Finite Group Databasebeta

← #17980333

Subgroups — #17980333

Order 4352.

1872 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545742C214yesmaximal, complemented
2#14545736C214yesmaximal, complemented
3#14545730C214yesmaximal, complemented
4#14545724C214yesmaximal, complemented
5#14545585C212yesmaximal, complemented
6#14545524C212yesmaximal, complemented
7#14545524C214yesmaximal, complemented
8#14545466C212yesmaximal, complemented
9#14545462C211yesmaximal, characteristic, complemented
10#14545428C212yesmaximal, complemented
11D17⋊#423C211yesmaximal, characteristic, complemented
12C2×#11763344C211yesmaximal, characteristic
13C2×D17⋊M16C2212yes—
14C2×D17⋊M16C2214yes—
15#11763861C2218yescomplemented
16#11763859C2214yescomplemented
17#11763858C2214yescomplemented
18#11763843C2214yescomplemented
19#11763843C2218yescomplemented
20#11763839C2218yescomplemented
21#11763839C2218yescomplemented
22#11763839C2218yescomplemented
23#11763837C2218yescomplemented
24#11763837C2214yescomplemented
25#11763834C2218yescomplemented
26#11763834C2218yescomplemented
27#11763832C2212yescomplemented
28#11763831C2212yescomplemented
29#11763828C2212yescomplemented
30#11763827C2212yescomplemented
31#11763816C2218yescomplemented
32#11763816C2218yescomplemented
33#11763814C2212yescomplemented
34#11763813C2212yescomplemented
35#11763812C2212yes—
36#11763812C2212yes—
37#11763812C2211yescharacteristic
38#11763812C2214yes—
39#11763812C2211yescharacteristic
40#11763810C2212yescomplemented
41#11763810C2212yescomplemented
42#11763781C2212yes—
43#11763781C2214yes—
44C4×#63247C2212yes—
45C4×#63247C2214yes—
46#11763344C412yes—
47#11763344C412yes—
48#11763344C412yes—
49#11763344C412yes—
50#11763344C2212yes—
51#11763344C2212yes—
52#11763344C2212yes—
53#11763344C2212yes—
54C2×#10587584C412yes—
55C2×#10587561C411yescharacteristic
56C2×#10587580C412yes—
57C2×#10587583C411yescharacteristic
58C2×#10587581C411yescharacteristic
59C2×#10587573C2211yescharacteristic
60C2×#10587579C2212yes—
61C2×#10587579C2211yescharacteristic
62C2×#10587578C2212yes—
63C2×C42×D17C2211yescharacteristic
64C2×C17×#125C411yescharacteristic
65C22×D68C2×C412yes—
66C22×D68C2×C411yescharacteristic
67C22×C4×D17C2×C411yescharacteristic
68C22×C4×D17C2×C411yescharacteristic
69C22×C4×D17C2311yescharacteristic
70C22×C4×D17C2312yes—
71C22×Dic34C2×C411yescharacteristic
72C2×#63247C2312yes—
73C2×#63247C2312yes—
74C2×#63247C2314yes—
75D17⋊M16—44no—
76D17⋊M16—48no—
77C2×#63243C2314yes—
78C2×#63243C2318yes—
79C2×#63242C2314yes—
80C2×#63242C2318yes—
81C17×#125C2×C412yes—
82C17×#125C2×C412yes—
83C17×#125C2×C412yes—
84C17×#125C2×C412yes—
85C2×C4⋊C4×C17C2×C412yes—
86C2×C4⋊C4×C17C2×C411yescharacteristic
87C2×C4⋊C4×C17C2×C412yes—
88C2×C4⋊C4×C17C2×C411yescharacteristic
89C2×C42×C17C2×C411yescharacteristic
