Finite Group Databasebeta

← C89×#27065 #36404913

Subgroups — C89×#27065 #36404913

Order 22784.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2513C211yesmaximal, characteristic, complemented
2C89×#2366C211yesmaximal, characteristic, complemented
3C89×#2092C211yesmaximal, characteristic, complemented
4C89×#2054C211yesmaximal, characteristic, complemented
5C89×#2041C211yesmaximal, characteristic, complemented
6C89×#2011C211yesmaximal, characteristic
7C89×#1970C211yesmaximal, characteristic, complemented
8C89×#1926C211yesmaximal, characteristic, complemented
9C89×#1926C211yesmaximal, characteristic, complemented
10C89×#1921C211yesmaximal, characteristic, complemented
11C89×#1916C211yesmaximal, characteristic, complemented
12C89×#1879C211yesmaximal, characteristic, complemented
13C89×#1879C211yesmaximal, characteristic, complemented
14C89×#1804C211yesmaximal, characteristic, complemented
15C4×#102×C89C211yesmaximal, characteristic, complemented
16C22×D8×C89C2211yescharacteristic
17C22×D8×C89C2211yescharacteristic
18C2×#127×C89C2211yescharacteristic
19C2×C4×D4×C89—21no—
20C2×C4×D4×C89C2211yescharacteristic
21C2×C4×D4×C89C2211yescharacteristic
22C2×#107×C89C2211yescharacteristic
23C2×#106×C89C2211yescharacteristic
24C2×C4⋊C8×C89C2211yescharacteristic
25C2×#102×C89C2211yescharacteristic
26C2×#102×C89C2211yescharacteristic
27C2×#102×C89C2211yescharacteristic
28C2×#102×C89C2211yescharacteristic
29C2×#102×C89C2211yescharacteristic
30C2×#102×C89C2211yescharacteristic
31C2×#102×C89C2211yescharacteristic
32C2×#102×C89C2211yescharacteristic
33C2×C4×C8×C89C2211yescharacteristic
34#397×C89—21no—
35#397×C89—21no—
36#390×C89—21no—
37#390×C89C2211yescharacteristic
38#390×C89C2211yescharacteristic
39#390×C89C2211yescharacteristic
40#390×C89C2211yescharacteristic
41#390×C89C2211yescharacteristic
42#389×C89C2211yescharacteristic
43#388×C89—21no—
44#388×C89—21no—
45#386×C89—21no—
46#386×C89—21no—
47#382×C89C2211yescharacteristic
48C4×C4⋊C4×C89C2211yescharacteristic
49C4×C4⋊C4×C89C2211yescharacteristic
50C4×C4⋊C4×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
63C22×D4×C89C2311yescharacteristic
64C23×C4×C89—21no—
65C23×C4×C89—21no—
66C2×D8×C89—22no—
67C2×D8×C89—22no—
68C2×D8×C89—22no—
69C2×D8×C89—41no—
70C2×D8×C89—41no—
71C2×D8×C89—41no—
72C22×C8×C89C2311yescharacteristic
73C22×C8×C89C2311yescharacteristic
74C22×C8×C89C2311yescharacteristic
75C22×C8×C89C2311yescharacteristic
76#127×C89—22no—
77#127×C89—22no—
78C4×D4×C89—22no—
79C4×D4×C89—22no—
80C4×D4×C89—41no—
81C4×D4×C89—41no—
82C4×D4×C89—44no—
83C2×C4⋊C4×C89—21no—
84C2×C4⋊C4×C89D411yescharacteristic
85C2×C4⋊C4×C89D411yescharacteristic
86C2×C4⋊C4×C89C2311yescharacteristic
87C2×C4⋊C4×C89C2311yescharacteristic
88C2×C4⋊C4×C89C2311yescharacteristic
89C2×C4⋊C4×C89C2311yescharacteristic
90C2×C4⋊C4×C89C2311yescharacteristic
91C2×C22⋊C4×C89—21no—
92C2×C22⋊C4×C89—21no—
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×C42×C89—21no—
104C2×C42×C89—21no—
105C2×C42×C89C2311yescharacteristic
106C2×C42×C89C2311yescharacteristic
107C2×C42×C89C2311yescharacteristic
108#107×C89—22no—
109#106×C89—41no—
110C4⋊C8×C89—41no—
111#102×C89—22no—
112#102×C89—22no—
113#102×C89—22no—
114#102×C89—22no—
115#102×C89—41no—
116#102×C89—41no—
117#102×C89—41no—
118#102×C89—41no—
119C4×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×C89D411yescharacteristic
126#95×C89D411yescharacteristic
