Finite Group Databasebeta

← #16956420

Subgroups — #16956420

Order 4352.

1746 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762697C212yesmaximal
2C2×#11762660C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic17C211yesmaximal, characteristic
4#14527047C212yesmaximal, complemented
5#14527027C212yesmaximal
6#14527016C212yesmaximal, complemented
7#14527012C211yesmaximal, characteristic, complemented
8#14527009C211yesmaximal, characteristic, complemented
9#14527008C211yesmaximal, characteristic, complemented
10#14527007C211yesmaximal, characteristic
11C2×C17×#380C211yesmaximal, characteristic
12C22×#63225C2212yes—
13C22×#63225C2212yes—
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C4×Dic17C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20#11762697—28no—
21#11762660—24no—
22C4×C22⋊Dic17C418yescomplemented
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C24×C4×C17C2211yescharacteristic
34C22×C4⋊C4×C17C2212yes—
35C22×C22⋊C4×C17C2212yes—
36C17×#380—24no—
37C2×C17×#95C2211yescharacteristic
38C2×C17×#95C2211yescharacteristic
39C25×C17C2311yescharacteristic
40C23×C4×C17—22no—
41C23×C4×C17—24no—
42C23×C4×C17—22no—
43C23×C4×C17—42no—
44C23×C4×C17C2×C414yes—
45C23×C4×C17C2312yes—
46C23×C4×C17C2312yes—
47C23×C4×C17C2311yescharacteristic
48C23×C4×C17C2311yescharacteristic
49C23×Dic17C2312yes—
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2312yes—
52C23×Dic17C2311yescharacteristic
53C23×Dic17C2311yescharacteristic
54C23×Dic17C2311yescharacteristic
55C2×C4⋊C4×C17—24no—
56C2×C4⋊C4×C17—24no—
57C2×C4⋊C4×C17—42no—
58C2×C22⋊C4×C17—24no—
59C2×C22⋊C4×C17—24no—
60C2×C22⋊C4×C17—42no—
61C2×C22⋊Dic17—24no—
62C2×C22⋊Dic17—24no—
63C2×C22⋊Dic17—24no—
64C2×C22⋊Dic17—42no—
65C2×C22⋊Dic17C2×C414yes—
66C2×C22⋊Dic17C2×C414yes—
67C2×C22⋊Dic17D414yes—
68C2×C22⋊Dic17Q814yes—
69C2×#63225—24no—
70C2×#63225—24no—
71C2×#63225—24no—
72C2×#63225—24no—
73C2×#63225—24no—
74C2×#63225—42no—
75C2×C4×Dic17—22no—
76C2×C4×Dic17—24no—
77C2×C4×Dic17—22no—
78C2×C4×Dic17—24no—
79C2×C4×Dic17—42no—
80C2×C4×Dic17—42no—
81C2×C4×Dic17C2×C414yes—
82C2×C4×Dic17C2×C414yes—
83C17×#95—22no—
84C17×#95D414yes—
85#10587502—22no—
86#10587502—24no—
87#10587502—22no—
88#10587502—24no—
89#10587502—24no—
90#10587502—24no—
91#10587502—42no—
92#10587502—42no—
93#10587502C2×C414yes—
94#10587502C2×C414yes—
95C24×C17—21no—
96C24×C17—21no—
97C24×C17—22no—
98C24×C17—22no—
99C24×C17—22no—
100C24×C17—22no—
101C24×C17—21no—
102C24×C17—21no—
103C24×C17C22×C412yes—
104C24×C17C2×D412yes—
105C24×C17C2×Q812yes—
106C24×C17C2411yescharacteristic
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—28no—
119C22×C4×C17—28no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—44no—
128C22×C4×C17—48no—
129C22×C4×C17—48no—
130C22×C4×C17C22×C412yes—
131C22×C4×C17C22×C412yes—
132C22×C4×C17C2×D414yes—
133C22×C4×C17C2×D412yes—
134C22×C4×C17#4112yes—
135C22×C4×C17#4114yes—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—21no—
143C22×Dic17—22no—
144C22×Dic17—21no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—21no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—21no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17C22×C412yes—
