Finite Group Databasebeta

← C2×#14529010 #17035178

Subgroups — C2×#14529010 #17035178

Order 4352.

1566 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762852C211yesmaximal, characteristic, complemented
2C22×#10587508C211yesmaximal, characteristic
3C2×#11762810C211yesmaximal, characteristic
4C2×#11762678C211yesmaximal, characteristic, complemented
5#14529010C218yesmaximal, direct product factor
6C2×#11762578C211yesmaximal, characteristic, complemented
7C2×#11762568C211yesmaximal, characteristic, complemented
8C2×C17×#520C211yesmaximal, characteristic
9C22×#63223C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63225—22no—
13C22×C4×Dic17C2211yescharacteristic
14#11762852—22no—
15#11762852C2214yescomplemented
16C2×#10587478—21no—
17C2×#10587479—21no—
18C2×#10587508C418yescomplemented
19C2×#10587508C2214yes—
20#11762810—22no—
21#11762810C2214yes—
22C2×#10587506—21no—
23C2×#10587503—21no—
24#11762678—22no—
25#11762678C2214yescomplemented
26#11762578C2214yescomplemented
27#11762568C2214yescomplemented
28C22×#41×C17C2211yescharacteristic
29C17×#520—22no—
30C17×#520—22no—
31C17×#520—22no—
32C17×#520C2214yes—
33C2×C4×Q8×C17—21no—
34C2×C4×D4×C17—21no—
35C2×C4×D4×C17—22no—
36C2×C17×#117—21no—
37C2×C17×#117C2211yescharacteristic
38C22×C4⋊C4×C17—21no—
39C22×C4⋊C4×C17C2211yescharacteristic
40C2×#41×C17—21no—
41C2×#41×C17—21no—
42C2×#41×C17—22no—
43C2×#41×C17—22no—
44C2×#41×C17C2×C414yes—
45C2×#41×C17D412yes—
46C2×#41×C17Q814yes—
47C2×#41×C17C2312yes—
48C22×Q8×C17D411yescharacteristic
49C22×D4×C17—21no—
50C22×D4×C17D411yescharacteristic
51C23×C4×C17—21no—
52C23×C4×C17—22no—
53C23×C4×C17D412yes—
54C23×C4×C17C2311yescharacteristic
55C23×Dic17—21no—
56C23×Dic17—21no—
57C4×Q8×C17—24no—
58C4×Q8×C17—24no—
59C4×D4×C17—28no—
60C4×D4×C17—24no—
61C4×D4×C17—24no—
62C4×D4×C17—28no—
63C17×#117—24no—
64C17×#117—21no—
65C17×#117—21no—
66C17×#117—24no—
67C17×#117D412yes—
68C17×#117C2312yes—
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—24no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×C4⋊C4×C17—21no—
75C2×C4⋊C4×C17—24no—
76C2×C4⋊C4×C17D412yes—
77C2×C4⋊C4×C17D411yescharacteristic
78C2×C4⋊C4×C17D411yescharacteristic
79C2×C4⋊C4×C17C2312yes—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—21no—
82C2×C42×C17—22no—
83C2×C42×C17—21no—
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17—21no—
89C2×C4⋊Dic17C2312yes—
90C2×#63225—28no—
91C2×#63225—48no—
92C2×C4×Dic17—21no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17C2×C414yescomplemented
95C2×C4×Dic17C2312yes—
96C2×#63223—21no—
97C2×#63223—21no—
98C2×#63223—22no—
99C2×#63223—22no—
100C2×#63223—22no—
101C2×#63223C2×C414yescomplemented
102C2×#63223C2312yes—
103C2×#63223C2312yes—
104C22×#3622—21no—
105C22×#3622—21no—
106#10587508C2×C4116yescomplemented
