Finite Group Databasebeta

← #16961355

Subgroups — #16961355

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762734C211yesmaximal, characteristic
2C2×#11762707C211yesmaximal, characteristic, complemented
3#14527051C211yesmaximal, characteristic, complemented
4#14527042C212yesmaximal, complemented
5#14527040C211yesmaximal, characteristic, complemented
6#14527029C211yesmaximal, characteristic
7#14527027C212yesmaximal
8#14527021C212yesmaximal
9#14527016C212yesmaximal, complemented
10C4×#10587502C211yesmaximal, characteristic, complemented
11C2×C17×#388C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×#63225C2212yes—
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×C4×Dic17C2212yes—
18#11762734C418yescomplemented
19#11762707—24no—
20C2×#10587502C2212yes—
21C2×#10587502C2211yescharacteristic
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2212yes—
30C22×C4⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2211yescharacteristic
32C22×C22⋊C4×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2211yescharacteristic
34C22×C42×C17C2211yescharacteristic
35C17×#388—24no—
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C25×C17C2311yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2312yes—
47C23×Dic17C2312yes—
48C23×Dic17C2312yes—
49C2×C4⋊C4×C17—22no—
50C2×C4⋊C4×C17—24no—
51C2×C22⋊C4×C17—22no—
52C2×C22⋊C4×C17—22no—
53C2×C22⋊C4×C17—22no—
54C2×C22⋊C4×C17—22no—
55C2×C22⋊C4×C17—24no—
56C2×C22⋊C4×C17—42no—
57C2×C22⋊C4×C17C2×C414yes—
58C2×C42×C17—42no—
59C2×C42×C17D414yes—
60C2×C22⋊Dic17—24no—
61C2×C22⋊Dic17—42no—
62C2×C22⋊Dic17—42no—
63C2×C22⋊Dic17—42no—
64C2×C22⋊Dic17—42no—
65C2×C22⋊Dic17C2×C418yes—
66C2×C4⋊Dic17—22no—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17—22no—
69C2×C4⋊Dic17—42no—
70C2×C4⋊Dic17C2×C414yes—
71C2×#63225—24no—
72C2×#63225—42no—
73C2×#63225—42no—
74C2×C4×Dic17—24no—
75C2×C4×Dic17—42no—
76C2×C4×Dic17—42no—
77C17×#95—22no—
78C17×#95—22no—
79#10587502—24no—
80#10587502—22no—
81#10587502—24no—
82#10587502—24no—
83#10587502—42no—
84#10587502—42no—
85#10587502—42no—
86#10587502—42no—
87#10587502C2×C414yes—
88#10587502C2×C418yes—
89C24×C17—21no—
90C24×C17—22no—
91C24×C17—21no—
92C24×C17—22no—
93C24×C17—21no—
94C24×C17—21no—
95C24×C17—21no—
96C24×C17—22no—
97C24×C17—22no—
98C24×C17—21no—
99C24×C17C22×C412yes—
100C24×C17C2411yescharacteristic
101C22×C4×C17—21no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—21no—
110C22×C4×C17—22no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—22no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—21no—
124C22×C4×C17C22×C412yes—
125C22×C4×C17C22×C412yes—
126C22×C4×C17C2×D412yes—
127C22×C4×C17C2×D412yes—
128C22×C4×C17C2×D412yes—
129C22×C4×C17#4112yes—
130C22×C4×C17#4114yes—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
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×Dic17C22×C414yes—
157C22×Dic17C22×C414yes—
158C22×Dic17#4114yes—
159C4⋊C4×C17—44no—
160C22⋊C4×C17—28no—
161C22⋊C4×C17—44no—
162C22⋊C4×C17—44no—
163C42×C17—44no—
164C22⋊Dic17—48no—
165C22⋊Dic17—48no—
166C4⋊Dic17—28no—
167C4⋊Dic17—44no—
168#63225—48no—
169C4×Dic17—48no—
170#14324—171nomaximal, Sylow
171C23×C17—22no—
172C23×C17—24no—
173C23×C17—22no—
174C23×C17—24no—
175C23×C17—22no—
176C23×C17—41no—
177C23×C17—42no—
178C23×C17—41no—
179C23×C17—41no—
180C23×C17—41no—
181C23×C17—41no—
182C23×C17—41no—
183C23×C17—42no—
184C23×C17—42no—
185C23×C17—42no—
186C23×C17—42no—
187C23×C17—42no—
188C23×C17—42no—
189C23×C17—41no—
190C23×C17—42no—
191C23×C17—42no—
192C23×C17—42no—
193C23×C17—41no—
194C23×C17C23×C411yescharacteristic
195C23×C17C22×D411yescharacteristic
196C23×C17C2×#4111yescharacteristic
