Finite Group Databasebeta

← #14517113

Subgroups — #14517113

Order 1944.

614 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 45 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×#92301C211yesmaximal, characteristic
2#11757604C212yesmaximal, complemented
3#10620150—31nomaximal
4#10619883—32nomaximal
5C2×C32⋊H(3,𝔽3)C2211yescharacteristic
6#92301C412yescomplemented
7C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic
8C32×C3⋊Dic3—32no—
9C2×C3⋊((C3⋊D3)⋊C3)—32no—
10C2×C3⋊((C3⋊D3)⋊C3)—61no—
11C3⋊#1084D312yescomplemented
12C3×(C3⋊Dic3)⋊C3—32no—
13C3×(C3⋊Dic3)⋊C3—62no—
14C32⋊H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
15#6294—91no—
16#6289—92no—
17#6289—96no—
18((C3⋊D3)⋊C3)⋊C4—96no—
19C2×C34C2×D311yescharacteristic
20C3⋊(C3⋊(C3⋊D3))Dic312yescomplemented
21C2×C3×H(3,𝔽3)—22no—
22C2×C3×H(3,𝔽3)—21no—
23C2×C3×H(3,𝔽3)—41no—
24C2×C3×H(3,𝔽3)C2×D312yes—
25C3⋊((C3⋊D3)⋊C3)—34no—
26C3⋊((C3⋊D3)⋊C3)—62no—
27C2×C3⋊(C3⋊D3)—32no—
28C2×C3⋊(C3⋊D3)—61no—
29C2×C3⋊(C3⋊D3)—96no—
30C2×C3⋊(C3⋊D3)—183no—
31C2×C3×C3⋊D3—91no—
32C3×C3⋊Dic3—36no—
33C3×C3⋊Dic3—32no—
34C3×C3⋊Dic3—32no—
35C3×C3⋊Dic3—62no—
36C32×Dic3—96no—
37C32×Dic3—92no—
38C2×(C3⋊D3)⋊C3—96no—
39C2×(C3⋊D3)⋊C3—183no—
40#1084—96no—
41(C3⋊Dic3)⋊C3—36no—
42(C3⋊Dic3)⋊C3—66no—
43C34C2×Dic311yescharacteristic, complemented
44C3×H(3,𝔽3)—22no—
45C3×H(3,𝔽3)—21no—
46C3×H(3,𝔽3)—41no—
47C3×H(3,𝔽3)C4×D312yescomplemented
48C4×C3⋊D3—272no—
49#624—276no—
50#624—271no—
51#624—279no—
52D3×Dic3—272no—
53C2×C33—21no—
54C2×C33—22no—
55C2×C33—36no—
56C2×C33—41no—
57C2×C33—63no—
58C2×C33D3211yescharacteristic
59C2×C33D3212yes—
60C3⋊(C3⋊D3)—34no—
61C3⋊(C3⋊D3)—62no—
62C3⋊(C3⋊D3)—912no—
63C3⋊(C3⋊D3)—186no—
64C3×C3⋊D3—92no—
65C2×H(3,𝔽3)—36no—
66C2×H(3,𝔽3)—63no—
67C2×H(3,𝔽3)—66no—
68C2×H(3,𝔽3)—123no—
69(C3⋊D3)⋊C3—912no—
70(C3⋊D3)⋊C3—186no—
71C2×C3⋊D3—91no—
72C2×C3⋊D3—96no—
73C2×C3⋊D3—183no—
74C2×C3⋊D3—272no—
75C2×C3⋊D3—279no—
76C2×C3⋊D3—542no—
77C2×C3⋊D3—542no—
78C2×C3⋊D3—541no—
79C2×C3⋊D3—549no—
80C2×C3×D3—272no—
81C2×C3×D3—541no—
82C32×C4—272no—
83C3⋊Dic3—32no—
84C3⋊Dic3—32no—
85C3⋊Dic3—62no—
86C3×Dic3—918no—
87C3×Dic3—96no—
88C3×Dic3—96no—
89C3×Dic3—92no—
90C3×Dic3—272no—
91C3×Dic3—542no—
92C33—21no—
93C33—22no—
94C33—36no—
95C33—41no—
96C33—63no—
97C33D3×Dic312yes—
98C33#62411yescharacteristic, complemented
99H(3,𝔽3)—36no—
100H(3,𝔽3)—63no—
101H(3,𝔽3)—66no—
102H(3,𝔽3)—123no—
103C2×Dic3—811no—
104C4×D3—812no—
105C4×D3—816no—
106C2×C32—23no—
107C2×C32—32no—
108C2×C32—39no—
109C2×C32—32no—
110C2×C32—62no—
111C2×C32—61no—
112C2×C32—61no—
113C2×C32—69no—
114C2×C32—62no—
115C2×C32—62no—
116C2×C32—62no—
117C2×C32—122no—
118C2×C32—121no—
119C2×C32—121no—
120C2×C32—122no—
121C2×C32((C3⋊D3)⋊C3)⋊C216yes—
122C2×C32#111311yescharacteristic
123C3⋊D3—92no—
124C3⋊D3—912no—
125C3⋊D3—186no—
126C3⋊D3—274no—
127C3⋊D3—2718no—
128C3⋊D3—544no—
129C3⋊D3—544no—
130C3⋊D3—542no—
131C3⋊D3—5418no—
132C3×D3—274no—
133C3×D3—542no—
134C22×C3—811no—
135C2×D3—272no—
136C2×D3—541no—
137C2×D3—816no—
138C2×D3—1623no—
139C3×C4—276no—
140C3×C4—272no—
141Dic3—96no—
142Dic3—92no—
143Dic3—272no—
144Dic3—542no—
145C32—23no—
146C32—32no—
147C32—39no—
148C32—32no—
149C32—62no—
150C32—61no—
151C32—61no—
152C32—69no—
153C32—62no—
154C32—62no—
155C32—62no—
156C32—122no—
157C32—121no—
158C32—121no—
159C32—122no—
160C32((C3⋊D3)⋊C3)⋊C416yescomplemented
161C32#629411yescharacteristic
162C2×C4—2431noSylow
163C2×C3—21no—
164C2×C3—36no—
165C2×C3—63no—
166C2×C3—91no—
167C2×C3—182no—
168C2×C3—361no—
169C2×C3—812no—
170C2×C3#6643212yes—
171D3—274no—
172D3—542no—
173D3—8112no—
174D3—1626no—
175C22—811no—
176C4—272no—
177C3—21no—
178C3—36no—
179C3—63no—
180C3—91no—
181C3—182no—
182C3—361no—
183C3#1061990112yes—
184C2—812no—
185C2#1175774911yescharacteristic
subgroupG/H
center, hypercenterC2#11757749
commutator, hypocenterC32⋊H(3,𝔽3)C2×C4
Frattini, socleC2×C32#1113
Fitting, cosocleC2×C32⋊H(3,𝔽3)C22
prime radicalC2×#92301C2
LCSG ▷ C32⋊H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757604C2semidirect
6. #92301C4semidirect
11. C3⋊#1084D3semidirect
14. C32⋊H(3,𝔽3)C2×C4semidirect
20. C3⋊(C3⋊(C3⋊D3))Dic3semidirect
43. C34C2×Dic3semidirect
47. C3×H(3,𝔽3)C4×D3semidirect
98. C33#624semidirect
160. C32((C3⋊D3)⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#923012
#117576042
#106201503
#106198833