Finite Group Databasebeta

← C89×#26033 #36403881

Subgroups — C89×#26033 #36403881

Order 22784.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2550C211yesmaximal, characteristic, complemented
2C89×#2354C211yesmaximal, characteristic
3C89×#2067C211yesmaximal, characteristic
4C89×#2067C211yesmaximal, characteristic
5C89×#2025C211yesmaximal, characteristic
6C89×#2023C211yesmaximal, characteristic
7C89×#1989C211yesmaximal, characteristic, complemented
8C89×#1987C211yesmaximal, characteristic, complemented
9C89×#1947C211yesmaximal, characteristic, complemented
10C89×#1940C211yesmaximal, characteristic, complemented
11C89×#1921C211yesmaximal, characteristic, complemented
12C89×#1918C211yesmaximal, characteristic, complemented
13C89×#1836C211yesmaximal, characteristic, complemented
14C89×#1804C211yesmaximal, characteristic
15C89×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C89C2211yescharacteristic
17C2×#125×C89C2211yescharacteristic
18C2×C4×D4×C89C2211yescharacteristic
19C2×#117×C89—21no—
20C2×#107×C89C2211yescharacteristic
21C2×#107×C89C2211yescharacteristic
22C2×C4⋊C8×C89C2211yescharacteristic
23C2×C4⋊C8×C89C2211yescharacteristic
24C2×C4⋊C8×C89C2211yescharacteristic
25C2×#102×C89C2211yescharacteristic
26C2×#102×C89C2211yescharacteristic
27C2×#102×C89C2211yescharacteristic
28C2×#102×C89C2211yescharacteristic
29C2×#97×C89C2211yescharacteristic
30#398×C89—21no—
31#395×C89—21no—
32#391×C89—21no—
33#390×C89C2211yescharacteristic
34#390×C89C2211yescharacteristic
35#389×C89—21no—
36#389×C89C2211yescharacteristic
37#389×C89C2211yescharacteristic
38#388×C89—21no—
39#388×C89—21no—
40#384×C89C2211yescharacteristic
41#382×C89C2211yescharacteristic
42#380×C89—21no—
43C4×C4⋊C4×C89C2211yescharacteristic
44C4×C4⋊C4×C89C2211yescharacteristic
45C4×C4⋊C4×C89C2211yescharacteristic
46C4×C4⋊C4×C89C2211yescharacteristic
47#340×C89C2211yescharacteristic
48#340×C89C2211yescharacteristic
49#340×C89C2211yescharacteristic
50#340×C89C2211yescharacteristic
51#340×C89C2211yescharacteristic
52#340×C89C2211yescharacteristic
53#340×C89C2211yescharacteristic
54#340×C89C2211yescharacteristic
55#340×C89C2211yescharacteristic
56#340×C89C2211yescharacteristic
57#336×C89C2211yescharacteristic
58#336×C89C2211yescharacteristic
59C22×Q8×C89—21no—
60C22×D4×C89C2311yescharacteristic
61C23×C4×C89—21no—
62C22×C8×C89C2311yescharacteristic
63C22×C8×C89C2311yescharacteristic
64C22×C8×C89C2311yescharacteristic
65C22×C8×C89C2311yescharacteristic
66C4⋊Q8×C89—22no—
67C4⋊Q8×C89—41no—
68#125×C89—22no—
69#125×C89—41no—
70C4×D4×C89—22no—
71C4×D4×C89Q814yescomplemented
72#117×C89—44no—
73C2×C4⋊C4×C89—21no—
74C2×C4⋊C4×C89—21no—
75C2×C4⋊C4×C89—21no—
76C2×C4⋊C4×C89—21no—
77C2×C4⋊C4×C89—21no—
78C2×C4⋊C4×C89—21no—
79C2×C4⋊C4×C89—21no—
80C2×C4⋊C4×C89D411yescharacteristic
81C2×C4⋊C4×C89D411yescharacteristic
82C2×C4⋊C4×C89C2311yescharacteristic
83C2×C4⋊C4×C89C2311yescharacteristic
84C2×C4⋊C4×C89C2311yescharacteristic
85C2×C4⋊C4×C89C2311yescharacteristic
86C2×C4⋊C4×C89C2311yescharacteristic
87C2×C4⋊C4×C89C2311yescharacteristic
88C2×C4⋊C4×C89C2311yescharacteristic
89C2×C22⋊C4×C89—21no—
90C2×C22⋊C4×C89—21no—
91C2×C22⋊C4×C89—21no—
92C2×C22⋊C4×C89—21no—
93C2×C22⋊C4×C89—21no—
94C2×C42×C89—21no—
95C2×C42×C89—21no—
96C2×C42×C89—21no—
97C2×C42×C89C2311yescharacteristic
98C2×C42×C89C2311yescharacteristic
99C2×C42×C89C2311yescharacteristic
100#107×C89—22no—
101#107×C89—22no—
