Finite Group Databasebeta

← C2×#14529968 #17061774

Subgroups — C2×#14529968 #17061774

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×#10587581C211yesmaximal, characteristic
2C22×#10587492C211yesmaximal, characteristic, complemented
3C22×#10587480C211yesmaximal, characteristic, complemented
4C22×#10587491C211yesmaximal, characteristic, complemented
5C2×#11762666C211yesmaximal, characteristic, complemented
6#14529968C218yesmaximal, direct product factor
7C2×#11762571C211yesmaximal, characteristic, complemented
8C22×C17×#107C211yesmaximal, characteristic, complemented
9C23×D68—21no—
10C23×D68C2211yescharacteristic
11C23×C4×D17C2211yescharacteristic
12C23×#3622C2211yescharacteristic
13C2×#10587581—24no—
14C2×#10587581—24no—
15C2×#10587581—22no—
16C2×#10587581C2214yes—
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63227—21no—
19C22×#63227—21no—
20C2×#10587492—24no—
21C2×#10587492C2214yescomplemented
22C2×#10587480—24no—
23C2×#10587480C2214yescomplemented
24C2×#10587491—24no—
25C2×#10587491C2214yescomplemented
26#11762666—22no—
27#11762666C2214yescomplemented
28C2×#10587502—21no—
29#11762571C2214yescomplemented
30C23×C8×C17C2211yescharacteristic
31C22×C4⋊C4×C17C2211yescharacteristic
32C22×C4⋊C4×C17C2211yescharacteristic
33C2×C17×#107—24no—
34C2×C17×#107C2214yescomplemented
35C24×D17—21no—
36C24×D17D411yescharacteristic
37C23×C4×C17—21no—
38C23×C4×C17—21no—
39C23×C4×C17C2311yescharacteristic
40C23×Dic17—21no—
41C23×Dic17D411yescharacteristic
42C22×D68—22no—
43C22×D68—22no—
44C22×D68—22no—
45C22×D68—22no—
46C22×D68—28no—
47C22×D68—24no—
48C22×D68—21no—
49C22×D68—22no—
50C22×D68—44no—
51C22×D68—44no—
52C22×D68D414yes—
53C22×D68C2312yes—
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×C17D414yescomplemented
65C22×C8×C17C2312yes—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—22no—
68C2×C4⋊C4×C17—22no—
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17D414yes—
72C2×C4⋊C4×C17C2312yes—
73C2×C4⋊C4×C17C2312yes—
74C2×#63227—28no—
75C2×#63227—24no—
76C2×#63227—24no—
77C2×#63227—44no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—22no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17C2312yes—
82C22×#3622—22no—
83C22×#3622—22no—
84C22×#3622—22no—
85C22×#3622C2312yes—
86#10587581—216no—
87#10587581—28no—
88#10587581—28no—
89C17×#107—28no—
90#10587502—24no—
91#10587492—28no—
92#10587491—28no—
93#10587480—28no—
94C24×C17C2×D411yescharacteristic
95C23×D17—22no—
96C23×D17—22no—
97C23×D17—22no—
98C23×D17—22no—
99C23×D17—22no—
100C23×D17—22no—
101C23×D17—24no—
102C23×D17—22no—
103C23×D17—42no—
104C23×D17—42no—
105C23×D17—42no—
106C23×D17—42no—
107C23×D17—42no—
108C23×D17—42no—
109C23×D17D814yes—
110C23×D17C2×D412yes—
111C22×C4×C17—24no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—42no—
115C22×C4×C17—42no—
116C22×C4×C17—42no—
117C22×C4×C17—42no—
118C22×C4×C17—42no—
119C22×C4×C17C2×D412yes—
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D412yes—
122C22×C4×C17C2×D412yes—
123C22×C4×C17#4112yes—
124C22×C4×C17#4112yes—
125C22×C4×C17#4112yes—
126C22×C4×C17C2411yescharacteristic
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—22no—
130C22×Dic17—22no—
131C22×Dic17—42no—
132C22×Dic17—42no—
133C22×Dic17—42no—
134C22×Dic17C2×D412yes—
