Finite Group Databasebeta

← C89×#29418 #36407266

Subgroups — C89×#29418 #36407266

Order 22784.

836 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2324C211yesmaximal, characteristic, complemented
2C89×#2324C211yesmaximal, characteristic, complemented
3C89×#2077C211yesmaximal, characteristic, complemented
4C89×#2034C211yesmaximal, characteristic, complemented
5C89×#2033C211yesmaximal, characteristic, complemented
6C89×#1999C211yesmaximal, characteristic
7C89×#1926C211yesmaximal, characteristic, complemented
8C89×#1925C211yesmaximal, characteristic, complemented
9C89×#1919C211yesmaximal, characteristic, complemented
10C89×#1918C211yesmaximal, characteristic, complemented
11C89×#1879C211yesmaximal, characteristic, complemented
12C89×#1879C211yesmaximal, characteristic, complemented
13C89×#1864C211yesmaximal, characteristic, complemented
14C89×#1864C211yesmaximal, characteristic, complemented
15C89×#1818C211yesmaximal, characteristic, complemented
16C22×D8×C89C2211yescharacteristic
17C2×#121×C89C2211yescharacteristic
18C2×#121×C89C2211yescharacteristic
19C2×C4×D4×C89C2211yescharacteristic
20C2×C4×D4×C89C2211yescharacteristic
21C2×#117×C89C2211yescharacteristic
22C2×#107×C89C2211yescharacteristic
23C2×#106×C89C2211yescharacteristic
24C2×#106×C89C2211yescharacteristic
25C2×#102×C89C2211yescharacteristic
26C2×#102×C89C2211yescharacteristic
27C2×#102×C89C2211yescharacteristic
28C2×#102×C89C2211yescharacteristic
29C2×#102×C89C2211yescharacteristic
30C2×#102×C89C2211yescharacteristic
31C2×C22⋊C8×C89C2211yescharacteristic
32C2×C22⋊C8×C89C2211yescharacteristic
33#390×C89—21no—
34#390×C89—21no—
35#390×C89C2211yescharacteristic
36#390×C89C2211yescharacteristic
37#389×C89C2211yescharacteristic
38#389×C89C2211yescharacteristic
39#388×C89—21no—
40#388×C89—21no—
41#386×C89—21no—
42#386×C89—21no—
43#385×C89—21no—
44#385×C89—21no—
45#380×C89C2211yescharacteristic
46#380×C89C2211yescharacteristic
47C4×C4⋊C4×C89C2211yescharacteristic
48C4×C4⋊C4×C89C2211yescharacteristic
49#340×C89C2211yescharacteristic
50#340×C89C2211yescharacteristic
51#340×C89C2211yescharacteristic
52#340×C89C2211yescharacteristic
53#340×C89C2211yescharacteristic
54#340×C89C2211yescharacteristic
55#336×C89C2211yescharacteristic
56#336×C89C2211yescharacteristic
57#336×C89C2211yescharacteristic
58#336×C89C2211yescharacteristic
59C22×D4×C89—21no—
60C22×D4×C89—21no—
61C22×D4×C89C2311yescharacteristic
62C22×D4×C89C2311yescharacteristic
63C23×C4×C89—21no—
64C23×C4×C89—21no—
65C23×C4×C89C2311yescharacteristic
66C2×D8×C89—22no—
67C2×D8×C89—22no—
68C2×D8×C89—41no—
69C22×C8×C89C2311yescharacteristic
70C22×C8×C89C2311yescharacteristic
71C22×C8×C89C2311yescharacteristic
72C22×C8×C89C2311yescharacteristic
73#121×C89—22no—
74#121×C89—22no—
75#121×C89—22no—
76#121×C89—22no—
77C4×D4×C89—41no—
78C4×D4×C89—41no—
79C4×D4×C89—41no—
80C4×D4×C89—41no—
81#117×C89—41no—
82#117×C89—41no—
83C2×C4⋊C4×C89—21no—
84C2×C4⋊C4×C89—21no—
85C2×C4⋊C4×C89D411yescharacteristic
86C2×C4⋊C4×C89D411yescharacteristic
