Finite Group Databasebeta

← C89×#35469 #36413317

Subgroups — C89×#35469 #36413317

Order 22784.

2246 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#539×C89C211yesmaximal, characteristic, complemented
2C22×#126×C89C211yesmaximal, characteristic, complemented
3C89×#2561C211yesmaximal, characteristic, complemented
4C89×#2560C214yesmaximal, complemented
5C89×#2554C214yesmaximal, complemented
6C89×#2539C211yesmaximal, characteristic
7C89×#2519C214yesmaximal, complemented
8C89×#2512C214yesmaximal, complemented
9C89×#2504C211yesmaximal, characteristic, complemented
10C89×#2502C211yesmaximal, characteristic, complemented
11C89×#2413C212yesmaximal, complemented
12C89×#2411C212yesmaximal, complemented
13C89×#2321C212yesmaximal, complemented
14C4×#123×C89C212yesmaximal, complemented
15C89×#2274C211yesmaximal, characteristic, complemented
16#539×C89—28no—
17C2×#126×C89—28no—
18C2×#126×C89C2214yes—
19C2×#126×C89C2214yes—
20C2×#126×C89C2212yescomplemented
21C2×#125×C89C2212yescomplemented
22C2×#123×C89C2212yes—
23C2×#123×C89C2212yes—
24C2×#123×C89C2212yescomplemented
25C2×C22⋊Q8×C89C2211yescharacteristic
26C2×C22⋊Q8×C89C2212yescomplemented
27C2×#121×C89C2211yescharacteristic
28C2×#120×C89C2212yes—
29C2×C4×D4×C89C2212yes—
30C2×#117×C89C2212yes—
31C22×C4⋊C4×C89C2211yescharacteristic
32C22×C4⋊C4×C89C2211yescharacteristic
33C22×C4⋊C4×C89C2211yescharacteristic
34C22×C22⋊C4×C89C2211yescharacteristic
35C22×C22⋊C4×C89C2211yescharacteristic
36C22×C22⋊C4×C89C2211yescharacteristic
37C22×C42×C89C2211yescharacteristic
38#399×C89C2212yes—
39#398×C89C2214yescomplemented
40#398×C89C2214yescomplemented
41#397×C89C2212yes—
42#397×C89C2214yescomplemented
43#396×C89C2214yes—
44#396×C89C2214yescomplemented
45#394×C89C2214yes—
46#393×C89C2212yes—
47#392×C89C2212yes—
48#391×C89C2212yescomplemented
49#390×C89C2214yes—
50#390×C89C2214yes—
51#390×C89C2214yes—
52#390×C89C2212yescomplemented
53#389×C89C2214yescomplemented
54#388×C89C2214yes—
55#388×C89C2214yes—
56#388×C89C2214yes—
57#388×C89C2214yes—
58#388×C89C2214yescomplemented
59#388×C89C2214yescomplemented
60#387×C89C2214yescomplemented
61#386×C89C2214yes—
62#386×C89C2212yes—
63#386×C89C2212yes—
64#385×C89C2212yes—
65#385×C89C2212yes—
66#384×C89C2212yescomplemented
67#382×C89C2212yescomplemented
68#381×C89C2212yes—
69#379×C89C2212yes—
70C4×C4⋊C4×C89C2214yescomplemented
71C4×C4⋊C4×C89C2214yescomplemented
72C4×C4⋊C4×C89C2214yescomplemented
73C4×C22⋊C4×C89C2212yes—
74C4×C22⋊C4×C89C2211yescharacteristic
75C4×C22⋊C4×C89C2211yescharacteristic
76C4×C22⋊C4×C89C2214yescomplemented
77C25×C89C2311yescharacteristic
78C22×Q8×C89C2311yescharacteristic
79C22×D4×C89C2312yes—
80C22×D4×C89C2314yes—
81C22×D4×C89C2311yescharacteristic
82C23×C4×C89C2311yescharacteristic
83C23×C4×C89C2311yescharacteristic
84C23×C4×C89C2312yes—
85C23×C4×C89C2311yescharacteristic
86C23×C4×C89C2311yescharacteristic
