Finite Group Databasebeta

← C2×#14529100 #17035523

Subgroups — C2×#14529100 #17035523

Order 4352.

2614 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587581C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C22×#10587492C211yesmaximal, characteristic, complemented
4C22×#10587480C211yesmaximal, characteristic, complemented
5C22×#10587491C211yesmaximal, characteristic, complemented
6#14529100C218yesmaximal, direct product factor
7C2×#11762571C211yesmaximal, characteristic, complemented
8C2×C17×#340C211yesmaximal, characteristic, complemented
9C23×D68—21no—
10C23×D68C2211yescharacteristic
11C23×C4×D17—21no—
12C23×C4×D17C2211yescharacteristic
13C23×#3622C2211yescharacteristic
14C2×#10587581—22no—
15C2×#10587581—24no—
16C2×#10587581C418yescomplemented
17C2×#10587581C2214yes—
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225—21no—
20C2×C4⋊C4×D17—24no—
21C2×C4⋊C4×D17—24no—
22C2×C4⋊C4×D17—22no—
23C2×C4⋊C4×D17C2214yescomplemented
24C22×#63227—21no—
25C2×#10587492—24no—
26C2×#10587492C2214yescomplemented
27C2×#10587480—24no—
28C2×#10587480C2214yescomplemented
29C2×#10587491—24no—
30C2×#10587491C2214yescomplemented
31#11762571C2214yescomplemented
32C23×C8×C17C2211yescharacteristic
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C4⋊C4×C17C2211yescharacteristic
35C17×#340C2214yescomplemented
36C24×D17—21no—
37C24×D17D411yescharacteristic
38C23×C4×C17—21no—
39C23×C4×C17—21no—
40C23×C4×C17C2311yescharacteristic
41C23×Dic17—21no—
42C23×Dic17D411yescharacteristic
43C22×D68—22no—
44C22×D68—22no—
45C22×D68—22no—
46C22×D68—22no—
47C22×D68—28no—
48C22×D68—24no—
49C22×D68—21no—
50C22×D68—22no—
51C22×D68—44no—
52C22×D68—44no—
53C22×D68C2×C414yescomplemented
54C22×D68C2312yes—
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17—22no—
58C22×C4×D17—22no—
59C22×C4×D17—28no—
60C22×C4×D17—24no—
61C22×C4×D17—44no—
62C22×C4×D17—44no—
63C22×C4×D17C2×C414yes—
64C22×C4×D17D412yes—
65C22×C4×D17D414yes—
66C22×C4×D17C2312yes—
67C22×C8×C17—22no—
68C22×C8×C17—22no—
69C22×C8×C17—22no—
70C22×C8×C17C2312yes—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17—22no—
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17—22no—
75C2×C4⋊C4×C17C2×C414yescomplemented
76C2×C4⋊C4×C17D414yescomplemented
77C2×C4⋊C4×C17C2312yes—
78C2×C4⋊C4×C17C2312yes—
79C2×#63227—28no—
80C2×#63227—24no—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17—21no—
83C2×C4⋊Dic17D414yescomplemented
84C2×C4⋊Dic17C2312yes—
85C2×#63225—28no—
86C2×#63225—24no—
87C22×#3622—22no—
88C22×#3622—22no—
89C22×#3622—22no—
90C22×#3622C2312yes—
91#10587581—216no—
92#10587581—28no—
93#10587581C2×C4116yescomplemented
94C4⋊C4×D17—216no—
95C4⋊C4×D17—28no—
96C4⋊C4×D17—28no—
97#10587492—28no—
98#10587491—28no—
99#10587480—28no—
100C24×C17C2×D411yescharacteristic
101C23×D17—22no—
102C23×D17—22no—
103C23×D17—22no—
104C23×D17—22no—
105C23×D17—24no—
106C23×D17—22no—
107C23×D17—42no—
108C23×D17—42no—
109C23×D17—42no—
110C23×D17—42no—
111C23×D17—42no—
112C23×D17—42no—
