Finite Group Databasebeta

← #17033730

Subgroups — #17033730

Order 4352.

1462 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763288C211yesmaximal, characteristic
2C2×#11762781C212yesmaximal
3#14531401C212yesmaximal, complemented
4#14528772C211yesmaximal, characteristic, complemented
5#14528771C212yesmaximal, complemented
6#14528770C212yesmaximal, complemented
7#14528769C212yesmaximal, complemented
8#14528515C212yesmaximal, complemented
9C17×#1799C211yesmaximal, characteristic, complemented
10C22×#63254C2211yescharacteristic
11#11763288—24no—
12#11763288—24no—
13C2×C4×Dic34C411yescharacteristic, complemented
14C2×#10587573C411yescharacteristic, complemented
15C2×D4×Dic17C2211yescharacteristic
16C2×C4×C22⋊D17C411yescharacteristic, complemented
17C2×C4×C22⋊D17C2211yescharacteristic
18C2×#10587567C411yescharacteristic, complemented
19C2×#10587567C2211yescharacteristic
20C2×#10587558C411yescharacteristic, complemented
21C2×#10587563C411yescharacteristic, complemented
22C2×#10587563C2214yes—
23C2×#10587563C2211yescharacteristic
24C22×#63225C411yescharacteristic, complemented
25C22×#63225C2211yescharacteristic
26C2×C4⋊C4×D17C411yescharacteristic, complemented
27#11762781—28no—
28C2×#10587505C2212yes—
29C2×#10587477C2214yes—
30#11762706—24no—
31#11762704—24no—
32#11762669C2212yes—
33#11762667C2214yes—
34#11762576C2212yes—
35#11762575C2214yes—
36C2×C4×D4×C17C2211yescharacteristic
37C2×C17×#99C2212yes—
38C17×#380C2212yes—
39C17×#342C2212yes—
40C22×D4×C17C2311yescharacteristic
41C23×C4×C17C2×C411yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C22×C22⋊D17C2×C411yescharacteristic
44C22×C22⋊D17C2311yescharacteristic
45C23×Dic17C2×C411yescharacteristic
46C23×Dic17C2×C411yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C2×#63254—24no—
50C2×#63254—24no—
51C2×#63254D414yes—
52C2×#63254Q814yes—
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C411yescharacteristic
55C22×C4×D17C2×C411yescharacteristic
56C22×Dic34C2×C411yescharacteristic
57C4×D4×C17—22no—
58C4×D4×C17—22no—
59C2×C4⋊C4×C17—22no—
60C2×C4⋊C4×C17C2×C411yescharacteristic
61C2×C22⋊C4×C17C2×C411yescharacteristic
62C2×C22⋊C4×C17C2314yes—
63C2×C22⋊C4×C17C2311yescharacteristic
64C2×C42×C17C2×C411yescharacteristic
65C2×C22⋊Dic17C2×C411yescharacteristic
66C2×C22⋊Dic17C2314yes—
67C2×C22⋊Dic17C2311yescharacteristic
68D4×Dic17—24no—
69C4×C22⋊D17—22no—
70C4×C22⋊D17—22no—
71C4×C22⋊D17—22no—
72C4×C22⋊D17—22no—
73C2×#63227C2×C411yescharacteristic
74C2×#63227C2×C411yescharacteristic
75C2×C4⋊Dic17—22no—
76C2×C4⋊Dic17C2×C411yescharacteristic
77C2×#63225—22no—
78C2×#63225—22no—
79C2×#63225—24no—
80C2×#63225—24no—
81C2×#63225C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×#63225C2×C411yescharacteristic
88C2×#63225C2×C411yescharacteristic
89C2×#63225D414yes—
90C2×#63225D414yes—
91C2×C4×Dic17—24no—
92C2×C4×Dic17C2×C411yescharacteristic