87C23×C4×C89C2311yescharacteristic
88C23×C4×C89C2311yescharacteristic
89#126×C89—216no—
90#126×C89—216no—
91#126×C89—28no—
92#125×C89—28no—
93#123×C89—28no—
94#123×C89—28no—
95#123×C89—28no—
96C22⋊Q8×C89—24no—
97C22⋊Q8×C89—28no—
98#121×C89—24no—
99#120×C89—28no—
100C4×D4×C89—28no—
101#117×C89—28no—
102C2×C4⋊C4×C89—24no—
103C2×C4⋊C4×C89—24no—
104C2×C4⋊C4×C89D418yescomplemented
105C2×C4⋊C4×C89C2314yes—
106C2×C4⋊C4×C89C2314yes—
107C2×C4⋊C4×C89C2311yescharacteristic
108C2×C4⋊C4×C89C2312yes—
109C2×C4⋊C4×C89C2311yescharacteristic
110C2×C4⋊C4×C89C2312yes—
111C2×C4⋊C4×C89C2312yes—
112C2×C4⋊C4×C89C2312yes—
113C2×C4⋊C4×C89C2312yes—
114C2×C4⋊C4×C89C2314yes—
115C2×C4⋊C4×C89C2312yes—
116C2×C4⋊C4×C89C2314yes—
117C2×C4⋊C4×C89C2314yes—
118C2×C4⋊C4×C89C2312yes—
119C2×C4⋊C4×C89C2312yes—
120C2×C22⋊C4×C89—24no—
121C2×C22⋊C4×C89—24no—
122C2×C22⋊C4×C89—24no—
123C2×C22⋊C4×C89C2312yes—
124C2×C22⋊C4×C89C2314yes—
125C2×C22⋊C4×C89C2312yes—
126C2×C22⋊C4×C89C2314yes—
127C2×C22⋊C4×C89C2314yes—
128C2×C22⋊C4×C89C2312yes—
129C2×C22⋊C4×C89C2314yes—
130C2×C22⋊C4×C89C2312yes—
131C2×C22⋊C4×C89C2312yes—
132C2×C22⋊C4×C89C2312yes—
133C2×C22⋊C4×C89C2312yes—
134C2×C22⋊C4×C89C2312yes—
135C2×C22⋊C4×C89C2314yes—
136C2×C22⋊C4×C89C2314yes—
137C2×C22⋊C4×C89C2314yes—
138C2×C22⋊C4×C89C2314yes—
139C2×C22⋊C4×C89C2312yes—
140C2×C42×C89—24no—
141C2×C42×C89C2314yes—
142C2×C42×C89C2312yes—
143C2×C42×C89C2314yes—
144C2×C42×C89C2314yes—
145C2×C42×C89C2312yes—
146C2×C42×C89C2312yes—
147#95×C89C2314yes—
148#95×C89C2312yes—
149#95×C89C2312yes—
150#95×C89C2314yes—
151#95×C89C2314yes—
152#95×C89C2314yes—
153#95×C89C2314yes—
154#95×C89C2314yes—
155#95×C89C2314yes—
156C24×C89—22no—
157C24×C89—24no—
158C24×C89—42no—
159C24×C89—42no—
160C24×C89C2412yes—
161C24×C89C2412yes—
162C24×C89C2411yescharacteristic
163C2×Q8×C89—22no—
164C2×Q8×C89—42no—
165C2×D4×C89—24no—
166C2×D4×C89—24no—
167C2×D4×C89—24no—
168C2×D4×C89—22no—
169C2×D4×C89—28no—
170C2×D4×C89—44no—
171C2×D4×C89—42no—
172C2×D4×C89—44no—
173C22×C4×C89—24no—
174C22×C4×C89—22no—
175C22×C4×C89—22no—
176C22×C4×C89—22no—
177C22×C4×C89—24no—
178C22×C4×C89—24no—
179C22×C4×C89—42no—
180C22×C4×C89—42no—
181C22×C4×C89—42no—
182C22×C4×C89—42no—
183C22×C4×C89—44no—
184C22×C4×C89C2×D414yes—
185C22×C4×C89C2×D414yes—
186C22×C4×C89C2×D414yes—
187C22×C4×C89C2414yes—
188C22×C4×C89C2412yes—
189C22×C4×C89C2412yes—
190C22×C4×C89C2412yes—
191C22×C4×C89C2412yes—
192C22×C4×C89C2412yes—
193C22×C4×C89C2412yes—
194C22×C4×C89C2412yes—
195C22×C4×C89C2411yescharacteristic
196C22×C4×C89C2411yescharacteristic
197C22×C4×C89C2412yes—
198C22×C4×C89C2414yes—
199C4⋊C4×C89—28no—
200C4⋊C4×C89—24no—
201C4⋊C4×C89—24no—
202C4⋊C4×C89—24no—
203C4⋊C4×C89—22no—
204C4⋊C4×C89—24no—
205C4⋊C4×C89—24no—
206C4⋊C4×C89—22no—
207C4⋊C4×C89—24no—
208C4⋊C4×C89—28no—
209C4⋊C4×C89—28no—
210C4⋊C4×C89—44no—
211C4⋊C4×C89—44no—
212C4⋊C4×C89C2×D418yes—