127C24×C89—21no—
128C24×C89—21no—
129C24×C89—21no—
130C2×D4×C89—24no—
131C2×D4×C89—24no—
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—21no—
142C2×D4×C89—21no—
143C2×D4×C89—21no—
144C2×D4×C89—21no—
145C2×D4×C89—21no—
146C2×D4×C89—21no—
147C2×D4×C89—21no—
148C2×D4×C89—42no—
149C2×D4×C89—42no—
150C2×D4×C89—81no—
151C2×D4×C89—81no—
152C2×D4×C89#4112yes—
153C2×D4×C89#4112yes—
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—42no—
162C22×C4×C89—42no—
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×C89C2×D411yescharacteristic
171C22×C4×C89C2411yescharacteristic
172D8×C89—44no—
173D8×C89—44no—
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—
184C2×C8×C89—21no—
185C2×C8×C89#4112yes—
186C4⋊C4×C89—22no—
187C4⋊C4×C89—22no—
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—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89—81no—
198C4⋊C4×C89#4112yes—
199C22⋊C4×C89—42no—
200C22⋊C4×C89—42no—
201C22⋊C4×C89—42no—
202C22⋊C4×C89—42no—
203C22⋊C4×C89—42no—
204C22⋊C4×C89—42no—
205C22⋊C4×C89—81no—
206C22⋊C4×C89—81no—
207C22⋊C4×C89—81no—
208C22⋊C4×C89—81no—
209C22⋊C4×C89—81no—
210C22⋊C4×C89—81no—
211C42×C89—21no—
212C42×C89—21no—
213C42×C89—21no—
214C42×C89—21no—
215C42×C89—21no—
216C42×C89—21no—
217C42×C89—42no—
218C42×C89—81no—
219C23×C89—22no—
220C23×C89—22no—
221C23×C89—41no—
222C23×C89—41no—
223C23×C89—41no—
224C23×C89—41no—
225C23×C89—41no—
226C23×C89—41no—
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×C89—41no—
240C23×C89C22×D411yescharacteristic
241D4×C89—22no—
242D4×C89—22no—
243D4×C89—22no—
244D4×C89—22no—
245D4×C89—48no—
246D4×C89—41no—
247D4×C89—41no—
248D4×C89—41no—
249D4×C89—41no—
250D4×C89—41no—
251D4×C89—41no—
252D4×C89—41no—
253D4×C89—41no—
254D4×C89—84no—
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—22no—
264C2×C4×C89—21no—
265C2×C4×C89—21no—
266C2×C4×C89—21no—
267C2×C4×C89—21no—
268C2×C4×C89—21no—
269C2×C4×C89—21no—
270C2×C4×C89—21no—
271C2×C4×C89—21no—
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—84no—
287C2×C4×C89—84no—
288C2×C4×C89#13512yes—
289C2×C4×C89AGL(1,ℤ/8)12yes—
290C2×C4×C89C2×#4111yescharacteristic
291C2×C4×C89C2×#4111yescharacteristic
292C2×C4×C89C2×#4111yescharacteristic
293C2×C4×C89C2×#4111yescharacteristic
294C2×C4×C89H(5,𝔽2)11yescharacteristic
295C2×C4×C89H(5,𝔽2)11yescharacteristic
296C8×C89—22no—
297C8×C89—41no—
298C8×C89—41no—
299C8×C89—41no—
300C22×C89—42no—
301C22×C89—42no—
302C22×C89—42no—
303C22×C89—42no—
304C22×C89—42no—
305C22×C89—42no—
306C22×C89—81no—
307C22×C89—81no—
308C22×C89—81no—
309C22×C89—81no—
310C22×C89—81no—
311C22×C89—81no—
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—81no—
321C22×C89#52511yescharacteristic
322C22×C89#54611yescharacteristic
323C22×C89#55011yescharacteristic
324C22×C89C2×#13511yescharacteristic
325C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C89#57611yescharacteristic
327C22×C89#57611yescharacteristic
328C4×C89—22no—
329C4×C89—22no—
330C4×C89—41no—
331C4×C89—41no—
332C4×C89—41no—
333C4×C89—41no—
334C4×C89—42no—
335C4×C89—81no—
336C4×C89—81no—
337C4×C89—81no—
338C4×C89—81no—
339C4×C89#52911yescharacteristic
340C4×C89#53811yescharacteristic
341C4×C89#55111yescharacteristic
342C4×C89#55311yescharacteristic
343#27065C8911yesmaximal, characteristic, direct product factor, Sylow
344C2×C89—82no—
345C2×C89—82no—
346C2×C89—161no—
347C2×C89#246711yescharacteristic