135C2×D68—28no—
136C2×D68—28no—
137C2×D68—22no—
138C2×D68—22no—
139C2×D68—22no—
140C2×D68—22no—
141C2×D68—216no—
142C2×D68—24no—
143C2×D68—22no—
144C2×D68—48no—
145C2×D68—432no—
146C2×D68—48no—
147C2×D68—42no—
148C2×D68—44no—
149C2×D68—42no—
150C2×D68—44no—
151C2×D68C2×D414yes—
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—28no—
166C2×C8×C17—22no—
167C2×C8×C17—22no—
168C2×C8×C17C2×D414yescomplemented
169C4⋊C4×C17—24no—
170C4⋊C4×C17—22no—
171C4⋊C4×C17—22no—
172C4⋊C4×C17—22no—
173C4⋊C4×C17—42no—
174C4⋊C4×C17C2×D414yes—
175#63227—216no—
176#63227—48no—
177C4⋊Dic17—22no—
178C4⋊Dic17—22no—
179C4⋊Dic17—42no—
180C2×#3622—22no—
181C2×#3622—22no—
182C2×#3622—22no—
183C2×#3622—44no—
184C2×#2033—171nomaximal, Sylow
185C23×C17#12012yes—
186C23×C17#12112yes—
187C23×C17#12312yes—
188C23×C17C2×D812yes—
189C23×C17#13512yes—
190C23×C17AGL(1,ℤ/8)12yes—
191C23×C17#13712yes—
192C23×C17C22×D411yescharacteristic
193C22×D17—22no—
194C22×D17—22no—
195C22×D17—22no—
196C22×D17—22no—
197C22×D17—22no—
198C22×D17—22no—
199C22×D17—28no—
200C22×D17—28no—
201C22×D17—28no—
202C22×D17—24no—
203C22×D17—44no—
204C22×D17—44no—
205C22×D17—44no—
206C22×D17—44no—
207C22×D17—42no—
208C22×D17—42no—
209C22×D17—42no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—42no—
213C22×D17—48no—
214C22×D17—48no—
215C22×D17—48no—
216C22×D17—84no—
217C22×D17—84no—
218C22×D17—84no—
219C22×D17—84no—
220C22×D17C2×D814yes—
221C2×C4×C17—24no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—48no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—84no—
229C2×C4×C17#12012yes—
230C2×C4×C17#12114yes—
231C2×C4×C17#12112yes—
232C2×C4×C17#12114yes—
233C2×C4×C17#12314yes—
234C2×C4×C17#12312yes—
235C2×C4×C17#12414yes—
236C2×C4×C17C22×D411yescharacteristic
237C2×C4×C17C22×D411yescharacteristic
238C2×C4×C17C22×D411yescharacteristic
239C2×C4×C17C2×#4111yescharacteristic
240C2×C4×C17C2×#4111yescharacteristic
241C2×C4×C17C2×#4111yescharacteristic
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—44no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—84no—
250D68—24no—
251D68—24no—
252D68—432no—
253D68—42no—
254D68—42no—
255D68—48no—
256C4×D17—42no—
257C4×D17—42no—
258C4×D17—42no—
259C4×D17—42no—
260C4×D17—48no—
261C8×C17—24no—
262#3622—42no—
263C22×#121—171no—
264C22×#107D1711yescharacteristic, complemented
265C22×#102—171no—
266C22×#102—171no—
267C22×C22⋊C8—171no—
268C2×#380—171no—
269#2033—178no—
270C2×#340—171no—
271C22×C17#39414yes—
272C22×C17#44714yes—
273C22×C17#45214yes—
274C22×C17#46614yes—
275C22×C17#46814yes—
276C22×C17#48014yes—
277C22×C17#48214yes—
278C22×C17C2×#12011yescharacteristic
279C22×C17C2×#12111yescharacteristic
280C22×C17C2×#12311yescharacteristic
281C22×C17C22×D811yescharacteristic
282C22×C17C2×#13511yescharacteristic
283C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C17C2×#13711yescharacteristic
285C2×D17—24no—
286C2×D17—24no—
287C2×D17—24no—
288C2×D17—42no—
289C2×D17—42no—
290C2×D17—42no—
291C2×D17—42no—
292C2×D17—416no—
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—44no—
302C4×C17—82no—
303C4×C17#39414yes—
304C4×C17C2×#12111yescharacteristic
305C4×C17C2×#12111yescharacteristic
306C4×C17C2×#12311yescharacteristic
307C4×C17C2×#12411yescharacteristic
308Dic17—42no—
309Dic17—82no—
