Finite Group Databasebeta

← C89×#24930 #36402778

Subgroups — C89×#24930 #36402778

Order 22784.

862 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3098C211yesmaximal, characteristic, complemented
2C89×#3013C211yesmaximal, characteristic
3C89×#2952C211yesmaximal, characteristic, complemented
4C89×#2898C211yesmaximal, characteristic, complemented
5C89×#2097C211yesmaximal, characteristic, complemented
6C89×#2079C211yesmaximal, characteristic, complemented
7C89×#2052C211yesmaximal, characteristic, complemented
8C89×#2040C211yesmaximal, characteristic, complemented
9C89×#1930C211yesmaximal, characteristic, complemented
10C89×#1929C211yesmaximal, characteristic, complemented
11C89×#1882C211yesmaximal, characteristic, complemented
12C89×#1876C211yesmaximal, characteristic, complemented
13C89×#1860C211yesmaximal, characteristic, complemented
14C89×#1816C211yesmaximal, characteristic, complemented
15C89×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C89C2211yescharacteristic
17C2×#137×C89C2211yescharacteristic
18C2×#135×C89C2211yescharacteristic
19C2×#131×C89C2211yescharacteristic
20#537×C89C2211yescharacteristic
21#520×C89C2211yescharacteristic
22#520×C89C2211yescharacteristic
23#485×C89—21no—
24#484×C89—21no—
25#482×C89—21no—
26#480×C89—21no—
27#452×C89—21no—
28#451×C89—21no—
29#449×C89—21no—
30#448×C89—21no—
31#442×C89—21no—
32#441×C89—21no—
33C4×SD16×C89—21no—
34C4×SD16×C89—21no—
35C2×#108×C89C2211yescharacteristic
36#428×C89C2211yescharacteristic
37C2×#107×C89C2211yescharacteristic
38C2×#106×C89C2211yescharacteristic
39C2×#104×C89C2211yescharacteristic
40C2×#104×C89C2211yescharacteristic
41C2×#104×C89C2211yescharacteristic
42#419×C89—21no—
43#419×C89C2211yescharacteristic
44#417×C89—21no—
45#417×C89C2211yescharacteristic
46#417×C89C2211yescharacteristic
47#417×C89C2211yescharacteristic
48#417×C89C2211yescharacteristic
49#417×C89C2211yescharacteristic
50#416×C89—21no—
51#416×C89C2211yescharacteristic
52C2×#103×C89—21no—
53C2×#103×C89C2211yescharacteristic
54C2×#103×C89C2211yescharacteristic
55C2×#101×C89C2211yescharacteristic
56#408×C89C2211yescharacteristic
57#408×C89C2211yescharacteristic
58#405×C89C2211yescharacteristic
59#391×C89C2211yescharacteristic
60#382×C89C2211yescharacteristic
61#343×C89C2211yescharacteristic
62#343×C89C2211yescharacteristic
63#343×C89C2211yescharacteristic
64#341×C89C2211yescharacteristic
65#339×C89C2211yescharacteristic
66#336×C89C2211yescharacteristic
672−1+4×C89—22no—
682−1+4×C89—22no—
692−1+4×C89—22no—
702−1+4×C89—41no—
71C2×#41×C89—21no—
72C2×#41×C89—21no—
73C2×#41×C89—41no—
74C2×#41×C89C2311yescharacteristic
75C2×#41×C89C2311yescharacteristic
76C2×#41×C89C2311yescharacteristic
77C22×Q8×C89—21no—
78C22×Q8×C89—21no—
79C22×Q8×C89C2311yescharacteristic
80#137×C89—22no—
81#137×C89—41no—
82#135×C89—22no—
83#135×C89—22no—
84C2×Q16×C89—21no—
85C2×Q16×C89D411yescharacteristic
86C2×SD16×C89—21no—
87C2×SD16×C89D411yescharacteristic
88C2×SD16×C89D411yescharacteristic
89C2×D8×C89D411yescharacteristic
90#131×C89—22no—
91#131×C89—41no—
92C2×M16×C89—21no—
93C2×M16×C89C2311yescharacteristic
94C2×M16×C89C2311yescharacteristic
95C2×M16×C89C2311yescharacteristic
96C2×M16×C89C2311yescharacteristic
97C22×C8×C89—21no—
98C22×C8×C89C2311yescharacteristic
99C22×C8×C89C2311yescharacteristic
100C22⋊Q8×C89—21no—
101C22⋊Q8×C89—21no—
102#121×C89—21no—
