Finite Group Databasebeta

← #16940876

Subgroups — #16940876

Order 4352.

1334 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
1C22×#10587555C211yesmaximal, characteristic
2C2×#11762819C211yesmaximal, characteristic
3C2×#11762817C211yesmaximal, characteristic
4C22×#10587495C211yesmaximal, characteristic
5#14531368C211yesmaximal, characteristic
6C2×#11762569C211yesmaximal, characteristic
7C2×C17×#339C211yesmaximal, characteristic
8C23×Dic34C2211yescharacteristic
9C23×Dic34C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C2×#10587555—22no—
12C2×#10587555—22no—
13C2×#10587555—22no—
14C2×#10587555—22no—
15C2×#10587555—22no—
16C2×#10587555C414yescomplemented
17C2×#10587612C2211yescharacteristic
18C22×C4⋊Dic17—22no—
19#11762819—22no—
20#11762819—22no—
21#11762817—22no—
22#11762817—22no—
23C2×#10587487—22no—
24C2×#10587481—22no—
25C2×#10587495—22no—
26C2×#10587495—22no—
27C2×#10587495—22no—
28#11762715—22no—
29#11762714—22no—
30#11762670—22no—
31#11762569—22no—
32C22×M16×C17C2211yescharacteristic
33C2×C17×#117C2211yescharacteristic
34C22×C42×C17C2211yescharacteristic
35C17×#339—22no—
36C23×C4×C17—21no—
37C23×C4×C17C2311yescharacteristic
38C23×Dic17—21no—
39C23×Dic17D412yes—
40C22×Dic34—21no—
41C22×Dic34—21no—
42C22×Dic34—21no—
43C22×Dic34—21no—
44C22×Dic34—21no—
45C22×Dic34—21no—
46C22×Dic34—21no—
47C22×Dic34—21no—
48C22×Dic34—21no—
49C22×Dic34—21no—
50C22×Dic34—21no—
51C22×Dic34—21no—
52C22×Dic34—21no—
53C22×Dic34—21no—
54C22×Dic34—21no—
55C22×Dic34—21no—
56C22×Dic34—21no—
57C22×Dic34—21no—
58C22×Dic34—21no—
59C22×Dic34—21no—
60C22×Dic34—21no—
61C22×Dic34—21no—
62C22×Dic34—21no—
63C22×Dic34C2×C412yes—
64C22×Dic34C2×C412yes—
65C22×Dic34D412yes—
66C22×Dic34D412yes—
67C22×Dic34D412yes—
68C2×M16×C17—21no—
69C2×M16×C17—21no—
70C2×M16×C17—21no—
71C2×M16×C17—21no—
72C2×M16×C17—21no—
73C2×M16×C17D412yes—
74C22×C8×C17—21no—
75C17×#117—21no—
76C17×#117—21no—
77C17×#117—21no—
78C17×#117—21no—
79C2×C4⋊C4×C17D412yes—
80C2×C22⋊C4×C17—21no—
81C2×C42×C17—21no—
82C2×C42×C17—21no—
83C2×C42×C17—21no—
84C2×C42×C17—21no—
85C2×C42×C17C2×C412yes—
86C2×C42×C17D412yes—
87C2×C42×C17D412yes—
88C2×C22⋊Dic17—21no—
89#10587612—21no—
90#10587612—21no—
91#10587612—21no—
92#10587612—21no—
93C2×C4⋊Dic17—28no—
94C2×C4⋊Dic17—28no—
95C2×C4⋊Dic17—28no—
96C2×C4⋊Dic17D412yes—
97C2×C4×Dic17—21no—
98C2×#63223—21no—
99C2×#63223—21no—
100C2×#63223—21no—
101C2×#63223—21no—
102C2×#63223—21no—
103C2×#63223D412yes—
104C22×#3622—21no—
105#10587555—28no—
106#10587555—28no—
107#10587555—28no—
108#10587555—28no—
109#10587502—28no—
110#10587495—28no—
111#10587487—28no—
112#10587481—28no—
113C24×C17C2×D411yescharacteristic
114C22×C4×C17—28no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17C22×C411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2×D411yescharacteristic
127C22×C4×C17C2×D411yescharacteristic
128C22×C4×C17C2×D411yescharacteristic
129C22×C4×C17#4111yescharacteristic
130C22×C4×C17#4111yescharacteristic
131C22×C4×C17#4111yescharacteristic
