Finite Group Databasebeta

← #92306⋊C4 #14517119

Subgroups — #92306⋊C4 #14517119

Order 1944.

295 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 295 conjugacy classes of subgroups — too many to draw. Only its 39 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×#92306C211yesmaximal, characteristic
2#11757609C211yesmaximal, characteristic, complemented
3#11757608C211yesmaximal, characteristic, complemented
4#10619883—31nomaximal
5#10619870—31nomaximal
6#4169⋊C4—31nomaximal
7C2×#6893C2211yescharacteristic
8#92306C412yescomplemented
9C2×C3⋊(C3⋊D9)D311yescharacteristic
10C2×C3⋊((C3⋊D3)⋊C3)—31no—
11C3⋊#1084D311yescharacteristic
12C9×C3⋊Dic3—31no—
13C3×3−1+2⋊C4—61no—
14C3×(C3⋊Dic3)⋊C3—31no—
15C32×Dic9—31no—
16C2×#4169—31no—
17C2×#4169—61no—
18#66328D311yescharacteristic, complemented
19(C3⋊Dic3)⋊C9—31no—
20(C3⋊Dic3)⋊C9—61no—
21#6893C2×C411yescharacteristic, complemented, Sylow
22#6294—91no—
23#6289—91no—
24((C3⋊D3)⋊C3)⋊C4—93no—
25(C3⋊D9)⋊C4—91no—
26(C3⋊D9)⋊C4—93no—
27C2×C3×3−1+2—21no—
28C2×C3×H(3,𝔽3)C2×D311yescharacteristic
29C2×C32×C9C2×D311yescharacteristic
30C3⋊(C3⋊D9)Dic312yescomplemented
31C3⋊((C3⋊D3)⋊C3)—32no—
32C2×C32⋊C9—21no—
33C2×C32⋊C9—21no—
34C2×C32⋊C9—41no—
35C2×C32⋊C9C2×D311yescharacteristic
36#4169—32no—
37#4169—62no—
38C2×C3⋊(C3⋊D3)—31no—
39C2×C3×C3⋊D3—91no—
40C3×C3⋊Dic3—31no—
41C3×C3⋊Dic3—31no—
42C3×C3⋊Dic3—31no—
43C3×C3⋊Dic3—61no—
44C32×Dic3—91no—
45C2×C3⋊D9—31no—
46C2×C3⋊D9—61no—
47C2×C3⋊D9—93no—
48C2×(C3⋊D3)⋊C3—93no—
49#1084—93no—
503−1+2⋊C4—63no—
51(C3⋊Dic3)⋊C3—33no—
52C9×Dic3—93no—
53C9×Dic3—91no—
54C3×Dic9—33no—
55C3×Dic9—31no—
56C3×Dic9—61no—
57C3×3−1+2—21no—
58C3×H(3,𝔽3)C4×D311yescharacteristic
59C32×C9C2×Dic311yescharacteristic, complemented
60C32⋊C9—21no—
61C32⋊C9—21no—
62C32⋊C9—41no—
63C32⋊C9C4×D311yescharacteristic, complemented
64C4×C3⋊D3—271no—
65#624—273no—
66#624—271no—
67D3×Dic3—271no—
68D3×Dic3—271no—
69C4×D9—271no—
70C2×C33—21no—
71C2×C33D3211yescharacteristic
72C2×C33D3211yescharacteristic
73C3⋊(C3⋊D3)—32no—
74C3×C3⋊D3—92no—
75C2×3−1+2—63no—
76C2×H(3,𝔽3)—33no—
77C2×C3×C9—21no—
78C2×C3×C9—21no—
79C2×C3×C9—33no—
80C2×C3×C9—41no—
81C2×C3×C9D3211yescharacteristic
82C3⋊D9—32no—
83C3⋊D9—62no—
84C3⋊D9—96no—
85(C3⋊D3)⋊C3—96no—
86C2×C3⋊D3—91no—
87C2×C3⋊D3—93no—
88C2×C3⋊D3—271no—
89C2×C3⋊D3—541no—
90C2×C3×D3—271no—
91C2×C3×D3—271no—
92C2×C3×D3—541no—
93C32×C4—271no—
