Finite Group Databasebeta

← #11778667

Subgroups — #11778667

Order 1152.

864 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 129 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#10595964C211yesmaximal, characteristic
2#10592648C211yesmaximal, characteristic, complemented
3#10592434C212yesmaximal, complemented
4C32×#323C211yesmaximal, characteristic, complemented
5#10589336C212yesmaximal, complemented
6#68112—34nomaximal
7C22×#638—21no—
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×#3757—21no—
10#64139—21no—
11#64139C2212yes—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
13C2×#3750—21no—
14#64095—22no—
15#64091—22no—
16C32×C22⋊C8C2212yescomplemented
17#63658C2211yescharacteristic, complemented
18#63648—22no—
19#63644—22no—
20#5493—34no—
21#4949—34no—
22#4735—38no—
23C3×#323D314yescomplemented
24#4470—38no—
25C24×C32D411yescharacteristic
26C23×C3⋊D3—21no—
27C22×C32×C4D411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C2×#638—22no—
30C2×#638—22no—
31C2×#638—42no—
32C2×#638—42no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)D412yes—
38C2×C32×C8—22no—
39C32×C22⋊C4—22no—
40#3757—42no—
41#3752—22no—
42#3752—22no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—22no—
45C4⋊(C3⋊Dic3)D412yes—
46#3750—42no—
47#1613—91noSylow
48C22×#67—64no—
49C2×C3×C22⋊C4C2×D314yes—
50C2×#217—64no—
51#930—38no—
52#930—64no—
53C2×C4⋊Dic3—34no—
54C2×Dic3⋊C4—64no—
55#886—68no—
56#882—68no—
57C3×C22⋊C8C2×D318yescomplemented
58C3⋊#95—34no—
59#821—68no—
60#817—68no—
61C23×C32—21no—
62C23×C32—21no—
63C23×C32—41no—
64C23×C32—41no—
65C23×C32SD1612yes—
66C23×C32C2×D411yescharacteristic
67C22×C3⋊D3—22no—
68C22×C3⋊D3—42no—
69C22×C3⋊D3—81no—
70C22×C3⋊D3—81no—
71C2×C32×C4—21no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4C2×D412yes—
75#638—44no—
76#638—42no—
77#638—42no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—42no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C4⋊(C3⋊D3)—42no—
87C4⋊(C3⋊D3)—81no—
88C32×C8—42no—
89#534—91no—
90#481—92no—
91#399—91no—
92#327—92no—
93#323C3⋊D311yescharacteristic, complemented
94C24×C3D1214yes—
95C23×D3—64no—
96C22×C3×C4D1214yes—
97C22×C3×C4C22×D314yes—
98C2×#67—68no—
99C2×#67—68no—
100C2×#67—128no—
101C2×#67—128no—
102C22×Dic3—64no—
103C22×Dic3—64no—
104C22×Dic3—64no—
105C2×D12—38no—
106C2×D12—64no—
107C2×C3×C8—28no—
108C3×C22⋊C4—28no—
109#217—128no—
110(C2×D3)⋊C4—68no—
111(C2×D3)⋊C4—68no—
112C4⋊Dic3—38no—
113C4⋊Dic3—64no—
114C4⋊Dic3—68no—
115Dic3⋊C4—128no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32—22no—
119C22×C32—42no—
120C22×C32—41no—
121C22×C32—41no—
122C22×C32—81no—
123C22×C32#12011yescharacteristic
124C22×C32C2×SD1611yescharacteristic
125C22×C32AGL(1,ℤ/8)11yescharacteristic
126C2×C3⋊D3—42no—
127C2×C3⋊D3—42no—
128C2×C3⋊D3—42no—
129C2×C3⋊D3—84no—
130C32×C4—22no—
131C32×C4—41no—
132C3⋊Dic3—42no—
133C3⋊Dic3—42no—