132C22×C4×C17#4111yescharacteristic
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—41no—
144C22×Dic17—41no—
145C22×Dic17—41no—
146C22×Dic17—41no—
147C22×Dic17C22⋊C414yes—
148C2×Dic34—22no—
149C2×Dic34—22no—
150C2×Dic34—22no—
151C2×Dic34—22no—
152C2×Dic34—22no—
153C2×Dic34—22no—
154C2×Dic34—22no—
155C2×Dic34—22no—
156C2×Dic34—22no—
157C2×Dic34—22no—
158C2×Dic34—22no—
159C2×Dic34—22no—
160C2×Dic34—22no—
161C2×Dic34—22no—
162C2×Dic34—22no—
163C2×Dic34—22no—
164C2×Dic34—22no—
165C2×Dic34—22no—
166C2×Dic34—22no—
167C2×Dic34—22no—
168C2×Dic34—22no—
169C2×Dic34—22no—
170C2×Dic34—22no—
171C2×Dic34—22no—
172C2×Dic34—22no—
173C2×Dic34—22no—
174C2×Dic34—22no—
175C2×Dic34—41no—
176C2×Dic34—41no—
177C2×Dic34—41no—
178C2×Dic34—41no—
179C2×Dic34—41no—
180C2×Dic34—41no—
181C2×Dic34—41no—
182C2×Dic34—41no—
183C2×Dic34—41no—
184C2×Dic34—41no—
185C2×Dic34—41no—
186C2×Dic34—41no—
187C2×Dic34—41no—
188C2×Dic34—41no—
189C2×Dic34—41no—
190C2×Dic34—41no—
191C2×Dic34—41no—
192C2×Dic34—41no—
193C2×Dic34—41no—
194C2×Dic34—41no—
195C2×Dic34—41no—
196C2×Dic34—41no—
197C2×Dic34—41no—
198C2×Dic34—41no—
199C2×Dic34—41no—
200C2×Dic34—41no—
201C2×Dic34—41no—
202C2×Dic34—41no—
203C2×Dic34C22⋊C414yes—
204M16×C17—22no—
205M16×C17—22no—
206M16×C17—41no—
207M16×C17—41no—
208C2×C8×C17—22no—
209C2×C8×C17—41no—
210C2×C8×C17—41no—
211C4⋊C4×C17—22no—
212C4⋊C4×C17—22no—
213C22⋊C4×C17—41no—
214C22⋊C4×C17—41no—
215C42×C17—22no—
216C42×C17—22no—
217C42×C17—22no—
218C42×C17—41no—
219C42×C17—41no—
220C42×C17C22⋊C414yes—
221C22⋊Dic17—41no—
222C22⋊Dic17—41no—
223C4⋊Dic17—232no—
224C4⋊Dic17—22no—
225C4⋊Dic17—22no—
226C4×Dic17—41no—
227C4×Dic17—41no—
228#63223—22no—
229#63223—22no—
230#63223—41no—
231#63223—41no—
232C2×#3622—22no—
233C2×#3622—41no—
234C2×#3622—41no—
235#10978—171nomaximal, Sylow
236C23×C17—24no—
237C23×C17C2×C22⋊C411yescharacteristic
238C23×C17#12011yescharacteristic
239C23×C17#12011yescharacteristic
240C23×C17#12011yescharacteristic
241C23×C17#12111yescharacteristic
242C23×C17#12111yescharacteristic
243C23×C17#12311yescharacteristic
244C2×C4×C17—28no—
245C2×C4×C17—28no—
246C2×C4×C17—28no—
247C2×C4×C17—24no—
248C2×C4×C17—42no—
249C2×C4×C17—44no—
250C2×C4×C17C2×C22⋊C411yescharacteristic
251C2×C4×C17C2×C22⋊C411yescharacteristic
252C2×C4×C17C4×D411yescharacteristic
253C2×C4×C17C4×D411yescharacteristic
254C2×C4×C17C4×D411yescharacteristic
255C2×C4×C17C4×D411yescharacteristic
256C2×C4×C17#12011yescharacteristic
257C2×C4×C17#12011yescharacteristic
258C2×C4×C17#12011yescharacteristic
259C2×C4×C17#12011yescharacteristic
260C2×C4×C17#12011yescharacteristic
261C2×C4×C17#12111yescharacteristic
262C2×C4×C17#12111yescharacteristic
263C2×C4×C17#12111yescharacteristic
264C2×C4×C17#12111yescharacteristic
265C2×C4×C17#12111yescharacteristic
266C2×C4×C17#12111yescharacteristic
267C2×C4×C17#12111yescharacteristic
268C2×C4×C17#12111yescharacteristic
269C2×C4×C17#12111yescharacteristic
270C2×C4×C17#12111yescharacteristic
271C2×C4×C17#12311yescharacteristic
272C2×C4×C17#12311yescharacteristic
