Finite Group Databasebeta

← C2×#14529963 #17061769

Subgroups — C2×#14529963 #17061769

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×#10587478C211yesmaximal, characteristic, complemented
2C22×#10587503C211yesmaximal, characteristic, complemented
3C22×#10587503C211yesmaximal, characteristic, complemented
4C22×C22⋊#3622C211yesmaximal, characteristic, complemented
5C2×#11762669C211yesmaximal, characteristic, complemented
6#14529963C218yesmaximal, direct product factor
7C2×#11762571C211yesmaximal, characteristic, complemented
8C22×C17×#121C211yesmaximal, characteristic
9C23×#3622C2211yescharacteristic
10C23×#3622C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C22⋊Dic17—21no—
14C2×#10587478—24no—
15C2×#10587478C2214yescomplemented
16C2×#10587503—24no—
17C2×#10587503—24no—
18C2×#10587503C2214yescomplemented
19C2×#10587503C2214yescomplemented
20C2×C22⋊#3622—24no—
21C2×C22⋊#3622C2214yescomplemented
22#11762669—22no—
23#11762669C2214yescomplemented
24C2×#10587502—21no—
25#11762571C2214yescomplemented
26C23×D4×C17—21no—
27C23×D4×C17C2211yescharacteristic
28C24×C4×C17C2211yescharacteristic
29C2×C17×#121—24no—
30C2×C17×#121—24no—
31C2×C17×#121—22no—
32C2×C17×#121C2214yes—
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17—21no—
35C25×C17—21no—
36C25×C17D411yescharacteristic
37C22×D4×C17—28no—
38C22×D4×C17—24no—
39C22×D4×C17—22no—
40C22×D4×C17—21no—
41C22×D4×C17—22no—
42C22×D4×C17—22no—
43C22×D4×C17—22no—
44C22×D4×C17—22no—
45C22×D4×C17—44no—
46C22×D4×C17—44no—
47C22×D4×C17D414yes—
48C22×D4×C17C2312yes—
49C23×C4×C17—21no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—22no—
54C23×C4×C17—22no—
55C23×C4×C17—22no—
56C23×C4×C17D411yescharacteristic
57C23×C4×C17D412yes—
58C23×C4×C17C2312yes—
59C23×C4×C17C2311yescharacteristic
60C23×Dic17—21no—
61C23×Dic17—21no—
62C17×#121—216no—
63C17×#121—28no—
64C17×#121—28no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—22no—
67C2×C4⋊C4×C17D414yes—
68C2×C4⋊C4×C17C2312yes—
69C2×C22⋊C4×C17—28no—
70C2×C22⋊C4×C17—24no—
71C2×C22⋊Dic17—24no—
72C2×C22⋊Dic17—44no—
73C2×C4⋊Dic17—21no—
74C2×C4⋊Dic17—21no—
75C2×C4⋊Dic17—22no—
76C2×C4⋊Dic17—22no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—22no—
79C2×C4⋊Dic17C2312yes—
80C2×C4⋊Dic17C2312yes—
81C22×#3622—22no—
82C22×#3622—22no—
83C22×#3622—22no—
84C22×#3622—22no—
85C22×#3622—22no—
86C22×#3622D414yescomplemented
87C22×#3622C2312yes—
88C22×#3622C2312yes—
89#10587503—28no—
90#10587503—28no—
91#10587502—24no—
92C22⋊#3622—28no—
93#10587478—28no—
94C24×C17—22no—
95C24×C17—22no—
96C24×C17—22no—
97C24×C17—22no—
98C24×C17—22no—
99C24×C17—22no—
100C24×C17—24no—
101C24×C17—22no—
102C24×C17—42no—
103C24×C17—42no—
104C24×C17—42no—
105C24×C17—42no—
106C24×C17—42no—
107C24×C17—42no—
108C24×C17D814yes—
109C24×C17C2×D412yes—
110C24×C17C2×D411yescharacteristic
111C2×D4×C17—216no—
112C2×D4×C17—24no—
113C2×D4×C17—28no—
114C2×D4×C17—28no—
115C2×D4×C17—22no—
116C2×D4×C17—22no—
117C2×D4×C17—22no—
118C2×D4×C17—22no—
119C2×D4×C17—22no—
120C2×D4×C17—48no—
121C2×D4×C17—432no—
122C2×D4×C17—48no—
123C2×D4×C17—44no—
124C2×D4×C17—42no—
125C2×D4×C17—42no—
