Finite Group Databasebeta

← #11872802

Subgroups — #11872802

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
1#10589623C211yesmaximal, characteristic
2#10589620C211yesmaximal, characteristic, complemented
3C9×#433C211yesmaximal, characteristic, complemented
4#10588531C212yesmaximal, complemented
5#10588525C212yesmaximal, complemented
6#10588413C212yesmaximal
7#10588403C212yesmaximal, complemented
8#10588391C212yesmaximal, complemented
9C4×#3664C212yesmaximal, complemented
10#79387—31nomaximal
11C22×D36C2211yescharacteristic
12C9×#117C2211yescharacteristic
13#63488C2211yescharacteristic
14#63486C2212yes—
15C2×#3664C2212yes—
16C2×#3664C2212yes—
17#63455—22no—
18#63451—22no—
19C22⋊C4×D9—22no—
20#63441—22no—
21C4×D36C2212yes—
22C4×D36C2212yes—
23#63432C2211yescharacteristic, complemented
24#63431C2211yescharacteristic, complemented
25C4×Dic18C2212yescomplemented
26C9×C4⋊C8C2212yescomplemented
27C9×C22⋊C8C2212yes—
28C9×#97C2211yescharacteristic, complemented
29C4×C8×C9C2211yescharacteristic, complemented
30#63380C2212yes—
31#63380C2212yes—
32#63378C2212yescomplemented
33#63377C2212yescomplemented
34#63376C2212yescomplemented
35#63376C2212yescomplemented
36#5521—31no—
37#5518—31no—
38C3×#433D311yescharacteristic
39#4847—32no—
40#4841—32no—
41#4731—32no—
42#4723—32no—
43#4710—32no—
44C4×#204—32no—
45C23×D9—21no—
46C22×C4×C9C2311yescharacteristic
47C2×D36—21no—
48C2×D36—24no—
49C2×D36C2312yes—
50C2×C4×D9—22no—
51C2×C4×D9—22no—
52C2×Dic18C2312yes—
53C2×C8×C9C2312yes—
54C2×C8×C9C2312yes—
55C9×C4⋊C4D412yes—
56C9×C22⋊C4D412yes—
57C42×C9C2311yescharacteristic
58C42×C9C2311yescharacteristic
59#3676—21no—
60#3676—22no—
61(C2×D9)⋊C4—22no—
62(C2×D9)⋊C4—22no—
63C4⋊Dic9—22no—
64C4⋊Dic9C2312yes—
65C4⋊Dic9C2312yes—
66Dic9⋊C4—22no—
67Dic9⋊C4—22no—
68Dic9⋊C4—22no—
69C4×Dic9—21no—
70C4×Dic9—22no—
71#3664—24no—
72#3664—24no—
73#3123—91noSylow
74C22×D12—31no—
75C3×#117C2×D311yescharacteristic
76#926—31no—
77#924—32no—
78C2×#204—32no—
79C2×#204—32no—
80#893—62no—
81#889—62no—
82D3×C22⋊C4—62no—
83#879—62no—
84C4×D12—32no—
85C4×D12—32no—
86#870—31no—
87#869—31no—
88C4×Dic6—32no—
89C3×C4⋊C8C2×D312yes—
90C3×C22⋊C8C2×D312yes—
91C3×#97C2×D311yescharacteristic
92C3×C4×C8C2×D311yescharacteristic
93#821—32no—
94#821—32no—
95#818—32no—
96#817—32no—
97#816—32no—
98#816—32no—
99C23×C9C2×D411yescharacteristic
100C22×D9—22no—
101C22×D9—24no—
102C22×D9—82no—
103C2×C4×C9—22no—
104C2×C4×C9C2×D411yescharacteristic
105C2×C4×C9C2×D412yes—
106C2×C4×C9C2×D412yes—
107C2×C4×C9C2411yescharacteristic
108C2×Dic9—22no—
109C2×Dic9—22no—
110C2×Dic9—22no—
111D36—24no—
112D36—22no—
113D36#4114yes—
114C4×D9—82no—
115C4×D9—82no—
116Dic18—22no—
117Dic18—22no—
118C8×C9—22no—
119C8×C9—22no—
120#541—91no—
121#518—91no—
122#485—92no—
123#478—92no—
124#461—92no—
125#450—92no—
126#440—92no—
127C4×SD16—92no—
128#433D911yescharacteristic, complemented
129C23×D3—61no—
130C22×C3×C4C22×D311yescharacteristic
131C2×D12—32no—
132C2×D12—64no—
133C2×D12—61no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×Dic6—32no—
137C2×C3×C8C22×D312yes—
138C2×C3×C8C22×D312yes—
139C3×C4⋊C4D1212yes—
140C3×C22⋊C4D1212yes—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#217—62no—
144#217—61no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—62no—
147C4⋊Dic3—32no—
148C4⋊Dic3—32no—
149C4⋊Dic3—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153C4×Dic3—62no—
154C4×Dic3—61no—
155#204—64no—
156#204—64no—
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×C9C2×#4112yes—