273C2×C4×C17#12311yescharacteristic
274C2×C4×C17#12411yescharacteristic
275C2×C4×C17#12411yescharacteristic
276C2×C4×C17#12711yescharacteristic
277C2×C4×C17#12711yescharacteristic
278C2×Dic17—24no—
279C2×Dic17—24no—
280C2×Dic17—24no—
281C2×Dic17—24no—
282C2×Dic17—42no—
283C2×Dic17—42no—
284C2×Dic17—42no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—42no—
288C2×Dic17—42no—
289C2×Dic17—42no—
290C2×Dic17—42no—
291C2×Dic17—42no—
292C2×Dic17—42no—
293C2×Dic17—44no—
294Dic34—24no—
295Dic34—24no—
296Dic34—42no—
297Dic34—42no—
298Dic34—42no—
299Dic34—42no—
300Dic34—42no—
301Dic34—42no—
302Dic34—42no—
303Dic34—42no—
304Dic34—42no—
305Dic34—42no—
306Dic34—42no—
307Dic34—42no—
308Dic34—42no—
309Dic34—42no—
310C8×C17—42no—
311#3622—42no—
312C22×C4⋊Q8—171no—
313C2×#419—171no—
314C2×#419—171no—
315C22×#101—171no—
316#2310—171no—
317C2×#339—171no—
318C2×#339D1711yescharacteristic
319C22×C17—22no—
320C22×C17—22no—
321C22×C17—22no—
322C22×C17—22no—
323C22×C17—22no—
324C22×C17—22no—
325C22×C17#37911yescharacteristic
326C22×C17#38611yescharacteristic
327C22×C17#38611yescharacteristic
328C22×C17#39211yescharacteristic
329C22×C17#39211yescharacteristic
330C22×C17#39411yescharacteristic
331C22×C17#39411yescharacteristic
332C22×C17#45614yes—
333C4×C17—28no—
334C4×C17—82no—
335C4×C17#38611yescharacteristic
336C4×C17#38611yescharacteristic
337C4×C17#39011yescharacteristic
338C4×C17#39011yescharacteristic
339C4×C17#39211yescharacteristic
340C4×C17#39211yescharacteristic
341C4×C17#39411yescharacteristic
342C4×C17#39411yescharacteristic
343Dic17—44no—
344Dic17—44no—
345Dic17—82no—
346C23×Q8—171no—
347C23×Q8—171no—
348C22×M16—171no—
349C22×M16C2×D1711yescharacteristic
350C2×C4⋊Q8—174no—
351C2×C4⋊Q8—342no—
352C2×C4⋊Q8—342no—
353C2×C4⋊Q8—342no—
354C2×C4⋊Q8—342no—
355C2×C4⋊Q8—342no—
356C2×#117—171no—
357C2×#117C2×D1711yescharacteristic
358C22×C4⋊C4—342no—
359C22×C42C2×D1711yescharacteristic
360#419—342no—
361#419—342no—
362#419—342no—
363#419—342no—
364C2×#103—342no—
365C2×#103—342no—
366C2×#101—342no—
367C2×#101—342no—
368C2×#101—342no—
369#391—342no—
370#391—342no—
371#381—342no—
372#339—22no—
373#339—342no—
374C2×C17—21no—
375C2×C17—21no—
376C2×C17—21no—
377C2×C17—21no—
378C2×C17#143811yescharacteristic
379C2×C17#188612yes—
380C2×C17#200512yes—
381C2×C17#200512yes—
382C22×Q8—172no—
383C22×Q8—172no—
384C22×Q8—172no—
385C22×Q8—172no—
386C22×Q8—172no—
387C22×Q8—341no—
388C22×Q8—341no—
389C22×Q8—341no—
390C22×Q8—341no—
391C22×Q8—341no—
392C22×Q8—341no—
393C22×Q8—341no—
394C22×Q8—341no—
395C22×Q8—341no—
396C22×Q8—341no—
397C22×Q8—341no—
398C22×Q8—341no—
399C22×Q8—341no—
400C22×Q8—341no—
401C22×Q8—341no—
402C22×Q8—341no—
403C22×Q8—341no—
404C22×Q8—341no—
405C22×Q8—341no—
406C22×Q8—341no—
407C22×Q8—341no—
408C22×Q8—341no—
409C22×Q8—341no—
410C23×C4—21no—
411C23×C4—172no—
412C23×C4—341no—
413C23×C4C22×D1711yescharacteristic
414C2×M16—21no—
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—172no—
420C2×M16—341no—
421C2×M16—341no—
422C2×M16—341no—
