/8)12yes—
211C23×C17C22×D411yescharacteristic
212C22×D17—22no—
213C22×D17—22no—
214C22×D17—22no—
215C22×D17—22no—
216C22×D17—22no—
217C22×D17—22no—
218C22×D17—28no—
219C22×D17—28no—
220C22×D17—28no—
221C22×D17—44no—
222C22×D17—44no—
223C22×D17—44no—
224C22×D17—44no—
225C22×D17C2×C22⋊C414yes—
226D4×C17—24no—
227D4×C17—24no—
228D4×C17—42no—
229D4×C17—42no—
230D4×C17—48no—
231C2×C4×C17—24no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17—48no—
235C2×C4×C17C2×C22⋊C412yes—
236C2×C4×C17C4×D414yes—
237C2×C4×C17C4×D414yes—
238C2×C4×C17#12012yes—
239C2×C4×C17#12114yes—
240C2×C4×C17#12114yes—
241C2×C4×C17#12312yes—
242C2×C4×C17C23×C411yescharacteristic
243C2×C4×C17C22×D411yescharacteristic
244C2×C4×C17C22×D411yescharacteristic
245C2×C4×C17C22×D411yescharacteristic
246C2×C4×C17C2×#4111yescharacteristic
247C2×C4×C17C2×#4111yescharacteristic
248C22⋊D17—432no—
249C2×Dic17—22no—
250C2×Dic17—22no—
251C2×Dic17—28no—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—48no—
259C2×Dic17—48no—
260C2×Dic17C2×C22⋊C414yes—
261C4×D17—24no—
262C4×D17—24no—
263C4×D17—24no—
264C4×D17—24no—
265C4×D17—216no—
266C8×C17—42no—
267#3622—42no—
268C22×#121—171no—
269C22×#117—171no—
270C22×#102—171no—
271C22×#102D1711yescharacteristic, complemented
272C22×C22⋊C8—171no—
273#1875—178no—
274C2×#340—171no—
275C2×#340—171no—
276C22×C17—44no—
277C22×C17—44no—
278C22×C17—44no—
279C22×C17—82no—
280C22×C17—82no—
281C22×C17—816no—
282C22×C17—82no—
283C22×C17—82no—
284C22×C17#38614yes—
285C22×C17#41614yes—
286C22×C17#41814yes—
287C22×C17#44914yes—
288C22×C17#44914yes—
289C22×C17#48214yes—
290C22×C17#48214yes—
291C22×C17C22×C22⋊C411yescharacteristic
292C22×C17C2×#12011yescharacteristic
293C22×C17C2×#12311yescharacteristic
294C22×C17C2×#13511yescharacteristic
295C22×C17C2×#13511yescharacteristic
296C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
298C2×D17—24no—
299C2×D17—24no—
300C2×D17—24no—
301C2×D17—42no—
302C2×D17—42no—
303C2×D17—416no—
304C2×D17—42no—
305C2×D17—42no—
306C4×C17—44no—
307C4×C17#38614yes—
308C4×C17C2×C4×D411yescharacteristic
309C4×C17C2×C4×D411yescharacteristic
310C4×C17C2×#12111yescharacteristic
311C4×C17C2×#12111yescharacteristic
312Dic17—24no—
313Dic17—44no—
314Dic17—44no—
315C23×D4—341no—
316C23×D4C2×D1711yescharacteristic
317C24×C4—171no—
318C23×C8—171no—
319C23×C8C2×D1711yescharacteristic
320C2×#121—178no—
321C2×#121—174no—
322C2×#121—342no—
323C2×#121—344no—
324C2×#117—174no—
325C2×#117—344no—
326C2×#117—342no—
327C2×#117—344no—
328C22×C4⋊C4—171no—
329C22×C4⋊C4—171no—
330C22×C4⋊C4C2×D1711yescharacteristic
331C22×C22⋊C4—341no—
332C22×C22⋊C4—341no—
333C22×C42—341no—
334C2×#102—24no—
335C2×#102—174no—
336C2×#102—344no—
337C2×#102C2×D1714yescomplemented
338C2×C22⋊C8—174no—
339C2×C22⋊C8—344no—
340#340—174no—
341#340—174no—
342C2×C17—84no—
343C2×C17#187518yescomplemented
344C2×C17C2×#38611yescharacteristic
345C2×C17C2×#41611yescharacteristic
346C2×C17C2×#41811yescharacteristic
347C2×C17C2×#44911yescharacteristic
348C2×C17C2×#44911yescharacteristic
349C2×C17C2×#48211yescharacteristic
350C2×C17C2×#48211yescharacteristic
351D17—44no—
352C25—21no—
