Finite Group Databasebeta

← C2×#14529098 #17035521

Subgroups — C2×#14529098 #17035521

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×#10587624C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C22×#10587503C211yesmaximal, characteristic, complemented
4C22×#10587491C211yesmaximal, characteristic, complemented
5#14529098C218yesmaximal, direct product factor
6C2×#11762572C211yesmaximal, characteristic, complemented
7C2×#11762571C211yesmaximal, characteristic, complemented
8C22×C17×#102C211yesmaximal, characteristic, complemented
9C23×C22⋊D17—21no—
10C23×C4×D17—21no—
11C23×C4×D17C2211yescharacteristic
12C23×#3622C2211yescharacteristic
13C2×#10587624—22no—
14C2×#10587624—24no—
15C2×#10587624C418yescomplemented
16C2×#10587624C2214yes—
17C22×C4⋊Dic17C2211yescharacteristic
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×C22⋊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×C414yescomplemented
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×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×C17D414yescomplemented
74C2×C4⋊C4×C17C2312yes—
75C2×C22⋊Dic17—28no—
76C2×C22⋊Dic17—24no—
77#10587624—216no—
78#10587624—28no—
79#10587624C2×C4116yescomplemented
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17—21no—
84C2×C4⋊Dic17C2×C414yescomplemented
85C2×C4⋊Dic17D414yescomplemented
86C2×C4⋊Dic17C2312yes—
87C2×C4⋊Dic17C2312yes—
88C2×#63225—28no—
89C2×#63225—24no—
90C22×#3622—22no—
91C22×#3622—22no—
92C22×#3622—22no—
93C22×#3622C2312yes—
94C4⋊C4×D17—216no—
95C4⋊C4×D17—28no—
96C4⋊C4×D17—28no—
97C17×#102—28no—
98#10587503—28no—
99#10587491—28no—
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×C17C2×D411yescharacteristic
109C23×D17—22no—
110C23×D17—22no—
111C23×D17—22no—
112C23×D17—22no—
113C23×D17C22⋊C414yes—
114C23×D17D814yes—
115C23×D17SD1614yes—
116C23×D17C2×D412yes—
117C2×D4×C17—24no—
118C2×D4×C17—28no—
119C2×D4×C17—28no—
120C2×D4×C17—22no—
121C2×D4×C17—22no—
122C2×D4×C17—22no—
123C2×D4×C17—22no—
124C2×D4×C17—22no—
125C2×D4×C17—42no—
126C2×D4×C17—44no—
127C2×D4×C17—44no—
128C2×D4×C17—42no—
129C2×D4×C17C22×C414yescomplemented
130C22×C4×C17—24no—
131C22×C4×C17—22no—
132C22×C4×C17—42no—
133C22×C4×C17—42no—
134C22×C4×C17C22×C412yes—
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D412yes—
137C22×C4×C17C2×D412yes—
138C22×C4×C17C2×D412yes—
139C22×C4×C17#4112yes—
140C22×C4×C17#4112yes—
141C22×C4×C17C2411yescharacteristic
142C2×C22⋊D17—216no—
143C2×C22⋊D17—432no—
144C2×C22⋊D17—48no—
145C2×C22⋊D17—48no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—24no—
149C22×Dic17—24no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—42no—
153C22×Dic17—42no—
154C22×Dic17—42no—
155C22×Dic17—42no—
156C22×Dic17C22⋊C414yes—
157C22×Dic17C2×D412yes—
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—22no—
181C4⋊C4×C17C2×D414yescomplemented
182C22⋊Dic17—216no—
183C4⋊Dic17—24no—
184C4⋊Dic17—24no—
185C4⋊Dic17—22no—
186C4⋊Dic17—22no—
187C4⋊Dic17C22×C414yescomplemented
188C4⋊Dic17C2×D414yescomplemented
189#63225—216no—
190C2×#3622—22no—
191C2×#3622—22no—
192C2×#3622—22no—
193C2×#3622—44no—
194C2×#1874—171nomaximal, Sylow
195C23×C17—24no—
196C23×C17—42no—
