Finite Group Databasebeta

← C2×#10590381 #11860126

Subgroups — C2×#10590381 #11860126

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C212yesmaximal
2C22×#3718C211yesmaximal, characteristic
3C2×#63630C211yesmaximal, characteristic
4C2×#63574C211yesmaximal, characteristic
5C2×#63565C212yesmaximal
6#10590381C218yesmaximal, direct product factor
7C2×#5030—32nomaximal
8C22×C3×Dic6C2212yes—
9C2×C32×C42C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4—22no—
14C2×C3×C4×Dic3—22no—
15C3×C4×Dic6—24no—
16C3×C4×Dic6C2218yes—
17C2×#3718C418yescomplemented
18C2×#3718C2214yes—
19#63630C2214yes—
20#63574C2214yes—
21#63565C2218yes—
22C2×C3×C4×Q8—32no—
23C22×#216—32no—
24C2×C4×Dic6D312yes—
25C2×#835—32no—
26#5030—316no—
27C2×#810—32no—
28C2×#808—32no—
29C2×#803—32no—
30C2×#803—61no—
31C22×C32×C4D412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3×Dic3—22no—
34C22×C3×Dic3—22no—
35C2×C3×Dic6—22no—
36C2×C3×Dic6—24no—
37C2×C3×Dic6C2×C418yes—
38C2×C3×Dic6C2314yes—
39C32×C42D412yes—
40C32×C42C2312yes—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)C2×C414yes—
43C2×C3⋊(C3⋊C8)C2312yes—
44C2×C3⋊(C3⋊C8)C2312yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3C2314yes—
47C3×Dic3⋊C4—28no—
48C3×C4×Dic3—28no—
49#3718C2×C4116yescomplemented
50C2×#441—91noSylow
51C22×C3×Q8—32no—
52C22×Dic6C2×D312yes—
53C3×C4×Q8—38no—
54C3×C4×Q8—64no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C4⋊C4—62no—
57C2×C3×C42—21no—
58C2×C3×C42—62no—
59C2×C3×C42C2×D312yes—
60C2×#216—316no—
61C2×#216—38no—
62C2×C4⋊Dic3C2×D312yes—
63C2×Dic3⋊C4—22no—
64C2×C4×Dic3—22no—
65C22×C3⋊C8—32no—
66C22×C3⋊C8—32no—
67C22×C3⋊C8—61no—
68C22×C3⋊C8—61no—
69C4×Dic6—24no—
70C4×Dic6C2×D318yes—
71#835—38no—
72#810—38no—
73#808—38no—
74#803—38no—
75#803—64no—
76C23×C32C2×D411yescharacteristic
77C2×C32×C4—24no—
78C2×C32×C4C22×C412yes—
79C2×C32×C4C2×D414yes—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C32×C4C2411yescharacteristic
83C2×C3×Dic3—28no—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—24no—
86C2×C3×Dic3—44no—
87C3×Dic6—28no—
88C3×Dic6—24no—
89C3×Dic6C22×C418yes—
90C3⋊(C3⋊C8)—22no—
91C3⋊(C3⋊C8)C22×C414yes—
92C22×Q16—91no—
93C2×C4×Q8—32no—
94#441—98no—
95C2×#106—91no—
96C2×#103—92no—
97C2×#97—91no—
98C2×C3×Q8—38no—
99C2×C3×Q8—34no—
100C2×C3×Q8—64no—
101C2×C3×Q8—62no—
102C22×C3×C4—22no—
103C22×C3×C4—21no—
104C22×C3×C4—62no—
105C22×C3×C4—62no—
106C22×C3×C4#6712yes—
107C22×C3×C4#6712yes—
108C22×C3×C4C22×D312yes—
109C22×Dic3—22no—
110C22×Dic3—22no—
111C2×Dic6—24no—
112C2×Dic6—22no—
113C2×Dic6C4×D318yes—
114C2×Dic6C22×D314yes—
115C3×C4⋊C4—34no—
116C3×C4⋊C4—68no—
117C3×C4⋊C4—62no—
118C3×C42—22no—
119C3×C42—22no—
120C3×C42—68no—
121C3×C42#6714yes—
122C3×C42C22×D314yes—
123#216—332no—
124C4⋊Dic3—22no—
125C4⋊Dic3C22×D314yes—
126Dic3⋊C4—28no—
127C4×Dic3—28no—
128C2×C3⋊C8—38no—
129C2×C3⋊C8—34no—
130C2×C3⋊C8—34no—
131C2×C3⋊C8—62no—
132C2×C3⋊C8—62no—
133C2×C3⋊C8—64no—
134C2×C3⋊C8—64no—
135C2×C3⋊C8—64no—
136C22×C32C4×D412yes—
137C22×C32#13714yes—
138C22×C32C22×D411yescharacteristic