353C25—171no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—344no—
361C22×D4—348no—
362C22×D4—684no—
363C22×D4—684no—
364C22×D4C4×D1714yes—
365C22×D4C22×D1712yes—
366C23×C4—21no—
367C23×C4—171no—
368C23×C4—174no—
369C23×C4—172no—
370C23×C4—174no—
371C23×C4—172no—
372C23×C4—342no—
373C23×C4—342no—
374C23×C4—342no—
375C23×C4—342no—
376C23×C4—341no—
377C23×C4—341no—
378C23×C4C22×D1711yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—172no—
383C22×C8—342no—
384C22×C8—342no—
385C22×C8—342no—
386C22×C8C22×D1712yes—
387#121—1716no—
388#121—348no—
389#121—3416no—
390#117—348no—
391#117—3416no—
392#117—348no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—174no—
396C2×C4⋊C4—174no—
397C2×C4⋊C4—172no—
398C2×C4⋊C4—172no—
399C2×C4⋊C4—341no—
400C2×C4⋊C4—342no—
401C2×C4⋊C4—341no—
402C2×C4⋊C4—342no—
403C2×C4⋊C4C22⋊D1714yescomplemented
404C2×C4⋊C4C22×D1712yes—
405C2×C22⋊C4—344no—
406C2×C22⋊C4—348no—
407C2×C22⋊C4—344no—
408C2×C22⋊C4—348no—
409C2×C42—344no—
410C2×C42—348no—
411#102—28no—
412#102—348no—
413C22⋊C8—348no—
414C17C2×#187511yescharacteristic, complemented, Sylow
415C24—22no—
416C24—24no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—172no—
424C24—174no—
425C24—342no—
426C24—342no—
427C24—342no—
428C24—342no—
429C24—342no—
430C24—342no—
431C24D4×D1711yescharacteristic
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—24no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—42no—
443C2×D4—44no—
444C2×D4—3416no—
445C2×D4—6832no—
446C2×D4—688no—
447C2×D4—688no—
448C2×D4C2×C4×D1714yes—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—172no—
454C22×C4—174no—
455C22×C4—174no—
456C22×C4—174no—
457C22×C4—178no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—348no—
465C22×C4—344no—
466C22×C4—348no—
467C22×C4—348no—
468C22×C4—344no—
469C22×C4—348no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—344no—
473C22×C4—344no—
474C22×C4—682no—
475C22×C4—682no—
476C22×C4—682no—
477C22×C4—682no—
478C22×C4C2×C4×D1712yes—
479C22×C4#6325212yes—
480C22×C4D4×D1712yes—
481C22×C4D4×D1712yes—
482C22×C4D4×D1711yescharacteristic
483C22×C4#6325412yes—
484C22×C4C2×C22⋊D1712yes—
485C22×C4C23×D1711yescharacteristic
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—44no—
490C2×C8—342no—
491C2×C8—342no—
492C2×C8—342no—
493C2×C8—684no—
494C4⋊C4—22no—
495C4⋊C4—24no—
496C4⋊C4—174no—
497C4⋊C4—174no—
498C4⋊C4—342no—
499C4⋊C4—342no—
500C4⋊C4—344no—
501C4⋊C4—344no—
502C4⋊C4C2×C22⋊D1714yescomplemented
503C22⋊C4—3416no—
504C22⋊C4—3416no—
505C42—3416no—
506C23—24no—
507C23—42no—
508C23—42no—
509C23—48no—
510C23—48no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—48no—
516C23—84no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—174no—
521C23—342no—
522C23—342no—
523C23—348no—
524C23—348no—
525C23—342no—
526C23—342no—
527C23—342no—
528C23—342no—
529C23—348no—
530C23—684no—
531C23—684no—
532C23—684no—
533C23—684no—
534C23C22⋊C4×D1712yes—
535C23#1058756912yes—
536C23#1058759712yes—
537C23#1058759812yes—
538C23#1058760012yes—
539C23#1058760212yes—
540C23#1058762312yes—
541C23C2×D4×D1711yescharacteristic
542D4—24no—
543D4—24no—
544D4—42no—
545D4—42no—
