Finite Group Databasebeta

← C89×#60499 #36438347

Subgroups — C89×#60499 #36438347

Order 22784.

1970 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3504C211yesmaximal, characteristic, complemented
2C4×2−1+4×C89C211yesmaximal, characteristic
3C89×#3084C213yesmaximal, complemented
4C89×#3083C213yesmaximal, complemented
5C89×#3082C213yesmaximal, complemented
6C89×#3082C213yesmaximal, complemented
7C89×#3080C213yesmaximal, complemented
8C89×#3078C213yesmaximal, complemented
9C89×#3076C213yesmaximal, complemented
10C2×#479×C89C213yesmaximal, complemented
11C89×#2913C211yesmaximal, characteristic, complemented
12C89×#2912C211yesmaximal, characteristic, complemented
13C89×#2906C211yesmaximal, characteristic, complemented
14C89×#2898C211yesmaximal, characteristic
15C89×#2898C211yesmaximal, characteristic
16C2×2−1+4×C89C2211yescharacteristic
17C2×#131×C89C2211yescharacteristic
18C2×#131×C89C2211yescharacteristic
19#557×C89—21no—
20#557×C89—21no—
21#554×C89—23no—
22#554×C89—23no—
23#544×C89C2213yes—
24#544×C89C2213yes—
25#533×C89C2213yes—
26C2×#125×C89C2213yes—
27#520×C89—23no—
28#520×C89C2213yes—
29#520×C89C2211yescharacteristic
30#520×C89C2211yescharacteristic
31#520×C89C2211yescharacteristic
32#519×C89—21no—
33#519×C89C2213yes—
34C4×#41×C89—23no—
35C4×#41×C89C2213yes—
36C4×#41×C89C2211yescharacteristic
37C2×C4×Q8×C89—21no—
38C2×C4×Q8×C89C2213yes—
39#479×C89C2213yes—
40#479×C89C2216yes—
41#479×C89C2216yes—
42#479×C89C2216yes—
43#479×C89C2213yes—
44#479×C89C2216yes—
45#478×C89C2211yescharacteristic
46#478×C89C2213yes—
47#478×C89C2216yes—
48#477×C89C2213yes—
49#477×C89C2216yes—
50#476×C89C2213yes—
51#475×C89C2213yes—
52#475×C89C2216yes—
53#474×C89C2213yes—
54#428×C89C2213yes—
55#428×C89C2213yes—
56#428×C89C2213yes—
57#428×C89C2213yes—
58#427×C89C2213yes—
59#427×C89C2213yes—
60C2×#107×C89C2213yes—
61C2×#106×C89C2213yes—
62#424×C89C2213yes—
63#424×C89C2213yes—
64#423×C89C2213yes—
65C2×C4⋊C8×C89C2213yes—
66#419×C89C2213yes—
67#419×C89C2213yes—
68#417×C89C2213yes—
69#417×C89C2213yes—
70#416×C89C2213yes—
71#416×C89C2213yes—
72C2×#103×C89C2213yes—
73C2×#103×C89C2213yes—
742−1+4×C89—24no—
752−1+4×C89Q818yescomplemented
76C2×#41×C89—23no—
77C2×#41×C89C2313yes—
78C2×#41×C89C2311yescharacteristic
79C22×Q8×C89—21no—
80C22×Q8×C89C2313yes—
81#131×C89—24no—
82#131×C89—24no—
83C2×M16×C89C2313yes—
84C2×M16×C89C2313yes—
85C22×C8×C89C2313yes—
86C22×C8×C89C2313yes—
87C4⋊Q8×C89—23no—
88C4⋊Q8×C89—23no—
89C4⋊Q8×C89C2313yes—
90C4⋊Q8×C89C2313yes—
91#125×C89—23no—
92#125×C89—23no—
93#125×C89—23no—
94#125×C89—23no—
95#125×C89C2313yes—
96#125×C89C2316yes—
97#125×C89C2311yescharacteristic
98C22⋊Q8×C89—23no—
99C22⋊Q8×C89—23no—
100C22⋊Q8×C89—26no—
101C22⋊Q8×C89—26no—
102C4×Q8×C89—21no—
103C4×Q8×C89—21no—
104C4×Q8×C89—21no—
105C4×Q8×C89—23no—
106C4×Q8×C89—23no—
107C4×Q8×C89—23no—
108C4×Q8×C89—23no—
109C4×Q8×C89—23no—
110C4×Q8×C89—23no—
111C4×Q8×C89D411yescharacteristic
112C4×Q8×C89D411yescharacteristic
