Finite Group Databasebeta

← C2×#14534525 #17200682

Subgroups — C2×#14534525 #17200682

Order 4352.

3718 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587569C212yesmaximal, complemented
2C22×#10587624C211yesmaximal, characteristic
3C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
4#14534525C2116yesmaximal, direct product factor
5C2×#11762741C211yesmaximal, characteristic, complemented
6C2×#11762739C211yesmaximal, characteristic, complemented
7C2×#11762732C212yesmaximal, complemented
8C2×#11762732C212yesmaximal, complemented
9C2×#11762723C211yesmaximal, characteristic, complemented
10C2×#11762685C212yesmaximal, complemented
11C2×#11762668C211yesmaximal, characteristic, complemented
12C2×C17×#394C211yesmaximal, characteristic, complemented
13C23×C22⋊D17C2212yes—
14C23×C4×D17C2211yescharacteristic
15C23×C4×D17C2211yescharacteristic
16C23×C4×D17C2211yescharacteristic
17C2×#10587569—216no—
18C2×#10587569C22116yescomplemented
19C2×#10587624—28no—
20C2×#10587624C2218yes—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2212yes—
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2212yes—
27C22×#63225C2212yes—
28C2×C4⋊C4×D17—28no—
29C2×C4⋊C4×D17C2218yescomplemented
30C22×C22⋊Dic17C2212yes—
31C22×C22⋊Dic17C2212yes—
32C22×C22⋊Dic17C2212yes—
33C22×#63227C2212yes—
34#11762741C2218yescomplemented
35#11762739C2218yescomplemented
36#11762732C22116yescomplemented
37#11762732C22116yescomplemented
38#11762723C2218yescomplemented
39#11762685C22116yescomplemented
40#11762668C2218yescomplemented
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2212yes—
43C2×#10587502C2212yes—
44C23×D4×C17C2211yescharacteristic
45C22×C4⋊C4×C17C2211yescharacteristic
46C22×C22⋊C4×C17C2212yes—
47C22×C22⋊C4×C17C2212yes—
48C17×#394C2218yescomplemented
49C2×C17×#95C2211yescharacteristic
50C25×C17C2312yes—
51C24×D17C2311yescharacteristic
52C22×D4×C17—24no—
53C22×D4×C17—44no—
54C22×D4×C17C2314yes—
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2312yes—
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C22×C22⋊D17—28no—
60C22×C22⋊D17—28no—
61C22×C22⋊D17—28no—
62C22×C22⋊D17C2318yes—
63C23×Dic17C2312yes—
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2312yes—
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C22×C4×D17—24no—
69C22×C4×D17—24no—
70C22×C4×D17—24no—
71C22×C4×D17—44no—
72C22×C4×D17—44no—
73C22×C4×D17D418yes—
74C22×C4×D17D418yescomplemented
75C22×C4×D17C2314yes—
76C22×C4×D17C2314yes—
77C22×C4×D17C2314yes—
78C2×C4⋊C4×C17—24no—
79C2×C4⋊C4×C17C2314yes—
80C2×C22⋊C4×C17—28no—
81C2×C22⋊C4×C17—44no—
82C2×C22⋊C4×C17C2318yes—
83C2×C22⋊C4×C17C2318yes—
84C2×C22⋊Dic17—28no—
85C2×C22⋊Dic17—28no—
86C2×C22⋊Dic17—44no—
