Finite Group Databasebeta

← #14517114

Subgroups — #14517114

Order 1944.

586 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 41 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×#92300C212yesmaximal, complemented
2#11757605C211yesmaximal, characteristic, complemented
3#10620151—31nomaximal
4#10619886—32nomaximal
5C2×C32⋊H(3,𝔽3)C2211yescharacteristic
6#92300—22no—
7C2×C32×C3⋊D3—32no—
8C3⋊(C3⋊(C3⋊Dic3))D311yescharacteristic, complemented
9C2×C3⋊#272D312yescomplemented
10C2×C3×(C3⋊D3)⋊C3—32no—
11C2×C3×(C3⋊D3)⋊C3—62no—
12C3⋊((C3⋊Dic3)⋊C3)—32no—
13C3⋊((C3⋊Dic3)⋊C3)—61no—
14C32⋊H(3,𝔽3)D411yescharacteristic, complemented, Sylow
15#6295—91no—
16#6290—92no—
17#6290—96no—
18#6200—96no—
19C2×C34C2×D311yescharacteristic
20C32×C3⋊D3—62no—
21C2×C3×H(3,𝔽3)—21no—
22C2×C3×H(3,𝔽3)—22no—
23C2×C3×H(3,𝔽3)—41no—
24C2×C3×H(3,𝔽3)C2×D312yes—
25C3⋊#272—22no—
26C3×(C3⋊D3)⋊C3—64no—
27C3×(C3⋊D3)⋊C3—62no—
28C2×C3×C3⋊D3—36no—
29C2×C3×C3⋊D3—32no—
30C2×C3×C3⋊D3—32no—
31C2×C3×C3⋊D3—62no—
32C2×C32×D3—96no—
33C2×C32×D3—92no—
34C3⋊(C3⋊Dic3)—32no—
35C3⋊(C3⋊Dic3)—61no—
36C3⋊(C3⋊Dic3)—96no—
37C3⋊(C3⋊Dic3)—183no—
38C3×C3⋊Dic3—91no—
39C2×#272—96no—
40C2×(C3⋊D3)⋊C3—36no—
41C2×(C3⋊D3)⋊C3—66no—
42(C3⋊Dic3)⋊C3—96no—
43(C3⋊Dic3)⋊C3—183no—
44C34D1211yescharacteristic, complemented
45C3×H(3,𝔽3)—21no—
46C3×H(3,𝔽3)—22no—
47C3×H(3,𝔽3)—41no—
48C3×H(3,𝔽3)#6712yescomplemented
49#638—272no—
50#626—272no—
51#625—276no—
52#625—271no—
53#625—279no—
54C2×C33—21no—
55C2×C33—22no—
56C2×C33—36no—
57C2×C33—41no—
58C2×C33—63no—
59C2×C33D3211yescharacteristic
60C2×C33D3212yes—
61C3×C3⋊D3—66no—
62C3×C3⋊D3—62no—
63C3×C3⋊D3—64no—
64C3×C3⋊D3—62no—
65C32×D3—186no—
66C32×D3—182no—
67C2×H(3,𝔽3)—36no—
68C2×H(3,𝔽3)—63no—
69C2×H(3,𝔽3)—66no—
70C2×H(3,𝔽3)—123no—
71#272—186no—
72(C3⋊D3)⋊C3—66no—
73(C3⋊D3)⋊C3—612no—
74C22×C32—272no—
75C2×C3⋊D3—32no—
76C2×C3⋊D3—32no—
77C2×C3⋊D3—62no—
78C2×C3×D3—918no—
79C2×C3×D3—96no—
80C2×C3×D3—96no—
81C2×C3×D3—92no—
82C2×C3×D3—272no—
83C2×C3×D3—542no—
84C3⋊Dic3—91no—
85C3⋊Dic3—96no—
86C3⋊Dic3—183no—
87C3⋊Dic3—272no—
88C3⋊Dic3—279no—
89C3⋊Dic3—542no—
90C3⋊Dic3—542no—
91C3⋊Dic3—541no—
92C3⋊Dic3—549no—
93C3×Dic3—272no—
94C3×Dic3—541no—
95C33—21no—
96C33—22no—
97C33—36no—
98C33—41no—
99C33—63no—
100C33#62511yescharacteristic, complemented
101C33#62612yes—
102H(3,𝔽3)—36no—
103H(3,𝔽3)—63no—
104H(3,𝔽3)—66no—
105H(3,𝔽3)—123no—
106#67—812no—
107#67—816no—
108D12—811no—
109C2×C32—23no—
110C2×C32—32no—
111C2×C32—39no—
112C2×C32—32no—
113C2×C32—62no—
114C2×C32—61no—
115C2×C32—61no—
116C2×C32—69no—
117C2×C32—62no—
118C2×C32—62no—
119C2×C32—62no—
120C2×C32—122no—
121C2×C32—121no—
122C2×C32—121no—
123C2×C32—122no—
124C2×C32—542no—
125C2×C32((C3⋊D3)⋊C3)⋊C216yes—
126C2×C32#111311yescharacteristic
127C3⋊D3—62no—
128C3⋊D3—62no—
129C3⋊D3—64no—
130C3×D3—1818no—
131C3×D3—186no—
132C3×D3—186no—
133C3×D3—182no—
134C3×D3—542no—
135C3×D3—544no—
136C22×C3—276no—
137C22×C3—272no—
138C2×D3—96no—
139C2×D3—92no—
140C2×D3—272no—
141C2×D3—542no—
142C3×C4—811no—
143Dic3—272no—
144Dic3—541no—
145Dic3—816no—
146Dic3—1623no—
147C32—23no—
148C32—32no—
149C32—39no—
150C32—32no—
151C32—62no—
152C32—61no—
153C32—61no—
154C32—69no—
155C32—62no—
156C32—62no—
157C32—62no—
158C32—122no—
159C32—121no—
160C32—121no—
161C32—122no—
162C32#620016yescomplemented
163C32#629511yescharacteristic
164D4—2431noSylow
165C2×C3—21no—
166C2×C3—36no—
167C2×C3—63no—
168C2×C3—91no—
169C2×C3—182no—
170C2×C3—361no—
171C2×C3—546no—
172C2×C3—542no—
173C2×C3#6643212yes—
174D3—186no—
175D3—182no—
176D3—542no—
177D3—544no—
178C22—272no—
179C4—811no—
180C3—21no—
181C3—36no—
182C3—63no—
183C3—91no—
184C3—182no—
185C3—361no—
186C3#1061990412yes—
187C2—542no—
188C2#1175774911yescharacteristic
subgroupG/H
center, hypercenterC2#11757749
commutator, Fitting, cosocleC2×C32⋊H(3,𝔽3)C22
Frattini, socleC2×C32#1113
hypocenterC32⋊H(3,𝔽3)D4
LCSG ▷ C2×C32⋊H(3,𝔽3) ▷ C32⋊H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92300C2semidirect
2. #11757605C2semidirect
8. C3⋊(C3⋊(C3⋊Dic3))D3semidirect
9. C2×C3⋊#272D3semidirect
14. C32⋊H(3,𝔽3)D4semidirect
44. C34D12semidirect
48. C3×H(3,𝔽3)#67semidirect
100. C33#625semidirect
162. C32#6200semidirect

Maximal subgroups

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

subgroupindex
C2×#923002
#117576052
#106201513
#106198863