Finite Group Databasebeta

← #11795131

Subgroups — #11795131

Order 1152.

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

normal subgroups only

This group has 276 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×AGL(1,𝔽9)⋊C4C212yesmaximal
2#10593548C211yesmaximal, characteristic
3#10593413C211yesmaximal, characteristic
4#10593267C211yesmaximal, characteristic
5#10593166C212yesmaximal
6C22×AGL(1,𝔽9)C2212yes—
7C2×C4×#157C2211yescharacteristic
8C2×#3777—21no—
9C2×#3777C2211yescharacteristic
10C2×#3777C2211yescharacteristic
11C2×#3773—21no—
12C2×#3773C2212yes—
13AGL(1,𝔽9)⋊C4—24no—
14#63900—21no—
15#63781—21no—
16C22×#157—21no—
17C22×#157—21no—
18C22×#157D411yescharacteristic
19C22×#157C2311yescharacteristic
20C2×AGL(1,𝔽9)—22no—
21C2×AGL(1,𝔽9)—22no—
22C2×AGL(1,𝔽9)Q814yes—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×#624—22no—
25C4×#157—22no—
26#3777—21no—
27#3777—22no—
28#3777—42no—
29#3777D412yes—
30#3773—22no—
31#3773—22no—
32#3773—42no—
33C3×C4⋊Dic3—41no—
34#3724—41no—
35#2084—91nomaximal, Sylow
36D3×C4⋊C4—121no—
37C22×C3⋊D3C2×D411yescharacteristic
38C2×#157—21no—
39C2×#157—21no—
40C2×#157—22no—
41C2×#157—41no—
42C2×#157—41no—
43C2×#157—41no—
44C2×#157—41no—
45C2×#157—41no—
46C2×#157SD1612yes—
47C2×#157C2×D411yescharacteristic
48C2×#157C2×Q812yes—
49C2×#157#4112yes—
50C2×#157#4111yescharacteristic
51AGL(1,𝔽9)—24no—
52C2×C32×C4SD1611yescharacteristic
53C2×C3⋊Dic3SD1611yescharacteristic
54C4×C3⋊D3—21no—
55C4×C3⋊D3—21no—
56C2×C3×Dic3—42no—
57#624—42no—
58#624—42no—
59C2×#106—92no—
60#389—91no—
61#384—91no—
62#340—92no—
63#336—91no—
64C2×C4×D3—121no—
65C2×C4×D3—122no—
66C3×C4⋊C4—121no—
67C4⋊Dic3—41no—
68Dic3⋊C4—122no—
69C22×C32C2×SD1611yescharacteristic
70C2×C3⋊D3#12111yescharacteristic
71C2×C3⋊D3#12311yescharacteristic
72C2×C3⋊D3C4⋊Q811yescharacteristic
73C2×C3⋊D3C2×SD1611yescharacteristic
74C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
75C2×C3⋊D3#13711yescharacteristic
76#157—22no—
77#157—42no—
78#157—81no—
79#157C22⋊Q812yes—
80#157#12512yes—
81C32×C4—21no—
82C3⋊Dic3—21no—
83C3×Dic3—82no—
84C22×C8—92no—
85C2×C4⋊C4—91no—
86C2×C4⋊C4—91no—
87C2×C4⋊C4—92no—
88C2×C4⋊C4—181no—
89C2×C4⋊C4—181no—
90C2×C4⋊C4—181no—
91C2×C42—91no—
92#106—184no—
93#95—181no—
94C22×D3—121no—
95C2×C3×C4—41no—
96C2×C3×C4—122no—
97C2×Dic3—42no—
98C2×Dic3—121no—
99C4×D3—122no—
100C4×D3—122no—
101C4×D3—242no—
102C4×D3—242no—
103C2×C32#46011yescharacteristic
104C2×C32#48311yescharacteristic
105C2×C32#49811yescharacteristic
106C3⋊D3#39811yescharacteristic
107C3⋊D3#46111yescharacteristic
108C3⋊D3#48111yescharacteristic
109C3⋊D3#50111yescharacteristic
110C22×C4—91no—
111C22×C4—91no—
112C22×C4—91no—
113C22×C4—182no—
114C22×C4—181no—
115C22×C4—181no—
116C2×C8—94no—
117C2×C8—182no—
118C2×C8—182no—
119C4⋊C4—92no—
120C4⋊C4—121no—
121C4⋊C4—181no—
122C4⋊C4—182no—
123C4⋊C4—182no—
124C4⋊C4—182no—
125C4⋊C4—361no—
126C4⋊C4—362no—
127C4⋊C4—362no—
128C42—182no—
129C22×C3—41no—
130C2×D3—121no—
131C2×D3—121no—
132C2×D3—121no—
133C2×D3—121no—
134C2×D3—121no—
135C2×D3—121no—
136C3×C4—42no—
137C3×C4—242no—
138Dic3—82no—
139Dic3—122no—
140C32#208411yescharacteristic, complemented, Sylow
141C23—91no—
142C2×C4—92no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—92no—
146C2×C4—92no—
147C2×C4—91no—
148C2×C4—122no—
149C2×C4—181no—
150C2×C4—181no—
151C2×C4—181no—
152C2×C4—181no—
153C2×C4—182no—
154C2×C4—362no—
155C2×C4—362no—
156C2×C4—361no—
157C2×C4—361no—
158C2×C4—361no—
159C2×C4—361no—
160C2×C4—361no—
161C2×C4AΓL(1,𝔽9)11yescharacteristic
162C8—184no—
163C2×C3—41no—
164C2×C3—41no—
165C2×C3—41no—
166D3—121no—
167D3—121no—
168D3—121no—
169D3—121no—
170C22—91no—
171C22—91no—
172C22—91no—
173C22—91no—
174C22—91no—
175C22—91no—
176C22C2×AΓL(1,𝔽9)11yescharacteristic
177C4—21no—
178C4—92no—
179C4—92no—
180C4—182no—
181C4—181no—
182C4—242no—
183C4—362no—
184C4—721no—
185C3—41no—
186C2—91no—
187C2—91no—
188C2—91no—
189C2—91no—
190C2AGL(1,𝔽9)⋊Q811yescharacteristic
191C2#1059641011yescharacteristic
192C2#1059641511yescharacteristic
subgroupG/H
center, FrattiniC22C2×AΓL(1,𝔽9)
commutator, cosocleC22×#157C23
FittingC2×C32×C4SD16
socleC22×C32C2×SD16
prime radicalC22×C3⋊D3C2×D4
hypercenterC2×C4AΓL(1,𝔽9)
hypocenterC32#2084
LCSG ▷ C22×#157 ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
140. C32#2084semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,𝔽9)⋊C42
#105935482
#105934132
#105932672
#105931662
#20849