107#10587506—24no—
108#10587503—24no—
109#10587479—24no—
110#10587478—24no—
111C24×C17—21no—
112C24×C17C2×D411yescharacteristic
113#41×C17—24no—
114#41×C17—24no—
115#41×C17—24no—
116#41×C17—24no—
117#41×C17—24no—
118#41×C17—22no—
119#41×C17—22no—
120#41×C17C4⋊C418yescomplemented
121#41×C17C22×C414yes—
122#41×C17C2×Q814yes—
123C2×Q8×C17—21no—
124C2×Q8×C17—22no—
125C2×Q8×C17C4⋊C414yescomplemented
126C2×Q8×C17C2×D412yes—
127C2×D4×C17—24no—
128C2×D4×C17—22no—
129C2×D4×C17—24no—
130C2×D4×C17—22no—
131C2×D4×C17—21no—
132C2×D4×C17—22no—
133C2×D4×C17C4⋊C414yescomplemented
134C2×D4×C17C2×D412yes—
135C22×C4×C17—21no—
136C22×C4×C17—24no—
137C22×C4×C17—22no—
138C22×C4×C17—24no—
139C22×C4×C17—22no—
140C22×C4×C17—21no—
141C22×C4×C17—22no—
142C22×C4×C17—21no—
143C22×C4×C17—28no—
144C22×C4×C17—22no—
145C22×C4×C17—44no—
146C22×C4×C17—84no—
147C22×C4×C17C22×C412yes—
148C22×C4×C17C2×D414yes—
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2×D411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×Q812yes—
155C22×C4×C17#4112yes—
156C22×C4×C17#4112yes—
157C22×C4×C17C2411yescharacteristic
158C22×Dic17—24no—
159C22×Dic17—24no—
160C22×Dic17—24no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—44no—
164C22×Dic17—41no—
165C22×Dic17—41no—
166C4⋊C4×C17—28no—
167C4⋊C4×C17—22no—
168C4⋊C4×C17—21no—
169C4⋊C4×C17—22no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—22no—
172C4⋊C4×C17—22no—
173C4⋊C4×C17C2×D412yes—
174C4⋊C4×C17C2×D412yes—
175C22⋊C4×C17—28no—
176C22⋊C4×C17—22no—
177C22⋊C4×C17—22no—
178C42×C17—28no—
179C42×C17—22no—
180C42×C17—22no—
181C4⋊Dic17—22no—
182C4⋊Dic17—22no—
183C4⋊Dic17—41no—
184C4⋊Dic17—41no—
185#63225—416no—
186C4×Dic17—24no—
187C4×Dic17—22no—
188C4×Dic17C22×C414yescomplemented
189#63223—24no—
190#63223—22no—
191#63223—22no—
192#63223—22no—
193#63223—42no—
194#63223C22×C414yescomplemented
195C2×#3622—24no—
196C2×#3622—22no—
197C2×#3622—22no—
198C2×#3622—42no—
199C2×#1859—171nomaximal, Sylow
200C23×C17—22no—
201C23×C17—22no—
202C23×C17—22no—
203C23×C17—24no—
204C23×C17—42no—
205C23×C17—42no—
206C23×C17C4×D412yes—
207C23×C17#12011yescharacteristic
208C23×C17#12011yescharacteristic
209C23×C17C22⋊Q812yes—
210C23×C17C22×D411yescharacteristic
211Q8×C17—22no—
212Q8×C17—24no—
213Q8×C17C2×C4⋊C414yescomplemented
214D4×C17—24no—
215D4×C17—24no—
216D4×C17—28no—
217D4×C17—22no—
218D4×C17—24no—
219D4×C17C2×C4⋊C414yescomplemented
220C2×C4×C17—22no—
221C2×C4×C17—24no—
222C2×C4×C17—24no—
223C2×C4×C17—24no—
224C2×C4×C17—28no—
225C2×C4×C17—22no—
226C2×C4×C17—24no—
227C2×C4×C17—22no—
228C2×C4×C17—44no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17—44no—
232C2×C4×C17—82no—
233C2×C4×C17—88no—
234C2×C4×C17C2×C4⋊C412yes—
235C2×C4×C17C2×C4⋊C412yes—
236C2×C4×C17C4×D412yes—
237C2×C4×C17C4×D412yes—
