Finite Group Databasebeta

← C89×#19417 #36397265

Subgroups — C89×#19417 #36397265

Order 22784.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3230C211yesmaximal, characteristic, complemented
2C89×#3079C211yesmaximal, characteristic
3C89×#3076C211yesmaximal, characteristic
4C89×#2988C211yesmaximal, characteristic
5C89×#1684C212yesmaximal, complemented
6C89×#1683C212yesmaximal, complemented
7C89×#1676C212yesmaximal, complemented
8C89×#1675C212yesmaximal, complemented
9C89×#1571C211yesmaximal, characteristic, complemented
10C89×#1550C211yesmaximal, characteristic, complemented
11C2×#333×C89C211yesmaximal, characteristic, complemented
12#533×C89C2211yescharacteristic
13C2×C4⋊Q8×C89C2211yescharacteristic
14C4×#41×C89C2211yescharacteristic
15#500×C89C2212yes—
16#487×C89C2212yes—
17#484×C89—22no—
18#479×C89—21no—
19#478×C89—21no—
20#477×C89—21no—
21#477×C89—21no—
22#477×C89C2211yescharacteristic
23#477×C89C2212yes—
24#476×C89C2211yescharacteristic
25#476×C89C2212yes—
26#475×C89—21no—
27#475×C89C2211yescharacteristic
28#474×C89—21no—
29#474×C89C2211yescharacteristic
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#333×C89C2212yes—
47#333×C89C2212yes—
48#332×C89C2212yes—
49C2×#41×C89D411yescharacteristic
50C22×Q8×C89—21no—
51C2×M16×C89—21no—
52C22×C8×C89—21no—
53C22×C8×C89—21no—
54C22×C8×C89—22no—
55C4⋊Q8×C89—21no—
56C4⋊Q8×C89—21no—
57C4⋊Q8×C89—21no—
58C4⋊Q8×C89C2311yescharacteristic
59C4⋊Q8×C89C2312yes—
60C4⋊Q8×C89C2311yescharacteristic
61#125×C89—21no—
62C22⋊Q8×C89—21no—
63C22⋊Q8×C89—21no—
64C4×Q8×C89—21no—
65C4×Q8×C89—21no—
66C4×Q8×C89D411yescharacteristic
67C4×Q8×C89C2311yescharacteristic
68C4×D4×C89—21no—
69C4×D4×C89—21no—
70C4×D4×C89D411yescharacteristic
71C4×D4×C89C2311yescharacteristic
72#117×C89—21no—
73#117×C89—21no—
74#117×C89D411yescharacteristic
75C2×C4⋊C4×C89—21no—
76C2×C4⋊C4×C89—21no—
77C2×C42×C89—21no—
78C2×C42×C89C2311yescharacteristic
79#107×C89—22no—
80#107×C89—22no—
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×C89Q1614yes—
111C2×Q8×C89—21no—
112C2×Q8×C89—21no—
113C2×Q8×C89—22no—
114C2×Q8×C89—41no—
115C2×Q8×C89—82no—
116C2×Q8×C89C2×D411yescharacteristic
117C2×D4×C89—21no—
118C2×D4×C89C2×D411yescharacteristic
119C22×C4×C89—21no—
120C22×C4×C89—21no—
121C22×C4×C89—21no—
122C22×C4×C89—41no—
123C22×C4×C89C2×D411yescharacteristic
124C22×C4×C89C2×D411yescharacteristic
125C22×C4×C89#4111yescharacteristic
126M16×C89—42no—
127C2×C8×C89—22no—
128C2×C8×C89—21no—
129C2×C8×C89—22no—
130C2×C8×C89—21no—
131C2×C8×C89—42no—
132C2×C8×C89—82no—
133C2×C8×C89—81no—
134C2×C8×C89C2×D412yes—
135C2×C8×C89C2×D412yes—
136C4⋊C4×C89—21no—
137C4⋊C4×C89—21no—
138C4⋊C4×C89—22no—
139C4⋊C4×C89—21no—
140C4⋊C4×C89—21no—
141C4⋊C4×C89—22no—
142C4⋊C4×C89—21no—
143C4⋊C4×C89—21no—
144C4⋊C4×C89—41no—
145C4⋊C4×C89—41no—
146C4⋊C4×C89—41no—
147C4⋊C4×C89—41no—
148C4⋊C4×C89C2×D411yescharacteristic
149C4⋊C4×C89C2×D411yescharacteristic
150C22⋊C4×C89—21no—
151C22⋊C4×C89—21no—
152C22⋊C4×C89—21no—
153C22⋊C4×C89—41no—
154C42×C89—21no—
155C42×C89—21no—
156C42×C89—21no—
157C42×C89—41no—
158C42×C89C2×D411yescharacteristic
159C42×C89C2×D411yescharacteristic
160C42×C89#4111yescharacteristic
161C42×C89C2411yescharacteristic
162C23×C89—21no—
163C23×C89#12111yescharacteristic
164Q8×C89—21no—
165Q8×C89—41no—