197C23×C17—42no—
198C23×C17—42no—
199C23×C17—42no—
200C23×C17—42no—
201C23×C17—42no—
202C23×C17—48no—
203C23×C17—48no—
204C23×C17—48no—
205C23×C17—84no—
206C23×C17—84no—
207C23×C17—84no—
208C23×C17—84no—
209C23×C17C2×C22⋊C412yes—
210C23×C17#12012yes—
211C23×C17#12312yes—
212C23×C17C2×D812yes—
213C23×C17C2×SD1612yes—
214C23×C17AGL(1,ℤ/8)12yes—
215C23×C17#13712yes—
216C23×C17C22×D411yescharacteristic
217C22×D17—22no—
218C22×D17—22no—
219C22×D17—22no—
220C22×D17—22no—
221C22×D17—28no—
222C22×D17—28no—
223C22×D17—28no—
224C22×D17—28no—
225C22×D17—28no—
226C22×D17—28no—
227C22×D17#102116yescomplemented
228C22×D17C2×C22⋊C414yes—
229C22×D17C2×D814yes—
230C22×D17C2×SD1614yes—
231D4×C17—24no—
232D4×C17—24no—
233D4×C17—42no—
234D4×C17—42no—
235D4×C17—48no—
236C2×C4×C17—24no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—48no—
240C2×C4×C17C2×C22⋊C412yes—
241C2×C4×C17C4×D414yes—
242C2×C4×C17C4×D414yes—
243C2×C4×C17#12012yes—
244C2×C4×C17#12114yes—
245C2×C4×C17#12114yes—
246C2×C4×C17#12312yes—
247C2×C4×C17C23×C411yescharacteristic
248C2×C4×C17C22×D411yescharacteristic
249C2×C4×C17C22×D411yescharacteristic
250C2×C4×C17C22×D411yescharacteristic
251C2×C4×C17C2×#4111yescharacteristic
252C2×C4×C17C2×#4111yescharacteristic
253C22⋊D17—432no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—28no—
257C2×Dic17—24no—
258C2×Dic17—24no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—48no—
264C2×Dic17—48no—
265C2×Dic17C2×C22⋊C414yes—
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×#102D1711yescharacteristic, complemented
278C22×C22⋊C8—171no—
279#1874—178no—
280C2×#340—171no—
281C2×#340—171no—
282C22×C17—44no—
283C22×C17—44no—
284C22×C17—44no—
285C22×C17—82no—
286C22×C17—82no—
287C22×C17—816no—
288C22×C17—82no—
289C22×C17—82no—
290C22×C17#38614yes—
291C22×C17C2×#10214yes—
292C22×C17#41714yes—
293C22×C17#44714yes—
294C22×C17#44814yes—
295C22×C17#48014yes—
296C22×C17#48114yes—
297C22×C17C22×C22⋊C411yescharacteristic
298C22×C17C2×#12011yescharacteristic
299C22×C17C2×#12311yescharacteristic
300C22×C17C22×D811yescharacteristic
301C22×C17C22×SD1611yescharacteristic
302C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C17C2×#13711yescharacteristic
304C2×D17—24no—
305C2×D17—24no—
306C2×D17—24no—
307C2×D17—232no—
308C2×D17—24no—
309C2×D17—24no—
310C2×D17—24no—
311C2×D17C2×#10218yescomplemented
312C4×C17—44no—
313C4×C17#38614yes—
314C4×C17C2×C4×D411yescharacteristic
315C4×C17C2×C4×D411yescharacteristic
316C4×C17C2×#12111yescharacteristic
317C4×C17C2×#12111yescharacteristic
318Dic17—24no—
319Dic17—44no—
320Dic17—44no—
321C23×D4—341no—
322C23×D4C2×D1711yescharacteristic
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—171no—
333C22×C4⋊C4—174no—
334C22×C4⋊C4—344no—
335C22×C4⋊C4—342no—
336C22×C4⋊C4—341no—
337C22×C4⋊C4—344no—
338C22×C4⋊C4C2×D1711yescharacteristic
339C22×C22⋊C4—341no—
340C2×#102—24no—
341C2×#102—174no—
342C2×#102—344no—
343C2×#102C2×D1714yescomplemented
344C2×C22⋊C8—174no—
345C2×C22⋊C8—344no—
346#340—174no—
347#340—174no—
348C2×C17—84no—
349C2×C17#187418yescomplemented
350C2×C17C2×#38611yescharacteristic
351C2×C17C22×#10211yescharacteristic
352C2×C17C2×#41711yescharacteristic