90C2×#63227C2×C412yes—
91C2×#63227C2×C412yes—
92C2×#63227C2×C412yes—
93C2×#63227C2×C412yes—
94C2×#63227C2×C412yes—
95C2×C4⋊Dic17C2×C412yes—
96C2×#63225C2×C412yes—
97C2×C4×Dic17C2×C411yescharacteristic
98C2×C4×Dic17C2311yescharacteristic
99C2×C4×Dic17C2311yescharacteristic
100C2×C4×Dic17C2312yes—
101#10587584C2×C414yes—
102#10587584C2×C414yes—
103#10587584C2×C414yes—
104#10587584C2×C414yes—
105#10587583C2×C412yes—
106#10587583C2×C412yes—
107#10587583C2×C412yes—
108#10587583C2×C412yes—
109#10587581C2×C412yes—
110#10587581C2×C412yes—
111#10587581C2×C412yes—
112#10587581C2×C412yes—
113#10587580C2×C414yes—
114#10587580C2×C414yes—
115#10587580C2×C414yes—
116#10587580C2×C414yes—
117#10587579C2×C412yes—
118#10587579C2×C412yes—
119#10587579C2×C414yes—
120#10587579C2×C414yes—
121#10587579C2314yes—
122#10587579C2312yes—
123#10587579C2312yes—
124#10587579C2314yes—
125#10587578C2×C414yes—
126#10587578C2×C414yes—
127#10587578C2314yes—
128#10587578C2314yes—
129#10587573C2×C412yes—
130#10587573C2×C412yes—
131#10587573C2312yes—
132#10587573C2312yes—
133#10587561C2×C412yes—
134#10587561C2×C412yes—
135#10587561C2×C412yes—
136#10587561C2×C412yes—
137C42×D17C2×C411yescharacteristic
138C42×D17C2×C411yescharacteristic
139C42×D17C2×C411yescharacteristic
140C42×D17C2×C411yescharacteristic
141C42×D17C2311yescharacteristic
142C42×D17C2311yescharacteristic
143C42×D17C2311yescharacteristic
144C42×D17C2311yescharacteristic
145#10587544C2314yes—
146#10587544C2314yes—
147#10587544C2312yes—
148#10587544C2318yes—
149#10587544C2312yes—
150#10587543C2314yes—
151#10587543C2314yes—
152#10587543C2318yes—
153#10587543C2318yes—
154#10587542C2314yes—
155#10587542C2318yes—
156C4⋊#3624C2314yes—
157C4⋊#3624C2314yes—
158C4⋊#3624C2312yes—
159C4⋊#3624C2318yes—
160C4⋊#3624C2312yes—
161C4×#3624C2314yes—
162C4×#3624C2318yes—
163C23×D17C22×C411yescharacteristic
164C23×D17C22×C412yes—
165C22×C4×C17C22×C411yescharacteristic
166C22×C4×C17C22×C411yescharacteristic
167C22×C4×C17C22×C412yes—
168C22×C4×C17C22×C411yescharacteristic
169C22×C4×C17C22×C412yes—
170C22×Dic17C22×C412yes—
171C22×Dic17C22×C411yescharacteristic
172C22×Dic17C22×C411yescharacteristic
173C22×Dic17C2411yescharacteristic
174C2×D68—42no—
175C2×D68—44no—
176C2×D68C22×C412yes—
177C2×D68C22×C414yes—
178C2×D68C22×C412yes—
179C2×D68C22×C414yes—
180C2×C4×D17—22no—
181C2×C4×D17—24no—
182C2×C4×D17—22no—
183C2×C4×D17—24no—
184C2×C4×D17—42no—
185C2×C4×D17—42no—
186C2×C4×D17C22×C411yescharacteristic
187C2×C4×D17C22×C411yescharacteristic
188C2×C4×D17C22×C411yescharacteristic
189C2×C4×D17C22×C411yescharacteristic
190C2×C4×D17C22×C411yescharacteristic
191C2×C4×D17C22×C411yescharacteristic
192C2×C4×D17C22×C414yes—
193C2×C4×D17C22×C411yescharacteristic
194C2×C4×D17C22×C411yescharacteristic
195C2×C4×D17C22×C411yescharacteristic