113C4×Q8×C89C2316yes—
114C4×Q8×C89C2313yes—
115C4×Q8×C89C2313yes—
116C4×D4×C89—23no—
117C4×D4×C89—23no—
118C4×D4×C89—23no—
119C4×D4×C89—23no—
120C4×D4×C89—23no—
121C4×D4×C89—26no—
122C4×D4×C89D413yes—
123C4×D4×C89D413yes—
124C4×D4×C89C2313yes—
125C4×D4×C89C2311yescharacteristic
126#117×C89—23no—
127#117×C89—26no—
128#117×C89—23no—
129#117×C89C2313yes—
130#117×C89C2313yes—
131#117×C89C2313yes—
132#117×C89C2313yes—
133C2×C4⋊C4×C89—23no—
134C2×C4⋊C4×C89—23no—
135C2×C4⋊C4×C89—23no—
136C2×C4⋊C4×C89—23no—
137C2×C4⋊C4×C89C2313yes—
138C2×C4⋊C4×C89C2313yes—
139C2×C4⋊C4×C89C2313yes—
140C2×C42×C89—23no—
141C2×C42×C89—23no—
142C2×C42×C89C2313yes—
143#107×C89C2313yes—
144#107×C89C2316yes—
145#107×C89C2311yescharacteristic
146#107×C89C2313yes—
147#107×C89C2313yes—
148#106×C89C2313yes—
149#106×C89C2316yes—
150#106×C89C2311yescharacteristic
151#106×C89C2313yes—
152#106×C89C2313yes—
153C4⋊C8×C89C2311yescharacteristic
154C4⋊C8×C89C2313yes—
155C4⋊C8×C89C2313yes—
156C4⋊C8×C89C2313yes—
157C4⋊C8×C89C2316yes—
158#103×C89C2313yes—
159#103×C89C2313yes—
160#103×C89C2316yes—
161#103×C89C2316yes—
162#103×C89C2313yes—
163#103×C89C2313yes—
164#102×C89C2311yescharacteristic
165#102×C89C2311yescharacteristic
166#102×C89C2313yes—
167#102×C89C2313yes—
168#41×C89—224no—
169#41×C89—26no—
170#41×C89C2×Q8112yes—
171#41×C89C2×Q814yes—
172#41×C89#4114yes—
173C2×Q8×C89—28no—
174C2×Q8×C89—23no—
175C2×Q8×C89—23no—
176C2×Q8×C89—23no—
177C2×Q8×C89—26no—
178C2×Q8×C89C2×D411yescharacteristic
179C2×Q8×C89C2×Q8112yes—
180C2×Q8×C89C2413yes—
181C2×D4×C89—23no—
182C2×D4×C89C2×D413yes—
183C2×D4×C89C2411yescharacteristic
184C22×C4×C89—23no—
185C22×C4×C89—23no—
186C22×C4×C89—23no—
187C22×C4×C89—23no—
188C22×C4×C89—23no—
189C22×C4×C89—21no—
190C22×C4×C89—23no—
191C22×C4×C89C2×D413yes—
192C22×C4×C89C2×D413yes—
193C22×C4×C89C2413yes—
194M16×C89—26no—
195M16×C89—26no—
196C2×C8×C89—26no—
197C2×C8×C89—26no—
198C2×C8×C89C2411yescharacteristic
199C2×C8×C89C2413yes—
200C2×C8×C89C2413yes—
201C2×C8×C89C2411yescharacteristic
202C4⋊C4×C89—26no—
203C4⋊C4×C89—23no—
204C4⋊C4×C89—23no—
205C4⋊C4×C89—23no—
206C4⋊C4×C89—23no—
207C4⋊C4×C89—26no—
208C4⋊C4×C89—26no—
209C4⋊C4×C89—23no—
210C4⋊C4×C89—23no—
211C4⋊C4×C89—23no—
212C4⋊C4×C89—21no—
213C4⋊C4×C89—21no—
214C4⋊C4×C89—23no—
215C4⋊C4×C89—23no—
216C4⋊C4×C89C2×D413yes—
217C4⋊C4×C89C2×D413yes—
218C4⋊C4×C89C2413yes—
219C4⋊C4×C89C2411yescharacteristic
220C4⋊C4×C89C2413yes—
221C4⋊C4×C89C2411yescharacteristic
222C4⋊C4×C89C2413yes—
223C4⋊C4×C89C2411yescharacteristic
224C22⋊C4×C89—23no—
225C22⋊C4×C89—23no—
226C22⋊C4×C89—23no—
227C22⋊C4×C89—21no—
228C22⋊C4×C89—23no—
229C22⋊C4×C89C2×D416yes—
230C42×C89—23no—
231C42×C89—23no—
232C42×C89—26no—
233C42×C89—23no—
234C42×C89—23no—
235C42×C89—23no—
236C42×C89C2×D413yes—
237C42×C89C2×D413yes—
238C42×C89C2411yescharacteristic
239C42×C89C2413yes—
240C23×C89—21no—
241C23×C89C22×D413yes—
242Q8×C89—212no—
243Q8×C89—23no—
244Q8×C89—83no—
245Q8×C89—83no—
