Finite Group Databasebeta

← C89×#19479 #36397327

Subgroups — C89×#19479 #36397327

Order 22784.

612 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3228C211yesmaximal, characteristic
2C89×#3104C211yesmaximal, characteristic, complemented
3C89×#3037C211yesmaximal, characteristic
4C89×#2984C211yesmaximal, characteristic, complemented
5C89×#1702C211yesmaximal, characteristic, complemented
6C89×#1698C211yesmaximal, characteristic, complemented
7C89×#1694C211yesmaximal, characteristic, complemented
8C89×#1692C211yesmaximal, characteristic, complemented
9C89×#1682C211yesmaximal, characteristic, complemented
10C89×#1678C211yesmaximal, characteristic, complemented
11C89×#1674C211yesmaximal, characteristic, complemented
12C89×#1672C211yesmaximal, characteristic, complemented
13C89×#1574C211yesmaximal, characteristic, complemented
14C89×#1559C211yesmaximal, characteristic, complemented
15C89×#1553C211yesmaximal, characteristic
16C2×#137×C89—21no—
17#533×C89C2211yescharacteristic
18#532×C89C2211yescharacteristic
19C2×C4×Q8×C89C2211yescharacteristic
20#500×C89C2211yescharacteristic
21#498×C89C2211yescharacteristic
22#486×C89C2211yescharacteristic
23#486×C89C2211yescharacteristic
24#484×C89—21no—
25#482×C89—21no—
26#482×C89—21no—
27#478×C89—21no—
28#478×C89—21no—
29#477×C89C2211yescharacteristic
30#477×C89C2211yescharacteristic
31#464×C89—21no—
32#464×C89—21no—
33#462×C89C2211yescharacteristic
34#462×C89C2211yescharacteristic
35#462×C89C2211yescharacteristic
36#462×C89C2211yescharacteristic
37#460×C89C2211yescharacteristic
38#460×C89C2211yescharacteristic
39#451×C89—21no—
40#446×C89—21no—
41#446×C89—21no—
42#446×C89C2211yescharacteristic
43#446×C89C2211yescharacteristic
44C8×Q8×C89C2211yescharacteristic
45C8×Q8×C89C2211yescharacteristic
46C4×Q16×C89—21no—
47C4×Q16×C89—21no—
48#432×C89—21no—
49#432×C89C2211yescharacteristic
50#431×C89—21no—
51#431×C89C2211yescharacteristic
52#431×C89C2211yescharacteristic
53#423×C89C2211yescharacteristic
54#417×C89—21no—
55#335×C89C2211yescharacteristic
56#335×C89C2211yescharacteristic
57#334×C89C2211yescharacteristic
58#334×C89C2211yescharacteristic
59#333×C89C2211yescharacteristic
60#333×C89C2211yescharacteristic
61#332×C89C2211yescharacteristic
62#332×C89C2211yescharacteristic
63#332×C89C2211yescharacteristic
64#332×C89C2211yescharacteristic
65#331×C89C2211yescharacteristic
66#331×C89C2211yescharacteristic
67C2×#41×C89—21no—
68C22×Q8×C89D411yescharacteristic
69#137×C89—44no—
70C2×Q16×C89—21no—
71C2×Q16×C89—21no—
72C2×Q16×C89—21no—
73C2×Q16×C89—21no—
74C2×SD16×C89—21no—
75C2×SD16×C89—21no—
76C2×M16×C89—21no—
77C4⋊Q8×C89C2311yescharacteristic
78C4⋊Q8×C89C2311yescharacteristic
79C4⋊Q8×C89C2311yescharacteristic
80#127×C89C2311yescharacteristic
81#125×C89—21no—
82#124×C89—21no—
83C22⋊Q8×C89—21no—
84C22⋊Q8×C89—21no—
85#121×C89—21no—
86#121×C89—21no—
87C4×Q8×C89—21no—
88C4×Q8×C89—21no—
89C4×Q8×C89—21no—
90C4×Q8×C89—21no—
91C4×Q8×C89D411yescharacteristic
92C4×Q8×C89D411yescharacteristic
93C4×Q8×C89C2311yescharacteristic
94C4×Q8×C89C2311yescharacteristic
95C4×D4×C89—21no—
96C4×D4×C89—21no—
97#117×C89—21no—
98C2×C4⋊C4×C89—21no—
99C2×C4⋊C4×C89D411yescharacteristic
100C2×C42×C89—21no—
101C2×C42×C89C2311yescharacteristic
102#107×C89—21no—
103#107×C89—21no—
104#107×C89—21no—
105#107×C89—21no—
106#106×C89—21no—
107#106×C89—21no—
108C4⋊C8×C89—21no—
109C4⋊C8×C89—21no—
110C4⋊C8×C89—21no—
111C4⋊C8×C89—21no—
112C4⋊C8×C89—21no—
