Finite Group Databasebeta

← C2×#14532191 #17203026

Subgroups — C2×#14532191 #17203026

Order 4352.

3570 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587615C211yesmaximal, characteristic
2C22×#10587615C211yesmaximal, characteristic
3C22×#10587612C211yesmaximal, characteristic, complemented
4#14532191C2116yesmaximal, direct product factor
5C2×#11762742C212yesmaximal, complemented
6C2×#11762731C212yesmaximal, complemented
7C2×#11762704C212yesmaximal, complemented
8C2×#11762699C212yesmaximal, complemented
9C2×#11762688C211yesmaximal, characteristic
10C2×#11762682C211yesmaximal, characteristic, complemented
11C2×#11762672C211yesmaximal, characteristic, complemented
12C23×C4⋊C4×C17C211yesmaximal, characteristic, complemented
13C23×C22⋊D17C2211yescharacteristic
14C2×#10587615—28no—
15C2×#10587615—28no—
16C2×#10587615C2218yes—
17C2×#10587615C2218yes—
18C2×#10587612—28no—
19C2×#10587612C2218yescomplemented
20C22×C4⋊Dic17C2212yes—
21C22×#63225C2212yes—
22C22×#63225C2211yescharacteristic
23C22×#63225C2212yes—
24C22×#63225C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×#63227C2212yes—
29C22×#63227C2211yescharacteristic
30C22×#63227C2212yes—
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2212yes—
33#11762742C22116yescomplemented
34#11762731C22116yescomplemented
35#11762704C22116yescomplemented
36#11762699C22116yescomplemented
37#11762688C2218yes—
38#11762682C2218yescomplemented
39#11762672C2218yescomplemented
40C2×#10587502C2212yes—
41C2×#10587502C2212yes—
42C2×#10587502C2212yes—
43C2×#10587502C2212yes—
44C24×C4×C17C2211yescharacteristic
45C24×C4×C17C2211yescharacteristic
46C24×C4×C17C2211yescharacteristic
47C22×C4⋊C4×C17—28no—
48C22×C4⋊C4×C17C2212yes—
49C22×C4⋊C4×C17C2212yes—
50C22×C4⋊C4×C17C2218yescomplemented
51C25×C17C2311yescharacteristic
52C24×D17C2311yescharacteristic
53C23×C4×C17—24no—
54C23×C4×C17—24no—
55C23×C4×C17—24no—
56C23×C4×C17—28no—
57C23×C4×C17—24no—
58C23×C4×C17—24no—
59C23×C4×C17—24no—
60C23×C4×C17D418yes—
61C23×C4×C17C2314yes—
62C23×C4×C17C2312yes—
63C23×C4×C17C2314yes—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2314yes—
67C23×C4×C17C2312yes—
68C22×C22⋊D17—24no—
69C22×C22⋊D17—24no—
70C22×C22⋊D17—24no—
71C22×C22⋊D17C2314yes—
72C23×Dic17C2312yes—
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2312yes—
77C2×C4⋊C4×C17—28no—
78C2×C4⋊C4×C17—28no—
79C2×C4⋊C4×C17—232no—
80C2×C4⋊C4×C17C2318yes—
81C2×C4⋊C4×C17C2318yes—
82C2×C22⋊Dic17—24no—
83C2×C22⋊Dic17—24no—
84C2×C22⋊Dic17D418yes—
85C2×C22⋊Dic17C2314yes—
86C2×C22⋊Dic17C2314yes—
87C2×C22⋊Dic17C2314yes—
88#10587615—232no—
89#10587615—232no—
90C2×#63227—24no—
91C2×#63227—24no—
92C2×#63227—28no—
93C2×#63227—28no—
94C2×#63227C2318yes—
95C2×#63227C2314yes—
96C2×#63227C2318yes—
97C2×#63227C2314yes—
98#10587612—232no—
99C2×C4⋊Dic17—28no—
100C2×C4⋊Dic17C2318yes—
101C2×#63225—24no—
102C2×#63225—24no—
103C2×#63225—28no—
104C2×#63225—28no—
105C2×#63225C2314yes—
106C2×#63225C2318yes—
107C2×#63225C2318yes—
108C2×#63225C2314yes—
109C2×C4×Dic17—28no—
110C2×C4×Dic17C2318yes—
111#10587502C2318yes—
112#10587502C2318yes—
113#10587502C2318yes—
114#10587502C2318yes—
115C24×C17—24no—
116C24×C17—24no—
117C24×C17C2×D414yes—
118C24×C17C2×D414yes—
119C24×C17#4114yes—
120C24×C17C2412yes—
121C24×C17C2411yescharacteristic
122C23×D17—22no—
123C23×D17—22no—