166Q8×C89—41no—
167Q8×C89—81no—
168Q8×C89—82no—
169Q8×C89—82no—
170Q8×C89C2×Q1612yes—
171D4×C89—24no—
172D4×C89—21no—
173D4×C89C2×Q1612yes—
174C2×C4×C89—21no—
175C2×C4×C89—21no—
176C2×C4×C89—21no—
177C2×C4×C89—24no—
178C2×C4×C89—21no—
179C2×C4×C89—21no—
180C2×C4×C89—41no—
181C2×C4×C89—41no—
182C2×C4×C89—41no—
183C2×C4×C89—41no—
184C2×C4×C89—41no—
185C2×C4×C89—42no—
186C2×C4×C89—81no—
187C2×C4×C89—82no—
188C2×C4×C89#12111yescharacteristic
189C2×C4×C89#12111yescharacteristic
190C2×C4×C89#12111yescharacteristic
191C2×C4×C89C2×Q1612yes—
192C2×C4×C89#13512yes—
193C2×C4×C89C22×D411yescharacteristic
194C2×C4×C89C22×D411yescharacteristic
195C2×C4×C89C2×#4111yescharacteristic
196C8×C89—22no—
197C8×C89—22no—
198C8×C89—41no—
199C8×C89—41no—
200C8×C89—42no—
201C8×C89—42no—
202C22×C89—21no—
203C22×C89—21no—
204C22×C89—22no—
205C22×C89—41no—
206C22×C89—41no—
207C22×C89#46712yes—
208C22×C89C2×#12111yescharacteristic
209C4×C89—21no—
210C4×C89—22no—
211C4×C89—21no—
212C4×C89—21no—
213C4×C89—41no—
214C4×C89—41no—
215C4×C89—81no—
216C4×C89—82no—
217C4×C89—81no—
218C4×C89#46712yes—
219C4×C89C22×Q1611yescharacteristic
220C4×C89C2×#13511yescharacteristic
221C4×C89#57711yescharacteristic
222C4×C89#57811yescharacteristic
223#19417C8911yesmaximal, characteristic, direct product factor, Sylow
224C2×C89—22no—
225C2×C89—42no—
226C2×C89#304611yescharacteristic
227C2×C89C2×#46711yescharacteristic
228C2×C89#306811yescharacteristic
229#3230C2×C8911yescharacteristic, complemented
230#3079C2×C8911yescharacteristic
231#3076C2×C8911yescharacteristic
232#2988C2×C8911yescharacteristic
233#1684C2×C8912yescomplemented
234#1683C2×C8912yescomplemented
235#1676C2×C8912yescomplemented
236#1675C2×C8912yescomplemented
237#1571C2×C8911yescharacteristic, complemented
238#1550C2×C8911yescharacteristic, complemented
239C2×#333C2×C8911yescharacteristic, complemented
240C89#1941711yescharacteristic, direct product factor, Sylow
241#533C22×C8911yescharacteristic
242C2×C4⋊Q8C22×C8911yescharacteristic
243C4×#41C22×C8911yescharacteristic
244#500C22×C8912yes—
245#487C22×C8912yes—
246#484—22no—
247#479—21no—
248#478—21no—
249#477—21no—
250#477—21no—
251#477C22×C8911yescharacteristic
252#477C22×C8912yes—
253#476C22×C8911yescharacteristic
254#476C22×C8912yes—
255#475—21no—
256#475C22×C8911yescharacteristic
257#474—21no—
258#474C22×C8911yescharacteristic
259C8×Q8C22×C8912yes—
260C8×D4—22no—
261C8×D4C22×C8912yes—
262#431—21no—
263#431C22×C8911yescharacteristic
264#428—21no—
265#427—21no—
266#423C22×C8911yescharacteristic
267C2×C4⋊C8—21no—
268C2×C4⋊C8C22×C8911yescharacteristic
269C2×C4⋊C8C22×C8911yescharacteristic
270#417—21no—
271#416—21no—
272#335C22×C8912yes—
273#335C22×C8912yes—
274#333C22×C8912yes—
275#333C22×C8912yes—
276#333C22×C8912yes—
277#332C22×C8912yes—
278C2×#41D4×C8911yescharacteristic
279C22×Q8—21no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—22no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C23×C8912yes—
288C4⋊Q8C23×C8911yescharacteristic
289C4⋊Q8C23×C8911yescharacteristic
290#125—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C8911yescharacteristic
296C4×Q8C23×C8911yescharacteristic
297C4×D4—21no—
298C4×D4—21no—
299C4×D4D4×C8911yescharacteristic
300C4×D4C23×C8911yescharacteristic
301#117—21no—
302#117—21no—
