Finite Group Databasebeta

← C2×#14544010 #17964197

Subgroups — C2×#14544010 #17964197

Order 4352.

2878 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×#11763777C212yesmaximal, complemented
2C2×#11763653C212yesmaximal, complemented
3#14544010C218yesmaximal, direct product factor
4C2×#11763652C212yesmaximal, complemented
5C22×C22⋊C4×D17C211yesmaximal, characteristic
6C22×#63242—22no—
7C2×#10587543—22no—
8#11763777—24no—
9#11763777C2218yescomplemented
10C2×C22⋊#3624C2214yescomplemented
11#11763653C2218yescomplemented
12#11763652C2218yescomplemented
13C25×D17C411yescharacteristic
14C23×C4×D17C411yescharacteristic
15C23×C4×D17C2211yescharacteristic
16C22×C22⋊Dic17C2211yescharacteristic
17C22×#63227C411yescharacteristic
18C22×#63227C2211yescharacteristic
19C2×C22⋊C4×D17—22no—
20C2×C22⋊C4×D17—24no—
21C2×C22⋊C4×D17—22no—
22C2×C22⋊C4×D17C414yes—
23C2×C22⋊C4×D17C2214yes—
24C22×C22⋊C4×C17C411yescharacteristic
25C25×C17C2×C411yescharacteristic
26C24×D17—22no—
27C24×D17—21no—
28C24×D17—21no—
29C24×D17—24no—
30C24×D17—44no—
31C24×D17—44no—
32C24×D17C818yescomplemented
33C24×D17C2×C411yescharacteristic
34C24×D17C2×C414yes—
35C24×D17C2×C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×C4×C17C2×C411yescharacteristic
38C23×Dic17C2×C411yescharacteristic
39C23×Dic17C2311yescharacteristic
40C22×C4×D17—21no—
41C22×C4×D17—22no—
42C22×C4×D17—21no—
43C22×C4×D17—44no—
44C22×C4×D17—44no—
45C22×C4×D17C2×C414yes—
46C22×C4×D17C2×C412yes—
47C22×C4×D17D412yes—
48C22×C4×D17D414yes—
49C22×C4×D17D412yes—
50C22×C4×D17C2312yes—
51C22×#3624—24no—
52C2×#63242—28no—
53C2×#63242—48no—
54C2×C22⋊C4×C17—22no—
55C2×C22⋊C4×C17—22no—
56C2×C22⋊C4×C17C2×C414yes—
57C2×C22⋊Dic17—22no—
58C2×C22⋊Dic17—22no—
59C2×C22⋊Dic17C2×C412yes—
60C2×C22⋊Dic17C2312yes—
61C2×#63227—22no—
62C2×#63227—22no—
63C2×#63227—22no—
64C2×#63227—22no—
65C2×#63227C2×C412yes—
66C2×#63227C2×C414yes—
67C2×#63227C2312yes—
68C22⋊C4×D17—28no—
69C22⋊C4×D17—28no—
70C22⋊C4×D17—28no—
71C22⋊C4×D17—28no—
72C22⋊#3624—24no—
73C22⋊#3624C2318yescomplemented
74#10587543—28no—
75C24×C17—21no—
76C24×C17—21no—
77C24×C17—22no—
78C24×C17—42no—
79C24×C17—42no—
80C24×C17C2×C814yescomplemented
81C24×C17C22×C411yescharacteristic
82C24×C17C22×C412yes—
83C23×D17—24no—
84C23×D17—24no—
85C23×D17—21no—
86C23×D17—21no—
87C23×D17—22no—
88C23×D17—216no—
89C23×D17—28no—
90C23×D17—28no—
91C23×D17—24no—
92C23×D17—24no—
93C23×D17—28no—
94C23×D17—44no—
95C23×D17—44no—
96C23×D17—432no—
97C23×D17—48no—
98C23×D17—48no—
99C23×D17—432no—
100C23×D17—48no—
101C23×D17—48no—
102C23×D17—44no—
103C23×D17—44no—
104C23×D17—42no—
105C23×D17—42no—
106C23×D17C22⋊C412yes—
107C23×D17C22⋊C411yescharacteristic
108C23×D17C22⋊C411yescharacteristic
109C23×D17C2×C814yes—
110C23×D17C2×C8116yescomplemented
111C23×D17C2×C814yescomplemented
112C23×D17M1614yes—
113C23×D17C22×C412yes—
114C23×D17C22×C412yes—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—42no—
118C22×C4×C17—42no—
119C22×C4×C17C22⋊C412yes—
120C22×C4×C17C22⋊C412yes—
121C22×C4×C17C22×C412yes—
122C22×C4×C17C22×C412yes—
123C22×Dic17—21no—
124C22×Dic17—21no—
125C22×Dic17—42no—
126C22×Dic17—42no—