113C4⋊C8×C89D411yescharacteristic
114C4⋊C8×C89D411yescharacteristic
115C4⋊C8×C89C2311yescharacteristic
116C4⋊C8×C89C2311yescharacteristic
117C4⋊C8×C89C2311yescharacteristic
118C4⋊C8×C89C2311yescharacteristic
119C4⋊C8×C89C2311yescharacteristic
120C4⋊C8×C89C2311yescharacteristic
121#103×C89—21no—
122#103×C89—21no—
123#103×C89—21no—
124#103×C89—21no—
125#103×C89—21no—
126#103×C89—21no—
127#102×C89—21no—
128#102×C89—21no—
129#102×C89—21no—
130#102×C89—21no—
131#102×C89—21no—
132#102×C89—21no—
133C22⋊C8×C89—21no—
134C22⋊C8×C89—21no—
135C22⋊C8×C89D411yescharacteristic
136C22⋊C8×C89D411yescharacteristic
137#97×C89—21no—
138#97×C89—21no—
139#97×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89—21no—
142C4×C8×C89—21no—
143C4×C8×C89C2311yescharacteristic
144C4×C8×C89C2311yescharacteristic
145#41×C89—42no—
146#41×C89—42no—
147C2×Q8×C89—21no—
148C2×Q8×C89—22no—
149C2×Q8×C89—21no—
150C2×Q8×C89—21no—
151C2×Q8×C89—21no—
152C2×Q8×C89—41no—
153C2×Q8×C89C2×D411yescharacteristic
154C2×Q8×C89C2×D411yescharacteristic
155C2×D4×C89—21no—
156C2×D4×C89—21no—
157C2×D4×C89—21no—
158C2×D4×C89—41no—
159C22×C4×C89—21no—
160C22×C4×C89—21no—
161C22×C4×C89—41no—
162C22×C4×C89C2×D411yescharacteristic
163C22×C4×C89C2×D411yescharacteristic
164C22×C4×C89#4111yescharacteristic
165Q16×C89—42no—
166Q16×C89—42no—
167Q16×C89—42no—
168Q16×C89—42no—
169SD16×C89—42no—
170SD16×C89—42no—
171M16×C89—42no—
172C2×C8×C89—21no—
173C2×C8×C89—21no—
174C2×C8×C89—21no—
175C2×C8×C89—21no—
176C2×C8×C89—21no—
177C2×C8×C89—21no—
178C2×C8×C89C2×D411yescharacteristic
179C2×C8×C89C2×D411yescharacteristic
180C2×C8×C89C2×D411yescharacteristic
181C2×C8×C89C2×D411yescharacteristic
182C4⋊C4×C89—21no—
183C4⋊C4×C89—21no—
184C4⋊C4×C89—21no—
185C4⋊C4×C89—21no—
186C4⋊C4×C89—21no—
187C4⋊C4×C89—21no—
188C4⋊C4×C89—21no—
189C4⋊C4×C89—21no—
190C4⋊C4×C89—21no—
191C4⋊C4×C89—21no—
192C4⋊C4×C89—21no—
193C4⋊C4×C89—41no—
194C4⋊C4×C89—41no—
195C4⋊C4×C89C2×D411yescharacteristic
196C4⋊C4×C89C2×D411yescharacteristic
197C22⋊C4×C89—41no—
198C22⋊C4×C89—41no—
199C22⋊C4×C89—41no—
200C42×C89—21no—
201C42×C89—21no—
202C42×C89—21no—
203C42×C89—21no—
204C42×C89—41no—
205C42×C89C2×D411yescharacteristic
206C42×C89C2×D411yescharacteristic
207C42×C89#4111yescharacteristic
208C42×C89C2411yescharacteristic
209C23×C89—41no—
210C23×C89#12111yescharacteristic
211Q8×C89—21no—
212Q8×C89—21no—
213Q8×C89—21no—
214Q8×C89—42no—
215Q8×C89—41no—
216Q8×C89—41no—
217Q8×C89—41no—
218Q8×C89—41no—
219Q8×C89—81no—
220Q8×C89AGL(1,ℤ/8)12yes—
221D4×C89—41no—
222D4×C89—41no—
223D4×C89—41no—
224D4×C89—41no—
225D4×C89—81no—
226D4×C89—82no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—21no—
232C2×C4×C89—21no—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—41no—
236C2×C4×C89—42no—
237C2×C4×C89—42no—
238C2×C4×C89—41no—
239C2×C4×C89—41no—
240C2×C4×C89—41no—
241C2×C4×C89—82no—
242C2×C4×C89#12111yescharacteristic
243C2×C4×C89#12111yescharacteristic
244C2×C4×C89#12111yescharacteristic
245C2×C4×C89C22×D411yescharacteristic
246C2×C4×C89C22×D411yescharacteristic
247C2×C4×C89C2×#4111yescharacteristic
248C8×C89—21no—
249C8×C89—21no—
250C8×C89—21no—
251C8×C89—21no—
252C8×C89—41no—
253C8×C89—41no—
254C8×C89—41no—
255C8×C89—41no—
256C8×C89—41no—
257C8×C89—41no—
258C22×C89—21no—
259C22×C89—21no—
260C22×C89—21no—
261C22×C89—81no—
262C22×C89—81no—
263C22×C89—81no—
264C22×C89C2×#12111yescharacteristic
265C4×C89—21no—
266C4×C89—21no—
267C4×C89—22no—
