Finite Group Databasebeta

← #16961347

Subgroups — #16961347

Order 4352.

1454 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762716C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic
3#14527055C211yesmaximal, characteristic, complemented
4#14527046C212yesmaximal, complemented
5#14527041C211yesmaximal, characteristic, complemented
6#14527033C212yesmaximal
7#14527029C211yesmaximal, characteristic
8#14527021C212yesmaximal
9#14527018C212yesmaximal, complemented
10#95×Dic17C211yesmaximal, characteristic, complemented
11C2×C17×#393C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C22⋊Dic17C2211yescharacteristic
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C4×Dic17C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19#11762716—24no—
20#11762702—24no—
21C2×#10587502C2211yescharacteristic
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2211yescharacteristic
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C23×Q8×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2212yes—
35C17×#393C418yescomplemented
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2212yes—
38C25×C17C2311yescharacteristic
39C22×Q8×C17—22no—
40C22×Q8×C17—22no—
41C22×Q8×C17—42no—
42C22×Q8×C17—42no—
43C22×Q8×C17C2×C414yes—
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2312yes—
47C23×C4×C17C2311yescharacteristic
48C23×Dic17C2312yes—
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2311yescharacteristic
54C2×C22⋊C4×C17—22no—
55C2×C22⋊C4×C17—22no—
56C2×C22⋊C4×C17—42no—
57C2×C22⋊C4×C17—42no—
58C2×C22⋊C4×C17C2×C414yes—
59C2×C22⋊C4×C17C2×C418yes—
60C2×C22⋊Dic17—22no—
61C2×C22⋊Dic17—22no—
62C2×C22⋊Dic17—24no—
63C2×C22⋊Dic17—24no—
64C2×C22⋊Dic17—42no—
65C2×C22⋊Dic17—42no—
66C2×C22⋊Dic17—42no—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17—22no—
69C2×C4⋊Dic17—24no—
70C2×C4⋊Dic17—42no—
71C2×C4×Dic17—24no—
72C2×C4×Dic17—42no—
73C2×C4×Dic17—42no—
74C2×C4×Dic17—42no—
75C2×C4×Dic17D414yes—
76C17×#95C2×C418yes—
77C17×#95C2×C414yes—
78#10587502—22no—
79#10587502—22no—
80#10587502—22no—
81#10587502—24no—
82#10587502—24no—
83#10587502—24no—
84#10587502—24no—
85#10587502—42no—
86#10587502—42no—
87#10587502—42no—
88#10587502—42no—
89C24×C17—21no—
90C24×C17—22no—
91C24×C17—22no—
92C24×C17—21no—
93C24×C17—21no—
94C24×C17—22no—
95C24×C17—22no—
96C24×C17—21no—
97C24×C17—21no—
98C24×C17—21no—
99C24×C17C22×C412yes—
100C24×C17C2411yescharacteristic
101C2×Q8×C17—28no—
102C2×Q8×C17—48no—
103C2×Q8×C17—44no—
104C2×Q8×C17—44no—
105C2×Q8×C17—48no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—21no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—21no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17C22×C414yes—
125C22×C4×C17C22×C412yes—
126C22×C4×C17C22×C414yes—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C2×D412yes—
129C22×C4×C17#4112yes—
130C22×Dic17—22no—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—21no—
141C22×Dic17—22no—
142C22×Dic17—21no—
143C22×Dic17—22no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—21no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—22no—
159C22×Dic17—21no—
160C22×Dic17C2×D412yes—
161C22×Dic17C2×D412yes—
162C22×Dic17#4114yes—
163C22×Dic17#4114yes—
164C22⋊C4×C17—28no—
165C22⋊C4×C17—48no—
166C22⋊Dic17—44no—
167C22⋊Dic17—48no—
168C22⋊Dic17—44no—
169C4⋊Dic17—44no—
170C4⋊Dic17—44no—
171C4×Dic17—44no—
172C4×Dic17—48no—
173#14323—171nomaximal, Sylow
174C23×C17—22no—
175C23×C17—24no—
176C23×C17—24no—
177C23×C17—22no—
178C23×C17—22no—
179C23×C17—41no—
180C23×C17—42no—
181C23×C17—41no—
182C23×C17—41no—
183C23×C17—41no—
184C23×C17—41no—
185C23×C17—41no—
186C23×C17—42no—
187C23×C17—42no—
188C23×C17—42no—
189C23×C17—42no—
190C23×C17—42no—
191C23×C17—41no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—41no—
197C23×C17C23×C411yescharacteristic
198C23×C17C22×D411yescharacteristic
199C23×C17C2×#4111yescharacteristic
200C23×C17C2×#4112yes—
