Finite Group Databasebeta

← #11778666

Subgroups — #11778666

Order 1152.

432 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 72 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#10589595C211yesmaximal, characteristic
2#10588629C211yesmaximal, characteristic, complemented
3#10588417C212yesmaximal, complemented
4C9×#323C211yesmaximal, characteristic, complemented
5#10588147C212yesmaximal, complemented
6#68112—31nomaximal
7C22×#611—21no—
8C2×C9×C22⋊C4C2211yescharacteristic
9C2×#3676—21no—
10#63492—21no—
11#63492C2212yes—
12C2×C4⋊Dic9C2211yescharacteristic, complemented
13C2×Dic9⋊C4—21no—
14#63448—22no—
15#63444—22no—
16C9×C22⋊C8C2212yescomplemented
17C9⋊#95C2211yescharacteristic, complemented
18#63380—22no—
19#63377—22no—
20#5493—31no—
21#4949—31no—
22#4735—32no—
23C3×#323D311yescharacteristic
24#4470—32no—
25C24×C9D411yescharacteristic
26C23×D9—21no—
27C22×C4×C9D411yescharacteristic
28C22×C4×C9C2311yescharacteristic
29C2×#611—22no—
30C2×#611—22no—
31C2×#611—42no—
32C2×#611—42no—
33C22×Dic9—21no—
34C22×Dic9—21no—
35C22×Dic9—21no—
36C2×D36—21no—
37C2×D36D412yes—
38C2×C8×C9—22no—
39C9×C22⋊C4—22no—
40#3676—42no—
41(C2×D9)⋊C4—22no—
42(C2×D9)⋊C4—22no—
43C4⋊Dic9—21no—
44C4⋊Dic9—22no—
45C4⋊Dic9D412yes—
46Dic9⋊C4—42no—
47#1613—91noSylow
48C22×#67—61no—
49C2×C3×C22⋊C4C2×D311yescharacteristic
50C2×#217—61no—
51#930—32no—
52#930—61no—
53C2×C4⋊Dic3—31no—
54C2×Dic3⋊C4—61no—
55#886—62no—
56#882—62no—
57C3×C22⋊C8C2×D312yes—
58C3⋊#95—31no—
59#821—62no—
60#817—62no—
61C23×C9—21no—
62C23×C9—21no—
63C23×C9—41no—
64C23×C9—41no—
65C23×C9SD1612yes—
66C23×C9C2×D411yescharacteristic
67C22×D9—22no—
68C22×D9—42no—
69C22×D9—81no—
70C22×D9—81no—
71C2×C4×C9—21no—
72C2×C4×C9—41no—
73C2×C4×C9—41no—
74C2×C4×C9C2×D412yes—
75#611—44no—
76#611—42no—
77#611—42no—
78C2×Dic9—22no—
79C2×Dic9—22no—
80C2×Dic9—41no—
81C2×Dic9—42no—
82C2×Dic9—41no—
83C2×Dic9—41no—
84C2×Dic9—41no—
85C2×Dic9—41no—
86D36—42no—
87D36—81no—
88C8×C9—42no—
89#534—91no—
90#481—92no—
91#399—91no—
92#327—92no—
93#323D911yescharacteristic, complemented
94C24×C3D1211yescharacteristic
95C23×D3—61no—
96C22×C3×C4D1211yescharacteristic
97C22×C3×C4C22×D311yescharacteristic
98C2×#67—62no—
99C2×#67—62no—
100C2×#67—122no—
101C2×#67—122no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×D12—32no—
106C2×D12—61no—
107C2×C3×C8—22no—
108C3×C22⋊C4—22no—
109#217—122no—
110(C2×D3)⋊C4—62no—
111(C2×D3)⋊C4—62no—
112C4⋊Dic3—32no—
113C4⋊Dic3—61no—
114C4⋊Dic3—62no—
115Dic3⋊C4—122no—
116C22×C9—21no—
117C22×C9—21no—
118C22×C9—22no—
119C22×C9—42no—
120C22×C9—41no—
121C22×C9—41no—
122C22×C9—81no—
123C22×C9#12011yescharacteristic
124C22×C9C2×SD1611yescharacteristic
125C22×C9AGL(1,ℤ/8)11yescharacteristic
126C2×D9—42no—
127C2×D9—42no—
128C2×D9—42no—
129C2×D9—84no—
130C4×C9—22no—
131C4×C9—41no—
132Dic9—42no—
133Dic9—42no—
134Dic9—81no—
135C22×D4—181no—
136#123—182no—
137#121—92no—
138#121—181no—
139#120—182no—
140C2×C4⋊C4—91no—
141C2×C4⋊C4—181no—
142C2×C22⋊C4—181no—
143C2×C22⋊C4C2×D911yescharacteristic
144#106—182no—
145#102—182no—
146C22⋊C8C2×D912yescomplemented
147#95—91no—
148C23×C3—21no—
