Finite Group Databasebeta

← #17005474

Subgroups — #17005474

Order 4352.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538831C211yesmaximal, characteristic
2#14537940C211yesmaximal, characteristic, complemented
3#14537819C211yesmaximal, characteristic, complemented
4#14527677C211yesmaximal, characteristic, complemented
5#14527666C211yesmaximal, characteristic, complemented
6#14527665C211yesmaximal, characteristic, complemented
7#14527651C211yesmaximal, characteristic, complemented
8#14527645C211yesmaximal, characteristic, complemented
9#14527638C211yesmaximal, characteristic, complemented
10#14527587C211yesmaximal, characteristic, complemented
11#14527576C211yesmaximal, characteristic, complemented
12#14527567C211yesmaximal, characteristic, complemented
13#14527245C211yesmaximal, characteristic, complemented
14#14527067C211yesmaximal, characteristic, complemented
15C2×C17×D4⋊C8C211yesmaximal, characteristic, complemented
16#11763343C2211yescharacteristic
17#11763144C411yescharacteristic
18#11763127C411yescharacteristic
19#11763109C411yescharacteristic
20#11763109C411yescharacteristic
21#11763024C411yescharacteristic
22#11763024C411yescharacteristic
23#11762960C411yescharacteristic
24#11762943C411yescharacteristic
25#11762936C2211yescharacteristic, complemented
26#11762933C2211yescharacteristic, complemented
27C4×#63229C2211yescharacteristic
28C4×#63229C2211yescharacteristic
29C4×#63228C2211yescharacteristic
30C4×#63228C2211yescharacteristic
31#11762887C2211yescharacteristic
32#11762887C2211yescharacteristic
33#11762886C2211yescharacteristic, complemented
34#11762881—21no—
35#11762881—21no—
36#11762880—21no—
37D4×#3622C2211yescharacteristic
38D4×#3622C2211yescharacteristic
39#11762874C2211yescharacteristic, complemented
40C8×C22⋊D17—21no—
41#11762869—21no—
42#11762866C2211yescharacteristic
43#11762862C2211yescharacteristic
44#11762862C2211yescharacteristic
45#11762834—21no—
46#11762773—21no—
47C2×C22⋊#3622—21no—
48#11762561C2211yescharacteristic, complemented
49#11762561C2211yescharacteristic, complemented
50#11762559C2211yescharacteristic, complemented
51#11762559C2211yescharacteristic, complemented
52#11762541C2211yescharacteristic, complemented
53#11762541C2211yescharacteristic, complemented
54#11762538C2211yescharacteristic, complemented
55#11762538C2211yescharacteristic, complemented
56#11762530C2211yescharacteristic, complemented
57#11762530C2211yescharacteristic, complemented
58C8×#3622C2211yescharacteristic, complemented
59C8×#3622C2211yescharacteristic, complemented
60C2×C4×D4×C17C2211yescharacteristic
61C2×C17×C4⋊C8C2211yescharacteristic
62C2×C4×C8×C17C2211yescharacteristic
63C17×D4⋊C8C2211yescharacteristic
64C17×D4⋊C8C2211yescharacteristic
65C17×D4⋊C8C2211yescharacteristic
66C17×D4⋊C8C2211yescharacteristic
67C22×D4×C17C2×C411yescharacteristic
68C23×C4×C17—21no—
69C22×C8×C17—21no—
70C22×C8×C17—21no—
71C4×D4×C17—21no—
72C4×D4×C17—21no—
73C4×D4×C17C2×C411yescharacteristic
74C4×D4×C17C2×C411yescharacteristic
75C4×D4×C17C2311yescharacteristic
76C4×D4×C17C2311yescharacteristic
77C2×C4⋊C4×C17C2×C411yescharacteristic
78C2×C22⋊C4×C17—21no—
79C2×C42×C17C2311yescharacteristic
80C2×#63229C2×C411yescharacteristic
81C2×#63229C2×C411yescharacteristic
82C2×#63228C2×C411yescharacteristic
83C2×#63228C2×C411yescharacteristic
84#10587616C2×C411yescharacteristic
85#10587615—21no—
86C4×C22⋊D17—21no—
87#10587610C2×C411yescharacteristic
88C2×#63223—21no—
89C2×#63223—21no—
90C22×#3622—21no—
91C22×#3622—21no—
92C2×#63218—21no—
93C2×C8×D17—21no—
94#10587562—21no—
95#10587561C2×C411yescharacteristic
96C4×D68C2311yescharacteristic
97#10587558—21no—
98#10587556C2×C411yescharacteristic
99C4×Dic34C2311yescharacteristic
