Finite Group Databasebeta

← #11785745

Subgroups — #11785745

Order 1152.

639 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 639 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C2×C3×#926C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4#10589167C214yesmaximal, complemented
5#71589—31nomaximal
6#69974—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×#3748C2212yes—
9C2×C3×#217C412yes—
10C3×#926—22no—
11C3×#926—22no—
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×C4×Dic3C412yes—
14C2×C3×#208C2212yes—
15#63657—22no—
16C3×#830—22no—
17C2×C3×#117—31no—
18C2×#926D311yescharacteristic
19C3×#407—31no—
20#5207—31no—
21#5207—31no—
22#5207—61no—
23#5207D311yescharacteristic
24#4554—34no—
25#4530—34no—
26C24×C32C2×C411yescharacteristic
27C22×C32×C4—24no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D412yes—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3×Dic3C2×C414yes—
33#3748—24no—
34C2×C3⋊(C3⋊C8)—22no—
35C3×#217—24no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C3×C4×Dic3—24no—
39C3×#208—24no—
40C2×C3×C3⋊C8—22no—
41#1822—91noSylow
42C23×C3×C4—21no—
43C23×C3×C4C2×D311yescharacteristic
44C23×C3×C4C2×D311yescharacteristic
45C2×C3×M16—32no—
46C3×#117—62no—
47C3×#117—62no—
48C2×C3×C4⋊C4—32no—
49C2×C3×C22⋊C4—32no—
50C2×C3×C42—32no—
51C2×#217Dic312yes—
52#926—22no—
53#926—22no—
54C2×C4⋊Dic3C2×D312yes—
55C2×C4×Dic3Dic312yes—
56C2×#208—32no—
57C2×#208—32no—
58C2×#208—62no—
59C2×#208C2×D312yes—
60C3×C22⋊C8—62no—
61#830—22no—
62#830—64no—
63#830—62no—
64#830—62no—
65C23×C32—22no—
66C23×C32—42no—
67C23×C32C22⋊C412yes—
68C23×C32C22×C411yescharacteristic
69C2×C32×C4—22no—
70C2×C32×C4—24no—
71C2×C32×C4—24no—
72C2×C32×C4C22⋊C412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4#4114yes—
76C2×C3×Dic3—24no—
77C2×C3×Dic3—44no—
78C3⋊(C3⋊C8)—42no—
79C3×C3⋊C8—42no—
80C2×#117—31no—
81#407—31no—
82#407—91no—
83#343—94no—
84C24×C3—21no—
85C24×C3C4×D311yescharacteristic
86C24×C3C2×Dic311yescharacteristic
87C22×C3×C4—24no—
88C22×C3×C4—24no—
89C22×C3×C4—21no—
90C22×C3×C4—22no—
91C22×C3×C4—22no—
92C22×C3×C4—21no—
93C22×C3×C4—34no—
94C22×C3×C4—44no—
95C22×C3×C4C4×D311yescharacteristic
96C22×C3×C4D1212yes—
97C22×C3×C4C2×Dic311yescharacteristic
98C22×C3×C4#6712yes—
99C22×C3×C4#6712yes—
100C22×C3×C4#6712yes—
101C22×C3×C4C22×D311yescharacteristic
102C22×C3×C4C22×D311yescharacteristic
103C22×Dic3C2×Dic314yes—
104C3×M16—64no—
105C2×C3×C8—62no—
106C3×C4⋊C4—62no—
107C3×C4⋊C4—62no—
108C3×C22⋊C4—64no—
109C3×C42—64no—
110#217—24no—
111C4⋊Dic3—22no—
112C4⋊Dic3—22no—
113C4×Dic3—24no—
114#208—24no—
115#208—64no—
116#208—64no—
117#208—124no—
118C2×C3⋊C8—22no—
119C2×C3⋊C8—64no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122C22×C32—22no—
123C22×C32—22no—
124C22×C32—22no—
125C22×C32—22no—
126C22×C32—44no—
127C22×C32C2×C22⋊C411yescharacteristic
128C22×C32#11712yes—
129C32×C4—22no—
130C32×C4#12312yes—
131C32×C4#12312yes—
132C3×Dic3—44no—
133C23×C4D3211yescharacteristic
134C2×M16—32no—
135C2×M16—92no—
136#117—62no—
