Finite Group Databasebeta

← #11808855

Subgroups — #11808855

Order 1152.

1097 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 1097 conjugacy classes of subgroups — too many to draw. Only its 268 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×C4×Dic6C212yesmaximal
2#10592631C211yesmaximal, characteristic
3#10591344C214yesmaximal
4C4×#3724C214yesmaximal
5#10591214C214yesmaximal
6#82467—32nomaximal
7C22×C3×Dic6C2212yes—
8C2×C32×C42C2211yescharacteristic
9C2×C4×C3⋊Dic3C2212yes—
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×Dic3⋊C4C2214yes—
12C2×C3×C4×Dic3C2214yes—
13C3×C4×Dic6—28no—
14C2×#3724C2218yes—
15#63658C2214yes—
16#63579C2214yes—
17#63579C2214yes—
18C2×C3×C4×Q8—32no—
19C2×C4×Dic6D312yes—
20#5230—34no—
21#4983—34no—
22#4981—34no—
23#4979—34no—
24#4932—32no—
25#4932—61no—
26C4×Dic3⋊C4—38no—
27C22×C32×C4C2312yes—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3C2314yes—
30C22×C3×Dic3C2314yes—
31C22×C3×Dic3C2314yes—
32C2×C3×Dic6—24no—
33C2×C3×Dic6—28no—
34C32×C42D414yes—
35C4×C3⋊Dic3Q818yescomplemented
36C3×C4⋊Dic3—24no—
37C3×Dic3⋊C4—28no—
38C3×C4×Dic3—28no—
39#3724—216no—
40#2399—91noSylow
41C22×C3×Q8—32no—
42C22×Dic6C2×D312yes—
43C3×C4×Q8—68no—
44C2×C3×C4⋊C4—34no—
45C2×C3×C4⋊C4—32no—
46C2×C3×C42—21no—
47C2×C3×C42—34no—
48C2×C3×C42C2×D312yes—
49C2×C4⋊Dic3C2×D312yes—
50C2×Dic3⋊C4—38no—
51C2×Dic3⋊C4—38no—
52C2×Dic3⋊C4C2×D314yes—
53C2×C4×Dic3—34no—
54C2×C4×Dic3—62no—
55C2×C4×Dic3C2×D314yes—
56C4×Dic6—28no—
57C3⋊#95—34no—
58C3⋊#95—34no—
59C3⋊#95—38no—
60C3⋊#95—38no—
61C3⋊#95—64no—
62C23×C32C2411yescharacteristic
63C2×C32×C4—24no—
64C2×C32×C4C2×D414yes—
65C2×C32×C4C2×D412yes—
66C2×C32×C4C2×Q814yes—
67C2×C3⋊Dic3—28no—
68C2×C3⋊Dic3C2×Q818yes—
69C2×C3×Dic3—24no—
70C2×C3×Dic3—24no—
71C2×C3×Dic3—24no—
72C2×C3×Dic3—28no—
73C2×C3×Dic3#4118yes—
74C3×Dic6—216no—
75C2×C4×Q8—32no—
76#398—94no—
77#395—94no—
78C4×C4⋊C4—94no—
79#376—91no—
80C2×C3×Q8—68no—
81C2×C3×Q8—64no—
82C22×C3×C4—22no—
83C22×C3×C4—21no—
84C22×C3×C4—34no—
85C22×C3×C4—34no—
86C22×C3×C4C22×D312yes—
87C22×C3×C4C22×D312yes—
88C22×C3×C4C22×D312yes—
89C22×Dic3—38no—
90C22×Dic3—64no—
91C22×Dic3C22×D314yes—
92C22×Dic3C22×D314yes—
93C2×Dic6—24no—
94C2×Dic6—28no—
95C3×C4⋊C4—68no—
96C3×C4⋊C4—64no—
97C3×C42—24no—
98C3×C42—68no—
99C3×C42#6718yes—
100C4⋊Dic3—24no—
101Dic3⋊C4—28no—
102Dic3⋊C4—616no—
103Dic3⋊C4—616no—
104C4×Dic3—28no—
105C4×Dic3—316no—
106C4×Dic3—68no—
107C22×C32C22×D411yescharacteristic