126C2×D4×C17—44no—
127C2×D4×C17C2×D414yes—
128C22×C4×C17—22no—
129C22×C4×C17—24no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—24no—
134C22×C4×C17—24no—
135C22×C4×C17—24no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—42no—
143C22×C4×C17—42no—
144C22×C4×C17—44no—
145C22×C4×C17—44no—
146C22×C4×C17—44no—
147C22×C4×C17—44no—
148C22×C4×C17C2×D412yes—
149C22×C4×C17C2×D412yes—
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D412yes—
152C22×C4×C17C2×D412yes—
153C22×C4×C17#4112yes—
154C22×C4×C17#4112yes—
155C22×C4×C17#4112yes—
156C22×C4×C17C2411yescharacteristic
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—42no—
160C22×Dic17—42no—
161C22×Dic17—42no—
162C22×Dic17—42no—
163C22×Dic17—42no—
164C22×Dic17—42no—
165C4⋊C4×C17—24no—
166C4⋊C4×C17—22no—
167C4⋊C4×C17C2×D414yes—
168C22⋊C4×C17—216no—
169C22⋊Dic17—48no—
170C4⋊Dic17—22no—
171C4⋊Dic17—22no—
172C4⋊Dic17—22no—
173C4⋊Dic17—22no—
174C4⋊Dic17—42no—
175C4⋊Dic17—42no—
176C2×#3622—28no—
177C2×#3622—22no—
178C2×#3622—22no—
179C2×#3622—22no—
180C2×#3622—22no—
181C2×#3622—22no—
182C2×#3622—44no—
183C2×#3622C2×D414yescomplemented
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—24no—
195C23×C17—44no—
196C23×C17—44no—
197C23×C17—44no—
198C23×C17—44no—
199C23×C17—42no—
200C23×C17—42no—
201C23×C17—42no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17—42no—
205C23×C17—48no—
206C23×C17—48no—
207C23×C17—48no—
208C23×C17—84no—
209C23×C17—84no—
210C23×C17—84no—
211C23×C17—84no—
212C23×C17#12012yes—
213C23×C17#12112yes—
214C23×C17#12312yes—
215C23×C17C2×D814yes—
216C23×C17C2×D812yes—
217C23×C17#13512yes—
218C23×C17AGL(1,ℤ/8)12yes—
219C23×C17#13712yes—
220C23×C17C22×D411yescharacteristic
221D4×C17—24no—
222D4×C17—24no—
223D4×C17—432no—
224D4×C17—42no—
225D4×C17—42no—
226D4×C17—48no—
227C2×C4×C17—22no—
228C2×C4×C17—24no—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17—44no—
234C2×C4×C17—48no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—48no—
240C2×C4×C17#12012yes—
241C2×C4×C17#12114yes—
242C2×C4×C17#12114yes—
243C2×C4×C17#12112yes—
244C2×C4×C17#12314yes—
245C2×C4×C17#12312yes—
246C2×C4×C17#12414yes—
247C2×C4×C17C22×D411yescharacteristic
248C2×C4×C17C22×D411yescharacteristic
249C2×C4×C17C22×D411yescharacteristic
250C2×C4×C17C2×#4111yescharacteristic
251C2×C4×C17C2×#4111yescharacteristic
252C2×C4×C17C2×#4111yescharacteristic
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—84no—
260C2×Dic17—84no—
261#3622—24no—
262#3622—42no—
263C22×#121D1711yescharacteristic
264C22×#107—171no—
265C22×#102—171no—
266C22×#102—171no—
267C22×C22⋊C8—171no—
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—44no—
280C22×C17—44no—
281C22×C17—44no—
282C22×C17—82no—
283C22×C17—82no—
284C22×C17—82no—
285C22×C17—82no—
286C22×C17—816no—
287C22×C17#39414yes—
288C22×C17#44714yes—
289C22×C17#45214yes—
290C22×C17#46614yes—
291C22×C17#46814yes—
292C22×C17#48014yes—
293C22×C17#48214yes—
294C22×C17C2×#12011yescharacteristic
295C22×C17C2×#12111yescharacteristic
296C22×C17C2×#12311yescharacteristic
297C22×C17C22×D811yescharacteristic
298C22×C17C2×#13511yescharacteristic