100C17×C4⋊C8—21no—
101C17×C4⋊C8C2311yescharacteristic
102C17×C4⋊C8C2311yescharacteristic
103C4×C8×C17—21no—
104C4×C8×C17C2311yescharacteristic
105C4×C8×C17C2311yescharacteristic
106#10587503C2×C411yescharacteristic
107#10587503C2×C411yescharacteristic
108#10587503C2×C411yescharacteristic
109#10587503C2×C411yescharacteristic
110C22⋊#3622—21no—
111C22⋊#3622—21no—
112C22⋊#3622—21no—
113C22⋊#3622—21no—
114C22⋊#3622—21no—
115C22⋊#3622C2×C411yescharacteristic
116C22⋊#3622C2×C411yescharacteristic
117C22⋊#3622D411yescharacteristic
118C22⋊#3622D411yescharacteristic
119#10587491—21no—
120#10587491—21no—
121#10587486—21no—
122#10587485—21no—
123#10587485—21no—
124C8×Dic17—21no—
125#10587481C2×C411yescharacteristic
126#10587481C2×C411yescharacteristic
127#10587480C2×C411yescharacteristic
128#10587480C2×C411yescharacteristic
129#10587479C2×C411yescharacteristic
130#10587479C2×C411yescharacteristic
131#10587478C2×C411yescharacteristic
132#10587478C2×C411yescharacteristic
133C4⋊#3622C2×C411yescharacteristic
134C4⋊#3622C2×C411yescharacteristic
135C4⋊#3622D411yescharacteristic
136C4⋊#3622D411yescharacteristic
137C4⋊#3622C2311yescharacteristic
138C4⋊#3622C2311yescharacteristic
139#10587474—21no—
140C4×#3622C2311yescharacteristic
141C4×#3622C2311yescharacteristic
142C4×#3622C2311yescharacteristic
143C4×#3622C2311yescharacteristic
144C24×C17—21no—
145C2×D4×C17—22no—
146C2×D4×C17—21no—
147C2×D4×C17—41no—
148C2×D4×C17C22×C411yescharacteristic
149C2×D4×C17C22×C411yescharacteristic
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—81no—
156C22×C4×C17—81no—
157C22×C4×C17C22×C411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17#4111yescharacteristic
160C2×C22⋊D17—21no—
161C2×D68C22×C411yescharacteristic
162C2×C4×D17—21no—
163C2×Dic34C22×C411yescharacteristic
164C2×C8×C17—24no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—81no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17C22×C411yescharacteristic
172C4⋊C4×C17C22×C411yescharacteristic
173C22⋊C4×C17—21no—
174C22⋊C4×C17—21no—
175C22⋊C4×C17—21no—
176C22⋊C4×C17—21no—
177C42×C17C22×C411yescharacteristic
178C42×C17C2×D411yescharacteristic
179C42×C17#4111yescharacteristic
180C42×C17C2411yescharacteristic
181C22⋊Dic17—21no—
182#63229—22no—
183#63229—41no—
184#63228—22no—
185#63228—41no—
186#63227—21no—
187#63227—21no—
188#63227—21no—
189#63227—21no—
190C4⋊Dic17C22×C411yescharacteristic
191C4⋊Dic17C22×C411yescharacteristic
192#63225—21no—
193#63225—21no—
194#63225—21no—
195#63225—21no—
196C4×Dic17—21no—
197#63223—81no—
198#63223—81no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—81no—
202C2×#3622—81no—
203C2×#3622C22×C411yescharacteristic
204C2×#3622C22×C411yescharacteristic
205C2×#3622C22×C411yescharacteristic
206C2×#3622C22×C411yescharacteristic
207C2×#3622C2×D411yescharacteristic
208C2×#3622C2×D411yescharacteristic
209C2×#3622C2×D411yescharacteristic
210C2×#3622C2×D411yescharacteristic
211#63218—81no—
212C8×D17—81no—
213#18014—171nomaximal, Sylow
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—42no—
217C23×C17—42no—
218C23×C17—81no—
219C23×C17C4×D411yescharacteristic
220C22×D17—21no—
221D4×C17—21no—
222D4×C17—21no—
223D4×C17—21no—
224D4×C17—42no—
225D4×C17#13112yes—
226C2×C4×C17—22no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—81no—
238C2×C4×C17—81no—
239C2×C4×C17—81no—
240C2×C4×C17C4×D411yescharacteristic
241C2×C4×C17C4×D411yescharacteristic
242C2×C4×C17C4×D411yescharacteristic
243C2×C4×C17C23×C411yescharacteristic
244C2×C4×C17C22×D411yescharacteristic
245C2×C4×C17C2×#4111yescharacteristic
246C22⋊D17—42no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250D68—21no—
251D68—21no—
252C4×D17—41no—
253C4×D17—41no—
254Dic34—21no—
255Dic34—21no—
256C8×C17—22no—
