Finite Group Databasebeta

← #11780699

Subgroups — #11780699

Order 1152.

258 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C9⋊#564C211yesmaximal, characteristic
2C9×#491C211yesmaximal, characteristic
3#10588761C212yesmaximal
4#10588220C211yesmaximal, characteristic
5#10588141C212yesmaximal
6#71252—31nomaximal
7C9×C4⋊Q8C2211yescharacteristic
8C9×#125C2211yescharacteristic
9#63452—22no—
10#63451—22no—
11#63451—22no—
12#63432C2212yes—
13C9×#103—22no—
14C9×#97C2211yescharacteristic
15#63367—22no—
16#63366—22no—
17#63362C2212yes—
18C3⋊#564—31no—
19C3×#491D311yescharacteristic
20#5081—32no—
21#4543—31no—
22#4465—32no—
23C2×Q8×C9—21no—
24C2×C8×C9—21no—
25C9×C4⋊C4—22no—
26C9×C4⋊C4—22no—
27C9×C4⋊C4D412yes—
28C42×C9C2311yescharacteristic
29C4⋊Dic9—22no—
30C4⋊Dic9D412yes—
31C4⋊Dic9D412yes—
32Dic9⋊C4—22no—
33Dic9⋊C4—22no—
34Dic9⋊C4—22no—
35Dic9⋊C4—22no—
36C4×Dic9—22no—
37C2×C9⋊C8—22no—
38#1663—91noSylow
39C3×C4⋊Q8C2×D311yescharacteristic
40C3×#125C2×D311yescharacteristic
41#890—62no—
42#889—62no—
43#889—62no—
44#870—32no—
45C3×#103—22no—
46C3×#97C2×D311yescharacteristic
47#808—62no—
48#807—62no—
49#803—32no—
50Q8×C9—42no—
51C2×C4×C9—22no—
52C2×C4×C9—41no—
53C2×C4×C9C2×D412yes—
54C2×C4×C9C2×D411yescharacteristic
55C2×Dic9—22no—
56C2×Dic9—22no—
57C8×C9—41no—
58C9⋊C8—24no—
59#564—91no—
60#501—92no—
61#491D911yescharacteristic
62#330—91no—
63#330—92no—
64C2×C3×Q8—21no—
65C2×C3×C8—21no—
66C3×C4⋊C4—22no—
67C3×C4⋊C4—22no—
68C3×C4⋊C4#6712yes—
69C3×C42C22×D311yescharacteristic
70C4⋊Dic3—32no—
71C4⋊Dic3—32no—
72C4⋊Dic3—62no—
73Dic3⋊C4—62no—
74Dic3⋊C4—62no—
75Dic3⋊C4—62no—
76Dic3⋊C4—62no—
77C4×Dic3—62no—
78C2×C3⋊C8—62no—
79C22×C9#12011yescharacteristic
80C4×C9—21no—
81C4×C9—22no—
82C4×C9—42no—
83C4×C9—81no—
84Dic9—42no—
85Dic9—42no—
86C4⋊Q8C2×D911yescharacteristic
87#125—92no—
88#125—182no—
89#125—182no—
90#125—182no—
91#125C2×D911yescharacteristic
92#107—182no—
93#106—182no—
94#103—22no—
95#97—92no—
96#97C2×D911yescharacteristic
97C3×Q8—42no—
98C2×C3×C4—22no—
99C2×C3×C4—41no—
100C2×C3×C4D3×D412yes—
101C2×C3×C4C2×#6711yescharacteristic
102C2×Dic3—62no—
103C2×Dic3—62no—
104C3×C8—41no—
105C3⋊C8—64no—
106C2×C9#45411yescharacteristic
107C2×C9#45612yes—
108C2×Q8—21no—
109C2×C8—21no—
110C2×C8—182no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4—92no—
114C4⋊C4—92no—
115C4⋊C4—182no—
116C4⋊C4—182no—
117C4⋊C4—182no—
118C4⋊C4—182no—
119C4⋊C4—182no—
120C4⋊C4#61112yes—
121C42—182no—
122C42C22×D911yescharacteristic
123C22×C3#93711yescharacteristic
124C3×C4—22no—
125C3×C4—21no—
126C3×C4—42no—
127C3×C4—81no—
128Dic3—122no—
129Dic3—122no—
130C9#166311yescharacteristic, complemented, Sylow
131Q8—42no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—182no—
135C2×C4—182no—
136C2×C4D4×D912yes—
137C2×C4C2×#61111yescharacteristic
138C8—41no—
139C8—184no—
140C2×C3#506211yescharacteristic
141C2×C3#520512yes—
142C22#6349911yescharacteristic
143C4—21no—
144C4—22no—
145C4—42no—
146C4—81no—
147C4—362no—
148C4—362no—
149C3#7125211yescharacteristic
150C2#1058874211yescharacteristic
151C2#1058888512yes—
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#491C2
socle, prime radicalC22×C3#937
hypercenter#491D9
hypocenterC9#1663
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
130. C9#1663semidirect

Maximal subgroups

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

subgroupindex
C9⋊#5642
C9×#4912
#105887612
#105882202
#105881412
#712523