Finite Group Databasebeta

← #11794639

Subgroups — #11794639

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#390C211yesmaximal, characteristic
2C2×#63659C212yesmaximal
3#10592634C211yesmaximal, characteristic, complemented
4#10589395C212yesmaximal, complemented
5#10589390C211yesmaximal, characteristic, complemented
6#69640—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C32×C22⋊C4—21no—
10C2×C32×C22⋊C4—21no—
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)—21no—
14C2×C4⋊(C3⋊Dic3)C2212yes—
15C22×C3⋊(C3⋊C8)C2212yes—
16#63659—24no—
17C3×#390D314yes—
18C2×#832—38no—
19#4935—34no—
20#4529—38no—
21#4524—34no—
22C24×C32—21no—
23C2×C32×D4—22no—
24C2×C32×D4—22no—
25C2×C32×D4—21no—
26C2×C32×D4D412yes—
27C22×C32×C4—21no—
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—22no—
32C32×C4⋊C4—22no—
33C32×C22⋊C4—42no—
34C32×C22⋊C4—42no—
35C32×C42—22no—
36C4⋊(C3⋊Dic3)—22no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)—42no—
39C4⋊(C3⋊Dic3)—42no—
40C2×C3⋊(C3⋊C8)—22no—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)—22no—
43#2071—91noSylow
44C22×C3×D4C2×D314yes—
45C2×C3×C4⋊C4C2×D314yes—
46C2×C3×C22⋊C4—24no—
47C2×C3×C22⋊C4—24no—
48C2×C3×C42C2×D314yes—
49C2×C4⋊Dic3—38no—
50C2×C4⋊Dic3—64no—
51C2×C4⋊Dic3—64no—
52C22×C3⋊C8—38no—
53#832—616no—
54C23×C32—22no—
55C23×C32—41no—
56C23×C32—41no—
57C23×C32—41no—
58C23×C32—41no—
59C23×C32—41no—
60C23×C32—41no—
61C23×C32C2×D411yescharacteristic
62C32×D4—24no—
63C32×D4—42no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4D812yes—
72C2×C32×C4SD1612yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C32×C4#4112yes—
76C2×C32×C4#4112yes—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3—42no—
79C2×C3⋊Dic3—42no—
80C3⋊(C3⋊C8)—42no—
81C2×#102—92no—
82#390C3⋊D311yescharacteristic
83#384—91no—
84#340—92no—
85#336—91no—
86C24×C3—24no—
87C2×C3×D4—24no—
88C2×C3×D4—28no—
89C2×C3×D4—28no—
90C2×C3×D4D1218yes—
91C22×C3×C4—24no—
92C22×C3×C4#6714yes—
93C22×C3×C4#6714yes—
94C22×C3×C4C22×D314yes—
95C22×Dic3—68no—
96C3×C4⋊C4—28no—
97C3×C22⋊C4—48no—
98C3×C22⋊C4—48no—
99C3×C42—28no—
100C4⋊Dic3—68no—
101C4⋊Dic3—68no—
102C4⋊Dic3—128no—
103C4⋊Dic3—128no—
104C2×C3⋊C8—68no—
105C2×C3⋊C8—68no—
106C2×C3⋊C8—68no—
107C22×C32—42no—
108C22×C32—42no—
109C22×C32—42no—
110C22×C32—81no—
111C22×C32—81no—
112C22×C32—81no—
113C22×C32—81no—
114C22×C32#12111yescharacteristic
115C22×C32#12311yescharacteristic
116C22×C32#12411yescharacteristic
117C22×C32C2×D811yescharacteristic
118C22×C32C2×SD1611yescharacteristic
119C22×C32AGL(1,ℤ/8)11yescharacteristic
120C22×C32#13711yescharacteristic
121C32×C4—22no—
122C32×C4—22no—
123C32×C4—81no—
124C32×C4#12312yes—
125C32×C4#12612yes—
126C3⋊Dic3—82no—
127C22×D4C2×C3⋊D311yescharacteristic
128C22×C8—92no—
129C2×C4⋊C4—92no—
130C2×C4⋊C4—181no—
131C2×C4⋊C4—181no—
132C2×C4⋊C4C2×C3⋊D311yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4—21no—
135C2×C42C2×C3⋊D311yescharacteristic
136#102—184no—
137C23×C3—28no—
138C23×C3—44no—
139C23×C3—44no—
140C23×C3—44no—
141C23×C3—44no—
142C23×C3—44no—
143C23×C3—44no—
144C23×C3C2×#6714yes—
