Finite Group Databasebeta

← #11779449

Subgroups — #11779449

Order 1152.

618 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 133 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#10596193C211yesmaximal, characteristic
2C32×#494C211yesmaximal, characteristic
3#10592790C212yesmaximal
4#10589412C211yesmaximal, characteristic
5#10589322C212yesmaximal
6#71307—34nomaximal
7C2×C32×Q16—22no—
8C32×C4⋊Q8C2211yescharacteristic
9C32×C4⋊Q8C2211yescharacteristic
10#64153—22no—
11#64097—22no—
12#64096—22no—
13C4×#634C2212yes—
14C32×C4×C8C2211yescharacteristic
15#63637—22no—
16#63634—22no—
17C4⋊(C3⋊(C3⋊C8))C2212yes—
18#5722—34no—
19C3×#494D314yes—
20#5091—38no—
21#4546—34no—
22#4456—38no—
23C2×C32×Q8—21no—
24C2×C32×Q8D412yes—
25C2×#634—22no—
26C2×#634D412yes—
27C32×Q16—44no—
28C2×C32×C8—21no—
29C32×C4⋊C4—22no—
30C32×C4⋊C4—22no—
31C32×C42C2311yescharacteristic
32C4⋊(C3⋊Dic3)D412yes—
33#3750—24no—
34#3750—22no—
35C4×C3⋊Dic3—22no—
36C4×C3⋊Dic3—22no—
37C2×C3⋊(C3⋊C8)—22no—
38#1633—91noSylow
39C2×C3×Q16—28no—
40C3×C4⋊Q8C2×D314yes—
41C3×C4⋊Q8C2×D314yes—
42#944—68no—
43#888—68no—
44#887—68no—
45C4×Dic6—38no—
46C3×C4×C8C2×D314yes—
47#810—68no—
48#807—68no—
49C4⋊(C3⋊C8)—38no—
50C32×Q8—42no—
51C32×Q8—42no—
52C2×C32×C4—22no—
53C2×C32×C4—41no—
54C2×C32×C4C2×D412yes—
55C2×C32×C4C2×D411yescharacteristic
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58#634—22no—
59#634—82no—
60#634Q1614yescomplemented
61C32×C8—22no—
62C3⋊(C3⋊C8)—42no—
63Q82—91no—
64#494C3⋊D311yescharacteristic
65#477—92no—
66#333—91no—
67Q8⋊C8—92no—
68C2×C3×Q8—24no—
69C2×C3×Q8#6718yes—
70C2×Dic6—38no—
71C2×Dic6—68no—
72C3×Q16—416no—
73C2×C3×C8—24no—
74C3×C4⋊C4—28no—
75C3×C4⋊C4—28no—
76C3×C42C22×D314yes—
77C4⋊Dic3—38no—
78Dic3⋊C4—616no—
79Dic3⋊C4—68no—
80C4×Dic3—68no—
81C4×Dic3—68no—
82C2×C3⋊C8—68no—
83C22×C32#12011yescharacteristic
84C32×C4—21no—
85C32×C4—42no—
86C32×C4—81no—
87C32×C4C2×Q1612yes—
88C32×C4#13712yes—
89C3⋊Dic3—24no—
90C3⋊Dic3—42no—
91C2×Q16—22no—
92C4⋊Q8—182no—
93C4⋊Q8—182no—
94C4⋊Q8C2×C3⋊D311yescharacteristic
95C4⋊Q8C2×C3⋊D311yescharacteristic
96C4×Q8—92no—
97C4×Q8—182no—
98#107—182no—
99C4⋊C8—92no—
100#103—182no—
101C4×C8C2×C3⋊D311yescharacteristic
102C3×Q8—48no—
103C3×Q8—48no—
104C2×C3×C4—28no—
105C2×C3×C4—44no—
106C2×C3×C4D3×D418yes—
107C2×C3×C4C2×#6714yes—
108C2×Dic3—68no—
109C2×Dic3—68no—
110Dic6—316no—
111Dic6—68no—
112Dic6—248no—
113C3×C8—28no—
114C3⋊C8—128no—
115C2×C32#45112yes—
116C2×C32#45311yescharacteristic
117C2×Q8—21no—
118C2×Q8—92no—
119C2×Q8—182no—
120C2×Q8#63812yes—
121Q16—44no—
122C2×C8—21no—
123C2×C8—182no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—92no—
127C4⋊C4—184no—
128C4⋊C4—182no—
129C42—182no—
130C42—182no—
131C42C22×C3⋊D311yescharacteristic
132C22×C3#93714yes—
133C3×C4—24no—
134C3×C4—48no—
135C3×C4—84no—
136C3×C4D3×Q1618yes—
137C3×C4#91818yes—
138Dic3—616no—
139Dic3—128no—
140C32#163311yescharacteristic, complemented, Sylow
141Q8—42no—
142Q8—42no—
143Q8—94no—
144Q8—182no—
145Q8—722no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—182no—
149C2×C4—182no—
150C2×C4D4×C3⋊D312yes—
151C2×C4C2×#63811yescharacteristic
152C8—22no—
153C8—362no—
154C2×C3#507714yes—
155C2×C3#518618yes—
156C22#6414611yescharacteristic
157C4—21no—
158C4—42no—
159C4—81no—
160C4—184no—
161C4—362no—
162C4Q16×C3⋊D312yes—
163C4#6412712yes—
164C3#7130714yescomplemented
165C2#1059277611yescharacteristic
166C2#1059288512yes—
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#494C2
socle, prime radicalC22×C32#120
hypercenter#494C3⋊D3
hypocenterC32#1633
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
60. #634Q16semidirect
140. C32#1633semidirect
164. C3#71307semidirect

Maximal subgroups

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

subgroupindex
#105961932
C32×#4942
#105927902
#105894122
#105893222
#713073