168Dic9—42no—
169Dic9—42no—
170Dic9—42no—
171C22×D4—91no—
172C2×SD16—92no—
173C2×SD16—92no—
174C4⋊Q8—91no—
175#126—182no—
176#125—91no—
177#125—182no—
178C22⋊Q8—92no—
179C4×Q8—92no—
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⋊C8C2×D912yescomplemented
189#103—92no—
190#103—92no—
191#102—92no—
192#102—92no—
193C22⋊C8C2×D912yes—
194#97C2×D911yescharacteristic, complemented
195C4×C8C2×D911yescharacteristic, complemented
196C23×C3C2×D1211yescharacteristic
197C22×D3—62no—
198C22×D3—64no—
199C22×D3—242no—
200C2×C3×C4—22no—
201C2×C3×C4C2×D1211yescharacteristic
202C2×C3×C4C2×D1212yes—
203C2×C3×C4C2×D1212yes—
204C2×C3×C4C23×D311yescharacteristic
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208D12—34no—
209D12—64no—
210D12—62no—
211C4×D3—242no—
212C4×D3—242no—
213Dic6—62no—
214Dic6—62no—
215C3×C8—22no—
216C3×C8—22no—
217C2×C9—41no—
218C2×C9#52511yescharacteristic
219C2×C9#57712yes—
220D9—44no—
221C24—181no—
222C2×Q8—92no—
223C2×D4—92no—
224C2×D4—184no—
225C2×D4—181no—
226C22×C4—182no—
227C22×C4—182no—
228C22×C4C22×D911yescharacteristic
229SD16—184no—
230SD16—184no—
231C2×C8C22×D912yes—
232C2×C8C22×D912yes—
233C4⋊C4—92no—
234C4⋊C4—92no—
235C4⋊C4—182no—
236C4⋊C4—182no—
237C4⋊C4—182no—
238C4⋊C4—182no—
239C4⋊C4D3612yes—
240C22⋊C4—181no—
241C22⋊C4—182no—
242C22⋊C4—182no—
243C22⋊C4—182no—
244C22⋊C4D3612yes—
245C42—181no—
246C42—182no—
247C42C22×D911yescharacteristic
248C42C22×D911yescharacteristic
249C22×C3—22no—
250C22×C3—21no—
251C22×C3C22×D1211yescharacteristic
252C2×D3—64no—
253C2×D3—122no—
254C2×D3—122no—
255C2×D3—244no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—21no—
259C3×C4D3×#4112yes—
260Dic3—122no—
261Dic3—122no—
262Dic3—122no—
263C9#312311yescharacteristic, complemented, Sylow
264C23—184no—
265C23—182no—
266C23—722no—
267C23C2×D3611yescharacteristic
268Q8—182no—
269Q8—182no—
270D4—94no—
271D4—184no—
272D4—182no—
273C2×C4—22no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—722no—
278C2×C4—722no—
279C2×C4C2×D3612yes—
280C2×C4C2×D3611yescharacteristic
281C2×C4C2×D3612yes—
282C2×C4C23×D911yescharacteristic
283C8—22no—
284C8—22no—
285C2×C3—41no—
286C2×C3#552411yescharacteristic
287C2×C3#575112yes—
288D3—124no—
289C22—22no—
290C22—21no—
291C22—184no—
292C22—362no—
293C22—362no—
294C22—724no—
295C22C22×D3611yescharacteristic
296C4—22no—
297C4—22no—
298C4—21no—
299C4—362no—
300C4—362no—
301C4—362no—
302C4#41×D912yes—
303C3#7938711yescharacteristic
304C2—41no—
305C2—364no—
306C2#1058962611yescharacteristic
307C2#1058985312yes—
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#433C2
socleC22×C3C22×D12
prime radicalC22×D36C22
hypercenter#433D9
hypocenterC9#3123
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #10589620C2semidirect
3. C9×#433C2semidirect
4. #10588531C2semidirect
5. #10588525C2semidirect
7. #10588403C2semidirect
8. #10588391C2semidirect
9. C4×#3664C2semidirect
23. #63432C22semidirect
24. #63431C22semidirect
25. C4×Dic18C22semidirect
26. C9×C4⋊C8C22semidirect
28. C9×#97C22semidirect
29. C4×C8×C9C22semidirect
32. #63378C22semidirect
33. #63377C22semidirect
34. #63376C22semidirect
35. #63376C22semidirect
128. #433D9semidirect
188. C4⋊C8C2×D9semidirect
194. #97C2×D9semidirect
195. C4×C8C2×D9semidirect
263. C9#3123semidirect

Maximal subgroups

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

subgroupindex
#105896232
#105896202
C9×#4332
#105885312
#105885252
#105884132
#105884032
#105883912
C4×#36642
#793873