Finite Group Databasebeta

← #16962783

Subgroups — #16962783

Order 4352.

1658 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762711C211yesmaximal, characteristic
2C2×#11762699C212yesmaximal, complemented
3#14527032C212yesmaximal, complemented
4#14527026C212yesmaximal, complemented
5#14527024C212yesmaximal
6#14527020C212yesmaximal, complemented
7#14527018C212yesmaximal, complemented
8#14527011C211yesmaximal, characteristic, complemented
9C17×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D68C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63227C2212yes—
13C22×#63227C2212yes—
14C22×#63227C2212yes—
15C22×#63227C2212yes—
16C22×#63227C2212yes—
17C22×#63227C2212yes—
18C22×C4×Dic17C2212yes—
19#11762711C418yescomplemented
20#11762699—28no—
21C2×#10587502C2212yes—
22C2×#10587502C2211yescharacteristic
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2211yescharacteristic
28C22×C4⋊C4×C17C2212yes—
29C22×C42×C17C2211yescharacteristic
30C2×C17×#95C2212yes—
31C2×C17×#95C2211yescharacteristic
32C2×C17×#95C2211yescharacteristic
33C24×D17C2312yes—
34C23×C4×C17C2312yes—
35C23×C4×C17C2311yescharacteristic
36C23×C4×C17C2312yes—
37C23×C4×C17C2311yescharacteristic
38C23×C4×C17C2311yescharacteristic
39C23×Dic17C2312yes—
40C23×Dic17C2312yes—
41C23×Dic17C2312yes—
42C22×D68—22no—
43C22×D68—22no—
44C22×D68—42no—
45C22×D68—42no—
46C22×D68C2×C414yes—
47C2×C4⋊C4×C17—24no—
48C2×C4⋊C4×C17—24no—
49C2×C4⋊C4×C17—42no—
50C2×C42×C17—42no—
51C2×C42×C17C2×C414yes—
52C2×#63227—24no—
53C2×#63227—24no—
54C2×#63227—24no—
55C2×#63227—24no—
56C2×#63227—24no—
57C2×#63227—24no—
58C2×#63227—42no—
59C2×#63227—42no—
60C2×#63227—42no—
61C2×#63227—42no—
62C2×#63227—42no—
63C2×#63227—42no—
64C2×#63227—42no—
65C2×#63227—42no—
66C2×#63227—42no—
67C2×#63227—42no—
68C2×#63227C2×C418yes—
69C2×#63227C2×C418yes—
70C2×C4⋊Dic17—42no—
71C2×C4⋊Dic17C2×C414yes—
72C2×C4×Dic17—24no—
73C2×C4×Dic17—42no—
74C2×C4×Dic17—42no—
75C17×#95—24no—
76C17×#95—41no—
77C17×#95—41no—
78#10587502—24no—
79#10587502—22no—
80#10587502—24no—
81#10587502—42no—
82#10587502—42no—
83#10587502—42no—
84#10587502D414yescomplemented
85C24×C17C2411yescharacteristic
86C23×D17—22no—
87C23×D17—22no—
88C23×D17—22no—
89C23×D17—22no—
90C23×D17—22no—
91C23×D17—22no—
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×D17C22×C414yes—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—22no—
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—21no—
115C22×C4×C17—22no—
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×C17C22×C412yes—
123C22×C4×C17C22×C412yes—
124C22×C4×C17C22×C412yes—
125C22×C4×C17C2×D412yes—
126C22×C4×C17#4114yes—
127C22×C4×C17#4112yes—
128C22×C4×C17#4112yes—
129C22×C4×C17#4112yes—
130C22×Dic17—22no—
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×Dic17C22×C414yes—
150C22×Dic17C2×D414yes—
151C2×D68—28no—
152C2×D68—44no—
153C2×D68—44no—
154C2×D68—48no—
