Finite Group Databasebeta

← #16963274

Subgroups — #16963274

Order 4352.

1918 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762710C211yesmaximal, characteristic
2C2×#11762687C212yesmaximal
3#14527037C211yesmaximal, characteristic, complemented
4#14527030C212yesmaximal, complemented
5#14527026C212yesmaximal, complemented
6#14527010C212yesmaximal, complemented
7#14527005C212yesmaximal, complemented
8#14527005C212yesmaximal, complemented
9C17×#1441C211yesmaximal, characteristic, complemented
10C23×D68C2211yescharacteristic
11C23×C4×D17C2212yes—
12C22×C4⋊Dic17C2211yescharacteristic
13C22×#63227C2212yes—
14C22×#63227C2212yes—
15C22×#63227C2212yes—
16C22×#63227C2212yes—
17C22×#63227C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19#11762710C418yescomplemented
20#11762687—28no—
21C2×#10587502C2212yes—
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C22×C4⋊C4×C17C2211yescharacteristic
29C22×C4⋊C4×C17C2211yescharacteristic
30C2×C17×#95C2212yes—
31C2×C17×#95C2211yescharacteristic
32C2×C17×#95C2212yes—
33C24×D17C2312yes—
34C23×C4×C17C2312yes—
35C23×C4×C17C2311yescharacteristic
36C23×C4×C17C2311yescharacteristic
37C23×C4×C17C2312yes—
38C23×C4×C17C2311yescharacteristic
39C23×Dic17C2312yes—
40C23×Dic17C2312yes—
41C23×Dic17C2312yes—
42C22×D68—41no—
43C22×D68—41no—
44C22×D68—41no—
45C22×D68—41no—
46C22×D68C2×C414yes—
47C22×D68D414yes—
48C22×D68Q814yes—
49C22×C4×D17—24no—
50C22×C4×D17—24no—
51C22×C4×D17—24no—
52C22×C4×D17—42no—
53C22×C4×D17—42no—
54C22×C4×D17—42no—
55C22×C4×D17—42no—
56C2×C4⋊C4×C17—41no—
57C2×C4⋊C4×C17—41no—
58C2×C4⋊C4×C17—42no—
59C2×C4⋊C4×C17—41no—
60C2×C4⋊C4×C17C2×C414yescomplemented
61C2×#63227—24no—
62C2×#63227—24no—
63C2×#63227—24no—
64C2×#63227—24no—
65C2×#63227—24no—
66C2×#63227—42no—
67C2×#63227—42no—
68C2×#63227—42no—
69C2×#63227—42no—
70C2×#63227—42no—
71C2×#63227—42no—
72C2×#63227—42no—
73C2×#63227—42no—
74C2×#63227C2×C418yescomplemented
75C2×#63227C2×C418yescomplemented
76C2×C4⋊Dic17—42no—
77C2×C4⋊Dic17—41no—
78C2×C4×Dic17—41no—
79C2×C4×Dic17—41no—
80C2×C4×Dic17C2×C414yescomplemented
81C17×#95—24no—
82C17×#95—41no—
83C17×#95—42no—
84#10587502—24no—
85#10587502—24no—
86#10587502—24no—
87#10587502—41no—
88#10587502—42no—
89#10587502—42no—
90#10587502—42no—
91C24×C17C2411yescharacteristic
92C23×D17—22no—
93C23×D17—22no—
94C23×D17—22no—
95C23×D17—22no—
96C23×D17—22no—
97C23×D17—22no—
98C23×D17—22no—
99C23×D17—22no—
100C23×D17—22no—
101C23×D17—22no—
102C23×D17—22no—
103C23×D17—22no—
104C23×D17C22×C414yes—
105C23×D17C2×D414yes—
106C23×D17C2×Q814yes—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
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—21no—
119C22×C4×C17—22no—
120C22×C4×C17—21no—
121C22×C4×C17—22no—
122C22×C4×C17—21no—
123C22×C4×C17—22no—
124C22×C4×C17—21no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17C22×C412yes—
133C22×C4×C17C22×C412yes—
134C22×C4×C17C22×C412yes—
135C22×C4×C17C2×D412yes—
136C22×C4×C17C2×Q812yes—
137C22×C4×C17#4114yes—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17C22×C414yes—
158C22×Dic17#4114yes—
159C2×D68—44no—
160C2×D68—44no—
161C2×D68—44no—
162C2×D68—44no—
163C2×D68—44no—
164C2×D68—44no—
165C2×D68C4⋊C4116yescomplemented
