Finite Group Databasebeta

← #17102484

Subgroups — #17102484

Order 4352.

860 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533147C211yesmaximal, characteristic, complemented
2#14530094C211yesmaximal, characteristic, complemented
3#14529970C211yesmaximal, characteristic, complemented
4#14529920C211yesmaximal, characteristic, complemented
5#14529780C211yesmaximal, characteristic
6#14529732C211yesmaximal, characteristic, complemented
7#14529466C211yesmaximal, characteristic, complemented
8#14529411C211yesmaximal, characteristic, complemented
9#14529392C211yesmaximal, characteristic, complemented
10#14529366C211yesmaximal, characteristic, complemented
11#14529132C211yesmaximal, characteristic, complemented
12#14529106C211yesmaximal, characteristic, complemented
13#14528879C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C17×#2363C211yesmaximal, characteristic, complemented
16C22×#63228C2211yescharacteristic
17C2×#10587555C2211yescharacteristic
18C2×#10587571—21no—
19C2×#10587616C2211yescharacteristic
20C2×#10587479C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587480C2211yescharacteristic
26C2×#10587480C2211yescharacteristic
27C2×#10587480C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×C4×#3622C2211yescharacteristic
31#11762725—21no—
32#11762722—21no—
33#11762711C2211yescharacteristic
34#11762711C2211yescharacteristic
35#11762701—21no—
36#11762669C2211yescharacteristic
37C4×C4⋊Dic17C2211yescharacteristic
38#11762571C2211yescharacteristic
39#11762571C2211yescharacteristic
40#11762571C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762564C2211yescharacteristic
47#11762564C2211yescharacteristic
48C2×C17×#121C2211yescharacteristic
49C2×C4×D4×C17C2211yescharacteristic
50C2×C17×#117C2211yescharacteristic
51C17×#390—21no—
52C17×#390C2211yescharacteristic
53C17×#389C2211yescharacteristic
54C17×#388—21no—
55C17×#386—21no—
56C4×C4⋊C4×C17C2211yescharacteristic
57C4×C22⋊C4×C17—21no—
58C4×C22⋊C4×C17C2211yescharacteristic
59C22×D4×C17—21no—
60C22×D4×C17C2311yescharacteristic
61C23×C4×C17—21no—
62C23×C4×C17C2311yescharacteristic
63C22×C22⋊D17—21no—
64C22×D68C2311yescharacteristic
65C22×Dic34—21no—
66C17×#121—22no—
67C17×#121—22no—
68C4×D4×C17—22no—
69C4×D4×C17—41no—
70C17×#117—22no—
71C17×#117—41no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C4⋊C4×C17C2311yescharacteristic
76C2×C22⋊C4×C17—21no—
77C2×C22⋊C4×C17—21no—
78C2×C22⋊C4×C17—21no—
79C2×C22⋊C4×C17—21no—
80C2×C22⋊C4×C17—21no—
81C2×C22⋊C4×C17D411yescharacteristic
82C2×C22⋊C4×C17D411yescharacteristic
83C2×C42×C17—21no—
84C2×C42×C17—21no—
85C2×C42×C17C2311yescharacteristic
86C2×C42×C17C2311yescharacteristic
87C2×C22⋊Dic17—21no—
88C2×#63228—22no—
89C2×#63228—41no—
90C2×#63228—41no—
91#10587616—22no—
92#10587616—41no—
93C2×#63227—21no—
94C2×#63227—21no—
95C2×#63227—21no—
96C2×#63227—21no—
97C2×#63227—21no—
98C2×C4⋊Dic17—21no—
99C2×C4⋊Dic17C2311yescharacteristic
100C2×C4⋊Dic17C2311yescharacteristic
101C2×C4⋊Dic17C2311yescharacteristic
102C2×C4×Dic17—21no—
103C22×#3622C2311yescharacteristic
104C22×#3622C2311yescharacteristic
105C22×#3622C2311yescharacteristic
106C22×#3622C2311yescharacteristic
107#10587571—44no—
108#10587555—22no—
109#10587555—41no—
110C17×#95—21no—
111C17×#95—21no—
112C17×#95D411yescharacteristic
113C17×#95D411yescharacteristic
114#10587503—22no—
115#10587503—22no—
116#10587503—41no—
117#10587502—21no—
118#10587502—21no—
119C22⋊#3622—41no—
120C22⋊#3622—41no—
121#10587480—22no—
122#10587480—22no—
123#10587480—41no—
124#10587479—22no—
125C4⋊#3622—41no—
126C4×#3622—41no—