93C2×C4×Dic17C2×C411yescharacteristic
94C2×C4×Dic17C2×C411yescharacteristic
95C2×C4×Dic17C2×C411yescharacteristic
96C2×C4×Dic17C2×C411yescharacteristic
97C4⋊C4×D17—24no—
98#10587573—24no—
99#10587567—24no—
100#10587567—24no—
101#10587563—24no—
102#10587563—24no—
103#10587563—28no—
104#10587563—28no—
105#10587558—22no—
106#10587558—22no—
107C4×Dic34—22no—
108C4×Dic34—22no—
109C17×#99—24no—
110C17×#95—22no—
111#10587505—24no—
112#10587502—22no—
113#10587502—24no—
114#10587477—28no—
115C24×C17C22×C411yescharacteristic
116C24×C17C2411yescharacteristic
117C23×D17C22×C411yescharacteristic
118C2×D4×C17—22no—
119C2×D4×C17—22no—
120C2×D4×C17C2×D412yes—
121C2×D4×C17C2×Q812yes—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—24no—
125C22×C4×C17—81no—
126C22×C4×C17—81no—
127C22×C4×C17C22×C411yescharacteristic
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C411yescharacteristic
130C22×C4×C17C22×C411yescharacteristic
131C22×C4×C17C22×C411yescharacteristic
132C22×C4×C17C2×D412yes—
133C22×C4×C17C2×D412yes—
134C2×C22⋊D17—22no—
135C2×C22⋊D17—22no—
136C2×C22⋊D17—22no—
137C2×C22⋊D17—22no—
138C2×C22⋊D17C4⋊C414yescomplemented
139C2×C22⋊D17C2×D412yes—
140C2×C22⋊D17C2×Q812yes—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—24no—
145C22×Dic17—81no—
146C22×Dic17—81no—
147C22×Dic17C4⋊C414yescomplemented
148C22×Dic17C22×C411yescharacteristic
149C22×Dic17C22×C411yescharacteristic
150C22×Dic17C22×C411yescharacteristic
151C22×Dic17C22×C411yescharacteristic
152C22×Dic17C22×C411yescharacteristic
153C22×Dic17C22×C411yescharacteristic
154C22×Dic17C22×C411yescharacteristic
155C22×Dic17C2×D414yes—
156C22×Dic17C2×D414yes—
157C22×Dic17C2×D412yes—
158C22×Dic17C2×Q812yes—
159C22×Dic17#4114yes—
160#63254—216no—
161#63254—216no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—81no—
167C2×C4×D17—81no—
168C2×C4×D17C4⋊C414yescomplemented
169C2×Dic34—22no—
170C2×Dic34—22no—
171C2×Dic34C4⋊C414yescomplemented
172C4⋊C4×C17—22no—
173C4⋊C4×C17—82no—
174C22⋊C4×C17—22no—
175C22⋊C4×C17—22no—
176C22⋊C4×C17—24no—
177C22⋊C4×C17—24no—
178C42×C17—21no—
179C42×C17—21no—
180C22⋊Dic17—22no—
181C22⋊Dic17—22no—
182C22⋊Dic17—24no—
183C22⋊Dic17—24no—
184#63227—21no—
185#63227—21no—
186#63227—22no—
187C4⋊Dic17—22no—
188C4⋊Dic17—82no—
189#63225—21no—
190#63225—21no—
191#63225—22no—
192#63225—22no—
193#63225—22no—
194#63225—48no—
195#63225—84no—
196#63225C22⋊C412yes—
197#63225C22⋊C412yes—
198#63225C22⋊C412yes—
199#63225C22⋊C412yes—
200#63225C22⋊C414yes—
201#63225C22⋊C414yes—
202C4×Dic17—22no—
203C4×Dic17—22no—
204C4×Dic17—22no—
205C4×Dic17—22no—
206C4×Dic17—22no—
207C4×Dic17—48no—
208#20634—171nomaximal, Sylow
209C23×C17—21no—
210C23×C17—21no—
211C23×C17—41no—
212C23×C17—41no—
213C23×C17—41no—
214C23×C17—41no—
215C23×C17C2×C4⋊C412yes—
216C23×C17C23×C411yescharacteristic
217C23×C17C22×D412yes—
218C23×C17C22×D411yescharacteristic
