Finite Group Databasebeta

← C2×#14529064 #17035404

Subgroups — C2×#14529064 #17035404

Order 4352.

1994 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763284C211yesmaximal, characteristic
2C22×#10587505C211yesmaximal, characteristic
3C2×#11762682C212yesmaximal, complemented
4#14529064C218yesmaximal, direct product factor
5C2×#11762575C212yesmaximal, complemented
6C2×C17×#386C211yesmaximal, characteristic
7#11763284—24no—
8#11763284—22no—
9#11763284C2214yes—
10C2×D4×Dic17—22no—
11C2×D4×Dic17—22no—
12C2×#10587612—21no—
13C22×#63225—22no—
14C22×C22⋊Dic17—21no—
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2212yes—
17C2×#10587505C418yescomplemented
18C2×#10587505C2214yes—
19#11762682—24no—
20#11762682C2218yescomplemented
21C2×#10587502—22no—
22#11762575C2218yescomplemented
23C23×D4×C17C2211yescharacteristic
24C24×C4×C17C2211yescharacteristic
25C22×C22⋊C4×C17—21no—
26C22×C22⋊C4×C17C2211yescharacteristic
27C17×#386—22no—
28C17×#386C2214yes—
29C2×C17×#95—21no—
30C25×C17D411yescharacteristic
31C25×C17C2311yescharacteristic
32C22×D4×C17—22no—
33C22×D4×C17—22no—
34C22×D4×C17—24no—
35C22×D4×C17C2×C414yes—
36C22×D4×C17D412yes—
37C22×D4×C17Q814yes—
38C22×D4×C17C2312yes—
39C23×C4×C17—21no—
40C23×C4×C17—22no—
41C23×C4×C17—21no—
42C23×C4×C17—21no—
43C23×C4×C17—22no—
44C23×C4×C17—44no—
45C23×C4×C17D411yescharacteristic
46C23×C4×C17C2312yes—
47C23×Dic17—22no—
48C23×Dic17—21no—
49C23×Dic17—21no—
50C23×Dic17D412yes—
51C23×Dic17D412yes—
52C2×C22⋊C4×C17—24no—
53C2×C22⋊C4×C17—24no—
54C2×C22⋊C4×C17—21no—
55C2×C22⋊C4×C17—44no—
56C2×C22⋊C4×C17C2312yes—
57C2×C22⋊Dic17—22no—
58C2×C22⋊Dic17—24no—
59C2×C22⋊Dic17—22no—
60C2×C22⋊Dic17—24no—
61C2×C22⋊Dic17—22no—
62C2×C22⋊Dic17—22no—
63C2×C22⋊Dic17—22no—
64C2×C22⋊Dic17—22no—
65C2×C22⋊Dic17—24no—
66C2×C22⋊Dic17C2×C418yescomplemented
67C2×C22⋊Dic17D414yes—
68C2×C22⋊Dic17C2314yes—
69C2×C22⋊Dic17C2314yes—
70D4×Dic17—28no—
71D4×Dic17—28no—
72D4×Dic17—28no—
73D4×Dic17—28no—
74#10587612—24no—
75#10587612—24no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—21no—
78C2×#63225—28no—
79C2×#63225—48no—
80C2×C4×Dic17—22no—
81C17×#95—24no—
82#10587505C2×C4116yescomplemented
83#10587502—28no—
84C24×C17—21no—
85C24×C17—21no—
86C24×C17—22no—
87C24×C17—42no—
88C24×C17—42no—
89C24×C17—42no—
90C24×C17—42no—
91C24×C17C4⋊C414yescomplemented
92C24×C17C22×C412yes—
93C24×C17C2×D412yes—
94C24×C17C2×D412yes—
95C24×C17C2×D411yescharacteristic
96C24×C17C2×D412yes—
97C24×C17C2×D411yescharacteristic
98C24×C17C2×Q812yes—
99C24×C17#4114yes—
100C24×C17C2411yescharacteristic
101C2×D4×C17—28no—
102C2×D4×C17—28no—
103C2×D4×C17—24no—
104C2×D4×C17—28no—
105C2×D4×C17—28no—
106C2×D4×C17—24no—
107C2×D4×C17—24no—
108C2×D4×C17—24no—
109C2×D4×C17C4⋊C418yescomplemented
110C2×D4×C17C22×C414yes—
111C2×D4×C17C2×Q814yes—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—22no—
115C22×C4×C17—28no—
116C22×C4×C17—24no—
117C22×C4×C17—24no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—44no—
121C22×C4×C17—44no—
122C22×C4×C17—48no—
123C22×C4×C17—44no—
124C22×C4×C17—42no—
125C22×C4×C17—41no—
126C22×C4×C17—42no—
127C22×C4×C17—41no—
128C22×C4×C17—42no—
129C22×C4×C17—42no—