127C24×C17—21no—
128C24×C17C2×D411yescharacteristic
129C23×D17—21no—
130C2×D4×C17—24no—
131C2×D4×C17—21no—
132C2×D4×C17—21no—
133C2×D4×C17—21no—
134C2×D4×C17—21no—
135C2×D4×C17—21no—
136C2×D4×C17—81no—
137C2×D4×C17—81no—
138C2×D4×C17#4112yes—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—42no—
149C22×C4×C17—42no—
150C22×C4×C17—81no—
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2×D411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2×D411yescharacteristic
156C22×C4×C17C2411yescharacteristic
157C2×C22⋊D17—42no—
158C2×C22⋊D17—42no—
159C2×C22⋊D17—81no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C2×D68—21no—
164C2×D68—21no—
165C2×D68—21no—
166C2×D68—21no—
167C2×D68—21no—
168C2×D68—21no—
169C2×Dic34—42no—
170C2×Dic34—42no—
171C2×Dic34—81no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17—21no—
174C4⋊C4×C17—21no—
175C4⋊C4×C17—21no—
176C4⋊C4×C17—81no—
177C4⋊C4×C17#4112yes—
178C4⋊C4×C17#4112yes—
179C22⋊C4×C17—24no—
180C22⋊C4×C17—22no—
181C22⋊C4×C17—22no—
182C22⋊C4×C17—42no—
183C22⋊C4×C17—42no—
184C22⋊C4×C17—42no—
185C22⋊C4×C17—81no—
186C42×C17—21no—
187C42×C17—21no—
188C42×C17—21no—
189C42×C17—21no—
190C42×C17—42no—
191C42×C17—81no—
192C22⋊Dic17—42no—
193#63228—44no—
194#63227—42no—
195#63227—42no—
196#63227—42no—
197#63227—42no—
198#63227—81no—
199C4⋊Dic17—21no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17—21no—
203C4⋊Dic17—21no—
204C4⋊Dic17—42no—
205C4⋊Dic17#4112yes—
206C4×Dic17—42no—
207C2×#3622—21no—
208C2×#3622—21no—
209C2×#3622—21no—
210C2×#3622—21no—
211C2×#3622—21no—
212C2×#3622—21no—
213C2×#3622—21no—
214C2×#3622—21no—
215C2×#3622—21no—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219#26729—171nomaximal, Sylow
220C23×C17—22no—
221C23×C17—21no—
222C23×C17—21no—
223C23×C17—21no—
224C23×C17—21no—
225C23×C17—21no—
226C23×C17—21no—
227C23×C17—21no—
228C23×C17—41no—
229C23×C17—41no—
230C23×C17—41no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—41no—
234C23×C17C22×D411yescharacteristic
235C22×D17—41no—
236C22×D17—41no—
237C22×D17—41no—
238C22×D17—41no—
239C22×D17—41no—
240C22×D17—41no—
241C22×D17—41no—
242D4×C17—22no—
243D4×C17—22no—
244D4×C17—41no—
245D4×C17—41no—
246D4×C17—84no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—22no—
253C2×C4×C17—21no—
254C2×C4×C17—21no—
255C2×C4×C17—21no—
256C2×C4×C17—22no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—41no—
270C2×C4×C17—41no—
271C2×C4×C17—41no—
272C2×C4×C17—41no—
273C2×C4×C17—84no—
274C2×C4×C17#13512yes—
275C2×C4×C17AGL(1,ℤ/8)12yes—
276C2×C4×C17C2×#4111yescharacteristic
277C2×C4×C17C2×#4111yescharacteristic
278C2×C4×C17C2×#4111yescharacteristic
279C2×C4×C17C2×#4111yescharacteristic
280C2×C4×C17H(5,𝔽2)11yescharacteristic
281C2×C4×C17H(5,𝔽2)11yescharacteristic
282C22⋊D17—84no—
283C2×Dic17—22no—
284C2×Dic17—41no—
285C2×Dic17—41no—
286C2×Dic17—41no—
287C2×Dic17—41no—
288C2×Dic17—41no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292D68—41no—
293D68—41no—
294D68—41no—
295D68—41no—
296Dic34—84no—
297#3622—41no—
298#3622—41no—
299#3622—41no—
300#3622—41no—
301#2491—171no—
302#2363D1711yescharacteristic, complemented
303#2054—171no—
304#2034—171no—
305#2023—171no—
306#1999—171no—
307#1987—171no—
308#1934—171no—
309#1926—171no—
310#1923—171no—
311#1920—171no—
312#1879—171no—
313#1875—171no—
314#1825—171no—
315C4×#102—171no—
316C22×C17—41no—
317C22×C17—42no—
318C22×C17—41no—
319C22×C17—42no—
320C22×C17—41no—
321C22×C17—42no—
322C22×C17—41no—
323C22×C17—41no—
324C22×C17—41no—
325C22×C17—41no—
326C22×C17—81no—
327C22×C17—81no—
328C22×C17—81no—
329C22×C17—81no—
