Finite Group Databasebeta

← C89×#25493 #36403341

Subgroups — C89×#25493 #36403341

Order 22784.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3166C211yesmaximal, characteristic, complemented
2C89×#3077C211yesmaximal, characteristic
3C2×#478×C89C211yesmaximal, characteristic
4C89×#2962C211yesmaximal, characteristic, complemented
5C89×#2090C211yesmaximal, characteristic, complemented
6C89×#2089C211yesmaximal, characteristic, complemented
7C89×#2063C211yesmaximal, characteristic
8C89×#2063C211yesmaximal, characteristic
9C89×#1998C211yesmaximal, characteristic, complemented
10C89×#1952C211yesmaximal, characteristic, complemented
11C89×#1951C211yesmaximal, characteristic, complemented
12C89×#1950C211yesmaximal, characteristic, complemented
13C89×#1931C211yesmaximal, characteristic
14C89×#1931C211yesmaximal, characteristic
15C4×#100×C89C211yesmaximal, characteristic
16#533×C89C2211yescharacteristic
17C2×#125×C89C2211yescharacteristic
18C2×C4×D4×C89C2211yescharacteristic
19#501×C89—21no—
20#501×C89—21no—
21#499×C89—21no—
22#499×C89—21no—
23#478×C89—21no—
24#478×C89—21no—
25#478×C89—21no—
26#478×C89—21no—
27#478×C89—21no—
28#478×C89—21no—
29#476×C89—21no—
30#474×C89—21no—
31#446×C89—21no—
32#446×C89—21no—
33#446×C89—21no—
34C8×Q8×C89—21no—
35C2×#108×C89C2211yescharacteristic
36C2×#108×C89C2211yescharacteristic
37#428×C89C2211yescharacteristic
38#428×C89C2211yescharacteristic
39#428×C89C2211yescharacteristic
40#428×C89C2211yescharacteristic
41#428×C89C2211yescharacteristic
42#428×C89C2211yescharacteristic
43C2×#107×C89C2211yescharacteristic
44C2×#106×C89C2211yescharacteristic
45#424×C89C2211yescharacteristic
46#424×C89C2211yescharacteristic
47#423×C89C2211yescharacteristic
48C2×C4⋊C8×C89C2211yescharacteristic
49#418×C89C2211yescharacteristic
50#418×C89C2211yescharacteristic
51C2×#102×C89C2211yescharacteristic
52C2×#102×C89C2211yescharacteristic
53C2×#100×C89C2211yescharacteristic
54C2×#100×C89C2211yescharacteristic
55#405×C89C2211yescharacteristic
56#405×C89C2211yescharacteristic
57C4×M16×C89C2211yescharacteristic
58C4×M16×C89C2211yescharacteristic
59#343×C89C2211yescharacteristic
60#343×C89C2211yescharacteristic
61#343×C89C2211yescharacteristic
62#343×C89C2211yescharacteristic
63#343×C89C2211yescharacteristic
64#343×C89C2211yescharacteristic
65#341×C89C2211yescharacteristic
66#341×C89C2211yescharacteristic
67C22×D4×C89C2311yescharacteristic
68C23×C4×C89—21no—
69C2×M16×C89C2311yescharacteristic
70C2×M16×C89C2311yescharacteristic
71C2×M16×C89C2311yescharacteristic
72C2×M16×C89C2311yescharacteristic
73C2×M16×C89C2311yescharacteristic
74C2×M16×C89C2311yescharacteristic
75C22×C8×C89C2311yescharacteristic
76C22×C8×C89C2311yescharacteristic
77C4⋊Q8×C89D411yescharacteristic
78C4⋊Q8×C89D411yescharacteristic
79#125×C89—21no—
80#125×C89—21no—
81#125×C89—21no—
82#125×C89—21no—
83#125×C89D411yescharacteristic
84#125×C89D411yescharacteristic
85C22⋊Q8×C89—21no—
86C22⋊Q8×C89—21no—
87C4×Q8×C89—21no—
88C4×Q8×C89—21no—
89C4×D4×C89—21no—
90C4×D4×C89—21no—
91C4×D4×C89—21no—
92C4×D4×C89—21no—
93#117×C89C2311yescharacteristic
94#117×C89C2311yescharacteristic
95C2×C4⋊C4×C89—21no—
96C2×C4⋊C4×C89—21no—
97C2×C4⋊C4×C89C2311yescharacteristic
98C2×C4⋊C4×C89C2311yescharacteristic
99C2×C4⋊C4×C89C2311yescharacteristic
100C2×C22⋊C4×C89—21no—
101C2×C42×C89C2311yescharacteristic
102#108×C89—22no—
103#108×C89—22no—
104#107×C89—21no—
105#107×C89—21no—
106#107×C89—21no—
107#107×C89—21no—
108#107×C89—21no—
109#107×C89—21no—
110#107×C89—21no—