102C4⋊C8×C89—22no—
103C4⋊C8×C89—41no—
104C4⋊C8×C89—41no—
105#102×C89—22no—
106#102×C89—22no—
107#102×C89—41no—
108#102×C89—41no—
109#97×C89—22no—
110#95×C89—21no—
111#95×C89—21no—
112#95×C89—21no—
113#95×C89—21no—
114#95×C89—21no—
115#95×C89—21no—
116#95×C89—21no—
117#95×C89D411yescharacteristic
118#95×C89D411yescharacteristic
119C24×C89—21no—
120C2×Q8×C89—42no—
121C2×Q8×C89—42no—
122C2×Q8×C89—81no—
123C2×D4×C89—21no—
124C2×D4×C89—21no—
125C2×D4×C89—21no—
126C2×D4×C89—21no—
127C2×D4×C89—21no—
128C2×D4×C89C2×Q812yes—
129C22×C4×C89—21no—
130C22×C4×C89—21no—
131C22×C4×C89—21no—
132C22×C4×C89—24no—
133C22×C4×C89—21no—
134C22×C4×C89—21no—
135C22×C4×C89—21no—
136C22×C4×C89—21no—
137C22×C4×C89—42no—
138C22×C4×C89—42no—
139C22×C4×C89C2×D411yescharacteristic
140C22×C4×C89C2×D411yescharacteristic
141C22×C4×C89C2×D411yescharacteristic
142C22×C4×C89C2×D411yescharacteristic
143C22×C4×C89C2×D411yescharacteristic
144C22×C4×C89C2×D411yescharacteristic
145C22×C4×C89C2411yescharacteristic
146C2×C8×C89—21no—
147C2×C8×C89—21no—
148C2×C8×C89—21no—
149C2×C8×C89—21no—
150C2×C8×C89—21no—
151C2×C8×C89—21no—
152C2×C8×C89—21no—
153C2×C8×C89—21no—
154C2×C8×C89—21no—
155C2×C8×C89—21no—
156C2×C8×C89—21no—
157C2×C8×C89—21no—
158C4⋊C4×C89—22no—
159C4⋊C4×C89—21no—
160C4⋊C4×C89—21no—
161C4⋊C4×C89—21no—
162C4⋊C4×C89—21no—
163C4⋊C4×C89—21no—
164C4⋊C4×C89—21no—
165C4⋊C4×C89—21no—
166C4⋊C4×C89—21no—
167C4⋊C4×C89—21no—
168C4⋊C4×C89—21no—
169C4⋊C4×C89—21no—
170C4⋊C4×C89—41no—
171C4⋊C4×C89—42no—
172C4⋊C4×C89—42no—
173C4⋊C4×C89—42no—
174C4⋊C4×C89—42no—
175C4⋊C4×C89—42no—
176C4⋊C4×C89—81no—
177C4⋊C4×C89—81no—
178C4⋊C4×C89C2×Q812yes—
179C4⋊C4×C89#4112yes—
180C4⋊C4×C89#4112yes—
181C22⋊C4×C89—24no—
182C22⋊C4×C89—42no—
183C22⋊C4×C89—42no—
184C22⋊C4×C89—81no—
185C22⋊C4×C89—81no—
186C42×C89—21no—
187C42×C89—21no—
188C42×C89—21no—
189C42×C89—21no—
190C42×C89—42no—
191C42×C89—42no—
192C42×C89—81no—
193C42×C89C2×Q812yes—
194C42×C89#4112yes—
195C23×C89—22no—
196C23×C89—41no—
197C23×C89—41no—
198C23×C89—41no—
199C23×C89—41no—
200C23×C89—41no—
201C23×C89—41no—
202C23×C89C22×D411yescharacteristic
203Q8×C89—84no—
204D4×C89—22no—
205D4×C89—22no—
206D4×C89—41no—
207D4×C89—41no—
208C2×C4×C89—21no—
209C2×C4×C89—21no—
210C2×C4×C89—21no—
211C2×C4×C89—21no—
212C2×C4×C89—21no—
213C2×C4×C89—21no—
214C2×C4×C89—22no—
215C2×C4×C89—21no—
216C2×C4×C89—21no—
217C2×C4×C89—21no—
218C2×C4×C89—22no—
219C2×C4×C89—22no—
220C2×C4×C89—21no—
221C2×C4×C89—21no—
222C2×C4×C89—21no—
223C2×C4×C89—21no—
224C2×C4×C89—21no—
225C2×C4×C89—21no—
226C2×C4×C89—48no—
227C2×C4×C89—41no—
228C2×C4×C89—41no—
229C2×C4×C89—41no—
230C2×C4×C89—41no—
231C2×C4×C89—41no—
232C2×C4×C89—41no—
233C2×C4×C89—41no—
234C2×C4×C89—41no—
235C2×C4×C89—41no—
236C2×C4×C89—41no—
237C2×C4×C89—41no—
238C2×C4×C89—41no—
239C2×C4×C89—41no—
240C2×C4×C89—41no—
241C2×C4×C89—41no—
242C2×C4×C89—41no—
243C2×C4×C89—41no—
244C2×C4×C89—41no—
245C2×C4×C89C22⋊Q812yes—
246C2×C4×C89C22⋊Q812yes—
247C2×C4×C89AGL(1,ℤ/8)12yes—
248C2×C4×C89C22×Q811yescharacteristic
249C2×C4×C89C2×#4111yescharacteristic
250C2×C4×C89C2×#4111yescharacteristic
251C2×C4×C89C2×#4111yescharacteristic
252C2×C4×C89H(5,𝔽2)11yescharacteristic
253C2×C4×C892−1+411yescharacteristic
254C8×C89—41no—
255C8×C89—41no—
256C8×C89—41no—
257C8×C89—41no—
258C22×C89—42no—
259C22×C89—42no—
260C22×C89—42no—
261C22×C89—81no—
262C22×C89—81no—
263C22×C89—81no—
264C22×C89—81no—
265C22×C89C2×C22⋊Q811yescharacteristic
