Finite Group Databasebeta

← #17063192

Subgroups — #17063192

Order 4352.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762851C211yesmaximal, characteristic, complemented
2#14531167C211yesmaximal, characteristic
3C2×#11762669C211yesmaximal, characteristic
4#14530217C212yesmaximal, complemented
5#14530217C212yesmaximal, complemented
6#14530212C212yesmaximal, complemented
7#14530207C212yesmaximal, complemented
8#14528504C211yesmaximal, characteristic, complemented
9#14528504C211yesmaximal, characteristic, complemented
10#14528504C211yesmaximal, characteristic, complemented
11C2×C17×#407C211yesmaximal, characteristic
12C2×#10587612C2211yescharacteristic
13C2×#10587612C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17—21no—
17#11762851—24no—
18C2×#10587489C2212yescomplemented
19C2×#10587488C2212yescomplemented
20#11762672—21no—
21#11762669—21no—
22#11762669—21no—
23#11762669C2212yes—
24#11762669C2212yes—
25#11762669C2211yescharacteristic
26#11762669C2211yescharacteristic
27#11762669C2211yescharacteristic
28#11762669C2211yescharacteristic
29#11762665—21no—
30C4×C22⋊Dic17—21no—
31C4×C22⋊Dic17—21no—
32C2×#10587502—21no—
33#11762572C2212yescomplemented
34#11762572C2212yescomplemented
35#11762572C2212yescomplemented
36#11762572C2212yescomplemented
37#11762572C2212yescomplemented
38#11762572C2212yescomplemented
39C24×C4×C17C2211yescharacteristic
40C22×M16×C17C2211yescharacteristic
41C22×M16×C17C2211yescharacteristic
42C17×#407—24no—
43C2×C17×C22⋊C8C2212yes—
44C2×C17×C22⋊C8C2212yes—
45C25×C17D411yescharacteristic
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—22no—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17D411yescharacteristic
53C23×C4×C17D411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×Dic17—21no—
59C23×Dic17—21no—
60C2×M16×C17—22no—
61C2×M16×C17—22no—
62C2×M16×C17—22no—
63C2×M16×C17—22no—
64C2×M16×C17—22no—
65C2×M16×C17D414yes—
66C22×C8×C17C2312yes—
67C22×C8×C17C2312yes—
68C2×C22⋊Dic17—22no—
69C2×C22⋊Dic17—22no—
70C2×C22⋊Dic17—21no—
71C2×C22⋊Dic17—21no—
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—44no—
77#10587612—22no—
78#10587612—22no—
79#10587612—22no—
80#10587612—22no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17—21no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—22no—
86C2×C4⋊Dic17—22no—
87C2×C4⋊Dic17C2312yes—
88C2×C4⋊Dic17C2312yes—
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4⋊Dic17C2311yescharacteristic
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C17×C22⋊C8—24no—
96C17×C22⋊C8—24no—
97#10587502—22no—
98#10587502—22no—
99#10587502—21no—
100#10587502—21no—
101#10587502—21no—
102#10587502—21no—
103#10587489—24no—
104#10587488—24no—
105C24×C17—22no—
106C24×C17—22no—
107C24×C17—22no—
108C24×C17—22no—
109C24×C17—22no—
110C24×C17—41no—
111C24×C17—41no—
112C24×C17C2×D411yescharacteristic
113C24×C17C2×D411yescharacteristic
114C24×C17C2×D411yescharacteristic
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—44no—
137C22×C4×C17—44no—
138C22×C4×C17—44no—
139C22×C4×C17—44no—