246Q8×C89C22⋊Q814yes—
247Q8×C89C22×Q816yes—
248D4×C89—212no—
249D4×C89—21no—
250D4×C89C22⋊Q8112yes—
251D4×C89C22×Q812yes—
252C2×C4×C89—212no—
253C2×C4×C89—23no—
254C2×C4×C89—212no—
255C2×C4×C89—21no—
256C2×C4×C89—23no—
257C2×C4×C89—21no—
258C2×C4×C89—21no—
259C2×C4×C89—23no—
260C2×C4×C89—23no—
261C2×C4×C89—43no—
262C2×C4×C89—43no—
263C2×C4×C89—42no—
264C2×C4×C89—83no—
265C2×C4×C89—83no—
266C2×C4×C89—83no—
267C2×C4×C89—83no—
268C2×C4×C89C22×D411yescharacteristic
269C2×C4×C89C22×D413yes—
270C2×C4×C89C22×D413yes—
271C2×C4×C89C22×D411yescharacteristic
272C2×C4×C89C22×D413yes—
273C2×C4×C89C22×Q816yes—
274C2×C4×C89C2×#4116yes—
275C2×C4×C89C2511yescharacteristic
276C8×C89—21no—
277C8×C89—21no—
278C8×C89—23no—
279C8×C89—23no—
280C22×C89—23no—
281C22×C89—23no—
282C22×C89—22no—
283C22×C89—41no—
284C22×C89—41no—
285C22×C89C2×C22⋊Q816yes—
286C22×C89C23×D411yescharacteristic
287C4×C89—21no—
288C4×C89—23no—
289C4×C89—21no—
290C4×C89—23no—
291C4×C89—26no—
292C4×C89—43no—
293C4×C89—43no—
294C4×C89—41no—
295C4×C89—41no—
296C4×C89—43no—
297C4×C89—41no—
298C4×C89C2×C22⋊Q816yes—
299C4×C89C23×Q811yescharacteristic
300C4×C89C22×#4111yescharacteristic
301#60499C8911yesmaximal, characteristic, direct product factor, Sylow
302C2×C89—26no—
303C2×C89—42no—
304C2×C89C22×C22⋊Q811yescharacteristic
305C2×C89#358411yescharacteristic
306C2×C89#358611yescharacteristic
307#3504C2×C8911yescharacteristic, complemented
308C4×2−1+4C2×C8911yescharacteristic
309#3084C2×C8913yescomplemented
310#3083C2×C8913yescomplemented
311#3082C2×C8913yescomplemented
312#3082C2×C8913yescomplemented
313#3080C2×C8913yescomplemented
314#3078C2×C8913yescomplemented
315#3076C2×C8913yescomplemented
316C2×#479C2×C8913yescomplemented
317#2913C2×C8911yescharacteristic, complemented
318#2912C2×C8911yescharacteristic, complemented
319#2906C2×C8911yescharacteristic, complemented
320#2898C2×C8911yescharacteristic
321#2898C2×C8911yescharacteristic
322C89#6049911yescharacteristic, direct product factor, Sylow
323C2×2−1+4C22×C8911yescharacteristic
324C2×#131C22×C8911yescharacteristic
325C2×#131C22×C8911yescharacteristic
326#557—21no—
327#557—21no—
328#554—23no—
329#554—23no—
330#544C22×C8913yes—
331#544C22×C8913yes—
332#533C22×C8913yes—
333C2×#125C22×C8913yes—
334#520—23no—
335#520C22×C8913yes—
336#520C22×C8911yescharacteristic
337#520C22×C8911yescharacteristic
338#520C22×C8911yescharacteristic
339#519—21no—
340#519C22×C8913yes—
341C4×#41—23no—
342C4×#41C22×C8913yes—
343C4×#41C22×C8911yescharacteristic
344C2×C4×Q8—21no—
345C2×C4×Q8C22×C8913yes—
346#479C22×C8913yes—
347#479C22×C8916yes—
348#479C22×C8916yes—
349#479C22×C8916yes—
350#479C22×C8913yes—
351#479C22×C8916yes—
352#478C22×C8911yescharacteristic
353#478C22×C8913yes—
354#478C22×C8916yes—
355#477C22×C8913yes—
356#477C22×C8916yes—
357#476C22×C8913yes—
358#475C22×C8913yes—
359#475C22×C8916yes—
360#474C22×C8913yes—
361#428C22×C8913yes—
362#428C22×C8913yes—
363#428C22×C8913yes—
364#428C22×C8913yes—
