Finite Group Databasebeta

← C89×#29406 #36407254

Subgroups — C89×#29406 #36407254

Order 22784.

664 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2330C211yesmaximal, characteristic, complemented
2C89×#2319C211yesmaximal, characteristic
3C89×#2084C211yesmaximal, characteristic, complemented
4C89×#2071C211yesmaximal, characteristic
5C89×#2059C211yesmaximal, characteristic, complemented
6C89×#2025C211yesmaximal, characteristic
7C89×#1926C211yesmaximal, characteristic
8C89×#1925C211yesmaximal, characteristic
9C89×#1920C211yesmaximal, characteristic, complemented
10C89×#1919C211yesmaximal, characteristic, complemented
11C89×#1919C211yesmaximal, characteristic, complemented
12C89×#1918C211yesmaximal, characteristic, complemented
13C89×#1864C211yesmaximal, characteristic
14C89×#1864C211yesmaximal, characteristic
15C89×#1840C211yesmaximal, characteristic, complemented
16C2×#125×C89C2211yescharacteristic
17C2×C4×D4×C89C2211yescharacteristic
18C2×#107×C89C2211yescharacteristic
19C2×#106×C89C2211yescharacteristic
20C2×#106×C89C2211yescharacteristic
21C2×#106×C89C2211yescharacteristic
22C2×#102×C89C2211yescharacteristic
23C2×#102×C89C2211yescharacteristic
24C2×#102×C89C2211yescharacteristic
25C2×#102×C89C2211yescharacteristic
26#390×C89C2211yescharacteristic
27#390×C89C2211yescharacteristic
28#389×C89—21no—
29#389×C89—21no—
30#389×C89C2211yescharacteristic
31#389×C89C2211yescharacteristic
32#389×C89C2211yescharacteristic
33#389×C89C2211yescharacteristic
34#388×C89—21no—
35#388×C89—21no—
36#387×C89—21no—
37#387×C89—21no—
38#384×C89C2211yescharacteristic
39#381×C89—21no—
40#380×C89—21no—
41C4×C4⋊C4×C89C2211yescharacteristic
42C4×C4⋊C4×C89C2211yescharacteristic
43C4×C4⋊C4×C89C2211yescharacteristic
44#376×C89C2211yescharacteristic
45#340×C89C2211yescharacteristic
46#340×C89C2211yescharacteristic
47#340×C89C2211yescharacteristic
48#340×C89C2211yescharacteristic
49#340×C89C2211yescharacteristic
50#340×C89C2211yescharacteristic
51#340×C89C2211yescharacteristic
52#340×C89C2211yescharacteristic
53#336×C89C2211yescharacteristic
54#336×C89C2211yescharacteristic
55#336×C89C2211yescharacteristic
56#336×C89C2211yescharacteristic
57#336×C89C2211yescharacteristic
58#336×C89C2211yescharacteristic
59C22×D4×C89C2311yescharacteristic
60C23×C4×C89—21no—
61C22×C8×C89C2311yescharacteristic
62C22×C8×C89C2311yescharacteristic
63C22×C8×C89C2311yescharacteristic
64C22×C8×C89C2311yescharacteristic
65#125×C89—22no—
66#125×C89—22no—
67C4×D4×C89—22no—
68C4×D4×C89—22no—
69C2×C4⋊C4×C89—21no—
70C2×C4⋊C4×C89—21no—
71C2×C4⋊C4×C89—21no—
72C2×C4⋊C4×C89—21no—
73C2×C4⋊C4×C89—21no—
74C2×C4⋊C4×C89—21no—
75C2×C4⋊C4×C89—21no—
76C2×C4⋊C4×C89—21no—
77C2×C4⋊C4×C89C2311yescharacteristic
78C2×C4⋊C4×C89C2311yescharacteristic
79C2×C4⋊C4×C89C2311yescharacteristic
80C2×C4⋊C4×C89C2311yescharacteristic
81C2×C4⋊C4×C89C2311yescharacteristic
82C2×C4⋊C4×C89C2311yescharacteristic
83C2×C4⋊C4×C89C2311yescharacteristic
84C2×C22⋊C4×C89—21no—
85C2×C22⋊C4×C89—21no—
86C2×C22⋊C4×C89—21no—
87C2×C22⋊C4×C89—21no—
88C2×C22⋊C4×C89—21no—
89C2×C42×C89—21no—
90C2×C42×C89—21no—
91C2×C42×C89—21no—
92C2×C42×C89C2311yescharacteristic
93C2×C42×C89C2311yescharacteristic
94C2×C42×C89C2311yescharacteristic
