Finite Group Databasebeta

← #16937620

Subgroups — #16937620

Order 4352.

694 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534589C211yesmaximal, characteristic
2#14529091C211yesmaximal, characteristic, complemented
3#14528977C211yesmaximal, characteristic, complemented
4C2×#11762545C211yesmaximal, characteristic, complemented
5C2×#11762533C211yesmaximal, characteristic
6#14526663C211yesmaximal, characteristic, complemented
7C17×#1439C211yesmaximal, characteristic
8C2×#10587610C2211yescharacteristic
9C2×#10587479—21no—
10C2×#10587481—21no—
11C2×C22⋊#3622C2211yescharacteristic
12C2×C22⋊#3622C2211yescharacteristic
13#11762745—21no—
14#11762732—21no—
15#11762732—21no—
16#11762721—21no—
17#11762682—21no—
18#11762669C2211yescharacteristic
19#11762665—21no—
20#11762571—21no—
21#11762571—21no—
22#11762545—22no—
23#11762533—22no—
24C22×C4⋊C4×C17C2211yescharacteristic
25C22×C22⋊C4×C17—21no—
26C22×C22⋊C4×C17C2211yescharacteristic
27C2×C17×#95—21no—
28C2×C17×#95C2211yescharacteristic
29C25×C17D411yescharacteristic
30C23×C4×C17—21no—
31C23×C4×C17—21no—
32C23×C4×C17D411yescharacteristic
33C23×C4×C17C2311yescharacteristic
34C22×Dic34D411yescharacteristic
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—42no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17—42no—
45C2×C22⋊C4×C17—42no—
46C2×C22⋊C4×C17—42no—
47C2×C22⋊Dic17—21no—
48C2×C22⋊Dic17—21no—
49C2×C22⋊Dic17—21no—
50C2×C22⋊Dic17—21no—
51C2×C22⋊Dic17—21no—
52C2×C22⋊Dic17—21no—
53C2×C4⋊Dic17D411yescharacteristic
54C2×C4⋊Dic17D411yescharacteristic
55C2×C4⋊Dic17D411yescharacteristic
56#10587610—21no—
57#10587610—21no—
58#10587610—21no—
59#10587610—21no—
60C2×#63225—21no—
61C2×#63225—21no—
62C2×#63225—21no—
63C22×#3622—21no—
64C22×#3622—21no—
65C17×#95—21no—
66C17×#95—21no—
67C17×#95—42no—
68#10587502—21no—
69#10587502—21no—
70#10587502—21no—
71C22⋊#3622—21no—
72C22⋊#3622—21no—
73C22⋊#3622—21no—
74C22⋊#3622D412yes—
75#10587481—42no—
76#10587479—42no—
77C24×C17—21no—
78C24×C17—21no—
79C24×C17—21no—
80C24×C17—21no—
81C24×C17—21no—
82C24×C17—21no—
83C24×C17—41no—
84C24×C17—41no—
85C24×C17—41no—
86C24×C17—41no—
87C24×C17SD1612yes—
88C24×C17C2×D411yescharacteristic
89C22×C4×C17—22no—
90C22×C4×C17—22no—
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17—41no—
101C22×C4×C17—41no—
102C22×C4×C17—41no—
103C22×C4×C17—41no—
104C22×C4×C17—41no—
105C22×C4×C17—41no—
106C22×C4×C17—41no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17—41no—
110C22×C4×C17C2×D411yescharacteristic
111C22×C4×C17C2×D411yescharacteristic
112C22×C4×C17C2×D411yescharacteristic
113C22×C4×C17#4111yescharacteristic
114C22×C4×C17#4111yescharacteristic
115C22×C4×C17#4111yescharacteristic
116C22×Dic17—21no—
117C22×Dic17—21no—
118C22×Dic17—21no—
119C22×Dic17—21no—
120C2×Dic34—21no—
121C2×Dic34—21no—
122C2×Dic34—41no—
123C2×Dic34—41no—
124C4⋊C4×C17—22no—
125C4⋊C4×C17—22no—
126C4⋊C4×C17—41no—
127C4⋊C4×C17—41no—
128C22⋊C4×C17—48no—
129C22⋊C4×C17—41no—
130C22⋊C4×C17—41no—
131C22⋊C4×C17—41no—
132C22⋊C4×C17—41no—
133C22⋊Dic17—41no—
134C22⋊Dic17—41no—
135C22⋊Dic17—41no—
136C22⋊Dic17—41no—
137C22⋊Dic17—81no—
138C22⋊Dic17—81no—
139C22⋊Dic17—81no—
140C22⋊Dic17—81no—
141C4⋊Dic17—21no—
142C4⋊Dic17—21no—
143C4⋊Dic17—41no—
144C4⋊Dic17—41no—
145#63225—41no—
146#63225—41no—
147#63225—81no—
148#63225—81no—
149C2×#3622—22no—
150C2×#3622—41no—
151C2×#3622—41no—
152C2×#3622—41no—
153C2×#3622—41no—
154C2×#3622—41no—
155#10398—171nomaximal, Sylow
156C23×C17—21no—
157C23×C17—21no—
158C23×C17—21no—
159C23×C17—21no—
160C23×C17—22no—