166C2×C4×D17—48no—
167C2×C4×D17—48no—
168C2×C4×D17—48no—
169C2×C4×D17—48no—
170C2×C4×D17—48no—
171C2×C4×D17—48no—
172C2×C4×D17—48no—
173C4⋊C4×C17—44no—
174C4⋊C4×C17—44no—
175#63227—48no—
176#63227—48no—
177#63227—48no—
178#63227—48no—
179#63227—48no—
180C4⋊Dic17—44no—
181C4×Dic17—44no—
182#14486—171nomaximal, Sylow
183C23×C17C23×C411yescharacteristic
184C23×C17C22×D411yescharacteristic
185C23×C17C22×Q811yescharacteristic
186C23×C17C2×#4112yes—
187C23×C17C2×#4112yes—
188C23×C17H(5,𝔽2)11yescharacteristic
189C23×C17H(5,𝔽2)11yescharacteristic
190C23×C17H(5,𝔽2)12yes—
191C23×C17H(5,𝔽2)11yescharacteristic
192C23×C17H(5,𝔽2)11yescharacteristic
193C23×C17H(5,𝔽2)12yes—
194C22×D17—24no—
195C22×D17—24no—
196C22×D17—24no—
197C22×D17—24no—
198C22×D17—24no—
199C22×D17—24no—
200C22×D17—24no—
201C22×D17—24no—
202C22×D17—24no—
203C22×D17—24no—
204C22×D17—24no—
205C22×D17—24no—
206C22×D17—24no—
207C22×D17—24no—
208C22×D17—24no—
209C22×D17—24no—
210C22×D17—24no—
211C22×D17—24no—
212C22×D17—42no—
213C22×D17—42no—
214C22×D17—42no—
215C22×D17—42no—
216C22×D17—42no—
217C22×D17—42no—
218C22×D17—42no—
219C22×D17—42no—
220C22×D17—42no—
221C22×D17—42no—
222C22×D17—42no—
223C22×D17—42no—
224C22×D17—42no—
225C22×D17—42no—
226C22×D17—42no—
227C22×D17—42no—
228C22×D17C2×C4⋊C418yes—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—22no—
233C2×C4×C17—22no—
234C2×C4×C17—22no—
235C2×C4×C17—22no—
236C2×C4×C17—22no—
237C2×C4×C17—24no—
238C2×C4×C17—24no—
239C2×C4×C17—24no—
240C2×C4×C17—24no—
241C2×C4×C17—24no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—42no—
245C2×C4×C17—41no—
246C2×C4×C17—42no—
247C2×C4×C17—42no—
248C2×C4×C17—42no—
249C2×C4×C17—41no—
250C2×C4×C17—41no—
251C2×C4×C17—41no—
252C2×C4×C17—42no—
253C2×C4×C17—42no—
254C2×C4×C17—42no—
255C2×C4×C17—42no—
256C2×C4×C17—42no—
257C2×C4×C17—42no—
258C2×C4×C17—42no—
259C2×C4×C17C2×C4⋊C414yes—
260C2×Dic17—24no—
261C2×Dic17—24no—
262C2×Dic17—24no—
263C2×Dic17—24no—
264C2×Dic17—24no—
265C2×Dic17—24no—
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×Dic17—42no—
276C2×Dic17—42no—
277C2×Dic17—42no—
278C2×Dic17—42no—
279C2×Dic17—42no—
280C2×Dic17—42no—
281D68—416no—
282C4×D17—432no—
283C2×#390—171no—
284C2×#386—172no—
285#1441—171no—
286#1441D1711yescharacteristic, complemented
287#1439—172no—
288#1439—172no—
289#1434—172no—
290C22⋊#95—172no—
291C22⋊#95—172no—
292C22×C17C22×C4⋊C411yescharacteristic
293C22×C17C4×#4112yes—
294C22×C17#51812yes—
295C22×C17#51811yescharacteristic
296C22×C17#51811yescharacteristic
297C22×C17#53411yescharacteristic
298C22×C17#53411yescharacteristic
299C22×C17#53812yes—
300C22×C17#53812yes—
301C22×C17#54012yes—
302C22×C17#54012yes—
303C22×C17#54311yescharacteristic
304C22×C17#54311yescharacteristic
305C22×C17#54612yes—
306C22×C17#54612yes—
307C22×C17#55112yes—
308C22×C17#55412yes—
309C22×C17#55412yes—
310C22×C17#55511yescharacteristic
311C22×C17#55511yescharacteristic
312C22×C17#56012yes—
313C22×C17#56011yescharacteristic
314C22×C17#56011yescharacteristic
315C2×D17—28no—
316C2×D17—28no—
317C2×D17—28no—
318C2×D17—44no—
319C2×D17—44no—
320C2×D17—44no—
321C2×D17—44no—
322C2×D17—44no—
323C2×D17—44no—
324C2×D17—44no—
325C2×D17—44no—
326C2×D17—44no—
327C2×D17—44no—