124C23×D17—22no—
125C23×D17—24no—
126C23×D17—24no—
127C23×D17C2412yes—
128C22×C4×C17—232no—
129C22×C4×C17—232no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—28no—
133C22×C4×C17—28no—
134C22×C4×C17—24no—
135C22×C4×C17—24no—
136C22×C4×C17—28no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—216no—
140C22×C4×C17—24no—
141C22×C4×C17—28no—
142C22×C4×C17—28no—
143C22×C4×C17—24no—
144C22×C4×C17—28no—
145C22×C4×C17—24no—
146C22×C4×C17—416no—
147C22×C4×C17C2×D414yes—
148C22×C4×C17C2×D414yes—
149C22×C4×C17C2×D4116yes—
150C22×C4×C17#4118yes—
151C22×C4×C17C2414yes—
152C22×C4×C17C2412yes—
153C22×C4×C17C2412yes—
154C22×C4×C17C2414yes—
155C2×C22⋊D17—28no—
156C2×C22⋊D17—28no—
157C2×C22⋊D17—28no—
158C2×C22⋊D17—416no—
159C22×Dic17—24no—
160C22×Dic17—24no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—24no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—24no—
168C22×Dic17—24no—
169C22×Dic17—24no—
170C22×Dic17—24no—
171C22×Dic17C2×D418yes—
172C22×Dic17C2412yes—
173C22×Dic17C2412yes—
174C22×Dic17C2414yes—
175C22×Dic17C2412yes—
176C22×Dic17C2414yes—
177C4⋊C4×C17—216no—
178C4⋊C4×C17—216no—
179C22⋊Dic17—28no—
180C22⋊Dic17—28no—
181C22⋊Dic17C2×D4116yes—
182#63227—28no—
183#63227—28no—
184#63227—216no—
185#63227—216no—
186C4⋊Dic17—216no—
187#63225—28no—
188#63225—28no—
189#63225—216no—
190#63225—216no—
191C4×Dic17—216no—
192C2×#2413—171nomaximal, Sylow
193C23×C17—28no—
194C23×C17—28no—
195C23×C17—216no—
196C23×C17—216no—
197C23×C17—24no—
198C23×C17—24no—
199C23×C17#121116yes—
200C23×C17C22×D414yes—
201C23×C17C22×D412yes—
202C23×C17C22×D414yes—
203C23×C17C22×D412yes—
204C23×C17C2×#4114yes—
205C23×C17C2×#4114yes—
206C23×C17C2×#4112yes—
207C23×C172−1+414yes—
208C23×C17C2511yescharacteristic
209C22×D17—22no—
210C22×D17—22no—
211C22×D17—22no—
212C22×D17—24no—
213C22×D17—24no—
214C22×D17—44no—
215C22×D17—44no—
216C22×D17—44no—
217C22×D17—48no—
218C22×D17—48no—
219C2×C4×C17—232no—
220C2×C4×C17—232no—
221C2×C4×C17—28no—
222C2×C4×C17—28no—
223C2×C4×C17—216no—
224C2×C4×C17—24no—
225C2×C4×C17—22no—
226C2×C4×C17—22no—
227C2×C4×C17—22no—
228C2×C4×C17—22no—
229C2×C4×C17—24no—
230C2×C4×C17—24no—
231C2×C4×C17—24no—
232C2×C4×C17—24no—
233C2×C4×C17—416no—
234C2×C4×C17—48no—
235C2×C4×C17C22×D414yes—
236C2×C4×C17C22×D414yes—
237C2×C4×C17C2×#4118yes—
238C22⋊D17—416no—
239C2×Dic17—216no—
240C2×Dic17—24no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—22no—
247C2×Dic17—22no—
248C2×Dic17—24no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—24no—
252C2×Dic17—44no—
253C2×Dic17—44no—
254C2×Dic17—44no—
255C2×Dic17—48no—
256C2×Dic17C22×D418yes—
257C22×#123—171no—
258C22×#123—171no—
259C22×#117—171no—
260C23×C4⋊C4D1711yescharacteristic, complemented
261#2413—1716no—
262C2×#398—172no—
263C2×#396—172no—
264C2×#389—172no—
265C2×#388—172no—
266C2×#386—171no—
267C2×#385—171no—
268C2×#381—171no—
269C22×C17—24no—
270C22×C17—232no—
271C22×C17—24no—
272C22×C17—28no—
273C22×C17—28no—
274C22×C17C2×#12118yes—
275C22×C17C2×#12114yes—
276C22×C17#52514yes—
277C22×C17#53614yes—
278C22×C17#54718yes—
279C22×C17#55218yes—
280C22×C17C23×D411yescharacteristic
281C22×C17C23×D411yescharacteristic
282C22×C17C22×#4111yescharacteristic
283C22×C17C22×#4112yes—
284C22×C17C2×2−1+412yes—
285C2×D17—42no—
286C2×D17—42no—
287C2×D17—42no—
288C2×D17—44no—
