Finite Group Databasebeta

← C89×#26975 #36404823

Subgroups — C89×#26975 #36404823

Order 22784.

956 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C89C211yesmaximal, characteristic
2C2×#440×C89C211yesmaximal, characteristic, complemented
3C89×#2426C211yesmaximal, characteristic, complemented
4C89×#2422C211yesmaximal, characteristic, complemented
5C89×#2083C211yesmaximal, characteristic, complemented
6C89×#2033C211yesmaximal, characteristic, complemented
7C89×#2012C211yesmaximal, characteristic, complemented
8C89×#2000C211yesmaximal, characteristic, complemented
9C89×#1959C211yesmaximal, characteristic, complemented
10C89×#1936C211yesmaximal, characteristic, complemented
11C89×#1936C211yesmaximal, characteristic, complemented
12C89×#1892C211yesmaximal, characteristic, complemented
13C89×#1879C211yesmaximal, characteristic, complemented
14C89×#1863C211yesmaximal, characteristic, complemented
15C89×#1752C211yesmaximal, characteristic, complemented
16C22×SD16×C89C2211yescharacteristic
17C22×D8×C89C2211yescharacteristic
18C23×C8×C89C2211yescharacteristic
19C2×#124×C89C2211yescharacteristic
20C2×#123×C89—21no—
21C2×C22⋊Q8×C89C2211yescharacteristic
22C2×#121×C89C2211yescharacteristic
23C2×#121×C89C2211yescharacteristic
24C2×C4×Q8×C89C2211yescharacteristic
25C2×C4×D4×C89C2211yescharacteristic
26#466×C89—24no—
27#440×C89—24no—
28C2×#107×C89C2211yescharacteristic
29C2×#107×C89C2211yescharacteristic
30C2×#103×C89C2211yescharacteristic
31C2×#103×C89C2211yescharacteristic
32C2×#103×C89C2211yescharacteristic
33C2×#102×C89C2211yescharacteristic
34C2×#102×C89C2211yescharacteristic
35C2×#102×C89C2211yescharacteristic
36C2×#102×C89C2211yescharacteristic
37C2×#102×C89C2211yescharacteristic
38C2×C22⋊C8×C89C2211yescharacteristic
39C2×#97×C89C2211yescharacteristic
40C2×#97×C89C2211yescharacteristic
41#397×C89—21no—
42#396×C89—21no—
43#394×C89—21no—
44#394×C89—21no—
45#390×C89—21no—
46#390×C89C2211yescharacteristic
47#390×C89C2211yescharacteristic
48#389×C89C2211yescharacteristic
49#389×C89C2211yescharacteristic
50#388×C89—21no—
51#385×C89—21no—
52#384×C89C2211yescharacteristic
53#380×C89C2211yescharacteristic
54C4×C22⋊C4×C89C2211yescharacteristic
55#340×C89C2211yescharacteristic
56#340×C89C2211yescharacteristic
57#340×C89C2211yescharacteristic
58#340×C89C2211yescharacteristic
59#336×C89C2211yescharacteristic
60#336×C89C2211yescharacteristic
61C22×Q8×C89C2311yescharacteristic
62C22×D4×C89—21no—
63C22×D4×C89—21no—
64C22×D4×C89C2311yescharacteristic
65C22×D4×C89C2311yescharacteristic
66C23×C4×C89—21no—
67C23×C4×C89C2311yescharacteristic
68C2×SD16×C89—22no—
69C2×SD16×C89—22no—
70C2×SD16×C89—22no—
71C2×D8×C89—22no—
72C2×D8×C89—22no—
73C2×D8×C89—41no—
74C22×C8×C89—22no—
75C22×C8×C89—22no—
76C22×C8×C89—41no—
77C22×C8×C89C2311yescharacteristic
78C22×C8×C89C2311yescharacteristic
79C22×C8×C89C2311yescharacteristic
80C22×C8×C89C2311yescharacteristic
81#124×C89—22no—
82#124×C89—41no—
83#123×C89—44no—
84C22⋊Q8×C89—22no—
85C22⋊Q8×C89—41no—
86#121×C89—22no—
87#121×C89—22no—
88#121×C89—41no—
89#121×C89—41no—
90C4×Q8×C89—22no—
91C4×Q8×C89—41no—
92C4×D4×C89—22no—
93C4×D4×C89—41no—
94C2×C4⋊C4×C89—21no—
95C2×C4⋊C4×C89—21no—
96C2×C4⋊C4×C89—21no—