238C2×C4×C17C4×D412yes—
239C2×C4×C17#12011yescharacteristic
240C2×C4×C17#12011yescharacteristic
241C2×C4×C17C22⋊Q812yes—
242C2×C4×C17C22⋊Q812yes—
243C2×C4×C17C22⋊Q812yes—
244C2×C4×C17#12312yes—
245C2×C4×C17#12312yes—
246C2×C4×C17C23×C411yescharacteristic
247C2×C4×C17C22×D411yescharacteristic
248C2×C4×C17C22×D411yescharacteristic
249C2×C4×C17C22×Q811yescharacteristic
250C2×C4×C17C2×#4111yescharacteristic
251C2×C4×C17C2×#4111yescharacteristic
252C2×Dic17—216no—
253C2×Dic17—24no—
254C2×Dic17—24no—
255C2×Dic17—24no—
256C2×Dic17—44no—
257C2×Dic17—42no—
258C2×Dic17—82no—
259C2×Dic17—82no—
260#3622—24no—
261#3622—42no—
262C2×#520D1711yescharacteristic
263C2×#428—171no—
264C22×#104—171no—
265C2×#417—171no—
266C2×#384—171no—
267#1859—178no—
268C2×#343—171no—
269C2×#339—171no—
270C22×C17—24no—
271C22×C17—24no—
272C22×C17—21no—
273C22×C17—21no—
274C22×C17—21no—
275C22×C17—21no—
276C22×C17—24no—
277C22×C17—48no—
278C22×C17—42no—
279C22×C17—42no—
280C22×C17#38512yes—
281C22×C17#38512yes—
282C22×C17#45312yes—
283C22×C17#45612yes—
284C22×C17C2×C4×D411yescharacteristic
285C22×C17C2×#12011yescharacteristic
286C22×C17C2×C22⋊Q811yescharacteristic
287C4×C17—24no—
288C4×C17—44no—
289C4×C17—42no—
290C4×C17—42no—
291C4×C17#38512yes—
292C4×C17#38512yes—
293C4×C17C22×C4⋊C411yescharacteristic
294C4×C17C2×C4×D411yescharacteristic
295C4×C17C2×C22⋊Q811yescharacteristic
296C4×C17C2×#12311yescharacteristic
297Dic17—28no—
298Dic17—82no—
299C22×#41C2×D1711yescharacteristic
300C22×M16—171no—
301C22×M16—171no—
302#520—22no—
303#520—22no—
304#520—22no—
305#520C2×D1714yes—
306C2×C4×Q8—21no—
307C2×C4×D4—21no—
308C2×C4×D4—22no—
309C2×#117—21no—
310C2×#117C2×D1711yescharacteristic
311C22×C4⋊C4—21no—
312C22×C4⋊C4—171no—
313C22×C4⋊C4—342no—
314C22×C4⋊C4C2×D1711yescharacteristic
315C22×C42—171no—
316#428—174no—
317#428—342no—
318C2×#107—341no—
319C2×#106—341no—
320C2×#104—178no—
321C2×#104—174no—
322#417—174no—
323#417—342no—
324C2×#103—341no—
325C2×#102—341no—
326#384—174no—
327#384—342no—
328#343—174no—
329#339—174no—
330C2×C17—21no—
331C2×C17—21no—
332C2×C17—22no—
333C2×C17—44no—
334C2×C17#185914yescomplemented
335C2×C17C2×#38511yescharacteristic
336C2×C17C2×#45311yescharacteristic
337C2×C17C2×#45611yescharacteristic
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41Dic3414yes—
343C2×#41C4×D1714yes—
344C2×#41C22⋊D1712yes—
345C2×#41C22×D1712yes—
346C22×Q8C22⋊D1711yescharacteristic
347C22×D4—21no—
348C22×D4C22⋊D1711yescharacteristic
349C23×C4—21no—
350C23×C4—22no—
351C23×C4—341no—
352C23×C4—341no—
353C23×C4C22⋊D1712yes—
354C23×C4C22×D1711yescharacteristic
355C2×M16—174no—
356C2×M16—172no—
357C2×M16—172no—
358C2×M16—342no—
359C2×M16—341no—
360C2×M16—341no—
361C2×M16—342no—
362C2×M16—342no—
363C22×C8—341no—
364C22×C8—341no—
365C4×Q8—24no—
366C4×Q8—24no—
