Finite Group Databasebeta

← #17043909

Subgroups — #17043909

Order 4352.

1170 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763339C211yesmaximal, characteristic
2C2×#11762859C211yesmaximal, characteristic, complemented
3C22×#10587485C211yesmaximal, characteristic, complemented
4#14529718C212yesmaximal, complemented
5#14529576C212yesmaximal, complemented
6#14529077C211yesmaximal, characteristic, complemented
7#14529076C211yesmaximal, characteristic, complemented
8#14529074C211yesmaximal, characteristic, complemented
9#14528767C212yesmaximal, complemented
10#14528766C212yesmaximal, complemented
11C17×#1869C211yesmaximal, characteristic, complemented
12C23×#3622C2211yescharacteristic
13#11763339—24no—
14#11763339—24no—
15C2×#10587584C411yescharacteristic
16C2×#10587565C411yescharacteristic
17C2×#10587575C411yescharacteristic
18C2×#10587571C411yescharacteristic
19C2×#10587572C411yescharacteristic
20C2×#10587621C411yescharacteristic
21C2×#10587564C411yescharacteristic
22C2×#10587625C411yescharacteristic
23C2×C4×Dic34C2211yescharacteristic
24C2×C4×C22⋊D17C2211yescharacteristic
25C2×C4×C22⋊D17C2211yescharacteristic
26C2×#10587612C2211yescharacteristic
27C2×#10587558C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762859—24no—
30C2×#10587485—24no—
31C2×#10587485C2212yes—
32C2×#10587485C2212yes—
33C2×#10587485C2212yes—
34C2×C22⋊#3622C2211yescharacteristic
35C2×C22⋊#3622C2212yes—
36C2×#10587491C2212yes—
37C2×#10587491C2212yes—
38C2×C8×Dic17C2212yes—
39#11762564C2212yes—
40#11762563C2212yes—
41#11762563C2212yes—
42C23×C8×C17C2211yescharacteristic
43C2×C4×D4×C17C2211yescharacteristic
44C2×C17×C22⋊C8C2211yescharacteristic
45C2×C17×C22⋊C8C2212yes—
46C17×#336C2212yes—
47C22×D4×C17C2×C411yescharacteristic
48C23×C4×C17C2311yescharacteristic
49C23×C4×C17C2311yescharacteristic
50C22×C22⋊D17C2×C411yescharacteristic
51C22×C22⋊D17C2×C411yescharacteristic
52C23×Dic17C2×C411yescharacteristic
53C23×Dic17C2×C411yescharacteristic
54C22×C4×D17C2311yescharacteristic
55C22×Dic34C2×C411yescharacteristic
56C22×C8×C17—22no—
57C22×C8×C17—42no—
58C22×C8×C17C2312yes—
59C22×C8×C17C2312yes—
60C4×D4×C17—22no—
61C4×D4×C17—22no—
62C2×C4⋊C4×C17C2×C411yescharacteristic
63C2×C22⋊C4×C17C2×C411yescharacteristic
64C2×C22⋊C4×C17C2×C411yescharacteristic
65C2×C42×C17C2311yescharacteristic
66C2×C22⋊Dic17C2×C411yescharacteristic
67C2×C22⋊Dic17C2×C411yescharacteristic
68C2×C22⋊Dic17C2×C411yescharacteristic
69C2×C22⋊Dic17C2×C411yescharacteristic
70#10587625—24no—
71#10587621—24no—
72C4×C22⋊D17—22no—
73C4×C22⋊D17—22no—
74C4×C22⋊D17—22no—
75C4×C22⋊D17—22no—
76C2×#63227C2×C411yescharacteristic
77C2×#63227C2×C411yescharacteristic
78C2×#63227C2×C411yescharacteristic
79C2×#63227C2×C411yescharacteristic
80#10587612—22no—
81#10587612—22no—
82C2×C4⋊Dic17C2×C411yescharacteristic
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×#63225C2×C411yescharacteristic
88C2×#63225C2×C411yescharacteristic
89C2×#63225C2×C411yescharacteristic
90C2×#63225C2×C411yescharacteristic
91C2×C4×Dic17C2×C411yescharacteristic
92C2×C4×Dic17C2×C411yescharacteristic
93C2×C4×Dic17D414yes—
94C2×C4×Dic17D414yes—
95C2×C4×Dic17C2311yescharacteristic
96C2×C4×Dic17C2311yescharacteristic
97C2×C4×Dic17C2311yescharacteristic
98C22×#3622—22no—
99C22×#3622—42no—
100C22×#3622C2312yes—
101C22×#3622C2312yes—
102#10587584—24no—
103#10587575—24no—
104#10587572—24no—
105#10587571—24no—
106#10587565—24no—