87C2×C4⋊C4×C89C2311yescharacteristic
88C2×C4⋊C4×C89C2311yescharacteristic
89C2×C4⋊C4×C89C2311yescharacteristic
90C2×C4⋊C4×C89C2311yescharacteristic
91C2×C4⋊C4×C89C2311yescharacteristic
92C2×C4⋊C4×C89C2311yescharacteristic
93C2×C22⋊C4×C89—21no—
94C2×C22⋊C4×C89—21no—
95C2×C22⋊C4×C89—21no—
96C2×C22⋊C4×C89—21no—
97C2×C22⋊C4×C89—21no—
98C2×C22⋊C4×C89—21no—
99C2×C22⋊C4×C89—21no—
100C2×C22⋊C4×C89—21no—
101C2×C22⋊C4×C89—21no—
102C2×C22⋊C4×C89—21no—
103C2×C22⋊C4×C89D411yescharacteristic
104C2×C22⋊C4×C89D411yescharacteristic
105C2×C42×C89—21no—
106C2×C42×C89—21no—
107C2×C42×C89C2311yescharacteristic
108C2×C42×C89C2311yescharacteristic
109#107×C89—22no—
110#106×C89—22no—
111#106×C89—41no—
112#102×C89—22no—
113#102×C89—22no—
114#102×C89—22no—
115#102×C89—22no—
116#102×C89—41no—
117#102×C89—41no—
118C22⋊C8×C89—41no—
119C22⋊C8×C89—41no—
120#95×C89—21no—
121#95×C89—21no—
122#95×C89—21no—
123#95×C89—21no—
124#95×C89—21no—
125#95×C89—21no—
126C24×C89—21no—
127C24×C89—21no—
128C24×C89C2×D411yescharacteristic
129C2×D4×C89—24no—
130C2×D4×C89—24no—
131C2×D4×C89—21no—
132C2×D4×C89—21no—
133C2×D4×C89—21no—
134C2×D4×C89—21no—
135C2×D4×C89—21no—
136C2×D4×C89—21no—
137C2×D4×C89—21no—
138C2×D4×C89—21no—
139C2×D4×C89—21no—
140C2×D4×C89—21no—
141C2×D4×C89—81no—
142C2×D4×C89—81no—
143C2×D4×C89—81no—
144C2×D4×C89—81no—
145C2×D4×C89#4112yes—
146C2×D4×C89#4112yes—
147C22×C4×C89—21no—
148C22×C4×C89—21no—
149C22×C4×C89—21no—
150C22×C4×C89—21no—
151C22×C4×C89—21no—
152C22×C4×C89—21no—
153C22×C4×C89—21no—
154C22×C4×C89—21no—
155C22×C4×C89—21no—
156C22×C4×C89—21no—
157C22×C4×C89—21no—
158C22×C4×C89—21no—
159C22×C4×C89—42no—
160C22×C4×C89—42no—
161C22×C4×C89—81no—
162C22×C4×C89—81no—
163C22×C4×C89—81no—
164C22×C4×C89—81no—
165C22×C4×C89C2×D411yescharacteristic
166C22×C4×C89C2×D411yescharacteristic
167C22×C4×C89C2×D411yescharacteristic
168C22×C4×C89C2×D411yescharacteristic
169C22×C4×C89C2×D411yescharacteristic
170C22×C4×C89C2411yescharacteristic
171D8×C89—44no—
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×C89—21no—
179C2×C8×C89—21no—
180C2×C8×C89—21no—
181C2×C8×C89—21no—
182C2×C8×C89—21no—
183C2×C8×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—21no—
194C4⋊C4×C89—41no—
195C4⋊C4×C89—41no—
196C4⋊C4×C89—81no—
197C4⋊C4×C89—81no—
198C4⋊C4×C89#4112yes—
199C4⋊C4×C89#4112yes—
200C22⋊C4×C89—24no—
201C22⋊C4×C89—24no—
202C22⋊C4×C89—41no—
203C22⋊C4×C89—41no—
204C22⋊C4×C89—42no—
205C22⋊C4×C89—42no—
206C22⋊C4×C89—81no—
207C22⋊C4×C89—81no—
208C22⋊C4×C89—81no—
209C22⋊C4×C89—81no—
210C22⋊C4×C89—81no—
211C22⋊C4×C89—81no—
212C42×C89—21no—
213C42×C89—21no—
214C42×C89—21no—
215C42×C89—21no—
216C42×C89—81no—
217C42×C89—81no—
218C23×C89—22no—
219C23×C89—22no—
220C23×C89—21no—
221C23×C89—21no—
222C23×C89—21no—
223C23×C89—21no—
224C23×C89—21no—
225C23×C89—21no—
226C23×C89—21no—
227C23×C89—41no—
228C23×C89—41no—
229C23×C89—41no—
230C23×C89—41no—
231C23×C89—41no—
232C23×C89—41no—
233C23×C89—41no—
234C23×C89—41no—
235C23×C89—41no—
236C23×C89—41no—
237C23×C89—41no—