145C3×D4—216no—
146C3×D4—48no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—24no—
151C2×C3×C4—44no—
152C2×C3×C4—44no—
153C2×C3×C4—44no—
154C2×C3×C4#21318yes—
155C2×C3×C4#21418yes—
156C2×C3×C4C2×D1214yes—
157C2×C3×C4#23514yes—
158C2×C3×C4#23718yes—
159C2×C3×C4#23718yes—
160C2×Dic3—128no—
161C2×Dic3—128no—
162C2×Dic3—128no—
163C3⋊C8—128no—
164C2×C32—82no—
165C2×C32#39711yescharacteristic
166C2×C32#45911yescharacteristic
167C2×C32#46111yescharacteristic
168C2×C32#48011yescharacteristic
169C2×C32#48111yescharacteristic
170C2×C32#48611yescharacteristic
171C2×C32#48911yescharacteristic
172C24—21no—
173C2×D4—21no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4C4⋊(C3⋊D3)12yes—
177C22×C4—21no—
178C22×C4—182no—
179C22×C4#63811yescharacteristic
180C22×C4#63811yescharacteristic
181C22×C4C22×C3⋊D311yescharacteristic
182C2×C8—182no—
183C2×C8—182no—
184C2×C8—182no—
185C4⋊C4—22no—
186C4⋊C4—182no—
187C4⋊C4—182no—
188C4⋊C4—362no—
189C4⋊C4—362no—
190C22⋊C4—42no—
191C22⋊C4—42no—
192C42—22no—
193C22×C3—48no—
194C22×C3—48no—
195C22×C3—48no—
196C22×C3—84no—
197C22×C3—84no—
198C22×C3—84no—
199C22×C3—84no—
200C22×C3#93014yes—
201C22×C3C2×#21314yes—
202C22×C3C2×#21414yes—
203C22×C3#93514yes—
204C22×C3#93614yes—
205C22×C3#94914yes—
206C22×C3#95114yes—
207C3×C4—28no—
208C3×C4—28no—
209C3×C4—84no—
210C3×C4#87918yes—
211C3×C4#88618yes—
212Dic3—248no—
213C32#207111yescharacteristic, complemented, Sylow
214C23—22no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—41no—
220C23—41no—
221C23C2×#63811yescharacteristic
222D4—24no—
223D4—42no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—362no—
232C2×C4—362no—
233C2×C4—362no—
234C2×C4#375312yes—
235C2×C4#375412yes—
236C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
237C2×C4#382811yescharacteristic
238C2×C4#383012yes—
239C2×C4#383012yes—
240C8—362no—
241C2×C3—88no—
242C2×C3#495314yes—
243C2×C3#501514yes—
244C2×C3#501914yes—
245C2×C3#503314yes—
246C2×C3#503414yes—
247C2×C3#505514yes—
248C2×C3#507014yes—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—81no—
253C22—81no—
254C22—81no—
255C22—81no—
256C22#6413911yescharacteristic
257C22C2×#375311yescharacteristic
258C22C2×#375411yescharacteristic
259C22#6414411yescharacteristic
260C22#6414511yescharacteristic
261C22#6415811yescharacteristic
262C22#6416011yescharacteristic
263C4—22no—
264C4—22no—
265C4—81no—
266C4—722no—
267C4#6408812yes—
268C4#6409512yes—
269C3#6964014yescomplemented
270C2—82no—
271C2#1059265211yescharacteristic
272C2#1059271411yescharacteristic
273C2#1059271811yescharacteristic
274C2#1059273211yescharacteristic
275C2#1059273311yescharacteristic
276C2#1059275411yescharacteristic
277C2#1059276911yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenter#390C3⋊D3
hypocenterC32#2071
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
3. #10592634C2semidirect
4. #10589395C2semidirect
5. #10589390C2semidirect
213. C32#2071semidirect
269. C3#69640semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C2×#636592
#105926342
#105893952
#105893902
#696403