353C2×C17C2×#44711yescharacteristic
354C2×C17C2×#44811yescharacteristic
355C2×C17C2×#48011yescharacteristic
356C2×C17C2×#48111yescharacteristic
357D17—28no—
358C25—21no—
359C25—171no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—21no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—344no—
367C22×D4—348no—
368C22×D4—684no—
369C22×D4—684no—
370C22×D4C4×D1714yescomplemented
371C22×D4C22×D1712yes—
372C23×C4—21no—
373C23×C4—171no—
374C23×C4—174no—
375C23×C4—172no—
376C23×C4—174no—
377C23×C4—172no—
378C23×C4—344no—
379C23×C4—348no—
380C23×C4—342no—
381C23×C4—342no—
382C23×C4—342no—
383C23×C4—342no—
384C23×C4—341no—
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—174no—
403C2×C4⋊C4—174no—
404C2×C4⋊C4—172no—
405C2×C4⋊C4—172no—
406C2×C4⋊C4—348no—
407C2×C4⋊C4—3416no—
408C2×C4⋊C4—344no—
409C2×C4⋊C4—348no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4—342no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—342no—
414C2×C4⋊C4—348no—
415C2×C4⋊C4C22⋊D1714yescomplemented
416C2×C4⋊C4C22×D1712yes—
417C2×C22⋊C4—344no—
418C2×C22⋊C4—348no—
419#102—28no—
420#102—348no—
421C22⋊C8—348no—
422C17C2×#187411yescharacteristic, complemented, Sylow
423C24—22no—
424C24—24no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—172no—
432C24—174no—
433C24—174no—
434C24—174no—
435C24—342no—
436C24—342no—
437C24—342no—
438C24—342no—
439C24D4×D1711yescharacteristic
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—44no—
452C2×D4—3416no—
453C2×D4—6832no—
454C2×D4—688no—
455C2×D4—688no—
456C2×D4C2×C4×D1714yescomplemented
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—172no—
462C22×C4—174no—
463C22×C4—174no—
464C22×C4—174no—
465C22×C4—178no—
466C22×C4—3416no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—348no—
474C22×C4—344no—
475C22×C4—348no—
476C22×C4—348no—
477C22×C4—344no—
478C22×C4—348no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—344no—
482C22×C4—344no—
483C22×C4—688no—
484C22×C4—688no—
485C22×C4—6832no—
486C22×C4—682no—
487C22×C4—682no—
488C22×C4—682no—
489C22×C4—682no—
490C22×C4C2×C4×D1712yes—
491C22×C4#6325212yes—
492C22×C4D4×D1712yes—
493C22×C4D4×D1712yes—
494C22×C4D4×D1711yescharacteristic
495C22×C4#6325412yes—
496C22×C4C2×C22⋊D1712yes—
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—24no—
508C4⋊C4—174no—
509C4⋊C4—174no—
510C4⋊C4—3416no—
511C4⋊C4—342no—
512C4⋊C4—342no—
513C4⋊C4—344no—
514C4⋊C4—344no—
515C4⋊C4C2×C22⋊D1714yescomplemented
516C22⋊C4—3416no—
517C23—24no—
518C23—42no—
519C23—48no—
520C23—42no—
521C23—48no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—48no—
527C23—84no—
528C23—84no—
529C23—84no—
530C23—84no—
531C23—174no—
532C23—1716no—
533C23—174no—
534C23—174no—
535C23—348no—
536C23—342no—
537C23—342no—
538C23—348no—
539C23—342no—
540C23—342no—
541C23—348no—
542C23—348no—
543C23—348no—
544C23—348no—
545C23C22⋊C4×D1712yes—
546C23#1058756912yes—
547C23D8×D1712yes—
548C23#1058759712yes—
549C23SD16×D1712yes—
550C23#1058760112yes—
551C23#1058762312yes—
552C23C2×D4×D1711yescharacteristic
553D4—24no—
554D4—24no—
555D4—42no—
556D4—42no—
557D4—48no—
558D4—6832no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—48no—