238C23×C89—41no—
239C23×C89C22×D411yescharacteristic
240D4×C89—22no—
241D4×C89—22no—
242D4×C89—22no—
243D4×C89—22no—
244D4×C89—41no—
245D4×C89—41no—
246D4×C89—41no—
247D4×C89—41no—
248D4×C89—84no—
249D4×C89—84no—
250C2×C4×C89—21no—
251C2×C4×C89—21no—
252C2×C4×C89—22no—
253C2×C4×C89—22no—
254C2×C4×C89—21no—
255C2×C4×C89—21no—
256C2×C4×C89—21no—
257C2×C4×C89—21no—
258C2×C4×C89—21no—
259C2×C4×C89—21no—
260C2×C4×C89—21no—
261C2×C4×C89—21no—
262C2×C4×C89—21no—
263C2×C4×C89—21no—
264C2×C4×C89—21no—
265C2×C4×C89—21no—
266C2×C4×C89—21no—
267C2×C4×C89—41no—
268C2×C4×C89—41no—
269C2×C4×C89—41no—
270C2×C4×C89—41no—
271C2×C4×C89—41no—
272C2×C4×C89—41no—
273C2×C4×C89—41no—
274C2×C4×C89—41no—
275C2×C4×C89—41no—
276C2×C4×C89—41no—
277C2×C4×C89—41no—
278C2×C4×C89—41no—
279C2×C4×C89—41no—
280C2×C4×C89—41no—
281C2×C4×C89—41no—
282C2×C4×C89—41no—
283C2×C4×C89—41no—
284C2×C4×C89—41no—
285C2×C4×C89—41no—
286C2×C4×C89—41no—
287C2×C4×C89—84no—
288C2×C4×C89—84no—
289C2×C4×C89C2×#4111yescharacteristic
290C2×C4×C89C2×#4111yescharacteristic
291C2×C4×C89C2×#4111yescharacteristic
292C2×C4×C89C2×#4111yescharacteristic
293C2×C4×C89H(5,𝔽2)11yescharacteristic
294C2×C4×C89H(5,𝔽2)11yescharacteristic
295C8×C89—41no—
296C8×C89—41no—
297C8×C89—41no—
298C8×C89—41no—
299C22×C89—41no—
300C22×C89—42no—
301C22×C89—42no—
302C22×C89—41no—
303C22×C89—42no—
304C22×C89—41no—
305C22×C89—42no—
306C22×C89—41no—
307C22×C89—42no—
308C22×C89—41no—
309C22×C89—42no—
310C22×C89—41no—
311C22×C89—41no—
312C22×C89—81no—
313C22×C89—81no—
314C22×C89—81no—
315C22×C89—81no—
316C22×C89—81no—
317C22×C89—81no—
318C22×C89—81no—
319C22×C89—81no—
320C22×C89#52511yescharacteristic
321C22×C89#52511yescharacteristic
322C22×C89#53411yescharacteristic
323C22×C89#57611yescharacteristic
324C22×C89#57611yescharacteristic
325C22×C89#57711yescharacteristic
326C22×C89#57711yescharacteristic
327C4×C89—41no—
328C4×C89—42no—
329C4×C89—42no—
330C4×C89—41no—
331C4×C89—41no—
332C4×C89—41no—
333C4×C89—41no—
334C4×C89—81no—
335C4×C89—81no—
336C4×C89—81no—
337C4×C89—81no—
338C4×C89#55111yescharacteristic
339C4×C89#55311yescharacteristic
340C4×C89#55311yescharacteristic
341C4×C89#55911yescharacteristic
342#29418C8911yesmaximal, characteristic, direct product factor, Sylow
343C2×C89—81no—
344C2×C89—82no—
345C2×C89—82no—
346C2×C89#260011yescharacteristic
347C2×C89#311811yescharacteristic
348C2×C89#311911yescharacteristic
349C2×C89#312211yescharacteristic
350C2×C89#312511yescharacteristic
351C2×C89#319811yescharacteristic
352C2×C89#319811yescharacteristic
353#2324C2×C8911yescharacteristic, complemented
354#2324C2×C8911yescharacteristic, complemented
355#2077C2×C8911yescharacteristic, complemented
356#2034C2×C8911yescharacteristic, complemented
357#2033C2×C8911yescharacteristic, complemented
358#1999C2×C8911yescharacteristic
359#1926C2×C8911yescharacteristic, complemented
360#1925C2×C8911yescharacteristic, complemented
361#1919C2×C8911yescharacteristic, complemented
362#1918C2×C8911yescharacteristic, complemented