113C23×D17C22⋊C414yes—
114C23×D17D814yes—
115C23×D17SD1614yes—
116C23×D17C2×D412yes—
117C22×C4×C17—24no—
118C22×C4×C17—24no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—42no—
122C22×C4×C17—42no—
123C22×C4×C17—42no—
124C22×C4×C17—42no—
125C22×C4×C17C22×C412yes—
126C22×C4×C17C2×D412yes—
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×D412yes—
129C22×C4×C17C2×D412yes—
130C22×C4×C17#4112yes—
131C22×C4×C17#4112yes—
132C22×C4×C17C2411yescharacteristic
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—24no—
136C22×Dic17—22no—
137C22×Dic17—42no—
138C22×Dic17—42no—
139C22×Dic17C22⋊C414yes—
140C22×Dic17C2×D412yes—
141C2×D68—28no—
142C2×D68—28no—
143C2×D68—22no—
144C2×D68—22no—
145C2×D68—22no—
146C2×D68—22no—
147C2×D68—216no—
148C2×D68—24no—
149C2×D68—22no—
150C2×D68—432no—
151C2×D68—48no—
152C2×D68—48no—
153C2×D68—42no—
154C2×D68—44no—
155C2×D68—44no—
156C2×D68—42no—
157C2×D68C22×C414yescomplemented
158C2×C4×D17—28no—
159C2×C4×D17—28no—
160C2×C4×D17—24no—
161C2×C4×D17—28no—
162C2×C4×D17—28no—
163C2×C4×D17—24no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—22no—
167C2×C4×D17—22no—
168C2×C4×D17—216no—
169C2×C4×D17—48no—
170C2×C4×D17—432no—
171C2×C4×D17—48no—
172C2×C4×D17C22⋊C418yes—
173C2×C4×D17C22×C414yes—
174C2×C4×D17C2×D414yes—
175C2×C8×C17—22no—
176C2×C8×C17—22no—
177C2×C8×C17—22no—
178C2×C8×C17—44no—
179C4⋊C4×C17—24no—
180C4⋊C4×C17—24no—
181C4⋊C4×C17—22no—
182C4⋊C4×C17—22no—
183C4⋊C4×C17C22×C414yescomplemented
184C4⋊C4×C17C2×D414yescomplemented
185#63227—216no—
186C4⋊Dic17—24no—
187C4⋊Dic17—22no—
188C4⋊Dic17C2×D414yescomplemented
189#63225—216no—
190C2×#3622—22no—
191C2×#3622—22no—
192C2×#3622—22no—
193C2×#3622—44no—
194C2×#1874—171nomaximal, Sylow
195C23×C17C2×C22⋊C412yes—
196C23×C17#12012yes—
197C23×C17#12312yes—
198C23×C17C2×D812yes—
199C23×C17C2×SD1612yes—
200C23×C17AGL(1,ℤ/8)12yes—
201C23×C17#13712yes—
202C23×C17C22×D411yescharacteristic
203C22×D17—22no—
204C22×D17—22no—
205C22×D17—22no—
206C22×D17—22no—
207C22×D17—28no—
208C22×D17—28no—
209C22×D17—28no—
210C22×D17—28no—
211C22×D17—28no—
212C22×D17—28no—
213C22×D17—24no—
214C22×D17—42no—
215C22×D17—42no—
216C22×D17—42no—
217C22×D17—42no—
218C22×D17—42no—
219C22×D17—42no—
220C22×D17—48no—
221C22×D17—48no—
222C22×D17—48no—
223C22×D17—84no—
224C22×D17—84no—
225C22×D17—84no—
226C22×D17—84no—
227C22×D17#102116yescomplemented
228C22×D17C2×C22⋊C414yes—
229C22×D17C2×D814yes—
230C22×D17C2×SD1614yes—
231C2×C4×C17—24no—
232C2×C4×C17—24no—
233C2×C4×C17—42no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—48no—
238C2×C4×C17—48no—
239C2×C4×C17C2×C22⋊C412yes—
240C2×C4×C17C4×D414yes—
241C2×C4×C17C4×D414yes—
242C2×C4×C17#12012yes—
243C2×C4×C17#12114yes—
244C2×C4×C17#12114yes—
245C2×C4×C17#12312yes—
246C2×C4×C17C23×C411yescharacteristic
247C2×C4×C17C22×D411yescharacteristic
248C2×C4×C17C22×D411yescharacteristic
249C2×C4×C17C22×D411yescharacteristic
250C2×C4×C17C2×#4111yescharacteristic
251C2×C4×C17C2×#4111yescharacteristic