328C2×D17—44no—
329C2×D17—44no—
330C4×C17—24no—
331C4×C17—42no—
332C4×C17—42no—
333C4×C17—44no—
334C4×C17—82no—
335Dic17—44no—
336Dic17—44no—
337Dic17—82no—
338C23×D4—171no—
339C24×C4—172no—
340C22×C4⋊C4—171no—
341C22×C4⋊C4C2×D1711yescharacteristic
342C22×C4⋊C4C2×D1711yescharacteristic
343C22×C22⋊C4—172no—
344C22×C22⋊C4—172no—
345C22×C22⋊C4—172no—
346C22×C22⋊C4—172no—
347C22×C22⋊C4—172no—
348C22×C42—171no—
349#390—178no—
350#386—348no—
351C2×#95—172no—
352C2×#95—172no—
353C2×#95—172no—
354C2×#95—172no—
355C2×#95—171no—
356C2×#95—172no—
357C2×#95—172no—
358C2×#95C2×D1712yes—
359C2×#95C2×D1711yescharacteristic
360C2×#95C2×D1712yes—
361C2×C17#231511yescharacteristic
362C2×C17#233312yes—
363C2×C17#234912yes—
364C2×C17#237211yescharacteristic
365C2×C17#238011yescharacteristic
366C2×C17#269712yes—
367C2×C17#269911yescharacteristic
368C2×C17#269911yescharacteristic
369C2×C17#274812yes—
370C2×C17#278411yescharacteristic
371C2×C17#278411yescharacteristic
372D17—48no—
373C25—172no—
374C22×D4—174no—
375C22×D4—174no—
376C22×D4—174no—
377C22×D4—681no—
378C22×D4—681no—
379C22×D4—681no—
380C22×D4—681no—
381C23×C4—172no—
382C23×C4—172no—
383C23×C4—172no—
384C23×C4—344no—
385C23×C4—344no—
386C23×C4—344no—
387C23×C4—682no—
388C23×C4—682no—
389C23×C4—682no—
390C23×C4—682no—
391C23×C4C22×D1712yes—
392C23×C4C22×D1711yescharacteristic
393C23×C4C22×D1711yescharacteristic
394C23×C4C22×D1712yes—
395C23×C4C22×D1711yescharacteristic
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—681no—
401C2×C4⋊C4—682no—
402C2×C4⋊C4C4×D1714yescomplemented
403C2×C22⋊C4—178no—
404C2×C22⋊C4—178no—
405C2×C22⋊C4—344no—
406C2×C22⋊C4—344no—
407C2×C22⋊C4—344no—
408C2×C22⋊C4—344no—
409C2×C22⋊C4—344no—
410C2×C22⋊C4—682no—
411C2×C22⋊C4—682no—
412C2×C22⋊C4—682no—
413C2×C22⋊C4—682no—
414C2×C22⋊C4—682no—
415C2×C22⋊C4—682no—
416C2×C22⋊C4—682no—
417C2×C22⋊C4—682no—
418C2×C42—174no—
419C2×C42—681no—
420C2×C42—681no—
421#95—24no—
422#95—42no—
423#95—41no—
424#95—344no—
425#95—344no—
426#95—344no—
427#95—681no—
428#95—682no—
429#95—682no—
430#95—682no—
431C17#1448611yescharacteristic, complemented, Sylow
432C24—174no—
433C24—174no—
434C24—174no—
435C24—342no—
436C24—342no—
437C24—342no—
438C24—342no—
439C24—342no—
440C24—342no—
441C24—342no—
442C24—342no—
443C24—342no—
444C24—342no—
445C24—342no—
446C24—342no—
447C24C23×D1711yescharacteristic
448C2×D4—1716no—
449C2×D4—684no—
450C2×D4—684no—
451C2×D4—684no—
452C2×D4—684no—
453C2×D4—684no—
454C2×D4—684no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—174no—
481C22×C4—174no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
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×C4—342no—
501C22×C4—688no—
502C22×C4—688no—
503C22×C4—688no—
504C22×C4—688no—
505C22×C4—688no—
506C22×C4—688no—
507C22×C4—688no—
508C22×C4C2×C4×D1712yes—
509C22×C4C2×C4×D1712yes—
510C22×C4C2×C4×D1712yes—
511C22×C4D4×D1712yes—
512C22×C4Q8×D1712yes—
513C22×C4#6325614yes—
514C4⋊C4—44no—
515C4⋊C4—44no—
516C4⋊C4—684no—
517C22⋊C4—688no—
518C22⋊C4—688no—
519C22⋊C4—688no—
520C22⋊C4—688no—
521C22⋊C4—688no—
522C42—684no—
523C23—178no—
524C23—344no—
525C23—344no—
526C23—344no—
527C23—344no—
528C23—344no—
529C23—344no—
530C23—344no—
531C23—344no—
532C23—344no—