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D412yes—
144C22×C4×C17#4112yes—
145C22×C4×C17#4112yes—
146C22×C4×C17#4112yes—
147C22×C4×C17#4112yes—
148C22×C4×C17#4112yes—
149C22×C4×C17C2411yescharacteristic
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—42no—
157C22×Dic17—42no—
158C22×Dic17—42no—
159C22×Dic17—42no—
160C22×Dic17—42no—
161C22×Dic17—42no—
162M16×C17—28no—
163M16×C17—44no—
164C2×C8×C17—22no—
165C2×C8×C17—22no—
166C2×C8×C17—22no—
167C2×C8×C17—22no—
168C2×C8×C17—22no—
169C2×C8×C17C2×D414yes—
170C22⋊Dic17—42no—
171C22⋊Dic17—42no—
172C22⋊Dic17—44no—
173C22⋊Dic17—42no—
174C22⋊Dic17—42no—
175C22⋊Dic17—42no—
176C22⋊Dic17—44no—
177C22⋊Dic17—42no—
178C4⋊Dic17—21no—
179C4⋊Dic17—22no—
180C4⋊Dic17—21no—
181C4⋊Dic17—22no—
182C4⋊Dic17—22no—
183C4⋊Dic17—22no—
184C4⋊Dic17—21no—
185C4⋊Dic17—21no—
186C4⋊Dic17—21no—
187C4⋊Dic17—21no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—42no—
191C4⋊Dic17—42no—
192C4×Dic17—42no—
193C4×Dic17—42no—
194#23642—171nomaximal, Sylow
195C23×C17—21no—
196C23×C17—21no—
197C23×C17—21no—
198C23×C17—21no—
199C23×C17—28no—
200C23×C17—21no—
201C23×C17—21no—
202C23×C17—21no—
203C23×C17—21no—
204C23×C17—21no—
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17—21no—
209C23×C17—21no—
210C23×C17—21no—
211C23×C17—21no—
212C23×C17—44no—
213C23×C17—44no—
214C23×C17—44no—
215C23×C17—44no—
216C23×C17—44no—
217C23×C17—44no—
218C23×C17#12112yes—
219C23×C17#12312yes—
220C23×C17#12312yes—
221C23×C17AGL(1,ℤ/8)12yes—
222C23×C17#13712yes—
223C23×C17C22×D411yescharacteristic
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—44no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—44no—
240C2×C4×C17—44no—
241C2×C4×C17#12112yes—
242C2×C4×C17#12312yes—
243C2×C4×C17#12312yes—
244C2×C4×C17#12314yes—
245C2×C4×C17#12414yes—
246C2×C4×C17#12614yes—
247C2×C4×C17#12614yes—
248C2×C4×C17C22×D411yescharacteristic
249C2×C4×C17C2×#4111yescharacteristic
250C2×C4×C17C2×#4111yescharacteristic
251C2×C4×C17C2×#4111yescharacteristic
252C2×C4×C17C2×#4111yescharacteristic
253C2×C4×C17C2×#4111yescharacteristic
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—42no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—84no—
273C2×Dic17—84no—
274C8×C17—24no—
275C8×C17—42no—
276C2×#428—171no—
277C2×#407D1711yescharacteristic
278#2280—171no—
279C2×#380—171no—
280#2077—172no—
281#2077—172no—
282#2076—172no—
283#2075—172no—
284#1736—171no—
285#1736—171no—
286#1736—171no—
287C22×C17—22no—
288C22×C17—22no—
289C22×C17—22no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—22no—
298C22×C17—22no—
299C22×C17—416no—
300C22×C17—41no—
301C22×C17—41no—
302C22×C17—41no—
303C22×C17—41no—
304C22×C17—41no—
305C22×C17—41no—
306C22×C17—41no—
307C22×C17—41no—
308C22×C17#39714yes—
309C22×C17C2×#12111yescharacteristic
310C22×C17C2×#12311yescharacteristic
311C22×C17C2×#12311yescharacteristic
312C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C17C2×#13711yescharacteristic
314C22×C17#57511yescharacteristic
315C22×C17#57511yescharacteristic
