Finite Group Databasebeta

← #11789045

Subgroups — #11789045

Order 1152.

690 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
1C2×C32×#107C211yesmaximal, characteristic
2#10592683C211yesmaximal, characteristic
3C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
4#10589417C211yesmaximal, characteristic
5#10589416C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#70609—34nomaximal
9C22×C32×C8C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C32×#107C414yescomplemented
19#63658—21no—
20#63658—21no—
21C2×C3×#107D314yes—
22#4984—34no—
23Dic3×C4⋊C4—34no—
24#4551—34no—
25#4550—34no—
26#4529—34no—
27#4529—34no—
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C32×C8—21no—
36C2×C32×C8—21no—
37C2×C32×C8C2×C412yes—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C412yes—
41C32×C4⋊C4C2×C412yes—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—42no—
46C4⋊(C3⋊Dic3)Q812yes—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3—42no—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53#1918—91noSylow
54C22×C3×C8C2×D314yes—
55C2×C3×C4⋊C4C2×D314yes—
56C2×C3×C4⋊C4C2×D314yes—
57C2×C4⋊Dic3—34no—
58C2×C4⋊Dic3—34no—
59C2×C4⋊Dic3—64no—
60C2×C4×Dic3—34no—
61C2×C4×Dic3—64no—
62C22×C3⋊C8—34no—
63C3×#107Dic3116yescomplemented
64C3⋊#95—64no—
65C3⋊#95—64no—
66C23×C32C2×D411yescharacteristic
67C2×C32×C4—22no—
68C2×C32×C4—22no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4C22×C411yescharacteristic
74C2×C32×C4C2×Q811yescharacteristic
75C2×C32×C4#4111yescharacteristic
76C2×C32×C4#4111yescharacteristic
77C2×C32×C4#4111yescharacteristic
78C2×C32×C4#4111yescharacteristic
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3D812yes—
91C32×C8—22no—
92C3⋊(C3⋊C8)—41no—
93C2×#107C3⋊D311yescharacteristic
94#389—91no—
95C4×C4⋊C4—91no—
96#340—91no—
97#340—91no—
98#340—91no—
99#336—91no—
100C22×C3×C4—24no—
101C22×C3×C4—24no—
102C22×C3×C4C22×D314yes—
103C22×Dic3—34no—
104C22×Dic3—34no—
105C22×Dic3—64no—
106C22×Dic3—64no—
107C2×C3×C8—24no—
108C2×C3×C8—24no—
109C2×C3×C8C2×Dic318yes—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4C2×Dic318yes—
113C3×C4⋊C4C2×Dic318yes—
114C4⋊Dic3—38no—
115C4⋊Dic3—64no—
116C4⋊Dic3—64no—
117C4⋊Dic3—64no—
118C4⋊Dic3—128no—
119C4×Dic3—64no—
120C4×Dic3—64no—
121C4×Dic3—128no—
122C2×C3⋊C8—64no—
123C2×C3⋊C8—64no—
124C2×C3⋊C8—64no—
125C22×C32C4×D411yescharacteristic
126C22×C32C22⋊Q811yescharacteristic
127C22×C32#12311yescharacteristic
128C22×C32C2×D811yescharacteristic
129C22×C32#13511yescharacteristic
130C22×C32#13711yescharacteristic
131C22×C32#13711yescharacteristic
132C32×C4—42no—
133C32×C4—42no—
134C32×C4#11711yescharacteristic
135C32×C4C4×Q811yescharacteristic
136C32×C4#12511yescharacteristic
137C32×C4#12611yescharacteristic
138C3⋊Dic3—22no—
139C3⋊Dic3—42no—
140C3⋊Dic3—41no—
141C3⋊Dic3—81no—
142C22×C8—91no—
143C22×C8C2×C3⋊D311yescharacteristic
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—181no—
147C2×C4⋊C4C2×C3⋊D311yescharacteristic
148C2×C4⋊C4C2×C3⋊D311yescharacteristic
149C2×C42—91no—
150C2×C42—181no—
151#107C3⋊Dic314yescomplemented
152#95—181no—
153#95—181no—
154C23×C3D3×D414yes—
155C2×C3×C4—28no—
156C2×C3×C4—28no—
157C2×C3×C4—44no—
158C2×C3×C4—44no—
