Finite Group Databasebeta

← #11780705

Subgroups — #11780705

Order 1152.

258 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 68 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
2#10588746C211yesmaximal, characteristic
3#10588743C212yesmaximal
4#10588220C212yesmaximal
5#10588220C211yesmaximal, characteristic
6#71961—31nomaximal
7C9×#125—22no—
8C9×#125—22no—
9C9×#125—22no—
10C9×#125C2212yes—
11C9×#125C2211yescharacteristic
12#63431C2211yescharacteristic
13#63368—22no—
14#63367—22no—
15#63366—22no—
16#63362C2212yes—
17#63362C2211yescharacteristic
18C3×#564D311yescharacteristic
19#5069—31no—
20#5064—32no—
21#4543—31no—
22#4543—32no—
23C2×Dic18—21no—
24C9×C4⋊C4—22no—
25C9×C4⋊C4—22no—
26C9×C4⋊C4—22no—
27C9×C4⋊C4—22no—
28C9×C4⋊C4—22no—
29C9×C4⋊C4—22no—
30C9×C4⋊C4D412yes—
31C9×C4⋊C4D412yes—
32C9×C4⋊C4D412yes—
33C42×C9—22no—
34C42×C9C2311yescharacteristic
35C4⋊Dic9—22no—
36C2×C9⋊C8—22no—
37C2×C9⋊C8—21no—
38#1663—91noSylow
39C3×#125—22no—
40C3×#125—22no—
41C3×#125—22no—
42C3×#125C2×D312yes—
43C3×#125C2×D311yescharacteristic
44#869—31no—
45#810—62no—
46#808—62no—
47#807—62no—
48#803—32no—
49#803—31no—
50C2×C4×C9—22no—
51C2×C4×C9—22no—
52C2×C4×C9—22no—
53C2×C4×C9C2×D412yes—
54C2×C4×C9C2×D411yescharacteristic
55C2×Dic9—41no—
56Dic18—42no—
57C9⋊C8—24no—
58C9⋊C8—41no—
59#564D911yescharacteristic
60#501—92no—
61#491—91no—
62#330—92no—
63#330—91no—
64C2×Dic6—61no—
65C3×C4⋊C4—22no—
66C3×C4⋊C4—22no—
67C3×C4⋊C4—22no—
68C3×C4⋊C4—22no—
69C3×C4⋊C4—22no—
70C3×C4⋊C4—22no—
71C3×C4⋊C4#6712yes—
72C3×C4⋊C4#6712yes—
73C3×C4⋊C4#6712yes—
74C3×C42—22no—
75C3×C42C22×D311yescharacteristic
76C4⋊Dic3—62no—
77C2×C3⋊C8—62no—
78C2×C3⋊C8—61no—
79C22×C9#12011yescharacteristic
80C4×C9—21no—
81C4×C9—22no—
82C4×C9—42no—
83C4×C9—42no—
84C4×C9—42no—
85Dic9—81no—
86C4⋊Q8—91no—
87#125—22no—
88#125—22no—
89#125—22no—
90#125C2×D911yescharacteristic
91#125C2×D912yes—
92#107—182no—
93#106—182no—
94#103—182no—
95#97—91no—
96#97—92no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4C2×#6712yes—
101C2×C3×C4C2×#6711yescharacteristic
102C2×Dic3—121no—
103Dic6—122no—
104C3⋊C8—64no—
105C3⋊C8—121no—
106C2×C9#45411yescharacteristic
107C2×C9#45612yes—
108C2×Q8—181no—
109C2×C8—182no—
110C2×C8—181no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—182no—
118C4⋊C4#61112yes—
119C4⋊C4#61112yes—
120C4⋊C4#61112yes—
121C42—22no—
122C42C22×D911yescharacteristic
123C22×C3#95311yescharacteristic
124C3×C4—21no—
125C3×C4—22no—
126C3×C4—42no—
127C3×C4—42no—
128C3×C4—42no—
129Dic3—241no—
130C9#166311yescharacteristic, complemented, Sylow
131Q8—362no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—361no—
136C2×C4C2×#61112yes—
137C2×C4C2×#61111yescharacteristic
138C8—184no—
139C8—361no—
140C2×C3#524511yescharacteristic
141C2×C3#524612yes—
142C22#6351511yescharacteristic
143C4—22no—
144C4—21no—
145C4—42no—
146C4—42no—
147C4—42no—
148C4—721no—
149C3#7196111yescharacteristic
150C2#1058892512yes—
151C2#1058892611yescharacteristic
subgroupG/H
centerC22#63515
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#564C2
socle, prime radicalC22×C3#953
hypercenter#564D9
hypocenterC9#1663
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #564

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
#105887462
#105887432
#105882202
#719613