103#121×C89—21no—
104#121×C89—41no—
105C4×Q8×C89—21no—
106C4×Q8×C89—21no—
107C4×D4×C89—21no—
108C4×D4×C89—21no—
109C4×D4×C89—41no—
110C4×D4×C89—41no—
111#117×C89—21no—
112#117×C89—21no—
113#117×C89C2311yescharacteristic
114C2×C4⋊C4×C89—21no—
115C2×C4⋊C4×C89—21no—
116C2×C4⋊C4×C89C2311yescharacteristic
117C2×C4⋊C4×C89C2311yescharacteristic
118C2×C4⋊C4×C89C2311yescharacteristic
119C2×C42×C89C2311yescharacteristic
120#108×C89—41no—
121#107×C89—21no—
122#107×C89—21no—
123#107×C89—21no—
124#106×C89—21no—
125#106×C89—21no—
126#106×C89—21no—
127#104×C89—22no—
128#104×C89—41no—
129#104×C89—41no—
130#103×C89—21no—
131#103×C89—21no—
132#103×C89—21no—
133#103×C89—21no—
134#103×C89—21no—
135#103×C89—21no—
136#103×C89—21no—
137#103×C89—21no—
138#103×C89—21no—
139#103×C89—21no—
140#103×C89—21no—
141#103×C89D411yescharacteristic
142#103×C89D411yescharacteristic
143#102×C89—21no—
144#102×C89—21no—
145#102×C89—21no—
146#102×C89—21no—
147#102×C89—21no—
148#102×C89D411yescharacteristic
149#102×C89D411yescharacteristic
150#101×C89—22no—
151C22⋊C8×C89—21no—
152C22⋊C8×C89—21no—
153C22⋊C8×C89—21no—
154C22⋊C8×C89—21no—
155#97×C89—21no—
156C4×C8×C89—21no—
157#95×C89—41no—
158#95×C89—41no—
159#41×C89—21no—
160#41×C89—21no—
161#41×C89—24no—
162#41×C89—21no—
163#41×C89—21no—
164#41×C89—21no—
165#41×C89—21no—
166#41×C89—21no—
167#41×C89—21no—
168#41×C89—21no—
169#41×C89—21no—
170#41×C89—42no—
171#41×C89—44no—
172#41×C89—42no—
173#41×C89—44no—
174#41×C89—42no—
175#41×C89#4112yes—
176#41×C89#4112yes—
177C2×Q8×C89—21no—
178C2×Q8×C89—24no—
179C2×Q8×C89—21no—
180C2×Q8×C89—21no—
181C2×Q8×C89—21no—
182C2×Q8×C89—21no—
183C2×Q8×C89—41no—
184C2×Q8×C89—42no—
185C2×Q8×C89—42no—
186C2×Q8×C89—42no—
187C2×Q8×C89C2×D411yescharacteristic
188C2×Q8×C89C2×D411yescharacteristic
189C2×Q8×C89C2×D411yescharacteristic
190C2×Q8×C89#4112yes—
191C2×D4×C89—21no—
192C2×D4×C89—21no—
193C2×D4×C89—21no—
194C2×D4×C89—41no—
195C2×D4×C89—41no—
196C2×D4×C89C2×D411yescharacteristic
197C2×D4×C89C2×D411yescharacteristic
198C2×D4×C89C2×D411yescharacteristic
199C22×C4×C89—21no—
200C22×C4×C89—21no—
201C22×C4×C89—21no—
202C22×C4×C89—21no—
203C22×C4×C89—21no—
204C22×C4×C89—21no—
205C22×C4×C89—21no—
206C22×C4×C89—21no—
207C22×C4×C89—41no—
208C22×C4×C89—41no—
209C22×C4×C89—41no—
210C22×C4×C89—41no—
211C22×C4×C89C2411yescharacteristic
212Q16×C89—22no—
213Q16×C89—42no—
214SD16×C89—22no—
215SD16×C89—22no—
216SD16×C89—42no—
217D8×C89—22no—
218M16×C89—21no—
219M16×C89—21no—
220M16×C89—21no—
221M16×C89—21no—
222M16×C89—21no—
223M16×C89—21no—
224M16×C89—21no—
225M16×C89—21no—
226M16×C89—42no—
227C2×C8×C89—21no—
228C2×C8×C89—21no—
229C2×C8×C89—21no—
230C2×C8×C89—21no—
231C2×C8×C89—21no—
232C2×C8×C89—21no—
233C2×C8×C89—21no—
234C2×C8×C89—21no—
235C2×C8×C89—42no—
236C2×C8×C89C2×D411yescharacteristic
237C2×C8×C89C2×D411yescharacteristic
238C2×C8×C89C2×D411yescharacteristic
239C2×C8×C89C2×D411yescharacteristic
240C4⋊C4×C89—21no—
241C4⋊C4×C89—21no—
242C4⋊C4×C89—21no—
243C4⋊C4×C89—21no—
244C4⋊C4×C89—21no—
245C4⋊C4×C89—21no—
246C4⋊C4×C89—41no—
247C4⋊C4×C89—41no—
248C4⋊C4×C89—41no—
249C4⋊C4×C89C2×D411yescharacteristic
250C4⋊C4×C89C2×D411yescharacteristic
251C22⋊C4×C89—21no—
252C22⋊C4×C89—41no—
253C22⋊C4×C89—41no—
254C22⋊C4×C89—41no—
255C22⋊C4×C89—41no—
256C42×C89—21no—
257C42×C89—21no—
258C42×C89—21no—
259C42×C89—41no—
260C42×C89—41no—
261C23×C89—21no—