94C3⋊Dic3—31no—
95C3⋊Dic3—31no—
96C3⋊Dic3—31no—
97C3⋊Dic3—61no—
98C3×Dic3—93no—
99C3×Dic3—93no—
100C3×Dic3—91no—
101C3×Dic3—91no—
102C3×Dic3—271no—
103C3×Dic3—271no—
104C3×Dic3—541no—
105C2×D9—271no—
106C2×D9—541no—
107C4×C9—271no—
108Dic9—31no—
109Dic9—61no—
110C33—21no—
111C33D3×Dic311yescharacteristic
112C33#62411yescharacteristic
1133−1+2—63no—
114H(3,𝔽3)—33no—
115C3×C9—21no—
116C3×C9—21no—
117C3×C9—33no—
118C3×C9—41no—
119C3×C9D3×Dic311yescharacteristic
120C2×Dic3—811no—
121C4×D3—811no—
122C4×D3—811no—
123C4×D3—813no—
124C2×C32—31no—
125C2×C32—31no—
126C2×C32—31no—
127C2×C32—61no—
128C2×C32—61no—
129C2×C32—61no—
130C2×C32—61no—
131C2×C32—121no—
132C2×C32((C3⋊D3)⋊C3)⋊C213yes—
133C2×C32#111311yescharacteristic
134C3⋊D3—92no—
135C3⋊D3—96no—
136C3⋊D3—272no—
137C3⋊D3—542no—
138C3×D3—272no—
139C3×D3—272no—
140C3×D3—542no—
141C2×C9—31no—
142C2×C9—61no—
143C2×C9—61no—
144C2×C9—121no—
145D9—272no—
146D9—542no—
147C22×C3—811no—
148C2×D3—271no—
149C2×D3—271no—
150C2×D3—541no—
151C2×D3—813no—
152C3×C4—273no—
153C3×C4—271no—
154C3×C4—271no—
155Dic3—93no—
156Dic3—91no—
157Dic3—91no—
158Dic3—271no—
159Dic3—271no—
160Dic3—541no—
161C32—31no—
162C32—31no—
163C32—31no—
164C32—61no—
165C32—61no—
166C32—61no—
167C32—61no—
168C32—121no—
169C32((C3⋊D3)⋊C3)⋊C413yes—
170C32#629411yescharacteristic
171C9—31no—
172C9—61no—
173C9—61no—
174C9—121no—
175C2×C4—2431noSylow
176C2×C3—21no—
177C2×C3—33no—
178C2×C3—91no—
179C2×C3—181no—
180C2×C3—812no—
181C2×C3#6643211yescharacteristic
182C2×C3#4207⋊C211yescharacteristic
183D3—272no—
184D3—272no—
185D3—542no—
186D3—816no—
187C22—811no—
188C4—271no—
189C4—271no—
190C3—21no—
191C3—33no—
192C3—91no—
193C3—181no—
194C3#1061990111yescharacteristic
195C3#4207⋊C411yescharacteristic
196C2—812no—
197C2#92304⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92304⋊C2
commutator, hypocenter#6893C2×C4
Frattini, socleC2×C32#1113
Fitting, cosocleC2×#6893C22
prime radicalC2×#92306C2
LCSG ▷ #6893
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757609C2semidirect
3. #11757608C2semidirect
8. #92306C4semidirect
18. #66328D3semidirect
21. #6893C2×C4semidirect
30. C3⋊(C3⋊D9)Dic3semidirect
59. C32×C9C2×Dic3semidirect
63. C32⋊C9C4×D3semidirect

Maximal subgroups

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

subgroupindex
C2×#923062
#117576092
#117576082
#106198833
#106198703
#4169⋊C43