365#427C22×C8913yes—
366#427C22×C8913yes—
367C2×#107C22×C8913yes—
368C2×#106C22×C8913yes—
369#424C22×C8913yes—
370#424C22×C8913yes—
371#423C22×C8913yes—
372C2×C4⋊C8C22×C8913yes—
373#419C22×C8913yes—
374#419C22×C8913yes—
375#417C22×C8913yes—
376#417C22×C8913yes—
377#416C22×C8913yes—
378#416C22×C8913yes—
379C2×#103C22×C8913yes—
380C2×#103C22×C8913yes—
3812−1+4—24no—
3822−1+4Q8×C8918yescomplemented
383C2×#41—23no—
384C2×#41C23×C8913yes—
385C2×#41C23×C8911yescharacteristic
386C22×Q8—21no—
387C22×Q8C23×C8913yes—
388#131—24no—
389#131—24no—
390C2×M16C23×C8913yes—
391C2×M16C23×C8913yes—
392C22×C8C23×C8913yes—
393C22×C8C23×C8913yes—
394C4⋊Q8—23no—
395C4⋊Q8—23no—
396C4⋊Q8C23×C8913yes—
397C4⋊Q8C23×C8913yes—
398#125—23no—
399#125—23no—
400#125—23no—
401#125—23no—
402#125C23×C8913yes—
403#125C23×C8916yes—
404#125C23×C8911yescharacteristic
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—26no—
408C22⋊Q8—26no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8D4×C8911yescharacteristic
419C4×Q8D4×C8911yescharacteristic
420C4×Q8C23×C8913yes—
421C4×Q8C23×C8916yes—
422C4×Q8C23×C8913yes—
423C4×D4—23no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—26no—
429C4×D4D4×C8913yes—
430C4×D4D4×C8913yes—
431C4×D4C23×C8911yescharacteristic
432C4×D4C23×C8913yes—
433#117—23no—
434#117—26no—
435#117—23no—
436#117C23×C8913yes—
437#117C23×C8913yes—
438#117C23×C8913yes—
439#117C23×C8913yes—
440C2×C4⋊C4—23no—
441C2×C4⋊C4—23no—
442C2×C4⋊C4—23no—
443C2×C4⋊C4—23no—
444C2×C4⋊C4C23×C8913yes—
445C2×C4⋊C4C23×C8913yes—
446C2×C4⋊C4C23×C8913yes—
447C2×C42—23no—
448C2×C42—23no—
449C2×C42C23×C8913yes—
450#107C23×C8913yes—
451#107C23×C8916yes—
452#107C23×C8911yescharacteristic
453#107C23×C8913yes—
454#107C23×C8913yes—
455#106C23×C8913yes—
456#106C23×C8916yes—
457#106C23×C8911yescharacteristic
458#106C23×C8913yes—
459#106C23×C8913yes—
460C4⋊C8C23×C8911yescharacteristic
461C4⋊C8C23×C8913yes—
462C4⋊C8C23×C8913yes—
463C4⋊C8C23×C8913yes—
464C4⋊C8C23×C8916yes—
465#103C23×C8913yes—
466#103C23×C8913yes—
467#103C23×C8916yes—
468#103C23×C8916yes—
469#103C23×C8913yes—
470#103C23×C8913yes—
471#102C23×C8911yescharacteristic
472#102C23×C8911yescharacteristic
473#102C23×C8913yes—
474#102C23×C8913yes—
475#41—224no—
476#41—26no—
477#41C2×Q8×C89112yes—
478#41C2×Q8×C8914yes—
479#41#41×C8914yes—
480C2×Q8—28no—
481C2×Q8—23no—
482C2×Q8—23no—
483C2×Q8—23no—
484C2×Q8—26no—
485C2×Q8C2×D4×C8911yescharacteristic
486C2×Q8C2×Q8×C89112yes—
487C2×Q8C24×C8913yes—
488C2×D4—23no—
489C2×D4C2×D4×C8913yes—
490C2×D4C24×C8911yescharacteristic
491C22×C4—23no—
492C22×C4—23no—
493C22×C4—23no—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—21no—
497C22×C4—23no—
498C22×C4C2×D4×C8913yes—
499C22×C4C2×D4×C8913yes—
500C22×C4C24×C8913yes—
501M16—26no—
502M16—26no—
503C2×C8—26no—
504C2×C8—26no—
505C2×C8C24×C8911yescharacteristic
506C2×C8C24×C8913yes—
507C2×C8C24×C8913yes—
508C2×C8C24×C8911yescharacteristic
509C4⋊C4—26no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—26no—
