Finite Group Databasebeta

← #11790174

Subgroups — #11790174

Order 1152.

553 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63630C211yesmaximal, characteristic
2C3×#4928C212yesmaximal
3C2×#63576C211yesmaximal, characteristic
4C2×#63574C211yesmaximal, characteristic
5#10589163C212yesmaximal
6#69620—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×Dic3⋊C4—22no—
13#63630—22no—
14C3×C3⋊#95—22no—
15#63576C414yescomplemented
16#63574—22no—
17C3×#389—32no—
18C2×#808—32no—
19C2×#807—32no—
20#4928D312yes—
21C2×#803—32no—
22C2×#803—61no—
23#4529—32no—
24#4529—32no—
25C22×C32×C4D412yes—
26C22×C32×C4C2311yescharacteristic
27C22×C3×Dic3—22no—
28C22×C3×Dic3—22no—
29C32×C42—21no—
30C32×C42—21no—
31C2×C3⋊(C3⋊C8)—21no—
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)C2×C412yes—
34C2×C3⋊(C3⋊C8)D412yes—
35C2×C3⋊(C3⋊C8)Q812yes—
36C2×C3⋊(C3⋊C8)Q812yes—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3C2×C414yes—
41C3×Dic3⋊C4—44no—
42#1943—91noSylow
43C2×C3×C4⋊C4—32no—
44C2×C3×C4⋊C4—32no—
45C2×C3×C4⋊C4—62no—
46C2×C3×C42—21no—
47C2×C3×C42C2×D312yes—
48C2×C4⋊Dic3C2×D312yes—
49C2×C4⋊Dic3C2×D312yes—
50C2×Dic3⋊C4—22no—
51C22×C3⋊C8—32no—
52C22×C3⋊C8—32no—
53C22×C3⋊C8—61no—
54C22×C3⋊C8—61no—
55C3×#95—62no—
56C3⋊#95—22no—
57#808—64no—
58#807—38no—
59#803—64no—
60#803—64no—
61C23×C32C2×D411yescharacteristic
62C2×C32×C4—22no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4C22×C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×Q811yescharacteristic
68C2×C32×C4C2×Q811yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C3×Dic3—24no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77C3⋊(C3⋊C8)—22no—
78C3⋊(C3⋊C8)C4⋊C414yescomplemented
79C2×#107—91no—
80C2×#106—91no—
81C2×#97—91no—
82#389—32no—
83#340—92no—
84C22×C3×C4—22no—
85C22×C3×C4—21no—
86C22×C3×C4—62no—
87C22×C3×C4—62no—
88C22×C3×C4#6712yes—
89C22×C3×C4#6712yes—
90C22×C3×C4C22×D312yes—
91C22×Dic3—22no—
92C22×Dic3—22no—
93C3×C4⋊C4—34no—
94C3×C4⋊C4—62no—
95C3×C4⋊C4—62no—
96C3×C4⋊C4—62no—
97C3×C4⋊C4—124no—
98C3×C42—22no—
99C3×C42—22no—
100C3×C42—22no—
101C3×C42—22no—
102C4⋊Dic3—22no—
103C4⋊Dic3—22no—
104C4⋊Dic3—22no—
105C4⋊Dic3C4×D314yes—
106Dic3⋊C4—44no—
107C2×C3⋊C8—34no—
108C2×C3⋊C8—34no—
109C2×C3⋊C8—34no—
110C2×C3⋊C8—34no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113C2×C3⋊C8—62no—
114C2×C3⋊C8—62no—
115C2×C3⋊C8—62no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8—62no—
119C22×C32C4×D411yescharacteristic
120C22×C32#12111yescharacteristic
121C22×C32C4⋊Q811yescharacteristic
122C22×C32AGL(1,ℤ/8)12yes—
123C22×C32#13712yes—
124C32×C4—42no—
125C32×C4C2×C4⋊C411yescharacteristic
126C32×C4C4×Q811yescharacteristic
127C32×C4C22⋊Q811yescharacteristic
128C32×C4#12511yescharacteristic
129C3×Dic3—44no—
130C3×Dic3—82no—
131C22×C8—91no—
132C22×C8—91no—
133C2×C4⋊C4—32no—
134C2×C4⋊C4—32no—
135C2×C4⋊C4—62no—
136C2×C42D3211yescharacteristic
137#107—94no—
138#106—182no—
139#97—182no—