299C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C17C2×#13711yescharacteristic
301C4×C17—42no—
302C4×C17—44no—
303C4×C17#39414yes—
304C4×C17C2×#12111yescharacteristic
305C4×C17C2×#12111yescharacteristic
306C4×C17C2×#12311yescharacteristic
307C4×C17C2×#12411yescharacteristic
308Dic17—82no—
309Dic17—82no—
310C23×D4—21no—
311C23×D4C2×D1711yescharacteristic
312C24×C4C2×D1711yescharacteristic
313C23×C8—171no—
314C23×C8—171no—
315C2×#121—24no—
316C2×#121—22no—
317C2×#121—24no—
318C2×#121C2×D1714yes—
319C22×C4⋊C4—171no—
320C22×C4⋊C4—171no—
321C22×C4⋊C4C2×D1711yescharacteristic
322C22×C22⋊C4—21no—
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—174no—
331C2×C22⋊C8—344no—
332#380—174no—
333#380—342no—
334C2×#95—341no—
335#340—174no—
336C2×C17—44no—
337C2×C17—84no—
338C2×C17#203318yescomplemented
339C2×C17C2×#39411yescharacteristic
340C2×C17C2×#44711yescharacteristic
341C2×C17C2×#45211yescharacteristic
342C2×C17C2×#46611yescharacteristic
343C2×C17C2×#46811yescharacteristic
344C2×C17C2×#48011yescharacteristic
345C2×C17C2×#48211yescharacteristic
346C25—21no—
347C25C22⋊D1711yescharacteristic
348C22×D4—28no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—44no—
357C22×D4—44no—
358C22×D4C22⋊D1714yes—
359C22×D4C22×D1712yes—
360C23×C4—21no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—341no—
368C23×C4—341no—
369C23×C4C22⋊D1712yes—
370C23×C4C22⋊D1711yescharacteristic
371C23×C4C22×D1712yes—
372C23×C4C22×D1711yescharacteristic
373C22×C8—174no—
374C22×C8—172no—
375C22×C8—172no—
376C22×C8—342no—
377C22×C8—342no—
378C22×C8—342no—
379C22×C8—342no—
380C22×C8—342no—
381#121—216no—
382#121—28no—
383#121—28no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—172no—
387C2×C4⋊C4—172no—
388C2×C4⋊C4—342no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4C22⋊D1714yes—
395C2×C4⋊C4C22×D1712yes—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—344no—
399C2×C22⋊C4—684no—
400#107—348no—
401#102—348no—
402#102—348no—
403C22⋊C8—348no—
404#95—344no—
405C17C2×#203311yescharacteristic, complemented, Sylow
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24#6322814yes—
421C24C2×C22⋊D1712yes—
422C24C2×C22⋊D1711yescharacteristic
423C2×D4—216no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—24no—
432C2×D4—48no—
433C2×D4—432no—
434C2×D4—48no—
435C2×D4—42no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—42no—
439C2×D4C2×C22⋊D1714yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—682no—
463C22×C4—682no—
464C22×C4—682no—
465C22×C4—682no—
466C22×C4—682no—
467C22×C4—682no—
468C22×C4D4×D1712yes—
469C22×C4#6325412yes—
470C22×C4#6325412yes—
471C22×C4#6325412yes—
472C22×C4C2×C22⋊D1712yes—
473C22×C4C2×C22⋊D1712yes—
474C22×C4C2×C22⋊D1712yes—
475C22×C4C2×C22⋊D1711yescharacteristic
476C22×C4C23×D1711yescharacteristic
477C2×C8—174no—
478C2×C8—342no—
479C2×C8—342no—
480C2×C8—348no—
481C2×C8—342no—
482C2×C8—342no—
483C2×C8—342no—
484C2×C8—684no—
485C4⋊C4—22no—
486C4⋊C4—24no—
487C4⋊C4—342no—
488C4⋊C4—342no—
489C4⋊C4—342no—
490C4⋊C4—342no—
491C4⋊C4—682no—
492C4⋊C4—682no—
493C4⋊C4C2×C22⋊D1714yes—
494C22⋊C4—216no—
495C22⋊C4—688no—
496C23—22no—