130C22×C4×C17—42no—
131C22×C4×C17C4⋊C414yescomplemented
132C22×C4×C17C2×D412yes—
133C22×Dic17—28no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—24no—
137C22×Dic17—24no—
138C22×Dic17—24no—
139C22×Dic17—22no—
140C22×Dic17—22no—
141C22×Dic17—44no—
142C22×Dic17—44no—
143C22×Dic17—44no—
144C22×Dic17—44no—
145C22×Dic17—82no—
146C22×Dic17—82no—
147C22×Dic17C2×D414yes—
148C22×Dic17C2×D414yes—
149C22⋊C4×C17—24no—
150C22⋊C4×C17—48no—
151C22⋊C4×C17—42no—
152C22⋊Dic17—28no—
153C22⋊Dic17—28no—
154C22⋊Dic17—24no—
155C22⋊Dic17—24no—
156C22⋊Dic17—24no—
157C22⋊Dic17—24no—
158C22⋊Dic17—24no—
159C22⋊Dic17C22×C418yescomplemented
160C4⋊Dic17—24no—
161C4⋊Dic17—24no—
162#63225—416no—
163C4×Dic17—28no—
164C2×#1867—171nomaximal, Sylow
165C23×C17—24no—
166C23×C17—22no—
167C23×C17—24no—
168C23×C17—22no—
169C23×C17—22no—
170C23×C17—24no—
171C23×C17—22no—
172C23×C17—24no—
173C23×C17—42no—
174C23×C17—41no—
175C23×C17—41no—
176C23×C17—44no—
177C23×C17—42no—
178C23×C17—41no—
179C23×C17—44no—
180C23×C17—48no—
181C23×C17—41no—
182C23×C17—42no—
183C23×C17—48no—
184C23×C17—42no—
185C23×C17—42no—
186C23×C17—42no—
187C23×C17—84no—
188C23×C17—81no—
189C23×C17—81no—
190C23×C17C2×C4⋊C412yes—
191C23×C17C2×C4⋊C412yes—
192C23×C17C2×C4⋊C414yescomplemented
193C23×C17C4×D414yes—
194C23×C17C4×D414yes—
195C23×C17#12011yescharacteristic
196C23×C17#12012yes—
197C23×C17#12011yescharacteristic
198C23×C17C22⋊Q814yes—
199C23×C17C22⋊Q814yes—
200C23×C17#12312yes—
201C23×C17#12312yes—
202C23×C17C23×C411yescharacteristic
203C23×C17C22×D412yes—
204C23×C17C22×D411yescharacteristic
205C23×C17C22×Q811yescharacteristic
206C23×C17C2×#4112yes—
207D4×C17—28no—
208D4×C17—28no—
209D4×C17—216no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—24no—
213C2×C4×C17—24no—
214C2×C4×C17—24no—
215C2×C4×C17—28no—
216C2×C4×C17—44no—
217C2×C4×C17—48no—
218C2×C4×C17—42no—
219C2×C4×C17—44no—
220C2×C4×C17—42no—
221C2×C4×C17—44no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—84no—
226C2×C4×C17C2×C4⋊C414yescomplemented
227C2×Dic17—28no—
228C2×Dic17—24no—
229C2×Dic17—24no—
230C2×Dic17—416no—
231C2×Dic17—44no—
232C2×Dic17—44no—
233C2×Dic17—44no—
234C2×Dic17—44no—
235C2×Dic17—44no—
236C2×Dic17—44no—
237C2×Dic17—82no—
238C2×Dic17—82no—
239C2×Dic17—84no—
240C2×Dic17—84no—
241C2×#518—171no—
242C22×#99—171no—
243C2×#386D1711yescharacteristic
244C2×#385—172no—
245#1867—178no—
246C2×#342—172no—
247C22×C17—28no—
248C22×C17—24no—
249C22×C17—24no—
250C22×C17—28no—
251C22×C17—22no—
252C22×C17—22no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—22no—
256C22×C17—22no—
257C22×C17—21no—
258C22×C17—21no—
259C22×C17—24no—
260C22×C17—42no—
261C22×C17—44no—
262C22×C17—44no—
263C22×C17—42no—
264C22×C17—41no—
265C22×C17—41no—
266C22×C17—42no—
267C22×C17—44no—
268C22×C17—48no—
269C22×C17—42no—
270C22×C17—42no—
271C22×C17—82no—
272C22×C17—84no—
273C22×C17#38512yes—
274C22×C17#38514yes—
275C22×C17#38512yes—
276C22×C17B(4,𝔽2)12yes—
277C22×C17#45812yes—
278C22×C17C22×C4⋊C411yescharacteristic
279C22×C17C2×C4×D412yes—
280C22×C17C2×#12011yescharacteristic
281C22×C17C2×C22⋊Q812yes—
282C22×C17C2×#12311yescharacteristic
283C4×C17—24no—
284C4×C17—44no—
285C4×C17—82no—
