Finite Group Databasebeta

← C89×#19411 #36397259

Subgroups — C89×#19411 #36397259

Order 22784.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3209C211yesmaximal, characteristic, complemented
2C89×#3079C211yesmaximal, characteristic
3C89×#3076C211yesmaximal, characteristic
4C89×#2988C211yesmaximal, characteristic
5C89×#1684C212yesmaximal, complemented
6C89×#1683C212yesmaximal, complemented
7C89×#1670C212yesmaximal, complemented
8C89×#1669C212yesmaximal, complemented
9C89×#1571C211yesmaximal, characteristic, complemented
10C89×#1550C211yesmaximal, characteristic, complemented
11C2×#332×C89C211yesmaximal, characteristic, complemented
12#533×C89C2211yescharacteristic
13C2×C4⋊Q8×C89C2211yescharacteristic
14C4×#41×C89C2211yescharacteristic
15#494×C89C2212yes—
16#487×C89C2212yes—
17#479×C89—21no—
18#478×C89—21no—
19#477×C89—21no—
20#477×C89C2211yescharacteristic
21#476×C89—21no—
22#476×C89C2211yescharacteristic
23#475×C89C2211yescharacteristic
24#475×C89C2212yes—
25#474×C89C2211yescharacteristic
26#474×C89C2212yes—
27#462×C89—21no—
28#462×C89—21no—
29#451×C89—22no—
30C8×Q8×C89C2212yes—
31C8×D4×C89—22no—
32C8×D4×C89C2212yes—
33#431×C89—21no—
34#431×C89C2211yescharacteristic
35#428×C89—21no—
36#427×C89—21no—
37#423×C89C2211yescharacteristic
38C2×C4⋊C8×C89—21no—
39C2×C4⋊C8×C89C2211yescharacteristic
40C2×C4⋊C8×C89C2211yescharacteristic
41#417×C89—21no—
42#416×C89—21no—
43#335×C89C2212yes—
44#335×C89C2212yes—
45#333×C89C2212yes—
46#332×C89C2212yes—
47#332×C89C2212yes—
48#332×C89C2212yes—
49C2×#41×C89D411yescharacteristic
50C22×Q8×C89—21no—
51C2×Q16×C89—22no—
52C2×Q16×C89—22no—
53C2×M16×C89—21no—
54C22×C8×C89—21no—
55C22×C8×C89—21no—
56C22×C8×C89—22no—
57C4⋊Q8×C89—21no—
58C4⋊Q8×C89—21no—
59C4⋊Q8×C89—21no—
60C4⋊Q8×C89C2312yes—
61C4⋊Q8×C89C2311yescharacteristic
62C4⋊Q8×C89C2311yescharacteristic
63#125×C89—21no—
64C22⋊Q8×C89—21no—
65C22⋊Q8×C89—21no—
66C4×Q8×C89—21no—
67C4×Q8×C89—21no—
68C4×Q8×C89D411yescharacteristic
69C4×Q8×C89C2311yescharacteristic
70C4×D4×C89—21no—
71C4×D4×C89—21no—
72C4×D4×C89D411yescharacteristic
73C4×D4×C89C2311yescharacteristic
74#117×C89—21no—
75#117×C89—21no—
76#117×C89D411yescharacteristic
77C2×C4⋊C4×C89—21no—
78C2×C4⋊C4×C89—21no—
79C2×C42×C89—21no—
80C2×C42×C89C2311yescharacteristic
81#107×C89—21no—
82#107×C89—21no—
83#107×C89—22no—
84#106×C89—21no—
85#106×C89—21no—
86#106×C89—22no—
87C4⋊C8×C89—22no—
88C4⋊C8×C89—21no—
89C4⋊C8×C89—21no—
90C4⋊C8×C89—21no—
91C4⋊C8×C89D411yescharacteristic
92C4⋊C8×C89D411yescharacteristic
93C4⋊C8×C89C2312yes—
94C4⋊C8×C89C2311yescharacteristic
95C4⋊C8×C89C2311yescharacteristic
96C4⋊C8×C89C2312yes—
97#103×C89—21no—
98#103×C89—21no—
99#103×C89—22no—
100#103×C89—22no—
101#103×C89—22no—
102#102×C89—21no—
