Finite Group Databasebeta

← #11796062

Subgroups — #11796062

Order 1152.

302 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 67 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×#64287C211yesmaximal, characteristic
2C2×#64218C212yesmaximal, complemented
3#10593274C212yesmaximal, complemented
4#10593266C212yesmaximal, complemented
5C2×#3830C411yescharacteristic
6C2×#3792C411yescharacteristic
7C2×#3792C2211yescharacteristic
8C22×#622C411yescharacteristic
9C22×#622C2211yescharacteristic
10#64287—22no—
11#64287—22no—
12C2×#3788C2211yescharacteristic
13C2×#3787C411yescharacteristic
14#64218—22no—
15#64218C2214yes—
16C2×#3771—22no—
17C2×C32×D4C811yescharacteristic
18C2×#638C811yescharacteristic
19C2×#638C811yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22#3830—22no—
23#3830—22no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×#634C811yescharacteristic
26#3792—22no—
27#3792—22no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622C2×C411yescharacteristic
31C2×#622C2×C411yescharacteristic
32C2×#622C2×C411yescharacteristic
33C2×#622D412yes—
34C2×#622D412yes—
35C2×#622C2311yescharacteristic
36#3788—22no—
37#3787—21no—
38#3787—21no—
39#3771—24no—
40#2115—91nomaximal, Sylow
41C2×#237—121no—
42C23×C32C2×C811yescharacteristic
43C23×C32C2×C811yescharacteristic
44C22×C3⋊D3C2×C811yescharacteristic
45C32×D4—22no—
46C2×C32×C4C2×C811yescharacteristic
47#638—22no—
48#638—22no—
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3—21no—
51C2×C3⋊Dic3C22⋊C412yes—
52C2×C3⋊Dic3C2×C811yescharacteristic
53C2×C3⋊Dic3C2×C811yescharacteristic
54C2×C3⋊Dic3M1612yes—
55C2×C3⋊Dic3C22×C411yescharacteristic
56C4×C3⋊D3—21no—
57C4×C3⋊D3—21no—
58#634—22no—
59#622—21no—
60#622—21no—
61#622C22⋊C411yescharacteristic
62#622C22⋊C411yescharacteristic
63#622C2×D412yes—
64C2×#131—91no—
65C2×M32—92no—
66#349—92no—
67#349—92no—
68C2×C3×D4—41no—
69C2×#67—121no—
70C2×#67—121no—
71C22×Dic3—121no—
72C22×Dic3—121no—
73#237—124no—
74#237—124no—
75C2×C4×D3—121no—
76C2×Dic6—121no—
77C22×C32—21no—
78C22×C32—41no—
79C22×C32—41no—
80C22×C32C22⋊C812yes—
81C22×C32C22×C811yescharacteristic
82C2×C3⋊D3—21no—
83C2×C3⋊D3—41no—
84C32×C4—21no—
85C3⋊Dic3—21no—
86C3⋊Dic3C22⋊C812yes—
87C3⋊Dic3C2×C22⋊C411yescharacteristic
88C3⋊Dic3C2×M1611yescharacteristic
89C2×#41—91no—
90#131—182no—
91#131—182no—
92C2×M16—91no—
93C2×M16—91no—
94C2×M16—91no—
95C22×C8—91no—
96C22×C8—91no—
97C22×C8—91no—
98M32—94no—
99M32—182no—
100C2×C16—182no—
101C23×C3—41no—
102C23×C3—41no—
103C22×D3—121no—
104C3×D4—44no—
105C2×C3×C4—41no—
106#67—124no—
107#67—124no—
108C2×Dic3—122no—
109C2×Dic3—121no—
110C2×Dic3—121no—
111C2×Dic3—122no—
112C2×Dic3—121no—
113C2×Dic3—122no—
114C2×Dic3—122no—
115C4×D3—122no—
116C4×D3—122no—
117Dic6—124no—
118C2×C32—21no—
119C2×C32—22no—
120C2×C32—41no—
121C2×C32C2×C22⋊C811yescharacteristic
122C3⋊D3—41no—
123#41—182no—
124#41—182no—
125C2×Q8—91no—
126C2×D4—91no—
127C2×D4—91no—
128C2×D4AGL(1,𝔽9)11yescharacteristic
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—91no—
132M16—182no—
133M16—182no—
134M16—182no—
135C2×C8—92no—
136C2×C8—91no—
137C2×C8—92no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—181no—
142C2×C8—181no—
143C2×C8—181no—
144C2×C8—181no—
145C16—184no—
146C22×C3—42no—
147C22×C3—41no—
148C22×C3—42no—
149C22×C3—82no—
150C22×C3—82no—
151C2×D3—122no—
152C2×D3—242no—
153C3×C4—42no—
154Dic3—122no—
155Dic3—121no—
156Dic3—121no—
157Dic3—122no—
158C32#211511yescharacteristic, complemented, Sylow
159C23—91no—
160C23C2×AGL(1,𝔽9)11yescharacteristic
161C23C2×AGL(1,𝔽9)11yescharacteristic
162Q8—182no—
163D4—22no—
164D4—182no—
165D4—182no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—92no—
169C2×C4—92no—
170C2×C4—91no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4C2×AGL(1,𝔽9)11yescharacteristic
176C8—92no—
177C8—91no—
178C8—91no—
179C8—181no—
180C8—181no—
181C2×C3—42no—
182C2×C3—41no—
183C2×C3—82no—
184C2×C3—82no—
185D3—242no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—181no—
190C22—361no—
191C22C22⋊AGL(1,𝔽9)12yes—
192C22C22×AGL(1,𝔽9)11yescharacteristic
193C4—21no—
194C4—91no—
195C4—91no—
196C4—92no—
197C4—181no—
198C3—41no—
199C2—21no—
200C2—22no—
201C2—41no—
202C2—361no—
203C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2C2×C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
FittingC2×C32×D4C8
socleC2×C32C2×C22⋊C8
prime radicalC2×#3830C4
cosocleC2×#622C23
hypercenterC2×D4AGL(1,𝔽9)
hypocenterC32#2115
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×#64218C2semidirect
3. #10593274C2semidirect
4. #10593266C2semidirect
158. C32#2115semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
C2×#642182
#105932742
#105932662
#21159