Finite Group Databasebeta

← #11778441

Subgroups — #11778441

Order 1152.

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

normal subgroups only

This group has 840 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#10592652C211yesmaximal, characteristic, complemented
3#10592435C212yesmaximal, complemented
4C32×#323C211yesmaximal, characteristic, complemented
5#10589336C212yesmaximal, complemented
6#68110—34nomaximal
7C22×#638—21no—
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×#3757—21no—
10#64139—21no—
11#64139C2212yes—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
13#64095—22no—
14#64091—22no—
15C32×C22⋊C8C2212yescomplemented
16#63658—21no—
17#63658C2211yescharacteristic, complemented
18#63648—22no—
19#63645—22no—
20#5493—34no—
21#4953—34no—
22#4736—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#1607—91noSylow
47C22×#67—64no—
48C2×C3×C22⋊C4C2×D314yes—
49C2×#217—64no—
50#930—38no—
51#930—64no—
52C2×C4⋊Dic3—34no—
53#886—68no—
54#882—68no—
55C3×C22⋊C8C2×D318yescomplemented
56C3⋊#95—34no—
57C3⋊#95—64no—
58#821—68no—
59#818—68no—
60C23×C32—21no—
61C23×C32—21no—
62C23×C32—41no—
63C23×C32—41no—
64C23×C32D812yes—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—42no—
68C22×C3⋊D3—81no—
69C22×C3⋊D3—81no—
70C2×C32×C4—21no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4C2×D412yes—
74#638—44no—
75#638—42no—
76#638—42no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—42no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C4⋊(C3⋊D3)—42no—
86C4⋊(C3⋊D3)—81no—
87C32×C8—42no—
88#534—91no—
89#480—92no—
90#397—91no—
91#327—92no—
92#323C3⋊D311yescharacteristic, complemented
93C24×C3D1214yes—
94C23×D3—64no—
95C22×C3×C4D1214yes—
96C22×C3×C4C22×D314yes—
97C2×#67—68no—
98C2×#67—68no—
99C2×#67—128no—
100C2×#67—128no—
101C22×Dic3—64no—
102C22×Dic3—64no—
103C22×Dic3—64no—
104C2×D12—38no—
105C2×D12—64no—
106C2×C3×C8—28no—
107C3×C22⋊C4—28no—
108#217—128no—
109(C2×D3)⋊C4—68no—
110(C2×D3)⋊C4—68no—
111C4⋊Dic3—38no—
112C4⋊Dic3—64no—
113C4⋊Dic3—68no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—22no—
117C22×C32—42no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—81no—
121C22×C32#12011yescharacteristic
122C22×C32C2×D811yescharacteristic
123C22×C32AGL(1,ℤ/8)11yescharacteristic
124C2×C3⋊D3—42no—
125C2×C3⋊D3—42no—
126C2×C3⋊D3—42no—
127C2×C3⋊D3—84no—
128C32×C4—22no—
129C32×C4—41no—
130C3⋊Dic3—42no—
131C3⋊Dic3—81no—
132C3⋊Dic3—81no—
133C22×D4—181no—
134#123—182no—
135#121—92no—
136#121—181no—
137#120—182no—
138C2×C4⋊C4—91no—
139C2×C22⋊C4—181no—
140C2×C22⋊C4C2×C3⋊D311yescharacteristic
141#107—182no—
142#102—182no—
143C22⋊C8C2×C3⋊D312yescomplemented
144#95—91no—
145#95—181no—
146C23×C3—24no—
147C23×C3—24no—
148C23×C3—44no—
149C23×C3—44no—
150C23×C3D2418yes—
151C23×C3C2×D1214yes—
152C22×D3—68no—
153C22×D3—128no—
154C22×D3—244no—
155C22×D3—244no—
156C2×C3×C4—24no—
157C2×C3×C4—44no—
158C2×C3×C4—44no—
159C2×C3×C4D3×D418yes—
160#67—1216no—
161#67—128no—
162#67—128no—
163C2×Dic3—68no—
164C2×Dic3—128no—
165C2×Dic3—124no—
166C2×Dic3—124no—
167C2×Dic3—124no—
168C2×Dic3—124no—
169C2×Dic3—124no—
170C2×Dic3—124no—
171D12—128no—
172D12—244no—
173C3×C8—48no—
174C2×C32—21no—
175C2×C32—21no—
176C2×C32—42no—
177C2×C32#44711yescharacteristic
178C2×C32#45511yescharacteristic
179C2×C32#45811yescharacteristic
180C3⋊D3—82no—
181C24—181no—
182C24C4⋊(C3⋊D3)11yescharacteristic
183C2×D4—92no—
184C2×D4—181no—
185C2×D4—182no—
186C2×D4—182no—
187C2×D4—362no—
188C2×D4—362no—
189C22×C4—181no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4C4⋊(C3⋊D3)11yescharacteristic
193C22×C4C22×C3⋊D311yescharacteristic
194C2×C8—22no—
195C4⋊C4—92no—
196C4⋊C4—181no—
197C4⋊C4—182no—
198C22⋊C4—22no—
199C22⋊C4—182no—
200C22⋊C4—182no—
201C22⋊C4—362no—
202C22×C3—24no—
203C22×C3—24no—
204C22×C3—28no—
205C22×C3—48no—
206C22×C3—44no—
207C22×C3—44no—
208C22×C3—84no—
209C22×C3#88214yes—
210C22×C3C2×D2414yes—
211C22×C3#90814yes—
212C2×D3—128no—
213C2×D3—128no—
214C2×D3—128no—
215C2×D3—2416no—
216C3×C4—28no—
217C3×C4—44no—
218Dic3—128no—
219Dic3—244no—
220Dic3—244no—
221C32#160711yescharacteristic, complemented, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23—182no—
227C23—362no—
228C23—721no—
229C23—721no—
230C23#374512yes—
231C23C2×C4⋊(C3⋊D3)11yescharacteristic
232D4—362no—
233D4—364no—
234D4—362no—
235D4—362no—
236D4—721no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—182no—
241C2×C4—362no—
242C2×C4—361no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4D4×C3⋊D312yes—
249C8—42no—
250C2×C3—24no—
251C2×C3—24no—
252C2×C3—48no—
253C2×C3#473214yes—
254C2×C3#474214yes—
255C2×C3#474614yes—
256D3—248no—
257C22—21no—
258C22—21no—
259C22—22no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—81no—
264C22—362no—
265C22—362no—
266C22—362no—
267C22—724no—
268C22#6409111yescharacteristic
269C22C2×#374511yescharacteristic
270C22#6411711yescharacteristic
271C4—22no—
272C4—41no—
273C4—362no—
274C4—721no—
275C4—721no—
276C3#6811014yescomplemented
277C2—21no—
278C2—21no—
279C2—42no—
280C2—722no—
281C2#1059243111yescharacteristic
282C2#1059244111yescharacteristic
283C2#1059244511yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32#120
prime radical#10595964C2
hypercenter#323C3⋊D3
hypocenterC32#1607
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. #10592652C2semidirect
3. #10592435C2semidirect
4. C32×#323C2semidirect
5. #10589336C2semidirect
12. C2×C4⋊(C3⋊Dic3)C22semidirect
15. C32×C22⋊C8C22semidirect
17. #63658C22semidirect
23. C3×#323D3semidirect
55. C3×C22⋊C8C2×D3semidirect
92. #323C3⋊D3semidirect
143. C22⋊C8C2×C3⋊D3semidirect
221. C32#1607semidirect
276. C3#68110semidirect

Maximal subgroups

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

subgroupindex
#105959642
#105926522
#105924352
C32×#3232
#105893362
#681103