423C2×M16—341no—
424C2×M16—341no—
425C2×M16D6812yes—
426C22×C8—21no—
427C22×C8—341no—
428C4⋊Q8—348no—
429C4⋊Q8—348no—
430C4⋊Q8—348no—
431C4⋊Q8—348no—
432#117—21no—
433#117—21no—
434#117—21no—
435#117—21no—
436#117—341no—
437#117—341no—
438#117—341no—
439#117—341no—
440C2×C4⋊C4—172no—
441C2×C4⋊C4—348no—
442C2×C4⋊C4—348no—
443C2×C4⋊C4—348no—
444C2×C4⋊C4D6812yes—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—341no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—341no—
452C2×C42C4×D1712yes—
453C2×C42D6812yes—
454C2×C42C22⋊D1712yes—
455#103—348no—
456#103—348no—
457#101—348no—
458#95—348no—
459C17#1097811yescharacteristic, complemented, Sylow
460C24D4×D1711yescharacteristic
461C2×Q8—174no—
462C2×Q8—342no—
463C2×Q8—342no—
464C2×Q8—342no—
465C2×Q8—342no—
466C2×Q8—342no—
467C2×Q8—342no—
468C2×Q8—342no—
469C2×Q8—342no—
470C2×Q8—342no—
471C2×Q8—342no—
472C2×Q8—342no—
473C2×Q8—342no—
474C2×Q8—342no—
475C2×Q8—342no—
476C2×Q8—342no—
477C2×Q8—342no—
478C2×Q8—342no—
479C2×Q8—342no—
480C2×Q8—342no—
481C2×Q8—342no—
482C2×Q8—342no—
483C2×Q8—342no—
484C2×Q8—342no—
485C2×Q8—342no—
486C2×Q8—342no—
487C2×Q8—342no—
488C2×Q8—342no—
489C2×Q8—681no—
490C2×Q8—681no—
491C2×Q8—681no—
492C2×Q8—681no—
493C2×Q8—681no—
494C2×Q8—681no—
495C2×Q8—681no—
496C2×Q8—681no—
497C2×Q8—681no—
498C2×Q8—681no—
499C2×Q8—681no—
500C2×Q8—681no—
501C2×Q8—681no—
502C2×Q8—681no—
503C2×Q8—681no—
504C2×Q8—681no—
505C2×Q8—681no—
506C2×Q8—681no—
507C2×Q8—681no—
508C2×Q8—681no—
509C2×Q8—681no—
510C2×Q8—681no—
511C2×Q8—681no—
512C2×Q8—681no—
513C2×Q8—681no—
514C2×Q8—681no—
515C2×Q8—681no—
516C2×Q8—681no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—174no—
523C22×C4—342no—
524C22×C4—342no—
525C22×C4—342no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—681no—
534C22×C4—681no—
535C22×C4—681no—
536C22×C4—681no—
537C22×C4C2×C4×D1711yescharacteristic
538C22×C4C2×D6811yescharacteristic
539C22×C4C2×D6811yescharacteristic
540C22×C4C2×D6811yescharacteristic
541C22×C4#6325211yescharacteristic
542C22×C4#6325211yescharacteristic
543C22×C4D4×D1711yescharacteristic
544C22×C4D4×D1711yescharacteristic
545C22×C4D4×D1711yescharacteristic
546C22×C4D4×D1711yescharacteristic
547C22×C4D4×D1711yescharacteristic
548C22×C4#6325611yescharacteristic
549C22×C4#6325611yescharacteristic
550C22×C4C2×C22⋊D1711yescharacteristic
551M16—22no—
552M16—22no—
553M16—41no—
554M16—41no—
555M16—342no—
556M16—342no—
557M16—681no—
558M16—681no—
559C2×C8—22no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—342no—
563C2×C8—681no—
564C2×C8—681no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—3432no—
568C4⋊C4—342no—
569C4⋊C4—342no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—681no—
573C22⋊C4—681no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—41no—
578C42—41no—
579C42—681no—
580C42—681no—
581C42#6322714yes—
582C23—24no—
583C23C22⋊C4×D1711yescharacteristic
584C23#1058756811yescharacteristic
585C23#1058756811yescharacteristic
586C23#1058757011yescharacteristic