289C2×D17—44no—
290C2×D17—88no—
291C4×C17—24no—
292C4×C17—24no—
293C4×C17—28no—
294C4×C17—44no—
295Dic17—28no—
296Dic17—42no—
297Dic17—42no—
298Dic17—42no—
299Dic17—44no—
300C23×D4—171no—
301C24×C4C2×D1711yescharacteristic
302C24×C4C2×D1711yescharacteristic
303C24×C4C2×D1711yescharacteristic
304C2×#123—178no—
305C2×#123—178no—
306C2×#123—348no—
307C2×#123—348no—
308C2×#117—178no—
309C2×#117—348no—
310C22×C4⋊C4—28no—
311C22×C4⋊C4—172no—
312C22×C4⋊C4—171no—
313C22×C4⋊C4—172no—
314C22×C4⋊C4—171no—
315C22×C4⋊C4—172no—
316C22×C4⋊C4C2×D1712yes—
317C22×C4⋊C4C2×D1712yes—
318C22×C4⋊C4C2×D1718yescomplemented
319C22×C22⋊C4—171no—
320C22×C22⋊C4—171no—
321C22×C22⋊C4—171no—
322C22×C22⋊C4—171no—
323C22×C22⋊C4—172no—
324C22×C22⋊C4—172no—
325C22×C22⋊C4—171no—
326C22×C42—172no—
327#398—1716no—
328#396—1716no—
329#389—1716no—
330#388—1716no—
331#386—178no—
332#385—178no—
333#381—178no—
334C2×#95—172no—
335C2×#95—172no—
336C2×#95—172no—
337C2×#95—172no—
338C2×C17—28no—
339C2×C17#241318yescomplemented
340C2×C17C22×#12111yescharacteristic
341C2×C17C2×#52511yescharacteristic
342C2×C17C2×#53611yescharacteristic
343C2×C17C2×#54712yes—
344C2×C17C2×#55212yes—
345D17—82no—
346C25—171no—
347C25C22×D1711yescharacteristic
348C22×D4—174no—
349C22×D4—344no—
350C22×D4—344no—
351C22×D4—344no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—28no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—172no—
360C23×C4—171no—
361C23×C4—171no—
362C23×C4—172no—
363C23×C4—171no—
364C23×C4C22⋊D1718yes—
365C23×C4C22×D1714yes—
366C23×C4C22×D1714yes—
367C23×C4C22×D1712yes—
368C23×C4C22×D1712yes—
369C23×C4C22×D1714yes—
370C23×C4C22×D1711yescharacteristic
371C23×C4C22×D1711yescharacteristic
372#123—3432no—
373#123—3432no—
374#117—3432no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—232no—
378C2×C4⋊C4—178no—
379C2×C4⋊C4—174no—
380C2×C4⋊C4—178no—
381C2×C4⋊C4—174no—
382C2×C4⋊C4—178no—
383C2×C4⋊C4—348no—
384C2×C4⋊C4—348no—
385C2×C4⋊C4—348no—
386C2×C4⋊C4—344no—
387C2×C4⋊C4—344no—
388C2×C4⋊C4C22×D1718yes—
389C2×C4⋊C4C22×D1718yes—
390C2×C22⋊C4—178no—
391C2×C22⋊C4—174no—
392C2×C22⋊C4—174no—
393C2×C22⋊C4—174no—
394C2×C22⋊C4—174no—
395C2×C22⋊C4—178no—
396C2×C22⋊C4—174no—
397C2×C22⋊C4—178no—
398C2×C22⋊C4—348no—
399C2×C22⋊C4—344no—
400C2×C22⋊C4—344no—
401C2×C22⋊C4—348no—
402C2×C22⋊C4—344no—
403C2×C22⋊C4—344no—
404C2×C42—178no—
405C2×C42—348no—
406#95—178no—
407#95—178no—
408#95—178no—
409#95—178no—
410C17C2×#241311yescharacteristic, complemented, Sylow
411C24—24no—
412C24—24no—
413C24—172no—
414C24—344no—
415C24—342no—
416C24—342no—
417C24—344no—
418C24—342no—
419C24D4×D1714yes—
420C24#6325414yes—
421C24C2×C22⋊D1714yes—
422C24C23×D1712yes—
423C24C23×D1711yescharacteristic
424C2×D4—348no—
425C2×D4—348no—
426C2×D4—348no—
427C2×D4—6816no—
428C22×C4—232no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—24no—
438C22×C4—232no—
439C22×C4—216no—
440C22×C4—24no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—24no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—416no—
447C22×C4—178no—
448C22×C4—174no—
449C22×C4—172no—
450C22×C4—174no—
451C22×C4—172no—
452C22×C4—172no—
453C22×C4—344no—
454C22×C4—344no—
455C22×C4—344no—
456C22×C4—344no—
457C22×C4—344no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—344no—
461C22×C4—344no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4#6325218yes—
