Finite Group Databasebeta

← D9×#484 #11869578

Subgroups — D9×#484 #11869578

Order 1152.

690 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D9×C22⋊Q8C211yesmaximal, characteristic
2C2×C4⋊C4×D9C211yesmaximal, characteristic
3C9×#484C211yesmaximal, characteristic, complemented
4#10588724C211yesmaximal, characteristic, complemented
5#10588646C211yesmaximal, characteristic, complemented
6#10588564C212yesmaximal, complemented
7D9×#107C212yesmaximal, complemented
8#10588491C212yesmaximal, complemented
9D9×#103C212yesmaximal, complemented
10D9×C22⋊C8C211yesmaximal, characteristic
11#10588402C211yesmaximal, characteristic, complemented
12D3×#484—31nomaximal
13C2×Q8×D9C2211yescharacteristic
14C22×C4×D9—21no—
15C22×C4×D9C2211yescharacteristic
16C9×C22⋊Q8C2211yescharacteristic
17C2×C9×C4⋊C4C2211yescharacteristic
18#63508C2211yescharacteristic
19C2×C4⋊Dic9C2211yescharacteristic
20#63486C2211yescharacteristic
21C2×Dic9⋊C4—21no—
22C2×C8×D9C2212yes—
23#63459C2211yescharacteristic
24#63458—21no—
25C4⋊C4×D9—21no—
26C4⋊C4×D9—21no—
27C4⋊C4×D9—21no—
28C4⋊C4×D9C2211yescharacteristic
29C4⋊C4×D9C2212yes—
30C4⋊C4×D9C2212yes—
31C22⋊C4×D9—21no—
32#63440—21no—
33C9×#107C2212yescomplemented
34C9×#103C2212yescomplemented
35C9×C22⋊C8C2211yescharacteristic
36#63395C2212yescomplemented
37#63389C2211yescharacteristic
38(C2×D9)⋊C8C2212yes—
39#63378C2212yescomplemented
40#63376C2212yescomplemented
41#63368C2212yescomplemented
42#63366C2212yescomplemented
43#63366C2212yescomplemented
44D3×C22⋊Q8—31no—
45C2×D3×C4⋊C4—31no—
46C3×#484D311yescharacteristic
47#5044—31no—
48#4970—31no—
49#4884—32no—
50D3×#107—32no—
51#4811—32no—
52D3×#103—32no—
53D3×C22⋊C8—31no—
54#4722—31no—
55C23×D9D411yescharacteristic
56C2×Q8×C9C2311yescharacteristic
57C22×C4×C9—21no—
58C22×C4×C9C2311yescharacteristic
59C22×Dic9—21no—
60C22×Dic9D411yescharacteristic
61Q8×D9—24no—
62C2×C4×D9—24no—
63C2×C4×D9—21no—
64C2×C4×D9—21no—
65C2×C4×D9—22no—
66C2×C4×D9—22no—
67C2×C4×D9—44no—
68C2×C4×D9D411yescharacteristic
69C2×C4×D9D411yescharacteristic
70C2×C4×D9C2311yescharacteristic
71C2×C4×D9C2311yescharacteristic
72C2×Dic18—21no—
73C2×Dic18C2311yescharacteristic
74C2×C8×C9C2312yes—
75C9×C4⋊C4—21no—
76C9×C4⋊C4—21no—
77C9×C4⋊C4C2312yes—
78C9×C4⋊C4C2311yescharacteristic
79C9×C22⋊C4—21no—
80#3676—21no—
81(C2×D9)⋊C4—21no—
82(C2×D9)⋊C4—21no—
83C4⋊Dic9—21no—
84C4⋊Dic9—21no—
85C4⋊Dic9C2311yescharacteristic
86C4⋊Dic9C2312yes—
87Dic9⋊C4—21no—
88Dic9⋊C4—21no—
89Dic9⋊C4—21no—
90Dic9⋊C4—22no—
91Dic9⋊C4—22no—
92C2×C9⋊C8C2312yes—
93C8×D9—24no—
94C2×#484—91noSylow
95C2×D3×Q8—31no—
96C22×C4×D3—31no—
97C22×C4×D3—61no—
98C3×C22⋊Q8C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100#946—31no—
101C2×C4⋊Dic3—31no—
102#924—31no—
103C2×Dic3⋊C4—61no—
104C2×D3×C8—32no—
105#897—31no—
106#896—61no—
107D3×C4⋊C4—31no—
108D3×C4⋊C4—32no—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—61no—
111D3×C4⋊C4—61no—
112D3×C4⋊C4—61no—
113D3×C22⋊C4—61no—
114#878—61no—
115C3×#107C2×D312yes—
116C3×#103C2×D312yes—
117C3×C22⋊C8C2×D311yescharacteristic
118#835—32no—
119#830—31no—
120(C2×D3)⋊C8—32no—
121#818—32no—
122#816—32no—
