Finite Group Databasebeta

← #11780677

Subgroups — #11780677

Order 1152.

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

normal subgroups only

This group has 294 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
1#10589802C211yesmaximal, characteristic
2#10588746C211yesmaximal, characteristic, complemented
3#10588395C212yesmaximal, complemented
4C9×#330C211yesmaximal, characteristic, complemented
5#10588142C212yesmaximal, complemented
6#68374—31nomaximal
7C9×#125C2211yescharacteristic
8#63458—22no—
9#63457—22no—
10#63456—22no—
11#63437C2212yes—
12#63431C2211yescharacteristic
13C9×#97C2212yes—
14#63380—22no—
15#63376—22no—
16#63368—22no—
17#63362C2211yescharacteristic
18#5700—31no—
19#5069—31no—
20#4714—32no—
21C3×#330D311yescharacteristic
22#4464—32no—
23C2×D36—22no—
24C2×D36D412yes—
25C2×C4×D9—22no—
26C2×Dic18—21no—
27C2×Dic18D412yes—
28C2×C8×C9—22no—
29C9×C4⋊C4—22no—
30C9×C4⋊C4D412yes—
31C42×C9C2311yescharacteristic
32(C2×D9)⋊C4—22no—
33(C2×D9)⋊C4—22no—
34(C2×D9)⋊C4—22no—
35C4⋊Dic9—22no—
36Dic9⋊C4—22no—
37C2×C9⋊C8—21no—
38#1662—91noSylow
39C3×#125C2×D311yescharacteristic
40#896—62no—
41#895—62no—
42#894—62no—
43#875—32no—
44#869—31no—
45C3×#97C2×D312yes—
46#821—62no—
47#816—62no—
48#810—62no—
49#803—31no—
50C22×D9—22no—
51C2×C4×C9—22no—
52C2×C4×C9C2×D411yescharacteristic
53C2×C4×C9C2×D412yes—
54C2×Dic9—22no—
55C2×Dic9—41no—
56D36—42no—
57D36—82no—
58C4×D9—82no—
59Dic18—42no—
60Dic18—42no—
61C8×C9—42no—
62C9⋊C8—41no—
63#562—91no—
64#491—91no—
65#489—92no—
66#330D911yescharacteristic, complemented
67#329—92no—
68C2×D12—32no—
69C2×D12—62no—
70C2×C4×D3—62no—
71C2×Dic6—32no—
72C2×Dic6—61no—
73C2×C3×C8—22no—
74C3×C4⋊C4—22no—
75C3×C4⋊C4D1212yes—
76C3×C42C22×D311yescharacteristic
77(C2×D3)⋊C4—62no—
78(C2×D3)⋊C4—62no—
79(C2×D3)⋊C4—62no—
80C4⋊Dic3—62no—
81Dic3⋊C4—62no—
82C2×C3⋊C8—61no—
83C22×C9#12011yescharacteristic
84C2×D9—42no—
85C2×D9—42no—
86C2×D9—42no—
87C4×C9—21no—
88C4×C9—22no—
89C4×C9—42no—
90Dic9—42no—
91Dic9—81no—
92C4⋊Q8—91no—
93#125C2×D911yescharacteristic
94#124—92no—
95#123—182no—
96C22⋊Q8—182no—
97#121—182no—
98#103—182no—
99#103—182no—
100#102—182no—
101#97—91no—
102#97C2×D912yes—
103C22×D3—62no—
104C2×C3×C4—22no—
105C2×C3×C4C2×D1211yescharacteristic
106C2×C3×C4D3×D412yes—
107C2×Dic3—62no—
108C2×Dic3—121no—
109D12—122no—
110D12—242no—
111C4×D3—242no—
112Dic6—122no—
113Dic6—122no—
114C3×C8—42no—
115C3⋊C8—121no—
116C2×C9#45411yescharacteristic
117C2×C9#45512yes—
118D9—82no—
119C2×Q8—92no—
120C2×Q8—181no—
121C2×D4—92no—
122C2×D4—182no—
123C22×C4—182no—
124C2×C8—22no—
125C2×C8—181no—
126C4⋊C4—22no—
127C4⋊C4—182no—
128C4⋊C4—182no—
129C4⋊C4D3612yes—
130C22⋊C4—182no—
131C22⋊C4—182no—
132C22⋊C4—182no—
133C42C22×D911yescharacteristic
134C22×C3#88211yescharacteristic
135C2×D3—122no—
136C2×D3—122no—
137C2×D3—122no—
138C3×C4—21no—
139C3×C4—22no—
140C3×C4—42no—
141Dic3—122no—
142Dic3—241no—
143C9#166211yescharacteristic, complemented, Sylow
144C23—182no—
145Q8—362no—
146Q8—362no—
147D4—362no—
148D4—722no—
149C2×C4—22no—
150C2×C4—182no—
151C2×C4—361no—
152C2×C4—722no—
153C2×C4C2×D3611yescharacteristic
154C2×C4D4×D912yes—
155C8—42no—
156C8—361no—
157C2×C3#475311yescharacteristic
158C2×C3#482512yes—
159D3—242no—
160C22—362no—
161C22—362no—
162C22—362no—
163C22#6344411yescharacteristic
164C4—21no—
165C4—22no—
166C4—42no—
167C4—362no—
168C4—721no—
169C3#6837411yescharacteristic
170C2—722no—
171C2#1058843311yescharacteristic
172C2#1058850512yes—
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#330C2
socleC22×C3#882
prime radical#10589802C2
hypercenter#330D9
hypocenterC9#1662
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #10588746C2semidirect
3. #10588395C2semidirect
4. C9×#330C2semidirect
5. #10588142C2semidirect
66. #330D9semidirect
143. C9#1662semidirect

Maximal subgroups

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

subgroupindex
#105898022
#105887462
#105883952
C9×#3302
#105881422
#683743