466C22×C4C2×C22⋊D1714yes—
467C22×C4C2×C22⋊D1714yes—
468C22×C4C2×C22⋊D17116yes—
469C22×C4C23×D1714yes—
470C22×C4C23×D1714yes—
471C22×C4C23×D1712yes—
472C22×C4C23×D1712yes—
473C4⋊C4—216no—
474C4⋊C4—216no—
475C4⋊C4—3416no—
476C4⋊C4—3416no—
477C4⋊C4—3416no—
478C4⋊C4—348no—
479C4⋊C4—348no—
480C22⋊C4—1716no—
481C22⋊C4—3416no—
482C22⋊C4—348no—
483C22⋊C4—348no—
484C22⋊C4—3416no—
485C22⋊C4—348no—
486C22⋊C4—348no—
487C42—3416no—
488C23—216no—
489C23—216no—
490C23—28no—
491C23—24no—
492C23—28no—
493C23—24no—
494C23—342no—
495C23—342no—
496C23—342no—
497C23—344no—
498C23—344no—
499C23—688no—
500C23—688no—
501C23—684no—
502C23—684no—
503C23—684no—
504C23#10587625116yes—
505C23C2×#6325214yes—
506C23C2×D4×D1714yes—
507C23C2×D4×D1712yes—
508C23C2×#6325414yes—
509C23C2×#6325412yes—
510C23#1058769414yes—
511C23C22×C22⋊D1714yes—
512C23C22×C22⋊D1712yes—
513C23C24×D1711yescharacteristic
514D4—6816no—
515C2×C4—232no—
516C2×C4—232no—
517C2×C4—28no—
518C2×C4—28no—
519C2×C4—216no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—416no—
530C2×C4—48no—
531C2×C4—178no—
532C2×C4—3416no—
533C2×C4—344no—
534C2×C4—344no—
535C2×C4—344no—
536C2×C4—342no—
537C2×C4—342no—
538C2×C4—342no—
539C2×C4—342no—
540C2×C4—342no—
541C2×C4—344no—
542C2×C4—344no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—688no—
546C2×C4—684no—
547C2×C4—684no—
548C2×C4—684no—
549C2×C4C2×#6325218yes—
550C2×C4C22×C22⋊D1714yes—
551C2×C4C22×C22⋊D1714yes—
552C22—24no—
553C22—232no—
554C22—28no—
555C22—24no—
556C22—28no—
557C22—682no—
558C22—684no—
559C22—682no—
560C22—682no—
561C22—684no—
562C22—1368no—
563C22C2×#1058762518yes—
564C22C2×#1058762514yes—
565C22#1176332014yes—
566C22#1176338314yes—
567C22#1176346018yes—
568C22#1176349418yes—
569C22C22×D4×D1711yescharacteristic
570C22C23×C22⋊D1711yescharacteristic
571C22C22×#6325411yescharacteristic
572C22C22×#6325212yes—
573C22C2×#1058769412yes—
574C4—24no—
575C4—24no—
576C4—28no—
577C4—44no—
578C4—348no—
579C4—682no—
580C4—684no—
581C4—682no—
582C4—682no—
583C2—28no—
584C2—1362no—
585C2#1453219118yesdirect product factor
586C2C22×#1058762511yescharacteristic
587C2C2×#1176332011yescharacteristic
588C2C2×#1176338311yescharacteristic
589C2C2×#1176346012yes—
590C2C2×#1176349412yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC23×C4⋊C4×C17C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC23×C4⋊C4D17
hypocenterC17C2×#2413
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#10587612C2semidirect
4. #14532191C2direct (N × H)
5. C2×#11762742C2semidirect
6. C2×#11762731C2semidirect
7. C2×#11762704C2semidirect
8. C2×#11762699C2semidirect
10. C2×#11762682C2semidirect
11. C2×#11762672C2semidirect
12. C23×C4⋊C4×C17C2semidirect
19. C2×#10587612C22semidirect
33. #11762742C22semidirect
34. #11762731C22semidirect
35. #11762704C22semidirect
36. #11762699C22semidirect
38. #11762682C22semidirect
39. #11762672C22semidirect
50. C22×C4⋊C4×C17C22semidirect
260. C23×C4⋊C4D17semidirect
318. C22×C4⋊C4C2×D17semidirect
339. C2×C17#2413semidirect
410. C17C2×#2413semidirect
585. C2#14532191direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876152
C22×#105876122
#145321912
C2×#117627422
C2×#117627312
C2×#117627042
C2×#117626992
C2×#117626882
C2×#117626822
C2×#117626722
C23×C4⋊C4×C172
C2×#241317