268C4×C89—21no—
269C4×C89—21no—
270C4×C89—41no—
271C4×C89—41no—
272C4×C89—41no—
273C4×C89—81no—
274C4×C89—81no—
275C4×C89—81no—
276C4×C89C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C89#57511yescharacteristic
278C4×C89#57811yescharacteristic
279C4×C89#57811yescharacteristic
280#19479C8911yesmaximal, characteristic, direct product factor, Sylow
281C2×C89—41no—
282C2×C89—161no—
283C2×C89#304411yescharacteristic
284C2×C89#305511yescharacteristic
285C2×C89#306711yescharacteristic
286#3228C2×C8911yescharacteristic
287#3104C2×C8911yescharacteristic, complemented
288#3037C2×C8911yescharacteristic
289#2984C2×C8911yescharacteristic, complemented
290#1702C2×C8911yescharacteristic, complemented
291#1698C2×C8911yescharacteristic, complemented
292#1694C2×C8911yescharacteristic, complemented
293#1692C2×C8911yescharacteristic, complemented
294#1682C2×C8911yescharacteristic, complemented
295#1678C2×C8911yescharacteristic, complemented
296#1674C2×C8911yescharacteristic, complemented
297#1672C2×C8911yescharacteristic, complemented
298#1574C2×C8911yescharacteristic, complemented
299#1559C2×C8911yescharacteristic, complemented
300#1553C2×C8911yescharacteristic
301C89#1947911yescharacteristic, direct product factor, Sylow
302C2×#137—21no—
303#533C22×C8911yescharacteristic
304#532C22×C8911yescharacteristic
305C2×C4×Q8C22×C8911yescharacteristic
306#500C22×C8911yescharacteristic
307#498C22×C8911yescharacteristic
308#486C22×C8911yescharacteristic
309#486C22×C8911yescharacteristic
310#484—21no—
311#482—21no—
312#482—21no—
313#478—21no—
314#478—21no—
315#477C22×C8911yescharacteristic
316#477C22×C8911yescharacteristic
317#464—21no—
318#464—21no—
319#462C22×C8911yescharacteristic
320#462C22×C8911yescharacteristic
321#462C22×C8911yescharacteristic
322#462C22×C8911yescharacteristic
323#460C22×C8911yescharacteristic
324#460C22×C8911yescharacteristic
325#451—21no—
326#446—21no—
327#446—21no—
328#446C22×C8911yescharacteristic
329#446C22×C8911yescharacteristic
330C8×Q8C22×C8911yescharacteristic
331C8×Q8C22×C8911yescharacteristic
332C4×Q16—21no—
333C4×Q16—21no—
334#432—21no—
335#432C22×C8911yescharacteristic
336#431—21no—
337#431C22×C8911yescharacteristic
338#431C22×C8911yescharacteristic
339#423C22×C8911yescharacteristic
340#417—21no—
341#335C22×C8911yescharacteristic
342#335C22×C8911yescharacteristic
343#334C22×C8911yescharacteristic
344#334C22×C8911yescharacteristic
345#333C22×C8911yescharacteristic
346#333C22×C8911yescharacteristic
347#332C22×C8911yescharacteristic
348#332C22×C8911yescharacteristic
349#332C22×C8911yescharacteristic
350#332C22×C8911yescharacteristic
351#331C22×C8911yescharacteristic
352#331C22×C8911yescharacteristic
353C2×#41—21no—
354C22×Q8D4×C8911yescharacteristic
355#137—44no—
356C2×Q16—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×M16—21no—
363C4⋊Q8C23×C8911yescharacteristic
364C4⋊Q8C23×C8911yescharacteristic
365C4⋊Q8C23×C8911yescharacteristic
366#127C23×C8911yescharacteristic
367#125—21no—
368#124—21no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371#121—21no—
372#121—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8D4×C8911yescharacteristic
378C4×Q8D4×C8911yescharacteristic
379C4×Q8C23×C8911yescharacteristic
380C4×Q8C23×C8911yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383#117—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C8911yescharacteristic
386C2×C42—21no—
