Finite Group Databasebeta

← #72246812

Subgroups — #72246812

Order 2016.

662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C23×C7×C3⋊D3C211yesmaximal, characteristic
2C2×#92693C212yesmaximal, complemented
3C3×#66636C212yesmaximal, complemented
4#11759226C212yesmaximal, complemented
5D3×C22⋊Dic7—32nomaximal
6C23×C32×C7C2211yescharacteristic
7C22×C7×C3⋊D3—24no—
8C22×C7×C3⋊D3C414yescomplemented
9C22×C7×C3⋊D3C2211yescharacteristic
10C22×C7×C3⋊D3C2211yescharacteristic
11C2×C3×Dic21C2214yescomplemented
12#92693—24no—
13C23×D3×C7—32no—
14C23×D3×C7—61no—
15C2×D3×Dic7—34no—
16#66636D312yescomplemented
17C3×C22⋊Dic7—32no—
18(C2×D3)⋊Dic7—34no—
19#63974—71nomaximal, Hall
20C22×C32×C7—22no—
21C22×C32×C7C2×C412yescomplemented
22C22×C32×C7C2311yescharacteristic
23C2×C7×C3⋊D3—22no—
24C2×C7×C3⋊D3—28no—
25C2×C7×C3⋊D3C2×C412yes—
26C2×C7×C3⋊D3C2×C412yescomplemented
27C2×C7×C3⋊D3D414yes—
28C3×Dic21—24no—
29C2×C22⋊Dic7—91noHall
30C23×C3×C7—21no—
31C23×C3×C7C2×D312yes—
32C22×D3×C7—32no—
33C22×D3×C7—38no—
34C22×D3×C7—32no—
35C22×D3×C7—61no—
36C22×D3×C7—64no—
37C22×D3×C7—61no—
38C22×D3×C7—68no—
39C22×D3×C7—64no—
40C22×D3×C7—64no—
41C2×Dic21C2×D314yescomplemented
42C2×C3×Dic7—34no—
43D3×Dic7—68no—
44C23×C3⋊D3D711yescharacteristic
45C2×#624—72no—
46C3×#217—72no—
47#3722—72no—
48C2×C32×C7—22no—
49C2×C32×C7C22×C411yescharacteristic
50C2×C32×C7C2×D412yes—
51C7×C3⋊D3—22no—
52C7×C3⋊D3C22⋊C414yescomplemented
53C24×C7—91no—
54C22×Dic7—92no—
55C22⋊Dic7—32no—
56C22⋊Dic7—92no—
57D3×C22⋊C4—212no—
58C22×C3×C7—22no—
59C22×C3×C7—22no—
60C22×C3×C7—24no—
61C22×C3×C7—22no—
62C22×C3×C7—21no—
63C22×C3×C7C4×D314yescomplemented
64C22×C3×C7C22×D312yes—
65C2×D3×C7—34no—
66C2×D3×C7—38no—
67C2×D3×C7—34no—
68C2×D3×C7—62no—
69C2×D3×C7—64no—
70C2×D3×C7—62no—
71C2×D3×C7—616no—
72C2×D3×C7—68no—
73C2×D3×C7—62no—
74C2×D3×C7—68no—
75C2×D3×C7—62no—
76C2×D3×C7—64no—
77Dic21—24no—
78C3×Dic7—64no—
79C23×C32C2×D711yescharacteristic
80C22×C3⋊D3—24no—
81C22×C3⋊D3Dic714yescomplemented
82C22×C3⋊D3C2×D711yescharacteristic
83C22×C3⋊D3C2×D711yescharacteristic
84C2×C3×Dic3—74no—
85#624—144no—
86C32×C7C2×C22⋊C411yescharacteristic, complemented, Hall
87C23×C7—91no—
88C23×C7—94no—
89C23×C7—91no—
90C23×C7—184no—
91C23×C7D3211yescharacteristic
92C2×Dic7—34no—
93C2×Dic7—184no—
94C23×D3—32no—
95C23×D3—61no—
96C2×C4×D3—214no—
97C3×C22⋊C4—212no—
98#217—72no—
99(C2×D3)⋊C4—214no—
100C2×C3×C7—22no—
101C2×C3×C7—22no—
102C2×C3×C7—24no—
103C2×C3×C7—21no—
104C2×C3×C7—22no—
105C2×C3×C7C2×C4×D312yes—
106C2×C3×C7D3×D414yes—
107D3×C7—38no—
108D3×C7—64no—
109D3×C7—62no—
110D3×C7—62no—
111D3×C7—64no—
112C22×C32—22no—
113C22×C32C2×Dic712yescomplemented
114C22×C32C22×D711yescharacteristic
115C2×C3⋊D3—22no—
116C2×C3⋊D3—28no—
117C2×C3⋊D3C2×Dic712yes—
118C2×C3⋊D3C2×Dic712yescomplemented
119C2×C3⋊D3C22⋊D714yes—
120C3×Dic3—144no—
121C2×C22⋊C4—631noSylow
122C22×C7—22no—