363#1879C2×C8911yescharacteristic, complemented
364#1879C2×C8911yescharacteristic, complemented
365#1864C2×C8911yescharacteristic, complemented
366#1864C2×C8911yescharacteristic, complemented
367#1818C2×C8911yescharacteristic, complemented
368C89#2941811yescharacteristic, direct product factor, Sylow
369C22×D8C22×C8911yescharacteristic
370C2×#121C22×C8911yescharacteristic
371C2×#121C22×C8911yescharacteristic
372C2×C4×D4C22×C8911yescharacteristic
373C2×C4×D4C22×C8911yescharacteristic
374C2×#117C22×C8911yescharacteristic
375C2×#107C22×C8911yescharacteristic
376C2×#106C22×C8911yescharacteristic
377C2×#106C22×C8911yescharacteristic
378C2×#102C22×C8911yescharacteristic
379C2×#102C22×C8911yescharacteristic
380C2×#102C22×C8911yescharacteristic
381C2×#102C22×C8911yescharacteristic
382C2×#102C22×C8911yescharacteristic
383C2×#102C22×C8911yescharacteristic
384C2×C22⋊C8C22×C8911yescharacteristic
385C2×C22⋊C8C22×C8911yescharacteristic
386#390—21no—
387#390—21no—
388#390C22×C8911yescharacteristic
389#390C22×C8911yescharacteristic
390#389C22×C8911yescharacteristic
391#389C22×C8911yescharacteristic
392#388—21no—
393#388—21no—
394#386—21no—
395#386—21no—
396#385—21no—
397#385—21no—
398#380C22×C8911yescharacteristic
399#380C22×C8911yescharacteristic
400C4×C4⋊C4C22×C8911yescharacteristic
401C4×C4⋊C4C22×C8911yescharacteristic
402#340C22×C8911yescharacteristic
403#340C22×C8911yescharacteristic
404#340C22×C8911yescharacteristic
405#340C22×C8911yescharacteristic
406#340C22×C8911yescharacteristic
407#340C22×C8911yescharacteristic
408#336C22×C8911yescharacteristic
409#336C22×C8911yescharacteristic
410#336C22×C8911yescharacteristic
411#336C22×C8911yescharacteristic
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C23×C8911yescharacteristic
415C22×D4C23×C8911yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4C23×C8911yescharacteristic
419C2×D8—22no—
420C2×D8—22no—
421C2×D8—41no—
422C22×C8C23×C8911yescharacteristic
423C22×C8C23×C8911yescharacteristic
424C22×C8C23×C8911yescharacteristic
425C22×C8C23×C8911yescharacteristic
426#121—22no—
427#121—22no—
428#121—22no—
429#121—22no—
430C4×D4—41no—
431C4×D4—41no—
432C4×D4—41no—
433C4×D4—41no—
434#117—41no—
435#117—41no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C8911yescharacteristic
439C2×C4⋊C4D4×C8911yescharacteristic
440C2×C4⋊C4C23×C8911yescharacteristic
441C2×C4⋊C4C23×C8911yescharacteristic
442C2×C4⋊C4C23×C8911yescharacteristic
443C2×C4⋊C4C23×C8911yescharacteristic
444C2×C4⋊C4C23×C8911yescharacteristic
445C2×C4⋊C4C23×C8911yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C8911yescharacteristic
457C2×C22⋊C4D4×C8911yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42C23×C8911yescharacteristic
461C2×C42C23×C8911yescharacteristic
462#107—22no—
463#106—22no—
464#106—41no—
465#102—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—41no—
470#102—41no—
471C22⋊C8—41no—
472C22⋊C8—41no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479C24—21no—
480C24—21no—
481C24C2×D4×C8911yescharacteristic