87C2×C22⋊Dic17C2318yes—
88C2×C22⋊Dic17C2318yes—
89C2×C22⋊Dic17C2318yes—
90#10587624—232no—
91C2×#63227—28no—
92C2×#63227C2318yes—
93C2×C4⋊Dic17—24no—
94C2×C4⋊Dic17—24no—
95C2×C4⋊Dic17—28no—
96C2×C4⋊Dic17C2314yes—
97C2×C4⋊Dic17C2318yes—
98C2×C4⋊Dic17C2314yes—
99C2×#63225—24no—
100C2×#63225—28no—
101C2×#63225—24no—
102C2×#63225—44no—
103C2×#63225C2314yes—
104C2×#63225C2314yes—
105C2×#63225C2318yes—
106C2×#63225C2318yes—
107C4⋊C4×D17—232no—
108#10587569—264no—
109C17×#95C2314yes—
110#10587502C2314yes—
111#10587502C2318yes—
112#10587502C2318yes—
113C24×C17—24no—
114C24×C17—24no—
115C24×C17—24no—
116C24×C17—24no—
117C24×C17—24no—
118C24×C17—24no—
119C24×C17—24no—
120C24×C17C2414yes—
121C24×C17C2411yescharacteristic
122C23×D17—24no—
123C23×D17—24no—
124C23×D17C2×D414yes—
125C23×D17C2×D414yes—
126C23×D17#4114yes—
127C23×D17C2412yes—
128C2×D4×C17—28no—
129C2×D4×C17—48no—
130C2×D4×C17—416no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—24no—
134C22×C4×C17—22no—
135C22×C4×C17—24no—
136C22×C4×C17—24no—
137C22×C4×C17—24no—
138C22×C4×C17—24no—
139C22×C4×C17C2×D414yes—
140C22×C4×C17C2×D414yes—
141C22×C4×C17C2412yes—
142C22×C4×C17C2414yes—
143C22×C4×C17C2412yes—
144C22×C4×C17C2412yes—
145C2×C22⋊D17—216no—
146C2×C22⋊D17—216no—
147C2×C22⋊D17—216no—
148C2×C22⋊D17—432no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—24no—
152C22×Dic17—22no—
153C22×Dic17—24no—
154C22×Dic17—24no—
155C22×Dic17—24no—
156C22×Dic17—24no—
157C22×Dic17—24no—
158C22×Dic17—24no—
159C22×Dic17—24no—
160C22×Dic17C2×D414yes—
161C22×Dic17C2×D414yes—
162C22×Dic17C2412yes—
163C22×Dic17C2414yes—
164C22×Dic17C2414yes—
165C22×Dic17C2412yes—
166C22×Dic17C2412yes—
167C2×C4×D17—232no—
168C2×C4×D17—28no—
169C2×C4×D17—28no—
170C2×C4×D17—28no—
171C2×C4×D17—416no—
172C2×C4×D17—48no—
173C2×C4×D17—48no—
174C2×C4×D17—416no—
175C2×C4×D17C2×D4116yes—
176C2×C4×D17C2×D4116yescomplemented
177C4⋊C4×C17—28no—
178C22⋊C4×C17—216no—
179C22⋊C4×C17—48no—
180C22⋊Dic17—216no—
181C22⋊Dic17—216no—
182C22⋊Dic17—48no—
183#63227—216no—
184C4⋊Dic17—28no—
185C4⋊Dic17—216no—
186C4⋊Dic17—28no—
187#63225—216no—
188#63225—28no—
189#63225—28no—
190#63225—48no—
191C2×#2618—171nomaximal, Sylow
192C23×C17—24no—
193C23×C17—24no—
194C23×C17—24no—
195C23×C17—24no—
196C23×C17—24no—
197C23×C17—24no—
198C23×C17—24no—
199C23×C17—48no—
200C23×C17—48no—
201C23×C17—48no—
202C23×C17—48no—
203C23×C17—48no—
204C23×C17—48no—
205C23×C17—48no—
206C23×C17C22×D412yes—
207C23×C17C22×D412yes—
208C23×C17C2×#4112yes—
209C23×C17H(5,𝔽2)14yes—
210C23×C172−1+414yes—
211C23×C17C2511yescharacteristic
212C22×D17—28no—
213C22×D17—28no—
214C22×D17—216no—
215C22×D17—216no—
216C22×D17—24no—
217C22×D17—24no—
218C22×D17#121116yes—