163C22×Dic17C22×C412yes—
164C22×Dic17C22×C412yes—
165C22×Dic17C22×C412yes—
166C22×Dic17C2×D412yes—
167C22×Dic17C2×D412yes—
168C22×Dic17C2×Q812yes—
169C22×Dic17C2×Q812yes—
170C22×Dic17#4114yes—
171C22×Dic17#4114yes—
172C4⋊C4×C17—48no—
173C22⋊C4×C17—48no—
174C22⋊Dic17—28no—
175C22⋊Dic17—48no—
176C22⋊Dic17C4⋊C4116yescomplemented
177#63225—216no—
178#63225—48no—
179C4×Dic17—28no—
180C4×Dic17—44no—
181C4×Dic17—48no—
182#13891—171nomaximal, Sylow
183C23×C17—22no—
184C23×C17—22no—
185C23×C17—22no—
186C23×C17—22no—
187C23×C17—22no—
188C23×C17—22no—
189C23×C17—24no—
190C23×C17—24no—
191C23×C17—22no—
192C23×C17—24no—
193C23×C17—22no—
194C23×C17—22no—
195C23×C17—24no—
196C23×C17—22no—
197C23×C17—42no—
198C23×C17—42no—
199C23×C17—42no—
200C23×C17—42no—
201C23×C17—42no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17—42no—
205C23×C17C2×C4⋊C414yes—
206C23×C17C23×C411yescharacteristic
207C23×C17C22×D411yescharacteristic
208C23×C17C22×D411yescharacteristic
209C23×C17C22×Q811yescharacteristic
210C23×C17C2×#4111yescharacteristic
211C23×C17C2×#4112yes—
212C23×C17C2×#4112yes—
213C23×C17C2×#4112yes—
214C23×C17H(5,𝔽2)12yes—
215C23×C17H(5,𝔽2)11yescharacteristic
216C23×C172−1+411yescharacteristic
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—22no—
220C2×C4×C17—22no—
221C2×C4×C17—24no—
222C2×C4×C17—24no—
223C2×C4×C17—24no—
224C2×C4×C17—24no—
225C2×C4×C17—24no—
226C2×C4×C17—24no—
227C2×C4×C17—24no—
228C2×C4×C17—416no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—42no—
240C2×C4×C17#11714yes—
241C2×C4×C17C4×D414yes—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—22no—
247C2×Dic17—22no—
248C2×Dic17—24no—
249C2×Dic17—24no—
250C2×Dic17—22no—
251C2×Dic17—24no—
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—24no—
255C2×Dic17—22no—
256C2×Dic17—22no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—24no—
260C2×Dic17—24no—
261C2×Dic17—24no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—42no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—42no—
275C2×Dic17C2×C4⋊C414yes—
276C2×Dic17C2×C4⋊C414yes—
277C2×Dic17#11714yes—
278C2×#388—172no—
279C2×#380D1711yescharacteristic
280C2×C4×C4⋊C4—171no—
281C2×C4×C22⋊C4—171no—
282#1444—172no—
283#1439—172no—
284#1436—172no—
285C4⋊#95—171no—
286#1434—171no—
287#1434—171no—
288C22⋊#95—171no—
289C22×C17—24no—
290C22×C17—24no—
291C22×C17—24no—
292C22×C17—42no—
293C22×C17—42no—
294C22×C17—42no—
295C22×C17—44no—
296C22×C17—44no—
297C22×C17—44no—
298C22×C17—44no—
299C22×C17—42no—
300C22×C17C22×C4⋊C411yescharacteristic
301C22×C17C2×#11711yescharacteristic
302C22×C17C2×#11711yescharacteristic
303C22×C17C2×C4×D411yescharacteristic
304C22×C17C4×#4111yescharacteristic
305C22×C17#51811yescharacteristic
306C22×C17#52011yescharacteristic
307C22×C17#52512yes—
308C22×C17#52912yes—
309C22×C17#53212yes—
310C22×C17#53312yes—
311C22×C17#54012yes—
312C22×C17#54212yes—
313C22×C17D4211yescharacteristic
314C22×C17#54612yes—
315C22×C17#54612yes—
316C22×C17#54711yescharacteristic
317C22×C17D4×Q811yescharacteristic
318C22×C17#55112yes—
319C22×C17#55312yes—