95#107×C89—22no—
96#106×C89—22no—
97#106×C89—22no—
98#106×C89—22no—
99#102×C89—22no—
100#102×C89—22no—
101#102×C89—22no—
102#102×C89—22no—
103#95×C89—21no—
104#95×C89—21no—
105#95×C89—21no—
106#95×C89—21no—
107#95×C89—21no—
108#95×C89—21no—
109#95×C89—21no—
110#95×C89D411yescharacteristic
111#95×C89D411yescharacteristic
112#95×C89D411yescharacteristic
113#95×C89D411yescharacteristic
114C24×C89—21no—
115C2×D4×C89—21no—
116C2×D4×C89—21no—
117C2×D4×C89—21no—
118C2×D4×C89—21no—
119C2×D4×C89—21no—
120C2×D4×C89#4112yes—
121C22×C4×C89—21no—
122C22×C4×C89—21no—
123C22×C4×C89—21no—
124C22×C4×C89—24no—
125C22×C4×C89—21no—
126C22×C4×C89—21no—
127C22×C4×C89—21no—
128C22×C4×C89—21no—
129C22×C4×C89—81no—
130C22×C4×C89—81no—
131C22×C4×C89C2×D411yescharacteristic
132C22×C4×C89C2×D411yescharacteristic
133C22×C4×C89C2×D411yescharacteristic
134C22×C4×C89C2×D411yescharacteristic
135C22×C4×C89C2×D411yescharacteristic
136C22×C4×C89C2×D411yescharacteristic
137C22×C4×C89C2411yescharacteristic
138C2×C8×C89—21no—
139C2×C8×C89—21no—
140C2×C8×C89—21no—
141C2×C8×C89—21no—
142C2×C8×C89—21no—
143C2×C8×C89—21no—
144C2×C8×C89—21no—
145C2×C8×C89—21no—
146C2×C8×C89—21no—
147C2×C8×C89—21no—
148C2×C8×C89—21no—
149C2×C8×C89—21no—
150C4⋊C4×C89—24no—
151C4⋊C4×C89—24no—
152C4⋊C4×C89—21no—
153C4⋊C4×C89—21no—
154C4⋊C4×C89—21no—
155C4⋊C4×C89—21no—
156C4⋊C4×C89—21no—
157C4⋊C4×C89—21no—
158C4⋊C4×C89—21no—
159C4⋊C4×C89—21no—
160C4⋊C4×C89—21no—
161C4⋊C4×C89—21no—
162C4⋊C4×C89—21no—
163C4⋊C4×C89—81no—
164C4⋊C4×C89—81no—
165C4⋊C4×C89—81no—
166C4⋊C4×C89—81no—
167C4⋊C4×C89—81no—
168C4⋊C4×C89—81no—
169C4⋊C4×C89#4112yes—
170C4⋊C4×C89#4112yes—
171C4⋊C4×C89#4112yes—
172C22⋊C4×C89—24no—
173C22⋊C4×C89—81no—
174C22⋊C4×C89—81no—
175C22⋊C4×C89—81no—
176C22⋊C4×C89—81no—
177C42×C89—21no—
178C42×C89—21no—
179C42×C89—21no—
180C42×C89—21no—
181C42×C89—21no—
182C42×C89—21no—
183C42×C89—81no—
184C42×C89—81no—
185C42×C89—81no—
186C23×C89—22no—
187C23×C89—41no—
188C23×C89—41no—
189C23×C89—41no—
190C23×C89—41no—
191C23×C89—41no—
192C23×C89—41no—
193C23×C89C22×D411yescharacteristic
194D4×C89—22no—
195D4×C89—22no—
196D4×C89—41no—
197D4×C89—41no—
198C2×C4×C89—21no—
199C2×C4×C89—21no—
200C2×C4×C89—21no—
201C2×C4×C89—21no—
202C2×C4×C89—22no—
203C2×C4×C89—22no—
204C2×C4×C89—22no—
205C2×C4×C89—21no—
206C2×C4×C89—21no—
207C2×C4×C89—21no—
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—21no—
215C2×C4×C89—21no—
216C2×C4×C89—21no—
217C2×C4×C89—21no—
218C2×C4×C89—21no—
219C2×C4×C89—41no—
220C2×C4×C89—41no—
221C2×C4×C89—41no—
222C2×C4×C89—41no—
223C2×C4×C89—41no—
224C2×C4×C89—41no—
225C2×C4×C89—41no—
226C2×C4×C89—41no—
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—84no—
238C2×C4×C89C2×#4111yescharacteristic
239C2×C4×C89C2×#4111yescharacteristic
240C2×C4×C89C2×#4111yescharacteristic
241C2×C4×C89C2×#4111yescharacteristic
242C2×C4×C892−1+411yescharacteristic
243C2×C4×C892−1+411yescharacteristic
244C8×C89—41no—
245C8×C89—41no—
246C8×C89—41no—
247C8×C89—41no—
248C22×C89—42no—
249C22×C89—42no—
250C22×C89—42no—
251C22×C89—81no—
252C22×C89—81no—
253C22×C89—81no—
254C22×C89—81no—
255C22×C89#52511yescharacteristic
256C22×C89#52511yescharacteristic
257C22×C89#53611yescharacteristic