127C22×Dic17C22×C412yes—
128C22×Dic17C22×C411yescharacteristic
129C22×Dic17C2×D412yes—
130C22×Dic17C2×D412yes—
131C22×Dic17C2411yescharacteristic
132C2×C4×D17—28no—
133C2×C4×D17—24no—
134C2×C4×D17—24no—
135C2×C4×D17—44no—
136C2×C4×D17—48no—
137C2×C4×D17—44no—
138C2×C4×D17—44no—
139C2×C4×D17—44no—
140C2×C4×D17—48no—
141C2×C4×D17—44no—
142C2×C4×D17—48no—
143C2×C4×D17C22⋊C414yes—
144C2×C4×D17C22⋊C414yes—
145C2×C4×D17C2×D414yes—
146C2×C4×D17C2×D414yes—
147C2×#3624—28no—
148C2×#3624—48no—
149#63242—416no—
150C22⋊C4×C17—28no—
151C22⋊Dic17—24no—
152C22⋊Dic17—24no—
153#63227—28no—
154#63227—24no—
155#63227—24no—
156C22×#323—171nomaximal, Sylow
157C23×C17—22no—
158C23×C17—22no—
159C23×C17—22no—
160C23×C17—22no—
161C23×C17—24no—
162C23×C17—24no—
163C23×C17—48no—
164C23×C17—42no—
165C23×C17—42no—
166C23×C17—42no—
167C23×C17—42no—
168C23×C17—48no—
169C23×C17—42no—
170C23×C17—42no—
171C23×C17C2×C22⋊C411yescharacteristic
172C23×C17C2×C22⋊C411yescharacteristic
173C23×C17C22×C812yes—
174C23×C17C22×C814yescomplemented
175C23×C17C2×M1612yes—
176C23×C17C23×C411yescharacteristic
177C22×D17—22no—
178C22×D17—22no—
179C22×D17—216no—
180C22×D17—216no—
181C22×D17—24no—
182C22×D17—24no—
183C22×D17—24no—
184C22×D17—24no—
185C22×D17—22no—
186C22×D17—22no—
187C22×D17—24no—
188C22×D17—24no—
189C22×D17—216no—
190C22×D17—216no—
191C22×D17—48no—
192C22×D17—48no—
193C22×D17—432no—
194C22×D17—464no—
195C22×D17—432no—
196C22×D17—432no—
197C22×D17—42no—
198C22×D17—42no—
199C22×D17—48no—
200C22×D17—42no—
201C22×D17—42no—
202C22×D17—432no—
203C22×D17—48no—
204C22×D17—48no—
205C22×D17—48no—
206C22×D17—42no—
207C22×D17—42no—
208C22×D17C22⋊C814yes—
209C22×D17C22⋊C818yes—
210C22×D17C22⋊C814yes—
211C22×D17#9914yes—
212C22×D17#10014yes—
213C22×D17C2×C22⋊C412yes—
214C22×D17C2×C22⋊C412yes—
215C22×D17C22×C814yes—
216C22×D17C22×C814yescomplemented
217C22×D17C2×M1614yes—
218C2×C4×C17—24no—
219C2×C4×C17—22no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17C2×C22⋊C414yes—
226C2×Dic17—24no—
227C2×Dic17—22no—
228C2×Dic17—41no—
229C2×Dic17—42no—
230C2×Dic17—41no—
231C2×Dic17—42no—
232C2×Dic17—42no—
233C2×Dic17—42no—
234C2×Dic17C2×C22⋊C412yes—
235C2×Dic17C22×D412yes—
236C4×D17—28no—
237C4×D17—28no—
238C4×D17—44no—
239C4×D17—44no—
240C4×D17—48no—
241C4×D17—48no—
242#3624—48no—
243C23×C22⋊C4—171no—
244C22×C22⋊C8—172no—
245C2×#323—172no—
246C2×#323—178no—
247C2×#323—172no—
248C22×C17—21no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—24no—
253C22×C17—24no—
254C22×C17—24no—
255C22×C17—44no—
256C22×C17—44no—
257C22×C17—48no—
258C22×C17—42no—
259C22×C17—42no—
260C22×C17—48no—
261C22×C17C2×C22⋊C812yes—
262C22×C17C2×C22⋊C812yes—
263C22×C17C2×#9912yes—
264C22×C17C2×#10012yes—
265C22×C17C22×C22⋊C411yescharacteristic
266C22×C17C23×C811yescharacteristic
267C22×C17C22×M1611yescharacteristic
268C2×D17—22no—
269C2×D17—22no—
270C2×D17—28no—
271C2×D17—216no—
272C2×D17—28no—
273C2×D17—28no—
274C2×D17—24no—
275C2×D17—432no—
276C2×D17—44no—
277C2×D17—48no—
278C2×D17—42no—
279C2×D17—42no—
280C2×D17—48no—
281C2×D17—432no—
282C2×D17—44no—
283C2×D17#323116yescomplemented
284C2×D17C2×C22⋊C814yes—
285C2×D17C2×C22⋊C814yes—