367C4×D4—28no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—28no—
371#117—24no—
372#117—21no—
373#117—21no—
374#117—24no—
375#117C22⋊D1712yes—
376#117C22×D1712yes—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—172no—
385C2×C4⋊C4—341no—
386C2×C4⋊C4—341no—
387C2×C4⋊C4—341no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—341no—
390C2×C4⋊C4—348no—
391C2×C4⋊C4—688no—
392C2×C4⋊C4C22⋊D1712yes—
393C2×C4⋊C4C22⋊D1711yescharacteristic
394C2×C4⋊C4C22⋊D1711yescharacteristic
395C2×C4⋊C4C22×D1712yes—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—21no—
398C2×C42—22no—
399C2×C42—21no—
400C2×C42—174no—
401C2×C42—172no—
402C2×C42—342no—
403C2×C42—341no—
404#107—344no—
405#106—344no—
406#104—1716no—
407#103—344no—
408#102—344no—
409C17C2×#185911yescharacteristic, complemented, Sylow
410C24—21no—
411C24C2×C22⋊D1711yescharacteristic
412#41—22no—
413#41—22no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—24no—
418#41—24no—
419#41#6322518yescomplemented
420#41C2×Dic3414yes—
421#41C2×C4×D1714yes—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8#6322514yescomplemented
425C2×Q8C2×C22⋊D1712yes—
426C2×D4—22no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4#6322514yescomplemented
433C2×D4C2×C22⋊D1712yes—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—28no—
443C22×C4—22no—
444C22×C4—44no—
445C22×C4—84no—
446C22×C4—344no—
447C22×C4—344no—
448C22×C4—342no—
449C22×C4—344no—
450C22×C4—342no—
451C22×C4—684no—
452C22×C4—681no—
453C22×C4—681no—
454C22×C4C2×Dic3412yes—
455C22×C4C2×C4×D1712yes—
456C22×C4#6325212yes—
457C22×C4#6325212yes—
458C22×C4C2×C22⋊D1714yes—
459C22×C4C2×C22⋊D1711yescharacteristic
460C22×C4C2×C22⋊D1711yescharacteristic
461C22×C4C2×C22⋊D1711yescharacteristic
462C22×C4C2×C22⋊D1711yescharacteristic
463C22×C4C2×C22⋊D1711yescharacteristic
464C22×C4C23×D1711yescharacteristic
465M16—174no—
466M16—342no—
467M16—344no—
468M16—342no—
469M16—342no—
470M16—682no—
471C2×C8—342no—
472C2×C8—344no—
473C2×C8—342no—
474C2×C8—682no—
475C4⋊C4—28no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—342no—
483C4⋊C4—342no—
484C4⋊C4—6816no—
485C4⋊C4—681no—
486C4⋊C4—681no—
487C4⋊C4C2×C22⋊D1712yes—
488C4⋊C4C2×C22⋊D1712yes—
489C22⋊C4—28no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C42—28no—
493C42—22no—
494C42—22no—
495C42—174no—
496C42—342no—
497C42—344no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—42no—
503C23—42no—
504C23#1058761012yes—
505C23C4×C22⋊D1712yes—
506C23#1058763911yescharacteristic
507C23#1058763911yescharacteristic
508C23C22×C22⋊D1711yescharacteristic
509Q8—22no—
510Q8—24no—
511Q8C2×#6322514yescomplemented
512D4—24no—
513D4—24no—
514D4—28no—
515D4—22no—
516D4—24no—
517D4C2×#6322514yescomplemented
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—28no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—82no—