310C23×D4—171no—
311C23×D4—341no—
312C24×C4—171no—
313C23×C8—171no—
314C23×C8C2×D1711yescharacteristic
315C2×#121—174no—
316C2×#121—342no—
317C2×#121—344no—
318C2×#121—344no—
319C22×C4⋊C4—171no—
320C22×C4⋊C4C2×D1711yescharacteristic
321C22×C4⋊C4C2×D1711yescharacteristic
322C22×C22⋊C4—341no—
323C22×C22⋊C4—341no—
324C2×#107—24no—
325C2×#107C2×D1714yescomplemented
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#203318yescomplemented
337C2×C17C2×#39411yescharacteristic
338C2×C17C2×#44711yescharacteristic
339C2×C17C2×#45211yescharacteristic
340C2×C17C2×#46611yescharacteristic
341C2×C17C2×#46811yescharacteristic
342C2×C17C2×#48011yescharacteristic
343C2×C17C2×#48211yescharacteristic
344D17—44no—
345D17—84no—
346C25—171no—
347C25—341no—
348C22×D4—174no—
349C22×D4—172no—
350C22×D4—344no—
351C22×D4—348no—
352C22×D4—342no—
353C22×D4—342no—
354C22×D4—341no—
355C22×D4—342no—
356C22×D4—342no—
357C22×D4—342no—
358C22×D4—684no—
359C22×D4—684no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—171no—
363C23×C4—172no—
364C23×C4—172no—
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—172no—
376C22×C8—342no—
377C22×C8—342no—
378C22×C8—342no—
379C22×C8D6814yescomplemented
380C22×C8C22×D1712yes—
381#121—348no—
382#121—3416no—
383#121—348no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—172no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4C22⋊D1714yes—
394C2×C4⋊C4C22×D1712yes—
395C2×C4⋊C4C22×D1712yes—
396C2×C22⋊C4—344no—
397C2×C22⋊C4—348no—
398C2×C22⋊C4—344no—
399C2×C22⋊C4—684no—
400#107—28no—
401#102—348no—
402#102—348no—
403C22⋊C8—348no—
404#95—344no—
405C17C2×#203311yescharacteristic, complemented, Sylow
406C24—172no—
407C24—174no—
408C24—342no—
409C24—342no—
410C24—342no—
411C24—342no—
412C24—342no—
413C24—342no—
414C24—342no—
415C24—344no—
416C24—682no—
417C24—682no—
418C24—682no—
419C24—682no—
420C24—682no—
421C24—682no—
422C24D4×D1711yescharacteristic
423C2×D4—174no—
424C2×D4—3416no—
425C2×D4—342no—
426C2×D4—342no—
427C2×D4—342no—
428C2×D4—342no—
429C2×D4—342no—
430C2×D4—348no—
431C2×D4—348no—
432C2×D4—344no—
433C2×D4—688no—
434C2×D4—688no—
435C2×D4—6832no—
436C2×D4—682no—
437C2×D4—682no—
438C2×D4—684no—
439C2×D4—684no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—172no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—344no—
459C22×C4—344no—
460C22×C4—344no—
461C22×C4—342no—
462C22×C4—684no—
463C22×C4—684no—
464C22×C4—684no—
465C22×C4—684no—
466C22×C4—682no—
467C22×C4—682no—
468C22×C4—682no—
469C22×C4C2×D6812yes—
470C22×C4#6325212yes—
471C22×C4D4×D1712yes—
472C22×C4D4×D1711yescharacteristic
473C22×C4#6325612yes—
474C22×C4#6325612yes—
475C22×C4C2×C22⋊D1712yes—
476C22×C4C23×D1711yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—28no—
480C2×C8—342no—
481C2×C8—342no—
482C2×C8—342no—
483C2×C8—684no—
484C2×C8C2×D6814yescomplemented
485C4⋊C4—22no—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—342no—
491C4⋊C4—342no—
492C4⋊C4—682no—
493C4⋊C4C2×C22⋊D1714yes—
494C22⋊C4—3416no—
495C22⋊C4—688no—
496C23—174no—
497C23—342no—
498C23—348no—
499C23—342no—
500C23—342no—
501C23—342no—
502C23—342no—
503C23—342no—
504C23—348no—
505C23—348no—
506C23—344no—
507C23—684no—
508C23—684no—
509C23—684no—
510C23—684no—
511C23—688no—
512C23—688no—
513C23—682no—