196C2×C4×D17C22×C411yescharacteristic
197C2×C4×D17C2411yescharacteristic
198C2×C4×D17C2414yes—
199C2×C4×D17C2411yescharacteristic
200C2×Dic34—42no—
201C2×Dic34C22×C412yes—
202C2×Dic34C22×C412yes—
203#63247—28no—
204#63247—24no—
205#63247—24no—
206C2×#3624C2418yes—
207C2×#3624C2414yes—
208C2×#3624C2414yes—
209#63243—48no—
210#63243—44no—
211#63242—44no—
212#63242—48no—
213C4⋊C4×C17C22×C412yes—
214C4⋊C4×C17C22×C412yes—
215C4⋊C4×C17C22×C414yes—
216C4⋊C4×C17C22×C414yes—
217C4⋊C4×C17C22×C412yes—
218C4⋊C4×C17C22×C412yes—
219C4⋊C4×C17C22×C414yes—
220C4⋊C4×C17C22×C414yes—
221C42×C17C22×C411yescharacteristic
222C42×C17C22×C411yescharacteristic
223C42×C17C22×C411yescharacteristic
224C42×C17C22×C411yescharacteristic
225#63227C22×C414yes—
226#63227C22×C414yes—
227#63227C22×C414yes—
228#63227C22×C414yes—
229#63227C22×C414yes—
230#63227C22×C414yes—
231#63227C22×C414yes—
232#63227C22×C414yes—
233#63227C22×C414yes—
234#63227C22×C414yes—
235C4⋊Dic17C22×C414yes—
236C4⋊Dic17C22×C414yes—
237#63225C22×C414yes—
238#63225C22×C414yes—
239C4×Dic17C22×C411yescharacteristic
240C4×Dic17C22×C411yescharacteristic
241C4×Dic17C22×C411yescharacteristic
242C4×Dic17C22×C411yescharacteristic
243C4×Dic17C22×C411yescharacteristic
244C4×Dic17C22×C411yescharacteristic
245C4×Dic17C22×C411yescharacteristic
246C4×Dic17C22×C411yescharacteristic
247C4×Dic17C22×C414yes—
248C4×Dic17C2411yescharacteristic
249C4×Dic17C2414yes—
250C4×Dic17C2411yescharacteristic
251C4×Dic17C2411yescharacteristic
252C4×Dic17C2411yescharacteristic
253#60264—171nomaximal, Sylow
254C23×C17C23×C411yescharacteristic
255C22×D17—22no—
256C22×D17—24no—
257C22×D17—22no—
258C22×D17—41no—
259C22×D17—42no—
260C22×D17—42no—
261C22×D17C23×C411yescharacteristic
262C22×D17C23×C414yes—
263C22×D17C23×C411yescharacteristic
264C2×C4×C17—22no—
265C2×C4×C17—24no—
266C2×C4×C17—22no—
267C2×C4×C17—41no—
268C2×C4×C17—42no—
269C2×C4×C17C23×C411yescharacteristic
270C2×C4×C17C23×C411yescharacteristic
271C2×C4×C17C23×C411yescharacteristic
272C2×C4×C17C23×C411yescharacteristic
273C2×C4×C17C23×C411yescharacteristic
274C2×C4×C17C23×C414yes—
275C2×C4×C17C23×C414yes—
276C2×C4×C17C23×C411yescharacteristic
277C2×Dic17—42no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17C23×C414yes—
281C2×Dic17C23×C411yescharacteristic
282C2×Dic17C23×C411yescharacteristic
283C2×Dic17C23×C411yescharacteristic
284C2×Dic17C23×C411yescharacteristic
285C2×Dic17C23×C411yescharacteristic
286C2×Dic17H(5,𝔽2)12yes—
287C2×Dic172−1+412yes—
288C2×Dic17C2511yescharacteristic
289D68—28no—
290D68—24no—
291D68—42no—
292D68—44no—
293C4×D17—22no—
294C4×D17—22no—
295C4×D17—22no—
296C4×D17—22no—
297C4×D17—22no—
298C4×D17—22no—
299C4×D17—28no—
300C4×D17—21no—
301C4×D17—24no—
302C4×D17—21no—
303C4×D17—21no—
304C4×D17—24no—
305C4×D17—21no—
