Finite Group Databasebeta

← C3×#2912⋊C3 #11919560

Subgroups — C3×#2912⋊C3 #11919560

Order 1152.

324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 94 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×C3×#131⋊C3C211yesmaximal, characteristic
2C3×#520⋊C3C212yesmaximal
3C3×#2912C311yesmaximal, characteristic, complemented
4#2912⋊C3C313yesmaximal, direct product factor
5C2×C3×#41⋊C3C2211yescharacteristic
6C3×#131⋊C3C412yescomplemented
7C3×C4×SL(2,𝔽3)—22no—
8C32×#106—41nomaximal
9C2×C3×#131C2×C311yescharacteristic
10C3×#520C2×C312yes—
11C2×#131⋊C3C2×C313yes—
12#520⋊C3C2×C316yes—
13C3×#428—32no—
14C3×#427—31no—
15C2×C3×#106—31no—
16C3×#41⋊C3C2×C411yescharacteristic
17C3×#41⋊C3Q811yescharacteristic
18C2×C3×SL(2,𝔽3)D411yescharacteristic
19C2×C32×C8—41no—
20C32×C4⋊C4—42no—
21#2912C3211yescharacteristic, complemented, Sylow
22C2×C3×#41C22×C311yescharacteristic
23C2×#41⋊C3C22×C313yes—
24C3×#131—32no—
25C3×#131C3×C412yescomplemented
26C2×C3×M16—31no—
27C22×C3×C8—31no—
28C3×C4×Q8—22no—
29C3×C4×D4—62no—
30C3×#117—32no—
31C2×C3×C4⋊C4—32no—
32#131⋊C3C3×C416yescomplemented
33C4×SL(2,𝔽3)—26no—
34C3×#107—32no—
35C3×#106—32no—
36C3×#106—31no—
37C3×#106—43no—
38C3×#106A411yescharacteristic
39C2×C32×C4—41no—
40C2×C32×C4—82no—
41C3×SL(2,𝔽3)C4⋊C411yescharacteristic
42C32×C8—42no—
43C2×#131C2×C3211yescharacteristic
44#520C2×C3212yes—
45#428—32no—
46#427—31no—
47C2×#106—31no—
48C3×#41—31no—
49C3×#41—31no—
50C3×#41C2×C3×C411yescharacteristic
51C3×#41C3×Q811yescharacteristic
52C2×C3×Q8C3×D411yescharacteristic
53C2×C3×D4—31no—
54C22×C3×C4—31no—
55C22×C3×C4—62no—
56#41⋊C3C2×C3×C413yes—
57#41⋊C3C3×Q813yes—
58C2×SL(2,𝔽3)C3×D413yes—
59C3×M16—32no—
60C3×M16—32no—
61C2×C3×C8—31no—
62C2×C3×C8—32no—
63C2×C3×C8—32no—
64C2×C3×C8—43no—
65C2×C3×C8C2×A411yescharacteristic
66C3×C4⋊C4—32no—
67C3×C4⋊C4—46no—
68C3×C4⋊C4—62no—
69C3×C4⋊C4C2×A412yes—
70C3×C22⋊C4—62no—
71C3×C42—62no—
72C22×C32—41no—
73C32×C4—41no—
74C32×C4—41no—
75C32×C4—162no—
76C2×#41C22×C3211yescharacteristic
77#131—32no—
78#131C32×C412yescomplemented
79C2×M16—31no—
80C22×C8—31no—
81C4×Q8—22no—
82C4×D4—62no—
83#117—32no—
84C2×C4⋊C4—32no—
85#107—32no—
86#106—32no—
87#106—31no—
88#106C3×A411yescharacteristic
89C23×C3—31no—
90C3×Q8—31no—
91C3×Q8C3×C4⋊C411yescharacteristic
92C3×D4—31no—
93C3×D4—31no—
94C3×D4—32no—
95C2×C3×C4—22no—
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—31no—
99C2×C3×C4—31no—
100C2×C3×C4—31no—
101C2×C3×C4—43no—
102C2×C3×C4—62no—
103C2×C3×C4—86no—
104C2×C3×C4—242no—
105C2×C3×C4C22×A411yescharacteristic
106SL(2,𝔽3)C3×C4⋊C413yes—
107C3×C8—32no—
108C3×C8—46no—
109C3×C8C4×A412yes—
110C2×C32—41no—
111C2×C32—42no—
112#41—31no—
113#41—31no—
114#41C2×C32×C411yescharacteristic
115#41C32×Q811yescharacteristic
116C2×Q8C32×D411yescharacteristic
117C2×D4—31no—
118C22×C4—31no—
119C22×C4—62no—
120M16—32no—
121M16—32no—
122C2×C8—31no—
123C2×C8—32no—
124C2×C8—32no—
125C2×C8C2×C3×A411yescharacteristic
126C4⋊C4—32no—
127C4⋊C4—62no—
128C4⋊C4C2×C3×A412yes—
129C22⋊C4—62no—
130C42—62no—
131C22×C3—31no—
132C22×C3—31no—
133C22×C3—43no—
134C22×C3—62no—
135C22×C3D4×A411yescharacteristic
136C3×C4—31no—
137C3×C4—31no—
138C3×C4—42no—
139C3×C4—43no—
140C3×C4—43no—
141C3×C4—122no—
142C3×C4—166no—
143C3×C4C2×C4×A411yescharacteristic
144C3×C4Q8×A411yescharacteristic
145C32—41noSylow
146C23—31no—
147Q8—31no—
148Q8C32×C4⋊C411yescharacteristic
149D4—31no—
150D4—31no—
151D4—32no—
152C2×C4—22no—
153C2×C4—31no—
154C2×C4—31no—
155C2×C4—31no—
156C2×C4—31no—
157C2×C4—31no—
158C2×C4—62no—
159C2×C4—242no—
160C2×C4C22×C3×A411yescharacteristic
161C8—32no—
162C8C3×C4×A412yes—
163C2×C3—43no—
164C2×C3—46no—
165C2×C3—61no—
166C2×C3—61no—
167C2×C3A4×C4⋊C411yescharacteristic
168C2×C3#577⋊C312yes—
169C22—31no—
170C22—31no—
171C22—62no—
172C22C3×D4×A411yescharacteristic
173C4—31no—
174C4—31no—
175C4—42no—
176C4—122no—
177C4C2×C3×C4×A411yescharacteristic
178C4C3×Q8×A411yescharacteristic
179C3—43no—
180C3#2912⋊C311yescharacteristic, direct product factor
181C2—61no—
182C2—61no—
183C2C3×A4×C4⋊C411yescharacteristic
184C2C3×#577⋊C312yes—
subgroupG/H
center, socleC22×C3D4×A4
commutator#41C2×C32×C4
FrattiniC2×C4C22×C3×A4
FittingC3×#2912C3
prime radicalC2×C3×#41⋊C3C22
cosocleC2×#41C22×C32
hypercenterC3×#106A4
hypocenterQ8C32×C4⋊C4
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#106

Complements

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

NH ≅ G/Ntype
3. C3×#2912C3semidirect
4. #2912⋊C3C3direct (N × H)
6. C3×#131⋊C3C4semidirect
21. #2912C32semidirect
25. C3×#131C3×C4semidirect
32. #131⋊C3C3×C4semidirect
78. #131C32×C4semidirect
180. C3#2912⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#131⋊C32
C3×#520⋊C32
C3×#29123
#2912⋊C33
C32×#1064