155C2×D68—48no—
156C4⋊C4×C17—48no—
157C42×C17—44no—
158#63227—216no—
159#63227—48no—
160#63227—48no—
161#63227—48no—
162#63227—48no—
163#63227—48no—
164C4⋊Dic17—44no—
165C4×Dic17—48no—
166#14444—171nomaximal, Sylow
167C23×C17C23×C411yescharacteristic
168C23×C17C22×D411yescharacteristic
169C23×C17C2×#4112yes—
170C23×C17C2×#4111yescharacteristic
171C23×C17C2×#4111yescharacteristic
172C23×C17C2×#4111yescharacteristic
173C23×C17H(5,𝔽2)12yes—
174C23×C17H(5,𝔽2)11yescharacteristic
175C23×C17H(5,𝔽2)12yes—
176C23×C17H(5,𝔽2)12yes—
177C23×C172−1+411yescharacteristic
178C22×D17—24no—
179C22×D17—24no—
180C22×D17—24no—
181C22×D17—24no—
182C22×D17—24no—
183C22×D17—24no—
184C22×D17—24no—
185C22×D17—42no—
186C22×D17—42no—
187C22×D17—42no—
188C22×D17—42no—
189C22×D17—42no—
190C22×D17—42no—
191C22×D17—42no—
192C22×D17—42no—
193C22×D17—42no—
194C22×D17—42no—
195C22×D17—42no—
196C22×D17—42no—
197C22×D17—42no—
198C22×D17—42no—
199C22×D17—42no—
200C22×D17—42no—
201C22×D17—42no—
202C22×D17—42no—
203C22×D17—42no—
204C22×D17—42no—
205C22×D17—42no—
206C22×D17—42no—
207C22×D17—42no—
208C22×D17—42no—
209C22×D17—42no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—42no—
213C2×C4×C17—22no—
214C2×C4×C17—22no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—24no—
220C2×C4×C17—24no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—24no—
225C2×C4×C17—24no—
226C2×C4×C17—24no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
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—24no—
243C2×Dic17—24no—
244C2×Dic17—24no—
245C2×Dic17—24no—
246C2×Dic17—24no—
247C2×Dic17—24no—
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—
263D68—416no—
264C2×#390—171no—
265C2×#388—172no—
266#1440—172no—
267#1439—172no—
268#1438—172no—
269#1437—172no—
270#1436—172no—
271C4⋊#95D1711yescharacteristic, complemented
272#1434—171no—
273C22×C17C2×#11711yescharacteristic
274C22×C17C2×C4×D411yescharacteristic
275C22×C17C4×#4111yescharacteristic
276C22×C17#51811yescharacteristic
277C22×C17#51811yescharacteristic
278C22×C17#51811yescharacteristic
279C22×C17#52011yescharacteristic
280C22×C17#53512yes—
281C22×C17#53812yes—
282C22×C17#53812yes—
283C22×C17#53812yes—
284C22×C17#54012yes—
285C22×C17#54212yes—
286C22×C17#54612yes—
287C22×C17#54711yescharacteristic
288C22×C17#55011yescharacteristic
289C22×C17#55312yes—
290C22×C17#55312yes—
291C22×C17#55511yescharacteristic
292C22×C17#55611yescharacteristic
293C22×C17#55912yes—
294C22×C17#56012yes—
295C22×C17#56212yes—
296C2×D17—44no—
297C2×D17—44no—
298C2×D17—44no—
299C2×D17—44no—
300C2×D17—44no—
301C2×D17—44no—
302C2×D17—44no—
303C2×D17—82no—
304C2×D17—82no—
305C2×D17—82no—
306C2×D17—82no—
307C2×D17—82no—
308C2×D17—82no—
309C2×D17—82no—
310C2×D17—82no—
311C4×C17—24no—
312C4×C17—24no—
313C4×C17—42no—
314C4×C17—44no—
315C4×C17—82no—
316Dic17—44no—
317Dic17—44no—
318Dic17—82no—
319C23×D4—171no—