201C23×C17C2×#4112yes—
202C23×C17H(5,𝔽2)12yes—
203C23×C17H(5,𝔽2)12yes—
204C23×C17H(5,𝔽2)11yescharacteristic
205C23×C172−1+411yescharacteristic
206C23×C172−1+411yescharacteristic
207C23×C172−1+411yescharacteristic
208Q8×C17—416no—
209C2×C4×C17—24no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—24no—
213C2×C4×C17—22no—
214C2×C4×C17—24no—
215C2×C4×C17—24no—
216C2×C4×C17—24no—
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—24no—
220C2×C4×C17—24no—
221C2×C4×C17—41no—
222C2×C4×C17—42no—
223C2×C4×C17—41no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17C4×D414yes—
233C2×Dic17—22no—
234C2×Dic17—22no—
235C2×Dic17—24no—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—42no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—42no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—42no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17#12414yes—
267C2×#393D1711yescharacteristic
268C2×#391—171no—
269C2×#388—171no—
270#1446—171no—
271#1443—172no—
272#1442—171no—
273#1440—172no—
274#1439—171no—
275#1437—172no—
276#1436—172no—
277C4×#95—171no—
278C22×C17—42no—
279C22×C17—42no—
280C22×C17—44no—
281C22×C17—44no—
282C22×C17—42no—
283C22×C17—81no—
284C22×C17—81no—
285C22×C17—82no—
286C22×C17—82no—
287C22×C17—81no—
288C22×C17—81no—
289C22×C17C2×C4×D411yescharacteristic
290C22×C17C4×#4112yes—
291C22×C17#51812yes—
292C22×C17#51911yescharacteristic
293C22×C17#52011yescharacteristic
294C22×C17C2×#12411yescharacteristic
295C22×C17#52912yes—
296C22×C17#53211yescharacteristic
297C22×C17#53411yescharacteristic
298C22×C17#53511yescharacteristic
299C22×C17#53611yescharacteristic
300C22×C17#53711yescharacteristic
301C22×C17#53812yes—
302C22×C17#53812yes—
303C22×C17#53812yes—
304C22×C17#53912yes—
305C22×C17#53912yes—
306C22×C17#54111yescharacteristic
307C22×C17#54212yes—
308C22×C17#54212yes—
309C22×C17#54212yes—
310C22×C17#54212yes—
311C22×C17#54211yescharacteristic
312C4×C17—24no—
313C4×C17—44no—
314C4×C17—44no—
315C4×C17—42no—
316Dic17—24no—
317Dic17—44no—
318Dic17—42no—
319Dic17—81no—
320Dic17—81no—
321Dic17—82no—
322C23×Q8C2×D1711yescharacteristic
323C22×C4⋊C4—171no—
324C22×C4⋊C4—171no—
325C22×C22⋊C4—171no—
326C22×C22⋊C4—172no—
327C22×C22⋊C4—171no—
328C22×C22⋊C4C2×D1711yescharacteristic
329C22×C22⋊C4C2×D1712yes—
330C22×C42—171no—
331C22×C42—172no—
332#393Dic1718yescomplemented
333#391—344no—
334#388—344no—
335C2×#95—171no—
336C2×#95—172no—
337C2×#95—172no—
338C2×#95—172no—
339C2×#95—172no—
340C2×#95—171no—
341C2×#95—171no—
342C2×#95—172no—
343C2×#95—172no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95C2×D1711yescharacteristic
347C2×#95C2×D1712yes—
348C2×C17—82no—
349C2×C17C4×#12411yescharacteristic
350C2×C17#232111yescharacteristic
351C2×C17#232311yescharacteristic
352C2×C17#233212yes—
353C2×C17#233712yes—
354C2×C17#263911yescharacteristic
355C2×C17#264011yescharacteristic
356C2×C17#265012yes—
357C2×C17#265312yes—
358C2×C17#266211yescharacteristic
359C2×C17#266311yescharacteristic
360C25C22×D1711yescharacteristic
361C22×Q8—22no—
362C22×Q8—22no—
363C22×Q8—42no—
364C22×Q8—42no—
365C22×Q8C2×Dic1714yes—
366C23×C4—171no—
367C23×C4—171no—
368C23×C4—172no—
369C23×C4—172no—
370C23×C4—171no—
371C23×C4—171no—
372C23×C4C22×D1711yescharacteristic
373C23×C4C22×D1712yes—
374C23×C4C22×D1712yes—
375C23×C4C22×D1711yescharacteristic
376C2×C4⋊C4—342no—
377C2×C4⋊C4—344no—
378C2×C4⋊C4—342no—
379C2×C4⋊C4—682no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—342no—
385C2×C22⋊C4—342no—
386C2×C22⋊C4—344no—
387C2×C22⋊C4—344no—
388C2×C22⋊C4—682no—
389C2×C22⋊C4—682no—
390C2×C22⋊C4—682no—
391C2×C22⋊C4C2×Dic1714yes—
392C2×C22⋊C4C2×Dic1718yes—
393C2×C42—174no—
394C2×C42—344no—
395C2×C42—682no—
396C2×C42—682no—
397C2×C42—682no—
398#95—344no—
399#95—344no—
400#95—342no—
401#95—344no—
402#95—344no—
403#95—342no—
404#95—342no—
405#95—682no—
406#95—682no—
407#95—682no—
408#95—682no—
409#95C2×Dic1718yes—
