Finite Group Databasebeta

← #11872784

Subgroups — #11872784

Order 1152.

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

normal subgroups only

This group has 591 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
1C9×#541C211yesmaximal, characteristic, complemented
2#10589623C211yesmaximal, characteristic
3#10588768C212yesmaximal, complemented
4#10588747C212yesmaximal, complemented
5#10588729C212yesmaximal
6#10588725C212yesmaximal, complemented
7#10588709C212yesmaximal, complemented
8C4×#3675C212yesmaximal, complemented
9#10588678C211yesmaximal, characteristic, complemented
10#83447—31nomaximal
11C22×D36C2211yescharacteristic
12C9×C4⋊Q8C2211yescharacteristic, complemented
13C9×#126—22no—
14C9×#125—22no—
15C9×#125C2211yescharacteristic, complemented
16C9×C22⋊Q8C2212yes—
17C4×Q8×C9C2212yescomplemented
18C9×#117C2211yescharacteristic
19C2×#3675C2212yes—
20C2×#3675C2212yes—
21#63488C2211yescharacteristic
22#63455—22no—
23C22⋊C4×D9—22no—
24C4×D36C2212yes—
25C4×D36C2212yes—
26#63395C2212yescomplemented
27#63395C2212yescomplemented
28#63389C2212yes—
29#63369C2212yes—
30#63369C2212yes—
31#63367C2212yescomplemented
32#63366C2212yescomplemented
33C4⋊(C9⋊C8)C2212yescomplemented
34#63362C2211yescharacteristic, complemented
35C4×C9⋊C8C2211yescharacteristic, complemented
36C3×#541D311yescharacteristic
37#5521—31no—
38#5083—32no—
39#5066—32no—
40#5046—32no—
41#5045—32no—
42#5026—32no—
43C4×#215—32no—
44#5000—31no—
45C23×D9—21no—
46C2×Q8×C9C2312yes—
47C22×C4×C9C2311yescharacteristic
48C2×D36—21no—
49C2×D36—24no—
50C2×D36C2312yes—
51C2×C4×D9—22no—
52C2×C4×D9—22no—
53C9×C4⋊C4—22no—
54C9×C4⋊C4—22no—
55C9×C4⋊C4—22no—
56C9×C4⋊C4—22no—
57C9×C4⋊C4D412yes—
58C9×C4⋊C4C2312yes—
59C9×C22⋊C4—22no—
60C9×C22⋊C4D412yes—
61C42×C9—22no—
62C42×C9C2311yescharacteristic
63C42×C9C2311yescharacteristic
64#3676—21no—
65#3675—24no—
66#3675—24no—
67(C2×D9)⋊C4—22no—
68(C2×D9)⋊C4—22no—
69C4⋊Dic9C2312yes—
70C4×Dic9—21no—
71C2×C9⋊C8C2312yes—
72C2×C9⋊C8C2312yes—
73#3123—91noSylow
74C22×D12—31no—
75C3×C4⋊Q8C2×D311yescharacteristic
76C3×#126—22no—
77C3×#125—22no—
78C3×#125C2×D311yescharacteristic
79C3×C22⋊Q8C2×D312yes—
80C3×C4×Q8C2×D312yes—
81C3×#117C2×D311yescharacteristic
82C2×#215—32no—
83C2×#215—32no—
84#926—31no—
85#893—62no—
86D3×C22⋊C4—62no—
87C4×D12—32no—
88C4×D12—32no—
89#835—32no—
90#835—32no—
91#830—32no—
92#809—32no—
93#809—32no—
94#808—32no—
95#807—32no—
96C4⋊(C3⋊C8)—32no—
97#803—31no—
98C4×C3⋊C8—31no—
99C23×C9C2×D411yescharacteristic
100C22×D9—22no—
101C22×D9—24no—
102C22×D9—82no—
103Q8×C9—22no—
104Q8×C9—22no—
105C2×C4×C9—22no—
106C2×C4×C9—22no—
107C2×C4×C9—22no—
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×D412yes—
110C2×C4×C9C2×D412yes—
111C2×C4×C9C2411yescharacteristic
112C2×Dic9—22no—
113D36—24no—
114D36—22no—
115D36#4114yes—
116C4×D9—82no—
117C4×D9—82no—
118C9⋊C8—22no—
119C9⋊C8—22no—
120#541D911yescharacteristic, complemented
121#518—91no—
122#485—92no—
123#478—92no—
124#461—92no—
125#450—92no—
126#440—92no—
127C4×SD16—92no—
128#433—91no—
129C23×D3—61no—
130C2×C3×Q8C22×D312yes—
131C22×C3×C4C22×D311yescharacteristic
132C2×D12—32no—
133C2×D12—64no—
134C2×D12—61no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4#6712yes—
142C3×C4⋊C4C22×D312yes—
143C3×C22⋊C4—22no—
144C3×C22⋊C4#6712yes—
145C3×C42—22no—
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148#217—61no—
149#215—64no—
150#215—64no—
151(C2×D3)⋊C4—62no—
152(C2×D3)⋊C4—62no—
153C4⋊Dic3—32no—
154C4×Dic3—61no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—32no—
157C22×C9—21no—
158C22×C9—22no—
159C22×C9C22×D411yescharacteristic
160C2×D9—24no—
