Finite Group Databasebeta

← #11775751

Subgroups — #11775751

Order 1152.

339 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 78 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#10589790C211yesmaximal, characteristic
2#10588388C212yesmaximal
3C9×#330C211yesmaximal, characteristic, complemented
4#10588220C211yesmaximal, characteristic, complemented
5#10588141C212yesmaximal, complemented
6#68362—31nomaximal
7C9×#125C2211yescharacteristic
8C2×#3663—22no—
9#63458—22no—
10#63454C412yes—
11#63450C412yes—
12#63449—22no—
13C42×D9C2211yescharacteristic
14#63432C2211yescharacteristic
15C9×#97C2212yes—
16C8×Dic9—22no—
17#63362C2212yes—
18#5688—31no—
19#4707—32no—
20C3×#330D311yescharacteristic
21#4543—31no—
22#4465—32no—
23C2×C4×D9C2×C411yescharacteristic
24C2×C4×D9D412yes—
25C2×Dic18—22no—
26C2×C8×C9—22no—
27C9×C4⋊C4—22no—
28C9×C4⋊C4C2×C412yes—
29C42×C9C2311yescharacteristic
30(C2×D9)⋊C4—22no—
31C4⋊Dic9C2×C412yes—
32Dic9⋊C4—22no—
33Dic9⋊C4—22no—
34C4×Dic9—22no—
35C4×Dic9C2×C411yescharacteristic
36C4×Dic9D412yes—
37C2×C9⋊C8—22no—
38#3663—28no—
39#1526—91noSylow
40C3×#125C2×D311yescharacteristic
41C2×ΓL(1,𝔽25)—62no—
42#896—62no—
43#892—32no—
44#888—32no—
45#887—62no—
46C42×D3—31no—
47#870—31no—
48C3×#97C2×D312yes—
49C8×Dic3—62no—
50#803—32no—
51C22×D9C22⋊C411yescharacteristic
52C2×C4×C9—22no—
53C2×C4×C9C22×C411yescharacteristic
54C2×C4×C9C2×D412yes—
55C2×Dic9—22no—
56C2×Dic9C22⋊C411yescharacteristic
57C2×Dic9C22⋊C412yes—
58C4×D9—22no—
59C4×D9—24no—
60Dic18—44no—
61C8×C9—24no—
62C9⋊C8—24no—
63#533—91no—
64C4×M16—92no—
65#330—91no—
66#330—92no—
67#330D911yescharacteristic, complemented
68C2×C4×D3—31no—
69C2×C4×D3—32no—
70C2×Dic6—62no—
71C2×C3×C8—22no—
72C3×C4⋊C4—22no—
73C3×C4⋊C4C4×D312yes—
74C3×C42C22×D311yescharacteristic
75(C2×D3)⋊C4—62no—
76C4⋊Dic3—32no—
77Dic3⋊C4—62no—
78Dic3⋊C4—62no—
79C4×Dic3—31no—
80C4×Dic3—32no—
81C4×Dic3—62no—
82C2×C3⋊C8—62no—
83ΓL(1,𝔽25)—68no—
84C22×C9C2×C22⋊C411yescharacteristic
85C2×D9—21no—
86C2×D9—22no—
87C4×C9—21no—
88C4×C9—22no—
89C4×C9—42no—
90Dic9—42no—
91Dic9#10112yes—
92Dic9#10414yes—
93C2×M16—182no—
94C4⋊Q8—92no—
95#125—91no—
96#125C2×D911yescharacteristic
97C22⋊Q8—182no—
98C4×Q8—182no—
99#117—92no—
100C2×C42—91no—
101#97—92no—
102#97C2×D912yes—
103C4×C8—182no—
104C22×D3—31no—
105C2×C3×C4—22no—
106C2×C3×C4C2×C4×D311yescharacteristic
107C2×C3×C4D3×D412yes—
108C2×Dic3—31no—
109C2×Dic3—32no—
110C2×Dic3—62no—
111C4×D3—64no—
112C4×D3—62no—
113Dic6—124no—
114C3×C8—24no—
115C3⋊C8—64no—
116C2×C9C2×#10111yescharacteristic
117C2×C9C2×#10412yes—
118D9—41no—
119C2×Q8—182no—
120C22×C4—91no—
121C22×C4—92no—
122M16—188no—
123C2×C8—22no—
124C2×C8—182no—
125C4⋊C4—22no—
126C4⋊C4—92no—
127C4⋊C4—182no—
128C4⋊C4—182no—
129C4⋊C4C4×D912yes—
130C22⋊C4—182no—
131C42—91no—
132C42—92no—
133C42—182no—
134C42C22×D911yescharacteristic
135C22×C3D3×C22⋊C411yescharacteristic
136C2×D3—61no—
137C2×D3—62no—
138C3×C4—21no—
139C3×C4—22no—
140C3×C4—42no—
141Dic3—32no—
142Dic3—34no—
143Dic3—122no—
144C9#152611yescharacteristic, complemented, Sylow
145C23—91no—
146Q8—364no—
147C2×C4—22no—
148C2×C4—91no—
149C2×C4—92no—
150C2×C4—184no—
151C2×C4—182no—
152C2×C4—182no—
153C2×C4C2×C4×D911yescharacteristic
154C2×C4D4×D912yes—
155C8—24no—
156C8—184no—
157C2×C3D3×#10111yescharacteristic
158C2×C3D3×#10412yes—
159D3—121no—
160C22—181no—
161C22—182no—
162C22C22⋊C4×D911yescharacteristic
163C4—21no—
164C4—22no—
165C4—42no—
166C4—92no—
167C4—94no—
168C4—362no—
169C3#6836211yescharacteristic
170C2—361no—
171C2D9×#10111yescharacteristic
172C2D9×#10412yes—
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×#330C2
socleC22×C3D3×C22⋊C4
prime radicalC22×D9C22⋊C4
cosocleC42×C9C23
hypercenter#330D9
hypocenterC9#1526
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. C9×#330C2semidirect
4. #10588220C2semidirect
5. #10588141C2semidirect
67. #330D9semidirect
144. C9#1526semidirect

Maximal subgroups

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

subgroupindex
#105897902
#105883882
C9×#3302
#105882202
#105881412
#683623