258C22×C89#57611yescharacteristic
259C22×C89#57711yescharacteristic
260C22×C89#57711yescharacteristic
261C22×C89#57711yescharacteristic
262C4×C89—41no—
263C4×C89—41no—
264C4×C89—42no—
265C4×C89—41no—
266C4×C89—42no—
267C4×C89—41no—
268C4×C89—42no—
269C4×C89—41no—
270C4×C89—41no—
271C4×C89—81no—
272C4×C89—81no—
273C4×C89—81no—
274C4×C89—81no—
275C4×C89#55211yescharacteristic
276C4×C89#55211yescharacteristic
277C4×C89#55611yescharacteristic
278C4×C89#55611yescharacteristic
279#29406C8911yesmaximal, characteristic, direct product factor, Sylow
280C2×C89—82no—
281C2×C89#259911yescharacteristic
282C2×C89#311911yescharacteristic
283C2×C89#311911yescharacteristic
284C2×C89#312311yescharacteristic
285C2×C89#312511yescharacteristic
286C2×C89#324111yescharacteristic
287C2×C89#324411yescharacteristic
288#2330C2×C8911yescharacteristic, complemented
289#2319C2×C8911yescharacteristic
290#2084C2×C8911yescharacteristic, complemented
291#2071C2×C8911yescharacteristic
292#2059C2×C8911yescharacteristic, complemented
293#2025C2×C8911yescharacteristic
294#1926C2×C8911yescharacteristic
295#1925C2×C8911yescharacteristic
296#1920C2×C8911yescharacteristic, complemented
297#1919C2×C8911yescharacteristic, complemented
298#1919C2×C8911yescharacteristic, complemented
299#1918C2×C8911yescharacteristic, complemented
300#1864C2×C8911yescharacteristic
301#1864C2×C8911yescharacteristic
302#1840C2×C8911yescharacteristic, complemented
303C89#2940611yescharacteristic, direct product factor, Sylow
304C2×#125C22×C8911yescharacteristic
305C2×C4×D4C22×C8911yescharacteristic
306C2×#107C22×C8911yescharacteristic
307C2×#106C22×C8911yescharacteristic
308C2×#106C22×C8911yescharacteristic
309C2×#106C22×C8911yescharacteristic
310C2×#102C22×C8911yescharacteristic
311C2×#102C22×C8911yescharacteristic
312C2×#102C22×C8911yescharacteristic
313C2×#102C22×C8911yescharacteristic
314#390C22×C8911yescharacteristic
315#390C22×C8911yescharacteristic
316#389—21no—
317#389—21no—
318#389C22×C8911yescharacteristic
319#389C22×C8911yescharacteristic
320#389C22×C8911yescharacteristic
321#389C22×C8911yescharacteristic
322#388—21no—
323#388—21no—
324#387—21no—
325#387—21no—
326#384C22×C8911yescharacteristic
327#381—21no—
328#380—21no—
329C4×C4⋊C4C22×C8911yescharacteristic
330C4×C4⋊C4C22×C8911yescharacteristic
331C4×C4⋊C4C22×C8911yescharacteristic
332#376C22×C8911yescharacteristic
333#340C22×C8911yescharacteristic
334#340C22×C8911yescharacteristic
335#340C22×C8911yescharacteristic
336#340C22×C8911yescharacteristic
337#340C22×C8911yescharacteristic
338#340C22×C8911yescharacteristic
339#340C22×C8911yescharacteristic
340#340C22×C8911yescharacteristic
341#336C22×C8911yescharacteristic
342#336C22×C8911yescharacteristic
343#336C22×C8911yescharacteristic
344#336C22×C8911yescharacteristic
345#336C22×C8911yescharacteristic
346#336C22×C8911yescharacteristic
347C22×D4C23×C8911yescharacteristic
348C23×C4—21no—
349C22×C8C23×C8911yescharacteristic
350C22×C8C23×C8911yescharacteristic
351C22×C8C23×C8911yescharacteristic
352C22×C8C23×C8911yescharacteristic
353#125—22no—
354#125—22no—
355C4×D4—22no—
356C4×D4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C23×C8911yescharacteristic