330C22×C17#52511yescharacteristic
331C22×C17#54611yescharacteristic
332C22×C17#54611yescharacteristic
333C22×C17C2×#13511yescharacteristic
334C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C17#57611yescharacteristic
336C22×C17#57711yescharacteristic
337C2×D17—81no—
338C2×D17—81no—
339C2×D17—81no—
340C2×D17—81no—
341C2×D17—81no—
342C2×D17—81no—
343C2×D17—81no—
344C4×C17—22no—
345C4×C17—22no—
346C4×C17—42no—
347C4×C17—41no—
348C4×C17—41no—
349C4×C17—42no—
350C4×C17—41no—
351C4×C17—81no—
352C4×C17#52911yescharacteristic
353C4×C17#53811yescharacteristic
354C4×C17#55511yescharacteristic
355C4×C17#55911yescharacteristic
356Dic17—42no—
357Dic17—81no—
358Dic17—81no—
359C22×D8—171no—
360C2×C4⋊Q8—171no—
361C2×#124—341no—
362C2×#121—171no—
363C2×#121C2×D1711yescharacteristic
364C2×C4×D4C2×D1711yescharacteristic
365C2×#117C2×D1711yescharacteristic
366C2×#106—171no—
367C2×C4⋊C8—171no—
368C2×#102—171no—
369C2×#102—171no—
370C2×#102—171no—
371C2×#102—171no—
372C2×#102—171no—
373C2×#102—171no—
374C2×C22⋊C8—171no—
375C2×C22⋊C8—171no—
376C2×C4×C8—171no—
377#394—341no—
378#393—341no—
379#390—21no—
380#390—171no—
381#390—171no—
382#390C2×D1711yescharacteristic
383#389C2×D1711yescharacteristic
384#388—21no—
385#388—341no—
386#386—21no—
387#380—171no—
388C4×C4⋊C4—171no—
389C4×C4⋊C4C2×D1711yescharacteristic
390C4×C22⋊C4—21no—
391C4×C22⋊C4C2×D1711yescharacteristic
392#340—171no—
393#340—171no—
394#340—171no—
395#340—171no—
396#340—171no—
397#340—171no—
398#340—171no—
399#340—171no—
400#336—171no—
401#336—171no—
402C2×C17—81no—
403C2×C17—82no—
404C2×C17#245911yescharacteristic
405C2×C17#310611yescharacteristic
406C2×C17#311811yescharacteristic
407C2×C17#330111yescharacteristic
408C2×C17#330511yescharacteristic
409C2×C17#330611yescharacteristic
410C2×C17#332511yescharacteristic
411D17—161no—
412C22×Q8—341no—
413C22×D4—21no—
414C22×D4—171no—
415C22×D4—341no—
416C22×D4C22×D1711yescharacteristic
417C23×C4—21no—
418C23×C4C22×D1711yescharacteristic
419C2×D8—342no—
420C2×D8—681no—
421C2×D8—681no—
422C22×C8—171no—
423C22×C8—171no—
424C22×C8—171no—
425C22×C8—171no—
426C4⋊Q8—342no—
427C4⋊Q8—681no—
428#124—684no—
429#121—22no—
430#121—22no—
431#121—342no—
432#121—681no—
433C4×D4—22no—
434C4×D4—41no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—171no—
439C2×C4⋊C4—171no—
440C2×C4⋊C4—171no—
441C2×C4⋊C4—341no—
442C2×C4⋊C4C22×D1711yescharacteristic
443C2×C4⋊C4C22×D1711yescharacteristic
444C2×C4⋊C4C22×D1711yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—341no—
451C2×C22⋊C4—341no—
452C2×C22⋊C4—341no—
453C2×C22⋊C4—341no—
454C2×C22⋊C4—341no—
455C2×C22⋊C4—341no—
456C2×C22⋊C4C22⋊D1711yescharacteristic
457C2×C22⋊C4C22⋊D1711yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—341no—
461C2×C42C22×D1711yescharacteristic
462C2×C42C22×D1711yescharacteristic
463#106—342no—
464C4⋊C8—681no—
465#102—342no—
466#102—342no—
467#102—342no—
468#102—342no—
469#102—681no—
470#102—681no—
471C22⋊C8—681no—
472C22⋊C8—681no—
473C4×C8—681no—
474#95—21no—
475#95—21no—
476#95—341no—
477#95—341no—
478#95C22⋊D1711yescharacteristic
479#95C22⋊D1711yescharacteristic
480C17#2672911yescharacteristic, complemented, Sylow
481C24—21no—
482C24—341no—
483C24C2×C22⋊D1711yescharacteristic
484C2×Q8—682no—
485C2×Q8—682no—
486C2×Q8—1361no—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—341no—
496C2×D4—341no—
497C2×D4—341no—
498C2×D4—341no—
499C2×D4—341no—
500C2×D4—341no—
501C2×D4—682no—
502C2×D4—682no—
503C2×D4—1361no—
504C2×D4#6325212yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—341no—
518C22×C4—341no—