303#117D4×C8911yescharacteristic
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C42—21no—
307C2×C42C23×C8911yescharacteristic
308#107—22no—
309#107—22no—
310#107—21no—
311#107—21no—
312#107—22no—
313#106—21no—
314#106—21no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8D4×C8911yescharacteristic
321C4⋊C8D4×C8911yescharacteristic
322C4⋊C8C23×C8912yes—
323C4⋊C8C23×C8912yes—
324C4⋊C8C23×C8911yescharacteristic
325C4⋊C8C23×C8911yescharacteristic
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#103—22no—
331#102—21no—
332#102—21no—
333#102—22no—
334C22⋊C8—22no—
335C22⋊C8D4×C8912yes—
336C4×C8—22no—
337C4×C8C23×C8912yes—
338#41—22no—
339#41Q16×C8914yes—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×Q8C2×D4×C8911yescharacteristic
346C2×D4—21no—
347C2×D4C2×D4×C8911yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4C2×D4×C8911yescharacteristic
353C22×C4C2×D4×C8911yescharacteristic
354C22×C4#41×C8911yescharacteristic
355M16—42no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8—42no—
361C2×C8—82no—
362C2×C8—81no—
363C2×C8C2×D4×C8912yes—
364C2×C8C2×D4×C8912yes—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4C2×D4×C8911yescharacteristic
378C4⋊C4C2×D4×C8911yescharacteristic
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—41no—
383C42—21no—
384C42—21no—
385C42—21no—
386C42—41no—
387C42C2×D4×C8911yescharacteristic
388C42C2×D4×C8911yescharacteristic
389C42#41×C8911yescharacteristic
390C42C24×C8911yescharacteristic
391C23—21no—
392C23#121×C8911yescharacteristic
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—81no—
397Q8—82no—
398Q8—82no—
399Q8C2×Q16×C8912yes—
400D4—24no—
401D4—21no—
402D4C2×Q16×C8912yes—
403C2×C4—21no—
404C2×C4—24no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4#121×C8911yescharacteristic
418C2×C4#121×C8911yescharacteristic
419C2×C4#121×C8911yescharacteristic
420C2×C4C2×Q16×C8912yes—
421C2×C4#135×C8912yes—
422C2×C4C22×D4×C8911yescharacteristic
423C2×C4C22×D4×C8911yescharacteristic
424C2×C4C2×#41×C8911yescharacteristic
425C8—22no—
426C8—22no—
427C8—41no—
428C8—41no—
429C8—42no—
430C8—42no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22#467×C8912yes—
437C22C2×#121×C8911yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—82no—
445C4—81no—
446C4—81no—
447C4#467×C8912yes—
448C4C22×Q16×C8911yescharacteristic
449C4C2×#135×C8911yescharacteristic
450C4#577×C8911yescharacteristic
451C4#578×C8911yescharacteristic
452C2—22no—
453C2—42no—
454C2C89×#304611yescharacteristic
455C2C2×#467×C8911yescharacteristic
456C2C89×#306811yescharacteristic
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×#3230C2semidirect
5. C89×#1684C2semidirect
6. C89×#1683C2semidirect
7. C89×#1676C2semidirect
8. C89×#1675C2semidirect
9. C89×#1571C2semidirect
10. C89×#1550C2semidirect
11. C2×#333×C89C2semidirect
223. #19417C89direct (N × H)
229. #3230C2×C89semidirect
233. #1684C2×C89semidirect
234. #1683C2×C89semidirect
235. #1676C2×C89semidirect
236. #1675C2×C89semidirect
237. #1571C2×C89semidirect
238. #1550C2×C89semidirect
239. C2×#333C2×C89semidirect
240. C89#19417direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#32302
C89×#30792
C89×#30762
C89×#29882
C89×#16842
C89×#16832
C89×#16762
C89×#16752
C89×#15712
C89×#15502
C2×#333×C892
#1941789