Finite Group Databasebeta

← #17979978

Subgroups — #17979978

Order 4352.

1960 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545620C214yesmaximal, complemented
2#14545613C214yesmaximal, complemented
3#14545608C214yesmaximal, complemented
4#14545601C214yesmaximal, complemented
5#14545585C212yesmaximal, complemented
6#14545524C212yesmaximal, complemented
7#14545524C214yesmaximal, complemented
8#14545466C212yesmaximal, complemented
9#14545462C211yesmaximal, characteristic, complemented
10#14545350C212yesmaximal, complemented
11C4×D17⋊M16C211yesmaximal, 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#11763812C2212yes—
32#11763812C2214yes—
33#11763781C2212yes—
34#11763781C2214yes—
35#11763774C2218yescomplemented
36#11763774C2218yescomplemented
37C4×#63243C2212yescomplemented
38C4×#63243C2212yescomplemented
39C4×#63247C2212yes—
40C4×#63247C2211yescharacteristic
41C4×#63247C2212yes—
42C4×#63247C2214yes—
43C4×#63247C2211yescharacteristic
44#11763768C2212yescomplemented
45C4×#63242C2212yescomplemented
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×#63247C2314yes—
73C2×#63247C2312yes—
74C2×#63247C2312yes—
75D17⋊M16—28no—
76D17⋊M16—216no—
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#10587544C2318yes—
147#10587543C2314yes—
148#10587543C2314yes—
149#10587543C2318yes—
150#10587543C2318yes—
151#10587542C2312yes—
152#10587542C2312yes—
153#10587542C2314yes—
154#10587542C2314yes—
155#10587542C2318yes—
156C4⋊#3624C2314yes—
157C4⋊#3624C2318yes—
158C4×#3624C2312yes—
159C4×#3624C2312yes—
160C4×#3624C2314yes—
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—24no—
181C2×C4×D17—28no—
182C2×C4×D17—42no—
183C2×C4×D17—42no—
184C2×C4×D17C22×C411yescharacteristic
185C2×C4×D17C22×C411yescharacteristic
186C2×C4×D17C22×C411yescharacteristic
187C2×C4×D17C22×C411yescharacteristic
188C2×C4×D17C22×C411yescharacteristic
189C2×C4×D17C22×C411yescharacteristic
190C2×C4×D17C22×C414yes—
191C2×C4×D17C22×C411yescharacteristic
192C2×C4×D17C22×C411yescharacteristic
193C2×C4×D17C22×C411yescharacteristic
194C2×C4×D17C22×C411yescharacteristic
195C2×C4×D17C2411yescharacteristic
196C2×C4×D17C2414yes—
197C2×C4×D17C2411yescharacteristic
198C2×Dic34—42no—
199C2×Dic34C22×C412yes—
200C2×Dic34C22×C412yes—
201#63247—24no—
202#63247—28no—
203#63247#4118yes—
204C2×#3624C2414yes—
205C2×#3624C2418yes—
206C2×#3624C2414yes—
207#63243—28no—
208#63243—216no—
209#63242—28no—
210#63242—216no—
211C4⋊C4×C17C22×C412yes—
212C4⋊C4×C17C22×C412yes—
213C4⋊C4×C17C22×C414yes—
214C4⋊C4×C17C22×C414yes—
215C4⋊C4×C17C22×C412yes—
216C4⋊C4×C17C22×C412yes—
217C4⋊C4×C17C22×C414yes—
218C4⋊C4×C17C22×C414yes—
219C42×C17C22×C411yescharacteristic
220C42×C17C22×C411yescharacteristic
221C42×C17C22×C411yescharacteristic
222C42×C17C22×C411yescharacteristic
223#63227C22×C414yes—
224#63227C22×C414yes—
225#63227C22×C414yes—
226#63227C22×C414yes—
227#63227C22×C414yes—
228#63227C22×C414yes—
229#63227C22×C414yes—
230#63227C22×C414yes—
231#63227C22×C414yes—
232#63227C22×C414yes—
233C4⋊Dic17C22×C414yes—
234C4⋊Dic17C22×C414yes—
235#63225C22×C414yes—
236#63225C22×C414yes—
237C4×Dic17C22×C411yescharacteristic
238C4×Dic17C22×C411yescharacteristic