213C4⋊C4×C89C2×D418yes—
214C22⋊C4×C89—24no—
215C22⋊C4×C89—24no—
216C22⋊C4×C89—28no—
217C22⋊C4×C89—24no—
218C22⋊C4×C89—24no—
219C22⋊C4×C89—28no—
220C22⋊C4×C89—24no—
221C22⋊C4×C89—24no—
222C22⋊C4×C89—24no—
223C22⋊C4×C89—24no—
224C22⋊C4×C89—28no—
225C22⋊C4×C89—28no—
226C22⋊C4×C89—44no—
227C22⋊C4×C89—44no—
228C22⋊C4×C89—44no—
229C22⋊C4×C89—44no—
230C22⋊C4×C89#4118yes—
231C42×C89—28no—
232C42×C89—24no—
233C42×C89—28no—
234C42×C89—42no—
235C42×C89—44no—
236C42×C89—42no—
237C23×C89—22no—
238C23×C89—22no—
239C23×C89—22no—
240C23×C89—22no—
241C23×C89—22no—
242C23×C89—24no—
243C23×C89—22no—
244C23×C89—24no—
245C23×C89—22no—
246C23×C89—24no—
247C23×C89—24no—
248C23×C89—22no—
249C23×C89—44no—
250C23×C89—44no—
251C23×C89—44no—
252C23×C89—88no—
253C23×C89C22×D412yes—
254C23×C89C2×#4114yes—
255C23×C89C2511yescharacteristic
256Q8×C89—82no—
257D4×C89—48no—
258D4×C89—82no—
259D4×C89—88no—
260C2×C4×C89—28no—
261C2×C4×C89—22no—
262C2×C4×C89—22no—
263C2×C4×C89—24no—
264C2×C4×C89—24no—
265C2×C4×C89—22no—
266C2×C4×C89—22no—
267C2×C4×C89—24no—
268C2×C4×C89—22no—
269C2×C4×C89—22no—
270C2×C4×C89—22no—
271C2×C4×C89—22no—
272C2×C4×C89—22no—
273C2×C4×C89—22no—
274C2×C4×C89—24no—
275C2×C4×C89—22no—
276C2×C4×C89—24no—
277C2×C4×C89—22no—
278C2×C4×C89—24no—
279C2×C4×C89—24no—
280C2×C4×C89—24no—
281C2×C4×C89—24no—
282C2×C4×C89—24no—
283C2×C4×C89—24no—
284C2×C4×C89—44no—
285C2×C4×C89—44no—
286C2×C4×C89—44no—
287C2×C4×C89—44no—
288C2×C4×C89—44no—
289C2×C4×C89—84no—
290C2×C4×C89C22×D414yes—
291C2×C4×C89C22×D414yes—
292C2×C4×C89C22×D412yes—
293C2×C4×C89C22×D412yes—
294C2×C4×C89C2×#4118yes—
295C22×C89—22no—
296C22×C89—22no—
297C22×C89—28no—
298C22×C89—42no—
299C22×C89—42no—
300C22×C89—42no—
301C22×C89—42no—
302C22×C89—42no—
303C22×C89—42no—
304C22×C89—44no—
305C22×C89—44no—
306C22×C89—44no—
307C22×C89—44no—
308C22×C89—88no—
309C22×C89#53214yes—
310C22×C89C23×D411yescharacteristic
311C22×C89C22×#4112yes—
312C22×C89#58512yes—
313C22×C89#58512yes—
314C4×C89—24no—
315C4×C89—24no—
316C4×C89—22no—
317C4×C89—22no—
318C4×C89—28no—
319C4×C89—42no—
320C4×C89—42no—
321C4×C89—42no—
322C4×C89—42no—
323C4×C89—42no—
324C4×C89—42no—
325C4×C89—44no—
326#35469C8911yesmaximal, characteristic, direct product factor, Sylow
327C2×C89—24no—
328C2×C89—82no—
329C2×C89—82no—
330C2×C89C2×#53211yescharacteristic
331C2×C89#348511yescharacteristic
332C2×C89#348711yescharacteristic
333C2×C89#352114yes—
334C2×#539C2×C8911yescharacteristic, complemented
335C22×#126C2×C8911yescharacteristic, complemented
336#2561C2×C8911yescharacteristic, complemented
337#2560C2×C8914yescomplemented
338#2554C2×C8914yescomplemented
339#2539C2×C8911yescharacteristic
340#2519C2×C8914yescomplemented
341#2512C2×C8914yescomplemented
342#2504C2×C8911yescharacteristic, complemented
343#2502C2×C8911yescharacteristic, complemented
344#2413C2×C8912yescomplemented
