Finite Group Databasebeta

← #11786426

Subgroups — #11786426

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3#10592911C211yesmaximal, characteristic
4C2×#63645C212yesmaximal, complemented
5#10589417C212yesmaximal, complemented
6#69927—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C22×C32×C8C2212yes—
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12C2×C4⋊(C3⋊Dic3)—24no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C32×C22⋊C8C414yescomplemented
17#63658—21no—
18#63645—24no—
19C22×C4⋊Dic3—34no—
20C2×C3×C22⋊C8D314yes—
21#5212—34no—
22C2×#818—38no—
23#4551—38no—
24C24×C32D411yescharacteristic
25C22×C32×C4—22no—
26C22×C32×C4—22no—
27C22×C32×C4C2×C412yes—
28C22×C32×C4D411yescharacteristic
29C22×C32×C4Q812yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—24no—
32C22×C3⋊Dic3—22no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—42no—
36C22×C3⋊Dic3—42no—
37C2×C32×C8—22no—
38C2×C32×C8—22no—
39C2×C32×C8C2×C414yescomplemented
40#3757—42no—
41C4⋊(C3⋊Dic3)—24no—
42C4⋊(C3⋊Dic3)—22no—
43C4⋊(C3⋊Dic3)—22no—
44C4⋊(C3⋊Dic3)—22no—
45C4⋊(C3⋊Dic3)D414yes—
46#1852—91noSylow
47C23×C3×C4C2×D314yes—
48C23×Dic3—64no—
49C22×C3×C8C2×D318yes—
50C2×#217—64no—
51C2×C4⋊Dic3—38no—
52C2×C4⋊Dic3—34no—
53C2×C4⋊Dic3—34no—
54C2×C4⋊Dic3—616no—
55C2×C4⋊Dic3—64no—
56C3×C22⋊C8Dic3116yescomplemented
57C3⋊#95—64no—
58#818—616no—
59C23×C32—21no—
60C23×C32—21no—
61C23×C32—21no—
62C23×C32—21no—
63C23×C32C4⋊C412yes—
64C23×C32D812yes—
65C23×C32Q1612yes—
66C23×C32C2×D411yescharacteristic
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4—24no—
70C2×C32×C4—24no—
71C2×C32×C4C4⋊C412yes—
72C2×C32×C4C22×C411yescharacteristic
73C2×C32×C4C2×D412yes—
74C2×C32×C4C2×Q811yescharacteristic
75C2×C32×C4#4112yes—
76C2×C3⋊Dic3—24no—
77C2×C3⋊Dic3—48no—
78C2×C3⋊Dic3—42no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C32×C8—24no—
87C22×C4⋊C4—91no—
88C2×#107—92no—
89C2×C22⋊C8C3⋊D311yescharacteristic
90#380—91no—
91#340—92no—
92C24×C3D1214yes—
93C22×C3×C4—28no—
94C22×C3×C4—28no—
95C22×C3×C4Dic618yes—
96C22×C3×C4D1214yes—
97C22×C3×C4C2×Dic318yes—
98C22×C3×C4C22×D314yes—
99C22×Dic3—616no—
100C22×Dic3—68no—
101C22×Dic3—64no—
102C22×Dic3—64no—
103C22×Dic3—128no—
104C22×Dic3—128no—
105C2×C3×C8—28no—
106C2×C3×C8—28no—
107C2×C3×C8C2×Dic3116yescomplemented
108#217—128no—
109C4⋊Dic3—316no—
110C4⋊Dic3—616no—
111C4⋊Dic3—68no—
112C4⋊Dic3—68no—
113C4⋊Dic3—68no—
114C22×C32—22no—
115C22×C32—22no—
116C22×C32—22no—
117C22×C32—22no—
118C22×C32—22no—
119C22×C32—22no—
120C22×C32#10714yescomplemented
121C22×C32C2×C4⋊C411yescharacteristic
122C22×C32#12011yescharacteristic
123C22×C32#12311yescharacteristic
124C22×C32C2×D811yescharacteristic
125C22×C32C2×Q1611yescharacteristic
126C22×C32AGL(1,ℤ/8)11yescharacteristic
127C22×C32#13711yescharacteristic
128C32×C4—22no—
129C32×C4C4×D412yes—
130C32×C4C22⋊Q812yes—
131C3⋊Dic3—44no—
132C3⋊Dic3—81no—
133C3⋊Dic3—81no—
134C23×C4—181no—
135C23×C4C2×C3⋊D311yescharacteristic
136C22×C8C2×C3⋊D312yes—
137C2×C4⋊C4—92no—
138C2×C4⋊C4—91no—
139C2×C4⋊C4—91no—
140C2×C4⋊C4—184no—
141C2×C4⋊C4—181no—
142C2×C22⋊C4—181no—
143#107—184no—
144C22⋊C8C3⋊Dic314yescomplemented
145#95—181no—
146C23×C3—24no—
147C23×C3—24no—
148C23×C3—24no—
149C23×C3—24no—
150C23×C3D2418yes—
151C23×C3Dic1218yes—
152C23×C3C4⋊Dic318yes—
153C23×C3C2×D1214yes—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4—216no—
157C2×C3×C4—216no—
158C2×C3×C4C4⋊Dic318yes—