320C22×C17#55412yes—
321C22×C17#55411yescharacteristic
322C22×C17#55612yes—
323C4×C17—24no—
324C4×C17—24no—
325C4×C17—44no—
326C4×C17—82no—
327Dic17—24no—
328Dic17—24no—
329Dic17—24no—
330Dic17—42no—
331Dic17—44no—
332Dic17—82no—
333C24×C4C2×D1711yescharacteristic
334C22×C4⋊C4—172no—
335C22×C4⋊C4—172no—
336C22×C4⋊C4C2×D1712yes—
337C22×C22⋊C4—171no—
338C22×C22⋊C4—171no—
339C22×C22⋊C4—172no—
340C22×C22⋊C4C2×D1712yes—
341C22×C42—171no—
342C22×C42—171no—
343C22×C42—172no—
344#388—348no—
345#380—24no—
346C4×C4⋊C4—344no—
347C4×C22⋊C4—178no—
348C2×#95—171no—
349C2×#95—171no—
350C2×#95—171no—
351C2×#95—171no—
352C2×#95—172no—
353C2×#95—172no—
354C2×#95—172no—
355C2×#95—172no—
356C2×#95—172no—
357C2×#95—172no—
358C2×#95C2×D1711yescharacteristic
359C2×#95C2×D1711yescharacteristic
360C2×C17—44no—
361C2×C17#228511yescharacteristic
362C2×C17#229011yescharacteristic
363C2×C17#231911yescharacteristic
364C2×C17#234211yescharacteristic
365C2×C17#234711yescharacteristic
366C2×C17D4×C4⋊C411yescharacteristic
367C2×C17#234911yescharacteristic
368C2×C17#246412yes—
369C2×C17#246512yes—
370C2×C17#252112yes—
371C2×C17#252212yes—
372C25C22×D1711yescharacteristic
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—42no—
377C23×C4—171no—
378C23×C4—171no—
379C23×C4—171no—
380C23×C4—172no—
381C23×C4—171no—
382C23×C4—172no—
383C23×C4C4×D1714yes—
384C23×C4C22×D1712yes—
385C23×C4C22×D1712yes—
386C23×C4C22×D1711yescharacteristic
387C23×C4C22×D1711yescharacteristic
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—344no—
392C2×C4⋊C4—344no—
393C2×C4⋊C4—344no—
394C2×C4⋊C4—344no—
395C2×C4⋊C4—344no—
396C2×C4⋊C4—682no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—174no—
401C2×C22⋊C4—174no—
402C2×C22⋊C4—174no—
403C2×C22⋊C4—174no—
404C2×C22⋊C4—344no—
405C2×C22⋊C4—344no—
406C2×C22⋊C4—344no—
407C2×C22⋊C4—682no—
408C2×C42—174no—
409C2×C42—174no—
410C2×C42—342no—
411C2×C42—342no—
412C2×C42—344no—
413C2×C42—344no—
414C2×C42—682no—
415C2×C42—682no—
416#95—22no—
417#95—174no—
418#95—174no—
419#95—344no—
420#95—344no—
421#95—344no—
422#95—342no—
423#95—344no—
424#95—342no—
425#95—682no—
426#95—682no—
427#95C22⋊D1714yes—
428C17#1389111yescharacteristic, complemented, Sylow
429C24—21no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24C2×C4×D1712yes—
438C24D4×D1712yes—
439C24Q8×D1712yes—
440C24C23×D1711yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—44no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—172no—
465C22×C4—172no—
466C22×C4—172no—
467C22×C4—172no—
468C22×C4—172no—
469C22×C4—172no—
470C22×C4—172no—
471C22×C4—174no—
472C22×C4—172no—
473C22×C4—174no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—342no—
478C22×C4—341no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—341no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—341no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4C2×C4×D1712yes—
501C22×C4C2×C4×D1712yes—
502C22×C4#6325212yes—
503C22×C4#6325414yes—
504C22×C4C2×C22⋊D1714yes—
505C22×C4C2×C22⋊D1712yes—
506C4⋊C4—48no—
507C4⋊C4—3416no—
508C4⋊C4—688no—
509C22⋊C4—48no—
510C22⋊C4—1716no—
511C22⋊C4—348no—
512C22⋊C4—688no—
513C42—348no—