161C23×C17—22no—
162C23×C17—22no—
163C23×C17—42no—
164C23×C17—42no—
165C23×C17—42no—
166C23×C17—42no—
167C23×C17—42no—
168C23×C17—42no—
169C23×C17—41no—
170C23×C17—41no—
171C23×C17—41no—
172C23×C17—41no—
173C23×C17—41no—
174C23×C17—41no—
175C23×C17—41no—
176C23×C17—41no—
177C23×C17—81no—
178C23×C17—81no—
179C23×C17—81no—
180C23×C17—81no—
181C23×C17—81no—
182C23×C17—81no—
183C23×C17#12011yescharacteristic
184C23×C17#12111yescharacteristic
185C23×C17#12311yescharacteristic
186C23×C17C2×SD1611yescharacteristic
187C23×C17#13511yescharacteristic
188C23×C17#13711yescharacteristic
189C23×C17#13711yescharacteristic
190C2×C4×C17—21no—
191C2×C4×C17—21no—
192C2×C4×C17—21no—
193C2×C4×C17—21no—
194C2×C4×C17—41no—
195C2×C4×C17—41no—
196C2×C4×C17—41no—
197C2×C4×C17—41no—
198C2×C4×C17—42no—
199C2×C4×C17—42no—
200C2×C4×C17—42no—
201C2×C4×C17—42no—
202C2×C4×C17—42no—
203C2×C4×C17—42no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—42no—
208C2×C4×C17—81no—
209C2×C4×C17—81no—
210C2×C4×C17—81no—
211C2×C4×C17—81no—
212C2×C4×C17—81no—
213C2×C4×C17—81no—
214C2×C4×C17—81no—
215C2×C4×C17—81no—
216C2×C4×C17—81no—
217C2×C4×C17#12111yescharacteristic
218C2×C4×C17#12111yescharacteristic
219C2×C4×C17#12311yescharacteristic
220C2×C4×C17#12411yescharacteristic
221C2×Dic17—41no—
222C2×Dic17—41no—
223C2×Dic17—41no—
224C2×Dic17—41no—
225C2×Dic17—41no—
226C2×Dic17—41no—
227C2×Dic17—41no—
228C2×Dic17—41no—
229C2×Dic17—41no—
230C2×Dic17—41no—
231C2×Dic17—41no—
232C2×Dic17—41no—
233Dic34—42no—
234Dic34—81no—
235#3622—42no—
236#3622—81no—
237#2626—171no—
238#1872—171no—
239#1853—171no—
240C2×#328—171no—
241C2×#323—171no—
242#1439D1711yescharacteristic
243#1294—171no—
244C22×C17—21no—
245C22×C17—21no—
246C22×C17—21no—
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—44no—
257C22×C17—42no—
258C22×C17—42no—
259C22×C17—42no—
260C22×C17—82no—
261C22×C17—82no—
262C22×C17—82no—
263C22×C17—81no—
264C22×C17—81no—
265C22×C17—81no—
266C22×C17—81no—
267C22×C17#39411yescharacteristic
268C22×C17#44811yescharacteristic
269C22×C17#45211yescharacteristic
270C22×C17#45311yescharacteristic
271C22×C17#45511yescharacteristic
272C22×C17B(4,𝔽2)11yescharacteristic
273C22×C17#45811yescharacteristic
274C22×C17#46511yescharacteristic
275C22×C17#47011yescharacteristic
276C22×C17#48311yescharacteristic
277C22×C17#48511yescharacteristic
278C4×C17—21no—
279C4×C17—21no—
280C4×C17—21no—
281C4×C17—21no—
282C4×C17—82no—
283C4×C17—82no—
284C4×C17—81no—
285Dic17—81no—
286Dic17—81no—
287Dic17—81no—
288Dic17—81no—
289C2×C22⋊Q8—171no—
290C22×C4⋊C4C2×D1711yescharacteristic
291C22×C22⋊C4—21no—
292C22×C22⋊C4C2×D1711yescharacteristic
293C2×#106—341no—
294C2×#103—341no—
295C2×C22⋊C8—171no—
296C2×C22⋊C8—171no—
297#399—341no—
298#396—341no—
299#396—341no—
300#393—341no—
301#385—341no—
302#380—171no—
303#379—341no—
304C2×#95—21no—
305C2×#95C2×D1711yescharacteristic
306#340—341no—
307#340—341no—
308#328—342no—
309#323—342no—
310C2×C17—21no—
311C2×C17—21no—
312C2×C17—21no—
313C2×C17—21no—
314C2×C17—82no—
315C2×C17#159611yescharacteristic
316C2×C17#160611yescharacteristic
317C2×C17#160811yescharacteristic
318C2×C17#161811yescharacteristic
319C2×C17#203511yescharacteristic
320C2×C17#203711yescharacteristic
321C2×C17#204411yescharacteristic
322C25C22⋊D1711yescharacteristic
323C22×Q8—171no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C22⋊D1711yescharacteristic
327C23×C4C22×D1711yescharacteristic
328C22×C8—341no—
329C22×C8—341no—
330C22⋊Q8—341no—
331C22⋊Q8—341no—
332C22⋊Q8—341no—