137#117—62no—
138C2×C4⋊C4—32no—
139C2×C22⋊C4—32no—
140C2×C42—32no—
141C22⋊C8—62no—
142C22⋊C8—182no—
143C23×C3—22no—
144C23×C3—22no—
145C23×C3—22no—
146C23×C3—21no—
147C23×C3—42no—
148C23×C3—42no—
149C23×C3—42no—
150C23×C3—44no—
151C23×C3(C2×D3)⋊C412yes—
152C23×C3#21712yes—
153C23×C3C2×C4×D311yescharacteristic
154C23×C3C22×Dic311yescharacteristic
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—22no—
162C2×C3×C4—24no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4—42no—
168C2×C3×C4—64no—
169C2×C3×C4—124no—
170C2×C3×C4(C2×D3)⋊C412yes—
171C2×C3×C4#21712yes—
172C2×C3×C4C2×D1211yescharacteristic
173C2×C3×C4#23514yes—
174C2×C3×C4#23714yes—
175C2×C3×C4C2×#6711yescharacteristic
176C2×C3×C4C2×#6711yescharacteristic
177C2×C3×C4C2×#6711yescharacteristic
178C2×Dic3—24no—
179C2×Dic3—44no—
180C3×C8—122no—
181C3⋊C8—42no—
182C3⋊C8—124no—
183C3⋊C8—122no—
184C3⋊C8—122no—
185C2×C32—22no—
186C2×C32—42no—
187C2×C32#38111yescharacteristic
188C2×C32#41312yes—
189C24D3×Dic311yescharacteristic
190C22×C4—24no—
191C22×C4—34no—
192C22×C4D3×Dic311yescharacteristic
193C22×C4#62512yes—
194C22×C4#62612yes—
195C22×C4C2×D3211yescharacteristic
196M16—64no—
197M16—184no—
198C2×C8—62no—
199C2×C8—182no—
200C4⋊C4—62no—
201C4⋊C4—62no—
202C22⋊C4—64no—
203C42—64no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—24no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—21no—
215C22×C3—42no—
216C22×C3—42no—
217C22×C3—42no—
218C22×C3—44no—
219C22×C3—44no—
220C22×C3—48no—
221C22×C3#87712yes—
222C22×C3#92612yes—
223C22×C3C2×(C2×D3)⋊C411yescharacteristic
224C22×C3C2×#21711yescharacteristic
225C3×C4—22no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—22no—
229C3×C4—42no—
230C3×C4—124no—
231C3×C4#88612yes—
232C3×C4#92912yes—
233C3×C4#92912yes—
234C3×C4#93512yes—
235Dic3—44no—
236C32#182211yescharacteristic, complemented, Sylow
237C23—22no—
238C23—42no—
239C23(C2×D3)⋊Dic312yes—
240C23C2×D3×Dic311yescharacteristic
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—24no—
244C2×C4—64no—
245C2×C4—124no—
246C2×C4(C2×D3)⋊Dic312yes—
247C2×C4#380414yes—
248C2×C4C2×#62511yescharacteristic
249C2×C4C2×#62611yescharacteristic
250C8—122no—
251C8—362no—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—21no—
256C2×C3—42no—
257C2×C3—44no—
258C2×C3—42no—
259C2×C3—42no—
260C2×C3#494311yescharacteristic
261C2×C3#513212yes—
262C2×C3#521111yescharacteristic
263C2×C3#523712yes—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—22no—
268C22—44no—
269C22#6395512yes—
270C22C2×(C2×D3)⋊Dic311yescharacteristic
271C4—22no—
272C4—124no—
273C4#6396112yes—
274C4#6396612yes—
275C3—21no—
276C3#6997411yescharacteristic, complemented
277C3#7158911yescharacteristic, complemented
278C2—22no—
279C2—42no—
280C2#1059107612yes—
281C2#1059169611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10589167C2semidirect
236. C32#1822semidirect
276. C3#69974semidirect
277. C3#71589semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
#105929062
C3×#52072
#105891672
#715893
#699743