286C2×D17C2×#9914yes—
287C2×D17C2×#10014yes—
288C4×C17—24no—
289C4×C17—42no—
290Dic17—22no—
291Dic17—22no—
292Dic17—42no—
293C26—171no—
294C24×C4—171no—
295C24×C4—171no—
296C23×C8—342no—
297C22×C22⋊C4—171no—
298C22×C22⋊C4—171no—
299C22×C22⋊C4—171no—
300C22×C22⋊C4—174no—
301C22×C22⋊C4—174no—
302C22×C22⋊C4—342no—
303C22×C22⋊C4—344no—
304C22×C22⋊C4—342no—
305C22×C22⋊C4#59511yescharacteristic
306C2×C22⋊C8—174no—
307C2×C22⋊C8—178no—
308C2×C22⋊C8—344no—
309C2×C22⋊C8—342no—
310#323—178no—
311#323—178no—
312C2×C17—21no—
313C2×C17—21no—
314C2×C17—22no—
315C2×C17—44no—
316C2×C17C2×#32314yescomplemented
317C2×C17C22×C22⋊C811yescharacteristic
318C2×C17C22×#9911yescharacteristic
319C2×C17C22×#10011yescharacteristic
320D17—24no—
321D17—44no—
322D17C2×#32318yescomplemented
323C25—171no—
324C25—178no—
325C25—174no—
326C25—171no—
327C25—342no—
328C25—341no—
329C25—341no—
330C25—344no—
331C25—684no—
332C25—684no—
333C25C2×#59511yescharacteristic
334C23×C4—171no—
335C23×C4—172no—
336C23×C4—172no—
337C23×C4—174no—
338C23×C4—172no—
339C23×C4—172no—
340C23×C4—171no—
341C23×C4—174no—
342C23×C4—342no—
343C23×C4—341no—
344C23×C4—341no—
345C23×C4—684no—
346C23×C4—684no—
347C23×C4C2×#59511yescharacteristic
348C23×C4C2×#59511yescharacteristic
349C22×C8—348no—
350C22×C8—344no—
351C22×C8—688no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—172no—
355C2×C22⋊C4—172no—
356C2×C22⋊C4—172no—
357C2×C22⋊C4—172no—
358C2×C22⋊C4—174no—
359C2×C22⋊C4—348no—
360C2×C22⋊C4—348no—
361C2×C22⋊C4—348no—
362C2×C22⋊C4—348no—
363C2×C22⋊C4—342no—
364C2×C22⋊C4—342no—
365C2×C22⋊C4—342no—
366C2×C22⋊C4—342no—
367C2×C22⋊C4—342no—
368C2×C22⋊C4—342no—
369C2×C22⋊C4C2×#59514yes—
370C22⋊C8—178no—
371C22⋊C8—348no—
372C22⋊C8—344no—
373C17C22×#32311yescharacteristic, complemented, Sylow
374C24—22no—
375C24—21no—
376C24—21no—
377C24—42no—
378C24—42no—
379C24—171no—
380C24—174no—
381C24—174no—
382C24—172no—
383C24—171no—
384C24—172no—
385C24—174no—
386C24—1716no—
387C24—172no—
388C24—344no—
389C24—344no—
390C24—344no—
391C24—344no—
392C24—348no—
393C24—3416no—
394C24—348no—
395C24—348no—
396C24—342no—
397C24—341no—
398C24—341no—
399C24—682no—
400C24—682no—
401C24—684no—
402C24—684no—
403C24—6832no—
404C24—688no—
405C24—688no—
406C24—688no—
407C24—688no—
408C24—6832no—
409C24—684no—
410C24—684no—
411C24#6324214yescomplemented
412C24C22×#59511yescharacteristic
413C24C22×#59512yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—172no—
419C22×C4—172no—
420C22×C4—171no—
421C22×C4—171no—
422C22×C4—174no—
423C22×C4—174no—
424C22×C4—174no—
425C22×C4—174no—
426C22×C4—172no—
427C22×C4—348no—
428C22×C4—344no—
429C22×C4—344no—
430C22×C4—341no—
431C22×C4—341no—
432C22×C4—684no—
433C22×C4—688no—
434C22×C4—684no—
435C22×C4—684no—
436C22×C4—684no—
437C22×C4—688no—
438C22×C4—684no—
439C22×C4—688no—
440C22×C4—682no—
441C22×C4—682no—
442C22×C4C22⋊#59512yes—
443C22×C4C22⋊#59512yes—
444C22×C4C22×#59512yes—
445C22×C4C22×#59512yes—
446C2×C8—348no—
447C2×C8—6816no—
448C2×C8—688no—
449C22⋊C4—28no—
450C22⋊C4—344no—
451C22⋊C4—344no—
452C22⋊C4—344no—
453C22⋊C4—344no—
454C22⋊C4—348no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—22no—