239C4×Dic17C22×C411yescharacteristic
240C4×Dic17C22×C411yescharacteristic
241C4×Dic17C22×C411yescharacteristic
242C4×Dic17C22×C411yescharacteristic
243C4×Dic17C22×C411yescharacteristic
244C4×Dic17C22×C411yescharacteristic
245C4×Dic17C22×C414yes—
246C4×Dic17C2411yescharacteristic
247C4×Dic17C2411yescharacteristic
248C4×Dic17C2411yescharacteristic
249C4×Dic17C2414yes—
250C4×Dic17C2411yescharacteristic
251#60214—171nomaximal, Sylow
252C23×C17C23×C411yescharacteristic
253C22×D17—22no—
254C22×D17—24no—
255C22×D17—22no—
256C22×D17—41no—
257C22×D17—42no—
258C22×D17—42no—
259C22×D17C23×C411yescharacteristic
260C22×D17C23×C414yes—
261C22×D17C23×C411yescharacteristic
262C2×C4×C17—22no—
263C2×C4×C17—24no—
264C2×C4×C17—22no—
265C2×C4×C17—41no—
266C2×C4×C17—42no—
267C2×C4×C17C23×C411yescharacteristic
268C2×C4×C17C23×C411yescharacteristic
269C2×C4×C17C23×C411yescharacteristic
270C2×C4×C17C23×C411yescharacteristic
271C2×C4×C17C23×C411yescharacteristic
272C2×C4×C17C23×C414yes—
273C2×C4×C17C23×C414yes—
274C2×C4×C17C23×C411yescharacteristic
275C2×Dic17—42no—
276C2×Dic17—41no—
277C2×Dic17—41no—
278C2×Dic17C23×C414yes—
279C2×Dic17C23×C411yescharacteristic
280C2×Dic17C23×C411yescharacteristic
281C2×Dic17C23×C411yescharacteristic
282C2×Dic17C23×C411yescharacteristic
283C2×Dic17C23×C411yescharacteristic
284C2×Dic17C2×#4114yes—
285C2×Dic17C2511yescharacteristic
286D68—28no—
287D68—24no—
288D68—42no—
289D68—44no—
290C4×D17—22no—
291C4×D17—22no—
292C4×D17—22no—
293C4×D17—22no—
294C4×D17—22no—
295C4×D17—22no—
296C4×D17—28no—
297C4×D17—22no—
298C4×D17—24no—
299C4×D17—24no—
300C4×D17—22no—
301C4×D17—41no—
302C4×D17—41no—
303C4×D17—41no—
304C4×D17—41no—
305Dic34—24no—
306Dic34—42no—
307#3624—24no—
308#3624—28no—
309#3624C2×#4118yes—
310C2×#529—171no—
311#2969—174no—
312#2968—174no—
313#2967—174no—
314#2966—174no—
315Q8×M16—172no—
316D4×M16—174no—
317D4×M16—172no—
318#2921—172no—
319#2920—171no—
320#2873—172no—
321C2×C4×M16—171no—
322C22×C17—21no—
323C22×C17—21no—
324C22×C17C4×#4112yes—
325C22×C17C24×C411yescharacteristic
326C2×D17—21no—
327C2×D17—21no—
328C2×D17—21no—
329C2×D17—24no—
330C2×D17—21no—
331C2×D17—21no—
332C2×D17—24no—
333C2×D17—24no—
334C2×D17—44no—
335C2×D17—84no—
336C2×D17#56812yes—
337C4×C17—21no—
338C4×C17—24no—
339C4×C17—21no—
340C4×C17—21no—
341C4×C17—21no—
342C4×C17—21no—
343C4×C17—24no—
344C4×C17#56812yes—
345Dic17—24no—
346Dic17—21no—
347Dic17—21no—
348Dic17—21no—
349Dic17—21no—
350Dic17C4×#4112yes—
351Dic17C22×#4112yes—
352C22×M16—172no—
353C22×M16—174no—
354#529—172no—
355#529—172no—
356#529—172no—
357#529—172no—
358#529—172no—
359#529—172no—
360#529—172no—
361#529—172no—
362C2×#126—172no—
363C2×#125#59511yescharacteristic
364C2×#124—171no—
365C2×#123—172no—
366C2×C22⋊Q8—171no—
367C2×#121—171no—
368C2×C4×Q8—171no—
369C2×C4×D4—172no—
370C2×C4×D4—171no—
371C2×#117—172no—
372C22×C42—171no—
373#446—174no—
374#446—178no—
375C8×Q8—174no—
376#436—174no—
377#436—178no—
378#435—178no—
379#435—178no—
380#435—178no—
381C8×D4—178no—
382C8×D4—174no—
383#433—178no—
384#433—178no—
385#432—172no—
386#432—172no—
387#431—172no—
388#431—172no—
389#423—172no—
390#423—174no—
391#407—172no—