97C2×C4⋊C4×C89—21no—
98C2×C4⋊C4×C89—21no—
99C2×C4⋊C4×C89—21no—
100C2×C4⋊C4×C89C2311yescharacteristic
101C2×C4⋊C4×C89C2311yescharacteristic
102C2×C4⋊C4×C89C2311yescharacteristic
103C2×C4⋊C4×C89C2311yescharacteristic
104C2×C4⋊C4×C89C2311yescharacteristic
105C2×C22⋊C4×C89—21no—
106C2×C22⋊C4×C89—21no—
107C2×C22⋊C4×C89—21no—
108C2×C22⋊C4×C89—21no—
109C2×C22⋊C4×C89—21no—
110C2×C22⋊C4×C89—21no—
111C2×C22⋊C4×C89—21no—
112C2×C22⋊C4×C89—21no—
113C2×C22⋊C4×C89—21no—
114C2×C22⋊C4×C89—21no—
115C2×C22⋊C4×C89—21no—
116C2×C22⋊C4×C89D411yescharacteristic
117C2×C22⋊C4×C89D411yescharacteristic
118C2×C42×C89—21no—
119C2×C42×C89C2311yescharacteristic
120C2×C42×C89C2311yescharacteristic
121#107×C89—22no—
122#107×C89—22no—
123#103×C89—22no—
124#103×C89—22no—
125#103×C89—41no—
126#102×C89—22no—
127#102×C89—22no—
128#102×C89—41no—
129#102×C89—41no—
130#102×C89D414yes—
131C22⋊C8×C89—22no—
132#97×C89—22no—
133#97×C89—41no—
134#95×C89—21no—
135#95×C89—21no—
136#95×C89—21no—
137#95×C89D411yescharacteristic
138#95×C89D411yescharacteristic
139C24×C89—21no—
140C24×C89—21no—
141C24×C89C2×D411yescharacteristic
142C2×Q8×C89—21no—
143C2×Q8×C89—21no—
144C2×Q8×C89—21no—
145C2×Q8×C89—21no—
146C2×Q8×C89—21no—
147C2×Q8×C89#4112yes—
148C2×D4×C89—21no—
149C2×D4×C89—21no—
150C2×D4×C89—21no—
151C2×D4×C89—21no—
152C2×D4×C89—21no—
153C2×D4×C89—21no—
154C2×D4×C89—21no—
155C2×D4×C89—21no—
156C2×D4×C89—21no—
157C2×D4×C89—21no—
158C2×D4×C89—21no—
159C2×D4×C89—42no—
160C2×D4×C89—42no—
161C2×D4×C89—42no—
162C2×D4×C89—42no—
163C2×D4×C89—81no—
164C2×D4×C89—81no—
165C2×D4×C89C2×D412yes—
166C22×C4×C89—21no—
167C22×C4×C89—21no—
168C22×C4×C89—21no—
169C22×C4×C89—21no—
170C22×C4×C89—21no—
171C22×C4×C89—21no—
172C22×C4×C89—21no—
173C22×C4×C89—21no—
174C22×C4×C89—21no—
175C22×C4×C89—21no—
176C22×C4×C89—21no—
177C22×C4×C89—21no—
178C22×C4×C89—42no—
179C22×C4×C89—42no—
180C22×C4×C89—81no—
181C22×C4×C89C2×D411yescharacteristic
182C22×C4×C89C2×D411yescharacteristic
183C22×C4×C89C2×D411yescharacteristic
184C22×C4×C89C2×D411yescharacteristic
185C22×C4×C89C2×D411yescharacteristic
186C22×C4×C89C2411yescharacteristic
187SD16×C89—28no—
188D8×C89—44no—
189C2×C8×C89—21no—
190C2×C8×C89—21no—
191C2×C8×C89—21no—
192C2×C8×C89—21no—
193C2×C8×C89—21no—
194C2×C8×C89—21no—
195C2×C8×C89—21no—
196C2×C8×C89—21no—
197C2×C8×C89—21no—
198C2×C8×C89—44no—
199C2×C8×C89C2×D412yes—
200C2×C8×C89#4112yes—
201C2×C8×C89#4112yes—
202C4⋊C4×C89—21no—
203C4⋊C4×C89—21no—
204C4⋊C4×C89—21no—
205C4⋊C4×C89—21no—
206C4⋊C4×C89—21no—
207C4⋊C4×C89—21no—
208C4⋊C4×C89—21no—
209C4⋊C4×C89—21no—
210C4⋊C4×C89—21no—
211C4⋊C4×C89—42no—
212C4⋊C4×C89—42no—
213C4⋊C4×C89—42no—
214C4⋊C4×C89—42no—
215C4⋊C4×C89—81no—
216C4⋊C4×C89—81no—
217C4⋊C4×C89C2×D412yes—
218C22⋊C4×C89—22no—
219C22⋊C4×C89—41no—
220C22⋊C4×C89—42no—
221C22⋊C4×C89—42no—
222C22⋊C4×C89—42no—
223C22⋊C4×C89—42no—
224C22⋊C4×C89—42no—
225C22⋊C4×C89—42no—
226C22⋊C4×C89—42no—
227C22⋊C4×C89—42no—
228C22⋊C4×C89—42no—
229C22⋊C4×C89—42no—
230C22⋊C4×C89—81no—
231C42×C89—21no—
232C42×C89—21no—
233C42×C89—21no—
234C42×C89—21no—
235C42×C89—42no—
236C23×C89—21no—
237C23×C89—21no—
238C23×C89—21no—
239C23×C89—21no—
240C23×C89—21no—
241C23×C89—21no—
242C23×C89—22no—