348C2×C89#310511yescharacteristic
349C2×C89#312211yescharacteristic
350C2×C89#330511yescharacteristic
351C2×C89#331811yescharacteristic
352C2×C89#339611yescharacteristic
353C2×C89#339911yescharacteristic
354#2513C2×C8911yescharacteristic, complemented
355#2366C2×C8911yescharacteristic, complemented
356#2092C2×C8911yescharacteristic, complemented
357#2054C2×C8911yescharacteristic, complemented
358#2041C2×C8911yescharacteristic, complemented
359#2011C2×C8911yescharacteristic
360#1970C2×C8911yescharacteristic, complemented
361#1926C2×C8911yescharacteristic, complemented
362#1926C2×C8911yescharacteristic, complemented
363#1921C2×C8911yescharacteristic, complemented
364#1916C2×C8911yescharacteristic, complemented
365#1879C2×C8911yescharacteristic, complemented
366#1879C2×C8911yescharacteristic, complemented
367#1804C2×C8911yescharacteristic, complemented
368C4×#102C2×C8911yescharacteristic, complemented
369C89#2706511yescharacteristic, direct product factor, Sylow
370C22×D8C22×C8911yescharacteristic
371C22×D8C22×C8911yescharacteristic
372C2×#127C22×C8911yescharacteristic
373C2×C4×D4—21no—
374C2×C4×D4C22×C8911yescharacteristic
375C2×C4×D4C22×C8911yescharacteristic
376C2×#107C22×C8911yescharacteristic
377C2×#106C22×C8911yescharacteristic
378C2×C4⋊C8C22×C8911yescharacteristic
379C2×#102C22×C8911yescharacteristic
380C2×#102C22×C8911yescharacteristic
381C2×#102C22×C8911yescharacteristic
382C2×#102C22×C8911yescharacteristic
383C2×#102C22×C8911yescharacteristic
384C2×#102C22×C8911yescharacteristic
385C2×#102C22×C8911yescharacteristic
386C2×#102C22×C8911yescharacteristic
387C2×C4×C8C22×C8911yescharacteristic
388#397—21no—
389#397—21no—
390#390—21no—
391#390C22×C8911yescharacteristic
392#390C22×C8911yescharacteristic
393#390C22×C8911yescharacteristic
394#390C22×C8911yescharacteristic
395#390C22×C8911yescharacteristic
396#389C22×C8911yescharacteristic
397#388—21no—
398#388—21no—
399#386—21no—
400#386—21no—
401#382C22×C8911yescharacteristic
402C4×C4⋊C4C22×C8911yescharacteristic
403C4×C4⋊C4C22×C8911yescharacteristic
404C4×C4⋊C4C22×C8911yescharacteristic
405#340C22×C8911yescharacteristic
406#340C22×C8911yescharacteristic
407#340C22×C8911yescharacteristic
408#340C22×C8911yescharacteristic
409#336C22×C8911yescharacteristic
410#336C22×C8911yescharacteristic
411#336C22×C8911yescharacteristic
412#336C22×C8911yescharacteristic
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C23×C8911yescharacteristic
416C22×D4C23×C8911yescharacteristic
417C22×D4C23×C8911yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C2×D8—22no—
421C2×D8—22no—
422C2×D8—22no—
423C2×D8—41no—
424C2×D8—41no—
425C2×D8—41no—
426C22×C8C23×C8911yescharacteristic
427C22×C8C23×C8911yescharacteristic
428C22×C8C23×C8911yescharacteristic
429C22×C8C23×C8911yescharacteristic
430#127—22no—
431#127—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—44no—
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×C22⋊C4—21no—
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⋊C4—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C8911yescharacteristic
460C2×C42C23×C8911yescharacteristic
461C2×C42C23×C8911yescharacteristic
462#107—22no—
463#106—41no—
464C4⋊C8—41no—
465#102—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—41no—
470#102—41no—
471#102—41no—
472#102—41no—
473C4×C8—41no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C8911yescharacteristic