111#107×C89—21no—
112#106×C89—21no—
113#106×C89—21no—
114#106×C89—21no—
115#106×C89—21no—
116#106×C89—21no—
117#106×C89—21no—
118#106×C89—21no—
119#106×C89—21no—
120C4⋊C8×C89—21no—
121C4⋊C8×C89—21no—
122C4⋊C8×C89—21no—
123C4⋊C8×C89—21no—
124C4⋊C8×C89—21no—
125C4⋊C8×C89—21no—
126C4⋊C8×C89D411yescharacteristic
127C4⋊C8×C89D411yescharacteristic
128C4⋊C8×C89D411yescharacteristic
129C4⋊C8×C89D411yescharacteristic
130#102×C89—21no—
131#102×C89—21no—
132#102×C89—21no—
133#102×C89—21no—
134#102×C89—21no—
135#102×C89—21no—
136#102×C89—21no—
137#102×C89—21no—
138#100×C89—22no—
139#100×C89Q814yescomplemented
140#97×C89—21no—
141#97×C89—21no—
142#97×C89—21no—
143#97×C89—21no—
144C4×C8×C89—21no—
145C4×C8×C89—21no—
146C4×C8×C89—21no—
147C4×C8×C89—21no—
148C24×C89—21no—
149C2×Q8×C89—21no—
150C2×Q8×C89—21no—
151C2×D4×C89—21no—
152C2×D4×C89—21no—
153C2×D4×C89—21no—
154C2×D4×C89—21no—
155C2×D4×C89—21no—
156C2×D4×C89C2×Q812yes—
157C22×C4×C89—21no—
158C22×C4×C89—21no—
159C22×C4×C89—21no—
160C22×C4×C89—41no—
161C22×C4×C89—41no—
162C22×C4×C89—82no—
163C22×C4×C89#4111yescharacteristic
164C22×C4×C89#4111yescharacteristic
165C22×C4×C89C2411yescharacteristic
166M16×C89—21no—
167M16×C89—21no—
168M16×C89—21no—
169M16×C89—21no—
170M16×C89—21no—
171M16×C89—21no—
172M16×C89—21no—
173M16×C89—21no—
174M16×C89—21no—
175M16×C89C2×Q812yes—
176M16×C89C2×Q812yes—
177M16×C89#4112yes—
178C2×C8×C89—21no—
179C2×C8×C89—21no—
180C2×C8×C89—21no—
181C2×C8×C89—21no—
182C2×C8×C89—21no—
183C2×C8×C89—21no—
184C2×C8×C89—21no—
185C2×C8×C89—21no—
186C2×C8×C89—21no—
187C2×C8×C89—21no—
188C2×C8×C89C2×D411yescharacteristic
189C2×C8×C89C2×D411yescharacteristic
190C2×C8×C89C2×D411yescharacteristic
191C2×C8×C89C2×D411yescharacteristic
192C4⋊C4×C89—21no—
193C4⋊C4×C89—21no—
194C4⋊C4×C89—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89—21no—
198C4⋊C4×C89—21no—
199C4⋊C4×C89—21no—
200C4⋊C4×C89—21no—
201C4⋊C4×C89—21no—
202C4⋊C4×C89—21no—
203C4⋊C4×C89—21no—
204C4⋊C4×C89—41no—
205C4⋊C4×C89—41no—
206C4⋊C4×C89—41no—
207C4⋊C4×C89—41no—
208C4⋊C4×C89C2×D411yescharacteristic
209C4⋊C4×C89C2×D411yescharacteristic
210C4⋊C4×C89C2×D411yescharacteristic
211C4⋊C4×C89C2×D411yescharacteristic
212C22⋊C4×C89—21no—
213C22⋊C4×C89—21no—
214C22⋊C4×C89—41no—
215C22⋊C4×C89—41no—
216C42×C89—21no—
217C42×C89—21no—
218C42×C89C2×D411yescharacteristic
219C42×C89C2×D411yescharacteristic
220C42×C89C2×D411yescharacteristic
221C42×C89C2×D411yescharacteristic
222C23×C89—22no—
223C23×C89—41no—
224C23×C89—41no—
225C23×C89—81no—
226C23×C89—81no—
227C23×C89C2×#4111yescharacteristic
228Q8×C89—42no—
229Q8×C89—81no—
230D4×C89—22no—
231D4×C89—22no—
232D4×C89—41no—
233D4×C89—41no—
234C2×C4×C89—21no—
235C2×C4×C89—21no—
236C2×C4×C89—21no—
237C2×C4×C89—21no—
238C2×C4×C89—41no—
239C2×C4×C89—41no—
240C2×C4×C89—41no—
241C2×C4×C89—41no—
242C2×C4×C89—41no—
243C2×C4×C89—82no—
244C2×C4×C89—82no—
245C2×C4×C89—81no—
246C2×C4×C89—81no—
247C2×C4×C89—81no—
248C2×C4×C89#12111yescharacteristic
249C2×C4×C89#12111yescharacteristic
250C2×C4×C89#12111yescharacteristic
251C2×C4×C89#12111yescharacteristic
252C2×C4×C89C22×D411yescharacteristic
253C2×C4×C89C22×D411yescharacteristic
254C2×C4×C89C22×Q811yescharacteristic
255C2×C4×C89C2×#4111yescharacteristic
256C2×C4×C892−1+411yescharacteristic
257C2×C4×C892−1+411yescharacteristic
258C8×C89—21no—
259C8×C89—21no—
260C8×C89—21no—
261C8×C89—21no—
262C8×C89—22no—
263C8×C89—22no—
264C8×C89—22no—
265C8×C89—41no—
266C8×C89—41no—
267C8×C89—41no—
268C22×C89—21no—
269C22×C89—21no—
