Finite Group Databasebeta

← #11773487

Subgroups — #11773487

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic
2C2×C3×C3⋊#95C212yesmaximal
3C2×#63579C214yesmaximal
4#69424—32nomaximal
5C23×C32×C4C2211yescharacteristic
6C23×C3⋊Dic3C2212yes—
7C22×#634—24no—
8C22×#634—28no—
9C22×#634C414yescomplemented
10C23×C3×Dic3C2214yes—
11C3×C3⋊#95—24no—
12#63579—28no—
13C23×Dic6—32no—
14C23×Dic6—61no—
15C2×C3×#95—32no—
16C2×C3⋊#95—38no—
17C2×C3⋊#95D312yes—
18C24×C32C2311yescharacteristic
19C22×C32×C4—24no—
20C22×C32×C4C2×C412yes—
21C22×C32×C4D414yes—
22C22×C3⋊Dic3—24no—
23C22×C3⋊Dic3—24no—
24C22×C3⋊Dic3C2×C414yes—
25C22×C3⋊Dic3D418yes—
26C2×#634—232no—
27C2×#634—28no—
28C2×#634—216no—
29C22×C3×Dic3—28no—
30C22×C3×Dic3—24no—
31C22×C3×Dic3—24no—
32C22×C3×Dic3—28no—
33C22×C3×Dic3Q818yescomplemented
34#1446—91noSylow
35C23×C3×C4—21no—
36C23×C3×C4—34no—
37C23×C3×C4C2×D312yes—
38C23×Dic3—34no—
39C23×Dic3—62no—
40C23×Dic3C2×D314yes—
41C22×Dic6—38no—
42C22×Dic6—64no—
43C22×Dic6—616no—
44C22×Dic6—616no—
45C22×Dic6—68no—
46C22×Dic6—64no—
47C22×Dic6—64no—
48C3×#95—64no—
49C3⋊#95—24no—
50C3⋊#95—616no—
51C23×C32C22×C411yescharacteristic
52C23×C32C2×D412yes—
53C23×C32C2×D414yes—
54C23×C32C2×Q814yes—
55C23×C32#4114yes—
56C2×C32×C4—24no—
57C2×C32×C4—28no—
58C2×C32×C4C22⋊C414yes—
59C2×C3⋊Dic3—24no—
60C2×C3⋊Dic3—24no—
61C2×C3⋊Dic3—216no—
62C2×C3⋊Dic3C22⋊C418yes—
63#634—232no—
64C2×C3×Dic3—216no—
65C2×C3×Dic3—28no—
66C2×C3×Dic3—44no—
67C2×C3×Dic3—48no—
68C2×C3×Dic3—44no—
69C23×Q8—91no—
70C2×#95—32no—
71C2×#95—94no—
72C24×C3—21no—
73C24×C3C22×D312yes—
74C22×C3×C4—28no—
75C22×C3×C4—28no—
76C22×C3×C4—22no—
77C22×C3×C4—24no—
78C22×C3×C4—38no—
79C22×C3×C4—64no—
80C22×C3×C4—68no—
81C22×C3×C4—68no—
82C22×C3×C4—64no—
83C22×C3×C4C4×D314yes—
84C22×C3×C4D1214yes—
85C22×C3×C4#6714yes—
86C22×Dic3—24no—
87C22×Dic3—28no—
88C22×Dic3—28no—
89C22×Dic3—24no—
90C22×Dic3—38no—
91C22×Dic3—316no—
92C22×Dic3—64no—
93C22×Dic3—68no—
94C22×Dic3—68no—
95C22×Dic3—68no—
96C22×Dic3—64no—
97C22×Dic3—68no—
98C22×Dic3—64no—
99C22×Dic3Dic618yescomplemented
100C2×Dic6—632no—
101C2×Dic6—632no—
102C2×Dic6—664no—
103C2×Dic6—632no—
104C2×Dic6—632no—
105C2×Dic6—616no—
106C2×Dic6—616no—
107C22×C32C2×C22⋊C412yes—
108C22×C32C2×C22⋊C411yescharacteristic
109C22×C32C4×Q814yes—
110C22×C32#12014yes—
111C22×C32C22⋊Q818yes—
112C22×C32C22⋊Q814yes—
113C22×C32#12412yes—
114C22×C32#12414yes—
115C22×C32C4⋊Q812yes—
116C22×C32C4⋊Q814yes—
117C32×C4—24no—
118C3⋊Dic3—28no—
119C3×Dic3—48no—
120C22×Q8—94no—
121C22×Q8—188no—
122C22×Q8—184no—
123C23×C4—34no—
124C23×C4—92no—
125C23×C4D3211yescharacteristic
126#95—64no—
127#95—188no—
128C23×C3—24no—
129C23×C3—24no—
130C23×C3—21no—
131C23×C3—22no—
132C23×C3—24no—
133C23×C3C2×Dic614yes—
134C23×C3C2×C4×D312yes—
135C23×C3C2×D1212yes—
136C23×C3#23514yes—
137C23×C3D3×D418yes—
138C23×C3#23714yes—
139C23×C3D3×Q814yes—
140C23×C3C2×#6712yes—
141C2×C3×C4—28no—