316C4×C17—41no—
317C4×C17—41no—
318C4×C17#39714yes—
319C4×C17C2×#12311yescharacteristic
320C4×C17C2×#12411yescharacteristic
321C4×C17C2×#12611yescharacteristic
322C4×C17C2×#12611yescharacteristic
323Dic17—81no—
324Dic17—81no—
325Dic17—82no—
326Dic17—81no—
327Dic17—82no—
328Dic17—81no—
329C24×C4C2×D1711yescharacteristic
330C22×M16C2×D1711yescharacteristic
331C22×M16C2×D1711yescharacteristic
332C2×#117—171no—
333C2×#117—171no—
334C22×C4⋊C4—171no—
335C22×C4⋊C4—171no—
336C22×C22⋊C4—341no—
337#428—344no—
338C2×#107—172no—
339C2×#106—172no—
340#407—24no—
341C2×C22⋊C8C2×D1712yes—
342C2×C22⋊C8C2×D1712yes—
343#381—341no—
344#380—171no—
345#380—172no—
346#380—171no—
347#380—172no—
348#380—171no—
349#380—171no—
350#380—341no—
351#380—341no—
352#379—341no—
353C4×C22⋊C4—341no—
354C4×C22⋊C4—341no—
355C2×#95—341no—
356#340—172no—
357#340—172no—
358#340—172no—
359#340—172no—
360#340—172no—
361#340—172no—
362C2×C17—24no—
363C2×C17—42no—
364C2×C17—42no—
365C2×C17C2×#39711yescharacteristic
366C2×C17#305511yescharacteristic
367C2×C17#305611yescharacteristic
368C2×C17#309211yescharacteristic
369C2×C17#309311yescharacteristic
370C2×C17#309411yescharacteristic
371C2×C17#309511yescharacteristic
372C25D6811yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—341no—
380C23×C4—341no—
381C23×C4D6811yescharacteristic
382C23×C4D6811yescharacteristic
383C23×C4D6811yescharacteristic
384C23×C4C22×D1711yescharacteristic
385C23×C4C22×D1711yescharacteristic
386C23×C4C22×D1711yescharacteristic
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16C22⋊D1714yes—
393C22×C8C22×D1712yes—
394C22×C8C22×D1712yes—
395#117—342no—
396#117—342no—
397#117—342no—
398#117—342no—
399C2×C4⋊C4—172no—
400C2×C4⋊C4—172no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—342no—
406C2×C4⋊C4—342no—
407C2×C4⋊C4—342no—
408C2×C4⋊C4—342no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—341no—
411C2×C22⋊C4—342no—
412C2×C22⋊C4—342no—
413C2×C22⋊C4—341no—
414C2×C22⋊C4—341no—
415C2×C22⋊C4—341no—
416C2×C22⋊C4—341no—
417C2×C22⋊C4—341no—
418C2×C22⋊C4—341no—
419C2×C22⋊C4—684no—
420C2×C42—341no—
421C2×C42—341no—
422#107—344no—
423#106—344no—
424C22⋊C8—24no—
425C22⋊C8—24no—
426#95—342no—
427#95—342no—
428#95—341no—
429#95—341no—
430#95—341no—
431#95—341no—
432C17#2364211yescharacteristic, complemented, Sylow
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—41no—
439C24—41no—
440C24C2×D6811yescharacteristic
441C24C2×D6811yescharacteristic
442C24C2×D6811yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—341no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—682no—
475C22×C4—682no—
476C22×C4—682no—
477C22×C4—682no—
478C22×C4—682no—
479C22×C4—682no—
480C22×C4C2×D6811yescharacteristic
481C22×C4C2×D6811yescharacteristic
482C22×C4C2×D6811yescharacteristic
483C22×C4#6325212yes—
484C22×C4#6325412yes—
485C22×C4#6325412yes—
486C22×C4#6325412yes—
487C22×C4#6325412yes—
488C22×C4C2×C22⋊D1712yes—
489C22×C4C23×D1711yescharacteristic
490M16—28no—
491M16—44no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8C2×C22⋊D1714yes—