333C22⋊Q8—341no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—171no—
338C2×C4⋊C4—171no—
339C2×C4⋊C4—171no—
340C2×C4⋊C4—341no—
341C2×C4⋊C4—341no—
342C2×C4⋊C4—341no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—341no—
353C2×C22⋊C4—341no—
354C2×C22⋊C4—341no—
355C2×C22⋊C4—341no—
356C2×C22⋊C4—341no—
357C2×C22⋊C4—341no—
358#106—682no—
359#103—682no—
360C22⋊C8—172no—
361C22⋊C8—341no—
362C22⋊C8—341no—
363C22⋊C8—341no—
364#95—21no—
365#95—21no—
366#95—42no—
367#95—341no—
368#95—341no—
369#95—341no—
370C17#1039811yescharacteristic, complemented, Sylow
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24#6322912yes—
382C24C2×C22⋊D1711yescharacteristic
383C2×Q8—341no—
384C2×Q8—341no—
385C2×Q8—681no—
386C2×Q8—681no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—341no—
409C22×C4—341no—
410C22×C4—341no—
411C22×C4—341no—
412C22×C4#6325211yescharacteristic
413C22×C4#6325211yescharacteristic
414C22×C4D4×D1711yescharacteristic
415C22×C4D4×D1711yescharacteristic
416C22×C4D4×D1711yescharacteristic
417C22×C4#6325411yescharacteristic
418C2×C8—342no—
419C2×C8—681no—
420C2×C8—681no—
421C2×C8—681no—
422C2×C8—681no—
423C2×C8—681no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—341no—
429C4⋊C4—341no—
430C4⋊C4—681no—
431C4⋊C4—681no—
432C4⋊C4—681no—
433C4⋊C4—681no—
434C4⋊C4—1361no—
435C4⋊C4—1361no—
436C22⋊C4—48no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—681no—
442C22⋊C4—681no—
443C22⋊C4—681no—
444C22⋊C4—681no—
445C22⋊C4—1361no—
446C22⋊C4—1361no—
447C22⋊C4—1361no—
448C22⋊C4—1361no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23#1058761511yescharacteristic
477C23C2×#6322911yescharacteristic
478C23#1058762311yescharacteristic
479C23#1058762511yescharacteristic
480C23#1058762811yescharacteristic
481C23#1058763611yescharacteristic
482C23#1058763711yescharacteristic
483Q8—682no—
484Q8—1361no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—681no—
513C2×C4—681no—
514C2×C4—681no—
515C2×C4—681no—
516C2×C4—681no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4#1058756911yescharacteristic
525C2×C4#1058757011yescharacteristic
526C2×C4#1058757011yescharacteristic
527C2×C4#1058757111yescharacteristic
528C8—682no—
529C8—1361no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#1176272411yescharacteristic
554C22#1176294711yescharacteristic
555C22#1176296911yescharacteristic
556C22#1176297611yescharacteristic
557C22#1176298611yescharacteristic
558C22#1176299511yescharacteristic
559C22#1176299811yescharacteristic
560C22#1176303611yescharacteristic
561C22#1176306511yescharacteristic
562C22#1176313911yescharacteristic
563C22#1176315011yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—82no—
569C4—81no—
570C4—82no—
571C4—1361no—
572C4—1361no—
573C4—1361no—
574C4—1361no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—82no—
580C2#1452770611yescharacteristic
581C2#1452776211yescharacteristic
582C2#1452777411yescharacteristic
583C2#1452783011yescharacteristic
584C2#1452998011yescharacteristic
585C2#1452999411yescharacteristic
586C2#1453003311yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1439C2
socleC23×C17#120
prime radicalC25×C17D4
hypercenter#1439D17
hypocenterC17#10398
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #14529091C2semidirect
3. #14528977C2semidirect
4. C2×#11762545C2semidirect
6. #14526663C2semidirect
370. C17#10398semidirect

Maximal subgroups

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

subgroupindex
#145345892
#145290912
#145289772
C2×#117625452
C2×#117625332
#145266632
C17×#14392
#1039817