197C23×C17C2×#4112yes—
198C23×C17C2×#4112yes—
199C23×C17H(5,𝔽2)12yes—
200C23×C17H(5,𝔽2)11yescharacteristic
201C23×C17H(5,𝔽2)11yescharacteristic
202C23×C17H(5,𝔽2)11yescharacteristic
203C23×C172−1+412yes—
204C23×C172−1+411yescharacteristic
205C2×C4×C17—24no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—24no—
211C2×C4×C17—24no—
212C2×C4×C17—24no—
213C2×C4×C17—22no—
214C2×C4×C17—24no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—41no—
219C2×C4×C17—42no—
220C2×C4×C17—41no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17C4×D414yes—
234C2×C4×C17#12414yes—
235C2×Dic17—24no—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—24no—
239C2×Dic17—24no—
240C2×Dic17—24no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×#397—171no—
264C2×#389—171no—
265C2×#388D1711yescharacteristic
266#1445—171no—
267#1442—171no—
268#1442—172no—
269#1439—172no—
270#1439—171no—
271#1437—172no—
272#1436—172no—
273C4×#95—171no—
274C22×C17—42no—
275C22×C17—42no—
276C22×C17—44no—
277C22×C17—44no—
278C22×C17—42no—
279C22×C17—81no—
280C22×C17—81no—
281C22×C17—82no—
282C22×C17—82no—
283C22×C17—81no—
284C22×C17—81no—
285C22×C17C2×C4×D411yescharacteristic
286C22×C17C4×#4112yes—
287C22×C17#51811yescharacteristic
288C22×C17#52012yes—
289C22×C17#52011yescharacteristic
290C22×C17C2×#12411yescharacteristic
291C22×C17#52912yes—
292C22×C17#53211yescharacteristic
293C22×C17#53411yescharacteristic
294C22×C17#53511yescharacteristic
295C22×C17#53611yescharacteristic
296C22×C17#53711yescharacteristic
297C22×C17#53812yes—
298C22×C17#53812yes—
299C22×C17#53912yes—
300C22×C17#53912yes—
301C22×C17#53912yes—
302C22×C17#54012yes—
303C22×C17#54011yescharacteristic
304C22×C17#54112yes—
305C22×C17#54212yes—
306C22×C17#54212yes—
307C22×C17#54211yescharacteristic
308C4×C17—24no—
309C4×C17—24no—
310C4×C17—42no—
311C4×C17—42no—
312C4×C17—81no—
313C4×C17—81no—
314Dic17—44no—
315Dic17—44no—
316Dic17—44no—
317Dic17—82no—
318C22×C4⋊C4—171no—
319C22×C4⋊C4—172no—
320C22×C4⋊C4—171no—
321C22×C4⋊C4C2×D1711yescharacteristic
322C22×C22⋊C4—172no—
323C22×C22⋊C4—172no—
324C22×C22⋊C4C2×D1711yescharacteristic
325C22×C22⋊C4C2×D1711yescharacteristic
326C22×C22⋊C4C2×D1711yescharacteristic
327C22×C42—172no—
328C22×C42C2×D1711yescharacteristic
329#397—178no—
330#389—344no—
331#388—24no—
332C2×#95—171no—
333C2×#95—172no—
334C2×#95—172no—
335C2×#95—171no—
336C2×#95—172no—
337C2×#95—172no—
338C2×#95—172no—
339C2×#95—172no—
340C2×#95—172no—
341C2×#95—172no—
342C2×#95C2×D1711yescharacteristic
343C2×#95C2×D1711yescharacteristic
344C2×C17—82no—
345C2×C17C4×#12411yescharacteristic
346C2×C17#232211yescharacteristic
347C2×C17#232411yescharacteristic
348C2×C17#233412yes—
349C2×C17#233512yes—
350C2×C17#263911yescharacteristic
351C2×C17#264011yescharacteristic
352C2×C17#264912yes—
353C2×C17#265412yes—
354C2×C17#266111yescharacteristic
355C2×C17#266411yescharacteristic
356C25C22×D1711yescharacteristic
357C23×C4—172no—
358C23×C4—172no—
359C23×C4—172no—
360C23×C4—172no—
361C23×C4C22×D1711yescharacteristic
362C23×C4C22×D1711yescharacteristic
363C23×C4C22×D1711yescharacteristic
364C23×C4C22×D1711yescharacteristic
365C23×C4C22×D1711yescharacteristic
366C23×C4C22×D1711yescharacteristic
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—174no—
370C2×C4⋊C4—342no—
371C2×C4⋊C4—342no—
372C2×C4⋊C4—344no—
373C2×C4⋊C4—342no—
374C2×C4⋊C4—682no—
375C2×C4⋊C4—682no—
376C2×C4⋊C4—682no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—178no—
384C2×C22⋊C4—344no—
385C2×C22⋊C4—682no—
386C2×C22⋊C4—682no—
387C2×C22⋊C4—682no—
388C2×C22⋊C4—682no—
389C2×C22⋊C4C4×D1714yes—
390C2×C42—42no—
391C2×C42—344no—
392C2×C42—682no—
393C2×C42—682no—