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—28no—
255C2×Dic17—24no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—48no—
259C2×Dic17C2×C22⋊C414yes—
260D68—24no—
261D68—24no—
262D68—432no—
263D68—42no—
264D68—42no—
265D68—48no—
266C4×D17—24no—
267C4×D17—24no—
268C4×D17—24no—
269C4×D17—24no—
270C4×D17—216no—
271C4×D17—432no—
272C8×C17—42no—
273#3622—42no—
274C22×#121—171no—
275C23×C4⋊C4—171no—
276C22×#102—171no—
277C22×#102—171no—
278C22×C22⋊C8—171no—
279#1874—178no—
280C2×#340—171no—
281C2×#340D1711yescharacteristic, complemented
282C22×C17#38614yes—
283C22×C17C2×#10214yes—
284C22×C17#41714yes—
285C22×C17#44714yes—
286C22×C17#44814yes—
287C22×C17#48014yes—
288C22×C17#48114yes—
289C22×C17C22×C22⋊C411yescharacteristic
290C22×C17C2×#12011yescharacteristic
291C22×C17C2×#12311yescharacteristic
292C22×C17C22×D811yescharacteristic
293C22×C17C22×SD1611yescharacteristic
294C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C17C2×#13711yescharacteristic
296C2×D17—24no—
297C2×D17—24no—
298C2×D17—24no—
299C2×D17—232no—
300C2×D17—24no—
301C2×D17—24no—
302C2×D17—24no—
303C2×D17—44no—
304C2×D17—44no—
305C2×D17—44no—
306C2×D17—82no—
307C2×D17—82no—
308C2×D17—816no—
309C2×D17—82no—
310C2×D17—82no—
311C2×D17C2×#10218yescomplemented
312C4×C17—44no—
313C4×C17—44no—
314C4×C17#38614yes—
315C4×C17C2×C4×D411yescharacteristic
316C4×C17C2×C4×D411yescharacteristic
317C4×C17C2×#12111yescharacteristic
318C4×C17C2×#12111yescharacteristic
319Dic17—24no—
320Dic17—44no—
321C23×D4—171no—
322C23×D4—341no—
323C24×C4—171no—
324C24×C4—341no—
325C23×C8—171no—
326C23×C8C2×D1711yescharacteristic
327C2×#121—178no—
328C2×#121—174no—
329C2×#121—342no—
330C2×#121—344no—
331C22×C4⋊C4—171no—
332C22×C4⋊C4—174no—
333C22×C4⋊C4—344no—
334C22×C4⋊C4—342no—
335C22×C4⋊C4—341no—
336C22×C4⋊C4—344no—
337C22×C4⋊C4C2×D1711yescharacteristic
338C22×C4⋊C4C2×D1711yescharacteristic
339C22×C22⋊C4—341no—
340C2×#102—174no—
341C2×#102—174no—
342C2×#102—344no—
343C2×#102—344no—
344C2×C22⋊C8—174no—
345C2×C22⋊C8—344no—
346#340—174no—
347#340C2×D1714yescomplemented
348C2×C17#187418yescomplemented
349C2×C17C2×#38611yescharacteristic
350C2×C17C22×#10211yescharacteristic
351C2×C17C2×#41711yescharacteristic
352C2×C17C2×#44711yescharacteristic
353C2×C17C2×#44811yescharacteristic
354C2×C17C2×#48011yescharacteristic
355C2×C17C2×#48111yescharacteristic
356D17—28no—
357D17—84no—
358C25—171no—
359C25—341no—
360C22×D4—174no—
361C22×D4—172no—
362C22×D4—344no—
363C22×D4—348no—
364C22×D4—342no—
365C22×D4—342no—
366C22×D4—342no—
367C22×D4—342no—
368C22×D4—341no—
369C22×D4—342no—
370C22×D4—684no—
371C22×D4—684no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—171no—
375C23×C4—174no—
376C23×C4—172no—
377C23×C4—174no—
378C23×C4—172no—
379C23×C4—344no—
380C23×C4—348no—
381C23×C4—342no—
382C23×C4—342no—
383C23×C4—342no—
384C23×C4—342no—
385C23×C4—341no—
386C23×C4—684no—
387C23×C4—684no—
388C23×C4C22×D1711yescharacteristic
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—172no—
