Finite Group Databasebeta

← C3×#5425 #10593611

Subgroups — C3×#5425 #10593611

Order 576.

161 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 161 conjugacy classes of subgroups — too many to draw. Only its 30 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×#41⋊C3C211yesmaximal, characteristic
2C2×C3×#226C211yesmaximal, characteristic, complemented
3C3×#859C211yesmaximal, characteristic, complemented
4#5425C311yesmaximal, characteristic, direct product factor
5C3×#452—31nomaximal
6C3×#41⋊C3—21no—
7C2×C3×SL(2,𝔽3)C2211yescharacteristic
8C3×#226—21no—
9C3×Dic3⋊C4—41nomaximal
10C2×C3×#41D311yescharacteristic
11C2×#41⋊C3—21no—
12C2×#41⋊C3C2×C311yescharacteristic
13C2×#226C2×C311yescharacteristic, complemented
14C2×C3×Q16—31no—
15C2×C3×SD16—31no—
16C3×C22⋊Q8—31no—
17#859C2×C311yescharacteristic, complemented
18C3×#103—31no—
19C3×#102—31no—
20C3×C22⋊C8—31no—
21C2×C32×C4—41no—
22C2×C3×Dic3—41no—
23C2×C3×Dic3—41no—
24C3×SL(2,𝔽3)D411yescharacteristic
25#452—31noSylow
26C3×#41—21no—
27C3×#41—61no—
28C2×C3×Q8—31no—
29C2×C3×Q8C2×D311yescharacteristic
30C2×C3×D4—31no—
31C22×C3×C4—31no—
32#41⋊C3—22no—
33#41⋊C3—21no—
34C2×SL(2,𝔽3)—21no—
35C2×SL(2,𝔽3)C22×C311yescharacteristic
36#226—21no—
37C3×Q16—61no—
38C3×Q16—61no—
39C3×SD16—62no—
40C2×C3×C8—31no—
41C2×C3×C8—31no—
42C3×C4⋊C4—31no—
43C3×C4⋊C4—61no—
44C3×C22⋊C4—61no—
45Dic3⋊C4—41no—
46C22×C32—41no—
47C32×C4—81no—
48C3×Dic3—42no—
49C3×Dic3—81no—
50C2×#41C3×D311yescharacteristic
51C2×Q16—31no—
52C2×SD16—31no—
53C22⋊Q8—31no—
54#103—31no—
55#102—31no—
56C22⋊C8—31no—
57C23×C3—31no—
58C3×Q8—31no—
59C3×Q8—61no—
60C3×Q8—61no—
61C3×Q8#6711yescharacteristic
62C3×D4—32no—
63C3×D4—61no—
64C2×C3×C4—31no—
65C2×C3×C4—41no—
66C2×C3×C4—61no—
67C2×C3×C4—61no—
68C2×C3×C4—61no—
69C2×C3×C4—61no—
70C2×C3×C4—81no—
71C2×C3×C4S411yescharacteristic
72C2×Dic3—41no—
73C2×Dic3—41no—
74SL(2,𝔽3)—21no—
75SL(2,𝔽3)C3×D411yescharacteristic
76C3×C8—61no—
77C3×C8—61no—
78C2×C32—41no—
79C2×C32—41no—
80C2×C32—41no—
81#41—21no—
82#41—61no—
83C2×Q8—31no—
84C2×Q8C2×C3×D311yescharacteristic
85C2×D4—31no—
86C22×C4—31no—
87Q16—61no—
88Q16—61no—
89SD16—62no—
90C2×C8—31no—
91C2×C8—31no—
92C4⋊C4—31no—
93C4⋊C4—61no—
94C22⋊C4—61no—
95C22×C3—41no—
96C22×C3—61no—
97C22×C3—61no—
98C22×C3—61no—
99C22×C3—81no—
100C22×C3C2×S411yescharacteristic
101C3×C4—21no—
102C3×C4—31no—
103C3×C4—31no—
104C3×C4—81no—
105C3×C4—82no—
106C3×C4—121no—
107C3×C4—121no—
108Dic3—42no—
109Dic3—81no—
110C32—41noSylow
111C23—31no—
112Q8—31no—
113Q8—61no—
114Q8—61no—
115Q8C3×#6711yescharacteristic
116D4—32no—
117D4—61no—
118C2×C4—31no—
119C2×C4—61no—
120C2×C4—61no—
121C2×C4—61no—
122C2×C4—61no—
123C2×C4C3×S411yescharacteristic
124C8—61no—
125C8—61no—
126C2×C3—41no—
127C2×C3—41no—
128C2×C3—41no—
129C2×C3—81no—
130C2×C3—81no—
131C2×C3—81no—
132C2×C3—121no—
133C2×C3#98411yescharacteristic
134C2×C3#98511yescharacteristic
135C2×C3GL(2,ℤ/4)11yescharacteristic
136C22—61no—
137C22—61no—
138C22—61no—
139C22C2×C3×S411yescharacteristic
140C4—21no—
141C4—31no—
142C4—31no—
143C4—121no—
144C4—121no—
145C3—41no—
146C3—81no—
147C3#542511yescharacteristic, direct product factor
148C2—121no—
149C2C3×#98411yescharacteristic
150C2C3×#98511yescharacteristic
151C2C3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, socleC22×C3C2×S4
commutator, cosocleC2×SL(2,𝔽3)C22×C3
FrattiniC22C2×C3×S4
FittingC2×C3×#41D3
prime radicalC2×C3×#41⋊C3C2
hypercenterC2×C3×C4S4
hypocenterSL(2,𝔽3)C3×D4
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#226C2semidirect
3. C3×#859C2semidirect
4. #5425C3direct (N × H)
13. C2×#226C2×C3semidirect
17. #859C2×C3semidirect
147. C3#5425direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41⋊C32
C2×C3×#2262
C3×#8592
#54253
C3×#4523
C3×Dic3⋊C44