Finite Group Databasebeta

← #11878832

Subgroups — #11878832

Order 1152.

732 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589830C211yesmaximal, characteristic, complemented
2D9×#127C211yesmaximal, characteristic
3C9×#486C211yesmaximal, characteristic, complemented
4#10588773C211yesmaximal, characteristic, complemented
5#10588753C211yesmaximal, characteristic, complemented
6#10588456C214yesmaximal, complemented
7#10588442C214yesmaximal, complemented
8#10588375C211yesmaximal, characteristic, complemented
9#10588367C211yesmaximal, characteristic, complemented
10#81568—31nomaximal
11C2×D4×D9—21no—
12C2×D4×D9—21no—
13C2×D4×D9C2212yes—
14C9×C4⋊Q8C2211yescharacteristic, complemented
15C9×#127C2211yescharacteristic
16#63508—21no—
17Q8×Dic9—21no—
18#63502—21no—
19#63502—21no—
20#63502C2212yes—
21C2×#3672C2214yescomplemented
22C2×#3664C2214yescomplemented
23#63459C2212yes—
24#63454—21no—
25#63452—21no—
26#63449C2212yescomplemented
27#63436C2211yescharacteristic
28C42×D9C2211yescharacteristic
29#63431C2211yescharacteristic, complemented
30C9×#102C2214yescomplemented
31C4×C8×C9C2211yescharacteristic, complemented
32(C2×D9)⋊C8C2212yes—
33Dic9⋊C8C2212yescomplemented
34#63369C2214yescomplemented
35C4×C9⋊C8C2211yescharacteristic, complemented
36#5728—31no—
37D3×#127—31no—
38C3×#486D311yescharacteristic
39#5088—31no—
40#5076—31no—
41#4776—34no—
42#4762—34no—
43#4693—31no—
44#4685—31no—
45C23×D9—22no—
46C2×Q8×C9—21no—
47C2×D4×C9—21no—
48C2×D4×C9—21no—
49C2×D4×C9C2312yes—
50C2×#611—22no—
51C2×#611—22no—
52C2×#611—22no—
53D4×D9—44no—
54D4×D9—44no—
55D4×D9—44no—
56C2×D36—21no—
57C2×D36—21no—
58C2×D36C2312yes—
59C2×C4×D9D411yescharacteristic
60C2×C4×D9D411yescharacteristic
61C2×C4×D9C2311yescharacteristic
62C2×Dic18C2312yes—
63C2×C8×C9C2312yes—
64C9×C4⋊C4—21no—
65C9×C4⋊C4C2312yes—
66C42×C9C2311yescharacteristic
67#3672—44no—
68(C2×D9)⋊C4—22no—
69C4⋊Dic9—21no—
70C4⋊Dic9—21no—
71C4⋊Dic9—22no—
72Dic9⋊C4—22no—
73C4×Dic9—22no—
74C4×Dic9D411yescharacteristic
75C4×Dic9D411yescharacteristic
76C4×Dic9C2311yescharacteristic
77C2×C9⋊C8C2312yes—
78#3664—44no—
79#3208—91noSylow
80C2×D3×D4—32no—
81C2×D3×D4—61no—
82C2×D3×D4—61no—
83C3×C4⋊Q8C2×D311yescharacteristic
84C3×#127C2×D311yescharacteristic
85#946—61no—
86Q8×Dic3—61no—
87#940—32no—
88#940—61no—
89#940—61no—
90C2×#214—34no—
91C2×#204—34no—
92#897—32no—
93#892—61no—
94#890—61no—
95#887—32no—
96#874—31no—
97C42×D3—31no—
98#869—31no—
99C3×#102C2×D314yes—
100C3×C4×C8C2×D311yescharacteristic
101(C2×D3)⋊C8—32no—
102Dic3⋊C8—32no—
103#809—34no—
104C4×C3⋊C8—31no—
105C23×C9—22no—
106C22×D9—22no—
107C22×D9—44no—
108C22×D9—44no—
109C22×D9—44no—
110C22×D9C2×D411yescharacteristic
111Q8×C9—42no—
112D4×C9—24no—
113D4×C9—42no—
114D4×C9—42no—
115C2×C4×C9—22no—
116C2×C4×C9C2×D411yescharacteristic
117C2×C4×C9C2×D411yescharacteristic