159C2×C3×C4—44no—
160C2×C3×C4—44no—
161C2×C3×C4#23514yes—
162C2×C3×C4#23514yes—
163C2×C3×C4#23714yes—
164C2×C3×C4D3×Q814yes—
165C2×C3×C4#23914yes—
166C2×C3×C4C22×Dic314yes—
167C2×Dic3—38no—
168C2×Dic3—64no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—68no—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—124no—
175C2×Dic3—124no—
176C2×Dic3—124no—
177C2×Dic3—124no—
178C2×Dic3—124no—
179C3×C8—28no—
180C3⋊C8—124no—
181C2×C32#38711yescharacteristic
182C2×C32C4×D811yescharacteristic
183C2×C32#44111yescharacteristic
184C2×C32#47411yescharacteristic
185C2×C32#47911yescharacteristic
186C2×C32#48011yescharacteristic
187C2×C32#48511yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—181no—
193C22×C4—181no—
194C22×C4C22×C3⋊D311yescharacteristic
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—181no—
198C2×C8—181no—
199C2×C8—181no—
200C2×C8C2×C3⋊Dic312yes—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—92no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4—362no—
208C4⋊C4C2×C3⋊Dic312yes—
209C4⋊C4C2×C3⋊Dic312yes—
210C42—181no—
211C42—181no—
212C42—362no—
213C22×C3#89414yes—
214C22×C3#89614yes—
215C22×C3D3×D814yes—
216C22×C3#91214yes—
217C22×C3#91814yes—
218C22×C3#91814yes—
219C22×C3D4×Dic314yes—
220C3×C4—48no—
221C3×C4—48no—
222C3×C4#88914yes—
223C3×C4#89814yes—
224C3×C4#92614yes—
225C3×C4Q8×Dic314yes—
226Dic3—68no—
227Dic3—124no—
228Dic3—128no—
229Dic3—244no—
230C32#191811yescharacteristic, complemented, Sylow
231C23D4×C3⋊D311yescharacteristic
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—92no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—182no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4—361no—
250C2×C4#382811yescharacteristic
251C2×C4#382811yescharacteristic
252C2×C4#383011yescharacteristic
253C2×C4Q8×C3⋊D311yescharacteristic
254C2×C4#383211yescharacteristic
255C2×C4C22×C3⋊Dic311yescharacteristic
256C8—22no—
257C8—361no—
258C2×C3#487714yes—
259C2×C3#488214yes—
260C2×C3#488814yes—
261C2×C3#489014yes—
262C2×C3#498014yes—
263C2×C3Dic3×D814yes—
264C2×C3#518414yes—
265C22#6410311yescharacteristic
266C22#6410511yescharacteristic
267C22D8×C3⋊D311yescharacteristic
268C22#6412111yescharacteristic
269C22#6412711yescharacteristic
270C22#6412711yescharacteristic
271C22D4×C3⋊Dic311yescharacteristic
272C4—42no—
273C4—42no—
274C4—182no—
275C4—361no—
276C4—362no—
277C4—721no—
278C4#6409811yescharacteristic
279C4#6410711yescharacteristic
280C4#6413511yescharacteristic
281C4Q8×C3⋊Dic311yescharacteristic
282C3#7060914yescomplemented
283C2#1059257611yescharacteristic
284C2#1059258111yescharacteristic
285C2#1059258711yescharacteristic
286C2#1059258911yescharacteristic
287C2#1059267911yescharacteristic
288C2D8×C3⋊Dic311yescharacteristic
289C2#1059288311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#107C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#107C3⋊D3
hypocenterC32#1918
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
18. C32×#107C4semidirect
63. C3×#107Dic3semidirect
151. #107C3⋊Dic3semidirect
230. C32#1918semidirect
282. C3#70609semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1072
#105926832
C4⋊C4×C3⋊Dic32
#105894172
#105894162
#105893952
#706093