219C23×C17C22×Q811yescharacteristic
220C23×C17C2×#4112yes—
221C22×D17—21no—
222C22×D17—21no—
223C22×D17—41no—
224C22×D17—41no—
225C22×D17C2×C4⋊C412yes—
226D4×C17—24no—
227D4×C17—24no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—42no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—42no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—44no—
239C2×C4×C17—44no—
240C2×C4×C17—44no—
241C2×C4×C17—81no—
242C2×C4×C17—81no—
243C2×C4×C17C2×C22⋊C411yescharacteristic
244C2×C4×C17C2×C22⋊C411yescharacteristic
245C2×C4×C17C2×C22⋊C412yes—
246C2×C4×C17C2×C4⋊C412yes—
247C22⋊D17—24no—
248C22⋊D17—24no—
249C22⋊D17—28no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—28no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—44no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—44no—
261C2×Dic17—44no—
262C2×Dic17—44no—
263C2×Dic17—82no—
264C2×Dic17C2×C22⋊C412yes—
265C2×Dic17C2×C22⋊C412yes—
266C2×Dic17C2×C22⋊C412yes—
267C2×Dic17C2×C22⋊C412yes—
268C2×Dic17C2×C4⋊C412yes—
269C2×Dic17C2×C4⋊C412yes—
270C2×Dic17C2×C4⋊C412yes—
271C2×Dic17#11712yes—
272C2×Dic17#11712yes—
273C2×Dic17#12118yes—
274C2×Dic17C22⋊Q818yes—
275C4×D17—28no—
276C4×D17—82no—
277C4×D17—82no—
278Dic34—28no—
279C2×#520—171no—
280C2×#410—172no—
281#2316—172no—
282#1799—172no—
283#1799—172no—
284#1799—172no—
285#1799—171no—
286#1799D1711yescharacteristic, complemented
287#1740—172no—
288C22×C17—22no—
289C22×C17—21no—
290C22×C17—22no—
291C22×C17—21no—
292C22×C17—22no—
293C22×C17—41no—
294C22×C17—41no—
295C22×C17—42no—
296C22×C17—42no—
297C22×C17—42no—
298C22×C17—41no—
299C22×C17—41no—
300C22×C17C22×C22⋊C411yescharacteristic
301C22×C17C22×C4⋊C411yescharacteristic
302C22×C17C2×#11711yescharacteristic
303C22×C17C2×#12112yes—
304C22×C17C2×C22⋊Q812yes—
305C2×D17—22no—
306C2×D17—42no—
307C2×D17—41no—
308C2×D17—41no—
309C2×D17—42no—
310C4×C17—22no—
311C4×C17—21no—
312C4×C17—21no—
313C4×C17—22no—
314C4×C17—41no—
315C4×C17—41no—
316C4×C17—84no—
317Dic17—22no—
318Dic17—22no—
319Dic17—22no—
320Dic17—41no—
321Dic17—41no—
322Dic17—84no—
323Dic17#38014yes—
324Dic17#38014yes—
325C22×#41—171no—
326#520—344no—
327#520—344no—
328C2×C4×Q8—171no—
329C2×C4×Q8—171no—
330C2×C4×D4—171no—
331C2×C4×D4—171no—
332C2×C4×D4—171no—
333C2×C4×D4—171no—
334C2×C4×D4—171no—
335C2×C4×D4C2×D1711yescharacteristic
336C2×#117—171no—
337C2×#117—171no—
338C2×#117—171no—
339C2×#117—174no—
340C22×C4⋊C4—171no—
341C22×C4⋊C4—171no—
342C22×C4⋊C4—171no—
343#410—348no—
344C2×#99—172no—
345C2×#99—174no—
346C2×#99C2×D1712yes—
347#389—344no—
348#389—344no—
349#380—172no—
350#380—174no—
351#380C2×D1712yes—
352#342—174no—
353#342—172no—
354#342C2×D1712yes—
355C2×C17—22no—
356C2×C17—21no—
357C2×C17—21no—
358C2×C17—22no—
359C2×C17—42no—
360C2×C17C2×#38011yescharacteristic
361C2×C17#288311yescharacteristic
362C2×C17#288411yescharacteristic
363D17—42no—
364C2×#41—174no—
365C2×#41—174no—
