Finite Group Databasebeta

← #64306

Subgroups — #64306

Order 288.

355 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 355 conjugacy classes of subgroups — too many to draw. Only its 110 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×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#235C212yesmaximal, complemented
3#3811C212yesmaximal, complemented
4#3805C212yesmaximal, complemented
5#3802C211yesmaximal, characteristic, complemented
6C4×D32C212yesmaximal, complemented
7#3798C212yesmaximal, complemented
8#3797C211yesmaximal, characteristic, complemented
9#3796C212yesmaximal, complemented
10D3×#41—32nomaximal
11C22×C3⋊D3C2211yescharacteristic
12C2×D32C2212yes—
13C2×C32×C4C2211yescharacteristic, complemented
14C2×C3⋊Dic3C2211yescharacteristic, complemented
15C4×C3⋊D3C2211yescharacteristic
16C4×C3⋊D3C2211yescharacteristic
17C4×C3⋊D3C2211yescharacteristic, complemented
18C4×C3⋊D3C2211yescharacteristic, complemented
19C3×#67C2214yescomplemented
20C3×D12C2212yescomplemented
21C3×C4×D3C2214yescomplemented
22C3×Dic6C2212yescomplemented
23#627C2212yescomplemented
24#626C2214yescomplemented
25#625C2212yescomplemented
26#624C2212yes—
27D3×Dic3C2214yescomplemented
28C3×#41—32no—
29#239—32no—
30D3×Q8—32no—
31#237—34no—
32#237—32no—
33D3×D4—34no—
34D3×D4—32no—
35#235—34no—
36#235D312yescomplemented
37C2×C4×D3—32no—
38C2×C4×D3—34no—
39C2×C4×D3—61no—
40C22×C32C2311yescharacteristic
41C2×C3⋊D3—22no—
42C2×C3⋊D3C2311yescharacteristic
43C2×C3⋊D3C2311yescharacteristic
44C2×C3×D3C2314yes—
45D32—24no—
46C32×C4C2311yescharacteristic
47C32×C4C2311yescharacteristic
48C3⋊Dic3C2311yescharacteristic
49C3⋊Dic3C2311yescharacteristic
50C3×Dic3C2314yes—
51C2×#41—91noSylow
52C22×D3—32no—
53C22×D3—34no—
54C22×D3—61no—
55C3×Q8—32no—
56C3×D4—34no—
57C3×D4—32no—
58C2×C3×C4—21no—
59C2×C3×C4—34no—
60C2×C3×C4C2×D312yescomplemented
61#67—34no—
62#67—34no—
63#67C2×D314yescomplemented
64C2×Dic3—32no—
65C2×Dic3—34no—
66C2×Dic3—61no—
67D12—34no—
68D12C2×D312yescomplemented
69C4×D3—34no—
70C4×D3—32no—
71C4×D3—32no—
72C4×D3—32no—
73C4×D3—32no—
74C4×D3—34no—
75C4×D3—61no—
76C4×D3—61no—
77C4×D3—61no—
78C4×D3—61no—
79C4×D3C2×D314yescomplemented
80Dic6—34no—
81Dic6C2×D312yescomplemented
82C2×C32—21no—
83C2×C32C2411yescharacteristic
84C3⋊D3—21no—
85C3⋊D3#4112yescomplemented
86C3×D3—24no—
87#41—32no—
88#41—92no—
89#41—92no—
90#41—92no—
91C2×Q8—91no—
92C2×D4—92no—
93C2×D4—91no—
94C22×C4—92no—
95C22×C4—91no—
96C22×C3—21no—
97C22×C3—34no—
98C22×C3C22×D312yes—
99C2×D3—32no—
100C2×D3—32no—
101C2×D3—61no—
102C2×D3—61no—
103C2×D3—68no—
104C2×D3—64no—
105C2×D3—64no—
106C2×D3C22×D314yes—
107C3×C4—21no—
108C3×C4—21no—
109C3×C4—34no—
110C3×C4C22×D312yes—
111C3×C4C22×D312yes—
112Dic3—32no—
113Dic3—32no—
114Dic3—61no—
115Dic3—61no—
116Dic3C22×D314yes—
117C32C2×#4111yescharacteristic, complemented, Sylow
118C23—92no—
119C23—91no—
120Q8—32no—
121Q8—92no—
122D4—34no—
123D4—32no—
124D4—94no—
125D4—92no—
126C2×C4—34no—
127C2×C4—92no—
128C2×C4—94no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4D3211yescharacteristic, complemented
135C2×C3—22no—
136C2×C3—22no—
137C2×C3—21no—
138C2×C3—64no—
139C2×C3C23×D312yes—
140D3—24no—
141D3—34no—
142D3—62no—
143D3—62no—
144D3—62no—
145C22—34no—
146C22—91no—
147C22—91no—
148C22—182no—
149C22—184no—
150C22C2×D3211yescharacteristic
151C4—34no—
152C4—91no—
153C4—91no—
154C4C2×D3211yescharacteristic
155C4C2×D3211yescharacteristic
156C3—21no—
157C3D3×#4112yescomplemented
158C2—21no—
159C2—64no—
160C2—92no—
161C2—181no—
162C2C22×D3211yescharacteristic
subgroupG/H
centerC4C2×D32
commutator, socle, cosocleC2×C32C24
FrattiniC2C22×D32
FittingC2×C32×C4C22
hypercenterC2×C4D32
hypocenterC32C2×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C3⋊D3C2semidirect
2. C3×#235C2semidirect
3. #3811C2semidirect
4. #3805C2semidirect
5. #3802C2semidirect
6. C4×D32C2semidirect
7. #3798C2semidirect
8. #3797C2semidirect
9. #3796C2semidirect
13. C2×C32×C4C22semidirect
14. C2×C3⋊Dic3C22semidirect
17. C4×C3⋊D3C22semidirect
18. C4×C3⋊D3C22semidirect
19. C3×#67C22semidirect
20. C3×D12C22semidirect
21. C3×C4×D3C22semidirect
22. C3×Dic6C22semidirect
23. #627C22semidirect
24. #626C22semidirect
25. #625C22semidirect
27. D3×Dic3C22semidirect
36. #235D3semidirect
60. C2×C3×C4C2×D3semidirect
63. #67C2×D3semidirect
68. D12C2×D3semidirect
79. C4×D3C2×D3semidirect
81. Dic6C2×D3semidirect
85. C3⋊D3#41semidirect
117. C32C2×#41semidirect
134. C2×C4D32semidirect
157. C3D3×#41semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D32
C3×#2352
#38112
#38052
#38022
C4×D322
#37982
#37972
#37962
D3×#413