159C2×C3×C4C2×Dic614yes—
160C2×C3×C4D3×D418yes—
161C2×C3×C4#23718yes—
162C2×C3×C4C22×Dic314yes—
163C2×Dic3—616no—
164C2×Dic3—1232no—
165C2×Dic3—128no—
166C2×Dic3—128no—
167C2×Dic3—124no—
168C2×Dic3—124no—
169C2×Dic3—124no—
170C2×Dic3—124no—
171C2×Dic3—124no—
172C2×Dic3—124no—
173C3×C8—216no—
174C2×C32—24no—
175C2×C32#38511yescharacteristic
176C2×C32C2×#10711yescharacteristic
177C2×C32#42811yescharacteristic
178C2×C32#44711yescharacteristic
179C2×C32#45111yescharacteristic
180C2×C32#48011yescharacteristic
181C2×C32#48411yescharacteristic
182C24C4⋊(C3⋊D3)11yescharacteristic
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—184no—
186C22×C4—182no—
187C22×C4—181no—
188C22×C4—181no—
189C22×C4—362no—
190C22×C4—362no—
191C22×C4#63412yes—
192C22×C4C4⋊(C3⋊D3)11yescharacteristic
193C22×C4C2×C3⋊Dic312yes—
194C22×C4C22×C3⋊D311yescharacteristic
195C2×C8—22no—
196C2×C8—22no—
197C2×C8C2×C3⋊Dic314yescomplemented
198C4⋊C4—94no—
199C4⋊C4—184no—
200C4⋊C4—182no—
201C4⋊C4—182no—
202C4⋊C4—182no—
203C22⋊C4—362no—
204C22×C3—28no—
205C22×C3—28no—
206C22×C3—28no—
207C22×C3—28no—
208C22×C3—28no—
209C22×C3—28no—
210C22×C3#818116yescomplemented
211C22×C3#88214yes—
212C22×C3#88614yes—
213C22×C3C2×D2414yes—
214C22×C3C2×Dic1214yes—
215C22×C3#90814yes—
216C22×C3#90914yes—
217C22×C3C2×C4⋊Dic314yes—
218C3×C4—28no—
219C3×C4#87818yes—
220C3×C4D4×Dic318yes—
221Dic3—1216no—
222Dic3—244no—
223Dic3—244no—
224C32#185211yescharacteristic, complemented, Sylow
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23#374512yes—
230C23#374612yes—
231C23C4⋊(C3⋊Dic3)12yes—
232C23C2×C4⋊(C3⋊D3)11yescharacteristic
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—184no—
238C2×C4—368no—
239C2×C4—362no—
240C2×C4—362no—
241C2×C4—361no—
242C2×C4—361no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4C4⋊(C3⋊Dic3)12yes—
248C2×C4C2×#63411yescharacteristic
249C2×C4D4×C3⋊D312yes—
250C2×C4#383012yes—
251C2×C4C22×C3⋊Dic311yescharacteristic
252C8—24no—
253C2×C3—216no—
254C2×C3#472214yes—
255C2×C3#473214yes—
256C2×C3#473614yes—
257C2×C3#473914yes—
258C2×C3#495014yes—
259C2×C3C2×#81814yes—
260C2×C3#512114yes—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22#6364514yescomplemented
268C22#6409111yescharacteristic
269C22#6409511yescharacteristic
270C22C2×#374511yescharacteristic
271C22C2×#374611yescharacteristic
272C22#6411711yescharacteristic
273C22#6411811yescharacteristic
274C22C2×C4⋊(C3⋊Dic3)11yescharacteristic
275C4—22no—
276C4—364no—
277C4—721no—
278C4—721no—
279C4#6408712yes—
280C4D4×C3⋊Dic312yes—
281C3#6992714yescomplemented
282C2—24no—
283C2#1059242111yescharacteristic
284C2#1059243111yescharacteristic
285C2#1059243511yescharacteristic
286C2#1059243811yescharacteristic
287C2#1059264911yescharacteristic
288C2C2×#6364511yescharacteristic
289C2#1059282011yescharacteristic
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C8C3⋊D3
hypocenterC32#1852
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#63645C2semidirect
5. #10589417C2semidirect
16. C32×C22⋊C8C4semidirect
39. C2×C32×C8C2×C4semidirect
56. C3×C22⋊C8Dic3semidirect
107. C2×C3×C8C2×Dic3semidirect
120. C22×C32#107semidirect
144. C22⋊C8C3⋊Dic3semidirect
197. C2×C8C2×C3⋊Dic3semidirect
210. C22×C3#818semidirect
224. C32#1852semidirect
267. C22#63645semidirect
281. C3#69927semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C2×C32×C22⋊C82
#105929112
C2×#636452
#105894172
#699273