345#2411C2×C8912yescomplemented
346#2321C2×C8912yescomplemented
347C4×#123C2×C8912yescomplemented
348#2274C2×C8911yescharacteristic, complemented
349C89#3546911yescharacteristic, direct product factor, Sylow
350#539—28no—
351C2×#126—28no—
352C2×#126C22×C8914yes—
353C2×#126C22×C8914yes—
354C2×#126C22×C8912yescomplemented
355C2×#125C22×C8912yescomplemented
356C2×#123C22×C8912yes—
357C2×#123C22×C8912yes—
358C2×#123C22×C8912yescomplemented
359C2×C22⋊Q8C22×C8911yescharacteristic
360C2×C22⋊Q8C22×C8912yescomplemented
361C2×#121C22×C8911yescharacteristic
362C2×#120C22×C8912yes—
363C2×C4×D4C22×C8912yes—
364C2×#117C22×C8912yes—
365C22×C4⋊C4C22×C8911yescharacteristic
366C22×C4⋊C4C22×C8911yescharacteristic
367C22×C4⋊C4C22×C8911yescharacteristic
368C22×C22⋊C4C22×C8911yescharacteristic
369C22×C22⋊C4C22×C8911yescharacteristic
370C22×C22⋊C4C22×C8911yescharacteristic
371C22×C42C22×C8911yescharacteristic
372#399C22×C8912yes—
373#398C22×C8914yescomplemented
374#398C22×C8914yescomplemented
375#397C22×C8912yes—
376#397C22×C8914yescomplemented
377#396C22×C8914yes—
378#396C22×C8914yescomplemented
379#394C22×C8914yes—
380#393C22×C8912yes—
381#392C22×C8912yes—
382#391C22×C8912yescomplemented
383#390C22×C8914yes—
384#390C22×C8914yes—
385#390C22×C8914yes—
386#390C22×C8912yescomplemented
387#389C22×C8914yescomplemented
388#388C22×C8914yes—
389#388C22×C8914yes—
390#388C22×C8914yes—
391#388C22×C8914yes—
392#388C22×C8914yescomplemented
393#388C22×C8914yescomplemented
394#387C22×C8914yescomplemented
395#386C22×C8914yes—
396#386C22×C8912yes—
397#386C22×C8912yes—
398#385C22×C8912yes—
399#385C22×C8912yes—
400#384C22×C8912yescomplemented
401#382C22×C8912yescomplemented
402#381C22×C8912yes—
403#379C22×C8912yes—
404C4×C4⋊C4C22×C8914yescomplemented
405C4×C4⋊C4C22×C8914yescomplemented
406C4×C4⋊C4C22×C8914yescomplemented
407C4×C22⋊C4C22×C8911yescharacteristic
408C4×C22⋊C4C22×C8912yes—
409C4×C22⋊C4C22×C8911yescharacteristic
410C4×C22⋊C4C22×C8914yescomplemented
411C25C23×C8911yescharacteristic
412C22×Q8C23×C8911yescharacteristic
413C22×D4C23×C8912yes—
414C22×D4C23×C8914yes—
415C22×D4C23×C8911yescharacteristic
416C23×C4C23×C8911yescharacteristic
417C23×C4C23×C8911yescharacteristic
418C23×C4C23×C8911yescharacteristic
419C23×C4C23×C8911yescharacteristic
420C23×C4C23×C8912yes—
421C23×C4C23×C8911yescharacteristic
422C23×C4C23×C8911yescharacteristic
423#126—216no—
424#126—216no—
425#126—28no—
426#125—28no—
427#123—28no—
428#123—28no—
429#123—28no—
430C22⋊Q8—24no—
431C22⋊Q8—28no—
432#121—24no—
433#120—28no—
434C4×D4—28no—
435#117—28no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4D4×C8918yescomplemented
439C2×C4⋊C4C23×C8912yes—
440C2×C4⋊C4C23×C8912yes—
441C2×C4⋊C4C23×C8914yes—
442C2×C4⋊C4C23×C8914yes—
443C2×C4⋊C4C23×C8912yes—
444C2×C4⋊C4C23×C8911yescharacteristic
445C2×C4⋊C4C23×C8912yes—
446C2×C4⋊C4C23×C8911yescharacteristic