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4#41×C8912yes—
499C2×D4#41×C8912yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4C2×D4×C8911yescharacteristic
519C22×C4C2×D4×C8911yescharacteristic
520C22×C4C2×D4×C8911yescharacteristic
521C22×C4C2×D4×C8911yescharacteristic
522C22×C4C2×D4×C8911yescharacteristic
523C22×C4C24×C8911yescharacteristic
524D8—44no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4#41×C8912yes—
552C4⋊C4#41×C8912yes—
553C22⋊C4—24no—
554C22⋊C4—24no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—81no—
571C23—22no—
572C23—22no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×D4×C8911yescharacteristic
593D4—22no—
594D4—22no—
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4C2×#41×C8911yescharacteristic
643C2×C4C2×#41×C8911yescharacteristic
644C2×C4C2×#41×C8911yescharacteristic
645C2×C4C2×#41×C8911yescharacteristic
646C2×C4H(5,𝔽2)×C8911yescharacteristic
647C2×C4H(5,𝔽2)×C8911yescharacteristic
648C8—41no—
649C8—41no—
650C8—41no—
651C8—41no—
652C22—41no—
653C22—42no—
654C22—42no—
655C22—41no—
656C22—42no—
657C22—41no—
658C22—42no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22#525×C8911yescharacteristic
674C22#525×C8911yescharacteristic
675C22#534×C8911yescharacteristic
676C22#576×C8911yescharacteristic
677C22#576×C8911yescharacteristic
678C22#577×C8911yescharacteristic
679C22#577×C8911yescharacteristic
680C4—41no—
681C4—42no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4#551×C8911yescharacteristic
692C4#553×C8911yescharacteristic
693C4#553×C8911yescharacteristic
694C4#559×C8911yescharacteristic
695C2—81no—
696C2—82no—
697C2—82no—
698C2C89×#260011yescharacteristic
699C2C89×#311811yescharacteristic
700C2C89×#311911yescharacteristic
701C2C89×#312211yescharacteristic
702C2C89×#312511yescharacteristic
703C2C89×#319811yescharacteristic
704C2C89×#319811yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC89×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C2×#117×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#2324C2semidirect
2. C89×#2324C2semidirect
3. C89×#2077C2semidirect
4. C89×#2034C2semidirect
5. C89×#2033C2semidirect
7. C89×#1926C2semidirect
8. C89×#1925C2semidirect
9. C89×#1919C2semidirect
10. C89×#1918C2semidirect
11. C89×#1879C2semidirect
12. C89×#1879C2semidirect
13. C89×#1864C2semidirect
14. C89×#1864C2semidirect
15. C89×#1818C2semidirect
342. #29418C89direct (N × H)
353. #2324C2×C89semidirect
354. #2324C2×C89semidirect
355. #2077C2×C89semidirect
356. #2034C2×C89semidirect
357. #2033C2×C89semidirect
359. #1926C2×C89semidirect
360. #1925C2×C89semidirect
361. #1919C2×C89semidirect
362. #1918C2×C89semidirect
363. #1879C2×C89semidirect
364. #1879C2×C89semidirect
365. #1864C2×C89semidirect
366. #1864C2×C89semidirect
367. #1818C2×C89semidirect
368. C89#29418direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#23242
C89×#20772
C89×#20342
C89×#20332
C89×#19992
C89×#19262
C89×#19252
C89×#19192
C89×#19182
C89×#18792
C89×#18642
C89×#18182
#2941889