Finite Group Databasebeta

← #11780708

Subgroups — #11780708

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
2#10588746C211yesmaximal, characteristic
3#10588382C212yesmaximal
4C9×#330C211yesmaximal, characteristic
5#10588141C212yesmaximal
6#68377—31nomaximal
7C9×#125C2211yescharacteristic
8#63452—22no—
9#63451—22no—
10#63451—22no—
11#63432C2212yes—
12#63431C2211yescharacteristic
13C9×#97C2212yes—
14#63378—22no—
15#63377—22no—
16#63368—22no—
17#63362C2211yescharacteristic
18C3⋊#564—31no—
19#5069—31no—
20#4702—32no—
21C3×#330D311yescharacteristic
22#4465—32no—
23C2×Dic18—21no—
24C2×C8×C9—22no—
25C9×C4⋊C4—22no—
26C9×C4⋊C4D412yes—
27C42×C9C2311yescharacteristic
28C4⋊Dic9—22no—
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—21no—
38#1663—91noSylow
39C3×#125C2×D311yescharacteristic
40#890—62no—
41#889—62no—
42#889—62no—
43#870—32no—
44#869—31no—
45C3×#97C2×D312yes—
46#818—62no—
47#817—62no—
48#810—62no—
49#803—31no—
50C2×C4×C9—22no—
51C2×C4×C9C2×D411yescharacteristic
52C2×C4×C9C2×D412yes—
53C2×Dic9—22no—
54C2×Dic9—22no—
55C2×Dic9—41no—
56Dic18—42no—
57C8×C9—24no—
58C9⋊C8—41no—
59#564—91no—
60#501—92no—
61#491—91no—
62#330—92no—
63#330D911yescharacteristic
64C2×Dic6—61no—
65C2×C3×C8—22no—
66C3×C4⋊C4—22no—
67C3×C4⋊C4D1212yes—
68C3×C42C22×D311yescharacteristic
69C4⋊Dic3—32no—
70C4⋊Dic3—32no—
71C4⋊Dic3—62no—
72C4⋊Dic3—62no—
73Dic3⋊C4—62no—
74Dic3⋊C4—62no—
75Dic3⋊C4—62no—
76Dic3⋊C4—62no—
77C4×Dic3—62no—
78C2×C3⋊C8—61no—
79C22×C9#12011yescharacteristic
80C4×C9—21no—
81C4×C9—22no—
82C4×C9—42no—
83Dic9—42no—
84Dic9—42no—
85Dic9—81no—
86C4⋊Q8—91no—
87#125—92no—
88#125—182no—
89#125—182no—
90#125—182no—
91#125C2×D911yescharacteristic
92#107—182no—
93#106—182no—
94#103—182no—
95#97—91no—
96#97C2×D912yes—
97C2×C3×C4—22no—
98C2×C3×C4C2×D1211yescharacteristic
99C2×C3×C4D3×D412yes—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C2×Dic3—121no—
103Dic6—122no—
104C3×C8—24no—
105C3⋊C8—121no—
106C2×C9#45411yescharacteristic
107C2×C9#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⋊C4D3612yes—
121C42—182no—
122C42C22×D911yescharacteristic
123C22×C3#88211yescharacteristic
124C3×C4—21no—
125C3×C4—22no—
126C3×C4—42no—
127Dic3—122no—
128Dic3—122no—
129Dic3—241no—
130C9#166311yescharacteristic, complemented, Sylow
131Q8—362no—
132C2×C4—22no—
133C2×C4—182no—
134C2×C4—182no—
135C2×C4—361no—
136C2×C4C2×D3611yescharacteristic
137C2×C4D4×D912yes—
138C8—24no—
139C8—361no—
140C2×C3#475311yescharacteristic
141C2×C3#482612yes—
142C22#6344411yescharacteristic
143C4—21no—
144C4—22no—
145C4—42no—
146C4—362no—
147C4—362no—
148C4—721no—
149C3#6837711yescharacteristic
150C2#1058843311yescharacteristic
151C2#1058850612yes—
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#330C2
socle, prime radicalC22×C3#882
hypercenter#330D9
hypocenterC9#1663
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #330

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
#105883822
C9×#3302
#105881412
#683773