447C2×C4⋊C4C23×C8912yes—
448C2×C4⋊C4C23×C8912yes—
449C2×C4⋊C4C23×C8914yes—
450C2×C4⋊C4C23×C8914yes—
451C2×C4⋊C4C23×C8914yes—
452C2×C4⋊C4C23×C8912yes—
453C2×C4⋊C4C23×C8912yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4C23×C8914yes—
458C2×C22⋊C4C23×C8912yes—
459C2×C22⋊C4C23×C8914yes—
460C2×C22⋊C4C23×C8912yes—
461C2×C22⋊C4C23×C8912yes—
462C2×C22⋊C4C23×C8912yes—
463C2×C22⋊C4C23×C8912yes—
464C2×C22⋊C4C23×C8914yes—
465C2×C22⋊C4C23×C8912yes—
466C2×C22⋊C4C23×C8912yes—
467C2×C22⋊C4C23×C8912yes—
468C2×C22⋊C4C23×C8914yes—
469C2×C22⋊C4C23×C8914yes—
470C2×C22⋊C4C23×C8914yes—
471C2×C22⋊C4C23×C8914yes—
472C2×C22⋊C4C23×C8914yes—
473C2×C22⋊C4C23×C8912yes—
474C2×C42—24no—
475C2×C42C23×C8914yes—
476C2×C42C23×C8912yes—
477C2×C42C23×C8914yes—
478C2×C42C23×C8914yes—
479C2×C42C23×C8912yes—
480C2×C42C23×C8912yes—
481#95C23×C8914yes—
482#95C23×C8912yes—
483#95C23×C8912yes—
484#95C23×C8914yes—
485#95C23×C8914yes—
486#95C23×C8914yes—
487#95C23×C8914yes—
488#95C23×C8914yes—
489#95C23×C8914yes—
490C24—22no—
491C24—24no—
492C24—42no—
493C24—42no—
494C24C24×C8912yes—
495C24C24×C8912yes—
496C24C24×C8911yescharacteristic
497C2×Q8—22no—
498C2×Q8—42no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—22no—
503C2×D4—28no—
504C2×D4—44no—
505C2×D4—42no—
506C2×D4—44no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4C2×D4×C8914yes—
519C22×C4C2×D4×C8914yes—
520C22×C4C2×D4×C8914yes—
521C22×C4C24×C8914yes—
522C22×C4C24×C8912yes—
523C22×C4C24×C8912yes—
524C22×C4C24×C8912yes—
525C22×C4C24×C8912yes—
526C22×C4C24×C8912yes—
527C22×C4C24×C8912yes—
528C22×C4C24×C8912yes—
529C22×C4C24×C8911yescharacteristic
530C22×C4C24×C8911yescharacteristic
531C22×C4C24×C8912yes—
532C22×C4C24×C8914yes—
533C4⋊C4—28no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—22no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—22no—
541C4⋊C4—24no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4C2×D4×C8918yes—
547C4⋊C4C2×D4×C8918yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—28no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—28no—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—44no—
561C22⋊C4—44no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4#41×C8918yes—
565C42—28no—
566C42—24no—
567C42—28no—
568C42—42no—
569C42—44no—
570C42—42no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—24no—
577C23—22no—
578C23—24no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—88no—
587C23C22×D4×C8912yes—
588C23C2×#41×C8914yes—
589C23C25×C8911yescharacteristic
590Q8—82no—
591D4—48no—
592D4—82no—
593D4—88no—
594C2×C4—28no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—84no—
624C2×C4C22×D4×C8914yes—
625C2×C4C22×D4×C8914yes—
626C2×C4C22×D4×C8912yes—
627C2×C4C22×D4×C8912yes—
628C2×C4C2×#41×C8918yes—
629C22—22no—
630C22—22no—
631C22—28no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—44no—
639C22—44no—
640C22—44no—