393C22×C8—342no—
394C22×C8—342no—
395C22×C8—342no—
396C22×C8C22×D1712yes—
397#121—1716no—
398#121—348no—
399#121—3416no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—174no—
405C2×C4⋊C4—172no—
406C2×C4⋊C4—348no—
407C2×C4⋊C4—3416no—
408C2×C4⋊C4—344no—
409C2×C4⋊C4—348no—
410C2×C4⋊C4—342no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—348no—
413C2×C4⋊C4C4×D1714yescomplemented
414C2×C4⋊C4D6814yescomplemented
415C2×C4⋊C4C22×D1712yes—
416C2×C4⋊C4C22×D1712yes—
417C2×C22⋊C4—344no—
418C2×C22⋊C4—348no—
419#102—348no—
420#102—348no—
421C22⋊C8—348no—
422C17C2×#187411yescharacteristic, complemented, Sylow
423C24—172no—
424C24—174no—
425C24—174no—
426C24—174no—
427C24—342no—
428C24—342no—
429C24—342no—
430C24—342no—
431C24—342no—
432C24—344no—
433C24—682no—
434C24—682no—
435C24—682no—
436C24—682no—
437C24—682no—
438C24—682no—
439C24D4×D1711yescharacteristic
440C2×D4—174no—
441C2×D4—3416no—
442C2×D4—342no—
443C2×D4—342no—
444C2×D4—342no—
445C2×D4—342no—
446C2×D4—342no—
447C2×D4—348no—
448C2×D4—344no—
449C2×D4—348no—
450C2×D4—6832no—
451C2×D4—688no—
452C2×D4—688no—
453C2×D4—682no—
454C2×D4—684no—
455C2×D4—682no—
456C2×D4—684no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—172no—
466C22×C4—174no—
467C22×C4—174no—
468C22×C4—174no—
469C22×C4—178no—
470C22×C4—3416no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—348no—
478C22×C4—344no—
479C22×C4—348no—
480C22×C4—348no—
481C22×C4—344no—
482C22×C4—348no—
483C22×C4—342no—
484C22×C4—344no—
485C22×C4—688no—
486C22×C4—6832no—
487C22×C4—688no—
488C22×C4—682no—
489C22×C4—682no—
490C22×C4C2×C4×D1712yes—
491C22×C4C2×D6812yes—
492C22×C4#6325212yes—
493C22×C4D4×D1712yes—
494C22×C4D4×D1712yes—
495C22×C4D4×D1711yescharacteristic
496C22×C4#6325612yes—
497C22×C4C23×D1711yescharacteristic
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—44no—
502C2×C8—342no—
503C2×C8—342no—
504C2×C8—342no—
505C2×C8—684no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—174no—
511C4⋊C4—3416no—
512C4⋊C4—342no—
513C4⋊C4—344no—
514C4⋊C4C2×C4×D1714yescomplemented
515C4⋊C4C2×D6814yescomplemented
516C22⋊C4—3416no—
517C23—174no—
518C23—1716no—
519C23—174no—
520C23—174no—
521C23—348no—
522C23—348no—
523C23—342no—
524C23—342no—
525C23—348no—
526C23—342no—
527C23—342no—
528C23—348no—
529C23—348no—
530C23—348no—
531C23—344no—
532C23—682no—
533C23—688no—
534C23—682no—
535C23—688no—
536C23—682no—
537C23—682no—
538C23—682no—
539C23—682no—
540C23—688no—
541C23—1364no—
542C23—1364no—
543C23—1364no—
544C23—1364no—
545C23C22⋊C4×D1712yes—
546C23#1058756812yes—
547C23#1058758012yes—
548C23D8×D1712yes—
549C23SD16×D1712yes—
550C23#1058760012yes—
551C23#1058760412yes—
552C23C2×D4×D1711yescharacteristic
553D4—344no—
554D4—344no—
555D4—6832no—
556D4—682no—
557D4—682no—
558D4—688no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—174no—
568C2×C4—342no—
569C2×C4—342no—
570C2×C4—348no—
571C2×C4—344no—
572C2×C4—344no—
573C2×C4—344no—
574C2×C4—344no—
575C2×C4—3416no—
576C2×C4—344no—
577C2×C4—6832no—
