Finite Group Databasebeta

← #11808026

Subgroups — #11808026

Order 1152.

1368 conjugacy classes of subgroups; only the 337 normal subgroups are shown.

normal subgroups only

This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 337 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×#64085C211yesmaximal, characteristic
2C32×#383C211yesmaximal, characteristic, complemented
3#10592634C211yesmaximal, characteristic, complemented
4#10592369C213yesmaximal
5#10592367C213yesmaximal
6#10592354C213yesmaximal, complemented
7#10592346C213yesmaximal, complemented
8#74299—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×#3752C2213yes—
12C2×#3752C2213yes—
13C2×C4⋊(C3⋊Dic3)C2213yes—
14C2×C4⋊(C3⋊Dic3)C2213yes—
15C2×#3750C2213yes—
16C2×#3750C2213yes—
17C2×C4×C3⋊Dic3C2213yes—
18#64085C418yescomplemented
19C32×#95C2213yes—
20C32×#95C2213yes—
21#63658C2213yes—
22#63658C2213yes—
23C2×#876—34no—
24C3×#383D314yescomplemented
25#4935—34no—
26#4670—312no—
27#4668—312no—
28#4655—312no—
29#4647—312no—
30C23×C3⋊D3C2311yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C22×C32×C4C2313yes—
33C22×C32×C4C2313yes—
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3⋊Dic3C2313yes—
36C22×C3⋊Dic3C2313yes—
37C2×C4×C3⋊D3—43no—
38C32×C42C2×C414yescomplemented
39#3752—43no—
40#3752C2×C4112yes—
41C4⋊(C3⋊Dic3)—43no—
42C4⋊(C3⋊Dic3)—43no—
43#3750—43no—
44#3750C2×C4112yescomplemented
45C4×C3⋊Dic3—43no—
46#2383—91noSylow
47C22×C4×D3—34no—
48C2×C3×C42C2×D314yes—
49C2×(C2×D3)⋊C4—312no—
50C2×(C2×D3)⋊C4—312no—
51C2×C4⋊Dic3—312no—
52C2×C4⋊Dic3—312no—
53C2×Dic3⋊C4—312no—
54C2×Dic3⋊C4—312no—
55C2×C4×Dic3—312no—
56#876—332no—
57C3×#95C2×D3112yes—
58C3×#95C2×D3112yes—
59C3⋊#95—312no—
60C3⋊#95—312no—
61C23×C32C2411yescharacteristic
62C22×C3⋊D3—23no—
63C22×C3⋊D3—23no—
64C22×C3⋊D3C22×C412yes—
65C2×C32×C4—23no—
66C2×C32×C4—23no—
67C2×C32×C4—23no—
68C2×C32×C4—23no—
69C2×C32×C4—26no—
70C2×C32×C4C22×C416yes—
71C2×C3⋊Dic3—23no—
72C2×C3⋊Dic3—23no—
73C2×C3⋊Dic3—23no—
74C2×C3⋊Dic3—23no—
75C2×C3⋊Dic3—23no—
76C2×C3⋊Dic3—23no—
77C2×C3⋊Dic3C22×C416yes—
78C4×C3⋊D3—44no—
79C2×#126—91no—
80#389—93no—
81#388—93no—
82#387—93no—
83#385—93no—
84#384—91no—
85#383C3⋊D311yescharacteristic, complemented
86C23×D3—34no—
87C22×C3×C4C22×D3112yes—
88C22×C3×C4C22×D314yes—
89C22×C3×C4C22×D3112yes—
90C22×Dic3—312no—
91C22×Dic3—34no—
92C22×Dic3—312no—
93C2×C4×D3—1212no—
94C3×C42C4×D3116yescomplemented
95(C2×D3)⋊C4—348no—
96(C2×D3)⋊C4—1212no—
97C4⋊Dic3—1212no—
98C4⋊Dic3—1212no—
99Dic3⋊C4—348no—
100Dic3⋊C4—1212no—
101C4×Dic3—1212no—
102C22×C32C23×C411yescharacteristic
103C22×C32H(5,𝔽2)13yes—
104C22×C322−1+413yes—
105C2×C3⋊D3—26no—
106C2×C3⋊D3—41no—
107C2×C3⋊D3—43no—
108C32×C4—26no—
109C32×C4—41no—