107#10587564—24no—
108#10587558—22no—
109#10587558—22no—
110C4×Dic34—22no—
111C4×Dic34—22no—
112C17×C22⋊C8—22no—
113C17×C22⋊C8—42no—
114C22⋊#3622—22no—
115C22⋊#3622—42no—
116#10587491—42no—
117#10587491—42no—
118#10587485—24no—
119#10587485—24no—
120#10587485—24no—
121C8×Dic17—24no—
122C24×C17C22×C411yescharacteristic
123C24×C17C22×C411yescharacteristic
124C23×D17C22×C411yescharacteristic
125C2×D4×C17—22no—
126C2×D4×C17—22no—
127C2×D4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C22×C4×C17C2×D412yes—
139C22×C4×C17C2×D412yes—
140C22×C4×C17C2411yescharacteristic
141C2×C22⋊D17—22no—
142C2×C22⋊D17—22no—
143C2×C22⋊D17—22no—
144C2×C22⋊D17—22no—
145C2×C22⋊D17—24no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—24no—
149C22×Dic17C22⋊C414yes—
150C22×Dic17C22⋊C414yes—
151C22×Dic17C22×C411yescharacteristic
152C22×Dic17C22×C411yescharacteristic
153C22×Dic17C22×C411yescharacteristic
154C22×Dic17C22×C411yescharacteristic
155C22×Dic17C22×C411yescharacteristic
156C22×Dic17C22×C411yescharacteristic
157C22×Dic17C22×C411yescharacteristic
158C2×C4×D17—21no—
159C2×C4×D17—21no—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×Dic34—22no—
163C2×Dic34—24no—
164C2×C8×C17—22no—
165C2×C8×C17—22no—
166C2×C8×C17—22no—
167C2×C8×C17—22no—
168C2×C8×C17—22no—
169C2×C8×C17—22no—
170C2×C8×C17—44no—
171C4⋊C4×C17—22no—
172C22⋊C4×C17—22no—
173C22⋊C4×C17—22no—
174C42×C17—21no—
175C42×C17—21no—
176C22⋊Dic17—22no—
177C22⋊Dic17—22no—
178C22⋊Dic17—22no—
179C22⋊Dic17—22no—
180#63227—22no—
181#63227—22no—
182#63227—22no—
183#63227—22no—
184C4⋊Dic17—22no—
185C4⋊Dic17—22no—
186C4⋊Dic17—22no—
187#63225—22no—
188#63225—22no—
189#63225—22no—
190#63225—22no—
191#63225—22no—
192#63225—22no—
193C4×Dic17—21no—
194C4×Dic17—21no—
195C4×Dic17C22⋊C414yes—
196C4×Dic17C22⋊C414yes—
197C4×Dic17C2×D412yes—
198C4×Dic17C2×D412yes—
199C4×Dic17C2×D412yes—
200C4×Dic17C2×D412yes—
201C2×#3622—22no—
202C2×#3622—22no—
203C2×#3622—22no—
204C2×#3622—22no—
205C2×#3622—22no—
206C2×#3622—22no—
207C2×#3622—44no—
208#21848—171nomaximal, Sylow
209C23×C17—22no—
210C23×C17—22no—
211C23×C17—21no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17C2×C22⋊C412yes—
217C23×C17#13112yes—
218C23×C17#13112yes—
219C23×C17C23×C411yescharacteristic
220C22×D17—21no—
221C22×D17—22no—
222C22×D17—22no—
223C22×D17—21no—
224C22×D17—21no—
225D4×C17—44no—
226C2×C4×C17—22no—
227C2×C4×C17—22no—
228C2×C4×C17—22no—
229C2×C4×C17—24no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—22no—
234C2×C4×C17—22no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—42no—
240C2×C4×C17C2×C22⋊C412yes—
241C2×C4×C17C22×D411yescharacteristic
242C2×C4×C17C22×D411yescharacteristic
243C2×C4×C17H(5,𝔽2)12yes—
244C2×C4×C172−1+412yes—
245C22⋊D17—44no—
246C22⋊D17—44no—
247C2×Dic17—22no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—28no—
253C2×Dic17—28no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17C2×C22⋊C412yes—
262C2×Dic17C2×C22⋊C412yes—
263C2×Dic17C2×C22⋊C412yes—
264C2×Dic17C2×C22⋊C412yes—
265C2×Dic17#13114yes—
266C4×D17—41no—
267C4×D17—41no—
268C4×D17—42no—
269Dic34—44no—
270C8×C17—42no—
271C8×C17—42no—
272#3622—42no—
273#3622—42no—
274C2×#529—171no—
275C2×#431—171no—
276C22×C4⋊C8—171no—
277#1984—172no—
278#1954—172no—
279#1869—171no—
280#1869—171no—
281#1869—171no—
282#1869D1711yescharacteristic, complemented
283#1798—172no—
284#1798—172no—
285C22×C17—22no—
286C22×C17—22no—
287C22×C17—24no—