460C23—22no—
461C23—48no—
462C23—42no—
463C23—42no—
464C23—48no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—174no—
470C23—174no—
471C23—174no—
472C23—172no—
473C23—178no—
474C23—174no—
475C23—172no—
476C23—174no—
477C23—174no—
478C23—174no—
479C23—344no—
480C23—344no—
481C23—344no—
482C23—344no—
483C23—3416no—
484C23—3416no—
485C23—3416no—
486C23—3416no—
487C23—342no—
488C23—342no—
489C23—344no—
490C23—344no—
491C23—342no—
492C23—342no—
493C23—688no—
494C23—682no—
495C23—682no—
496C23—688no—
497C23—682no—
498C23—682no—
499C23—6832no—
500C23—688no—
501C23—688no—
502C23—6832no—
503C23—6864no—
504C23—6832no—
505C23—6832no—
506C23—688no—
507C23—688no—
508C23—682no—
509C23—682no—
510C23C2×#6324212yes—
511C23C2×#6324214yescomplemented
512C23D17⋊M1612yes—
513C23C2×C22⋊#59511yescharacteristic
514C23C2×C22⋊#59511yescharacteristic
515C23C23×#59511yescharacteristic
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—172no—
524C2×C4—172no—
525C2×C4—348no—
526C2×C4—348no—
527C2×C4—344no—
528C2×C4—342no—
529C2×C4—684no—
530C2×C4—684no—
531C2×C4—688no—
532C2×C4—688no—
533C2×C4—681no—
534C2×C4—682no—
535C2×C4—681no—
536C2×C4—682no—
537C2×C4—682no—
538C2×C4—682no—
539C2×C4C2×C22⋊#59514yes—
540C8—688no—
541C22—24no—
542C22—24no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—24no—
548C22—44no—
549C22—48no—
550C22—44no—
551C22—48no—
552C22—42no—
553C22—42no—
554C22—1716no—
555C22—174no—
556C22—174no—
557C22—174no—
558C22—174no—
559C22—3416no—
560C22—348no—
561C22—348no—
562C22—348no—
563C22—342no—
564C22—342no—
565C22—344no—
566C22—684no—
567C22—688no—
568C22—684no—
569C22—6832no—
570C22—6832no—
571C22—688no—
572C22—682no—
573C22—682no—
574C22#1176377712yes—
575C22#1176377712yes—
576C22D17⋊#9912yes—
577C22D17⋊#10012yes—
578C22C22×C22⋊#59511yescharacteristic
579C22C22×#6324211yescharacteristic
580C22C2×D17⋊M1611yescharacteristic
581C4—24no—
582C4—42no—
583C4—342no—
584C4—342no—
585C4—682no—
586C2—22no—
587C2—21no—
588C2—21no—
589C2—44no—
590C2—178no—
591C2—344no—
592C2—684no—
593C2#1454401014yesdirect product factor
594C2C2×#1176377711yescharacteristic
595C2C2×D17⋊#9911yescharacteristic
596C2C2×D17⋊#10011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C17C23×C8
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×D17C4
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C22×#323
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11763777C2semidirect
2. C2×#11763653C2semidirect
3. #14544010C2direct (N × H)
4. C2×#11763652C2semidirect
9. #11763777C22semidirect
10. C2×C22⋊#3624C22semidirect
11. #11763653C22semidirect
12. #11763652C22semidirect
32. C24×D17C8semidirect
73. C22⋊#3624C23semidirect
80. C24×C17C2×C8semidirect
110. C23×D17C2×C8semidirect
111. C23×D17C2×C8semidirect
174. C23×C17C22×C8semidirect
216. C22×D17C22×C8semidirect
283. C2×D17#323semidirect
316. C2×C17C2×#323semidirect
322. D17C2×#323semidirect
373. C17C22×#323semidirect
411. C24#63242semidirect
511. C23C2×#63242semidirect
593. C2#14544010direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×#117636532
#145440102
C2×#117636522
C22×C22⋊C4×D172
C22×#32317