392#407—174no—
393#405—178no—
394#405—178no—
395C4×M16—171no—
396C4×M16—171no—
397C4×M16—172no—
398C4×M16—172no—
399C4×M16—172no—
400C4×M16—172no—
401C4×M16—174no—
402C2×#97—172no—
403C2×C4×C8—172no—
404C2×C17—22no—
405C2×C17C2×C4×#4111yescharacteristic
406C2×C17C2×#56811yescharacteristic
407C2×C17C2×#56811yescharacteristic
408D17—22no—
409D17—41no—
410D17—44no—
411C22×Q8—171no—
412C22×D4—172no—
413C22×D4—171no—
414C23×C4—172no—
415C23×C4—171no—
416C23×C4—171no—
417C23×C4—171no—
418C2×M16—172no—
419C2×M16—174no—
420C2×M16—178no—
421C2×M16—172no—
422C2×M16—174no—
423C2×M16—348no—
424C2×M16—3416no—
425C22×C8—174no—
426C22×C8—178no—
427#126—174no—
428#126—174no—
429#126—174no—
430#126—174no—
431#125C2×#59512yes—
432#125C2×#59512yes—
433#125C2×#59512yes—
434#125C2×#59512yes—
435#124—172no—
436#124—172no—
437#124—172no—
438#124—172no—
439#123—174no—
440#123—174no—
441#123—174no—
442#123—174no—
443C22⋊Q8—172no—
444C22⋊Q8—172no—
445C22⋊Q8—172no—
446C22⋊Q8—172no—
447#121—172no—
448#121—172no—
449#121—172no—
450#121—172no—
451C4×Q8—172no—
452C4×Q8—172no—
453C4×Q8—172no—
454C4×Q8—172no—
455C4×D4—174no—
456C4×D4—172no—
457C4×D4—172no—
458C4×D4—174no—
459C4×D4—172no—
460C4×D4—172no—
461C4×D4—174no—
462C4×D4—174no—
463#117—174no—
464#117—174no—
465#117—174no—
466#117—174no—
467C2×C4⋊C4—172no—
468C2×C4⋊C4—172no—
469C2×C4⋊C4C2×#59512yes—
470C2×C4⋊C4C2×#59511yescharacteristic
471C2×C4⋊C4C2×#59512yes—
472C2×C4⋊C4C2×#59511yescharacteristic
473C2×C22⋊C4—172no—
474C2×C22⋊C4—172no—
475C2×C22⋊C4—172no—
476C2×C22⋊C4—172no—
477C2×C22⋊C4—172no—
478C2×C42—171no—
479C2×C42—172no—
480C2×C42—171no—
481C2×C42—171no—
482C2×C42—171no—
483C2×C42—171no—
484C2×C42—171no—
485C2×C42—171no—
486C2×C42—171no—
487C2×C42—171no—
488C2×C42—171no—
489C2×C42—171no—
490C2×C42C2×#59511yescharacteristic
491C4⋊C8—174no—
492C4⋊C8—178no—
493C4⋊C8—174no—
494C4⋊C8—178no—
495C22⋊C8—174no—
496C22⋊C8—174no—
497C22⋊C8—178no—
498C22⋊C8—178no—
499#97—172no—
500#97—172no—
501#97—174no—
502#97—174no—
503#97—178no—
504C4×C8—172no—
505C4×C8—172no—
506C4×C8—174no—
507C4×C8—174no—
508C4×C8—178no—
509C17#6021411yescharacteristic, complemented, Sylow
510C24—171no—
511C24—172no—
512C2×Q8—172no—
513C2×Q8—172no—
514C2×Q8—682no—
515C2×D4—174no—
516C2×D4—172no—
517C2×D4—174no—
518C2×D4—172no—
519C2×D4—682no—
520C2×D4—684no—
521C22×C4—171no—
522C22×C4—171no—
523C22×C4—171no—
524C22×C4—172no—
525C22×C4—171no—
526C22×C4—171no—
527C22×C4—171no—
528C22×C4—171no—
529C22×C4—171no—
530C22×C4—171no—
531C22×C4—174no—
532C22×C4—171no—
533C22×C4—171no—
534C22×C4—174no—
535C22×C4—171no—
536C22×C4—171no—
537C22×C4—171no—
538C22×C4—171no—
539C22×C4—344no—
540C22×C4—348no—
541C22×C4—682no—
542C22×C4—682no—
543C22×C4C22×#59511yescharacteristic
544C22×C4C22×#59511yescharacteristic
545C22×C4C22×#59512yes—
546C22×C4C22×#59511yescharacteristic
547C22×C4C22×#59512yes—
548M16—178no—
549M16—348no—
550M16—3416no—
551M16—344no—
552M16—348no—
553C2×C8—174no—
554C2×C8—174no—
555C2×C8—178no—
556C2×C8—348no—
557C2×C8—3416no—
558C4⋊C4—174no—
559C4⋊C4—174no—
560C4⋊C4—174no—
561C4⋊C4—174no—
562C4⋊C4C22×#59514yes—
563C4⋊C4C22×#59514yes—
564C4⋊C4C22×#59512yes—
565C4⋊C4C22×#59512yes—