270C22×C89—42no—
271C22×C89—82no—
272C22×C89—82no—
273C22×C89—81no—
274C22×C89—81no—
275C22×C89C2×#12111yescharacteristic
276C22×C89#53311yescharacteristic
277C22×C89#54111yescharacteristic
278C4×C89—21no—
279C4×C89—21no—
280C4×C89—21no—
281C4×C89—21no—
282C4×C89—41no—
283C4×C89—41no—
284C4×C89—41no—
285C4×C89—41no—
286C4×C89—81no—
287C4×C89—81no—
288C4×C89—81no—
289C4×C89#54711yescharacteristic
290C4×C89#54811yescharacteristic
291C4×C89D4×Q811yescharacteristic
292C4×C89D4×Q811yescharacteristic
293#25493C8911yesmaximal, characteristic, direct product factor, Sylow
294C2×C89—21no—
295C2×C89—21no—
296C2×C89—82no—
297C2×C89#242911yescharacteristic
298C2×C89#306711yescharacteristic
299C2×C89#306811yescharacteristic
300#3166C2×C8911yescharacteristic, complemented
301#3077C2×C8911yescharacteristic
302C2×#478C2×C8911yescharacteristic
303#2962C2×C8911yescharacteristic, complemented
304#2090C2×C8911yescharacteristic, complemented
305#2089C2×C8911yescharacteristic, complemented
306#2063C2×C8911yescharacteristic
307#2063C2×C8911yescharacteristic
308#1998C2×C8911yescharacteristic, complemented
309#1952C2×C8911yescharacteristic, complemented
310#1951C2×C8911yescharacteristic, complemented
311#1950C2×C8911yescharacteristic, complemented
312#1931C2×C8911yescharacteristic
313#1931C2×C8911yescharacteristic
314C4×#100C2×C8911yescharacteristic
315C89#2549311yescharacteristic, direct product factor, Sylow
316#533C22×C8911yescharacteristic
317C2×#125C22×C8911yescharacteristic
318C2×C4×D4C22×C8911yescharacteristic
319#501—21no—
320#501—21no—
321#499—21no—
322#499—21no—
323#478—21no—
324#478—21no—
325#478—21no—
326#478—21no—
327#478—21no—
328#478—21no—
329#476—21no—
330#474—21no—
331#446—21no—
332#446—21no—
333#446—21no—
334C8×Q8—21no—
335C2×#108C22×C8911yescharacteristic
336C2×#108C22×C8911yescharacteristic
337#428C22×C8911yescharacteristic
338#428C22×C8911yescharacteristic
339#428C22×C8911yescharacteristic
340#428C22×C8911yescharacteristic
341#428C22×C8911yescharacteristic
342#428C22×C8911yescharacteristic
343C2×#107C22×C8911yescharacteristic
344C2×#106C22×C8911yescharacteristic
345#424C22×C8911yescharacteristic
346#424C22×C8911yescharacteristic
347#423C22×C8911yescharacteristic
348C2×C4⋊C8C22×C8911yescharacteristic
349#418C22×C8911yescharacteristic
350#418C22×C8911yescharacteristic
351C2×#102C22×C8911yescharacteristic
352C2×#102C22×C8911yescharacteristic
353C2×#100C22×C8911yescharacteristic
354C2×#100C22×C8911yescharacteristic
355#405C22×C8911yescharacteristic
356#405C22×C8911yescharacteristic
357C4×M16C22×C8911yescharacteristic
358C4×M16C22×C8911yescharacteristic
359#343C22×C8911yescharacteristic
360#343C22×C8911yescharacteristic
361#343C22×C8911yescharacteristic
362#343C22×C8911yescharacteristic
363#343C22×C8911yescharacteristic
364#343C22×C8911yescharacteristic
365#341C22×C8911yescharacteristic
366#341C22×C8911yescharacteristic
367C22×D4C23×C8911yescharacteristic
368C23×C4—21no—
369C2×M16C23×C8911yescharacteristic
370C2×M16C23×C8911yescharacteristic
371C2×M16C23×C8911yescharacteristic
372C2×M16C23×C8911yescharacteristic
373C2×M16C23×C8911yescharacteristic
374C2×M16C23×C8911yescharacteristic
375C22×C8C23×C8911yescharacteristic
376C22×C8C23×C8911yescharacteristic
377C4⋊Q8D4×C8911yescharacteristic
378C4⋊Q8D4×C8911yescharacteristic
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C8911yescharacteristic
384#125D4×C8911yescharacteristic
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117C23×C8911yescharacteristic