118C2×C4×C9C2411yescharacteristic
119#611—44no—
120#611—44no—
121#611—44no—
122C2×Dic9—22no—
123C2×Dic9C2×D411yescharacteristic
124C2×Dic9C2×D411yescharacteristic
125C2×Dic9C2×D411yescharacteristic
126D36—24no—
127D36—42no—
128D36—42no—
129C4×D9—22no—
130C4×D9—22no—
131C4×D9SD1614yescomplemented
132Dic18—24no—
133C8×C9—22no—
134C9⋊C8—22no—
135#533—91no—
136C2×#127—91no—
137#492—91no—
138#492—91no—
139#486—91no—
140#486D911yescharacteristic, complemented
141#460—94no—
142#450—94no—
143#431—91no—
144C23×D3—62no—
145C2×C3×Q8—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4C22×D312yes—
149C2×#67—62no—
150C2×#67—62no—
151C2×#67—62no—
152D3×D4—124no—
153D3×D4—124no—
154D3×D4—124no—
155C2×D12—32no—
156C2×D12—61no—
157C2×D12—61no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—31no—
161C2×Dic6—32no—
162C2×C3×C8C22×D312yes—
163C3×C4⋊C4—21no—
164C3×C4⋊C4C22×D312yes—
165C3×C42C22×D311yescharacteristic
166#214—124no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—62no—
169C4⋊Dic3—61no—
170C4⋊Dic3—61no—
171Dic3⋊C4—62no—
172C4×Dic3—31no—
173C4×Dic3—31no—
174C4×Dic3—31no—
175C4×Dic3—62no—
176C2×C3⋊C8—32no—
177#204—124no—
178C22×C9—42no—
179C22×C9—42no—
180C22×C9—42no—
181C22×C9C22×D411yescharacteristic
182C2×D9—21no—
183C2×D9—21no—
184C2×D9—42no—
185C2×D9—42no—
186C2×D9—42no—
187C2×D9—88no—
188C2×D9C2×SD1612yes—
189C4×C9—42no—
190C4×C9C2×SD1612yes—
191C4×C9AGL(1,ℤ/8)12yes—
192C4×C9H(5,𝔽2)12yes—
193Dic9—21no—
194Dic9—21no—
195Dic9—42no—
196Dic9C2×SD1612yes—
197C22×D4—92no—
198C22×D4—181no—
199C22×D4—181no—
200C2×SD16—94no—
201C2×SD16—94no—
202C4⋊Q8—91no—
203C4⋊Q8C2×D911yescharacteristic, complemented
204#127—92no—
205#127—91no—
206#127—181no—
207#127—181no—
208#127C2×D911yescharacteristic
209#125—181no—
210C22⋊Q8—92no—
211C22⋊Q8—181no—
212C4×Q8—92no—
213C4×Q8—181no—
214#117—181no—
215C2×C42—91no—
216C4⋊C8—92no—
217#102—94no—
218#102C2×D914yescomplemented
219C22⋊C8—92no—
220C4×C8—91no—
221C4×C8C2×D911yescharacteristic, complemented
222C23×C3—22no—
223C22×D3—31no—
224C22×D3—62no—
225C22×D3—124no—
226C22×D3—124no—
227C22×D3—124no—
228C3×Q8—42no—
229C3×D4—24no—
230C3×D4—42no—
231C3×D4—42no—
232C2×C3×C4—22no—
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4C23×D311yescharacteristic
236#67—124no—
237#67—124no—
238#67—124no—
239C2×Dic3—31no—
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—62no—
243D12—64no—
244D12—122no—
245D12—122no—
246C4×D3—34no—
247C4×D3—62no—
248C4×D3—62no—
249Dic6—64no—
250C3×C8—22no—
251C3⋊C8—62no—
252C2×C9—82no—
253C2×C9#53511yescharacteristic
254C2×C9C22×SD1611yescharacteristic
255C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
256D9—22no—
257D9—82no—
258C24—182no—
259C2×Q8—21no—
260C2×Q8—92no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—92no—
264C2×D4—182no—
265C2×D4—182no—