103#102×C89—21no—
104#102×C89—22no—
105C22⋊C8×C89—22no—
106C22⋊C8×C89D412yes—
107C4×C8×C89—22no—
108C4×C8×C89C2312yes—
109#41×C89—22no—
110#41×C89Q1614yescomplemented
111C2×Q8×C89—22no—
112C2×Q8×C89—21no—
113C2×Q8×C89—21no—
114C2×Q8×C89—41no—
115C2×Q8×C89—81no—
116C2×Q8×C89—81no—
117C2×Q8×C89C2×D411yescharacteristic
118C2×D4×C89—21no—
119C2×D4×C89C2×D411yescharacteristic
120C22×C4×C89—21no—
121C22×C4×C89—21no—
122C22×C4×C89—21no—
123C22×C4×C89—41no—
124C22×C4×C89C2×D411yescharacteristic
125C22×C4×C89C2×D411yescharacteristic
126C22×C4×C89#4111yescharacteristic
127Q16×C89—82no—
128Q16×C89—82no—
129M16×C89—42no—
130C2×C8×C89—22no—
131C2×C8×C89—21no—
132C2×C8×C89—22no—
133C2×C8×C89—21no—
134C2×C8×C89—42no—
135C2×C8×C89—82no—
136C2×C8×C89—81no—
137C2×C8×C89C2×D412yes—
138C2×C8×C89C2×D412yes—
139C4⋊C4×C89—21no—
140C4⋊C4×C89—21no—
141C4⋊C4×C89—22no—
142C4⋊C4×C89—21no—
143C4⋊C4×C89—21no—
144C4⋊C4×C89—21no—
145C4⋊C4×C89—22no—
146C4⋊C4×C89—21no—
147C4⋊C4×C89—41no—
148C4⋊C4×C89—41no—
149C4⋊C4×C89—41no—
150C4⋊C4×C89—41no—
151C4⋊C4×C89C2×D411yescharacteristic
152C4⋊C4×C89C2×D411yescharacteristic
153C22⋊C4×C89—21no—
154C22⋊C4×C89—21no—
155C22⋊C4×C89—21no—
156C22⋊C4×C89—41no—
157C42×C89—21no—
158C42×C89—21no—
159C42×C89—21no—
160C42×C89—41no—
161C42×C89C2×D411yescharacteristic
162C42×C89C2×D411yescharacteristic
163C42×C89#4111yescharacteristic
164C42×C89C2411yescharacteristic
165C23×C89—21no—
166C23×C89#12111yescharacteristic
167Q8×C89—21no—
168Q8×C89—41no—
169Q8×C89—42no—
170Q8×C89—41no—
171Q8×C89—42no—
172Q8×C89—81no—
173Q8×C89—82no—
174Q8×C89C2×Q1612yes—
175D4×C89—24no—
176D4×C89—21no—
177D4×C89C2×Q1612yes—
178C2×C4×C89—21no—
179C2×C4×C89—21no—
180C2×C4×C89—21no—
181C2×C4×C89—24no—
182C2×C4×C89—21no—
183C2×C4×C89—21no—
184C2×C4×C89—41no—
185C2×C4×C89—41no—
186C2×C4×C89—41no—
187C2×C4×C89—41no—
188C2×C4×C89—41no—
189C2×C4×C89—42no—
190C2×C4×C89—81no—
191C2×C4×C89—82no—
192C2×C4×C89#12111yescharacteristic
193C2×C4×C89#12111yescharacteristic
194C2×C4×C89#12111yescharacteristic
195C2×C4×C89C2×Q1612yes—
196C2×C4×C89#13512yes—
197C2×C4×C89C22×D411yescharacteristic
198C2×C4×C89C22×D411yescharacteristic
199C2×C4×C89C2×#4111yescharacteristic
200C8×C89—22no—
201C8×C89—22no—
202C8×C89—41no—
203C8×C89—41no—
204C8×C89—42no—
205C8×C89—42no—
206C22×C89—21no—
207C22×C89—21no—
208C22×C89—22no—
209C22×C89—41no—
210C22×C89—41no—
211C22×C89#46712yes—
212C22×C89C2×#12111yescharacteristic
213C4×C89—21no—
214C4×C89—22no—
215C4×C89—21no—
216C4×C89—21no—
217C4×C89—41no—
218C4×C89—41no—
219C4×C89—82no—
220C4×C89—81no—
221C4×C89—81no—
222C4×C89#46712yes—
223C4×C89C22×Q1611yescharacteristic
224C4×C89C2×#13511yescharacteristic
225C4×C89#57611yescharacteristic
226C4×C89#57711yescharacteristic