306C4×D17—41no—
307C4×D17—41no—
308C4×D17—41no—
309C4×D17—41no—
310Dic34—24no—
311Dic34—42no—
312#3624—28no—
313#3624—24no—
314#3624—24no—
315C2×#529—171no—
316#2995—174no—
317#2994—174no—
318#2993—174no—
319#2992—174no—
320Q8×M16—172no—
321D4×M16—174no—
322D4×M16—172no—
323#2921—172no—
324#2920—171no—
325#2905—172no—
326C2×#423—171no—
327C22×C17—21no—
328C22×C17—21no—
329C22×C17#52012yes—
330C22×C17C24×C411yescharacteristic
331C2×D17—21no—
332C2×D17—21no—
333C2×D17—21no—
334C2×D17—24no—
335C2×D17—21no—
336C2×D17—21no—
337C2×D17—24no—
338C2×D17—24no—
339C2×D17—44no—
340C2×D17—84no—
341C2×D17#56812yes—
342C4×C17—21no—
343C4×C17—24no—
344C4×C17—21no—
345C4×C17—21no—
346C4×C17—21no—
347C4×C17—21no—
348C4×C17—24no—
349C4×C17#56812yes—
350Dic17—24no—
351Dic17—21no—
352Dic17—21no—
353Dic17—21no—
354Dic17—21no—
355Dic17#52012yes—
356Dic17C2×H(5,𝔽2)11yescharacteristic
357Dic17C2×2−1+411yescharacteristic
358C22×M16—172no—
359C22×M16—174no—
360#529—172no—
361#529—172no—
362#529—172no—
363#529—172no—
364#529—172no—
365#529—172no—
366#529—172no—
367#529—172no—
368C2×#126—172no—
369C2×#125#59511yescharacteristic
370C2×#124—171no—
371C2×#123—172no—
372C2×C22⋊Q8—171no—
373C2×#121—171no—
374C2×C4×Q8—171no—
375C2×C4×D4—172no—
376C2×C4×D4—171no—
377C2×#117—172no—
378C22×C42—171no—
379#446—174no—
380#446—178no—
381C8×Q8—174no—
382#436—174no—
383#436—178no—
384#435—178no—
385#435—178no—
386#435—178no—
387C8×D4—178no—
388C8×D4—174no—
389#433—178no—
390#433—178no—
391#432—172no—
392#432—172no—
393#431—172no—
394#431—172no—
395#424—178no—
396#424—178no—
397#423—172no—
398#423—172no—
399#423—172no—
400#423—172no—
401#423—171no—
402#423—174no—
403#423—171no—
404C2×C4⋊C8—172no—
405C2×C4⋊C8—172no—
406#407—172no—
407#407—174no—
408C4×M16—172no—
409C4×M16—174no—
410C2×C17—22no—
411C2×C17C2×#52011yescharacteristic
412C2×C17C2×#56811yescharacteristic
413C2×C17C2×#56811yescharacteristic
414D17—22no—
415D17—41no—
416D17—44no—
417C22×Q8—171no—
418C22×D4—172no—
419C22×D4—171no—
420C23×C4—172no—
421C23×C4—171no—
422C23×C4—171no—
423C23×C4—171no—
424C2×M16—174no—
425C2×M16—172no—
426C2×M16—172no—
427C2×M16—174no—
428C2×M16—178no—
429C2×M16—684no—
430C2×M16—688no—
431C22×C8—174no—
432C22×C8—178no—
433#126—174no—
434#126—174no—
435#126—174no—
436#126—174no—
437#125C2×#59512yes—
438#125C2×#59512yes—
439#125C2×#59512yes—
440#125C2×#59512yes—
441#124—172no—
442#124—172no—
443#124—172no—
444#124—172no—
445#123—174no—
446#123—174no—
447#123—174no—
448#123—174no—
449C22⋊Q8—172no—
450C22⋊Q8—172no—
451C22⋊Q8—172no—
452C22⋊Q8—172no—
453#121—172no—
454#121—172no—
455#121—172no—
456#121—172no—
457C4×Q8—172no—
458C4×Q8—172no—
459C4×Q8—172no—
460C4×Q8—172no—
461C4×D4—174no—
462C4×D4—172no—
463C4×D4—172no—
464C4×D4—174no—
465C4×D4—172no—
466C4×D4—172no—