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—28no—
504C23—28no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—48no—
511C23—48no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—48no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—84no—
523C23C2×#6322814yes—
524C23C2×#6322812yes—
525C23#1058761812yes—
526C23#1058762112yes—
527C23#1058762512yes—
528C23#1058763612yes—
529C23#1058763712yes—
530C23#1058763912yes—
531C23C22×C22⋊D1711yescharacteristic
532D4—24no—
533D4—24no—
534D4—432no—
535D4—48no—
536D4—42no—
537D4—42no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—48no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
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#1058762112yes—
560C2×C4#1058762114yes—
561C2×C4#1058762214yes—
562C2×C4#1058762414yes—
563C2×C4#1058762512yes—
564C2×C4#1058762514yes—
565C2×C4#1058763912yes—
566C2×C4C2×D4×D1711yescharacteristic
567C2×C4C2×#6325411yescharacteristic
568C2×C4C2×#6325411yescharacteristic
569C2×C4C2×#6325411yescharacteristic
570C2×C4C22×C22⋊D1711yescharacteristic
571C2×C4C22×C22⋊D1711yescharacteristic
572C8—344no—
573C8—682no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—416no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—816no—
590C22#1176272314yes—
591C22#1176294314yes—
592C22#1176297114yes—
593C22#1176304314yes—
594C22#1176305314yes—
595C22#1176312014yes—
596C22#1176313014yes—
597C22C2×#1058763911yescharacteristic
598C22C2×#1058762511yescharacteristic
599C22C2×#1058762111yescharacteristic
600C22C22×#6322811yescharacteristic
601C22C2×#1058763611yescharacteristic
602C22C2×#1058761811yescharacteristic
603C22C2×#1058763711yescharacteristic
604C4—42no—
605C4—44no—
606C4—1362no—
607C4—1362no—
608C4#1176272314yes—
609C4C2×#1058762411yescharacteristic
610C4C2×#1058762511yescharacteristic
611C4C2×#1058762111yescharacteristic
612C4C2×#1058762211yescharacteristic
613C2—44no—
614C2—84no—
615C2#1452996318yesdirect product factor
616C2C2×#1176272311yescharacteristic
617C2C2×#1176294311yescharacteristic
618C2C2×#1176297111yescharacteristic
619C2C2×#1176304311yescharacteristic
620C2C2×#1176305311yescharacteristic
621C2C2×#1176312011yescharacteristic
622C2C2×#1176313011yescharacteristic
subgroupG/H
centerC24C2×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
Fitting, prime radicalC22×C17×#121C2
socleC24×C17C2×D4
hypercenterC22×#121D17
hypocenterC17C2×#2033
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#10587478C2semidirect
2. C22×#10587503C2semidirect
3. C22×#10587503C2semidirect
4. C22×C22⋊#3622C2semidirect
5. C2×#11762669C2semidirect
6. #14529963C2direct (N × H)
7. C2×#11762571C2semidirect
15. C2×#10587478C22semidirect
18. C2×#10587503C22semidirect
19. C2×#10587503C22semidirect
21. C2×C22⋊#3622C22semidirect
23. #11762669C22semidirect
25. #11762571C22semidirect
86. C22×#3622D4semidirect
183. C2×#3622C2×D4semidirect
338. C2×C17#2033semidirect
405. C17C2×#2033semidirect
615. C2#14529963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105874782
C22×#105875032
C22×C22⋊#36222
C2×#117626692
#145299632
C2×#117625712
C22×C17×#1212
C2×#203317