641C22—44no—
642C22—88no—
643C22#532×C8914yes—
644C22C23×D4×C8911yescharacteristic
645C22C22×#41×C8912yes—
646C22#585×C8912yes—
647C22#585×C8912yes—
648C4—24no—
649C4—24no—
650C4—22no—
651C4—22no—
652C4—28no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—44no—
660C2—24no—
661C2—82no—
662C2—82no—
663C2C2×#532×C8911yescharacteristic
664C2C89×#348511yescharacteristic
665C2C89×#348711yescharacteristic
666C2C89×#352114yes—
subgroupG/H
center, socleC23×C89C25
commutator, Frattini, cosocleC23C25×C89
prime radicalC89×#2539C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#539×C89C2semidirect
2. C22×#126×C89C2semidirect
3. C89×#2561C2semidirect
4. C89×#2560C2semidirect
5. C89×#2554C2semidirect
7. C89×#2519C2semidirect
8. C89×#2512C2semidirect
9. C89×#2504C2semidirect
10. C89×#2502C2semidirect
11. C89×#2413C2semidirect
12. C89×#2411C2semidirect
13. C89×#2321C2semidirect
14. C4×#123×C89C2semidirect
15. C89×#2274C2semidirect
20. C2×#126×C89C22semidirect
21. C2×#125×C89C22semidirect
24. C2×#123×C89C22semidirect
26. C2×C22⋊Q8×C89C22semidirect
39. #398×C89C22semidirect
40. #398×C89C22semidirect
42. #397×C89C22semidirect
44. #396×C89C22semidirect
48. #391×C89C22semidirect
52. #390×C89C22semidirect
53. #389×C89C22semidirect
58. #388×C89C22semidirect
59. #388×C89C22semidirect
60. #387×C89C22semidirect
66. #384×C89C22semidirect
67. #382×C89C22semidirect
70. C4×C4⋊C4×C89C22semidirect
71. C4×C4⋊C4×C89C22semidirect
72. C4×C4⋊C4×C89C22semidirect
76. C4×C22⋊C4×C89C22semidirect
104. C2×C4⋊C4×C89D4semidirect
326. #35469C89direct (N × H)
334. C2×#539C2×C89semidirect
335. C22×#126C2×C89semidirect
336. #2561C2×C89semidirect
337. #2560C2×C89semidirect
338. #2554C2×C89semidirect
340. #2519C2×C89semidirect
341. #2512C2×C89semidirect
342. #2504C2×C89semidirect
343. #2502C2×C89semidirect
344. #2413C2×C89semidirect
345. #2411C2×C89semidirect
346. #2321C2×C89semidirect
347. C4×#123C2×C89semidirect
348. #2274C2×C89semidirect
349. C89#35469direct (N × H)
354. C2×#126C22×C89semidirect
355. C2×#125C22×C89semidirect
358. C2×#123C22×C89semidirect
360. C2×C22⋊Q8C22×C89semidirect
373. #398C22×C89semidirect
374. #398C22×C89semidirect
376. #397C22×C89semidirect
378. #396C22×C89semidirect
382. #391C22×C89semidirect
386. #390C22×C89semidirect
387. #389C22×C89semidirect
392. #388C22×C89semidirect
393. #388C22×C89semidirect
394. #387C22×C89semidirect
400. #384C22×C89semidirect
401. #382C22×C89semidirect
404. C4×C4⋊C4C22×C89semidirect
405. C4×C4⋊C4C22×C89semidirect
406. C4×C4⋊C4C22×C89semidirect
410. C4×C22⋊C4C22×C89semidirect
438. C2×C4⋊C4D4×C89semidirect

Maximal subgroups

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

subgroupindex
C2×#539×C892
C22×#126×C892
C89×#25612
C89×#25602
C89×#25542
C89×#25392
C89×#25192
C89×#25122
C89×#25042
C89×#25022
C89×#24132
C89×#24112
C89×#23212
C4×#123×C892
C89×#22742
#3546989