Finite Group Databasebeta

← #11808038

Subgroups — #11808038

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×#384C211yesmaximal, characteristic, complemented
3#10592689C213yesmaximal
4#10592688C213yesmaximal
5#10592677C213yesmaximal, complemented
6#10592675C213yesmaximal, complemented
7#10592636C211yesmaximal, characteristic, complemented
8#74361—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C4⋊C4C2213yes—
11C2×C32×C4⋊C4C2213yes—
12C2×C32×C42C2211yescharacteristic
13C2×#3752C2213yes—
14C2×#3752C2213yes—
15C2×#3750C2213yes—
16C2×#3750C2213yes—
17C2×C4×C3⋊Dic3C2213yes—
18#64085C418yescomplemented
19#63658C2213yes—
20#63658C2213yes—
21#63658C2213yes—
22#63658C2213yes—
23C2×#876—34no—
24C3×#384D314yescomplemented
25#4990—312no—
26#4989—312no—
27#4978—312no—
28#4976—312no—
29#4937—34no—
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×C4⋊C4—43no—
39C32×C4⋊C4—43no—
40C32×C42C2×C414yescomplemented
41#3752—43no—
42#3752C2×C4112yes—
43#3750—43no—
44#3750C2×C4112yescomplemented
45C4×C3⋊Dic3—43no—
46#2383—91noSylow
47C22×C4×D3—34no—
48C2×C3×C4⋊C4C2×D3112yes—
49C2×C3×C4⋊C4C2×D3112yes—
50C2×C3×C42C2×D314yes—
51C2×(C2×D3)⋊C4—312no—
52C2×(C2×D3)⋊C4—312no—
53C2×Dic3⋊C4—312no—
54C2×Dic3⋊C4—312no—
55C2×C4×Dic3—312no—
56#876—332no—
57C3⋊#95—312no—
58C3⋊#95—312no—
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—23no—
70C2×C32×C4—23no—
71C2×C32×C4C22×C416yes—
72C2×C3⋊Dic3—23no—
73C2×C3⋊Dic3—23no—
74C2×C3⋊Dic3—23no—
75C2×C3⋊Dic3—23no—
76C2×C3⋊Dic3—26no—
77C2×C3⋊Dic3C22×C416yes—
78C4×C3⋊D3—44no—
79C2×#126—91no—
80#389—93no—
81#388—93no—
82#387—93no—
83#385—93no—
84#384C3⋊D311yescharacteristic, complemented
85#383—91no—
86C23×D3—34no—
87C22×C3×C4C22×D314yes—
88C22×C3×C4C22×D3112yes—
89C22×C3×C4C22×D3112yes—
90C22×Dic3—312no—
91C22×Dic3—312no—
92C22×Dic3—34no—
93C2×C4×D3—1212no—
94C3×C4⋊C4—412no—
95C3×C4⋊C4—412no—
96C3×C42C4×D3116yescomplemented
97(C2×D3)⋊C4—348no—
98(C2×D3)⋊C4—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⋊C4C2×C3⋊D313yes—
119C2×C4⋊C4C2×C3⋊D313yes—
120C2×C22⋊C4—93no—
121C2×C22⋊C4—93no—
122C2×C42—93no—
123C2×C42C2×C3⋊D311yescharacteristic
124#95—93no—
125#95—93no—
126#95—93no—
127#95—93no—
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—212no—
137C2×C3×C4—212no—
138C2×C3×C4C2×C4×D3124yes—
139C2×Dic3—324no—
140C2×Dic3—612no—
141C2×Dic3—612no—
142C2×Dic3—612no—
143C2×Dic3—612no—
144C2×Dic3—624no—
145C4×D3—1216no—
146C2×C32#52013yes—
147C2×C32#56011yescharacteristic
148C2×C32#56313yes—
149C3⋊D3—42no—
150C24—91no—
151C22×C4—93no—
152C22×C4—93no—
153C22×C4—91no—
154C22×C4—363no—
155C22×C4C22×C3⋊D311yescharacteristic
156C22×C4C22×C3⋊D313yes—
157C22×C4C22×C3⋊D313yes—
158C4⋊C4—43no—
159C4⋊C4—43no—
160C4⋊C4—912no—
161C4⋊C4—363no—
162C22⋊C4—912no—
163C22⋊C4—363no—
164C42—363no—
165C42C4×C3⋊D314yescomplemented
166C22×C3C22×C4×D314yes—
167C22×C3#1004112yes—
168C22×C3#1007112yes—
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—23no—
188C2×C4—23no—
189C2×C4—96no—
190C2×C4—183no—
191C2×C4—183no—
192C2×C4—183no—
193C2×C4—183no—
194C2×C4—186no—
195C2×C4—364no—
196C2×C4C2×C4×C3⋊D316yes—
197C2×C3#5504112yes—
198C2×C3#572014yes—
199C2×C3#5735112yes—
200D3—128no—
201C22—186no—
202C22—361no—
203C22—363no—
204C22C22×C4×C3⋊D311yescharacteristic
205C22#6436113yes—
206C22#6436413yes—
207C4—26no—
208C4—41no—
209C4—43no—
210C4—186no—
211C4—361no—
212C4—363no—
213C3#7436114yescomplemented
214C2—362no—
215C2#1059597513yes—
216C2#1059619111yescharacteristic
217C2#1059620613yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#384C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#384C3⋊D3
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C32×#384C2semidirect
5. #10592677C2semidirect
6. #10592675C2semidirect
7. #10592636C2semidirect
18. #64085C4semidirect
24. C3×#384D3semidirect
40. C32×C42C2×C4semidirect
44. #3750C2×C4semidirect
84. #384C3⋊D3semidirect
96. C3×C42C4×D3semidirect
165. C42C4×C3⋊D3semidirect
178. C32#2383semidirect
213. C3#74361semidirect

Maximal subgroups

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

subgroupindex
C2×#640852
C32×#3842
#105926892
#105926882
#105926772
#105926752
#105926362
#743613