219C22×D17C22×D414yes—
220C22×D17C22×D414yes—
221C22×D17C2×#4114yes—
222D4×C17—416no—
223C2×C4×C17—28no—
224C2×C4×C17—28no—
225C2×C4×C17—22no—
226C2×C4×C17—22no—
227C2×C4×C17—24no—
228C2×C4×C17—24no—
229C2×C4×C17—22no—
230C2×C4×C17—24no—
231C2×C4×C17—24no—
232C2×C4×C17—24no—
233C2×C4×C17—44no—
234C2×C4×C17—48no—
235C2×C4×C17C22×D414yes—
236C2×C4×C17C22×D414yes—
237C22⋊D17—432no—
238C2×Dic17—28no—
239C2×Dic17—28no—
240C2×Dic17—22no—
241C2×Dic17—22no—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—24no—
245C2×Dic17—22no—
246C2×Dic17—24no—
247C2×Dic17—24no—
248C2×Dic17—24no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—48no—
252C2×Dic17—44no—
253C2×Dic17—48no—
254C2×Dic17C22×D414yes—
255C2×Dic17C22×D414yes—
256C4×D17—232no—
257C4×D17—416no—
258C4×D17—416no—
259C22×#123—172no—
260C22×#121—171no—
261C23×C4⋊C4—171no—
262#2618—1716no—
263C2×#398—171no—
264C2×#398—171no—
265C2×#396—172no—
266C2×#396—172no—
267C2×#394—171no—
268C2×#394D1711yescharacteristic, complemented
269C2×#386—172no—
270C2×#380—171no—
271C22×C17—44no—
272C22×C17—44no—
273C22×C17—44no—
274C22×C17—44no—
275C22×C17—44no—
276C22×C17—44no—
277C22×C17—44no—
278C22×C17—816no—
279C22×C17C2×#12114yes—
280C22×C17#53414yes—
281C22×C17#53614yes—
282C22×C17#53718yes—
283C22×C17#53918yes—
284C22×C17C23×D411yescharacteristic
285C22×C17C23×D411yescharacteristic
286C22×C17C22×#4111yescharacteristic
287C22×C17C2×H(5,𝔽2)12yes—
288C22×C17C2×2−1+412yes—
289C2×D17—232no—
290C2×D17—24no—
291C2×D17—24no—
292C2×D17—28no—
293C2×D17—28no—
294C2×D17C2×#12118yes—
295C4×C17—24no—
296C4×C17—24no—
297C4×C17—42no—
298C4×C17—44no—
299Dic17—24no—
300Dic17—24no—
301Dic17—44no—
302Dic17—42no—
303Dic17—44no—
304C23×D4—172no—
305C23×D4C2×D1711yescharacteristic
306C24×C4—171no—
307C24×C4—171no—
308C24×C4—171no—
309C2×#123—1716no—
310C2×#123—3416no—
311C2×#121—178no—
312C2×#121—348no—
313C22×C4⋊C4—171no—
314C22×C4⋊C4—171no—
315C22×C4⋊C4—172no—
316C22×C4⋊C4—171no—
317C22×C4⋊C4—172no—
318C22×C4⋊C4—171no—
319C22×C4⋊C4—172no—
320C22×C4⋊C4—178no—
321C22×C4⋊C4—348no—
322C22×C4⋊C4C2×D1711yescharacteristic
323C22×C22⋊C4—172no—
324C22×C22⋊C4—172no—
325C22×C22⋊C4—172no—
326C22×C22⋊C4—172no—
327C22×C22⋊C4C2×D1712yes—
328C22×C22⋊C4C2×D1712yes—
329#398—178no—
330#398—178no—
331#396—1716no—
332#396—1716no—
333#394—178no—
334#394C2×D1718yescomplemented
335#386—1716no—
336#380—178no—
337C2×#95—171no—
338C2×#95—172no—
339C2×#95—172no—
340C2×#95C2×D1711yescharacteristic
341C2×C17—84no—
342C2×C17#261818yescomplemented
343C2×C17C22×#12111yescharacteristic
344C2×C17C2×#53411yescharacteristic
345C2×C17C2×#53611yescharacteristic
346C2×C17C2×#53712yes—
347C2×C17C2×#53912yes—
348D17—28no—
349C25—171no—