480#95D4×C8911yescharacteristic
481C24—21no—
482C24—21no—
483C24—21no—
484C2×D4—24no—
485C2×D4—24no—
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—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4#41×C8912yes—
507C2×D4#41×C8912yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C2×D4×C8911yescharacteristic
520C22×C4C2×D4×C8911yescharacteristic
521C22×C4C2×D4×C8911yescharacteristic
522C22×C4C2×D4×C8911yescharacteristic
523C22×C4C2×D4×C8911yescharacteristic
524C22×C4C2×D4×C8911yescharacteristic
525C22×C4C24×C8911yescharacteristic
526D8—44no—
527D8—44no—
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—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8#41×C8912yes—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—81no—
552C4⋊C4#41×C8912yes—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
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—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22×D4×C8911yescharacteristic
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
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—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
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×C4#135×C8912yes—
643C2×C4AGL(1,ℤ/8)×C8912yes—
644C2×C4C2×#41×C8911yescharacteristic
645C2×C4C2×#41×C8911yescharacteristic
646C2×C4C2×#41×C8911yescharacteristic
647C2×C4C2×#41×C8911yescharacteristic
648C2×C4H(5,𝔽2)×C8911yescharacteristic
649C2×C4H(5,𝔽2)×C8911yescharacteristic
650C8—22no—
651C8—41no—
652C8—41no—
653C8—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22#525×C8911yescharacteristic
676C22#546×C8911yescharacteristic
677C22#550×C8911yescharacteristic
678C22C2×#135×C8911yescharacteristic
679C22C2×AGL(1,ℤ/8)×C8911yescharacteristic
680C22#576×C8911yescharacteristic
681C22#576×C8911yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4#529×C8911yescharacteristic
694C4#538×C8911yescharacteristic
695C4#551×C8911yescharacteristic
696C4#553×C8911yescharacteristic
697C2—82no—
698C2—82no—
699C2—161no—
700C2C89×#246711yescharacteristic
701C2C89×#310511yescharacteristic
702C2C89×#312211yescharacteristic
703C2C89×#330511yescharacteristic
704C2C89×#331811yescharacteristic
705C2C89×#339611yescharacteristic
706C2C89×#339911yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC89×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C4×C4⋊C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#2513C2semidirect
2. C89×#2366C2semidirect
3. C89×#2092C2semidirect
4. C89×#2054C2semidirect
5. C89×#2041C2semidirect
7. C89×#1970C2semidirect
8. C89×#1926C2semidirect
9. C89×#1926C2semidirect
10. C89×#1921C2semidirect
11. C89×#1916C2semidirect
12. C89×#1879C2semidirect
13. C89×#1879C2semidirect
14. C89×#1804C2semidirect
15. C4×#102×C89C2semidirect
343. #27065C89direct (N × H)
354. #2513C2×C89semidirect
355. #2366C2×C89semidirect
356. #2092C2×C89semidirect
357. #2054C2×C89semidirect
358. #2041C2×C89semidirect
360. #1970C2×C89semidirect
361. #1926C2×C89semidirect
362. #1926C2×C89semidirect
363. #1921C2×C89semidirect
364. #1916C2×C89semidirect
365. #1879C2×C89semidirect
366. #1879C2×C89semidirect
367. #1804C2×C89semidirect
368. C4×#102C2×C89semidirect
369. C89#27065direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#25132
C89×#23662
C89×#20922
C89×#20542
C89×#20412
C89×#20112
C89×#19702
C89×#19262
C89×#19212
C89×#19162
C89×#18792
C89×#18042
C4×#102×C892
#2706589