546D4—48no—
547D4—6832no—
548C2×C4—24no—
549C2×C4—48no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—174no—
553C2×C4—342no—
554C2×C4—342no—
555C2×C4—348no—
556C2×C4—344no—
557C2×C4—344no—
558C2×C4—344no—
559C2×C4—344no—
560C2×C4—3416no—
561C2×C4—344no—
562C2×C4—344no—
563C2×C4—688no—
564C2×C4—688no—
565C2×C4—682no—
566C2×C4—682no—
567C2×C4—682no—
568C2×C4—682no—
569C2×C4C22⋊C4×D1712yes—
570C2×C4#1058756714yes—
571C2×C4#1058756912yes—
572C2×C4#1058757014yes—
573C2×C4C4×C22⋊D1714yes—
574C2×C4#1058762312yes—
575C2×C4#1058762414yes—
576C2×C4C22×C4×D1711yescharacteristic
577C2×C4C2×#6325211yescharacteristic
578C2×C4C2×D4×D1711yescharacteristic
579C2×C4C2×D4×D1711yescharacteristic
580C2×C4C2×#6325411yescharacteristic
581C2×C4C22×C22⋊D1711yescharacteristic
582C8—42no—
583C8—682no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—82no—
588C22—816no—
589C22—82no—
590C22—82no—
591C22—82no—
592C22—344no—
593C22—344no—
594C22—344no—
595C22—682no—
596C22—6816no—
597C22—682no—
598C22—682no—
599C22—682no—
600C22#1176268514yes—
601C22#1176280214yes—
602C22#1176281214yes—
603C22#1176295114yes—
604C22#1176295314yes—
605C22#1176313114yes—
606C22#1176313214yes—
607C22C2×C22⋊C4×D1711yescharacteristic
608C22C2×#1058762311yescharacteristic
609C22C2×#1058756911yescharacteristic
610C22C2×#1058759811yescharacteristic
611C22C2×#1058760211yescharacteristic
612C22C2×#1058759711yescharacteristic
613C22C2×#1058760011yescharacteristic
614C4—44no—
615C4—344no—
616C4—684no—
617C4—684no—
618C4#1176268514yes—
619C4C2×#1058756711yescharacteristic
620C4C2×C4×C22⋊D1711yescharacteristic
621C4C2×#1058762411yescharacteristic
622C4C2×#1058757011yescharacteristic
623C2—84no—
624C2—684no—
625C2#1452910318yesdirect product factor
626C2C2×#1176268511yescharacteristic
627C2C2×#1176280211yescharacteristic
628C2C2×#1176281211yescharacteristic
629C2C2×#1176295111yescharacteristic
630C2C2×#1176295311yescharacteristic
631C2C2×#1176313111yescharacteristic
632C2C2×#1176313211yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#102C2
socleC24×C17C2×D4
prime radicalC22×#10587624C2
cosocleC22×C4×C17C24
hypercenterC22×#102D17
hypocenterC17C2×#1875
LCSG ▷ C2×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×#10587578C2semidirect
3. C22×#10587503C2semidirect
4. C22×#10587491C2semidirect
5. #14529103C2direct (N × H)
6. C2×#11762572C2semidirect
7. C2×#11762571C2semidirect
8. C22×C17×#102C2semidirect
14. C2×#10587624C4semidirect
19. C2×#10587578C22semidirect
26. C2×#10587503C22semidirect
28. C2×#10587491C22semidirect
29. #11762572C22semidirect
30. #11762571C22semidirect
35. C2×C17×#102C22semidirect
69. C2×C4⋊C4×C17D4semidirect
75. #10587624C2×C4semidirect
83. C2×C4⋊Dic17D4semidirect
175. C4⋊C4×C17C2×D4semidirect
183. C4⋊Dic17C2×D4semidirect
271. C22×#102D17semidirect
337. C2×#102C2×D17semidirect
343. C2×C17#1875semidirect
403. C2×C4⋊C4C22⋊D17semidirect
414. C17C2×#1875semidirect
502. C4⋊C4C2×C22⋊D17semidirect
625. C2#14529103direct (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×#105875782
C22×#105875032
C22×#105874912
#145291032
C2×#117625722
C2×#117625712
C22×C17×#1022
C2×#187517