587C23#1058758011yescharacteristic
588C23#1058758111yescharacteristic
589C23#1058762311yescharacteristic
590Q8—344no—
591Q8—344no—
592Q8—682no—
593Q8—682no—
594Q8—682no—
595Q8—682no—
596Q8—682no—
597Q8—682no—
598Q8—682no—
599Q8—682no—
600Q8—682no—
601Q8—682no—
602Q8—682no—
603Q8—682no—
604Q8—682no—
605Q8—682no—
606C2×C4—28no—
607C2×C4—28no—
608C2×C4—28no—
609C2×C4—24no—
610C2×C4—42no—
611C2×C4—44no—
612C2×C4—344no—
613C2×C4—344no—
614C2×C4—344no—
615C2×C4—344no—
616C2×C4—682no—
617C2×C4—682no—
618C2×C4—682no—
619C2×C4—682no—
620C2×C4—682no—
621C2×C4—682no—
622C2×C4—682no—
623C2×C4—682no—
624C2×C4—682no—
625C2×C4—682no—
626C2×C4—682no—
627C2×C4—684no—
628C2×C4C4×D6811yescharacteristic
629C2×C4C4×D6811yescharacteristic
630C2×C4#1058756011yescharacteristic
631C2×C4#1058756111yescharacteristic
632C2×C4C22⋊C4×D1711yescharacteristic
633C2×C4#1058756811yescharacteristic
634C2×C4#1058756811yescharacteristic
635C2×C4#1058756811yescharacteristic
636C2×C4#1058756811yescharacteristic
637C2×C4#1058757011yescharacteristic
638C2×C4#1058757011yescharacteristic
639C2×C4#1058757011yescharacteristic
640C2×C4#1058757911yescharacteristic
641C2×C4#1058757911yescharacteristic
642C2×C4#1058758011yescharacteristic
643C2×C4#1058758011yescharacteristic
644C2×C4#1058758011yescharacteristic
645C2×C4#1058758111yescharacteristic
646C2×C4#1058758111yescharacteristic
647C2×C4#1058758111yescharacteristic
648C2×C4#1058758111yescharacteristic
649C2×C4#1058758111yescharacteristic
650C2×C4C2×#6322711yescharacteristic
651C2×C4#1058761611yescharacteristic
652C2×C4#1058761611yescharacteristic
653C2×C4#1058762311yescharacteristic
654C2×C4#1058762611yescharacteristic
655C2×C4#1058763311yescharacteristic
656C8—42no—
657C8—682no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22#1176266411yescharacteristic
665C22#1176268711yescharacteristic
666C22#1176268711yescharacteristic
667C22#1176271811yescharacteristic
668C22#1176271911yescharacteristic
669C22#1176272611yescharacteristic
670C22#1176272711yescharacteristic
671C22#1176299314yes—
672C4—28no—
673C4—82no—
674C4—684no—
675C4—684no—
676C4—1362no—
677C4#1176268711yescharacteristic
678C4#1176268711yescharacteristic
679C4#1176271011yescharacteristic
680C4#1176271111yescharacteristic
681C4#1176271811yescharacteristic
682C4#1176271911yescharacteristic
683C4#1176272611yescharacteristic
684C4#1176272711yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2#1452702411yescharacteristic
690C2#1452917612yes—
691C2#1452981912yes—
692C2#1452982312yes—
subgroupG/H
centerC23#10587568
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC2×C17×#339C2
socleC23×C17#120
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#339D17
hypocenterC17#10978
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
16. C2×#10587555C4semidirect
459. C17#10978semidirect

Maximal subgroups

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

subgroupindex
C22×#105875552
C2×#117628192
C2×#117628172
C22×#105874952
#145313682
C2×#117625692
C2×C17×#3392
#1097817