514C42—684no—
515C42—688no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—22no—
529C23—24no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23C4⋊C4×D1714yes—
539C23C22×C4×D1711yescharacteristic
540C23C2×#6325211yescharacteristic
541C23C2×D4×D1711yescharacteristic
542C23C2×#6325412yes—
543C23#1058769112yes—
544C23#1058769111yescharacteristic
545C23C2×Q8×D1711yescharacteristic
546C23#1058769411yescharacteristic
547C23#41×D1712yes—
548C23#41×D1712yes—
549C23C22×C22⋊D1711yescharacteristic
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—416no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—174no—
574C2×C4—174no—
575C2×C4—174no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—344no—
579C2×C4—342no—
580C2×C4—342no—
581C2×C4—342no—
582C2×C4—342no—
583C2×C4—342no—
584C2×C4—342no—
585C2×C4—342no—
586C2×C4—344no—
587C2×C4—344no—
588C2×C4—342no—
589C2×C4—344no—
590C2×C4—344no—
591C2×C4—342no—
592C2×C4—342no—
593C2×C4—342no—
594C2×C4—344no—
595C2×C4—344no—
596C2×C4—682no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—682no—
600C2×C4—682no—
601C2×C4—682no—
602C2×C4—682no—
603C2×C4—682no—
604C2×C4—682no—
605C2×C4—682no—
606C2×C4—682no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4#1058756314yes—
610C2×C4C4×C22⋊D1714yes—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22C2×C4⋊C4×D1711yescharacteristic
623C22#117×D1711yescharacteristic
624C22C2×#1058756311yescharacteristic
625C22C2×C4×C22⋊D1711yescharacteristic
626C22#1176327711yescharacteristic
627C22#1176328211yescharacteristic
628C22#1176329011yescharacteristic
629C22#1176331612yes—
630C22#1176333712yes—
631C22#1176335412yes—
632C22#1176336112yes—
633C22#1176340912yes—
634C22#1176342912yes—
635C22D4×C22⋊D1711yescharacteristic
636C22#1176344812yes—
637C22#1176345312yes—
638C22#1176346011yescharacteristic
639C22Q8×C22⋊D1711yescharacteristic
640C22#1176348512yes—
641C22#1176350612yes—
642C22#1176351312yes—
643C22#1176351411yescharacteristic
644C22#1176353012yes—
645C4—24no—
646C4—24no—
647C4—44no—
648C4—82no—
649C4—344no—
650C4—344no—
651C4—344no—
652C4—682no—
653C4—684no—
654C4—1362no—
655C2—44no—
656C2#1453118611yescharacteristic
657C2#1453122111yescharacteristic
658C2#1453142611yescharacteristic
659C2#1453162911yescharacteristic
660C2#1453167911yescharacteristic
661C2C4⋊C4×C22⋊D1711yescharacteristic
662C2#1453168811yescharacteristic
663C2#1453278612yes—
664C2#1453280112yes—
665C2#1453348312yes—
666C2#1453349812yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#380C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#380D17
hypocenterC17#13891
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11762660C2semidirect
4. #14527047C2semidirect
6. #14527016C2semidirect
7. #14527012C2semidirect
8. #14527009C2semidirect
9. #14527008C2semidirect
22. C4×C22⋊Dic17C4semidirect
176. C22⋊Dic17C4⋊C4semidirect
428. C17#13891semidirect

Maximal subgroups

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

subgroupindex
C2×#117626972
C2×#117626602
C2×C4×C22⋊Dic172
#145270472
#145270272
#145270162
#145270122
#145270092
#145270082
#145270072
C2×C17×#3802
#1389117