108C22×C32C22×Q812yes—
109C22×C32C2×#4114yes—
110C32×C4—24no—
111C32×C4C4⋊Q814yes—
112C3⋊Dic3—28no—
113C3×Dic3—28no—
114C3×Dic3—44no—
115C22×Q8—32no—
116C4×Q8—68no—
117C2×C4⋊C4—34no—
118C2×C4⋊C4—32no—
119C2×C4⋊C4—98no—
120C2×C42—34no—
121C2×C42—92no—
122C2×C42D3211yescharacteristic
123#95—94no—
124#95—94no—
125#95—94no—
126C23×C3—21no—
127C23×C3C23×D312yes—
128C3×Q8—616no—
129C2×C3×C4—24no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—22no—
133C2×C3×C4—24no—
134C2×C3×C4—38no—
135C2×C3×C4—44no—
136C2×C3×C4—64no—
137C2×C3×C4—64no—
138C2×C3×C4—68no—
139C2×C3×C4—64no—
140C2×C3×C4D3×Q818yes—
141C2×C3×C4C2×#6714yes—
142C2×C3×C4C2×#6714yes—
143C2×C3×C4C2×#6714yes—
144C2×Dic3—24no—
145C2×Dic3—24no—
146C2×Dic3—28no—
147C2×Dic3—24no—
148C2×Dic3—316no—
149C2×Dic3—68no—
150C2×Dic3—68no—
151C2×Dic3—68no—
152C2×Dic3—128no—
153C2×Dic3#23518yes—
154Dic6—216no—
155C2×C32#52512yes—
156C2×C32C2×C4⋊Q811yescharacteristic
157C2×C32#53314yes—
158C2×Q8—68no—
159C2×Q8—64no—
160C22×C4—34no—
161C22×C4—34no—
162C22×C4—94no—
163C22×C4C2×D3212yes—
164C22×C4C2×D3211yescharacteristic
165C4⋊C4—68no—
166C4⋊C4—64no—
167C4⋊C4—1816no—
168C42—68no—
169C42—98no—
170C42#62514yes—
171C22×C3—22no—
172C22×C3—24no—
173C22×C3—21no—
174C22×C3C2×#23514yes—
175C22×C3C2×D3×Q814yes—
176C22×C3D3×#4114yes—
177C22×C3C22×#6712yes—
178C3×C4—24no—
179C3×C4—24no—
180C3×C4—24no—
181C3×C4—44no—
182C3×C4—68no—
183C3×C4—124no—
184C3×C4#94418yes—
185Dic3—28no—
186Dic3—44no—
187Dic3—616no—
188Dic3—128no—
189C32#239911yescharacteristic, complemented, Sylow
190C23C22×D3211yescharacteristic
191Q8—616no—
192C2×C4—24no—
193C2×C4—38no—
194C2×C4—64no—
195C2×C4—64no—
196C2×C4—68no—
197C2×C4—64no—
198C2×C4—98no—
199C2×C4—188no—
200C2×C4#379714yes—
201C2×C4C2×#62514yes—
202C2×C4C2×#62512yes—
203C2×C3—21no—
204C2×C3—24no—
205C2×C3—22no—
206C2×C3#557818yes—
207C2×C3#579112yes—
208C2×C3C2×#94412yes—
209C2×C3#582812yes—
210C22C2×#379712yes—
211C22D3×#23514yes—
212C22C22×#62511yescharacteristic
213C4—24no—
214C4—68no—
215C4—124no—
216C4—188no—
217C4#6387314yes—
218C3—21no—
219C3#8246712yescomplemented
220C2#1059393514yes—
221C2C2×#6387311yescharacteristic
222C2#1059502212yes—
subgroupG/H
centerC22×C4C2×D32
commutator, socle, prime radical, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
35. C4×C3⋊Dic3Q8semidirect
189. C32#2399semidirect
219. C3#82467semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
#105926312
#105913442
C4×#37242
#105912142
#824673