243C23×C89—41no—
244C23×C89—41no—
245C23×C89—41no—
246C23×C89—41no—
247C23×C89—41no—
248C23×C89—41no—
249C23×C89—41no—
250C23×C89—41no—
251C23×C89—41no—
252C23×C89—41no—
253C23×C89—41no—
254C23×C89—41no—
255C23×C89—41no—
256C23×C89AGL(1,ℤ/8)12yes—
257C23×C89C22×D411yescharacteristic
258Q8×C89—22no—
259Q8×C89—22no—
260Q8×C89—41no—
261Q8×C89—41no—
262D4×C89—22no—
263D4×C89—22no—
264D4×C89—41no—
265D4×C89—41no—
266D4×C89—41no—
267D4×C89—41no—
268D4×C89—41no—
269D4×C89—41no—
270D4×C89—84no—
271D4×C89—84no—
272C2×C4×C89—21no—
273C2×C4×C89—21no—
274C2×C4×C89—21no—
275C2×C4×C89—22no—
276C2×C4×C89—21no—
277C2×C4×C89—21no—
278C2×C4×C89—21no—
279C2×C4×C89—22no—
280C2×C4×C89—21no—
281C2×C4×C89—21no—
282C2×C4×C89—21no—
283C2×C4×C89—21no—
284C2×C4×C89—21no—
285C2×C4×C89—21no—
286C2×C4×C89—21no—
287C2×C4×C89—21no—
288C2×C4×C89—21no—
289C2×C4×C89—41no—
290C2×C4×C89—41no—
291C2×C4×C89—41no—
292C2×C4×C89—41no—
293C2×C4×C89—41no—
294C2×C4×C89—41no—
295C2×C4×C89—41no—
296C2×C4×C89—41no—
297C2×C4×C89—41no—
298C2×C4×C89—41no—
299C2×C4×C89—41no—
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—84no—
310C2×C4×C89C22×D411yescharacteristic
311C2×C4×C89C2×#4111yescharacteristic
312C2×C4×C89C2×#4111yescharacteristic
313C2×C4×C89C2×#4111yescharacteristic
314C2×C4×C89H(5,𝔽2)11yescharacteristic
315C2×C4×C89H(5,𝔽2)11yescharacteristic
316C8×C89—22no—
317C8×C89—22no—
318C8×C89—22no—
319C8×C89—41no—
320C22×C89—22no—
321C22×C89—22no—
322C22×C89—22no—
323C22×C89—41no—
324C22×C89—41no—
325C22×C89—41no—
326C22×C89—41no—
327C22×C89—42no—
328C22×C89—42no—
329C22×C89—42no—
330C22×C89—81no—
331C22×C89—81no—
332C22×C89—81no—
333C22×C89—81no—
334C22×C89—81no—
335C22×C89—81no—
336C22×C89—81no—
337C22×C89—81no—
338C22×C89—81no—
339C22×C89—81no—
340C22×C89—81no—
341C22×C89#53211yescharacteristic
342C22×C89D4211yescharacteristic
343C22×C89#54611yescharacteristic
344C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C89#57511yescharacteristic
346C22×C89#57611yescharacteristic
347C22×C89#57811yescharacteristic
348C4×C89—41no—
349C4×C89—42no—
350C4×C89—41no—
351C4×C89—42no—
352C4×C89—41no—
353C4×C89—41no—
354C4×C89—41no—
355C4×C89—81no—
356C4×C89—81no—
357C4×C89—81no—
358C4×C89—81no—
359C4×C89#52511yescharacteristic
360C4×C89#54011yescharacteristic
361C4×C89#54611yescharacteristic
362C4×C89#55311yescharacteristic
363#26975C8911yesmaximal, characteristic, direct product factor, Sylow
364C2×C89—42no—
365C2×C89—82no—
366C2×C89—161no—
367C2×C89#246411yescharacteristic
368C2×C89#317511yescharacteristic
369C2×C89#318011yescharacteristic
370C2×C89#326411yescharacteristic
371C2×C89#326911yescharacteristic
372C2×C89#330811yescharacteristic
373C2×C89#330911yescharacteristic
374C2×#466C2×C8911yescharacteristic
375C2×#440C2×C8911yescharacteristic, complemented
376#2426C2×C8911yescharacteristic, complemented
377#2422C2×C8911yescharacteristic, complemented
378#2083C2×C8911yescharacteristic, complemented
379#2033C2×C8911yescharacteristic, complemented
380#2012C2×C8911yescharacteristic, complemented
381#2000C2×C8911yescharacteristic, complemented
382#1959C2×C8911yescharacteristic, complemented
383#1936C2×C8911yescharacteristic, complemented
384#1936C2×C8911yescharacteristic, complemented