366C2×C4⋊C4C23×C8911yescharacteristic
367C2×C4⋊C4C23×C8911yescharacteristic
368C2×C4⋊C4C23×C8911yescharacteristic
369C2×C4⋊C4C23×C8911yescharacteristic
370C2×C4⋊C4C23×C8911yescharacteristic
371C2×C4⋊C4C23×C8911yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C23×C8911yescharacteristic
381C2×C42C23×C8911yescharacteristic
382C2×C42C23×C8911yescharacteristic
383#107—22no—
384#106—22no—
385#106—22no—
386#106—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95D4×C8911yescharacteristic
399#95D4×C8911yescharacteristic
400#95D4×C8911yescharacteristic
401#95D4×C8911yescharacteristic
402C24—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4#41×C8912yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—81no—
418C22×C4—81no—
419C22×C4C2×D4×C8911yescharacteristic
420C22×C4C2×D4×C8911yescharacteristic
421C22×C4C2×D4×C8911yescharacteristic
422C22×C4C2×D4×C8911yescharacteristic
423C22×C4C2×D4×C8911yescharacteristic
424C22×C4C2×D4×C8911yescharacteristic
425C22×C4C24×C8911yescharacteristic
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4#41×C8912yes—
458C4⋊C4#41×C8912yes—
459C4⋊C4#41×C8912yes—
460C22⋊C4—24no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—81no—
472C42—81no—
473C42—81no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×D4×C8911yescharacteristic
482D4—22no—
483D4—22no—
484D4—41no—
485D4—41no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4C2×#41×C8911yescharacteristic
527C2×C4C2×#41×C8911yescharacteristic
528C2×C4C2×#41×C8911yescharacteristic
529C2×C4C2×#41×C8911yescharacteristic
530C2×C42−1+4×C8911yescharacteristic
531C2×C42−1+4×C8911yescharacteristic
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22#525×C8911yescharacteristic
544C22#525×C8911yescharacteristic
545C22#536×C8911yescharacteristic
546C22#576×C8911yescharacteristic
547C22#577×C8911yescharacteristic
548C22#577×C8911yescharacteristic
549C22#577×C8911yescharacteristic
550C4—41no—
551C4—41no—
552C4—42no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4#552×C8911yescharacteristic
564C4#552×C8911yescharacteristic
565C4#556×C8911yescharacteristic
566C4#556×C8911yescharacteristic
567C2—82no—
568C2C89×#259911yescharacteristic
569C2C89×#311911yescharacteristic
570C2C89×#311911yescharacteristic
571C2C89×#312311yescharacteristic
572C2C89×#312511yescharacteristic
573C2C89×#324111yescharacteristic
574C2C89×#324411yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC22×D4×C89C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ #376×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#2330C2semidirect
3. C89×#2084C2semidirect
5. C89×#2059C2semidirect
9. C89×#1920C2semidirect
10. C89×#1919C2semidirect
11. C89×#1919C2semidirect
12. C89×#1918C2semidirect
15. C89×#1840C2semidirect
279. #29406C89direct (N × H)
288. #2330C2×C89semidirect
290. #2084C2×C89semidirect
292. #2059C2×C89semidirect
296. #1920C2×C89semidirect
297. #1919C2×C89semidirect
298. #1919C2×C89semidirect
299. #1918C2×C89semidirect
302. #1840C2×C89semidirect
303. C89#29406direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#23302
C89×#23192
C89×#20842
C89×#20712
C89×#20592
C89×#20252
C89×#19262
C89×#19252
C89×#19202
C89×#19192
C89×#19182
C89×#18642
C89×#18402
#2940689