140#95—62no—
141C23×C3—21no—
142C23×C3C2×#6712yes—
143C2×C3×C4—24no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—42no—
157C2×C3×C4—42no—
158C2×C3×C4—64no—
159C2×C3×C4—122no—
160C2×C3×C4—122no—
161C2×C3×C4—122no—
162C2×C3×C4—122no—
163C2×C3×C4—122no—
164C2×C3×C4C2×C4×D312yes—
165C2×C3×C4#23512yes—
166C2×C3×C4D3×D412yes—
167C2×C3×C4#23712yes—
168C2×C3×C4D3×Q812yes—
169C2×C3×C4D3×Q812yes—
170C2×Dic3—24no—
171C2×Dic3—42no—
172C2×Dic3—42no—
173C2×Dic3—42no—
174C2×Dic3—42no—
175C2×Dic3—42no—
176C3⋊C8—38no—
177C3⋊C8—64no—
178C3⋊C8—64no—
179C3⋊C8—64no—
180C2×C32#38911yescharacteristic
181C2×C32#44111yescharacteristic
182C2×C32#44211yescharacteristic
183C2×C32#46812yes—
184C2×C32#50112yes—
185C22×C4—62no—
186C22×C4—62no—
187C22×C4#62512yes—
188C22×C4C2×D3211yescharacteristic
189C2×C8—92no—
190C2×C8—92no—
191C2×C8—92no—
192C2×C8—92no—
193C2×C8—181no—
194C2×C8—181no—
195C4⋊C4—34no—
196C4⋊C4—62no—
197C4⋊C4—62no—
198C4⋊C4—62no—
199C4⋊C4—124no—
200C42—21no—
201C42—21no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3C4×#6712yes—
208C22×C3#93212yes—
209C22×C3#93912yes—
210C22×C3#94212yes—
211C22×C3#94412yes—
212C22×C3#94912yes—
213C22×C3#95112yes—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—44no—
219C3×C4—42no—
220C3×C4—42no—
221C3×C4—124no—
222C3×C4—242no—
223C3×C4#88712yes—
224C3×C4#88912yes—
225C3×C4D3×C4⋊C412yes—
226C3×C4#89612yes—
227Dic3—44no—
228Dic3—82no—
229C32#194311yescharacteristic, complemented, Sylow
230C23C2×#62511yescharacteristic
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—64no—
235C2×C4—122no—
236C2×C4—122no—
237C2×C4—122no—
238C2×C4—122no—
239C2×C4—122no—
240C2×C4#379711yescharacteristic
241C2×C4#379711yescharacteristic
242C2×C4#379811yescharacteristic
243C2×C4C4×D3211yescharacteristic
244C2×C4#380511yescharacteristic
245C2×C4#381111yescharacteristic
246C8—94no—
247C8—182no—
248C2×C3—21no—
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—22no—
253C2×C3#497612yes—
254C2×C3#501412yes—
255C2×C3#503012yes—
256C2×C3#504212yes—
257C2×C3#504912yes—
258C2×C3#506412yes—
259C2×C3#508112yes—
260C22#6382312yes—
261C22#6382712yes—
262C22#6387311yescharacteristic
263C22C4×#62511yescharacteristic
264C22#6398011yescharacteristic
265C4—42no—
266C4—124no—
267C4—242no—
268C4#6383811yescharacteristic
269C4#6386511yescharacteristic
270C4#6387011yescharacteristic
271C4#6388311yescharacteristic
272C3—21no—
273C3#6962012yescomplemented
274C2#1059031512yes—
275C2#1059034411yescharacteristic
276C2#1059038111yescharacteristic
277C2#1059118012yes—
278C2#1059133711yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1943
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
15. #63576C4semidirect
78. C3⋊(C3⋊C8)C4⋊C4semidirect
229. C32#1943semidirect
273. C3#69620semidirect

Maximal subgroups

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

subgroupindex
C2×#636302
C3×#49282
C2×#635762
C2×#635742
#105891632
#696203