161C2×D9—42no—
162C2×D9—42no—
163C2×D9—84no—
164C4×C9—21no—
165C4×C9—22no—
166C4×C9—22no—
167C4×C9—42no—
168C4×C9—42no—
169C4×C9C2×#4112yes—
170Dic9—42no—
171C22×D4—91no—
172C2×SD16—92no—
173C2×SD16—92no—
174C4⋊Q8C2×D911yescharacteristic, complemented
175#126—22no—
176#125—22no—
177#125C2×D911yescharacteristic, complemented
178C22⋊Q8C2×D912yes—
179C4×Q8C2×D912yescomplemented
180C4×D4—92no—
181C4×D4—92no—
182C4×D4—182no—
183#117—91no—
184#117C2×D911yescharacteristic
185C2×C22⋊C4—182no—
186#107—92no—
187#106—92no—
188C4⋊C8—92no—
189#103—92no—
190#103—92no—
191#102—92no—
192#102—92no—
193C22⋊C8—92no—
194#97—91no—
195C4×C8—91no—
196C23×C3C2×#6711yescharacteristic
197C22×D3—62no—
198C22×D3—64no—
199C22×D3—242no—
200C3×Q8—22no—
201C3×Q8—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4C2×#6711yescharacteristic
206C2×C3×C4C2×#6712yes—
207C2×C3×C4C2×#6712yes—
208C2×C3×C4C23×D311yescharacteristic
209C2×Dic3—62no—
210D12—34no—
211D12—64no—
212D12—62no—
213C4×D3—242no—
214C4×D3—242no—
215C3⋊C8—62no—
216C3⋊C8—62no—
217C2×C9—41no—
218C2×C9#52511yescharacteristic
219C2×C9#57712yes—
220D9—44no—
221C24—181no—
222C2×Q8C22×D912yes—
223C2×D4—92no—
224C2×D4—184no—
225C2×D4—181no—
226C22×C4—182no—
227C22×C4—182no—
228C22×C4C22×D911yescharacteristic
229SD16—184no—
230SD16—184no—
231C2×C8—92no—
232C2×C8—92no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—92no—
238C4⋊C4#61112yes—
239C4⋊C4C22×D912yes—
240C22⋊C4—22no—
241C22⋊C4—181no—
242C22⋊C4—182no—
243C22⋊C4—182no—
244C22⋊C4#61112yes—
245C42—22no—
246C42—181no—
247C42C22×D911yescharacteristic
248C42C22×D911yescharacteristic
249C22×C3—21no—
250C22×C3—22no—
251C22×C3C22×#6711yescharacteristic
252C2×D3—64no—
253C2×D3—122no—
254C2×D3—122no—
255C2×D3—244no—
256C3×C4—21no—
257C3×C4—22no—
258C3×C4—22no—
259C3×C4—42no—
260C3×C4—42no—
261C3×C4D3×#4112yes—
262Dic3—122no—
263C9#312311yescharacteristic, complemented, Sylow
264C23—184no—
265C23—182no—
266C23—722no—
267C23C2×#61111yescharacteristic
268Q8—22no—
269Q8—22no—
270D4—94no—
271D4—184no—
272D4—182no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—182no—
277C2×C4—722no—
278C2×C4—722no—
279C2×C4C2×#61112yes—
280C2×C4C2×#61111yescharacteristic
281C2×C4C2×#61112yes—
282C2×C4C23×D911yescharacteristic
283C8—182no—
284C8—182no—
285C2×C3—41no—
286C2×C3#582811yescharacteristic
287C2×C3#583712yes—
288D3—124no—
289C22—21no—
290C22—22no—
291C22—184no—
292C22—362no—
293C22—362no—
294C22—724no—
295C22C22×#61111yescharacteristic
296C4—21no—
297C4—22no—
298C4—22no—
299C4—42no—
300C4—42no—
301C4—362no—
302C4#41×D912yes—
303C3#8344711yescharacteristic
304C2—41no—
305C2—364no—
306C2#1058993011yescharacteristic
307C2#1058993912yes—
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#541C2
socleC22×C3C22×#67
prime radicalC22×D36C22
hypercenter#541D9
hypocenterC9#3123
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C9×#541C2semidirect
3. #10588768C2semidirect
4. #10588747C2semidirect
6. #10588725C2semidirect
7. #10588709C2semidirect
8. C4×#3675C2semidirect
9. #10588678C2semidirect
12. C9×C4⋊Q8C22semidirect
15. C9×#125C22semidirect
17. C4×Q8×C9C22semidirect
26. #63395C22semidirect
27. #63395C22semidirect
31. #63367C22semidirect
32. #63366C22semidirect
33. C4⋊(C9⋊C8)C22semidirect
34. #63362C22semidirect
35. C4×C9⋊C8C22semidirect
120. #541D9semidirect
174. C4⋊Q8C2×D9semidirect
177. #125C2×D9semidirect
179. C4×Q8C2×D9semidirect
263. C9#3123semidirect

Maximal subgroups

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

subgroupindex
C9×#5412
#105896232
#105887682
#105887472
#105887292
#105887252
#105887092
C4×#36752
#105886782
#834473