387C2×C42C23×C8911yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8D4×C8911yescharacteristic
400C4⋊C8D4×C8911yescharacteristic
401C4⋊C8C23×C8911yescharacteristic
402C4⋊C8C23×C8911yescharacteristic
403C4⋊C8C23×C8911yescharacteristic
404C4⋊C8C23×C8911yescharacteristic
405C4⋊C8C23×C8911yescharacteristic
406C4⋊C8C23×C8911yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8D4×C8911yescharacteristic
422C22⋊C8D4×C8911yescharacteristic
423#97—21no—
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8C23×C8911yescharacteristic
430C4×C8C23×C8911yescharacteristic
431#41—42no—
432#41—42no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8C2×D4×C8911yescharacteristic
440C2×Q8C2×D4×C8911yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4C2×D4×C8911yescharacteristic
449C22×C4C2×D4×C8911yescharacteristic
450C22×C4#41×C8911yescharacteristic
451Q16—42no—
452Q16—42no—
453Q16—42no—
454Q16—42no—
455SD16—42no—
456SD16—42no—
457M16—42no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8C2×D4×C8911yescharacteristic
465C2×C8C2×D4×C8911yescharacteristic
466C2×C8C2×D4×C8911yescharacteristic
467C2×C8C2×D4×C8911yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C8911yescharacteristic
482C4⋊C4C2×D4×C8911yescharacteristic
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42C2×D4×C8911yescharacteristic
492C42C2×D4×C8911yescharacteristic
493C42#41×C8911yescharacteristic
494C42C24×C8911yescharacteristic
495C23—41no—
496C23#121×C8911yescharacteristic
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—42no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8AGL(1,ℤ/8)×C8912yes—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—82no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4#121×C8911yescharacteristic
529C2×C4#121×C8911yescharacteristic
530C2×C4#121×C8911yescharacteristic
531C2×C4C22×D4×C8911yescharacteristic
532C2×C4C22×D4×C8911yescharacteristic
533C2×C4C2×#41×C8911yescharacteristic
534C8—21no—
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22C2×#121×C8911yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—22no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×AGL(1,ℤ/8)×C8911yescharacteristic
563C4#575×C8911yescharacteristic
564C4#578×C8911yescharacteristic
565C4#578×C8911yescharacteristic
566C2—41no—
567C2—161no—
568C2C89×#304411yescharacteristic
569C2C89×#305511yescharacteristic
570C2C89×#306711yescharacteristic
subgroupG/H
center, socleC22×C89C2×#121
commutator, Frattini, cosocleC42C24×C89
prime radical#532×C89C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#3104C2semidirect
4. C89×#2984C2semidirect
5. C89×#1702C2semidirect
6. C89×#1698C2semidirect
7. C89×#1694C2semidirect
8. C89×#1692C2semidirect
9. C89×#1682C2semidirect
10. C89×#1678C2semidirect
11. C89×#1674C2semidirect
12. C89×#1672C2semidirect
13. C89×#1574C2semidirect
14. C89×#1559C2semidirect
280. #19479C89direct (N × H)
287. #3104C2×C89semidirect
289. #2984C2×C89semidirect
290. #1702C2×C89semidirect
291. #1698C2×C89semidirect
292. #1694C2×C89semidirect
293. #1692C2×C89semidirect
294. #1682C2×C89semidirect
295. #1678C2×C89semidirect
296. #1674C2×C89semidirect
297. #1672C2×C89semidirect
298. #1574C2×C89semidirect
299. #1559C2×C89semidirect
301. C89#19479direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#32282
C89×#31042
C89×#30372
C89×#29842
C89×#17022
C89×#16982
C89×#16942
C89×#16922
C89×#16822
C89×#16782
C89×#16742
C89×#16722
C89×#15742
C89×#15592
C89×#15532
#1947989