139C32×C4—24no—
140C32×C4C4×D412yes—
141C32×C4C23×C411yescharacteristic
142C32×C4C2×#4111yescharacteristic
143C3×Dic3—28no—
144C3×Dic3—44no—
145C22×Q8—32no—
146C2×Q16—98no—
147C2×Q16—94no—
148C22×C8—91no—
149C22×C8—91no—
150C4×Q8—38no—
151C4×Q8—64no—
152C2×C4⋊C4—32no—
153C2×C4⋊C4—62no—
154C2×C42—62no—
155C2×C42D3211yescharacteristic
156#106—94no—
157#103—98no—
158#97—94no—
159C23×C3—21no—
160C23×C3C2×#6712yes—
161C3×Q8—38no—
162C3×Q8—68no—
163C3×Q8—64no—
164C2×C3×C4—24no—
165C2×C3×C4—24no—
166C2×C3×C4—21no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—21no—
170C2×C3×C4—24no—
171C2×C3×C4—44no—
172C2×C3×C4—68no—
173C2×C3×C4—64no—
174C2×C3×C4—64no—
175C2×C3×C4—124no—
176C2×C3×C4C2×C4×D314yes—
177C2×C3×C4#23514yes—
178C2×C3×C4C2×#6714yes—
179C2×C3×C4C2×#6714yes—
180C2×C3×C4C2×#6712yes—
181C2×C3×C4C23×D312yes—
182C2×Dic3—28no—
183C2×Dic3—24no—
184C2×Dic3—24no—
185C2×Dic3—44no—
186Dic6—28no—
187Dic6—24no—
188Dic6C2×C4×D318yes—
189C3⋊C8—38no—
190C3⋊C8—64no—
191C3⋊C8—64no—
192C3⋊C8—64no—
193C2×C32#44114yescomplemented
194C2×C32C2×C4×D411yescharacteristic
195C2×C32C2×#13712yes—
196C2×Q8—34no—
197C2×Q8—38no—
198C2×Q8—64no—
199C2×Q8—62no—
200C22×C4—62no—
201C22×C4—62no—
202C22×C4#62512yes—
203C22×C4C2×D3211yescharacteristic
204Q16—916no—
205C2×C8—92no—
206C2×C8—94no—
207C2×C8—92no—
208C2×C8—182no—
209C4⋊C4—34no—
210C4⋊C4—62no—
211C4⋊C4—68no—
212C42—68no—
213C42#62512yes—
214C42C2×D3212yes—
215C22×C3—21no—
216C22×C3—24no—
217C22×C3—22no—
218C22×C3C4×#6714yes—
219C22×C3#94214yes—
220C22×C3#95114yes—
221C22×C3C22×#6712yes—
222C3×C4—24no—
223C3×C4—24no—
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—22no—
227C3×C4—44no—
228C3×C4—68no—
229C3×C4—124no—
230C3×C4C4×#6714yes—
231C3×C4C22×C4×D312yes—
232C3×C4C2×#23512yes—
233Dic3—28no—
234Dic3—44no—
235C32C2×#44111yescharacteristic, complemented, Sylow
236C23C2×#62511yescharacteristic
237Q8—38no—
238Q8—64no—
239Q8—68no—
240C2×C4—24no—
241C2×C4—64no—
242C2×C4—68no—
243C2×C4—64no—
244C2×C4—124no—
245C2×C4#379812yes—
246C2×C4C4×D3212yes—
247C2×C4C2×#62514yes—
248C2×C4C2×#62511yescharacteristic
249C2×C4C22×D3211yescharacteristic
250C8—94no—
251C8—182no—
252C2×C3—24no—
253C2×C3—21no—
254C2×C3—22no—
255C2×C3#503018yescomplemented
256C2×C3C2×C4×#6712yes—
257C2×C3C2×#94212yes—
258C2×C3C2×#95112yes—
259C22#6382714yes—
260C22C4×#62512yes—
261C22C22×#62511yescharacteristic
262C4—24no—
263C4—68no—
264C4—124no—
265C4C4×#62512yes—
266C4C2×#379811yescharacteristic
267C4C2×C4×D3211yescharacteristic
268C3—21no—
269C3C2×#503012yescomplemented
270C2#1059038114yesdirect product factor
271C2C2×#6382712yes—
272C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#441
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. #10590381C2direct (N × H)
17. C2×#3718C4semidirect
49. #3718C2×C4semidirect
193. C2×C32#441semidirect
235. C32C2×#441semidirect
255. C2×C3#5030semidirect
269. C3C2×#5030semidirect
270. C2#10590381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C22×#37182
C2×#636302
C2×#635742
C2×#635652
#105903812
C2×#50303