467C4×D4—174no—
468C4×D4—174no—
469#117—174no—
470#117—174no—
471#117—174no—
472#117—174no—
473C2×C4⋊C4—172no—
474C2×C4⋊C4—172no—
475C2×C4⋊C4C2×#59512yes—
476C2×C4⋊C4C2×#59511yescharacteristic
477C2×C4⋊C4C2×#59512yes—
478C2×C4⋊C4C2×#59511yescharacteristic
479C2×C22⋊C4—172no—
480C2×C22⋊C4—172no—
481C2×C22⋊C4—172no—
482C2×C22⋊C4—172no—
483C2×C22⋊C4—172no—
484C2×C42—171no—
485C2×C42—172no—
486C2×C42—171no—
487C2×C42—171no—
488C2×C42—171no—
489C2×C42—171no—
490C2×C42—171no—
491C2×C42—171no—
492C2×C42—171no—
493C2×C42—171no—
494C2×C42—171no—
495C2×C42—171no—
496C2×C42C2×#59511yescharacteristic
497C4⋊C8—174no—
498C4⋊C8—174no—
499C4⋊C8—172no—
500C4⋊C8—178no—
501C4⋊C8—172no—
502C4⋊C8—174no—
503C4⋊C8—174no—
504C4⋊C8—172no—
505C4⋊C8—178no—
506C4⋊C8—172no—
507C22⋊C8—174no—
508C22⋊C8—174no—
509C22⋊C8—178no—
510C22⋊C8—178no—
511#97—174no—
512#97—178no—
513C4×C8—174no—
514C4×C8—178no—
515C17#6026411yescharacteristic, complemented, Sylow
516C24—171no—
517C24—172no—
518C2×Q8—172no—
519C2×Q8—172no—
520C2×Q8—682no—
521C2×D4—174no—
522C2×D4—172no—
523C2×D4—174no—
524C2×D4—172no—
525C2×D4—682no—
526C2×D4—684no—
527C22×C4—171no—
528C22×C4—171no—
529C22×C4—171no—
530C22×C4—172no—
531C22×C4—171no—
532C22×C4—171no—
533C22×C4—171no—
534C22×C4—171no—
535C22×C4—171no—
536C22×C4—171no—
537C22×C4—174no—
538C22×C4—171no—
539C22×C4—171no—
540C22×C4—174no—
541C22×C4—171no—
542C22×C4—171no—
543C22×C4—171no—
544C22×C4—171no—
545C22×C4—342no—
546C22×C4—344no—
547C22×C4—342no—
548C22×C4—344no—
549C22×C4—682no—
550C22×C4—682no—
551C22×C4C22×#59511yescharacteristic
552C22×C4C22×#59511yescharacteristic
553C22×C4C22×#59512yes—
554C22×C4C22×#59511yescharacteristic
555C22×C4C22×#59512yes—
556M16—344no—
557M16—348no—
558M16—344no—
559M16—688no—
560M16—684no—
561C2×C8—174no—
562C2×C8—174no—
563C2×C8—178no—
564C2×C8—684no—
565C2×C8—688no—
566C4⋊C4—174no—
567C4⋊C4—174no—
568C4⋊C4—174no—
569C4⋊C4—174no—
570C4⋊C4C22×#59514yes—
571C4⋊C4C22×#59514yes—
572C4⋊C4C22×#59512yes—
573C4⋊C4C22×#59512yes—
574C4⋊C4C22×#59514yes—
575C4⋊C4C22×#59514yes—
576C4⋊C4C22×#59512yes—
577C4⋊C4C22×#59512yes—
578C22⋊C4—174no—
579C22⋊C4—174no—
580C22⋊C4—174no—
581C22⋊C4—174no—
582C22⋊C4—174no—
583C22⋊C4—174no—
584C22⋊C4—174no—
585C22⋊C4—174no—
586C22⋊C4—174no—
587C22⋊C4—174no—
588C42—171no—
589C42—174no—
590C42—171no—
591C42—171no—
592C42—171no—
593C42—171no—
594C42—171no—
595C42—171no—
596C42—171no—
597C42—171no—
598C42—171no—
599C42—171no—
600C42—171no—
601C42—174no—
602C42C22×#59511yescharacteristic
603C42C22×#59511yescharacteristic
604C42C22×#59511yescharacteristic
605C42C22×#59511yescharacteristic
606C23—171no—
607C23—174no—
608C23—171no—
609C23—342no—
610C23—342no—
611C23—344no—
612C23—681no—
613C23—682no—
614C23—682no—
615C23C23×#59511yescharacteristic
616Q8—344no—
617Q8—682no—
