Finite Group Databasebeta

← #11779323

Subgroups — #11779323

Order 1152.

654 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#10596184C211yesmaximal, characteristic
2C32×#492C211yesmaximal, characteristic
3#10592790C212yesmaximal, complemented
4#10589410C211yesmaximal, characteristic
5#10589322C212yesmaximal, complemented
6#71270—34nomaximal
7C2×C32×SD16—22no—
8C32×C4⋊Q8C2211yescharacteristic
9C32×#127C2211yescharacteristic
10#64145—22no—
11#64144—22no—
12D4×C3⋊Dic3—22no—
13C4×#634C2212yes—
14C32×C4×C8C2211yescharacteristic
15#63637—22no—
16#63634—22no—
17C4⋊(C3⋊(C3⋊C8))C2212yes—
18#5713—34no—
19C3×#492D314yes—
20#5091—38no—
21#4544—34no—
22#4456—38no—
23C2×C32×Q8—21no—
24C2×C32×D4—22no—
25C2×C32×D4D412yes—
26C22×C3⋊Dic3—22no—
27C2×#634D412yes—
28C32×SD16—44no—
29C2×C32×C8—21no—
30C32×C4⋊C4—22no—
31C32×C42C2311yescharacteristic
32#3757—24no—
33#3757—22no—
34C4⋊(C3⋊Dic3)D412yes—
35#3750—22no—
36C4×C3⋊Dic3—22no—
37C2×C3⋊(C3⋊C8)—22no—
38#1630—91noSylow
39C2×C3×SD16—28no—
40C3×C4⋊Q8C2×D314yes—
41C3×#127C2×D314yes—
42#936—68no—
43#935—68no—
44D4×Dic3—68no—
45C4×Dic6—38no—
46C3×C4×C8C2×D314yes—
47#810—68no—
48#807—68no—
49C4⋊(C3⋊C8)—38no—
50C23×C32—22no—
51C32×Q8—42no—
52C32×D4—42no—
53C32×D4—42no—
54C32×D4—42no—
55C2×C32×C4—41no—
56C2×C32×C4C2×D412yes—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—82no—
61#634—22no—
62#634—22no—
63C32×C8—22no—
64C3⋊(C3⋊C8)—42no—
65#559—91no—
66#492C3⋊D311yescharacteristic
67#477—92no—
68#331—91no—
69Q8⋊C8—92no—
70C2×C3×Q8—24no—
71C2×C3×D4—28no—
72C2×C3×D4#6718yes—
73C22×Dic3—68no—
74C2×Dic6—38no—
75C3×SD16—416no—
76C2×C3×C8—24no—
77C3×C4⋊C4—28no—
78C3×C42C22×D314yes—
79#217—616no—
80#217—68no—
81C4⋊Dic3—38no—
82Dic3⋊C4—68no—
83C4×Dic3—68no—
84C2×C3⋊C8—68no—
85C22×C32—44no—
86C22×C32—42no—
87C22×C32#12011yescharacteristic
88C32×C4—21no—
89C32×C4—81no—
90C32×C4#13512yes—
91C32×C4#13712yes—
92C3⋊Dic3—42no—
93C3⋊Dic3—42no—
94C2×SD16—22no—
95C4⋊Q8C2×C3⋊D311yescharacteristic
96#127C2×C3⋊D311yescharacteristic
97#124—182no—
98#123—182no—
99C4×Q8—92no—
100C4×D4—182no—
101#107—182no—
102C4⋊C8—92no—
103#103—182no—
104C4×C8C2×C3⋊D311yescharacteristic
105C23×C3—28no—
106C3×Q8—48no—
107C3×D4—48no—
108C3×D4—48no—
109C3×D4—48no—
110C2×C3×C4—44no—
111C2×C3×C4D3×D418yes—
112C2×C3×C4C2×#6714yes—
113C2×Dic3—68no—
114C2×Dic3—68no—
115C2×Dic3—248no—
116Dic6—68no—
117Dic6—68no—
118C3×C8—28no—
119C3⋊C8—128no—
120C2×C32—82no—
121C2×C32#45212yes—
122C2×C32#45311yescharacteristic
123C2×Q8—21no—
124C2×Q8—92no—
125C2×D4—22no—
126C2×D4#63812yes—
127C22×C4—182no—
128SD16—44no—
129C2×C8—21no—
130C2×C8—182no—
131C4⋊C4—22no—
132C4⋊C4—92no—
133C4⋊C4—182no—
134C22⋊C4—184no—
135C22⋊C4—182no—
136C42—182no—
137C42C22×C3⋊D311yescharacteristic
138C22×C3—416no—
139C22×C3—48no—
140C22×C3#93714yes—
141C3×C4—24no—
142C3×C4—84no—
143C3×C4#91518yes—
144C3×C4#91618yes—
145Dic3—128no—
146Dic3—128no—
147C32#163011yescharacteristic, complemented, Sylow
148C23—22no—
149Q8—42no—
150Q8—182no—
151Q8—182no—
152D4—42no—
153D4—42no—
154D4—42no—
155C2×C4—41no—
156C2×C4—182no—
157C2×C4—182no—
158C2×C4—722no—
159C2×C4D4×C3⋊D312yes—
160C2×C4C2×#63811yescharacteristic
161C8—22no—
162C8—362no—
163C2×C3—88no—
164C2×C3#507714yes—
165C2×C3#517318yes—
166C22—42no—
167C22—44no—
168C22#6414611yescharacteristic
169C4—21no—
170C4—81no—
171C4—362no—
172C4—362no—
173C4#6412412yes—
174C4#6412512yes—
175C3#7127014yescomplemented
176C2—82no—
177C2#1059277611yescharacteristic
178C2#1059287212yes—
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#492C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenter#492C3⋊D3
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
3. #10592790C2semidirect
5. #10589322C2semidirect
147. C32#1630semidirect
175. C3#71270semidirect

Maximal subgroups

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

subgroupindex
#105961842
C32×#4922
#105927902
#105894102
#105893222
#712703