262C23×C89—21no—
263C23×C89—21no—
264C23×C89H(5,𝔽2)11yescharacteristic
265Q8×C89—21no—
266Q8×C89—21no—
267Q8×C89—21no—
268Q8×C89—22no—
269Q8×C89—22no—
270Q8×C89—21no—
271Q8×C89—21no—
272Q8×C89—44no—
273Q8×C89—41no—
274Q8×C89—41no—
275Q8×C89#12312yes—
276D4×C89—22no—
277D4×C89—22no—
278D4×C89—21no—
279D4×C89—21no—
280D4×C89—21no—
281D4×C89—21no—
282D4×C89—21no—
283D4×C89—44no—
284D4×C89—41no—
285D4×C89—41no—
286D4×C89—41no—
287D4×C89—41no—
288D4×C89—161no—
289D4×C89#12312yes—
290C2×C4×C89—21no—
291C2×C4×C89—22no—
292C2×C4×C89—22no—
293C2×C4×C89—21no—
294C2×C4×C89—21no—
295C2×C4×C89—21no—
296C2×C4×C89—21no—
297C2×C4×C89—22no—
298C2×C4×C89—44no—
299C2×C4×C89—44no—
300C2×C4×C89—41no—
301C2×C4×C89—41no—
302C2×C4×C89—41no—
303C2×C4×C89—41no—
304C2×C4×C89—41no—
305C2×C4×C89—41no—
306C2×C4×C89—41no—
307C2×C4×C89—41no—
308C2×C4×C89—41no—
309C2×C4×C89—41no—
310C2×C4×C89—41no—
311C2×C4×C89—41no—
312C2×C4×C89—81no—
313C2×C4×C89—81no—
314C2×C4×C89—81no—
315C2×C4×C89—161no—
316C2×C4×C89—161no—
317C2×C4×C89C22×D411yescharacteristic
318C2×C4×C89C22×D411yescharacteristic
319C2×C4×C89C2×#4111yescharacteristic
320C2×C4×C89C2×#4111yescharacteristic
321C2×C4×C89C2×#4111yescharacteristic
322C2×C4×C89H(5,𝔽2)11yescharacteristic
323C8×C89—21no—
324C8×C89—21no—
325C8×C89—21no—
326C8×C89—21no—
327C8×C89—41no—
328C8×C89—41no—
329C8×C89—41no—
330C8×C89—41no—
331C22×C89—21no—
332C22×C89—21no—
333C22×C89—22no—
334C22×C89—41no—
335C22×C89—41no—
336C22×C89—41no—
337C22×C89—41no—
338C22×C89—41no—
339C22×C89—41no—
340C22×C89—41no—
341C22×C89—41no—
342C22×C89#53811yescharacteristic
343C22×C89D4211yescharacteristic
344C22×C89#55111yescharacteristic
345C4×C89—22no—
346C4×C89—41no—
347C4×C89—42no—
348C4×C89—41no—
349C4×C89—41no—
350C4×C89—41no—
351C4×C89—81no—
352C4×C89—81no—
353C4×C89—81no—
354C4×C89—81no—
355C4×C89C2×#12311yescharacteristic
356C4×C89#52511yescharacteristic
357C4×C89#54611yescharacteristic
358C4×C89#54611yescharacteristic
359#24930C8911yesmaximal, characteristic, direct product factor, Sylow
360C2×C89—21no—
361C2×C89—21no—
362C2×C89—42no—
363C2×C89—81no—
364C2×C89—81no—
365C2×C89#241811yescharacteristic
366C2×C89#328911yescharacteristic
367C2×C89#329011yescharacteristic
368#3098C2×C8911yescharacteristic, complemented
369#3013C2×C8911yescharacteristic
370#2952C2×C8911yescharacteristic, complemented
371#2898C2×C8911yescharacteristic, complemented
372#2097C2×C8911yescharacteristic, complemented
373#2079C2×C8911yescharacteristic, complemented
374#2052C2×C8911yescharacteristic, complemented
375#2040C2×C8911yescharacteristic, complemented
376#1930C2×C8911yescharacteristic, complemented
377#1929C2×C8911yescharacteristic, complemented
378#1882C2×C8911yescharacteristic, complemented
379#1876C2×C8911yescharacteristic, complemented
380#1860C2×C8911yescharacteristic, complemented
381#1816C2×C8911yescharacteristic, complemented
382#1793C2×C8911yescharacteristic, complemented
383C89#2493011yescharacteristic, direct product factor, Sylow
384C2×2−1+4C22×C8911yescharacteristic
385C2×#137C22×C8911yescharacteristic
386C2×#135C22×C8911yescharacteristic
387C2×#131C22×C8911yescharacteristic
388#537C22×C8911yescharacteristic
389#520C22×C8911yescharacteristic
390#520C22×C8911yescharacteristic
391#485—21no—
392#484—21no—
393#482—21no—
394#480—21no—
395#452—21no—
396#451—21no—
397#449—21no—
398#448—21no—