350C25C22×D1712yes—
351C22×D4—24no—
352C22×D4—44no—
353C22×D4—178no—
354C22×D4—348no—
355C22×D4—348no—
356C22×D4—348no—
357C22×D4C22×D1714yes—
358C23×C4—171no—
359C23×C4—171no—
360C23×C4—178no—
361C23×C4—174no—
362C23×C4—178no—
363C23×C4—174no—
364C23×C4—172no—
365C23×C4—171no—
366C23×C4—172no—
367C23×C4—174no—
368C23×C4—344no—
369C23×C4—344no—
370C23×C4—344no—
371C23×C4—684no—
372C23×C4—684no—
373C23×C4C22×D1712yes—
374C23×C4C22×D1711yescharacteristic
375C23×C4C22×D1711yescharacteristic
376C23×C4C22×D1711yescharacteristic
377#123—3464no—
378#121—3432no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—174no—
381C2×C4⋊C4—174no—
382C2×C4⋊C4—174no—
383C2×C4⋊C4—174no—
384C2×C4⋊C4—178no—
385C2×C4⋊C4—178no—
386C2×C4⋊C4—178no—
387C2×C4⋊C4—3432no—
388C2×C4⋊C4—344no—
389C2×C4⋊C4—344no—
390C2×C4⋊C4—348no—
391C2×C4⋊C4—344no—
392C2×C4⋊C4—344no—
393C2×C4⋊C4—348no—
394C2×C4⋊C4—684no—
395C2×C4⋊C4C22×D1714yes—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—178no—
399C2×C22⋊C4—178no—
400C2×C22⋊C4—178no—
401C2×C22⋊C4—178no—
402C2×C22⋊C4—348no—
403C2×C22⋊C4—348no—
404C2×C22⋊C4—348no—
405C2×C22⋊C4—684no—
406C2×C22⋊C4C22×D1718yes—
407C2×C22⋊C4C22×D1718yes—
408#95—174no—
409#95—178no—
410#95—178no—
411#95C22×D1714yes—
412C17C2×#261811yescharacteristic, complemented, Sylow
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—174no—
421C24—174no—
422C24—174no—
423C24—172no—
424C24—344no—
425C24—344no—
426C24C23×D1714yes—
427C24C23×D1711yescharacteristic
428C2×D4—28no—
429C2×D4—48no—
430C2×D4—416no—
431C2×D4—3416no—
432C2×D4—3416no—
433C2×D4—3416no—
434C2×D4—6832no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—174no—
444C22×C4—174no—
445C22×C4—172no—
446C22×C4—172no—
447C22×C4—1716no—
448C22×C4—1716no—
449C22×C4—174no—
450C22×C4—172no—
451C22×C4—174no—
452C22×C4—348no—
453C22×C4—3432no—
454C22×C4—348no—
455C22×C4—348no—
456C22×C4—342no—
457C22×C4—344no—
458C22×C4—342no—
459C22×C4—344no—
460C22×C4—344no—
461C22×C4—342no—
462C22×C4—344no—
463C22×C4—344no—
464C22×C4—344no—
465C22×C4—344no—
466C22×C4—344no—
467C22×C4—6816no—
468C22×C4—688no—
469C22×C4—688no—
470C22×C4—6816no—
471C22×C4D4×D1714yes—
472C22×C4D4×D1714yes—
473C22×C4C23×D1712yes—
474C22×C4C23×D1714yes—
475C22×C4C23×D1712yes—
476C22×C4C23×D1712yes—
477C4⋊C4—28no—
478C4⋊C4—348no—
479C4⋊C4—348no—
480C4⋊C4—3416no—
481C4⋊C4—348no—
482C4⋊C4—348no—
483C4⋊C4—3416no—
484C4⋊C4—688no—
485C22⋊C4—216no—
486C22⋊C4—48no—
487C22⋊C4—3416no—
488C22⋊C4—3416no—
489C22⋊C4—3416no—
490C22⋊C4—688no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—48no—
499C23—48no—
500C23—48no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—48no—
505C23—1716no—
506C23—174no—
507C23—174no—
508C23—174no—