227#19411C8911yesmaximal, characteristic, direct product factor, Sylow
228C2×C89—22no—
229C2×C89—42no—
230C2×C89#304511yescharacteristic
231C2×C89C2×#46711yescharacteristic
232C2×C89#306911yescharacteristic
233#3209C2×C8911yescharacteristic, complemented
234#3079C2×C8911yescharacteristic
235#3076C2×C8911yescharacteristic
236#2988C2×C8911yescharacteristic
237#1684C2×C8912yescomplemented
238#1683C2×C8912yescomplemented
239#1670C2×C8912yescomplemented
240#1669C2×C8912yescomplemented
241#1571C2×C8911yescharacteristic, complemented
242#1550C2×C8911yescharacteristic, complemented
243C2×#332C2×C8911yescharacteristic, complemented
244C89#1941111yescharacteristic, direct product factor, Sylow
245#533C22×C8911yescharacteristic
246C2×C4⋊Q8C22×C8911yescharacteristic
247C4×#41C22×C8911yescharacteristic
248#494C22×C8912yes—
249#487C22×C8912yes—
250#479—21no—
251#478—21no—
252#477—21no—
253#477C22×C8911yescharacteristic
254#476—21no—
255#476C22×C8911yescharacteristic
256#475C22×C8911yescharacteristic
257#475C22×C8912yes—
258#474C22×C8911yescharacteristic
259#474C22×C8912yes—
260#462—21no—
261#462—21no—
262#451—22no—
263C8×Q8C22×C8912yes—
264C8×D4—22no—
265C8×D4C22×C8912yes—
266#431—21no—
267#431C22×C8911yescharacteristic
268#428—21no—
269#427—21no—
270#423C22×C8911yescharacteristic
271C2×C4⋊C8—21no—
272C2×C4⋊C8C22×C8911yescharacteristic
273C2×C4⋊C8C22×C8911yescharacteristic
274#417—21no—
275#416—21no—
276#335C22×C8912yes—
277#335C22×C8912yes—
278#333C22×C8912yes—
279#332C22×C8912yes—
280#332C22×C8912yes—
281#332C22×C8912yes—
282C2×#41D4×C8911yescharacteristic
283C22×Q8—21no—
284C2×Q16—22no—
285C2×Q16—22no—
286C2×M16—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C23×C8912yes—
294C4⋊Q8C23×C8911yescharacteristic
295C4⋊Q8C23×C8911yescharacteristic
296#125—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8D4×C8911yescharacteristic
302C4×Q8C23×C8911yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C4×D4D4×C8911yescharacteristic
306C4×D4C23×C8911yescharacteristic
307#117—21no—
308#117—21no—
309#117D4×C8911yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—21no—
313C2×C42C23×C8911yescharacteristic
314#107—21no—
315#107—21no—
316#107—22no—
317#106—21no—
318#106—21no—
319#106—22no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8D4×C8911yescharacteristic
325C4⋊C8D4×C8911yescharacteristic
326C4⋊C8C23×C8912yes—
327C4⋊C8C23×C8911yescharacteristic
328C4⋊C8C23×C8911yescharacteristic
329C4⋊C8C23×C8912yes—
330#103—21no—
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#102—21no—
336#102—21no—
337#102—22no—
338C22⋊C8—22no—
339C22⋊C8D4×C8912yes—
340C4×C8—22no—
341C4×C8C23×C8912yes—
342#41—22no—
343#41Q16×C8914yescomplemented
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—81no—
