Finite Group Databasebeta

← #11785474

Subgroups — #11785474

Order 1152.

390 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22×#3792C211yesmaximal, characteristic
2#10593845C212yesmaximal
3C2×#63748C212yesmaximal, complemented
4#10590097C212yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C2×#3792—24no—
7C2×#3792C414yes—
8C2×#3792C2214yes—
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C22⋊#622—24no—
12#63748—24no—
13C24×C32Q811yescharacteristic
14C22×C3⋊Dic3—22no—
15C22×C3⋊Dic3—22no—
16C22×C3⋊Dic3C2×C412yes—
17C22×C3⋊Dic3D412yes—
18C22×C3⋊Dic3Q811yescharacteristic
19C22×C3⋊Dic3C2311yescharacteristic
20#3792—28no—
21#3792—24no—
22#3792—24no—
23C2×#622—22no—
24C2×#622—24no—
25C2×#622C2×C412yes—
26C2×#622C2×C412yes—
27C2×#622D414yes—
28#1811—91nomaximal, Sylow
29C23×Dic3—121no—
30C23×C32—22no—
31C23×C32—42no—
32C23×C32C4⋊C412yes—
33C23×C32C2×Q811yescharacteristic
34C2×C3⋊Dic3—22no—
35C2×C3⋊Dic3—22no—
36C2×C3⋊Dic3—22no—
37C2×C3⋊Dic3—24no—
38C2×C3⋊Dic3C4⋊C412yes—
39C2×C3⋊Dic3C22×C411yescharacteristic
40C2×C3⋊Dic3C2×D412yes—
41C2×C3⋊Dic3C2×D411yescharacteristic
42C2×C3⋊Dic3#4112yes—
43#622—22no—
44#622—44no—
45#622C22⋊C414yes—
46C22×M16—91no—
47C2×#108—92no—
48#407—92no—
49#341—92no—
50C24×C3—41no—
51C22×Dic3—122no—
52C22×Dic3—122no—
53C22×Dic3—121no—
54C22×Dic3—121no—
55C22×Dic3—124no—
56C22×Dic3—124no—
57C22×C32—22no—
58C22×C32—22no—
59C22×C32—24no—
60C22×C32—44no—
61C22×C32C2×C4⋊C411yescharacteristic
62C22×C32C22⋊Q812yes—
63C3⋊Dic3—22no—
64C3⋊Dic3C2×C22⋊C411yescharacteristic
65C3⋊Dic3#11711yescharacteristic
66C3⋊Dic3#12112yes—
67C23×C4—91no—
68C2×M16—94no—
69C2×M16—94no—
70C2×M16—184no—
71C22×C8—91no—
72C22×C8—91no—
73#108—184no—
74C22⋊C8—184no—
75C23×C3—44no—
76C23×C3—48no—
77C23×C3—41no—
78C23×C3—42no—
79C2×Dic3—122no—
80C2×Dic3—121no—
81C2×Dic3—121no—
82C2×Dic3—122no—
83C2×Dic3—122no—
84C2×Dic3—124no—
85C2×Dic3—124no—
86C2×Dic3—128no—
87C2×Dic3—124no—
88C2×C32—22no—
89C2×C32—42no—
90C2×C32#38011yescharacteristic
91C2×C32#43012yes—
92C24PSU(3,𝔽2)11yescharacteristic
93C22×C4—91no—
94C22×C4—91no—
95C22×C4—92no—
96C22×C4—92no—
97C22×C4—182no—
98C22×C4—182no—
99M16—188no—
100M16—184no—
101M16—184no—
102C2×C8—94no—
103C2×C8—92no—
104C2×C8—92no—
105C2×C8—182no—
106C2×C8—184no—
107C22×C3—44no—
108C22×C3—44no—
109C22×C3—48no—
110C22×C3—416no—
111C22×C3—41no—
112C22×C3—42no—
113Dic3—121no—
114Dic3—121no—
115Dic3—122no—
116Dic3—124no—
117C32#181111yescharacteristic, complemented, Sylow
118C23—22no—
119C23—42no—
120C23#377712yes—
121C23C2×PSU(3,𝔽2)11yescharacteristic
122C2×C4—91no—
123C2×C4—91no—
124C2×C4—92no—
125C2×C4—92no—
126C2×C4—92no—
127C2×C4—182no—
128C2×C4—184no—
129C2×C4—182no—
130C2×C4—182no—
131C8—94no—
132C8—182no—
133C8—364no—
134C2×C3—44no—
135C2×C3—48no—
136C2×C3—42no—
137C2×C3—41no—
138C22—22no—
139C22—24no—
140C22—22no—
141C22—44no—
142C22C2×#377711yescharacteristic
143C22C22⋊PSU(3,𝔽2)12yes—
144C4—91no—
145C4—92no—
146C4—91no—
147C4—182no—
148C3—41no—
149C2—22no—
150C2—42no—
151C2#1059356512yes—
152C2#1059356811yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×PSU(3,𝔽2)
Fitting, prime radicalC24×C32Q8
socleC22×C32C2×C4⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC24PSU(3,𝔽2)
hypocenterC32#1811
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
3. C2×#63748C2semidirect
4. #10590097C2semidirect
117. C32#1811semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
#105938452
C2×#637482
#105900972
#18119