514C23—682no—
515C23—682no—
516C23—682no—
517C23—682no—
518C23—682no—
519C23—688no—
520C23—1364no—
521C23—1364no—
522C23—1364no—
523C23—1364no—
524C23#1058758012yes—
525C23#1058758112yes—
526C23D8×D1712yes—
527C23#1058759712yes—
528C23#1058760412yes—
529C23#1058760512yes—
530C23#1058762312yes—
531C23C2×D4×D1711yescharacteristic
532D4—344no—
533D4—344no—
534D4—6832no—
535D4—688no—
536D4—682no—
537D4—682no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—48no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4—342no—
547C2×C4—342no—
548C2×C4—342no—
549C2×C4—684no—
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#1058758012yes—
560C2×C4#1058758014yes—
561C2×C4#1058758112yes—
562C2×C4#1058758114yes—
563C2×C4#1058761614yes—
564C2×C4#1058762312yes—
565C2×C4#1058763314yes—
566C2×C4C22×D6811yescharacteristic
567C2×C4C2×#6325211yescharacteristic
568C2×C4C2×D4×D1711yescharacteristic
569C2×C4C2×#6325611yescharacteristic
570C2×C4C2×#6325611yescharacteristic
571C2×C4C22×C22⋊D1711yescharacteristic
572C8—24no—
573C8—682no—
574C22—344no—
575C22—344no—
576C22—344no—
577C22—682no—
578C22—682no—
579C22—682no—
580C22—682no—
581C22—6816no—
582C22—684no—
583C22—684no—
584C22—684no—
585C22—1362no—
586C22—1362no—
587C22—1362no—
588C22—1362no—
589C22—13616no—
590C22#1176272614yes—
591C22#1176294114yes—
592C22#1176297014yes—
593C22#1176304614yes—
594C22#1176305614yes—
595C22#1176312414yes—
596C22#1176313614yes—
597C22C2×#1058762311yescharacteristic
598C22C2×#1058758111yescharacteristic
599C22C2×#1058758011yescharacteristic
600C22C2×D8×D1711yescharacteristic
601C22C2×#1058760511yescharacteristic
602C22C2×#1058759711yescharacteristic
603C22C2×#1058760411yescharacteristic
604C4—44no—
605C4—82no—
606C4—682no—
607C4—1362no—
608C4#1176272614yes—
609C4C2×#1058761611yescharacteristic
610C4C2×#1058758111yescharacteristic
611C4C2×#1058758011yescharacteristic
612C4C2×#1058763311yescharacteristic
613C2—684no—
614C2—1364no—
615C2#1452996818yesdirect product factor
616C2C2×#1176272611yescharacteristic
617C2C2×#1176294111yescharacteristic
618C2C2×#1176297011yescharacteristic
619C2C2×#1176304611yescharacteristic
620C2C2×#1176305611yescharacteristic
621C2C2×#1176312411yescharacteristic
622C2C2×#1176313611yescharacteristic
subgroupG/H
centerC24D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#107C2
socleC24×C17C2×D4
prime radicalC22×#10587581C2
hypercenterC22×#107D17
hypocenterC17C2×#2033
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C22×#10587492C2semidirect
3. C22×#10587480C2semidirect
4. C22×#10587491C2semidirect
5. C2×#11762666C2semidirect
6. #14529968C2direct (N × H)
7. C2×#11762571C2semidirect
8. C22×C17×#107C2semidirect
21. C2×#10587492C22semidirect
23. C2×#10587480C22semidirect
25. C2×#10587491C22semidirect
27. #11762666C22semidirect
29. #11762571C22semidirect
34. C2×C17×#107C22semidirect
64. C22×C8×C17D4semidirect
168. C2×C8×C17C2×D4semidirect
264. C22×#107D17semidirect
325. C2×#107C2×D17semidirect
336. C2×C17#2033semidirect
379. C22×C8D68semidirect
405. C17C2×#2033semidirect
484. C2×C8C2×D68semidirect
615. C2#14529968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875812
C22×#105874922
C22×#105874802
C22×#105874912
C2×#117626662
#145299682
C2×#117625712
C22×C17×#1072
C2×#203317