Finite Group Databasebeta

← C3×#73137 #11920915

Subgroups — C3×#73137 #11920915

Order 1152.

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

normal subgroups only

This group has 207 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×#576⋊C3C211yesmaximal, characteristic, complemented
2C3×#5407C211yesmaximal, characteristic, complemented
3C3×#4628C211yesmaximal, characteristic, complemented
4#73137C311yesmaximal, characteristic, direct product factor
5C3×#2192—31nomaximal
6C3×#994—21no—
7C3×#986—21no—
8C3×#131⋊C3C2211yescharacteristic
9C3×#828—41nomaximal
10C3×#576D311yescharacteristic, complemented
11#576⋊C3—21no—
12#576⋊C3C2×C311yescharacteristic, complemented
13#5407C2×C311yescharacteristic, complemented
14C3×#509—31no—
15C2×C3×D16—31no—
16C3×#472—31no—
17#4628C2×C311yescharacteristic, complemented
18C3×#361—31no—
19C3×#359—31no—
20C3×#350—31no—
21C3×#41⋊C3—41no—
22C3×#41⋊C3D411yescharacteristic
23C3×GL(2,𝔽3)—41no—
24C32×Q16—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27#2192—31noSylow
28C3×H(5,𝔽2)—21no—
29#994—22no—
30#994—21no—
31#986—21no—
32C3×AGL(1,ℤ/8)—61no—
33C3×AGL(1,ℤ/8)—61no—
34C3×#135—31no—
35C2×C3×D8—31no—
36C2×C3×D8—31no—
37C3×#131C2×D311yescharacteristic
38#131⋊C3—21no—
39#131⋊C3C22×C311yescharacteristic
40C3×SD32—61no—
41C3×D16—62no—
42C3×D16—61no—
43C3×M32—31no—
44C2×C3×C16—31no—
45C3×#108—31no—
46C3×#100—61no—
47#828—41no—
48C32×Q8—81no—
49C3×D12—81no—
50C3×SL(2,𝔽3)D811yescharacteristic
51C32×C8—41no—
52#576C3×D311yescharacteristic, complemented
53#509—31no—
54C2×D16—31no—
55#472—31no—
56#361—31no—
57#359—31no—
58#350—31no—
59C3×#41—41no—
60C3×#41—61no—
61C3×#41#6711yescharacteristic
62C2×C3×D4—61no—
63C2×C3×D4—61no—
64C2×C3×D4—121no—
65#41⋊C3—21no—
66#41⋊C3—42no—
67#41⋊C3—41no—
68#41⋊C3C3×D411yescharacteristic
69GL(2,𝔽3)—41no—
70C3×Q16—41no—
71C3×Q16—81no—
72C3×Q16S411yescharacteristic
73C3×SD16—61no—
74C3×SD16—121no—
75C3×D8—32no—
76C3×D8—31no—
77C3×D8—61no—
78C3×D8—61no—
79C3×D8—121no—
80C3×M16—31no—
81C3×M16—61no—
82C2×C3×C8—31no—
83D24—41no—
84C3×C16—61no—
85C3×C16—61no—
86C3⋊C16—41no—
87C2×C3×D3—161no—
88C32×C4—41no—
89C32×C4—161no—
90H(5,𝔽2)—21no—
91AGL(1,ℤ/8)—61no—
92AGL(1,ℤ/8)—61no—
93#135—31no—
94C2×D8—31no—
95C2×D8—31no—
96#131C2×C3×D311yescharacteristic
97SD32—61no—
98D16—62no—
99D16—61no—
100M32—31no—
101C2×C16—31no—
102#108—31no—
103#100—61no—
104C23×C3—121no—
105C23×C3—121no—
106C3×Q8—21no—
107C3×Q8—81no—
108C3×Q8—82no—
109C3×Q8#21311yescharacteristic
110C3×D4—31no—
111C3×D4—61no—
112C3×D4—121no—
113C3×D4—121no—
114C3×D4—121no—
115C3×D4—121no—
116C2×C3×C4—31no—
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—
127C3×D3—321no—
128#41—41no—
129#41—61no—
130#41C3×#6711yescharacteristic
131C2×D4—61no—
132C2×D4—61no—
133C2×D4—121no—
134Q16C3×S411yescharacteristic
135SD16—61no—
136SD16—121no—
137D8—32no—
138D8—31no—
139D8—61no—
140D8—61no—
141D8—121no—
142M16—31no—
143M16—61no—
144C2×C8—31no—
145C16—61no—
146C16—61no—
147C22×C3—31no—
148C22×C3—121no—
149C22×C3—241no—
150C22×C3—481no—
151C22×C3—481no—
152C2×D3—161no—
153C3×C4—31no—
154C3×C4—41no—
155C3×C4—41no—
156C3×C4—81no—
157C3×C4—161no—
158C3×C4—162no—
159C3×C4GL(2,ℤ/4)11yescharacteristic
160C32—41noSylow
161C23—121no—
162C23—121no—
163Q8—21no—
164Q8C3×#21311yescharacteristic
165D4—31no—
166D4—61no—
167D4—121no—
168D4—121no—
169D4—121no—
170D4—121no—
171C2×C4—31no—
172C2×C4—121no—
173C8—31no—
174C8—121no—
175C8C2×C3×S411yescharacteristic
176C2×C3—41no—
177C2×C3—61no—
178C2×C3—81no—
179C2×C3—241no—
180C2×C3—481no—
181C2×C3#541511yescharacteristic
182D3—321no—
183C22—31no—
184C22—121no—
185C22—241no—
186C22—481no—
187C22—481no—
188C4—31no—
189C4—41no—
190C4C3×GL(2,ℤ/4)11yescharacteristic
191C3—41no—
192C3—81no—
193C3#7313711yescharacteristic, direct product factor
194C2—61no—
195C2—241no—
196C2—481no—
197C2C3×#541511yescharacteristic
subgroupG/H
center, socleC2×C3#5415
commutator, cosocle#131⋊C3C22×C3
FrattiniC8C2×C3×S4
FittingC3×#576D3
hypercenterC3×Q16S4
hypocenterSL(2,𝔽3)C3×D8
LCSG ▷ #131⋊C3 ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#576⋊C3C2semidirect
2. C3×#5407C2semidirect
3. C3×#4628C2semidirect
4. #73137C3direct (N × H)
10. C3×#576D3semidirect
12. #576⋊C3C2×C3semidirect
13. #5407C2×C3semidirect
17. #4628C2×C3semidirect
52. #576C3×D3semidirect
193. C3#73137direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#576⋊C32
C3×#54072
C3×#46282
#731373
C3×#21923
C3×#8284