410#95C2×Dic1714yes—
411C17#1432311yescharacteristic, complemented, Sylow
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24C22×Dic1712yes—
423C24C23×D1711yescharacteristic
424C2×Q8—28no—
425C2×Q8—48no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—48no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—172no—
448C22×C4—174no—
449C22×C4—172no—
450C22×C4—174no—
451C22×C4—342no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—341no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—342no—
466C22×C4—341no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—341no—
479C22×C4—342no—
480C22×C4—341no—
481C22×C4D4×D1712yes—
482C22×C4#6325412yes—
483C22×C4C22×Dic1712yes—
484C22×C4C22×Dic1714yes—
485C22×C4C22×Dic1714yes—
486C22×C4C22×Dic1712yes—
487C4⋊C4—684no—
488C4⋊C4—684no—
489C22⋊C4—28no—
490C22⋊C4—48no—
491C22⋊C4—684no—
492C22⋊C4—684no—
493C22⋊C4—688no—
494C42—684no—
495C42—688no—
496C23—22no—
497C23—24no—
498C23—24no—
499C23—22no—
500C23—22no—
501C23—41no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23C2×D4×D1711yescharacteristic
520C23C2×#6325411yescharacteristic
521C23#1058769112yes—
522C23#1058769112yes—
523C23#1058769411yescharacteristic
524C23#1058769411yescharacteristic
525C23#41×D1712yes—
526C23#41×D1712yes—
527C23#1058769611yescharacteristic
528C23#1058769711yescharacteristic
529C23C23×Dic1711yescharacteristic
530Q8—416no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—174no—
555C2×C4—342no—
556C2×C4—342no—
557C2×C4—344no—
558C2×C4—344no—
559C2×C4—344no—
560C2×C4—342no—
561C2×C4—342no—
562C2×C4—342no—
563C2×C4—344no—
564C2×C4—344no—
565C2×C4—682no—
566C2×C4—682no—
567C2×C4—682no—
568C2×C4—682no—
569C2×C4—682no—
570C2×C4—682no—
571C2×C4—681no—
572C2×C4—681no—
573C2×C4—682no—
574C2×C4—681no—
575C2×C4—682no—
576C2×C4—681no—
577C2×C4—681no—
578C2×C4—682no—
579C2×C4—681no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—682no—
583C2×C4—682no—
584C2×C4—682no—
585C2×C4—682no—
586C2×C4—682no—
587C2×C4—682no—
588C2×C4D4×Dic1714yes—
589C22—42no—
590C22—44no—
591C22—42no—
592C22—42no—
593C22—44no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22C2×D4×Dic1711yescharacteristic
601C22#41×Dic1712yes—
602C22#1176328412yes—
603C22#1176328711yescharacteristic
604C22#1176329211yescharacteristic
605C22#124×D1711yescharacteristic
606C22#1176333812yes—
607C22#1176335811yescharacteristic
608C22#1176336911yescharacteristic
609C22#1176337411yescharacteristic
610C22#1176338211yescharacteristic
611C22#1176338911yescharacteristic
612C22#1176339312yes—
613C22#1176339312yes—
614C22#1176339412yes—
615C22#1176340512yes—
616C22#1176340512yes—
617C22#1176341911yescharacteristic
618C22#1176342312yes—
619C22#1176342312yes—
620C22#1176342912yes—
621C22#1176342912yes—
622C22#1176343211yescharacteristic
623C4—24no—
624C4—42no—
625C4—44no—
626C4—44no—
627C4—344no—
628C4—682no—
629C4—684no—
630C4—1362no—
631C4—1361no—
632C4—1361no—
633C2—82no—
634C2#124×Dic1711yescharacteristic
635C2#1453144511yescharacteristic
636C2#1453146811yescharacteristic
637C2#1453154212yes—
638C2#1453159912yes—
639C2#1453471311yescharacteristic
640C2#1453472211yescharacteristic
641C2#1453479912yes—
642C2#1453484412yes—
643C2#1453493011yescharacteristic
644C2#1453494011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#393C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#393D17
hypocenterC17#14323
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×#11762716C2semidirect
3. #14527055C2semidirect
4. #14527046C2semidirect
5. #14527041C2semidirect
9. #14527018C2semidirect
10. #95×Dic17C2semidirect
35. C17×#393C4semidirect
332. #393Dic17semidirect
411. C17#14323semidirect

Maximal subgroups

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

subgroupindex
C2×#117627162
C2×#117627022
#145270552
#145270462
#145270412
#145270332
#145270292
#145270212
#145270182
#95×Dic172
C2×C17×#3932
#1432317