288C22×C17—24no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17—41no—
292C22×C17—42no—
293C22×C17—42no—
294C22×C17#40814yes—
295C22×C17C22×C22⋊C411yescharacteristic
296C22×C17#52012yes—
297C22×C17C2×#13112yes—
298C22×C17C2×#13111yescharacteristic
299C22×C17C2×#13111yescharacteristic
300C2×D17—41no—
301C2×D17—41no—
302C2×D17—41no—
303C2×D17—42no—
304C2×D17—42no—
305C4×C17—22no—
306C4×C17—41no—
307C4×C17—41no—
308C4×C17—41no—
309C4×C17#53511yescharacteristic
310C4×C17#53611yescharacteristic
311C4×C17#53712yes—
312Dic17—22no—
313Dic17—22no—
314Dic17—22no—
315Dic17—41no—
316Dic17—41no—
317Dic17—41no—
318Dic17#40814yes—
319C23×C8—171no—
320C23×C8C2×D1711yescharacteristic
321#529—344no—
322#529—344no—
323C2×#126—171no—
324C2×#126—171no—
325C2×#125—171no—
326C2×#124—171no—
327C2×#123—171no—
328C2×#123—171no—
329C2×C22⋊Q8—171no—
330C2×#121—171no—
331C2×C4×Q8—171no—
332C2×C4×D4—171no—
333C2×C4×D4—171no—
334C2×C4×D4C2×D1711yescharacteristic
335C2×#117—171no—
336C2×#117—171no—
337C22×C42—171no—
338#431—344no—
339C2×C4⋊C8—172no—
340C2×C4⋊C8—172no—
341C2×C4⋊C8—172no—
342C2×C4⋊C8—344no—
343C2×C22⋊C8—171no—
344C2×C22⋊C8—172no—
345C2×C22⋊C8—172no—
346C2×C22⋊C8—172no—
347C2×C22⋊C8C2×D1711yescharacteristic
348C2×C22⋊C8C2×D1712yes—
349C2×C4×C8—172no—
350#336—172no—
351#336—172no—
352#336—172no—
353#336C2×D1712yes—
354C2×C17—24no—
355C2×C17—81no—
356C2×C17#231111yescharacteristic
357C2×C17C2×#40811yescharacteristic
358C2×C17C2×#40811yescharacteristic
359C2×C17#299412yes—
360C2×C17#299412yes—
361D17—81no—
362C22×Q8—171no—
363C22×D4—171no—
364C22×D4—171no—
365C22×D4C4×D1711yescharacteristic
366C23×C4—171no—
367C23×C4—171no—
368C23×C4—171no—
369C23×C4C22×D1711yescharacteristic
370C23×C4C22×D1711yescharacteristic
371C22×C8—22no—
372C22×C8—42no—
373C22×C8—172no—
374C22×C8—172no—
375C22×C8—342no—
376C22×C8—682no—
377C22×C8C22×D1712yes—
378C22×C8C22×D1712yes—
379#126—344no—
380#126—344no—
381#125—344no—
382#124—344no—
383#123—344no—
384#123—344no—
385C22⋊Q8—344no—
386#121—344no—
387C4×Q8—342no—
388C4×Q8—342no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—342no—
392C4×D4—342no—
393C4×D4—342no—
394C4×D4—342no—
395#117—342no—
396#117—342no—
397#117—342no—
398#117—342no—
399C2×C4⋊C4—171no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—171no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—171no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—171no—
408C2×C4⋊C4C4×D1711yescharacteristic
409C2×C22⋊C4—171no—
410C2×C22⋊C4—171no—
411C2×C22⋊C4—171no—
412C2×C22⋊C4—171no—
413C2×C22⋊C4—171no—
414C2×C22⋊C4—171no—
415C2×C22⋊C4—171no—
416C2×C22⋊C4—171no—
417C2×C22⋊C4C4×D1711yescharacteristic
418C2×C22⋊C4C4×D1711yescharacteristic
419C2×C42—171no—
420C2×C42—171no—
421C2×C42—174no—
422C2×C42—174no—
423C2×C42—171no—
424C2×C42—171no—
425C2×C42—171no—
426C2×C42C22×D1711yescharacteristic
427C4⋊C8—344no—
428C4⋊C8—344no—
429C4⋊C8—344no—
430C22⋊C8—22no—
431C22⋊C8—42no—
432C22⋊C8—342no—
433C22⋊C8—682no—
434C22⋊C8—682no—
435C22⋊C8—682no—
436C4×C8—344no—
437C17#2184811yescharacteristic, complemented, Sylow
438C24—171no—
439C24C2×C4×D1711yescharacteristic
440C24C2×C4×D1711yescharacteristic
441C2×Q8—342no—
442C2×Q8—344no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—342no—
447C2×D4—344no—
448C2×D4—342no—
449C2×D4—342no—
450C2×D4—342no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—171no—
458C22×C4—171no—
459C22×C4—171no—
460C22×C4—171no—
461C22×C4—174no—
