Finite Group Databasebeta

← #11786039

Subgroups — #11786039

Order 1152.

434 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×#622C211yesmaximal, characteristic
2#10591359C212yesmaximal
3#10590075C214yesmaximal
4C22×#622C2212yes—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×C4⋊Dic3—22no—
7C2×#3724—22no—
8C2×#3724C2214yes—
9C4×#622C414yescomplemented
10#4975—62no—
11C22×C32×C4D411yescharacteristic
12C22×C3⋊Dic3D411yescharacteristic
13C22×C3⋊Dic3C2311yescharacteristic
14C22×C3×Dic3—24no—
15C2×#622—24no—
16C2×#622C2×C414yes—
17C4×C3⋊Dic3C2×C412yes—
18C4×C3⋊Dic3Q812yes—
19C3×C4⋊Dic3—44no—
20#3724—28no—
21#3724—44no—
22#1834—91nomaximal, Sylow
23C2×C3×C4⋊C4—62no—
24C2×C4⋊Dic3—22no—
25C2×Dic3⋊C4—64no—
26C2×Dic3⋊C4—64no—
27C2×C4×Dic3—62no—
28C23×C32C2×D411yescharacteristic
29C2×C32×C4C4⋊C412yes—
30C2×C32×C4D812yes—
31C2×C32×C4Q1612yes—
32C2×C3⋊Dic3C4⋊C412yes—
33C2×C3⋊Dic3SD1614yes—
34C2×C3⋊Dic3C22×C411yescharacteristic
35C2×C3⋊Dic3C2×Q811yescharacteristic
36C2×C3⋊Dic3#4114yes—
37C2×C3×Dic3—44no—
38C2×C3×Dic3—44no—
39C2×C3×Dic3—44no—
40#622—24no—
41C2×C4×C8—91no—
42#384—92no—
43#340—94no—
44C22×C3×C4—22no—
45C22×C3×C4—64no—
46C22×Dic3—24no—
47C22×Dic3—62no—
48C22×Dic3—62no—
49C3×C4⋊C4—124no—
50C4⋊Dic3—44no—
51Dic3⋊C4—128no—
52Dic3⋊C4—128no—
53C4×Dic3—64no—
54C4×Dic3—64no—
55C22×C32C2×C4⋊C411yescharacteristic
56C22×C32#12412yes—
57C22×C32C2×D811yescharacteristic
58C22×C32C2×SD1612yes—
59C22×C32C2×Q1611yescharacteristic
60C32×C4#10714yes—
61C3⋊Dic3#10614yes—
62C3⋊Dic3#11712yes—
63C3⋊Dic3#12512yes—
64C3×Dic3—84no—
65C22×C8—92no—
66C2×C4⋊C4—62no—
67C2×C4⋊C4—94no—
68C2×C4⋊C4—182no—
69C2×C42—91no—
70C4×C8—94no—
71C23×C3—22no—
72C2×C3×C4—24no—
73C2×C3×C4—24no—
74C2×C3×C4—24no—
75C2×C3×C4—124no—
76C2×C3×C4—124no—
77C2×C3×C4—124no—
78C2×Dic3—44no—
79C2×Dic3—44no—
80C2×Dic3—44no—
81C2×Dic3—64no—
82C2×Dic3—64no—
83C2×Dic3—64no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—64no—
87C2×Dic3—64no—
88C2×C32#38211yescharacteristic
89C2×C32C2×#10611yescharacteristic
90C2×C32C2×#10711yescharacteristic
91C2×C32#48612yes—
92C2×C32#48712yes—
93C22×C4—64no—
94C22×C4—91no—
95C22×C4—91no—
96C22×C4GO+(4,𝔽2)11yescharacteristic
97C2×C8—94no—
98C2×C8—184no—
99C4⋊C4—124no—
100C4⋊C4—188no—
101C4⋊C4—364no—
102C42—92no—
103C42—92no—
104C22×C3—22no—
105C22×C3—22no—
106C22×C3—22no—
107C22×C3—22no—
108C22×C3—22no—
109C22×C3—22no—
110C22×C3—22no—
111C3×C4—28no—
112C3×C4—244no—
113Dic3—68no—
114Dic3—64no—
115Dic3—64no—
116Dic3—84no—
117C32#183411yescharacteristic, complemented, Sylow
118C23C2×GO+(4,𝔽2)11yescharacteristic
119C2×C4—94no—
120C2×C4—94no—
121C2×C4—91no—
122C2×C4—91no—
123C2×C4—92no—
124C2×C4—124no—
125C2×C4—124no—
126C2×C4—124no—
127C2×C4#377312yes—
128C2×C4#377412yes—
129C2×C4#377612yes—
130C8—184no—
131C2×C3—22no—
132C2×C3—22no—
133C2×C3—22no—
134C2×C3—22no—
135C2×C3—22no—
136C2×C3—22no—
137C2×C3—22no—
138C22#6422112yes—
139C22#6422712yes—
140C22C2×#377311yescharacteristic
141C22C2×#377411yescharacteristic
142C22C2×#377611yescharacteristic
143C4—92no—
144C4—92no—
145C4—94no—
146C4—244no—
147C4#6374314yes—
148C3—22no—
149C2#1059334411yescharacteristic
150C2#1059334812yes—
151C2#1059337912yes—
152C2#1059338711yescharacteristic
153C2C2×#6374311yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1834
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
9. C4×#622C4semidirect
117. C32#1834semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
#105913592
#105900752
#18349