394#117C23×C8911yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C23×C8911yescharacteristic
398C2×C4⋊C4C23×C8911yescharacteristic
399C2×C4⋊C4C23×C8911yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C23×C8911yescharacteristic
402#108—22no—
403#108—22no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8D4×C8911yescharacteristic
427C4⋊C8D4×C8911yescharacteristic
428C4⋊C8D4×C8911yescharacteristic
429C4⋊C8D4×C8911yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#100—22no—
439#100Q8×C8914yescomplemented
440#97—21no—
441#97—21no—
442#97—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8—21no—
447C4×C8—21no—
448C24—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C2×Q8×C8912yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—82no—
463C22×C4#41×C8911yescharacteristic
464C22×C4#41×C8911yescharacteristic
465C22×C4C24×C8911yescharacteristic
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—21no—
471M16—21no—
472M16—21no—
473M16—21no—
474M16—21no—
475M16C2×Q8×C8912yes—
476M16C2×Q8×C8912yes—
477M16#41×C8912yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8C2×D4×C8911yescharacteristic
489C2×C8C2×D4×C8911yescharacteristic
490C2×C8C2×D4×C8911yescharacteristic
491C2×C8C2×D4×C8911yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C8911yescharacteristic
509C4⋊C4C2×D4×C8911yescharacteristic
510C4⋊C4C2×D4×C8911yescharacteristic
511C4⋊C4C2×D4×C8911yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—21no—
517C42—21no—
518C42C2×D4×C8911yescharacteristic
519C42C2×D4×C8911yescharacteristic
520C42C2×D4×C8911yescharacteristic
521C42C2×D4×C8911yescharacteristic
522C23—22no—
523C23—41no—
524C23—41no—
525C23—81no—
526C23—81no—
527C23C2×#41×C8911yescharacteristic
528Q8—42no—
529Q8—81no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4#121×C8911yescharacteristic
549C2×C4#121×C8911yescharacteristic
550C2×C4#121×C8911yescharacteristic
551C2×C4#121×C8911yescharacteristic
552C2×C4C22×D4×C8911yescharacteristic
553C2×C4C22×D4×C8911yescharacteristic
554C2×C4C22×Q8×C8911yescharacteristic
555C2×C4C2×#41×C8911yescharacteristic
556C2×C42−1+4×C8911yescharacteristic
557C2×C42−1+4×C8911yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22C2×#121×C8911yescharacteristic
576C22#533×C8911yescharacteristic
577C22#541×C8911yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4#547×C8911yescharacteristic
590C4#548×C8911yescharacteristic
591C4D4×Q8×C8911yescharacteristic
592C4D4×Q8×C8911yescharacteristic
593C2—21no—
594C2—21no—
595C2—82no—
596C2C89×#242911yescharacteristic
597C2C89×#306711yescharacteristic
598C2C89×#306811yescharacteristic
subgroupG/H
center, socleC22×C89C2×#121
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC22×D4×C89C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3166C2semidirect
4. C89×#2962C2semidirect
5. C89×#2090C2semidirect
6. C89×#2089C2semidirect
9. C89×#1998C2semidirect
10. C89×#1952C2semidirect
11. C89×#1951C2semidirect
12. C89×#1950C2semidirect
139. #100×C89Q8semidirect
293. #25493C89direct (N × H)
300. #3166C2×C89semidirect
303. #2962C2×C89semidirect
304. #2090C2×C89semidirect
305. #2089C2×C89semidirect
308. #1998C2×C89semidirect
309. #1952C2×C89semidirect
310. #1951C2×C89semidirect
311. #1950C2×C89semidirect
315. C89#25493direct (N × H)
439. #100Q8×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#31662
C89×#30772
C2×#478×C892
C89×#29622
C89×#20902
C89×#20892
C89×#20632
C89×#19982
C89×#19522
C89×#19512
C89×#19502
C89×#19312
C4×#100×C892
#2549389