110C32×C4—43no—
111C3⋊Dic3—26no—
112C3⋊Dic3—41no—
113C3⋊Dic3—43no—
114C23×C4—91no—
115#126—98no—
116C2×C4⋊C4—93no—
117C2×C4⋊C4—93no—
118C2×C4⋊C4—93no—
119C2×C4⋊C4—93no—
120C2×C22⋊C4—93no—
121C2×C22⋊C4—93no—
122C2×C42—93no—
123C2×C42C2×C3⋊D311yescharacteristic
124#95—93no—
125#95—93no—
126#95C2×C3⋊D313yes—
127#95C2×C3⋊D313yes—
128C23×C3C23×D314yes—
129C22×D3—38no—
130C22×D3—612no—
131C22×D3—612no—
132C2×C3×C4—212no—
133C2×C3×C4—212no—
134C2×C3×C4—212no—
135C2×C3×C4—212no—
136C2×C3×C4—224no—
137C2×C3×C4C2×C4×D3124yes—
138C2×Dic3—324no—
139C2×Dic3—612no—
140C2×Dic3—612no—
141C2×Dic3—612no—
142C2×Dic3—612no—
143C2×Dic3—612no—
144C2×Dic3—612no—
145C4×D3—1216no—
146C2×C32#52013yes—
147C2×C32#56011yescharacteristic
148C2×C32#56313yes—
149C3⋊D3—42no—
150C24—91no—
151C22×C4—93no—
152C22×C4—91no—
153C22×C4—93no—
154C22×C4—363no—
155C22×C4C22×C3⋊D313yes—
156C22×C4C22×C3⋊D311yescharacteristic
157C22×C4C22×C3⋊D313yes—
158C4⋊C4—912no—
159C4⋊C4—363no—
160C4⋊C4—363no—
161C4⋊C4—363no—
162C22⋊C4—912no—
163C22⋊C4—363no—
164C42—363no—
165C42C4×C3⋊D314yescomplemented
166C22×C3C22×C4×D314yes—
167C22×C3#1009112yes—
168C22×C3#1010112yes—
169C2×D3—624no—
170C2×D3—124no—
171C2×D3—1212no—
172C3×C4—224no—
173C3×C4—44no—
174C3×C4—412no—
175Dic3—624no—
176Dic3—124no—
177Dic3—1212no—
178C32#238311yescharacteristic, complemented, Sylow
179C23—92no—
180C23—183no—
181C23—183no—
182C23C23×C3⋊D311yescharacteristic
183C2×C4—23no—
184C2×C4—23no—
185C2×C4—23no—
186C2×C4—23no—
187C2×C4—26no—
188C2×C4—96no—
189C2×C4—183no—
190C2×C4—183no—
191C2×C4—183no—
192C2×C4—183no—
193C2×C4—183no—
194C2×C4—183no—
195C2×C4—364no—
196C2×C4C2×C4×C3⋊D316yes—
197C2×C3#5523112yes—
198C2×C3#571114yes—
199C2×C3#5712112yes—
200D3—128no—
201C22—186no—
202C22—361no—
203C22—363no—
204C22C22×C4×C3⋊D311yescharacteristic
205C22#6436613yes—
206C22#6436713yes—
207C4—26no—
208C4—41no—
209C4—43no—
210C4—186no—
211C4—361no—
212C4—363no—
213C3#7429914yescomplemented
214C2—362no—
215C2#1059599413yes—
216C2#1059618211yescharacteristic
217C2#1059618313yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#383C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#383C3⋊D3
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. C32×#383C2semidirect
3. #10592634C2semidirect
6. #10592354C2semidirect
7. #10592346C2semidirect
18. #64085C4semidirect
24. C3×#383D3semidirect
38. C32×C42C2×C4semidirect
44. #3750C2×C4semidirect
85. #383C3⋊D3semidirect
94. C3×C42C4×D3semidirect
165. C42C4×C3⋊D3semidirect
178. C32#2383semidirect
213. C3#74299semidirect

Maximal subgroups

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

subgroupindex
C2×#640852
C32×#3832
#105926342
#105923692
#105923672
#105923542
#105923462
#742993