349C2×Q8—81no—
350C2×Q8C2×D4×C8911yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C8911yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C8911yescharacteristic
358C22×C4C2×D4×C8911yescharacteristic
359C22×C4#41×C8911yescharacteristic
360Q16—82no—
361Q16—82no—
362M16—42no—
363C2×C8—22no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—42no—
368C2×C8—82no—
369C2×C8—81no—
370C2×C8C2×D4×C8912yes—
371C2×C8C2×D4×C8912yes—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C8911yescharacteristic
385C4⋊C4C2×D4×C8911yescharacteristic
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—41no—
394C42C2×D4×C8911yescharacteristic
395C42C2×D4×C8911yescharacteristic
396C42#41×C8911yescharacteristic
397C42C24×C8911yescharacteristic
398C23—21no—
399C23#121×C8911yescharacteristic
400Q8—21no—
401Q8—41no—
402Q8—42no—
403Q8—41no—
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8C2×Q16×C8912yes—
408D4—24no—
409D4—21no—
410D4C2×Q16×C8912yes—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4#121×C8911yescharacteristic
426C2×C4#121×C8911yescharacteristic
427C2×C4#121×C8911yescharacteristic
428C2×C4C2×Q16×C8912yes—
429C2×C4#135×C8912yes—
430C2×C4C22×D4×C8911yescharacteristic
431C2×C4C22×D4×C8911yescharacteristic
432C2×C4C2×#41×C8911yescharacteristic
433C8—22no—
434C8—22no—
435C8—41no—
436C8—41no—
437C8—42no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22#467×C8912yes—
445C22C2×#121×C8911yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—22no—
450C4—41no—
451C4—41no—
452C4—81no—
453C4—82no—
454C4—81no—
455C4#467×C8912yes—
456C4C22×Q16×C8911yescharacteristic
457C4C2×#135×C8911yescharacteristic
458C4#576×C8911yescharacteristic
459C4#577×C8911yescharacteristic
460C2—22no—
461C2—42no—
462C2C89×#304511yescharacteristic
463C2C2×#467×C8911yescharacteristic
464C2C89×#306911yescharacteristic
subgroupG/H
center, socleC22×C89C2×#121
commutator, Frattini, cosocleC42C24×C89
prime radicalC2×#41×C89D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3209C2semidirect
5. C89×#1684C2semidirect
6. C89×#1683C2semidirect
7. C89×#1670C2semidirect
8. C89×#1669C2semidirect
9. C89×#1571C2semidirect
10. C89×#1550C2semidirect
11. C2×#332×C89C2semidirect
110. #41×C89Q16semidirect
227. #19411C89direct (N × H)
233. #3209C2×C89semidirect
237. #1684C2×C89semidirect
238. #1683C2×C89semidirect
239. #1670C2×C89semidirect
240. #1669C2×C89semidirect
241. #1571C2×C89semidirect
242. #1550C2×C89semidirect
243. C2×#332C2×C89semidirect
244. C89#19411direct (N × H)
343. #41Q16×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#32092
C89×#30792
C89×#30762
C89×#29882
C89×#16842
C89×#16832
C89×#16702
C89×#16692
C89×#15712
C89×#15502
C2×#332×C892
#1941189