385#1892C2×C8911yescharacteristic, complemented
386#1879C2×C8911yescharacteristic, complemented
387#1863C2×C8911yescharacteristic, complemented
388#1752C2×C8911yescharacteristic, complemented
389C89#2697511yescharacteristic, direct product factor, Sylow
390C22×SD16C22×C8911yescharacteristic
391C22×D8C22×C8911yescharacteristic
392C23×C8C22×C8911yescharacteristic
393C2×#124C22×C8911yescharacteristic
394C2×#123—21no—
395C2×C22⋊Q8C22×C8911yescharacteristic
396C2×#121C22×C8911yescharacteristic
397C2×#121C22×C8911yescharacteristic
398C2×C4×Q8C22×C8911yescharacteristic
399C2×C4×D4C22×C8911yescharacteristic
400#466—24no—
401#440—24no—
402C2×#107C22×C8911yescharacteristic
403C2×#107C22×C8911yescharacteristic
404C2×#103C22×C8911yescharacteristic
405C2×#103C22×C8911yescharacteristic
406C2×#103C22×C8911yescharacteristic
407C2×#102C22×C8911yescharacteristic
408C2×#102C22×C8911yescharacteristic
409C2×#102C22×C8911yescharacteristic
410C2×#102C22×C8911yescharacteristic
411C2×#102C22×C8911yescharacteristic
412C2×C22⋊C8C22×C8911yescharacteristic
413C2×#97C22×C8911yescharacteristic
414C2×#97C22×C8911yescharacteristic
415#397—21no—
416#396—21no—
417#394—21no—
418#394—21no—
419#390—21no—
420#390C22×C8911yescharacteristic
421#390C22×C8911yescharacteristic
422#389C22×C8911yescharacteristic
423#389C22×C8911yescharacteristic
424#388—21no—
425#385—21no—
426#384C22×C8911yescharacteristic
427#380C22×C8911yescharacteristic
428C4×C22⋊C4C22×C8911yescharacteristic
429#340C22×C8911yescharacteristic
430#340C22×C8911yescharacteristic
431#340C22×C8911yescharacteristic
432#340C22×C8911yescharacteristic
433#336C22×C8911yescharacteristic
434#336C22×C8911yescharacteristic
435C22×Q8C23×C8911yescharacteristic
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C23×C8911yescharacteristic
439C22×D4C23×C8911yescharacteristic
440C23×C4—21no—
441C23×C4C23×C8911yescharacteristic
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×D8—22no—
446C2×D8—22no—
447C2×D8—41no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—41no—
451C22×C8C23×C8911yescharacteristic
452C22×C8C23×C8911yescharacteristic
453C22×C8C23×C8911yescharacteristic
454C22×C8C23×C8911yescharacteristic
455#124—22no—
456#124—41no—
457#123—44no—
458C22⋊Q8—22no—
459C22⋊Q8—41no—
460#121—22no—
461#121—22no—
462#121—41no—
463#121—41no—
464C4×Q8—22no—
465C4×Q8—41no—
466C4×D4—22no—
467C4×D4—41no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4C23×C8911yescharacteristic
475C2×C4⋊C4C23×C8911yescharacteristic
476C2×C4⋊C4C23×C8911yescharacteristic
477C2×C4⋊C4C23×C8911yescharacteristic
478C2×C4⋊C4C23×C8911yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4D4×C8911yescharacteristic
491C2×C22⋊C4D4×C8911yescharacteristic
492C2×C42—21no—
493C2×C42C23×C8911yescharacteristic
494C2×C42C23×C8911yescharacteristic
495#107—22no—
496#107—22no—
497#103—22no—
498#103—22no—
499#103—41no—
500#102—22no—
501#102—22no—
502#102—41no—
503#102—41no—
504#102D4×C8914yes—
505C22⋊C8—22no—
506#97—22no—
507#97—41no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95D4×C8911yescharacteristic
512#95D4×C8911yescharacteristic
513C24—21no—
514C24—21no—