142C2×C3×C4—216no—
143C2×C3×C4—28no—
144C2×C3×C4—28no—
145C2×C3×C4—28no—
146C2×C3×C4—24no—
147C2×C3×C4—616no—
148C2×C3×C4—68no—
149C2×C3×C4—124no—
150C2×C3×C4—124no—
151C2×C3×C4—128no—
152C2×C3×C4(C2×D3)⋊C418yes—
153C2×Dic3—216no—
154C2×Dic3—28no—
155C2×Dic3—316no—
156C2×Dic3—48no—
157C2×Dic3—44no—
158C2×Dic3—44no—
159C2×Dic3—68no—
160C2×Dic3—68no—
161C2×Dic3—68no—
162C2×Dic3—632no—
163C2×Dic3—68no—
164C2×Dic3—616no—
165C2×Dic3—68no—
166C2×Dic3—616no—
167Dic6—664no—
168Dic6—664no—
169C2×C32#37911yescharacteristic
170C2×C32#39114yes—
171C2×C32#39112yes—
172C2×C32#39314yes—
173C2×C32#39514yes—
174C24C2×D3211yescharacteristic
175C2×Q8—1816no—
176C2×Q8—1832no—
177C2×Q8—188no—
178C22×C4—24no—
179C22×C4—38no—
180C22×C4—64no—
181C22×C4—68no—
182C22×C4—64no—
183C22×C4—68no—
184C22×C4—94no—
185C22×C4—98no—
186C22×C4—184no—
187C22×C4—184no—
188C22×C4#62412yes—
189C22×C4#62614yes—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—24no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—28no—
196C22×C3—24no—
197C22×C3—21no—
198C22×C3—22no—
199C22×C3—24no—
200C22×C3C4×Dic614yes—
201C22×C3#86912yes—
202C22×C3#87512yes—
203C22×C3#87818yes—
204C22×C3D3×C22⋊C414yes—
205C22×C3#88214yes—
206C22×C3#88518yes—
207C22×C3#88714yes—
208C22×C3#88818yes—
209C22×C3#89618yes—
210C22×C3#89714yes—
211C22×C3#92414yes—
212C22×C3C2×(C2×D3)⋊C412yes—
213C22×C3#93612yes—
214C22×C3#93714yes—
215C22×C3#94412yes—
216C3×C4—28no—
217C3×C4—28no—
218C3×C4—128no—
219Dic3—48no—
220Dic3—616no—
221Dic3—616no—
222C32#144611yescharacteristic, complemented, Sylow
223C23D3×Dic614yes—
224C23#379514yes—
225C23C2×#62411yescharacteristic
226C23C2×#62612yes—
227C23#381114yes—
228Q8—1832no—
229C2×C4—24no—
230C2×C4—28no—
231C2×C4—68no—
232C2×C4—616no—
233C2×C4—98no—
234C2×C4—124no—
235C2×C4—128no—
236C2×C4—124no—
237C2×C4—184no—
238C2×C4—184no—
239C2×C4—1816no—
240C2×C4#372214yes—
241C2×C3—24no—
242C2×C3—24no—
243C2×C3—24no—
244C2×C3—21no—
245C2×C3—22no—
246C2×C3#464618yes—
247C2×C3#465614yes—
248C2×C3#467314yes—
249C2×C3#492912yes—
250C2×C3#494714yes—
251C2×C3#495512yes—
252C2×C3#497312yes—
253C2×C3#497914yes—
254C22#6384014yes—
255C22#6384414yes—
256C22#6385714yes—
257C22#6386012yes—
258C22#6386612yes—
259C22#6389618yes—
260C22#6391314yes—
261C22C2×#372211yescharacteristic
262C22#6397412yes—
263C22#6398114yes—
264C4—24no—
265C4—128no—
266C4—188no—
267C3—21no—
268C3#6942412yescomplemented
269C2#1059121312yes—
270C2#1059127314yes—
271C2#1059132214yes—
272C2#1059135414yes—
273C2#1059171411yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1446
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
9. C22×#634C4semidirect
33. C22×C3×Dic3Q8semidirect
99. C22×Dic3Dic6semidirect
222. C32#1446semidirect
268. C3#69424semidirect

Maximal subgroups

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

subgroupindex
C23×#6342
C2×C3×C3⋊#952
C2×#635792
#694243