462C22×C4—174no—
463C22×C4—171no—
464C22×C4—171no—
465C22×C4—171no—
466C22×C4—344no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4C2×C4×D1711yescharacteristic
474C22×C4C2×C4×D1711yescharacteristic
475C22×C4C2×C4×D1711yescharacteristic
476C22×C4C2×C4×D1711yescharacteristic
477C22×C4D4×D1712yes—
478C22×C4D4×D1712yes—
479C22×C4C23×D1711yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—44no—
487C2×C8—342no—
488C2×C8—342no—
489C2×C8—342no—
490C2×C8—342no—
491C2×C8—342no—
492C2×C8—342no—
493C2×C8—684no—
494C4⋊C4—22no—
495C4⋊C4—342no—
496C4⋊C4—342no—
497C4⋊C4—342no—
498C4⋊C4—342no—
499C4⋊C4—342no—
500C4⋊C4—342no—
501C4⋊C4—342no—
502C4⋊C4—342no—
503C4⋊C4—342no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—342no—
507C22⋊C4—342no—
508C22⋊C4—342no—
509C22⋊C4—342no—
510C22⋊C4—342no—
511C22⋊C4—342no—
512C22⋊C4—342no—
513C22⋊C4—342no—
514C42—21no—
515C42—21no—
516C42—172no—
517C42—172no—
518C42—172no—
519C42—172no—
520C42—174no—
521C42—174no—
522C42—341no—
523C42—341no—
524C23—22no—
525C23—22no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—21no—
530C23—21no—
531C23—341no—
532C23—342no—
533C23—342no—
534C23—341no—
535C23—341no—
536C23C22⋊C4×D1712yes—
537C23#1058758712yes—
538C23#1058759312yes—
539C23C22×C4×D1711yescharacteristic
540Q8—684no—
541D4—44no—
542D4—684no—
543D4—684no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—172no—
559C2×C4—174no—
560C2×C4—172no—
561C2×C4—172no—
562C2×C4—172no—
563C2×C4—348no—
564C2×C4—348no—
565C2×C4—342no—
566C2×C4—341no—
567C2×C4—341no—
568C2×C4—341no—
569C2×C4—341no—
570C2×C4—341no—
571C2×C4—341no—
572C2×C4—341no—
573C2×C4—342no—
574C2×C4—342no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—682no—
580C2×C4C22⋊C4×D1712yes—
581C2×C4C2×D4×D1711yescharacteristic
582C2×C4C2×D4×D1711yescharacteristic
583C2×C4#1058769112yes—
584C2×C4#1058769712yes—
585C8—42no—
586C8—42no—
587C8—682no—
588C8—682no—
589C22—22no—
590C22—22no—
591C22—24no—
592C22—24no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—42no—
598C22—681no—
599C22—681no—
600C22—681no—
601C22—682no—
602C22—682no—
603C22#1176277414yes—
604C22C2×C22⋊C4×D1711yescharacteristic
605C22#1176328812yes—
606C22#131×D1712yes—
607C22C2×#1058758711yescharacteristic
608C22C2×#1058759311yescharacteristic
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—174no—
614C4—342no—
615C4—342no—
616C4—342no—
617C4—681no—
618C4—681no—
619C4—681no—
620C4#1176337411yescharacteristic
621C4#1176338111yescharacteristic
622C4#1176338612yes—
623C2—24no—
624C2—81no—
625C2—1361no—
626C2#1453137111yescharacteristic
627C2D17×#40811yescharacteristic
628C2C2×#1176277411yescharacteristic
629C2#1453793712yes—
630C2#1453794112yes—
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1869C2
prime radicalC2×#10587625C4
cosocleC22×C4×C17C24
hypercenter#1869D17
hypocenterC17#21848
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#11762859C2semidirect
3. C22×#10587485C2semidirect
4. #14529718C2semidirect
5. #14529576C2semidirect
6. #14529077C2semidirect
7. #14529076C2semidirect
8. #14529074C2semidirect
9. #14528767C2semidirect
10. #14528766C2semidirect
11. C17×#1869C2semidirect
282. #1869D17semidirect
437. C17#21848semidirect

Maximal subgroups

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

subgroupindex
C2×#117633392
C2×#117628592
C22×#105874852
#145297182
#145295762
#145290772
#145290762
#145290742
#145287672
#145287662
C17×#18692
#2184817