515C24C2×D4×C8911yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8#41×C8912yes—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4C2×D4×C8912yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4C2×D4×C8911yescharacteristic
556C22×C4C2×D4×C8911yescharacteristic
557C22×C4C2×D4×C8911yescharacteristic
558C22×C4C2×D4×C8911yescharacteristic
559C22×C4C2×D4×C8911yescharacteristic
560C22×C4C24×C8911yescharacteristic
561SD16—28no—
562D8—44no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—44no—
573C2×C8C2×D4×C8912yes—
574C2×C8#41×C8912yes—
575C2×C8#41×C8912yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C4⋊C4—81no—
591C4⋊C4C2×D4×C8912yes—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—42no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23AGL(1,ℤ/8)×C8912yes—
631C23C22×D4×C8911yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4—84no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
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—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—84no—
684C2×C4C22×D4×C8911yescharacteristic
685C2×C4C2×#41×C8911yescharacteristic
686C2×C4C2×#41×C8911yescharacteristic
687C2×C4C2×#41×C8911yescharacteristic
688C2×C4H(5,𝔽2)×C8911yescharacteristic
689C2×C4H(5,𝔽2)×C8911yescharacteristic
690C8—22no—
691C8—22no—
692C8—22no—
693C8—41no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22#532×C8911yescharacteristic
716C22D42×C8911yescharacteristic
717C22#546×C8911yescharacteristic
718C22C2×AGL(1,ℤ/8)×C8911yescharacteristic
719C22#575×C8911yescharacteristic
720C22#576×C8911yescharacteristic
721C22#578×C8911yescharacteristic
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4#525×C8911yescharacteristic
734C4#540×C8911yescharacteristic
735C4#546×C8911yescharacteristic
736C4#553×C8911yescharacteristic
737C2—42no—
738C2—82no—
739C2—161no—
740C2C89×#246411yescharacteristic
741C2C89×#317511yescharacteristic
742C2C89×#318011yescharacteristic
743C2C89×#326411yescharacteristic
744C2C89×#326911yescharacteristic
745C2C89×#330811yescharacteristic
746C2C89×#330911yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC2×#466×C89C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C4×C22⋊C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C89C2semidirect
3. C89×#2426C2semidirect
4. C89×#2422C2semidirect
5. C89×#2083C2semidirect
6. C89×#2033C2semidirect
7. C89×#2012C2semidirect
8. C89×#2000C2semidirect
9. C89×#1959C2semidirect
10. C89×#1936C2semidirect
11. C89×#1936C2semidirect
12. C89×#1892C2semidirect
13. C89×#1879C2semidirect
14. C89×#1863C2semidirect
15. C89×#1752C2semidirect
363. #26975C89direct (N × H)
375. C2×#440C2×C89semidirect
376. #2426C2×C89semidirect
377. #2422C2×C89semidirect
378. #2083C2×C89semidirect
379. #2033C2×C89semidirect
380. #2012C2×C89semidirect
381. #2000C2×C89semidirect
382. #1959C2×C89semidirect
383. #1936C2×C89semidirect
384. #1936C2×C89semidirect
385. #1892C2×C89semidirect
386. #1879C2×C89semidirect
387. #1863C2×C89semidirect
388. #1752C2×C89semidirect
389. C89#26975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#466×C892
C2×#440×C892
C89×#24262
C89×#24222
C89×#20832
C89×#20332
C89×#20122
C89×#20002
C89×#19592
C89×#19362
C89×#18922
C89×#18792
C89×#18632
C89×#17522
#2697589