123#810—32no—
124#807—32no—
125#807—32no—
126C23×C9C2×D411yescharacteristic
127C22×D9—22no—
128C22×D9—22no—
129C22×D9Q1614yes—
130C22×D9C2×D411yescharacteristic
131C22×D9C2×D411yescharacteristic
132Q8×C9—22no—
133C2×C4×C9—22no—
134C2×C4×C9—22no—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9—42no—
138C2×C4×C9C2×D411yescharacteristic
139C2×C4×C9C2411yescharacteristic
140C2×Dic9—22no—
141C2×Dic9—21no—
142C2×Dic9—22no—
143C2×Dic9—21no—
144C2×Dic9—42no—
145C2×Dic9C2×D411yescharacteristic
146C2×Dic9C2×D411yescharacteristic
147C4×D9—22no—
148C4×D9—22no—
149C4×D9—22no—
150C4×D9—44no—
151C4×D9—42no—
152C4×D9—42no—
153C4×D9—44no—
154C4×D9#4114yes—
155Dic18—22no—
156Dic18—42no—
157C8×C9—22no—
158C9⋊C8—22no—
159C2×C22⋊Q8—91no—
160C22×C4⋊C4—91no—
161#484—91no—
162#484—91no—
163#484—92no—
164#484—92no—
165#484—91no—
166#484D911yescharacteristic, direct product factor
167C2×#107—92no—
168C2×#103—92no—
169C2×C22⋊C8—91no—
170C23×D3—31no—
171C2×C3×Q8C22×D311yescharacteristic
172C22×C3×C4—21no—
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—31no—
175C22×Dic3—61no—
176D3×Q8—64no—
177C2×C4×D3—31no—
178C2×C4×D3—31no—
179C2×C4×D3—31no—
180C2×C4×D3—31no—
181C2×C4×D3—64no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—124no—
187C2×Dic6—31no—
188C2×Dic6—61no—
189C2×C3×C8C22×D312yes—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4C22×D311yescharacteristic
193C3×C4⋊C4C22×D312yes—
194C3×C22⋊C4—21no—
195#217—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198C4⋊Dic3—31no—
199C4⋊Dic3—32no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—61no—
207C2×C3⋊C8—32no—
208D3×C8—64no—
209C22×C9—21no—
210C22×C9—21no—
211C22×C9C2×Q1612yes—
212C22×C9C22×D411yescharacteristic
213C2×D9—21no—
214C2×D9—21no—
215C2×D9—28no—
216C2×D9#12312yes—
217C2×D9C2×Q1612yes—
218C2×D9C2×Q1612yes—
219C2×D9AGL(1,ℤ/8)12yes—
220C4×C9—21no—
221C4×C9—41no—
222C4×C9—42no—
223C4×C9—41no—
224C4×C9C2×#4112yes—
225Dic9—21no—
226Dic9—41no—
227Dic9—42no—
228Dic9—41no—
229Dic9#12312yes—
230C22×Q8—91no—
231C23×C4—91no—
232C23×C4—181no—
233C22×C8—92no—
234C22⋊Q8—91no—
235C22⋊Q8—91no—
236C22⋊Q8—91no—
237C22⋊Q8—181no—
238C22⋊Q8—181no—
239C22⋊Q8C2×D911yescharacteristic
240C2×C4⋊C4—91no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4C2×D911yescharacteristic
249C2×C22⋊C4—181no—
250#107—92no—
251#107—92no—
252#107—92no—
253#107C2×D912yescomplemented
254#103—92no—
255#103—92no—
256#103—92no—
257#103C2×D912yescomplemented
258C22⋊C8—91no—
259C22⋊C8—92no—
260C22⋊C8C2×D911yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—31no—
263C22×D3—34no—
264C22×D3—31no—
265C22×D3—62no—
266C22×D3—62no—
267C3×Q8—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—42no—
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4C23×D311yescharacteristic
275C2×Dic3—31no—
276C2×Dic3—31no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—62no—
280C2×Dic3—61no—
281C2×Dic3—122no—
282C4×D3—34no—
283C4×D3—62no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—122no—
287C4×D3—124no—
288C4×D3—122no—
289C4×D3—124no—
290Dic6—62no—
291Dic6—122no—
292C3×C8—22no—
293C3⋊C8—62no—
294C2×C9—22no—