266C22×C89#54611yescharacteristic
267C22×C89#54811yescharacteristic
268C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C89#57511yescharacteristic
270C22×C89#57611yescharacteristic
271C22×C89#57811yescharacteristic
272C4×C89—22no—
273C4×C89—22no—
274C4×C89—22no—
275C4×C89—42no—
276C4×C89—42no—
277C4×C89—41no—
278C4×C89—41no—
279C4×C89—41no—
280C4×C89—42no—
281C4×C89—81no—
282C4×C89—81no—
283C4×C89—81no—
284C4×C89—81no—
285C4×C89#53311yescharacteristic
286C4×C89#54411yescharacteristic
287C4×C89#55511yescharacteristic
288C4×C89#55611yescharacteristic
289#26033C8911yesmaximal, characteristic, direct product factor, Sylow
290C2×C89—82no—
291C2×C89#243911yescharacteristic
292C2×C89#307711yescharacteristic
293C2×C89#308311yescharacteristic
294C2×C89#330811yescharacteristic
295C2×C89#331911yescharacteristic
296C2×C89#336611yescharacteristic
297C2×C89#337711yescharacteristic
298#2550C2×C8911yescharacteristic, complemented
299#2354C2×C8911yescharacteristic
300#2067C2×C8911yescharacteristic
301#2067C2×C8911yescharacteristic
302#2025C2×C8911yescharacteristic
303#2023C2×C8911yescharacteristic
304#1989C2×C8911yescharacteristic, complemented
305#1987C2×C8911yescharacteristic, complemented
306#1947C2×C8911yescharacteristic, complemented
307#1940C2×C8911yescharacteristic, complemented
308#1921C2×C8911yescharacteristic, complemented
309#1918C2×C8911yescharacteristic, complemented
310#1836C2×C8911yescharacteristic, complemented
311#1804C2×C8911yescharacteristic
312#1762C2×C8911yescharacteristic
313C89#2603311yescharacteristic, direct product factor, Sylow
314C2×C4⋊Q8C22×C8911yescharacteristic
315C2×#125C22×C8911yescharacteristic
316C2×C4×D4C22×C8911yescharacteristic
317C2×#117—21no—
318C2×#107C22×C8911yescharacteristic
319C2×#107C22×C8911yescharacteristic
320C2×C4⋊C8C22×C8911yescharacteristic
321C2×C4⋊C8C22×C8911yescharacteristic
322C2×C4⋊C8C22×C8911yescharacteristic
323C2×#102C22×C8911yescharacteristic
324C2×#102C22×C8911yescharacteristic
325C2×#102C22×C8911yescharacteristic
326C2×#102C22×C8911yescharacteristic
327C2×#97C22×C8911yescharacteristic
328#398—21no—
329#395—21no—
330#391—21no—
331#390C22×C8911yescharacteristic
332#390C22×C8911yescharacteristic
333#389—21no—
334#389C22×C8911yescharacteristic
335#389C22×C8911yescharacteristic
336#388—21no—
337#388—21no—
338#384C22×C8911yescharacteristic
339#382C22×C8911yescharacteristic
340#380—21no—
341C4×C4⋊C4C22×C8911yescharacteristic
342C4×C4⋊C4C22×C8911yescharacteristic
343C4×C4⋊C4C22×C8911yescharacteristic
344C4×C4⋊C4C22×C8911yescharacteristic
345#340C22×C8911yescharacteristic
346#340C22×C8911yescharacteristic
347#340C22×C8911yescharacteristic
348#340C22×C8911yescharacteristic
349#340C22×C8911yescharacteristic
350#340C22×C8911yescharacteristic
351#340C22×C8911yescharacteristic
352#340C22×C8911yescharacteristic
353#340C22×C8911yescharacteristic
354#340C22×C8911yescharacteristic
355#336C22×C8911yescharacteristic
356#336C22×C8911yescharacteristic
357C22×Q8—21no—
358C22×D4C23×C8911yescharacteristic
359C23×C4—21no—
360C22×C8C23×C8911yescharacteristic
361C22×C8C23×C8911yescharacteristic
362C22×C8C23×C8911yescharacteristic
363C22×C8C23×C8911yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8—41no—
366#125—22no—
367#125—41no—
368C4×D4—22no—
369C4×D4Q8×C8914yescomplemented
370#117—44no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C8911yescharacteristic