123C22×C7—92no—
124C22×C7—94no—
125C22×C7—92no—
126C22×C7—188no—
127C22×C7—182no—
128C22×C7#62412yescomplemented
129C22×C7C2×D3211yescharacteristic
130Dic7—64no—
131C23×C3—21no—
132C23×C3D3×D712yes—
133C22×D3—32no—
134C22×D3—38no—
135C22×D3—32no—
136C22×D3—61no—
137C22×D3—64no—
138C22×D3—61no—
139C22×D3—68no—
140C22×D3—64no—
141C22×D3—64no—
142C2×C3×C4—214no—
143C2×Dic3—74no—
144C4×D3—428no—
145C3×C7—21no—
146C3×C7D3×C22⋊C412yescomplemented
147C2×C32—22no—
148C2×C32C22×Dic711yescharacteristic
149C2×C32C2×C22⋊D712yes—
150C3⋊D3—22no—
151C3⋊D3C22⋊Dic714yescomplemented
152C24—91no—
153C22×C4—632no—
154C22⋊C4—212no—
155C22⋊C4—632no—
156C2×C7—22no—
157C2×C7—94no—
158C2×C7—182no—
159C2×C7C2×#62411yescharacteristic
160C2×C7#381112yes—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—24no—
164C22×C3—22no—
165C22×C3—21no—
166C22×C3D3×Dic714yescomplemented
167C22×C3C2×D3×D712yes—
168C2×D3—34no—
169C2×D3—38no—
170C2×D3—34no—
171C2×D3—62no—
172C2×D3—64no—
173C2×D3—62no—
174C2×D3—616no—
175C2×D3—68no—
176C2×D3—62no—
177C2×D3—68no—
178C2×D3—62no—
179C2×D3—64no—
180C3×C4—424no—
181Dic3—144no—
182C32C2×C22⋊Dic711yescharacteristic, complemented, Sylow
183C23—91no—
184C23—94no—
185C23—91no—
186C23—184no—
187C23(C3⋊D3)⋊D711yescharacteristic
188C2×C4—214no—
189C2×C4—1264no—
190C7#6397411yescharacteristic, complemented, Sylow
191C2×C3—22no—
192C2×C3—22no—
193C2×C3—24no—
194C2×C3—21no—
195C2×C3—22no—
196C2×C3C2×D3×Dic712yes—
197C2×C3D3×C22⋊D714yes—
198D3—38no—
199D3—64no—
200D3—62no—
201D3—62no—
202D3—64no—
203C22—22no—
204C22—92no—
205C22—94no—
206C22—92no—
207C22—188no—
208C22—182no—
209C22#9269312yescomplemented
210C22C2×(C3⋊D3)⋊D711yescharacteristic
211C4—424no—
212C3—21no—
213C3D3×C22⋊Dic712yescomplemented
214C2—22no—
215C2—94no—
216C2—182no—
217C2C2×#9269311yescharacteristic
218C2#1175964412yes—
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D7
commutatorC2×C32×C7C22×C4
FittingC23×C32×C7C22
socle, cosocleC22×C32×C7C23
prime radicalC23×C7×C3⋊D3C2
hypercenterC23(C3⋊D3)⋊D7
hypocenterC32×C7C2×C22⋊C4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#92693C2semidirect
3. C3×#66636C2semidirect
4. #11759226C2semidirect
8. C22×C7×C3⋊D3C4semidirect
11. C2×C3×Dic21C22semidirect
16. #66636D3semidirect
21. C22×C32×C7C2×C4semidirect
26. C2×C7×C3⋊D3C2×C4semidirect
41. C2×Dic21C2×D3semidirect
52. C7×C3⋊D3C22⋊C4semidirect
63. C22×C3×C7C4×D3semidirect
81. C22×C3⋊D3Dic7semidirect
86. C32×C7C2×C22⋊C4semidirect
113. C22×C32C2×Dic7semidirect
118. C2×C3⋊D3C2×Dic7semidirect
128. C22×C7#624semidirect
146. C3×C7D3×C22⋊C4semidirect
151. C3⋊D3C22⋊Dic7semidirect
166. C22×C3D3×Dic7semidirect
182. C32C2×C22⋊Dic7semidirect
190. C7#63974semidirect
209. C22#92693semidirect
213. C3D3×C22⋊Dic7semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C3⋊D32
C2×#926932
C3×#666362
#117592262
D3×C22⋊Dic73
#639747