257C8×C17—22no—
258C8×C17—41no—
259C8×C17—41no—
260#3622—21no—
261#3622—21no—
262#3622—21no—
263#3622—21no—
264#3622—21no—
265#3622—21no—
266#3622—21no—
267#3622—21no—
268#3622—41no—
269#3622—41no—
270#3105—171no—
271#2994—171no—
272#2974—171no—
273#1590—171no—
274#1589—171no—
275#1588—171no—
276#1586—171no—
277#1586—171no—
278#1585—171no—
279C8×SD16—171no—
280C8×D8—171no—
281#1573—171no—
282#1494—171no—
283C2×D4⋊C8D1711yescharacteristic, complemented
284#1450—171no—
285C22×C17—21no—
286C22×C17—21no—
287C22×C17—22no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17—41no—
292C22×C17—41no—
293C22×C17—84no—
294C22×C17#44312yes—
295C22×C17C2×C4×D411yescharacteristic
296C2×D17—41no—
297C2×D17—41no—
298C2×D17—41no—
299C4×C17—21no—
300C4×C17—21no—
301C4×C17—21no—
302C4×C17—21no—
303C4×C17—41no—
304C4×C17—41no—
305C4×C17C2×#13111yescharacteristic
306C4×C17#56811yescharacteristic
307C4×C17#57611yescharacteristic
308C4×C17#57711yescharacteristic
309Dic17—41no—
310Dic17—41no—
311Dic17—41no—
312#529—171no—
313C2×C4×D4C2×D1711yescharacteristic
314#484—171no—
315#481—171no—
316#478—171no—
317#478—171no—
318#463—171no—
319#463—171no—
320#450—171no—
321#447—171no—
322#446—171no—
323C8×Q8—171no—
324C4×SD16—171no—
325C4×SD16—171no—
326C4×D8—171no—
327C4×D8—171no—
328#436—171no—
329#436—171no—
330#436—171no—
331#435—341no—
332#435—341no—
333#435—341no—
334C8×D4—171no—
335C8×D4—171no—
336C8×D4—171no—
337C8×D4—341no—
338#433—341no—
339#432—171no—
340#431—171no—
341#431—171no—
342#424—341no—
343C2×C4⋊C8C2×D1711yescharacteristic
344#407—341no—
345C2×C22⋊C8—341no—
346C2×C4×C8C2×D1711yescharacteristic
347#335—171no—
348#335—171no—
349#334—171no—
350#334—171no—
351Q8⋊C8—171no—
352Q8⋊C8—171no—
353D4⋊C8—171no—
354D4⋊C8—171no—
355D4⋊C8C2×D1711yescharacteristic
356D4⋊C8C2×D1711yescharacteristic
357D4⋊C8C2×D1711yescharacteristic
358D4⋊C8C2×D1711yescharacteristic
359#322—171no—
360#322—171no—
361C82—171no—
362C82—171no—
363C2×C17—22no—
364C2×C17—42no—
365C2×C17—81no—
366C2×C17#293311yescharacteristic
367C2×C17#294611yescharacteristic
368C2×C17C2×#44311yescharacteristic
369D17—81no—
370C22×D4C4×D1711yescharacteristic
371C23×C4—21no—
372C2×SD16—171no—
373C2×SD16—171no—
374C2×D8—171no—
375C2×D8—171no—
376C2×M16—341no—
377C2×M16—341no—
378C2×M16—341no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—341no—
382C22×C8—341no—
383C22×C8—341no—
384#126—341no—
385#125—171no—
386#124—171no—
387#123—341no—
388C22⋊Q8—171no—
389#121—171no—
390C4×Q8—171no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—171no—
394C4×D4—341no—
395C4×D4C4×D1711yescharacteristic
396C4×D4C4×D1711yescharacteristic
397C4×D4C22×D1711yescharacteristic
398C4×D4C22×D1711yescharacteristic
399#117—341no—
400C2×C4⋊C4C4×D1711yescharacteristic
401C2×C22⋊C4—21no—
402C2×C42C22×D1711yescharacteristic
403#107—171no—
404#107—171no—
405#106—171no—
406#106—171no—
407C4⋊C8—21no—
408C4⋊C8—171no—
409C4⋊C8—171no—
410C4⋊C8—171no—
411C4⋊C8—171no—
412C4⋊C8—171no—
413C4⋊C8—171no—
414C4⋊C8—341no—
415C4⋊C8—341no—
416C4⋊C8C22×D1711yescharacteristic
417C4⋊C8C22×D1711yescharacteristic
418#103—171no—
419#103—171no—
420#102—171no—
421#102—171no—
422#102—171no—
423#102—171no—
424#102—171no—
425#102—171no—
426C22⋊C8—171no—
427C22⋊C8—171no—
428C22⋊C8—171no—
429C22⋊C8—171no—
430C22⋊C8—341no—
431C22⋊C8—341no—
432C22⋊C8—341no—
433C22⋊C8—341no—
434C22⋊C8—341no—
435C22⋊C8—341no—
436C22⋊C8—341no—
437#97—341no—
438#97—341no—
439C4×C8—21no—
440C4×C8—171no—
441C4×C8—171no—
442C4×C8—171no—
443C4×C8—171no—
444C4×C8—341no—
445C4×C8C22×D1711yescharacteristic
446C4×C8C22×D1711yescharacteristic
447C17#1801411yescharacteristic, complemented, Sylow
448C24—21no—
449C2×Q8—171no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—171no—