379C2×C4⋊C4D4×C8911yescharacteristic
380C2×C4⋊C4C23×C8911yescharacteristic
381C2×C4⋊C4C23×C8911yescharacteristic
382C2×C4⋊C4C23×C8911yescharacteristic
383C2×C4⋊C4C23×C8911yescharacteristic
384C2×C4⋊C4C23×C8911yescharacteristic
385C2×C4⋊C4C23×C8911yescharacteristic
386C2×C4⋊C4C23×C8911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42C23×C8911yescharacteristic
396C2×C42C23×C8911yescharacteristic
397C2×C42C23×C8911yescharacteristic
398#107—22no—
399#107—22no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—22no—
404#102—22no—
405#102—41no—
406#102—41no—
407#97—22no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95D4×C8911yescharacteristic
416#95D4×C8911yescharacteristic
417C24—21no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—81no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×Q8×C8912yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4C2×D4×C8911yescharacteristic
438C22×C4C2×D4×C8911yescharacteristic
439C22×C4C2×D4×C8911yescharacteristic
440C22×C4C2×D4×C8911yescharacteristic
441C22×C4C2×D4×C8911yescharacteristic
442C22×C4C2×D4×C8911yescharacteristic
443C22×C4C24×C8911yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4C2×Q8×C8912yes—
477C4⋊C4#41×C8912yes—
478C4⋊C4#41×C8912yes—
479C22⋊C4—24no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—42no—
489C42—42no—
490C42—81no—
491C42C2×Q8×C8912yes—
492C42#41×C8912yes—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×D4×C8911yescharacteristic
501Q8—84no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—48no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4C22⋊Q8×C8912yes—
544C2×C4C22⋊Q8×C8912yes—
545C2×C4AGL(1,ℤ/8)×C8912yes—
546C2×C4C22×Q8×C8911yescharacteristic
547C2×C4C2×#41×C8911yescharacteristic
548C2×C4C2×#41×C8911yescharacteristic
549C2×C4C2×#41×C8911yescharacteristic
550C2×C4H(5,𝔽2)×C8911yescharacteristic
551C2×C42−1+4×C8911yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C2×C22⋊Q8×C8911yescharacteristic
564C22#546×C8911yescharacteristic
565C22#548×C8911yescharacteristic
566C22C2×AGL(1,ℤ/8)×C8911yescharacteristic
567C22#575×C8911yescharacteristic
568C22#576×C8911yescharacteristic
569C22#578×C8911yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4#533×C8911yescharacteristic
584C4#544×C8911yescharacteristic
585C4#555×C8911yescharacteristic
586C4#556×C8911yescharacteristic
587C2—82no—
588C2C89×#243911yescharacteristic
589C2C89×#307711yescharacteristic
590C2C89×#308311yescharacteristic
591C2C89×#330811yescharacteristic
592C2C89×#331911yescharacteristic
593C2C89×#336611yescharacteristic
594C2C89×#337711yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC22×D4×C89C23
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×#2550C2semidirect
7. C89×#1989C2semidirect
8. C89×#1987C2semidirect
9. C89×#1947C2semidirect
10. C89×#1940C2semidirect
11. C89×#1921C2semidirect
12. C89×#1918C2semidirect
13. C89×#1836C2semidirect
71. C4×D4×C89Q8semidirect
289. #26033C89direct (N × H)
298. #2550C2×C89semidirect
304. #1989C2×C89semidirect
305. #1987C2×C89semidirect
306. #1947C2×C89semidirect
307. #1940C2×C89semidirect
308. #1921C2×C89semidirect
309. #1918C2×C89semidirect
310. #1836C2×C89semidirect
313. C89#26033direct (N × H)
369. C4×D4Q8×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#25502
C89×#23542
C89×#20672
C89×#20252
C89×#20232
C89×#19892
C89×#19872
C89×#19472
C89×#19402
C89×#19212
C89×#19182
C89×#18362
C89×#18042
C89×#17622
#2603389