Finite Group Databasebeta

← C3×#73139 #11920917

Subgroups — C3×#73139 #11920917

Order 1152.

209 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 209 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C3×#578⋊C3C211yesmaximal, characteristic, complemented
2C3×#5407C211yesmaximal, characteristic, complemented
3C3×#4628C211yesmaximal, characteristic, complemented
4#73139C311yesmaximal, characteristic, direct product factor
5C3×#2193—31nomaximal
6C3×2−1+4⋊C3—21no—
7C3×#986—21no—
8C3×#131⋊C3C2211yescharacteristic
9C3×#826—41nomaximal
10C3×#578D311yescharacteristic, complemented
11#578⋊C3—21no—
12#578⋊C3C2×C311yescharacteristic, complemented
13#5407C2×C311yescharacteristic, complemented
14C3×#509—31no—
15C2×C3×SD32—31no—
16C3×#472—31no—
17#4628C2×C311yescharacteristic, complemented
18C3×#362—31no—
19C3×#359—31no—
20C3×#350—31no—
21C3×#41⋊C3D411yescharacteristic
22C2×C3×SL(2,𝔽3)—41no—
23C3×GL(2,𝔽3)—41no—
24C32×D8—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27#2193—31noSylow
28C3×2−1+4—21no—
292−1+4⋊C3—22no—
302−1+4⋊C3—21no—
31#986—21no—
32C3×#137—61no—
33C3×AGL(1,ℤ/8)—61no—
34C3×#135—31no—
35C2×C3×Q16—31no—
36C2×C3×D8—31no—
37C3×#131C2×D311yescharacteristic
38#131⋊C3—21no—
39#131⋊C3C22×C311yescharacteristic
40C3×SD32—62no—
41C3×SD32—61no—
42C3×D16—61no—
43C3×M32—31no—
44C2×C3×C16—31no—
45C3×#108—31no—
46C3×#100—61no—
47#826—41no—
48C32×D4—81no—
49C3×D12—81no—
50C3×SL(2,𝔽3)D811yescharacteristic
51C32×C8—41no—
52#578C3×D311yescharacteristic, complemented
53#509—31no—
54C2×SD32—31no—
55#472—31no—
56#362—31no—
57#359—31no—
58#350—31no—
59C3×#41—61no—
60C3×#41—121no—
61C3×#41#6711yescharacteristic
62C2×C3×Q8—41no—
63C2×C3×Q8—61no—
64C2×C3×D4—61no—
65#41⋊C3—21no—
66#41⋊C3C3×D411yescharacteristic
67C2×SL(2,𝔽3)—42no—
68C2×SL(2,𝔽3)—41no—
69GL(2,𝔽3)—41no—
70C3×Q16—32no—
71C3×Q16—31no—
72C3×SD16—61no—
73C3×SD16—121no—
74C3×D8—41no—
75C3×D8—61no—
76C3×D8—61no—
77C3×D8—81no—
78C3×D8—121no—
79C3×D8S411yescharacteristic
80C3×M16—31no—
81C3×M16—61no—
82C2×C3×C8—31no—
83D24—41no—
84C3×C16—61no—
85C3×C16—61no—
86C3⋊C16—41no—
87C22×C32—161no—
88C2×C3×D3—161no—
89C32×C4—41no—
902−1+4—21no—
91#137—61no—
92AGL(1,ℤ/8)—61no—
93#135—31no—
94C2×Q16—31no—
95C2×D8—31no—
96#131C2×C3×D311yescharacteristic
97SD32—62no—
98SD32—61no—
99D16—61no—
100M32—31no—
101C2×C16—31no—
102#108—31no—
103#100—61no—
104C23×C3—121no—
105C3×Q8—61no—
106C3×Q8—121no—
107C3×Q8#21311yescharacteristic
108C3×D4—21no—
109C3×D4—31no—
110C3×D4—81no—
111C3×D4—82no—
112C3×D4—121no—
113C3×D4—121no—
114C3×D4—121no—
115C2×C3×C4—31no—
116C2×C3×C4—121no—
117C2×C3×C4—121no—
118D12—81no—
119SL(2,𝔽3)—21no—
120SL(2,𝔽3)C3×D811yescharacteristic
121C3×C8—31no—
122C3×C8—41no—
123C3×C8—81no—
124C3×C8—121no—
125C3×C8C2×S411yescharacteristic
126C2×C32—41no—
127C2×C32—321no—
128C3×D3—321no—
129#41—61no—
130#41—121no—
131#41C3×#6711yescharacteristic
132C2×Q8—41no—
133C2×Q8—61no—
134C2×D4—61no—
135Q16—32no—
136Q16—31no—
137SD16—61no—
138SD16—121no—
139D8—61no—
140D8—61no—
141D8—121no—
142D8C3×S411yescharacteristic
143M16—31no—
144M16—61no—
145C2×C8—31no—
146C16—61no—
147C16—61no—
148C22×C3—31no—
149C22×C3—41no—
150C22×C3—161no—
151C22×C3—162no—
152C22×C3—241no—
153C22×C3—481no—
154C2×D3—161no—
155C3×C4—31no—
156C3×C4—41no—
157C3×C4—81no—
158C3×C4—121no—
159C3×C4GL(2,ℤ/4)11yescharacteristic
160C32—41noSylow
161C23—121no—
162Q8—61no—
163Q8—121no—
164Q8C3×#21311yescharacteristic
165D4—21no—
166D4—31no—
167D4—121no—
168D4—121no—
169D4—121no—
170C2×C4—31no—
171C2×C4—121no—
172C2×C4—121no—
173C8—31no—
174C8—121no—
175C8C2×C3×S411yescharacteristic
176C2×C3—41no—
177C2×C3—61no—
178C2×C3—81no—
179C2×C3—81no—
180C2×C3—321no—
181C2×C3—322no—
182C2×C3—481no—
183C2×C3#541511yescharacteristic
184D3—321no—
185C22—31no—
186C22—41no—
187C22—241no—
188C22—481no—
189C4—31no—
190C4—121no—
191C4C3×GL(2,ℤ/4)11yescharacteristic
192C3—41no—
193C3—81no—
194C3#7313911yescharacteristic, direct product factor
195C2—61no—
196C2—81no—
197C2—481no—
198C2C3×#541511yescharacteristic
subgroupG/H
center, socleC2×C3#5415
commutator, cosocle#131⋊C3C22×C3
FrattiniC8C2×C3×S4
FittingC3×#578D3
hypercenterC3×D8S4
hypocenterSL(2,𝔽3)C3×D8
LCSG ▷ #131⋊C3 ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D8

Complements

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

NH ≅ G/Ntype
1. C3×#578⋊C3C2semidirect
2. C3×#5407C2semidirect
3. C3×#4628C2semidirect
4. #73139C3direct (N × H)
10. C3×#578D3semidirect
12. #578⋊C3C2×C3semidirect
13. #5407C2×C3semidirect
17. #4628C2×C3semidirect
52. #578C3×D3semidirect
194. C3#73139direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#578⋊C32
C3×#54072
C3×#46282
#731393
C3×#21933
C3×#8264