Finite Group Databasebeta

← #11795328

Subgroups — #11795328

Order 1152.

528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 167 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×C32×#106C211yesmaximal, characteristic
2#10592801C211yesmaximal, characteristic
3#10592663C212yesmaximal
4#10589418C211yesmaximal, characteristic
5#10589396C212yesmaximal
6#70573—34nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C32×C4⋊C4C2212yes—
9#64135C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×#3748C2212yes—
12C32×#106—22no—
13#63641—22no—
14#63635—22no—
15#63634—22no—
16C2×C3×#106D314yes—
17#5102—34no—
18#4964—38no—
19#4552—34no—
20#4530—38no—
21C22×C32×C4—22no—
22C22×C32×C4C2311yescharacteristic
23C2×C32×C8—22no—
24C2×C32×C8D412yes—
25C32×C4⋊C4—22no—
26C32×C4⋊C4—22no—
27#3757—21no—
28C4⋊(C3⋊Dic3)D412yes—
29C4×C3⋊Dic3—21no—
30#3748—22no—
31#3748—22no—
32#3748Q814yes—
33C2×C3⋊(C3⋊C8)—22no—
34C2×C3⋊(C3⋊C8)—21no—
35#2090—91noSylow
36C22×C3×C8C2×D314yes—
37C2×C3×C4⋊C4C2×D318yes—
38#926—34no—
39C2×#208—38no—
40C2×#208—34no—
41C3×#106—28no—
42Dic3⋊C8—68no—
43#808—68no—
44#807—68no—
45C23×C32#4111yescharacteristic
46C2×C32×C4—42no—
47C2×C32×C4—82no—
48C2×C32×C4C2×D411yescharacteristic
49C2×C32×C4C2×D411yescharacteristic
50C2×C32×C4C2×Q812yes—
51C2×C32×C4#4112yes—
52C2×C3⋊Dic3—22no—
53C32×C8—22no—
54C3⋊(C3⋊C8)—24no—
55C3⋊(C3⋊C8)—41no—
56#428—92no—
57C2×#106C3⋊D311yescharacteristic
58#424—91no—
59#343—92no—
60#341—91no—
61C22×C3×C4—28no—
62C22×C3×C4C22×D314yes—
63C2×C3×C8—28no—
64C2×C3×C8#6718yes—
65C3×C4⋊C4—28no—
66C3×C4⋊C4—28no—
67#217—64no—
68C4⋊Dic3—38no—
69C4×Dic3—64no—
70#208—316no—
71#208—68no—
72#208—68no—
73C2×C3⋊C8—68no—
74C2×C3⋊C8—64no—
75C22×C32—22no—
76C22×C32#12111yescharacteristic
77C22×C32#12512yes—
78C32×C4—82no—
79C32×C4C22⋊Q812yes—
80C32×C4#12311yescharacteristic
81C32×C4C4⋊Q811yescharacteristic
82C3⋊Dic3—42no—
83C2×M16—92no—
84C2×M16—91no—
85C22×C8C2×C3⋊D311yescharacteristic
86#117—91no—
87C2×C4⋊C4C2×C3⋊D312yes—
88#107—182no—
89#106—22no—
90#106—182no—
91C4⋊C8—182no—
92C23×C3#23714yes—
93C2×C3×C4—48no—
94C2×C3×C4—88no—
95C2×C3×C4#23518yes—
96C2×C3×C4D3×D414yes—
97C2×C3×C4D3×Q818yes—
98C2×C3×C4C2×#6714yes—
99C2×Dic3—68no—
100C3×C8—28no—
101C3⋊C8—616no—
102C3⋊C8—124no—
103C2×C32—22no—
104C2×C32#39811yescharacteristic
105C2×C32#47112yes—
106C22×C4—22no—
107C22×C4C22×C3⋊D311yescharacteristic
108M16—94no—
109M16—182no—
110M16—182no—
111C2×C8—22no—
112C2×C8—182no—
113C2×C8—181no—
114C2×C8#63812yes—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—92no—
118C22⋊C4—181no—
119C42—181no—
120C22×C3—28no—
121C22×C3#88918yes—
122C22×C3#93814yes—
123C3×C4—88no—
124C3×C4#89618yes—
125C3×C4#92914yes—
126C3×C4#94414yes—
127Dic3—128no—
128C32#209011yescharacteristic, complemented, Sylow
129C23#383011yescharacteristic
130C2×C4—42no—
131C2×C4—82no—
132C2×C4—182no—
133C2×C4#382812yes—
134C2×C4D4×C3⋊D311yescharacteristic
135C2×C4Q8×C3⋊D312yes—
136C2×C4C2×#63811yescharacteristic
137C8—22no—
138C8—184no—
139C8—361no—
140C2×C3—28no—
141C2×C3#498314yes—
142C2×C3#517718yes—
143C22—22no—
144C22#6409812yes—
145C22#6414711yescharacteristic
146C4—82no—
147C4—362no—
148C4#6410512yes—
149C4#6413811yescharacteristic
150C4#6415311yescharacteristic
151C3#7057314yescomplemented
152C2—22no—
153C2#1059268211yescharacteristic
154C2#1059287612yes—
subgroupG/H
centerC22#64147
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#106C2
socleC22×C32#121
prime radicalC23×C32#41
hypercenterC2×#106C3⋊D3
hypocenterC32#2090
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
128. C32#2090semidirect
151. C3#70573semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1062
#105928012
#105926632
#105894182
#105893962
#705733