531C2×C4—88no—
532C2×C4—344no—
533C2×C4—344no—
534C2×C4—3416no—
535C2×C4—344no—
536C2×C4—684no—
537C2×C4—682no—
538C2×C4—1362no—
539C2×C4—1362no—
540C2×C4C2×#6322512yes—
541C2×C4C2×#6322512yes—
542C2×C4#1058761012yes—
543C2×C4#1058761012yes—
544C2×C4#1058761012yes—
545C2×C4C4×C22⋊D1712yes—
546C2×C4C4×C22⋊D1712yes—
547C2×C4C4×C22⋊D1712yes—
548C2×C4#1058761512yes—
549C2×C4#1058761512yes—
550C2×C4#1058763911yescharacteristic
551C2×C4#1058763911yescharacteristic
552C2×C4C22×Dic3411yescharacteristic
553C2×C4C22×C4×D1711yescharacteristic
554C2×C4C2×#6325211yescharacteristic
555C2×C4C2×#6325211yescharacteristic
556C2×C4C22×C22⋊D1711yescharacteristic
557C2×C4C22×C22⋊D1711yescharacteristic
558C8—344no—
559C8—682no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—24no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—48no—
570C22#1176268212yes—
571C22#1176268212yes—
572C22#1176297712yes—
573C22#1176299212yes—
574C22C2×C4×C22⋊D1711yescharacteristic
575C22C2×#1058763911yescharacteristic
576C22C2×#1058761011yescharacteristic
577C4—24no—
578C4—44no—
579C4—42no—
580C4—42no—
581C4—348no—
582C4—1362no—
583C4#1176268212yes—
584C4#1176268212yes—
585C4C22×#6322511yescharacteristic
586C4C2×C4×C22⋊D1711yescharacteristic
587C4C2×#1058761011yescharacteristic
588C4C2×#1058761511yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—44no—
593C2#1452901014yesdirect product factor
594C2C2×#1176268211yescharacteristic
595C2C2×#1176297711yescharacteristic
596C2C2×#1176299211yescharacteristic
subgroupG/H
centerC23#10587639
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#520C2
socleC23×C17#120
prime radicalC22×#41×C17C22
cosocleC22×C4×C17C24
hypercenterC2×#520D17
hypocenterC17C2×#1859
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11762852C2semidirect
4. C2×#11762678C2semidirect
5. #14529010C2direct (N × H)
6. C2×#11762578C2semidirect
7. C2×#11762568C2semidirect
15. #11762852C22semidirect
18. C2×#10587508C4semidirect
25. #11762678C22semidirect
26. #11762578C22semidirect
27. #11762568C22semidirect
94. C2×C4×Dic17C2×C4semidirect
101. C2×#63223C2×C4semidirect
106. #10587508C2×C4semidirect
120. #41×C17C4⋊C4semidirect
125. C2×Q8×C17C4⋊C4semidirect
133. C2×D4×C17C4⋊C4semidirect
188. C4×Dic17C22×C4semidirect
194. #63223C22×C4semidirect
213. Q8×C17C2×C4⋊C4semidirect
219. D4×C17C2×C4⋊C4semidirect
334. C2×C17#1859semidirect
409. C17C2×#1859semidirect
419. #41#63225semidirect
424. C2×Q8#63225semidirect
432. C2×D4#63225semidirect
511. Q8C2×#63225semidirect
517. D4C2×#63225semidirect
593. C2#14529010direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117628522
C22×#105875082
C2×#117628102
C2×#117626782
#145290102
C2×#117625782
C2×#117625682
C2×C17×#5202
C2×#185917