563C2×C4—174no—
564C2×C4—342no—
565C2×C4—342no—
566C2×C4—348no—
567C2×C4—344no—
568C2×C4—344no—
569C2×C4—344no—
570C2×C4—344no—
571C2×C4—3416no—
572C2×C4—344no—
573C2×C4—344no—
574C2×C4—6832no—
575C2×C4—688no—
576C2×C4—682no—
577C2×C4—682no—
578C2×C4—682no—
579C2×C4—682no—
580C2×C4—688no—
581C2×C4C22⋊C4×D1712yes—
582C2×C4#1058756714yes—
583C2×C4#1058756912yes—
584C2×C4#1058757014yes—
585C2×C4C4×C22⋊D1714yes—
586C2×C4#1058762312yes—
587C2×C4#1058762414yes—
588C2×C4C22×C4×D1711yescharacteristic
589C2×C4C2×#6325211yescharacteristic
590C2×C4C2×D4×D1711yescharacteristic
591C2×C4C2×D4×D1711yescharacteristic
592C2×C4C2×#6325411yescharacteristic
593C2×C4C22×C22⋊D1711yescharacteristic
594C8—42no—
595C8—682no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—816no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—178no—
605C22—3432no—
606C22—344no—
607C22—344no—
608C22—344no—
609C22—344no—
610C22—344no—
611C22—344no—
612C22#1176268514yes—
613C22#102×D1714yes—
614C22#1176280714yes—
615C22#1176294114yes—
616C22#1176294614yes—
617C22#1176312114yes—
618C22#1176312614yes—
619C22C2×C22⋊C4×D1711yescharacteristic
620C22C2×#1058762311yescharacteristic
621C22C2×#1058756911yescharacteristic
622C22C2×D8×D1711yescharacteristic
623C22C2×SD16×D1711yescharacteristic
624C22C2×#1058759711yescharacteristic
625C22C2×#1058760111yescharacteristic
626C4—44no—
627C4—344no—
628C4—684no—
629C4—684no—
630C4#1176268514yes—
631C4C2×#1058756711yescharacteristic
632C4C2×C4×C22⋊D1711yescharacteristic
633C4C2×#1058762411yescharacteristic
634C4C2×#1058757011yescharacteristic
635C2—84no—
636C2—348no—
637C2#1452909818yesdirect product factor
638C2C2×#1176268511yescharacteristic
639C2C2×#102×D1711yescharacteristic
640C2C2×#1176280711yescharacteristic
641C2C2×#1176294111yescharacteristic
642C2C2×#1176294611yescharacteristic
643C2C2×#1176312111yescharacteristic
644C2C2×#1176312611yescharacteristic
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×#1874
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×C4⋊C4×D17C2semidirect
3. C22×#10587503C2semidirect
4. C22×#10587491C2semidirect
5. #14529098C2direct (N × H)
6. C2×#11762572C2semidirect
7. C2×#11762571C2semidirect
8. C22×C17×#102C2semidirect
15. C2×#10587624C4semidirect
23. C2×C4⋊C4×D17C22semidirect
26. C2×#10587503C22semidirect
28. C2×#10587491C22semidirect
29. #11762572C22semidirect
30. #11762571C22semidirect
35. C2×C17×#102C22semidirect
44. C22×D4×C17C2×C4semidirect
73. C2×C4⋊C4×C17D4semidirect
79. #10587624C2×C4semidirect
84. C2×C4⋊Dic17C2×C4semidirect
85. C2×C4⋊Dic17D4semidirect
129. C2×D4×C17C22×C4semidirect
181. C4⋊C4×C17C2×D4semidirect
187. C4⋊Dic17C22×C4semidirect
188. C4⋊Dic17C2×D4semidirect
227. C22×D17#102semidirect
277. C22×#102D17semidirect
311. C2×D17C2×#102semidirect
343. C2×#102C2×D17semidirect
349. C2×C17#1874semidirect
370. C22×D4C4×D17semidirect
415. C2×C4⋊C4C22⋊D17semidirect
422. C17C2×#1874semidirect
456. C2×D4C2×C4×D17semidirect
515. C4⋊C4C2×C22⋊D17semidirect
637. C2#14529098direct (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×C4⋊C4×D172
C22×#105875032
C22×#105874912
#145290982
C2×#117625722
C2×#117625712
C22×C17×#1022
C2×#187417