366C2×#41—344no—
367C2×#41—344no—
368C22×Q8—171no—
369C22×D4—171no—
370C22×D4—171no—
371C22×D4C22×D1711yescharacteristic
372C23×C4—171no—
373C23×C4—171no—
374C23×C4—171no—
375C23×C4—171no—
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—171no—
379C23×C4C4×D1711yescharacteristic
380C23×C4C22×D1711yescharacteristic
381C4×Q8—342no—
382C4×Q8—342no—
383C4×Q8—344no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—344no—
387C4×D4—344no—
388C4×D4—342no—
389C4×D4—342no—
390C4×D4—344no—
391C4×D4—342no—
392C4×D4—342no—
393#117—342no—
394#117—342no—
395#117—344no—
396#117—344no—
397#117—348no—
398#117—348no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—174no—
405C2×C4⋊C4—174no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—171no—
408C2×C4⋊C4—171no—
409C2×C4⋊C4—171no—
410C2×C4⋊C4—171no—
411C2×C4⋊C4—344no—
412C2×C4⋊C4—342no—
413C2×C4⋊C4—342no—
414C2×C4⋊C4—344no—
415C2×C4⋊C4—344no—
416C2×C4⋊C4—342no—
417C2×C4⋊C4C4×D1711yescharacteristic
418C2×C22⋊C4—171no—
419C2×C22⋊C4—171no—
420C2×C22⋊C4—171no—
421C2×C22⋊C4—171no—
422C2×C22⋊C4—174no—
423C2×C22⋊C4C4×D1711yescharacteristic
424C2×C22⋊C4C22×D1714yes—
425C2×C22⋊C4C22×D1711yescharacteristic
426C2×C42—171no—
427C2×C42—171no—
428C2×C42—171no—
429C2×C42—171no—
430C2×C42—171no—
431C2×C42—344no—
432C2×C42C4×D1711yescharacteristic
433#99—24no—
434#99—348no—
435#99—344no—
436#95—22no—
437#95—344no—
438#95—342no—
439C17#2063411yescharacteristic, complemented, Sylow
440C24—171no—
441C24C2×C4×D1711yescharacteristic
442C24C23×D1711yescharacteristic
443#41—3416no—
444#41—3416no—
445C2×Q8—174no—
446C2×Q8—342no—
447C2×Q8—342no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—172no—
451C2×D4—172no—
452C2×D4—174no—
453C2×D4—342no—
454C2×D4—342no—
455C2×D4—342no—
456C2×D4—342no—
457C2×D4D4×D1712yes—
458C2×D4Q8×D1712yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—171no—
465C22×C4—171no—
466C22×C4—174no—
467C22×C4—172no—
468C22×C4—172no—
469C22×C4—174no—
470C22×C4—171no—
471C22×C4—174no—
472C22×C4—171no—
473C22×C4—171no—
474C22×C4—174no—
475C22×C4—174no—
476C22×C4—171no—
477C22×C4—171no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—344no—
486C22×C4—1361no—
487C22×C4—1361no—
488C22×C4—1361no—
489C22×C4—1361no—
490C22×C4C2×C4×D1711yescharacteristic
491C22×C4C2×C4×D1711yescharacteristic
492C22×C4C2×C4×D1711yescharacteristic
493C22×C4C2×C4×D1711yescharacteristic
494C22×C4C2×C4×D1711yescharacteristic
495C22×C4D4×D1712yes—
496C22×C4D4×D1712yes—
497C4⋊C4—22no—
498C4⋊C4—82no—
499C4⋊C4—172no—
500C4⋊C4—172no—
501C4⋊C4—174no—
502C4⋊C4—172no—
503C4⋊C4—172no—
504C4⋊C4—174no—
505C4⋊C4—342no—
506C4⋊C4—342no—
507C4⋊C4—342no—
508C4⋊C4—342no—
509C4⋊C4—341no—
510C4⋊C4—341no—
511C4⋊C4—688no—
512C4⋊C4—1364no—
513C4⋊C4—1362no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—342no—
519C22⋊C4—342no—
520C22⋊C4—342no—
521C22⋊C4—341no—
522C22⋊C4—341no—
523C22⋊C4—344no—