399#442—21no—
400#441—21no—
401C4×SD16—21no—
402C4×SD16—21no—
403C2×#108C22×C8911yescharacteristic
404#428C22×C8911yescharacteristic
405C2×#107C22×C8911yescharacteristic
406C2×#106C22×C8911yescharacteristic
407C2×#104C22×C8911yescharacteristic
408C2×#104C22×C8911yescharacteristic
409C2×#104C22×C8911yescharacteristic
410#419—21no—
411#419C22×C8911yescharacteristic
412#417—21no—
413#417C22×C8911yescharacteristic
414#417C22×C8911yescharacteristic
415#417C22×C8911yescharacteristic
416#417C22×C8911yescharacteristic
417#417C22×C8911yescharacteristic
418#416—21no—
419#416C22×C8911yescharacteristic
420C2×#103—21no—
421C2×#103C22×C8911yescharacteristic
422C2×#103C22×C8911yescharacteristic
423C2×#101C22×C8911yescharacteristic
424#408C22×C8911yescharacteristic
425#408C22×C8911yescharacteristic
426#405C22×C8911yescharacteristic
427#391C22×C8911yescharacteristic
428#382C22×C8911yescharacteristic
429#343C22×C8911yescharacteristic
430#343C22×C8911yescharacteristic
431#343C22×C8911yescharacteristic
432#341C22×C8911yescharacteristic
433#339C22×C8911yescharacteristic
434#336C22×C8911yescharacteristic
4352−1+4—22no—
4362−1+4—22no—
4372−1+4—22no—
4382−1+4—41no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—41no—
442C2×#41C23×C8911yescharacteristic
443C2×#41C23×C8911yescharacteristic
444C2×#41C23×C8911yescharacteristic
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8C23×C8911yescharacteristic
448#137—22no—
449#137—41no—
450#135—22no—
451#135—22no—
452C2×Q16—21no—
453C2×Q16D4×C8911yescharacteristic
454C2×SD16—21no—
455C2×SD16D4×C8911yescharacteristic
456C2×SD16D4×C8911yescharacteristic
457C2×D8D4×C8911yescharacteristic
458#131—22no—
459#131—41no—
460C2×M16—21no—
461C2×M16C23×C8911yescharacteristic
462C2×M16C23×C8911yescharacteristic
463C2×M16C23×C8911yescharacteristic
464C2×M16C23×C8911yescharacteristic
465C22×C8—21no—
466C22×C8C23×C8911yescharacteristic
467C22×C8C23×C8911yescharacteristic
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470#121—21no—
471#121—21no—
472#121—41no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—41no—
478C4×D4—41no—
479#117—21no—
480#117—21no—
481#117C23×C8911yescharacteristic
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4C23×C8911yescharacteristic
485C2×C4⋊C4C23×C8911yescharacteristic
486C2×C4⋊C4C23×C8911yescharacteristic
487C2×C42C23×C8911yescharacteristic
488#108—41no—
489#107—21no—
490#107—21no—
491#107—21no—
492#106—21no—
493#106—21no—
494#106—21no—
495#104—22no—
496#104—41no—
497#104—41no—
498#103—21no—
499#103—21no—
500#103—21no—
501#103—21no—
502#103—21no—
503#103—21no—
504#103—21no—
505#103—21no—
506#103—21no—
507#103—21no—
508#103—21no—
509#103D4×C8911yescharacteristic
510#103D4×C8911yescharacteristic
511#102—21no—
512#102—21no—
513#102—21no—
514#102—21no—
515#102—21no—
516#102D4×C8911yescharacteristic
517#102D4×C8911yescharacteristic
518#101—22no—
519C22⋊C8—21no—
520C22⋊C8—21no—
521C22⋊C8—21no—
522C22⋊C8—21no—
523#97—21no—
524C4×C8—21no—
525#95—41no—
526#95—41no—
527#41—21no—
528#41—21no—
529#41—24no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—42no—
539#41—44no—
540#41—42no—
541#41—44no—
542#41—42no—
543#41#41×C8912yes—
544#41#41×C8912yes—
545C2×Q8—21no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—41no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8C2×D4×C8911yescharacteristic