286Dic17—48no—
287Dic17—44no—
288Dic17—44no—
289C23×D4C2×D1711yescharacteristic
290C24×C4C2×D1711yescharacteristic
291#518—174no—
292#518—344no—
293#518—342no—
294C2×C4×D4—342no—
295C2×C4×D4—342no—
296C2×#117—341no—
297C22×C4⋊C4—342no—
298C22×C22⋊C4—21no—
299C22×C22⋊C4—172no—
300C22×C22⋊C4—172no—
301C22×C22⋊C4—341no—
302C22×C22⋊C4C2×D1711yescharacteristic
303C2×#99—178no—
304C2×#99—174no—
305#386—22no—
306#386C2×D1714yes—
307#385—178no—
308#385—344no—
309C2×#95—21no—
310C2×#95—342no—
311#342—178no—
312C2×C17—22no—
313C2×C17—21no—
314C2×C17—21no—
315C2×C17—22no—
316C2×C17—22no—
317C2×C17—24no—
318C2×C17—44no—
319C2×C17#186714yescomplemented
320C2×C17C2×#38511yescharacteristic
321C2×C17C2×B(4,𝔽2)11yescharacteristic
322C2×C17C2×#45811yescharacteristic
323C25C22⋊D1711yescharacteristic
324C25C22×D1711yescharacteristic
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—24no—
328C22×D4Dic3414yes—
329C22×D4C4×D1714yes—
330C22×D4C22⋊D1712yes—
331C22×D4C22×D1712yes—
332C23×C4—22no—
333C23×C4—21no—
334C23×C4—22no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—44no—
338C23×C4—172no—
339C23×C4—172no—
340C23×C4—342no—
341C23×C4—341no—
342C23×C4—341no—
343C23×C4C22⋊D1711yescharacteristic
344C23×C4C22×D1712yes—
345C4×D4—348no—
346C4×D4—348no—
347C4×D4—348no—
348C4×D4—348no—
349#117—344no—
350#117—344no—
351C2×C4⋊C4—341no—
352C2×C4⋊C4—341no—
353C2×C4⋊C4—348no—
354C2×C4⋊C4—688no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—178no—
360C2×C22⋊C4—174no—
361C2×C22⋊C4—174no—
362C2×C22⋊C4—174no—
363C2×C22⋊C4—342no—
364C2×C22⋊C4—344no—
365C2×C22⋊C4—342no—
366C2×C22⋊C4—342no—
367C2×C22⋊C4—342no—
368C2×C22⋊C4—344no—
369C2×C22⋊C4—342no—
370C2×C22⋊C4—342no—
371C2×C22⋊C4—344no—
372C2×C22⋊C4C22×D1712yes—
373C2×C42—342no—
374#99—1716no—
375#95—24no—
376#95—348no—
377C17C2×#186711yescharacteristic, complemented, Sylow
378C24—21no—
379C24—22no—
380C24—21no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24#6322514yescomplemented
386C24C2×Dic3412yes—
387C24C2×C4×D1712yes—
388C24D4×D1712yes—
389C24D4×D1712yes—
390C24#6325414yes—
391C24C2×C22⋊D1711yescharacteristic
392C24C2×C22⋊D1712yes—
393C24C2×C22⋊D1711yescharacteristic
394C24C23×D1711yescharacteristic
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4#6322518yescomplemented
404C2×D4C2×Dic3414yes—
405C2×D4C2×C4×D1714yes—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—28no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—48no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4—41no—
420C22×C4—42no—
421C22×C4—41no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—174no—
426C22×C4—174no—
427C22×C4—344no—
428C22×C4—348no—
429C22×C4—342no—
430C22×C4—342no—
431C22×C4—344no—
432C22×C4—344no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—684no—
436C22×C4—684no—
437C22×C4—684no—
438C22×C4—684no—
439C22×C4—1362no—
440C22×C4—1362no—
441C22×C4#6322514yescomplemented
442C22×C4C2×C22⋊D1712yes—
443C4⋊C4—344no—
444C4⋊C4—344no—
445C4⋊C4—6816no—
446C22⋊C4—24no—
447C22⋊C4—48no—
448C22⋊C4—42no—
449C22⋊C4—178no—
450C22⋊C4—348no—
451C22⋊C4—344no—
452C22⋊C4—344no—
453C22⋊C4—344no—
454C22⋊C4—348no—
455C22⋊C4—344no—