618D4—348no—
619D4—344no—
620D4—684no—
621D4—682no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—172no—
628C2×C4—172no—
629C2×C4—171no—
630C2×C4—171no—
631C2×C4—171no—
632C2×C4—171no—
633C2×C4—171no—
634C2×C4—171no—
635C2×C4—174no—
636C2×C4—341no—
637C2×C4—344no—
638C2×C4—341no—
639C2×C4—341no—
640C2×C4—341no—
641C2×C4—344no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—348no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—681no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—681no—
654C2×C4—681no—
655C2×C4—682no—
656C2×C4C23×#59511yescharacteristic
657C2×C4C23×#59511yescharacteristic
658C2×C4C23×#59511yescharacteristic
659C2×C4C23×#59511yescharacteristic
660C2×C4C23×#59511yescharacteristic
661C2×C4C23×#59514yes—
662C2×C4C23×#59514yes—
663C2×C4C23×#59511yescharacteristic
664C8—344no—
665C8—348no—
666C8—344no—
667C22—21no—
668C22—21no—
669C22—172no—
670C22—341no—
671C22—341no—
672C22—341no—
673C22—344no—
674C22—341no—
675C22—344no—
676C22—341no—
677C22—344no—
678C22—684no—
679C22—1364no—
680C22#1176387812yes—
681C22C24×#59511yescharacteristic
682C4—21no—
683C4—24no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—24no—
688C4—21no—
689C4—171no—
690C4—171no—
691C4—172no—
692C4—341no—
693C4—341no—
694C4—341no—
695C4—341no—
696C4—344no—
697C4#1176388912yes—
698C2—22no—
699C2—342no—
700C2—681no—
701C2—684no—
702C2C2×#1176387811yescharacteristic
703C2D17⋊#56811yescharacteristic
704C2C2×#1176388911yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC2×C17×#125C4
prime radicalC2×#10587581C4
cosocleC2×Dic17C25
hypercenterC2×#125#595
hypocenterC17#60264
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14545742C2semidirect
2. #14545736C2semidirect
3. #14545730C2semidirect
4. #14545724C2semidirect
5. #14545585C2semidirect
6. #14545524C2semidirect
7. #14545524C2semidirect
8. #14545466C2semidirect
9. #14545462C2semidirect
10. #14545428C2semidirect
11. D17⋊#423C2semidirect
15. #11763861C22semidirect
16. #11763859C22semidirect
17. #11763858C22semidirect
18. #11763843C22semidirect
19. #11763843C22semidirect
20. #11763839C22semidirect
21. #11763839C22semidirect
22. #11763839C22semidirect
23. #11763837C22semidirect
24. #11763837C22semidirect
25. #11763834C22semidirect
26. #11763834C22semidirect
27. #11763832C22semidirect
28. #11763831C22semidirect
29. #11763828C22semidirect
30. #11763827C22semidirect
31. #11763816C22semidirect
32. #11763816C22semidirect
33. #11763814C22semidirect
34. #11763813C22semidirect
40. #11763810C22semidirect
41. #11763810C22semidirect
515. C17#60264semidirect

Maximal subgroups

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

subgroupindex
#145457422
#145457362
#145457302
#145457242
#145455852
#145455242
#145454662
#145454622
#145454282
D17⋊#4232
C2×#117633442
#6026417