Finite Group Databasebeta

← C3×#73125 #11920902

Subgroups — C3×#73125 #11920902

Order 1152.

269 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 269 conjugacy classes of subgroups — too many to draw. Only its 60 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×#5426C212yesmaximal
3#73125C311yesmaximal, characteristic, direct product factor
4C3×#1815—31nomaximal
5C2×C3×#41⋊C3C2211yescharacteristic
6C3×#131⋊C3C412yescomplemented
7C3×#859—22no—
8C3×#817—41nomaximal
9C2×C3×#131D311yescharacteristic
10C2×#131⋊C3—21no—
11C2×#131⋊C3C2×C311yescharacteristic
12#5426C2×C312yes—
13C2×C3×#108—31no—
14C2×C3×#106—31no—
15C3×#417—32no—
16C3×#343—32no—
17C3×#41⋊C3C2×C411yescharacteristic
18C3×#41⋊C3Q811yescharacteristic
19C2×C3×SL(2,𝔽3)D411yescharacteristic
20C2×C32×C8—41no—
21C3×C4⋊Dic3—42no—
22#1815—31noSylow
23C2×C3×#41C2×D311yescharacteristic
24C2×#41⋊C3—21no—
25C2×#41⋊C3C22×C311yescharacteristic
26C3×#131—32no—
27C3×#131Dic312yescomplemented
28C2×C3×M16—31no—
29C2×C3×M16—32no—
30C22×C3×C8—31no—
31C2×C3×C4⋊C4—32no—
32#131⋊C3—22no—
33#131⋊C3C3×C412yescomplemented
34#859—22no—
35C3×#108—62no—
36C3×#106—61no—
37C3×#106—61no—
38C3×#103—62no—
39C3×#102—62no—
40#817—41no—
41C2×C32×C4—41no—
42C2×C3×Dic3—82no—
43C3×SL(2,𝔽3)C4⋊C411yescharacteristic
44C32×C8—42no—
45C2×#131C3×D311yescharacteristic
46C2×#108—31no—
47C2×#106—31no—
48#417—32no—
49#343—32no—
50C3×#41—31no—
51C3×#41—31no—
52C3×#41Dic611yescharacteristic
53C3×#41C2×Dic311yescharacteristic
54C2×C3×Q8D1211yescharacteristic
55C2×C3×D4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—62no—
58#41⋊C3—21no—
59#41⋊C3—21no—
60#41⋊C3C2×C3×C411yescharacteristic
61#41⋊C3C3×Q811yescharacteristic
62C2×SL(2,𝔽3)—21no—
63C2×SL(2,𝔽3)C3×D411yescharacteristic
64C3×M16—32no—
65C3×M16—61no—
66C3×M16—62no—
67C3×M16—62no—
68C2×C3×C8—31no—
69C2×C3×C8—32no—
70C2×C3×C8—32no—
71C2×C3×C8—41no—
72C2×C3×C8—62no—
73C2×C3×C8—81no—
74C2×C3×C8S411yescharacteristic
75C3×C4⋊C4—62no—
76C3×C4⋊C4—62no—
77C4⋊Dic3—42no—
78C22×C32—41no—
79C32×C4—41no—
80C32×C4—41no—
81C3×Dic3—162no—
82C2×#41C2×C3×D311yescharacteristic
83#131—32no—
84#131C3×Dic312yescomplemented
85C2×M16—31no—
86C2×M16—32no—
87C22×C8—31no—
88C2×C4⋊C4—32no—
89#108—62no—
90#106—61no—
91#106—61no—
92#103—62no—
93#102—62no—
94C23×C3—31no—
95C3×Q8—31no—
96C3×Q8C4⋊Dic311yescharacteristic
97C3×D4—31no—
98C3×D4—31no—
99C3×D4—61no—
100C2×C3×C4—31no—
101C2×C3×C4—31no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—41no—
106C2×C3×C4—81no—
107C2×C3×C4—122no—
108C2×C3×C4—242no—
109C2×C3×C4C2×S411yescharacteristic
110C2×Dic3—82no—
111SL(2,𝔽3)—21no—
112SL(2,𝔽3)C3×C4⋊C411yescharacteristic
113C3×C8—32no—
114C3×C8—42no—
115C3×C8—82no—
116C3×C8—122no—
117C3×C8SL(2,ℤ/4)12yes—
118C2×C32—42no—
119C2×C32—41no—
120#41—31no—
121#41—31no—
122#41C3×Dic611yescharacteristic
123#41C2×C3×Dic311yescharacteristic
124C2×Q8C3×D1211yescharacteristic
125C2×D4—31no—
126C22×C4—31no—
127C22×C4—62no—
128M16—32no—
129M16—61no—
130M16—62no—
131M16—62no—
132C2×C8—31no—
133C2×C8—32no—
134C2×C8—32no—
135C2×C8—62no—
136C2×C8C3×S411yescharacteristic
137C4⋊C4—62no—
138C4⋊C4—62no—
139C22×C3—31no—
140C22×C3—31no—
141C22×C3—41no—
142C22×C3—62no—
143C22×C3—81no—
144C22×C3C4⋊S411yescharacteristic
145C3×C4—31no—
146C3×C4—31no—
147C3×C4—41no—
148C3×C4—41no—
149C3×C4—81no—
150C3×C4—81no—
151C3×C4—242no—
152C3×C4A4⋊Q811yescharacteristic
153C3×C4C2×SL(2,ℤ/4)11yescharacteristic
154Dic3—162no—
155C32—41noSylow
156C23—31no—
157Q8—31no—
158Q8C3×C4⋊Dic311yescharacteristic
159D4—31no—
160D4—31no—
161D4—61no—
162C2×C4—31no—
163C2×C4—31no—
164C2×C4—31no—
165C2×C4—31no—
166C2×C4—31no—
167C2×C4—122no—
168C2×C4—242no—
169C2×C4C2×C3×S411yescharacteristic
170C8—32no—
171C8—122no—
172C8C3×SL(2,ℤ/4)12yes—
173C2×C3—42no—
174C2×C3—41no—
175C2×C3—61no—
176C2×C3—61no—
177C2×C3—82no—
178C2×C3—81no—
179C2×C3#540612yes—
180C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
181C22—31no—
182C22—31no—
183C22—62no—
184C22C3×C4⋊S411yescharacteristic
185C4—31no—
186C4—31no—
187C4—242no—
188C4C3×A4⋊Q811yescharacteristic
189C4C2×C3×SL(2,ℤ/4)11yescharacteristic
190C3—41no—
191C3—81no—
192C3#7312511yescharacteristic, direct product factor
193C2—61no—
194C2—61no—
195C2C3×#540612yes—
196C2C3×C4⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, socleC22×C3C4⋊S4
commutator#41⋊C3C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC2×C3×#131D3
prime radicalC2×C3×#41⋊C3C22
cosocleC2×#41⋊C3C22×C3
hypercenterC2×C3×C8S4
hypocenterSL(2,𝔽3)C3×C4⋊C4
LCSG ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
3. #73125C3direct (N × H)
6. C3×#131⋊C3C4semidirect
27. C3×#131Dic3semidirect
33. #131⋊C3C3×C4semidirect
84. #131C3×Dic3semidirect
192. C3#73125direct (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×#54262
#731253
C3×#18153
C3×#8174