524C22⋊C4—344no—
525C42—21no—
526C42—21no—
527C42—342no—
528C42—342no—
529C42—342no—
530C42—342no—
531C42—342no—
532C42—688no—
533C23—21no—
534C23—21no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—172no—
540C23—341no—
541C23—341no—
542C23—681no—
543C23—681no—
544C23C4⋊C4×D1712yes—
545C23C22×C4×D1711yescharacteristic
546C23C2×D4×D1712yes—
547C23C2×D4×D1711yescharacteristic
548C23C2×Q8×D1711yescharacteristic
549C23#41×D1712yes—
550Q8—348no—
551D4—24no—
552D4—24no—
553D4—348no—
554D4—344no—
555D4—344no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—172no—
572C2×C4—172no—
573C2×C4—172no—
574C2×C4—172no—
575C2×C4—172no—
576C2×C4—172no—
577C2×C4—178no—
578C2×C4—178no—
579C2×C4—172no—
580C2×C4—172no—
581C2×C4—172no—
582C2×C4—348no—
583C2×C4—348no—
584C2×C4—341no—
585C2×C4—341no—
586C2×C4—341no—
587C2×C4—341no—
588C2×C4—684no—
589C2×C4—681no—
590C2×C4—681no—
591C2×C4—681no—
592C2×C4—681no—
593C2×C4—684no—
594C2×C4—684no—
595C2×C4—684no—
596C2×C4—1362no—
597C2×C4—1362no—
598C2×C4—1362no—
599C2×C4C22⋊C4×D1711yescharacteristic
600C2×C4C22⋊C4×D1711yescharacteristic
601C2×C4C22⋊C4×D1712yes—
602C2×C4C4⋊C4×D1712yes—
603C22—22no—
604C22—21no—
605C22—22no—
606C22—21no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—41no—
615C22—342no—
616C22—682no—
617C22—682no—
618C22—681no—
619C22—681no—
620C22C2×C22⋊C4×D1711yescharacteristic
621C22C2×C4⋊C4×D1711yescharacteristic
622C22#117×D1711yescharacteristic
623C22#121×D1712yes—
624C22C22⋊Q8×D1712yes—
625C4—21no—
626C4—21no—
627C4—22no—
628C4—22no—
629C4—41no—
630C4—41no—
631C4—84no—
632C4—174no—
633C4—174no—
634C4—342no—
635C4—342no—
636C4—342no—
637C4—681no—
638C4—681no—
639C4—1364no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—22no—
644C2—42no—
645C2—682no—
646C2D17×#38011yescharacteristic
647C2#1453724211yescharacteristic
648C2#1453724611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC17×#1799C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#63254C22
cosocleC24×C17C24
hypercenter#1799D17
hypocenterC17#20634
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #14531401C2semidirect
4. #14528772C2semidirect
5. #14528771C2semidirect
6. #14528770C2semidirect
7. #14528769C2semidirect
8. #14528515C2semidirect
9. C17×#1799C2semidirect
13. C2×C4×Dic34C4semidirect
14. C2×#10587573C4semidirect
16. C2×C4×C22⋊D17C4semidirect
18. C2×#10587567C4semidirect
20. C2×#10587558C4semidirect
21. C2×#10587563C4semidirect
24. C22×#63225C4semidirect
26. C2×C4⋊C4×D17C4semidirect
138. C2×C22⋊D17C4⋊C4semidirect
147. C22×Dic17C4⋊C4semidirect
168. C2×C4×D17C4⋊C4semidirect
171. C2×Dic34C4⋊C4semidirect
286. #1799D17semidirect
439. C17#20634semidirect

Maximal subgroups

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

subgroupindex
C2×#117632882
C2×#117627812
#145314012
#145287722
#145287712
#145287702
#145287692
#145285152
C17×#17992
#2063417