515C4⋊C4—26no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4C2×D4×C8913yes—
524C4⋊C4C2×D4×C8913yes—
525C4⋊C4C24×C8913yes—
526C4⋊C4C24×C8911yescharacteristic
527C4⋊C4C24×C8913yes—
528C4⋊C4C24×C8911yescharacteristic
529C4⋊C4C24×C8913yes—
530C4⋊C4C24×C8911yescharacteristic
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—23no—
534C22⋊C4—21no—
535C22⋊C4—23no—
536C22⋊C4C2×D4×C8916yes—
537C42—23no—
538C42—23no—
539C42—26no—
540C42—23no—
541C42—23no—
542C42—23no—
543C42C2×D4×C8913yes—
544C42C2×D4×C8913yes—
545C42C24×C8911yescharacteristic
546C42C24×C8913yes—
547C23—21no—
548C23C22×D4×C8913yes—
549Q8—212no—
550Q8—23no—
551Q8—83no—
552Q8—83no—
553Q8C22⋊Q8×C8914yes—
554Q8C22×Q8×C8916yes—
555D4—212no—
556D4—21no—
557D4C22⋊Q8×C89112yes—
558D4C22×Q8×C8912yes—
559C2×C4—212no—
560C2×C4—23no—
561C2×C4—212no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—43no—
569C2×C4—43no—
570C2×C4—42no—
571C2×C4—83no—
572C2×C4—83no—
573C2×C4—83no—
574C2×C4—83no—
575C2×C4C22×D4×C8911yescharacteristic
576C2×C4C22×D4×C8913yes—
577C2×C4C22×D4×C8913yes—
578C2×C4C22×D4×C8911yescharacteristic
579C2×C4C22×D4×C8913yes—
580C2×C4C22×Q8×C8916yes—
581C2×C4C2×#41×C8916yes—
582C2×C4C25×C8911yescharacteristic
583C8—21no—
584C8—21no—
585C8—23no—
586C8—23no—
587C22—23no—
588C22—23no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22C2×C22⋊Q8×C8916yes—
593C22C23×D4×C8911yescharacteristic
594C4—21no—
595C4—23no—
596C4—21no—
597C4—23no—
598C4—26no—
599C4—43no—
600C4—43no—
601C4—41no—
602C4—41no—
603C4—43no—
604C4—41no—
605C4C2×C22⋊Q8×C8916yes—
606C4C23×Q8×C8911yescharacteristic
607C4C22×#41×C8911yescharacteristic
608C2—26no—
609C2—42no—
610C2C22×C22⋊Q8×C8911yescharacteristic
611C2C89×#358411yescharacteristic
612C2C89×#358611yescharacteristic
subgroupG/H
center, socleC22×C89C23×D4
commutator, Frattini, cosocleC2×C4C25×C89
prime radicalC2×2−1+4×C89C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ C4×#41×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3504C2semidirect
3. C89×#3084C2semidirect
4. C89×#3083C2semidirect
5. C89×#3082C2semidirect
6. C89×#3082C2semidirect
7. C89×#3080C2semidirect
8. C89×#3078C2semidirect
9. C89×#3076C2semidirect
10. C2×#479×C89C2semidirect
11. C89×#2913C2semidirect
12. C89×#2912C2semidirect
13. C89×#2906C2semidirect
75. 2−1+4×C89Q8semidirect
301. #60499C89direct (N × H)
307. #3504C2×C89semidirect
309. #3084C2×C89semidirect
310. #3083C2×C89semidirect
311. #3082C2×C89semidirect
312. #3082C2×C89semidirect
313. #3080C2×C89semidirect
314. #3078C2×C89semidirect
315. #3076C2×C89semidirect
316. C2×#479C2×C89semidirect
317. #2913C2×C89semidirect
318. #2912C2×C89semidirect
319. #2906C2×C89semidirect
322. C89#60499direct (N × H)
382. 2−1+4Q8×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#35042
C4×2−1+4×C892
C89×#30842
C89×#30832
C89×#30822
C89×#30802
C89×#30782
C89×#30762
C2×#479×C892
C89×#29132
C89×#29122
C89×#29062
C89×#28982
#6049989