566C4⋊C4C22×#59514yes—
567C4⋊C4C22×#59514yes—
568C4⋊C4C22×#59512yes—
569C4⋊C4C22×#59512yes—
570C22⋊C4—174no—
571C22⋊C4—174no—
572C22⋊C4—174no—
573C22⋊C4—174no—
574C22⋊C4—174no—
575C22⋊C4—174no—
576C22⋊C4—174no—
577C22⋊C4—174no—
578C22⋊C4—174no—
579C22⋊C4—174no—
580C42—171no—
581C42—171no—
582C42—171no—
583C42—174no—
584C42—171no—
585C42—171no—
586C42—171no—
587C42—171no—
588C42—171no—
589C42—171no—
590C42—171no—
591C42—171no—
592C42—171no—
593C42—174no—
594C42C22×#59511yescharacteristic
595C42C22×#59511yescharacteristic
596C42C22×#59511yescharacteristic
597C42C22×#59511yescharacteristic
598C23—171no—
599C23—174no—
600C23—171no—
601C23—342no—
602C23—342no—
603C23—344no—
604C23—681no—
605C23—682no—
606C23—682no—
607C23C23×#59511yescharacteristic
608Q8—344no—
609Q8—682no—
610D4—348no—
611D4—344no—
612D4—684no—
613D4—682no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—174no—
620C2×C4—171no—
621C2×C4—171no—
622C2×C4—171no—
623C2×C4—171no—
624C2×C4—171no—
625C2×C4—171no—
626C2×C4—174no—
627C2×C4—342no—
628C2×C4—344no—
629C2×C4—342no—
630C2×C4—344no—
631C2×C4—342no—
632C2×C4—342no—
633C2×C4—348no—
634C2×C4—342no—
635C2×C4—342no—
636C2×C4—342no—
637C2×C4—342no—
638C2×C4—681no—
639C2×C4—681no—
640C2×C4—681no—
641C2×C4—681no—
642C2×C4—681no—
643C2×C4—681no—
644C2×C4—682no—
645C2×C4C23×#59511yescharacteristic
646C2×C4C23×#59511yescharacteristic
647C2×C4C23×#59511yescharacteristic
648C2×C4C23×#59511yescharacteristic
649C2×C4C23×#59511yescharacteristic
650C2×C4C23×#59514yes—
651C2×C4C23×#59514yes—
652C2×C4C23×#59511yescharacteristic
653C8—178no—
654C8—344no—
655C8—348no—
656C22—21no—
657C22—21no—
658C22—172no—
659C22—341no—
660C22—341no—
661C22—341no—
662C22—344no—
663C22—341no—
664C22—344no—
665C22—341no—
666C22—344no—
667C22—684no—
668C22—1364no—
669C22#41×#59512yes—
670C22C24×#59511yescharacteristic
671C4—21no—
672C4—24no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—24no—
677C4—21no—
678C4—172no—
679C4—172no—
680C4—341no—
681C4—341no—
682C4—341no—
683C4—341no—
684C4—344no—
685C4#1176388912yes—
686C2—22no—
687C2—342no—
688C2—681no—
689C2—684no—
690C2C2×#41×#59511yescharacteristic
691C2D17⋊#56811yescharacteristic
692C2C2×#1176388911yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC2×C17×#125C4
prime radicalC2×#10587581C4
cosocleC2×Dic17C25
hypercenterC2×#125#595
hypocenterC17#60214
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14545620C2semidirect
2. #14545613C2semidirect
3. #14545608C2semidirect
4. #14545601C2semidirect
5. #14545585C2semidirect
6. #14545524C2semidirect
7. #14545524C2semidirect
8. #14545466C2semidirect
9. #14545462C2semidirect
10. #14545350C2semidirect
11. C4×D17⋊M16C2semidirect
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
35. #11763774C22semidirect
36. #11763774C22semidirect
37. C4×#63243C22semidirect
38. C4×#63243C22semidirect
44. #11763768C22semidirect
45. C4×#63242C22semidirect
509. C17#60214semidirect

Maximal subgroups

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

subgroupindex
#145456202
#145456132
#145456082
#145456012
#145455852
#145455242
#145454662
#145454622
#145453502
C4×D17⋊M162
C2×#117633442
#6021417