394C2×C42C22⋊D1714yes—
395#95—22no—
396#95—22no—
397#95—174no—
398#95—178no—
399#95—344no—
400#95—344no—
401#95—342no—
402#95—344no—
403#95—682no—
404#95—682no—
405#95—682no—
406#95—682no—
407C17#1432411yescharacteristic, complemented, Sylow
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24C2×C4×D1712yes—
419C24C23×D1711yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—174no—
444C22×C4—174no—
445C22×C4—174no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—342no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4C2×C4×D1712yes—
472C22×C4C2×C4×D1712yes—
473C22×C4#6325212yes—
474C22×C4#6325414yes—
475C22×C4C2×C22⋊D1712yes—
476C22×C4C2×C22⋊D1712yes—
477C22×C4C2×C22⋊D1712yes—
478C4⋊C4—44no—
479C4⋊C4—348no—
480C4⋊C4—688no—
481C4⋊C4—684no—
482C22⋊C4—28no—
483C22⋊C4—44no—
484C22⋊C4—44no—
485C22⋊C4—688no—
486C22⋊C4—688no—
487C42—44no—
488C42—688no—
489C23—22no—
490C23—24no—
491C23—22no—
492C23—24no—
493C23—22no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23C22×C4×D1711yescharacteristic
513C23C2×#6325211yescharacteristic
514C23C2×#6325412yes—
515C23#1058769112yes—
516C23#41×D1712yes—
517C23#1058769611yescharacteristic
518C23#1058769611yescharacteristic
519C23#1058769611yescharacteristic
520C23#1058769712yes—
521C23#1058769711yescharacteristic
522C23C22×C22⋊D1711yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—344no—
552C2×C4—344no—
553C2×C4—344no—
554C2×C4—344no—
555C2×C4—344no—
556C2×C4—344no—
557C2×C4—344no—
558C2×C4—344no—
559C2×C4—344no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4—682no—
564C2×C4—682no—
565C2×C4—682no—
566C2×C4—682no—
567C2×C4—682no—
568C2×C4—682no—
569C2×C4—682no—
570C2×C4—682no—
571C2×C4—682no—
572C2×C4—682no—
573C2×C4—682no—
574C2×C4—682no—
575C2×C4—682no—
576C2×C4—682no—
577C2×C4—682no—
578C2×C4—682no—
579C2×C4C4×C22⋊D1714yes—
580C2×C4#1058762214yes—
581C22—42no—
582C22—42no—
583C22—44no—
584C22—44no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—82no—
591C22—82no—
592C22C2×C4×C22⋊D1711yescharacteristic
593C22C4×#6325412yes—
594C22#1176328311yescharacteristic
595C22#1176328812yes—
596C22#1176328911yescharacteristic
597C22C2×#1058762211yescharacteristic
598C22#1176334112yes—
599C22#1176335511yescharacteristic
600C22#1176336811yescharacteristic
601C22#1176337311yescharacteristic
602C22#1176338011yescharacteristic
603C22#1176338711yescharacteristic
604C22#1176339512yes—
605C22#1176339612yes—
606C22#1176340012yes—
607C22#1176340112yes—
608C22#1176340412yes—
609C22#1176341112yes—
610C22#1176341411yescharacteristic
611C22#1176341612yes—
612C22#1176342812yes—
613C22#1176342812yes—
614C22#1176343011yescharacteristic
615C4—24no—
616C4—24no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—684no—
622C4—684no—
623C4—684no—
624C4—1362no—
625C2—82no—
626C2C4×#1058762211yescharacteristic
627C2#1453144911yescharacteristic
628C2#1453147711yescharacteristic
629C2#1453155612yes—
630C2#1453156712yes—
631C2#1453471711yescharacteristic
632C2#1453472411yescharacteristic
633C2#1453479112yes—
634C2#1453486612yes—
635C2#1453491211yescharacteristic
636C2#1453494611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#14324
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762707C2semidirect
3. #14527051C2semidirect
4. #14527042C2semidirect
5. #14527040C2semidirect
9. #14527016C2semidirect
10. C4×#10587502C2semidirect
18. #11762734C4semidirect
407. C17#14324semidirect

Maximal subgroups

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

subgroupindex
C2×#117627342
C2×#117627072
#145270512
#145270422
#145270402
#145270292
#145270272
#145270212
#145270162
C4×#105875022
C2×C17×#3882
#1432417