533C23—344no—
534C23—344no—
535C23—344no—
536C23—344no—
537C23—344no—
538C23—344no—
539C23—344no—
540C23—344no—
541C23—344no—
542C23—682no—
543C23—682no—
544C23—682no—
545C23—682no—
546C23—682no—
547C23—682no—
548C23—682no—
549C23—682no—
550C23—682no—
551C23—682no—
552C23—682no—
553C23—682no—
554C23—682no—
555C23—682no—
556C23—682no—
557C23—682no—
558C23C22×C4×D1711yescharacteristic
559C23C2×D4×D1711yescharacteristic
560C23#1058769112yes—
561C23#1058769111yescharacteristic
562C23#1058769111yescharacteristic
563C23C2×Q8×D1711yescharacteristic
564C23C2×#6325612yes—
565C23#41×D1712yes—
566C23#1058769612yes—
567C23#1058769611yescharacteristic
568C23#1058769611yescharacteristic
569D4—6816no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—344no—
601C2×C4—344no—
602C2×C4—344no—
603C2×C4—344no—
604C2×C4—344no—
605C2×C4—344no—
606C2×C4—6832no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4—682no—
610C2×C4—682no—
611C2×C4—682no—
612C2×C4—682no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—682no—
616C2×C4—682no—
617C2×C4—682no—
618C2×C4—682no—
619C2×C4—682no—
620C2×C4—682no—
621C2×C4—682no—
622C2×C4C4⋊C4×D1714yes—
623C22—348no—
624C22—348no—
625C22—348no—
626C22—684no—
627C22—684no—
628C22—684no—
629C22—684no—
630C22—684no—
631C22—684no—
632C22—684no—
633C22—684no—
634C22—684no—
635C22—684no—
636C22—684no—
637C22—684no—
638C22C2×C4⋊C4×D1711yescharacteristic
639C22C4×#6325612yes—
640C22#1176328112yes—
641C22#1176328211yescharacteristic
642C22#1176328311yescharacteristic
643C22#1176336711yescharacteristic
644C22#1176336711yescharacteristic
645C22#1176339812yes—
646C22#1176339912yes—
647C22#1176341112yes—
648C22#1176341512yes—
649C22#1176343411yescharacteristic
650C22#1176343411yescharacteristic
651C22#1176345012yes—
652C22#1176345612yes—
653C22#1176348612yes—
654C22#1176351512yes—
655C22#1176352012yes—
656C22#1176352111yescharacteristic
657C22#1176352511yescharacteristic
658C22#1176354712yes—
659C22#1176354811yescharacteristic
660C22#1176354911yescharacteristic
661C4—24no—
662C4—42no—
663C4—42no—
664C4—44no—
665C4—82no—
666C4—684no—
667C4—684no—
668C4—1362no—
669C2—688no—
670C2#1453139711yescharacteristic
671C2#1453154812yes—
672C2#1453169312yes—
673C2#1453189511yescharacteristic
674C2#1453195911yescharacteristic
675C2#1453534212yes—
676C2#1453536611yescharacteristic
677C2#1453537011yescharacteristic
678C2#1453599612yes—
679C2#1453648411yescharacteristic
680C2#1453648711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1441D17
hypocenterC17#14486
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #14527037C2semidirect
4. #14527030C2semidirect
5. #14527026C2semidirect
6. #14527010C2semidirect
7. #14527005C2semidirect
8. #14527005C2semidirect
9. C17×#1441C2semidirect
19. #11762710C4semidirect
60. C2×C4⋊C4×C17C2×C4semidirect
74. C2×#63227C2×C4semidirect
75. C2×#63227C2×C4semidirect
80. C2×C4×Dic17C2×C4semidirect
165. C2×D68C4⋊C4semidirect
286. #1441D17semidirect
402. C2×C4⋊C4C4×D17semidirect
431. C17#14486semidirect

Maximal subgroups

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

subgroupindex
C2×#117627102
C2×#117626872
#145270372
#145270302
#145270262
#145270102
#145270052
C17×#14412
#1448617