Finite Group Databasebeta

← #11780709

Subgroups — #11780709

Order 1152.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#10596157C211yesmaximal, characteristic
2#10592768C211yesmaximal, characteristic
3#10592401C212yesmaximal
4C32×#330C211yesmaximal, characteristic
5#10589331C212yesmaximal
6#68377—34nomaximal
7C32×#125C2211yescharacteristic
8#64099—22no—
9#64098—22no—
10#64098—22no—
11#64079C2212yes—
12#64078C2211yescharacteristic
13C32×#97C2212yes—
14#63645—22no—
15#63644—22no—
16#63637—22no—
17#63630C2211yescharacteristic
18C3⋊#564—34no—
19#5069—34no—
20#4702—38no—
21C3×#330D314yes—
22#4465—38no—
23C2×#634—21no—
24C2×C32×C8—22no—
25C32×C4⋊C4—22no—
26C32×C4⋊C4D412yes—
27C32×C42C2311yescharacteristic
28C4⋊(C3⋊Dic3)—22no—
29C4⋊(C3⋊Dic3)—22no—
30C4⋊(C3⋊Dic3)D412yes—
31C4⋊(C3⋊Dic3)D412yes—
32#3750—22no—
33#3750—22no—
34#3750—22no—
35#3750—22no—
36C4×C3⋊Dic3—22no—
37C2×C3⋊(C3⋊C8)—21no—
38#1663—91noSylow
39C3×#125C2×D314yes—
40#890—68no—
41#889—68no—
42#889—68no—
43#870—38no—
44#869—34no—
45C3×#97C2×D318yes—
46#818—68no—
47#817—68no—
48#810—68no—
49#803—34no—
50C2×C32×C4—22no—
51C2×C32×C4C2×D411yescharacteristic
52C2×C32×C4C2×D412yes—
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—41no—
56#634—42no—
57C32×C8—24no—
58C3⋊(C3⋊C8)—41no—
59#564—91no—
60#501—92no—
61#491—91no—
62#330—92no—
63#330C3⋊D311yescharacteristic
64C2×Dic6—64no—
65C2×C3×C8—28no—
66C3×C4⋊C4—28no—
67C3×C4⋊C4D1218yes—
68C3×C42C22×D314yes—
69C4⋊Dic3—38no—
70C4⋊Dic3—38no—
71C4⋊Dic3—68no—
72C4⋊Dic3—68no—
73Dic3⋊C4—68no—
74Dic3⋊C4—68no—
75Dic3⋊C4—68no—
76Dic3⋊C4—68no—
77C4×Dic3—68no—
78C2×C3⋊C8—64no—
79C22×C32#12011yescharacteristic
80C32×C4—21no—
81C32×C4—22no—
82C32×C4—42no—
83C3⋊Dic3—42no—
84C3⋊Dic3—42no—
85C3⋊Dic3—81no—
86C4⋊Q8—91no—
87#125—92no—
88#125—182no—
89#125—182no—
90#125—182no—
91#125C2×C3⋊D311yescharacteristic
92#107—182no—
93#106—182no—
94#103—182no—
95#97—91no—
96#97C2×C3⋊D312yes—
97C2×C3×C4—28no—
98C2×C3×C4C2×D1214yes—
99C2×C3×C4D3×D418yes—
100C2×Dic3—68no—
101C2×Dic3—68no—
102C2×Dic3—124no—
103Dic6—128no—
104C3×C8—216no—
105C3⋊C8—124no—
106C2×C32#45411yescharacteristic
107C2×C32#45612yes—
108C2×Q8—181no—
109C2×C8—22no—
110C2×C8—181no—
111C4⋊C4—22no—
112C4⋊C4—92no—
113C4⋊C4—92no—
114C4⋊C4—182no—
115C4⋊C4—182no—
116C4⋊C4—182no—
117C4⋊C4—182no—
118C4⋊C4—182no—
119C4⋊C4—182no—
120C4⋊C4C4⋊(C3⋊D3)12yes—
121C42—182no—
122C42C22×C3⋊D311yescharacteristic
123C22×C3#88214yes—
124C3×C4—24no—
125C3×C4—28no—
126C3×C4—48no—
127Dic3—128no—
128Dic3—128no—
129Dic3—244no—
130C32#166311yescharacteristic, complemented, Sylow
131Q8—362no—
132C2×C4—22no—
133C2×C4—182no—
134C2×C4—182no—
135C2×C4—361no—
136C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
137C2×C4D4×C3⋊D312yes—
138C8—24no—
139C8—361no—
140C2×C3#475314yes—
141C2×C3#482618yes—
142C22#6409111yescharacteristic
143C4—22no—
144C4—21no—
145C4—42no—
146C4—362no—
147C4—362no—
148C4—721no—
149C3#6837714yescomplemented
150C2#1059245211yescharacteristic
151C2#1059252512yes—
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#330C2
socle, prime radicalC22×C32#120
hypercenter#330C3⋊D3
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
130. C32#1663semidirect
149. C3#68377semidirect

Maximal subgroups

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

subgroupindex
#105961572
#105927682
#105924012
C32×#3302
#105893312
#683773