Finite Group Databasebeta

← #11910447

Subgroups — #11910447

Order 1152.

2790 conjugacy classes of subgroups; only the 735 normal subgroups are shown.

normal subgroups only

This group has 2790 conjugacy classes of subgroups — too many to draw. Only its 735 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
1C32×#564C211yesmaximal, characteristic, complemented
2#10596171C215yesmaximal, complemented
3#10596170C2110yesmaximal, complemented
4#10596162C2110yesmaximal, complemented
5#10596159C215yesmaximal, complemented
6#87139—34nomaximal
7C32×#125C2215yes—
8C32×#125C22110yes—
9#64107C22120yes—
10#64106C22110yes—
11#64105C22120yes—
12#64104C22110yes—
13#64103C22120yes—
14#64102C22110yes—
15#64101C22110yes—
16#64097C22110yes—
17#64096C22110yes—
18#64084C22110yes—
19C42×C3⋊D3C2215yes—
20#64079C2215yes—
21C3×#564D314yescomplemented
22#5700—320no—
23#5699—340no—
24#5691—340no—
25#5688—320no—
26C2×C4⋊(C3⋊D3)C23110yes—
27C2×C4×C3⋊D3C2315yes—
28C2×C4×C3⋊D3C23110yes—
29C2×#634C23110yes—
30C32×C4⋊C4C23110yes—
31C32×C4⋊C4C23110yes—
32C32×C4⋊C4C23110yes—
33C32×C42C2315yes—
34#3752C23120yes—
35#3752C23120yes—
36C4⋊(C3⋊Dic3)C23110yes—
37#3750C23120yes—
38C4×C3⋊Dic3C23110yes—
39C4×C3⋊Dic3C2315yes—
40#3531—91noSylow
41C3×#125C2×D3120yes—
42C3×#125C2×D3140yes—
43#898—380no—
44#897—340no—
45#896—380no—
46#895—340no—
47#894—380no—
48#893—340no—
49#892—340no—
50#888—340no—
51#887—340no—
52#875—340no—
53C42×D3—320no—
54#870—320no—
55C22×C3⋊D3C2415yes—
56C2×C32×C4C24110yes—
57C2×C32×C4C2415yes—
58C2×C3⋊Dic3C24110yes—
59C2×C3⋊Dic3C2411yescharacteristic
60C4⋊(C3⋊D3)—410no—
61C4×C3⋊D3—210no—
62C4×C3⋊D3—410no—
63#634—410no—
64#564C3⋊D311yescharacteristic, complemented
65#563—910no—
66#562—95no—
67#533—95no—
68#529—910no—
69C2×D12—340no—
70C2×C4×D3—320no—
71C2×C4×D3—340no—
72C2×Dic6—340no—
73C3×C4⋊C4C22×D3140yes—
74C3×C4⋊C4C22×D3140yes—
75C3×C4⋊C4C22×D3140yes—
76C3×C42C22×D3120yes—
77(C2×D3)⋊C4—380no—
78(C2×D3)⋊C4—380no—
79C4⋊Dic3—340no—
80Dic3⋊C4—380no—
81C4×Dic3—340no—
82C4×Dic3—320no—
83C22×C32C2511yescharacteristic
84C2×C3⋊D3—25no—
85C2×C3⋊D3—210no—
86C32×C4—25no—
87C32×C4—210no—
88C3⋊Dic3—210no—
89C3⋊Dic32−1+412yes—
90C4⋊Q8—910no—
91#126—920no—
92#125—95no—
93#125C2×C3⋊D3110yes—
94#125C2×C3⋊D315yes—
95#124—910no—
96#123—920no—
97C22⋊Q8—910no—
98C22⋊Q8—920no—
99#121—910no—
100C4×Q8—910no—
101C4×D4—910no—
102#117—910no—
103C2×C42—95no—
104C22×D3—320no—
105C2×C3×C4C23×D3140yes—
106C2×C3×C4C23×D3120yes—
107C2×Dic3—34no—
108C2×Dic3—340no—
109D12—1240no—
110C4×D3—640no—
111C4×D3—1240no—
112Dic6—1240no—
113C2×C32C2×2−1+411yescharacteristic
114C2×C32#58512yes—
115C3⋊D3—45no—
116C2×Q8—910no—
117C2×D4—910no—
118C22×C4—95no—
119C22×C4—910no—
120C4⋊C4—910no—
121C4⋊C4—920no—
122C4⋊C4C22×C3⋊D3110yes—
123C4⋊C4C22×C3⋊D3110yes—
124C4⋊C4C22×C3⋊D3110yes—
125C22⋊C4—920no—
126C22⋊C4—920no—
127C42—910no—
128C42—95no—
129C42C22×C3⋊D315yes—
130C22×C3C24×D314yes—
131C2×D3—620no—
132C2×D3—640no—
133C3×C4—220no—
134C3×C4—240no—
135Dic3—38no—
136Dic3—640no—
137C32#353111yescharacteristic, complemented, Sylow
138C23—95no—
139Q8—3610no—
140D4—3610no—
141C2×C4—91no—
142C2×C4—910no—
143C2×C4—1810no—
144C2×C4—3610no—
145C2×C4C23×C3⋊D315yes—
146C2×C4C23×C3⋊D3110yes—
147C2×C3D3×2−1+414yes—
148C2×C3#596818yes—
149D3—1220no—
150C22—185no—
151C22—1810no—
152C22C24×C3⋊D311yescharacteristic
153C4—25no—
154C4—210no—
155C4—92no—
156C4—1810no—
157C3#8713914yescomplemented
158C2—365no—
159C2C3⋊D3×2−1+411yescharacteristic
160C2#1059676012yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#564C2
hypercenter#564C3⋊D3
hypocenterC32#3531
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C32×#564C2semidirect
2. #10596171C2semidirect
3. #10596170C2semidirect
4. #10596162C2semidirect
5. #10596159C2semidirect
21. C3×#564D3semidirect
64. #564C3⋊D3semidirect
137. C32#3531semidirect
157. C3#87139semidirect

Maximal subgroups

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

subgroupindex
C32×#5642
#105961712
#105961702
#105961622
#105961592
#871393