320C22×C4⋊C4—171no—
321C22×C4⋊C4C2×D1712yes—
322C22×C22⋊C4—172no—
323C22×C22⋊C4—172no—
324C22×C22⋊C4—172no—
325C22×C22⋊C4—172no—
326C22×C22⋊C4—172no—
327C22×C22⋊C4—172no—
328C22×C42—172no—
329C22×C42C2×D1711yescharacteristic
330#390—178no—
331#388—348no—
332C2×#95—171no—
333C2×#95—172no—
334C2×#95—171no—
335C2×#95—172no—
336C2×#95—172no—
337C2×#95—172no—
338C2×#95—172no—
339C2×#95C2×D1712yes—
340C2×#95C2×D1711yescharacteristic
341C2×#95C2×D1711yescharacteristic
342C2×C17#231211yescharacteristic
343C2×C17#232811yescharacteristic
344C2×C17#233711yescharacteristic
345C2×C17#235411yescharacteristic
346C2×C17#235711yescharacteristic
347C2×C17#236411yescharacteristic
348C2×C17#237711yescharacteristic
349C2×C17#271012yes—
350C2×C17#271412yes—
351C2×C17#280012yes—
352C2×C17#280312yes—
353D17—84no—
354C25—172no—
355C22×D4—174no—
356C22×D4—342no—
357C22×D4—342no—
358C22×D4—682no—
359C22×D4—682no—
360C23×C4—172no—
361C23×C4—172no—
362C23×C4—172no—
363C23×C4C22×D1712yes—
364C23×C4C22×D1711yescharacteristic
365C23×C4C22×D1712yes—
366C23×C4C22×D1711yescharacteristic
367C23×C4C22×D1711yescharacteristic
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—174no—
372C2×C4⋊C4—682no—
373C2×C22⋊C4—178no—
374C2×C22⋊C4—178no—
375C2×C22⋊C4—344no—
376C2×C22⋊C4—344no—
377C2×C22⋊C4—344no—
378C2×C22⋊C4—344no—
379C2×C22⋊C4—344no—
380C2×C22⋊C4—344no—
381C2×C22⋊C4—682no—
382C2×C22⋊C4—682no—
383C2×C22⋊C4—682no—
384C2×C22⋊C4—682no—
385C2×C22⋊C4—682no—
386C2×C22⋊C4—682no—
387C2×C22⋊C4—682no—
388C2×C22⋊C4—682no—
389C2×C22⋊C4—682no—
390C2×C22⋊C4—682no—
391C2×C42—42no—
392C2×C42—344no—
393C2×C42—682no—
394C2×C42—682no—
395C2×C42C4×D1714yes—
396#95—24no—
397#95—41no—
398#95—41no—
399#95—174no—
400#95—344no—
401#95—344no—
402#95—342no—
403#95—682no—
404#95—682no—
405#95—682no—
406C17#1444411yescharacteristic, complemented, Sylow
407C24—174no—
408C24—342no—
409C24—342no—
410C24—342no—
411C24—342no—
412C24—342no—
413C24—342no—
414C24—342no—
415C24—342no—
416C24—342no—
417C24—342no—
418C24—342no—
419C24—342no—
420C24—342no—
421C24—342no—
422C24C23×D1711yescharacteristic
423C2×D4—348no—
424C2×D4—684no—
425C2×D4—684no—
426C2×D4—688no—
427C2×D4—688no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
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—22no—
448C22×C4—22no—
449C22×C4—174no—
450C22×C4—174no—
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×C4C2×C4×D1712yes—
471C22×C4C2×C4×D1712yes—
472C22×C4C2×C4×D1712yes—
473C22×C4#6325214yes—
474C22×C4D4×D1712yes—
475C22×C4#6325412yes—
476C22×C4#6325612yes—
477C22×C4#6325612yes—
478C4⋊C4—48no—
479C4⋊C4—684no—
480C22⋊C4—3416no—
481C22⋊C4—688no—
482C22⋊C4—688no—
483C22⋊C4—688no—
484C22⋊C4—688no—
485C22⋊C4—688no—
486C42—44no—
487C42—688no—
488C23—344no—
489C23—344no—
490C23—344no—
491C23—344no—
492C23—344no—
493C23—344no—
494C23—344no—
495C23—682no—
496C23—682no—
497C23—682no—
498C23—682no—