456C22⋊C4—344no—
457C42—348no—
458C23—22no—
459C23—24no—
460C23—22no—
461C23—24no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—24no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—44no—
470C23—44no—
471C23—42no—
472C23—48no—
473C23—41no—
474C23—41no—
475C23—42no—
476C23—42no—
477C23—48no—
478C23—42no—
479C23—42no—
480C23—84no—
481C23—81no—
482C23—81no—
483C23#1058756414yes—
484C23#1058756414yes—
485C23#1058756714yes—
486C23#1058756714yes—
487C23C2×#6322512yes—
488C23C2×#6322512yes—
489C23C2×#6322514yescomplemented
490C23#1058762112yes—
491C23#1058762112yes—
492C23#1058762311yescharacteristic
493C23#1058762312yes—
494C23#1058762311yescharacteristic
495C23C22×Dic3411yescharacteristic
496C23C22×C4×D1711yescharacteristic
497C23C2×D4×D1712yes—
498C23C2×#6325412yes—
499C23C22×C22⋊D1711yescharacteristic
500D4—28no—
501D4—28no—
502D4—216no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—28no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—48no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4—348no—
520C2×C4—344no—
521C2×C4—344no—
522C2×C4—684no—
523C2×C4—6816no—
524C2×C4—684no—
525C2×C4—684no—
526C2×C4—684no—
527C2×C4—684no—
528C2×C4—684no—
529C2×C4—1362no—
530C2×C4—1362no—
531C2×C4—1364no—
532C2×C4—1364no—
533C2×C4C2×#6322514yescomplemented
534C22—24no—
535C22—28no—
536C22—24no—
537C22—28no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—22no—
545C22—21no—
546C22—24no—
547C22—41no—
548C22—41no—
549C22—42no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—44no—
555C22—48no—
556C22—42no—
557C22—42no—
558C22—82no—
559C22—84no—
560C22#1176268112yes—
561C22#1176268114yes—
562C22#1176268112yes—
563C22#1176299512yes—
564C22#1176299812yes—
565C22C22×#6322511yescharacteristic
566C22C2×#1058756712yes—
567C22C2×#1058762311yescharacteristic
568C22C2×#1058756412yes—
569C22C2×#1058762111yescharacteristic
570C4—24no—
571C4—44no—
572C4—82no—
573C4—688no—
574C4—684no—
575C4—684no—
576C2—21no—
577C2—22no—
578C2—21no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—44no—
583C2#1452906414yesdirect product factor
584C2C2×#1176268111yescharacteristic
585C2C2×#1176299511yescharacteristic
586C2C2×#1176299811yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#386C2
socleC23×C17#120
prime radicalC23×D4×C17C22
cosocleC24×C17C24
hypercenterC2×#386D17
hypocenterC17C2×#1867
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#11762682C2semidirect
4. #14529064C2direct (N × H)
5. C2×#11762575C2semidirect
17. C2×#10587505C4semidirect
20. #11762682C22semidirect
22. #11762575C22semidirect
66. C2×C22⋊Dic17C2×C4semidirect
82. #10587505C2×C4semidirect
91. C24×C17C4⋊C4semidirect
109. C2×D4×C17C4⋊C4semidirect
131. C22×C4×C17C4⋊C4semidirect
159. C22⋊Dic17C22×C4semidirect
192. C23×C17C2×C4⋊C4semidirect
226. C2×C4×C17C2×C4⋊C4semidirect
319. C2×C17#1867semidirect
377. C17C2×#1867semidirect
385. C24#63225semidirect
403. C2×D4#63225semidirect
441. C22×C4#63225semidirect
489. C23C2×#63225semidirect
533. C2×C4C2×#63225semidirect
583. C2#14529064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117632842
C22×#105875052
C2×#117626822
#145290642
C2×#117625752
C2×C17×#3862
C2×#186717