Finite Group Databasebeta

← #11800786

Subgroups — #11800786

Order 1152.

1753 conjugacy classes of subgroups; only the 444 normal subgroups are shown.

normal subgroups only

This group has 1753 conjugacy classes of subgroups — too many to draw. Only its 444 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×C42×C3⋊D3C211yesmaximal, characteristic
2C2×#63874C212yesmaximal
3C3×#4932C212yesmaximal, complemented
4#10591260C214yesmaximal
5#10591257C214yesmaximal, complemented
6C4×Dic32C212yesmaximal, complemented
7#73382—32nomaximal
8C22×C4×C3⋊D3C2212yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2212yes—
13C42×C3⋊D3C418yescomplemented
14C2×C3×C4×Dic3C2214yes—
15C2×#3724C2214yes—
16C2×#3722C2214yes—
17C2×Dic32C2218yes—
18#63874C4116yescomplemented
19C3×C3⋊#95C2218yes—
20C2×#872—34no—
21C2×C42×D3—32no—
22C2×C42×D3—61no—
23C3×#376—32no—
24#4932D312yescomplemented
25C42×Dic3—34no—
26#4666—38no—
27#4649—38no—
28C23×C3⋊D3C2311yescharacteristic
29C22×C32×C4C2312yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C22×C3⋊Dic3C2312yes—
33C2×C4×C3⋊D3—28no—
34C2×C4×C3⋊D3C2×C418yes—
35C2×C4×C3⋊D3C2×C414yes—
36C2×C4×C3⋊D3C2×C418yes—
37C22×C3×Dic3C2318yes—
38C32×C42C2×C414yes—
39C4×C3⋊Dic3C2×C418yes—
40C4×C3⋊Dic3C2×C414yes—
41C3×C4×Dic3C2×C4116yescomplemented
42#3724C2×C4116yescomplemented
43#3722C2×C4116yes—
44Dic32—216no—
45C4×#117—91noSylow
46C22×C4×D3—32no—
47C22×C4×D3—34no—
48C22×C4×D3—61no—
49C22×C4×D3—62no—
50C2×C3×C42—21no—
51C2×C3×C42—34no—
52C2×C3×C42C2×D312yes—
53C2×(C2×D3)⋊C4—38no—
54C2×Dic3⋊C4—38no—
55C2×C4×Dic3—34no—
56C2×C4×Dic3—32no—
57C2×C4×Dic3—316no—
58C2×C4×Dic3—62no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3C2×D314yes—
61#872—332no—
62C42×D3—316no—
63C42×D3—68no—
64C3×#95—38no—
65C3⋊#95C2×D318yes—
66C23×C32C2411yescharacteristic
67C22×C3⋊D3—24no—
68C22×C3⋊D3C22×C414yes—
69C22×C3⋊D3C22×C412yes—
70C2×C32×C4—24no—
71C2×C32×C4C22×C414yes—
72C2×C32×C4C22×C414yes—
73C2×C32×C4C22×C412yes—
74C2×C3⋊Dic3C22×C414yes—
75C2×C3⋊Dic3C22×C412yes—
76C2×C3⋊Dic3C22×C414yes—
77C2×C3⋊Dic3#4118yes—
78C4×C3⋊D3—216no—
79C4×C3⋊D3C42116yescomplemented
80C2×C3×Dic3—216no—
81C2×C3×Dic3C22×C4116yes—
82C2×#117—92no—
83C22×C42—91no—
84C4×C4⋊C4—94no—
85C4×C22⋊C4—94no—
86#376—32no—
87C43—92no—
88C23×D3—32no—
89C23×D3—61no—
90C22×C3×C4—22no—
91C22×C3×C4—21no—
92C22×C3×C4—38no—
93C22×C3×C4C22×D314yes—
94C22×C3×C4C22×D312yes—
95C22×Dic3—34no—
96C22×Dic3—32no—
97C22×Dic3—62no—
98C22×Dic3—61no—
99C22×Dic3C22×D318yes—
100C2×C4×D3—38no—
101C2×C4×D3—316no—
102C2×C4×D3—316no—
103C2×C4×D3—64no—
104C2×C4×D3—68no—
105C2×C4×D3—68no—
106C2×C4×D3—616no—
107C2×C4×D3—616no—
108C3×C42—24no—
109C3×C42—316no—
110C3×C42C4×D318yes—
111(C2×D3)⋊C4—332no—
112Dic3⋊C4—332no—
113C4×Dic3—316no—
114C4×Dic3—38no—
115C4×Dic3—68no—
116C4×Dic3—64no—
117C4×Dic3—632no—
118C4×Dic3C4×D3116yescomplemented
119C22×C32C23×C411yescharacteristic
120C22×C32C23×C412yes—
121C22×C32C2×#4114yes—
122C2×C3⋊D3—24no—
123C2×C3⋊D3—28no—