556C2×Q8C2×D4×C8911yescharacteristic
557C2×Q8C2×D4×C8911yescharacteristic
558C2×Q8#41×C8912yes—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4C2×D4×C8911yescharacteristic
565C2×D4C2×D4×C8911yescharacteristic
566C2×D4C2×D4×C8911yescharacteristic
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4C24×C8911yescharacteristic
580Q16—22no—
581Q16—42no—
582SD16—22no—
583SD16—22no—
584SD16—42no—
585D8—22no—
586M16—21no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16—42no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C2×C8C2×D4×C8911yescharacteristic
605C2×C8C2×D4×C8911yescharacteristic
606C2×C8C2×D4×C8911yescharacteristic
607C2×C8C2×D4×C8911yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4C2×D4×C8911yescharacteristic
618C4⋊C4C2×D4×C8911yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—41no—
628C42—41no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23H(5,𝔽2)×C8911yescharacteristic
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—22no—
637Q8—22no—
638Q8—21no—
639Q8—21no—
640Q8—44no—
641Q8—41no—
642Q8—41no—
643Q8#123×C8912yes—
644D4—22no—
645D4—22no—
646D4—21no—
647D4—21no—
648D4—21no—
649D4—21no—
650D4—21no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—161no—
657D4#123×C8912yes—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—161no—
684C2×C4—161no—
685C2×C4C22×D4×C8911yescharacteristic
686C2×C4C22×D4×C8911yescharacteristic
687C2×C4C2×#41×C8911yescharacteristic
688C2×C4C2×#41×C8911yescharacteristic
689C2×C4C2×#41×C8911yescharacteristic
690C2×C4H(5,𝔽2)×C8911yescharacteristic
691C8—21no—
692C8—21no—
693C8—21no—
694C8—21no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C22—21no—
700C22—21no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22#538×C8911yescharacteristic
711C22D42×C8911yescharacteristic
712C22#551×C8911yescharacteristic
713C4—22no—
714C4—41no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4C2×#123×C8911yescharacteristic
724C4#525×C8911yescharacteristic
725C4#546×C8911yescharacteristic
726C4#546×C8911yescharacteristic
727C2—21no—
728C2—21no—
729C2—42no—
730C2—81no—
731C2—81no—
732C2C89×#241811yescharacteristic
733C2C89×#328911yescharacteristic
734C2C89×#329011yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC89×#3013C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ C22×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3098C2semidirect
3. C89×#2952C2semidirect
4. C89×#2898C2semidirect
5. C89×#2097C2semidirect
6. C89×#2079C2semidirect
7. C89×#2052C2semidirect
8. C89×#2040C2semidirect
9. C89×#1930C2semidirect
10. C89×#1929C2semidirect
11. C89×#1882C2semidirect
12. C89×#1876C2semidirect
13. C89×#1860C2semidirect
14. C89×#1816C2semidirect
15. C89×#1793C2semidirect
359. #24930C89direct (N × H)
368. #3098C2×C89semidirect
370. #2952C2×C89semidirect
371. #2898C2×C89semidirect
372. #2097C2×C89semidirect
373. #2079C2×C89semidirect
374. #2052C2×C89semidirect
375. #2040C2×C89semidirect
376. #1930C2×C89semidirect
377. #1929C2×C89semidirect
378. #1882C2×C89semidirect
379. #1876C2×C89semidirect
380. #1860C2×C89semidirect
381. #1816C2×C89semidirect
382. #1793C2×C89semidirect
383. C89#24930direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#30982
C89×#30132
C89×#29522
C89×#28982
C89×#20972
C89×#20792
C89×#20522
C89×#20402
C89×#19302
C89×#19292
C89×#18822
C89×#18762
C89×#18602
C89×#18162
C89×#17932
#2493089