134C3⋊Dic3—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×C3⋊D311yescharacteristic
144#106—182no—
145#102—182no—
146C22⋊C8C2×C3⋊D312yescomplemented
147#95—91no—
148C23×C3—24no—
149C23×C3—24no—
150C23×C3—44no—
151C23×C3—44no—
152C23×C3#20418yes—
153C23×C3C2×D1214yes—
154C22×D3—68no—
155C22×D3—128no—
156C22×D3—244no—
157C22×D3—244no—
158C2×C3×C4—24no—
159C2×C3×C4—44no—
160C2×C3×C4—44no—
161C2×C3×C4D3×D418yes—
162#67—1216no—
163#67—128no—
164#67—128no—
165C2×Dic3—68no—
166C2×Dic3—68no—
167C2×Dic3—124no—
168C2×Dic3—128no—
169C2×Dic3—124no—
170C2×Dic3—124no—
171C2×Dic3—124no—
172C2×Dic3—124no—
173D12—128no—
174D12—244no—
175C3×C8—48no—
176C2×C32—21no—
177C2×C32—21no—
178C2×C32—42no—
179C2×C32#45011yescharacteristic
180C2×C32#45311yescharacteristic
181C2×C32#45811yescharacteristic
182C3⋊D3—82no—
183C24—181no—
184C24C4⋊(C3⋊D3)11yescharacteristic
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×C4C4⋊(C3⋊D3)11yescharacteristic
195C22×C4C22×C3⋊D311yescharacteristic
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—24no—
206C22×C3—24no—
207C22×C3—28no—
208C22×C3—48no—
209C22×C3—44no—
210C22×C3—44no—
211C22×C3—84no—
212C22×C3#88214yes—
213C22×C3C2×#20414yes—
214C22×C3#90814yes—
215C2×D3—128no—
216C2×D3—128no—
217C2×D3—128no—
218C2×D3—2416no—
219C3×C4—28no—
220C3×C4—44no—
221Dic3—128no—
222Dic3—128no—
223Dic3—244no—
224C32#161311yescharacteristic, complemented, Sylow
225C23—21no—
226C23—21no—
227C23—41no—
228C23—41no—
229C23—182no—
230C23—362no—
231C23—721no—
232C23—721no—
233C23#374412yes—
234C23C2×C4⋊(C3⋊D3)11yescharacteristic
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×C3⋊D312yes—
252C8—42no—
253C2×C3—24no—
254C2×C3—24no—
255C2×C3—48no—
256C2×C3#473114yes—
257C2×C3#474214yes—
258C2×C3#474714yes—
259D3—248no—
260C22—21no—
261C22—21no—
262C22—22no—
263C22—42no—
264C22—41no—
265C22—41no—
266C22—81no—
267C22—362no—
268C22—362no—
269C22—362no—
270C22—724no—
271C22#6409111yescharacteristic
272C22C2×#374411yescharacteristic
273C22#6411711yescharacteristic
274C4—22no—
275C4—41no—
276C4—362no—
277C4—362no—
278C4—721no—
279C3#6811214yescomplemented
280C2—21no—
281C2—21no—
282C2—42no—
283C2—722no—
284C2#1059243011yescharacteristic
285C2#1059244111yescharacteristic
286C2#1059244611yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32#120
prime radical#10595964C2
hypercenter#323C3⋊D3
hypocenterC32#1613
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10592648C2semidirect
3. #10592434C2semidirect
4. C32×#323C2semidirect
5. #10589336C2semidirect
12. C2×C4⋊(C3⋊Dic3)C22semidirect
16. C32×C22⋊C8C22semidirect
17. #63658C22semidirect
23. C3×#323D3semidirect
57. C3×C22⋊C8C2×D3semidirect
93. #323C3⋊D3semidirect
146. C22⋊C8C2×C3⋊D3semidirect
224. C32#1613semidirect
279. C3#68112semidirect

Maximal subgroups

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

subgroupindex
#105959642
#105926482
#105924342
C32×#3232
#105893362
#681123