454C2×D4—341no—
455C2×D4C2×C4×D1711yescharacteristic
456C2×D4C2×C4×D1711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—341no—
465C22×C4C2×C4×D1711yescharacteristic
466C22×C4D4×D1711yescharacteristic
467C22×C4#6325411yescharacteristic
468SD16—342no—
469SD16—681no—
470D8—342no—
471D8—681no—
472M16—1361no—
473M16—1361no—
474M16—1361no—
475C2×C8—24no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—81no—
481C2×C8—171no—
482C2×C8—171no—
483C2×C8—171no—
484C2×C8—171no—
485C2×C8—171no—
486C2×C8—171no—
487C2×C8—171no—
488C2×C8—171no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—1361no—
492C2×C8—1361no—
493C2×C8—1361no—
494C4⋊C4—21no—
495C4⋊C4—171no—
496C4⋊C4—171no—
497C4⋊C4—341no—
498C4⋊C4—341no—
499C4⋊C4—341no—
500C4⋊C4—341no—
501C4⋊C4C2×C4×D1711yescharacteristic
502C4⋊C4C2×C4×D1711yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—341no—
508C22⋊C4—341no—
509C22⋊C4—341no—
510C22⋊C4—341no—
511C22⋊C4—341no—
512C42—341no—
513C42C2×C4×D1711yescharacteristic
514C42D4×D1711yescharacteristic
515C42#6325411yescharacteristic
516C42C23×D1711yescharacteristic
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—341no—
523C23#1058756711yescharacteristic
524Q8—341no—
525Q8—341no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—341no—
531D4—341no—
532D4—682no—
533D4#1058758712yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—341no—
549C2×C4—341no—
550C2×C4—341no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4#1058756711yescharacteristic
554C2×C4#1058756711yescharacteristic
555C2×C4#1058756711yescharacteristic
556C2×C4C22×C4×D1711yescharacteristic
557C2×C4C2×D4×D1711yescharacteristic
558C2×C4C2×#6325411yescharacteristic
559C8—22no—
560C8—22no—
561C8—41no—
562C8—41no—
563C8—341no—
564C8—341no—
565C8—341no—
566C8—341no—
567C8—341no—
568C8—341no—
569C8—341no—
570C8—341no—
571C8—681no—
572C8—681no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—681no—
583C22—681no—
584C22—681no—
585C22#1176292312yes—
586C22C2×#1058756711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—681no—
594C4—681no—
595C4—681no—
596C4C2×#1058758711yescharacteristic
597C4#1176357511yescharacteristic
598C4#1176361011yescharacteristic
599C4#1176361511yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—1361no—
604C2#1453750511yescharacteristic
605C2#1453761011yescharacteristic
606C2C2×#1176292311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC2×C17×D4⋊C8C2
socleC22×C17C2×C4×D4
prime radical#11762943C4
cosocleC42×C17C24
hypercenterC2×D4⋊C8D17
hypocenterC17#18014
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14537940C2semidirect
3. #14537819C2semidirect
4. #14527677C2semidirect
5. #14527666C2semidirect
6. #14527665C2semidirect
7. #14527651C2semidirect
8. #14527645C2semidirect
9. #14527638C2semidirect
10. #14527587C2semidirect
11. #14527576C2semidirect
12. #14527567C2semidirect
13. #14527245C2semidirect
14. #14527067C2semidirect
15. C2×C17×D4⋊C8C2semidirect
25. #11762936C22semidirect
26. #11762933C22semidirect
33. #11762886C22semidirect
39. #11762874C22semidirect
48. #11762561C22semidirect
49. #11762561C22semidirect
50. #11762559C22semidirect
51. #11762559C22semidirect
52. #11762541C22semidirect
53. #11762541C22semidirect
54. #11762538C22semidirect
55. #11762538C22semidirect
56. #11762530C22semidirect
57. #11762530C22semidirect
58. C8×#3622C22semidirect
59. C8×#3622C22semidirect
283. C2×D4⋊C8D17semidirect
447. C17#18014semidirect

Maximal subgroups

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

subgroupindex
#145388312
#145379402
#145378192
#145276772
#145276662
#145276652
#145276512
#145276452
#145276382
#145275872
#145275762
#145275672
#145272452
#145270672
C2×C17×D4⋊C82
#1801417