498C4⋊C4—342no—
499C4⋊C4—341no—
500C4⋊C4—341no—
501C4⋊C4—342no—
502C4⋊C4—342no—
503C4⋊C4—341no—
504C4⋊C4—341no—
505C4⋊C4—341no—
506C4⋊C4—341no—
507C4⋊C4—341no—
508C4⋊C4—342no—
509C4⋊C4—341no—
510C4⋊C4—682no—
511C4⋊C4—682no—
512C22⋊C4—682no—
513C22⋊C4—682no—
514C22⋊C4—684no—
515C22⋊C4—682no—
516C22⋊C4—682no—
517C22⋊C4—684no—
518C22⋊C4—682no—
519C22⋊C4—682no—
520C42—682no—
521C42—682no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23#1058757212yes—
546C23#1058757212yes—
547C23#1058759412yes—
548C23#1058759512yes—
549C23#1058761612yes—
550C23C22×D6811yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—681no—
569C2×C4—681no—
570C2×C4—682no—
571C2×C4—681no—
572C2×C4—681no—
573C2×C4—682no—
574C2×C4—682no—
575C2×C4—682no—
576C2×C4—681no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—682no—
585C2×C4—682no—
586C2×C4—1364no—
587C2×C4—1364no—
588C2×C4#1058756514yes—
589C2×C4#1058756514yes—
590C2×C4#1058757212yes—
591C2×C4#1058757212yes—
592C2×C4#1058761612yes—
593C2×C4#1058762114yes—
594C2×C4#1058762214yes—
595C2×C4C2×#6325211yescharacteristic
596C2×C4C2×#6325411yescharacteristic
597C2×C4C2×#6325411yescharacteristic
598C2×C4C2×#6325411yescharacteristic
599C2×C4C2×#6325411yescharacteristic
600C2×C4C22×C22⋊D1711yescharacteristic
601C8—24no—
602C8—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22#1176273414yes—
625C22C2×#1058761611yescharacteristic
626C22C2×#1058757211yescharacteristic
627C22C2×#1058757211yescharacteristic
628C22C2×#1058759411yescharacteristic
629C22C2×#1058759511yescharacteristic
630C22#1176360911yescharacteristic
631C22#1176360911yescharacteristic
632C4—41no—
633C4—41no—
634C4—1362no—
635C4—1361no—
636C4—1361no—
637C4—1361no—
638C4—1361no—
639C4—1362no—
640C4#1176273414yes—
641C4C2×#1058762111yescharacteristic
642C4C2×#1058762211yescharacteristic
643C4C2×#1058756511yescharacteristic
644C4C2×#1058756511yescharacteristic
645C2—24no—
646C2—42no—
647C2—42no—
648C2C2×#1176273411yescharacteristic
649C2#1453840311yescharacteristic
650C2#1453841411yescharacteristic
651C2#1453870911yescharacteristic
652C2#1453871711yescharacteristic
653C2#1453872511yescharacteristic
654C2#1453873311yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#407C2
socleC23×C17C22×D4
prime radicalC25×C17D4
hypercenterC2×#407D17
hypocenterC17#23642
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#11762851C2semidirect
4. #14530217C2semidirect
5. #14530217C2semidirect
6. #14530212C2semidirect
7. #14530207C2semidirect
8. #14528504C2semidirect
9. #14528504C2semidirect
10. #14528504C2semidirect
18. C2×#10587489C22semidirect
19. C2×#10587488C22semidirect
33. #11762572C22semidirect
34. #11762572C22semidirect
35. #11762572C22semidirect
36. #11762572C22semidirect
37. #11762572C22semidirect
38. #11762572C22semidirect
432. C17#23642semidirect

Maximal subgroups

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

subgroupindex
C2×#117628512
#145311672
C2×#117626692
#145302172
#145302122
#145302072
#145285042
C2×C17×#4072
#2364217