266C2×D4—182no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—364no—
270C2×D4—364no—
271C2×D4—364no—
272C2×D4C22×D912yes—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276SD16—364no—
277SD16—364no—
278C2×C8—92no—
279C2×C8C22×D912yes—
280C4⋊C4—21no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4C22×D912yes—
286C22⋊C4—182no—
287C42—91no—
288C42—91no—
289C42—91no—
290C42—182no—
291C42C22×D911yescharacteristic
292C22×C3—42no—
293C22×C3—42no—
294C22×C3—42no—
295C22×C3C2×D3×D411yescharacteristic
296C2×D3—32no—
297C2×D3—61no—
298C2×D3—61no—
299C2×D3—122no—
300C2×D3—122no—
301C2×D3—122no—
302C2×D3—248no—
303C3×C4—42no—
304C3×C4#91112yes—
305C3×C4D3×SD1612yes—
306C3×C4#100912yes—
307Dic3—32no—
308Dic3—61no—
309Dic3—61no—
310Dic3—122no—
311C9#320811yescharacteristic, complemented, Sylow
312C23—22no—
313C23—91no—
314C23—182no—
315C23—364no—
316C23—364no—
317C23—364no—
318Q8—42no—
319Q8—184no—
320D4—24no—
321D4—42no—
322D4—42no—
323D4—184no—
324D4—364no—
325D4—364no—
326D4—364no—
327D4—362no—
328D4—362no—
329C2×C4—22no—
330C2×C4—91no—
331C2×C4—94no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4D4×D911yescharacteristic
338C2×C4D4×D911yescharacteristic
339C2×C4C23×D911yescharacteristic
340C8—22no—
341C8—182no—
342C2×C3—82no—
343C2×C3#567411yescharacteristic
344C2×C3C2×#91111yescharacteristic
345C2×C3C2×D3×SD1611yescharacteristic
346D3—62no—
347D3—242no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—92no—
352C22—181no—
353C22—181no—
354C22—362no—
355C22—362no—
356C22—362no—
357C22—728no—
358C22C2×D4×D911yescharacteristic
359C4—42no—
360C4—92no—
361C4—181no—
362C4—181no—
363C4—362no—
364C4#6347312yes—
365C4SD16×D912yes—
366C4#6371512yes—
367C3#8156811yescharacteristic
368C2—82no—
369C2—182no—
370C2—722no—
371C2#1058977611yescharacteristic
372C2C2×#6347311yescharacteristic
373C2C2×SD16×D911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#486C2
socleC22×C3C2×D3×D4
prime radicalD9×#127C2
hypercenter#486D9
hypocenterC9#3208
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10589830C2semidirect
3. C9×#486C2semidirect
4. #10588773C2semidirect
5. #10588753C2semidirect
6. #10588456C2semidirect
7. #10588442C2semidirect
8. #10588375C2semidirect
9. #10588367C2semidirect
14. C9×C4⋊Q8C22semidirect
21. C2×#3672C22semidirect
22. C2×#3664C22semidirect
26. #63449C22semidirect
29. #63431C22semidirect
30. C9×#102C22semidirect
31. C4×C8×C9C22semidirect
33. Dic9⋊C8C22semidirect
34. #63369C22semidirect
35. C4×C9⋊C8C22semidirect
131. C4×D9SD16semidirect
140. #486D9semidirect
203. C4⋊Q8C2×D9semidirect
218. #102C2×D9semidirect
221. C4×C8C2×D9semidirect
311. C9#3208semidirect

Maximal subgroups

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

subgroupindex
#105898302
D9×#1272
C9×#4862
#105887732
#105887532
#105884562
#105884422
#105883752
#105883672
#815683