578C2×C4—688no—
579C2×C4—682no—
580C2×C4—682no—
581C2×C4C4×D6814yes—
582C2×C4C22⋊C4×D1712yes—
583C2×C4#1058756812yes—
584C2×C4#1058757014yes—
585C2×C4#1058757914yes—
586C2×C4#1058758012yes—
587C2×C4#1058758114yes—
588C2×C4C22×C4×D1711yescharacteristic
589C2×C4C22×D6811yescharacteristic
590C2×C4C2×#6325211yescharacteristic
591C2×C4C2×D4×D1711yescharacteristic
592C2×C4C2×D4×D1711yescharacteristic
593C2×C4C2×#6325611yescharacteristic
594C8—42no—
595C8—682no—
596C22—178no—
597C22—3432no—
598C22—344no—
599C22—344no—
600C22—344no—
601C22—344no—
602C22—344no—
603C22—344no—
604C22—684no—
605C22—684no—
606C22—684no—
607C22—13616no—
608C22—1362no—
609C22—1362no—
610C22—1362no—
611C22—1362no—
612C22#1176268714yes—
613C22#102×D1714yes—
614C22#1176280914yes—
615C22#1176294414yes—
616C22#1176294914yes—
617C22#1176312414yes—
618C22#1176312914yes—
619C22C2×C22⋊C4×D1711yescharacteristic
620C22C2×#1058756811yescharacteristic
621C22C2×#1058758011yescharacteristic
622C22C2×D8×D1711yescharacteristic
623C22C2×SD16×D1711yescharacteristic
624C22C2×#1058760011yescharacteristic
625C22C2×#1058760411yescharacteristic
626C4—44no—
627C4—44no—
628C4—344no—
629C4—684no—
630C4#1176268714yes—
631C4C2×#1058757911yescharacteristic
632C4C2×C4×D6811yescharacteristic
633C4C2×#1058757011yescharacteristic
634C4C2×#1058758111yescharacteristic
635C2—348no—
636C2—1364no—
637C2#1452910018yesdirect product factor
638C2C2×#1176268711yescharacteristic
639C2C2×#102×D1711yescharacteristic
640C2C2×#1176280911yescharacteristic
641C2C2×#1176294411yescharacteristic
642C2C2×#1176294911yescharacteristic
643C2C2×#1176312411yescharacteristic
644C2C2×#1176312911yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#340C2
socleC24×C17C2×D4
prime radicalC22×#10587581C2
cosocleC22×C4×C17C24
hypercenterC2×#340D17
hypocenterC17C2×#1874
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
3. C22×#10587492C2semidirect
4. C22×#10587480C2semidirect
5. C22×#10587491C2semidirect
6. #14529100C2direct (N × H)
7. C2×#11762571C2semidirect
8. C2×C17×#340C2semidirect
16. C2×#10587581C4semidirect
23. C2×C4⋊C4×D17C22semidirect
26. C2×#10587492C22semidirect
28. C2×#10587480C22semidirect
30. C2×#10587491C22semidirect
31. #11762571C22semidirect
35. C17×#340C22semidirect
53. C22×D68C2×C4semidirect
75. C2×C4⋊C4×C17C2×C4semidirect
76. C2×C4⋊C4×C17D4semidirect
83. C2×C4⋊Dic17D4semidirect
93. #10587581C2×C4semidirect
157. C2×D68C22×C4semidirect
183. C4⋊C4×C17C22×C4semidirect
184. C4⋊C4×C17C2×D4semidirect
188. C4⋊Dic17C2×D4semidirect
227. C22×D17#102semidirect
281. C2×#340D17semidirect
311. C2×D17C2×#102semidirect
347. #340C2×D17semidirect
348. C2×C17#1874semidirect
413. C2×C4⋊C4C4×D17semidirect
414. C2×C4⋊C4D68semidirect
422. C17C2×#1874semidirect
514. C4⋊C4C2×C4×D17semidirect
515. C4⋊C4C2×D68semidirect
637. C2#14529100direct (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×C4⋊C4×D172
C22×#105874922
C22×#105874802
C22×#105874912
#145291002
C2×#117625712
C2×C17×#3402
C2×#187417