149C23×C3—21no—
150C23×C3—41no—
151C23×C3—41no—
152C23×C3#20412yes—
153C23×C3C2×D1211yescharacteristic
154C22×D3—62no—
155C22×D3—122no—
156C22×D3—241no—
157C22×D3—241no—
158C2×C3×C4—21no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4D3×D412yes—
162#67—124no—
163#67—122no—
164#67—122no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—121no—
168C2×Dic3—122no—
169C2×Dic3—121no—
170C2×Dic3—121no—
171C2×Dic3—121no—
172C2×Dic3—121no—
173D12—122no—
174D12—241no—
175C3×C8—42no—
176C2×C9—21no—
177C2×C9—21no—
178C2×C9—42no—
179C2×C9#45011yescharacteristic
180C2×C9#45311yescharacteristic
181C2×C9#45811yescharacteristic
182D9—82no—
183C24—181no—
184C24D3611yescharacteristic
185C2×D4—92no—
186C2×D4—181no—
187C2×D4—182no—
188C2×D4—182no—
189C2×D4—362no—
190C2×D4—362no—
191C22×C4—181no—
192C22×C4—181no—
193C22×C4—181no—
194C22×C4D3611yescharacteristic
195C22×C4C22×D911yescharacteristic
196C2×C8—22no—
197C4⋊C4—92no—
198C4⋊C4—181no—
199C4⋊C4—182no—
200C4⋊C4—362no—
201C22⋊C4—22no—
202C22⋊C4—182no—
203C22⋊C4—182no—
204C22⋊C4—362no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—22no—
208C22×C3—42no—
209C22×C3—41no—
210C22×C3—41no—
211C22×C3—81no—
212C22×C3#88211yescharacteristic
213C22×C3C2×#20411yescharacteristic
214C22×C3#90811yescharacteristic
215C2×D3—122no—
216C2×D3—122no—
217C2×D3—122no—
218C2×D3—244no—
219C3×C4—22no—
220C3×C4—41no—
221Dic3—122no—
222Dic3—122no—
223Dic3—241no—
224C9#161311yescharacteristic, complemented, Sylow
225C23—21no—
226C23—21no—
227C23—41no—
228C23—41no—
229C23—182no—
230C23—362no—
231C23—721no—
232C23—721no—
233C23#366412yes—
234C23C2×D3611yescharacteristic
235D4—362no—
236D4—364no—
237D4—362no—
238D4—362no—
239D4—721no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4—362no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4—361no—
250C2×C4—361no—
251C2×C4D4×D912yes—
252C8—42no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—42no—
256C2×C3#473111yescharacteristic
257C2×C3#474211yescharacteristic
258C2×C3#474711yescharacteristic
259D3—242no—
260C22—21no—
261C22—21no—
262C22—22no—
263C22—42no—
264C22—41no—
265C22—41no—
266C22—81no—
267C22—362no—
268C22—362no—
269C22—362no—
270C22—724no—
271C22#6344411yescharacteristic
272C22C2×#366411yescharacteristic
273C22#6347011yescharacteristic
274C4—22no—
275C4—41no—
276C4—362no—
277C4—362no—
278C4—721no—
279C3#6811211yescharacteristic
280C2—21no—
281C2—21no—
282C2—42no—
283C2—722no—
284C2#1058841311yescharacteristic
285C2#1058842211yescharacteristic
286C2#1058842711yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#323C2
socleC22×C3#882
prime radical#10589595C2
hypercenter#323D9
hypocenterC9#1613
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10588629C2semidirect
3. #10588417C2semidirect
4. C9×#323C2semidirect
5. #10588147C2semidirect
12. C2×C4⋊Dic9C22semidirect
16. C9×C22⋊C8C22semidirect
17. C9⋊#95C22semidirect
93. #323D9semidirect
146. C22⋊C8C2×D9semidirect
224. C9#1613semidirect

Maximal subgroups

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

subgroupindex
#105895952
#105886292
#105884172
C9×#3232
#105881472
#681123