519C22×C4—341no—
520C22×C4C2×C22⋊D1711yescharacteristic
521C22×C4C2×C22⋊D1711yescharacteristic
522C22×C4C2×C22⋊D1711yescharacteristic
523C22×C4C2×C22⋊D1711yescharacteristic
524C22×C4C2×C22⋊D1711yescharacteristic
525C22×C4C23×D1711yescharacteristic
526D8—684no—
527C2×C8—341no—
528C2×C8—341no—
529C2×C8—341no—
530C2×C8—341no—
531C2×C8—341no—
532C2×C8—341no—
533C2×C8—341no—
534C2×C8—341no—
535C2×C8—341no—
536C2×C8—341no—
537C2×C8—341no—
538C2×C8—341no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—81no—
544C4⋊C4—172no—
545C4⋊C4—341no—
546C4⋊C4—341no—
547C4⋊C4—341no—
548C4⋊C4—341no—
549C4⋊C4—341no—
550C4⋊C4—682no—
551C4⋊C4#6325212yes—
552C4⋊C4#6325412yes—
553C22⋊C4—24no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—682no—
561C22⋊C4—682no—
562C22⋊C4—682no—
563C22⋊C4—682no—
564C22⋊C4—682no—
565C22⋊C4—1361no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—81no—
572C42—682no—
573C23—22no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—681no—
588C23—681no—
589C23—681no—
590C23—681no—
591C23—681no—
592C23—681no—
593C23—681no—
594C23C22×C22⋊D1711yescharacteristic
595Q8—1364no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—681no—
602D4—681no—
603D4—681no—
604D4—681no—
605D4—1364no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—84no—
633C2×C4—342no—
634C2×C4—681no—
635C2×C4—681no—
636C2×C4—681no—
637C2×C4—681no—
638C2×C4—681no—
639C2×C4—681no—
640C2×C4—681no—
641C2×C4—681no—
642C2×C4#1058763512yes—
643C2×C4#1058763612yes—
644C2×C4C2×#6325211yescharacteristic
645C2×C4C2×#6325211yescharacteristic
646C2×C4C2×#6325411yescharacteristic
647C2×C4#1058769111yescharacteristic
648C2×C4#41×D1711yescharacteristic
649C2×C4#1058769611yescharacteristic
650C8—681no—
651C8—681no—
652C8—681no—
653C8—681no—
654C22—41no—
655C22—42no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—1361no—
669C22—1361no—
670C22—1361no—
671C22—1361no—
672C22—1361no—
673C22—1361no—
674C22—1361no—
675C22#1176332011yescharacteristic
676C22#1176344711yescharacteristic
677C22#1176345311yescharacteristic
678C22C2×#1058763611yescharacteristic
679C22C2×#1058763511yescharacteristic
680C22#1176361211yescharacteristic
681C22#1176362011yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—41no—
689C4—81no—
690C4—682no—
691C4—1361no—
692C4—1361no—
693C4#1176333911yescharacteristic
694C4#1176339211yescharacteristic
695C4#1176352411yescharacteristic
696C4#1176354211yescharacteristic
697C2—81no—
698C2—82no—
699C2—2721no—
700C2#1453271511yescharacteristic
701C2#1453884411yescharacteristic
702C2#1453896811yescharacteristic
703C2#1454068011yescharacteristic
704C2#1454073411yescharacteristic
705C2#1454074511yescharacteristic
706C2#1454102011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2363C2
socleC23×C17C22×D4
prime radical#14529780C2
hypercenter#2363D17
hypocenterC17#26729
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #14533147C2semidirect
2. #14530094C2semidirect
3. #14529970C2semidirect
4. #14529920C2semidirect
6. #14529732C2semidirect
7. #14529466C2semidirect
8. #14529411C2semidirect
9. #14529392C2semidirect
10. #14529366C2semidirect
11. #14529132C2semidirect
12. #14529106C2semidirect
13. #14528879C2semidirect
14. C4×#10587503C2semidirect
15. C17×#2363C2semidirect
302. #2363D17semidirect
480. C17#26729semidirect

Maximal subgroups

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

subgroupindex
#145331472
#145300942
#145299702
#145299202
#145297802
#145297322
#145294662
#145294112
#145293922
#145293662
#145291322
#145291062
#145288792
C4×#105875032
C17×#23632
#2672917