124C2×C3⋊D3C2×C4214yes—
125C32×C4—24no—
126C32×C4C2×C4214yes—
127C3⋊Dic3C2×C4214yes—
128C3⋊Dic3#11718yescomplemented
129C3×Dic3—216no—
130C23×C4—91no—
131C23×C4—92no—
132#117—916no—
133C2×C4⋊C4—94no—
134C2×C22⋊C4—94no—
135C2×C42—34no—
136C2×C42—92no—
137C2×C42—91no—
138C2×C42—98no—
139C2×C42—98no—
140C2×C42D3211yescharacteristic
141#95—38no—
142C23×C3—21no—
143C23×C3C23×D312yes—
144C22×D3—38no—
145C22×D3—34no—
146C22×D3—62no—
147C22×D3—64no—
148C22×D3—68no—
149C22×D3—68no—
150C2×C3×C4—28no—
151C2×C3×C4—28no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—316no—
156C2×C3×C4—616no—
157C2×C3×C4C2×C4×D318yes—
158C2×C3×C4C2×C4×D318yes—
159C2×C3×C4C2×C4×D314yes—
160C2×Dic3—216no—
161C2×Dic3—34no—
162C2×Dic3—38no—
163C2×Dic3—38no—
164C2×Dic3—316no—
165C2×Dic3—62no—
166C2×Dic3—64no—
167C2×Dic3—64no—
168C2×Dic3—68no—
169C2×Dic3C2×C4×D3116yes—
170C4×D3—332no—
171C4×D3—616no—
172C4×D3—632no—
173C4×D3—632no—
174C2×C32C22×C4211yescharacteristic
175C2×C32C2×#11712yes—
176C2×C32C4×#4114yes—
177C3⋊D3—24no—
178C24—91no—
179C22×C4—38no—
180C22×C4—92no—
181C22×C4—91no—
182C22×C4—98no—
183C22×C4—94no—
184C22×C4—98no—
185C22×C4—188no—
186C22×C4C2×D3212yes—
187C22×C4C2×D3211yescharacteristic
188C4⋊C4—916no—
189C22⋊C4—916no—
190C42—316no—
191C42—98no—
192C42—94no—
193C42—1816no—
194C42#62414yes—
195C22×C3—22no—
196C22×C3—24no—
197C22×C3—21no—
198C22×C3C22×C4×D314yes—
199C22×C3C22×C4×D312yes—
200C22×C3D3×#4118yes—
201C2×D3—38no—
202C2×D3—64no—
203C2×D3—68no—
204C2×D3—616no—
205C2×D3—68no—
206C2×D3—616no—
207C3×C4—28no—
208C3×C4—28no—
209C3×C4—24no—
210C3×C4—616no—
211C3×C4C42×D318yes—
212Dic3—216no—
213Dic3—38no—
214Dic3—316no—
215Dic3—64no—
216Dic3—68no—
217C32C4×#11711yescharacteristic, complemented, Sylow
218C23—94no—
219C23—92no—
220C23—184no—
221C23C22×D3211yescharacteristic
222C2×C4—24no—
223C2×C4—316no—
224C2×C4—616no—
225C2×C4—94no—
226C2×C4—98no—
227C2×C4—92no—
228C2×C4—94no—
229C2×C4—916no—
230C2×C4—1816no—
231C2×C4C4×D3214yes—
232C2×C4C2×#62414yes—
233C2×C4C2×#62412yes—
234C2×C3—21no—
235C2×C3—22no—
236C2×C3—24no—
237C2×C3C2×C42×D312yes—
238C2×C3D3×#11714yes—
239C2×C3#552218yes—
240D3—68no—
241D3—68no—
242C22—94no—
243C22—184no—
244C22—188no—
245C22C2×C4×D3212yes—
246C22#6430614yes—
247C22C22×#62411yescharacteristic
248C4—24no—
249C4—616no—
250C4—94no—
251C4—98no—
252C4C4×#62414yes—
253C3—21no—
254C3#7338212yescomplemented
255C2—184no—
256C2#1059396614yes—
257C2C2×C4×#62411yescharacteristic
258C2#1059496912yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4932C2semidirect
5. #10591257C2semidirect
6. C4×Dic32C2semidirect
13. C42×C3⋊D3C4semidirect
18. #63874C4semidirect
24. #4932D3semidirect
41. C3×C4×Dic3C2×C4semidirect
42. #3724C2×C4semidirect
79. C4×C3⋊D3C42semidirect
118. C4×Dic3C4×D3semidirect
128. C3⋊Dic3#117semidirect
217. C32C4×#117semidirect
254. C3#73382semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#638742
C3×#49322
#105912602
#105912572
C4×Dic322
#733823