295C2×C9C2×#12311yescharacteristic
296C2×C9C22×Q1611yescharacteristic
297C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
298D9—22no—
299D9#48414yesdirect product factor
300C24—91no—
301C2×Q8—91no—
302C2×Q8—181no—
303C2×Q8—184no—
304C2×Q8C22×D911yescharacteristic
305C22×C4—21no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—184no—
312C22×C4—181no—
313C22×C4—181no—
314C22×C4—182no—
315C22×C4—182no—
316C22×C4—181no—
317C22×C4—364no—
318C22×C4C22×D911yescharacteristic
319C2×C8—92no—
320C2×C8—184no—
321C2×C8C22×D912yes—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—92no—
325C4⋊C4—91no—
326C4⋊C4—182no—
327C4⋊C4—182no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4C22×D912yes—
334C4⋊C4C22×D911yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3D3×Q1612yes—
342C22×C3C2×D3×D411yescharacteristic
343C2×D3—32no—
344C2×D3—32no—
345C2×D3—32no—
346C2×D3—32no—
347C2×D3—68no—
348C2×D3—61no—
349C2×D3—61no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4D3×#4112yes—
355Dic3—32no—
356Dic3—61no—
357Dic3—121no—
358Dic3—122no—
359Dic3—121no—
360C9C2×#48411yescharacteristic, complemented, Sylow
361C23—91no—
362C23—91no—
363C23—94no—
364C23—182no—
365C23—182no—
366C23D4×D911yescharacteristic
367Q8—22no—
368Q8—182no—
369Q8—362no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—91no—
376C2×C4—94no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—364no—
386C2×C4—362no—
387C2×C4—362no—
388C2×C4—364no—
389C2×C4—362no—
390C2×C4D4×D911yescharacteristic
391C2×C4C23×D911yescharacteristic
392C8—22no—
393C8—182no—
394C2×C3—22no—
395C2×C3D3×#12311yescharacteristic
396C2×C3C2×D3×Q1611yescharacteristic
397C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
398D3—34no—
399D3—62no—
400C22—21no—
401C22—21no—
402C22—92no—
403C22—92no—
404C22—92no—
405C22—92no—
406C22—188no—
407C22—181no—
408C22—181no—
409C22Q16×D912yes—
410C22C2×D4×D911yescharacteristic
411C4—21no—
412C4—41no—
413C4—42no—
414C4—41no—
415C4—92no—
416C4—181no—
417C4—361no—
418C4—362no—
419C4—361no—
420C4#41×D912yes—
421C3D3×#48411yescharacteristic
422C2—22no—
423C2—94no—
424C2—182no—
425C2D9×#12311yescharacteristic
426C2C2×Q16×D911yescharacteristic
427C2D9×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#484C2
socleC22×C3C2×D3×D4
prime radicalC23×D9D4
hypercenter#484D9
hypocenterC9C2×#484
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C9×#484C2semidirect
4. #10588724C2semidirect
5. #10588646C2semidirect
6. #10588564C2semidirect
7. D9×#107C2semidirect
8. #10588491C2semidirect
9. D9×#103C2semidirect
11. #10588402C2semidirect
33. C9×#107C22semidirect
34. C9×#103C22semidirect
36. #63395C22semidirect
39. #63378C22semidirect
40. #63376C22semidirect
41. #63368C22semidirect
42. #63366C22semidirect
43. #63366C22semidirect
166. #484D9direct (N × H)
253. #107C2×D9semidirect
257. #103C2×D9semidirect
299. D9#484direct (N × H)
360. C9C2×#484semidirect

Maximal subgroups

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

subgroupindex
D9×C22⋊Q82
C2×C4⋊C4×D92
C9×#4842
#105887242
#105886462
#105885642
D9×#1072
#105884912
D9×#1032
D9×C22⋊C82
#105884022
D3×#4843