509C23—348no—
510C23—348no—
511C23—344no—
512C23—344no—
513C23—3416no—
514C23—3416no—
515C23C2×D4×D1712yes—
516C23C2×D4×D1712yes—
517C23#1058769114yes—
518C23#41×D1712yes—
519C23#1058769714yes—
520C23C24×D1711yescharacteristic
521D4—416no—
522D4—6832no—
523C2×C4—28no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—48no—
535C2×C4—174no—
536C2×C4—174no—
537C2×C4—3432no—
538C2×C4—348no—
539C2×C4—348no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—344no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—342no—
546C2×C4—344no—
547C2×C4—344no—
548C2×C4—344no—
549C2×C4—344no—
550C2×C4—344no—
551C2×C4—6816no—
552C2×C4—6816no—
553C2×C4—688no—
554C2×C4—684no—
555C2×C4—688no—
556C2×C4C2×D4×D1714yes—
557C2×C4C2×D4×D1714yes—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—816no—
566C22—178no—
567C22—344no—
568C22—344no—
569C22—348no—
570C22—348no—
571C22—3432no—
572C22#121×D1714yes—
573C22#1176336914yes—
574C22#1176337914yes—
575C22#1176338818yes—
576C22#1176340218yes—
577C22C22×D4×D1711yescharacteristic
578C22C22×D4×D1711yescharacteristic
579C22C2×#41×D1711yescharacteristic
580C22C2×#1058769112yes—
581C22C2×#1058769712yes—
582C4—24no—
583C4—24no—
584C4—42no—
585C4—44no—
586C4—344no—
587C4—344no—
588C4—682no—
589C4—684no—
590C4—684no—
591C2—84no—
592C2—348no—
593C2#1453452518yesdirect product factor
594C2C2×#121×D1711yescharacteristic
595C2C2×#1176336911yescharacteristic
596C2C2×#1176337911yescharacteristic
597C2C2×#1176338812yes—
598C2C2×#1176340212yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#394C2
socleC24×C17C24
prime radicalC22×#10587624C2
hypercenterC2×#394D17
hypocenterC17C2×#2618
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#10587569C2semidirect
3. C22×C4⋊C4×D17C2semidirect
4. #14534525C2direct (N × H)
5. C2×#11762741C2semidirect
6. C2×#11762739C2semidirect
7. C2×#11762732C2semidirect
8. C2×#11762732C2semidirect
9. C2×#11762723C2semidirect
10. C2×#11762685C2semidirect
11. C2×#11762668C2semidirect
12. C2×C17×#394C2semidirect
18. C2×#10587569C22semidirect
29. C2×C4⋊C4×D17C22semidirect
34. #11762741C22semidirect
35. #11762739C22semidirect
36. #11762732C22semidirect
37. #11762732C22semidirect
38. #11762723C22semidirect
39. #11762685C22semidirect
40. #11762668C22semidirect
48. C17×#394C22semidirect
74. C22×C4×D17D4semidirect
176. C2×C4×D17C2×D4semidirect
268. C2×#394D17semidirect
334. #394C2×D17semidirect
342. C2×C17#2618semidirect
412. C17C2×#2618semidirect
593. C2#14534525direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875692
C22×#105876242
C22×C4⋊C4×D172
#145345252
C2×#117627412
C2×#117627392
C2×#117627322
C2×#117627232
C2×#117626852
C2×#117626682
C2×C17×#3942
C2×#261817