499C23—682no—
500C23—682no—
501C23—682no—
502C23—682no—
503C23—682no—
504C23—682no—
505C23—682no—
506C23—682no—
507C23—682no—
508C23—682no—
509C23—682no—
510C23—682no—
511C23—682no—
512C23—682no—
513C23—682no—
514C23—682no—
515C23—682no—
516C23—682no—
517C23—682no—
518C23—682no—
519C23—682no—
520C23—682no—
521C23—682no—
522C23—682no—
523C23C22×C4×D1711yescharacteristic
524C23C2×#6325212yes—
525C23C2×D4×D1711yescharacteristic
526C23C2×#6325411yescharacteristic
527C23#1058769111yescharacteristic
528C23#1058769112yes—
529C23C2×#6325611yescharacteristic
530C23C2×#6325611yescharacteristic
531C23#1058769411yescharacteristic
532C23#1058769612yes—
533C23#1058769612yes—
534D4—6816no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—344no—
563C2×C4—344no—
564C2×C4—344no—
565C2×C4—344no—
566C2×C4—344no—
567C2×C4—344no—
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×C4—682no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—682no—
583C2×C4#1058757814yes—
584C2×C4#1058757914yes—
585C22—684no—
586C22—684no—
587C22—684no—
588C22—684no—
589C22—684no—
590C22—684no—
591C22—684no—
592C22—1362no—
593C22—1362no—
594C22—1362no—
595C22—1362no—
596C22—1362no—
597C22—1362no—
598C22—1362no—
599C22—1362no—
600C22C2×#1058757811yescharacteristic
601C22C2×#1058757911yescharacteristic
602C22C4×#6325211yescharacteristic
603C22#1176328211yescharacteristic
604C22#1176328311yescharacteristic
605C22#1176328311yescharacteristic
606C22#1176329011yescharacteristic
607C22#1176337712yes—
608C22#1176339212yes—
609C22#1176339612yes—
610C22#1176339912yes—
611C22#1176341512yes—
612C22#1176343112yes—
613C22#1176344912yes—
614C22#1176346211yescharacteristic
615C22#1176347911yescharacteristic
616C22#1176350512yes—
617C22#1176350712yes—
618C22#1176352511yescharacteristic
619C22#1176353311yescharacteristic
620C22#1176354412yes—
621C22#1176354712yes—
622C22#1176355512yes—
623C4—24no—
624C4—24no—
625C4—42no—
626C4—44no—
627C4—82no—
628C4—684no—
629C4—684no—
630C4—1362no—
631C2—1364no—
632C2#1453138111yescharacteristic
633C2#1453150711yescharacteristic
634C2#1453159711yescharacteristic
635C2#1453173511yescharacteristic
636C2#1453175511yescharacteristic
637C2#1453183111yescharacteristic
638C2#1453193811yescharacteristic
639C2#1453552112yes—
640C2#1453557512yes—
641C2#1453667412yes—
642C2#1453671112yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC4⋊#95D17
hypocenterC17#14444
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11762699C2semidirect
3. #14527032C2semidirect
4. #14527026C2semidirect
6. #14527020C2semidirect
7. #14527018C2semidirect
8. #14527011C2semidirect
9. C17×C4⋊#95C2semidirect
19. #11762711C4semidirect
84. #10587502D4semidirect
271. C4⋊#95D17semidirect
406. C17#14444semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117626992
#145270322
#145270262
#145270242
#145270202
#145270182
#145270112
C17×C4⋊#952
#1444417