Finite Group Databasebeta

← #11800167

Subgroups — #11800167

Order 1152.

276 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 43 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#10590352C211yesmaximal, characteristic
2#10590314C211yesmaximal, characteristic, complemented
3#10590148C211yesmaximal, characteristic, complemented
4#10590061C214yesmaximal, complemented
5C3×#874—21no—
6C3×#870—21no—
7C2×#3713—21no—
8C2×#3713C2212yes—
9C2×#3708C2212yes—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#63576C2212yes—
12#63574—21no—
13#5073—61no—
14#5065—61no—
15C2×C3×D12—22no—
16C2×C3×D12—42no—
17C32×C42D411yescharacteristic
18C2×C3⋊(C3⋊C8)D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2311yescharacteristic
20C3×C4⋊Dic3—22no—
21C3×Dic3⋊C4—42no—
22#3713—24no—
23#3713—42no—
24#3708—22no—
25#2244—91nomaximal, Sylow
26C3×#127—61no—
27C3×#125—61no—
28C2×#213—62no—
29C2×#213—62no—
30#874—21no—
31#870—21no—
32#808—62no—
33#807—62no—
34C4×C3⋊C8—61no—
35C4×C3⋊C8—61no—
36C22×C3×D3—42no—
37C2×C32×C4D812yes—
38C2×C32×C4C2×D411yescharacteristic
39C2×C3×Dic3—42no—
40C3×D12—42no—
41C3×D12—42no—
42C3×D12—84no—
43C3⋊(C3⋊C8)SD1612yes—
44C3⋊(C3⋊C8)#4112yes—
45#499—91no—
46#493—91no—
47#357—94no—
48#346—91no—
49C2×C3×D4—62no—
50C2×C3×D4—122no—
51C2×D12—22no—
52C2×D12—42no—
53C3×C4⋊C4—62no—
54C3×C4⋊C4—122no—
55C3×C42—21no—
56C3×C42—21no—
57#213—124no—
58#213—124no—
59C4⋊Dic3—22no—
60Dic3⋊C4—42no—
61C2×C3⋊C8—61no—
62C2×C3⋊C8—61no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65C22×C32C2×D811yescharacteristic
66C2×C3×D3—82no—
67C2×C3×D3—84no—
68C32×C4—22no—
69C32×C4#12411yescharacteristic
70C32×C4C2×SD1611yescharacteristic
71C3×Dic3—82no—
72C2×D8—92no—
73C2×D8—181no—
74#127—61no—
75#125—61no—
76C2×C16—92no—
77#107—92no—
78#106—181no—
79C4×C8—91no—
80C23×C3—122no—
81C22×D3—42no—
82C3×D4—122no—
83C3×D4—122no—
84C3×D4—244no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—122no—
90C2×Dic3—42no—
91D12—42no—
92D12—42no—
93D12—84no—
94C3⋊C8—62no—
95C3⋊C8—62no—
96C3⋊C8—62no—
97C3⋊C8—62no—
98C2×C32#48611yescharacteristic
99C2×C32#50912yes—
100C3×D3—162no—
101C2×D4—62no—
102C2×D4—122no—
103D8—184no—
104D8—362no—
105C2×C8—91no—
106C2×C8—91no—
107C4⋊C4—62no—
108C4⋊C4—122no—
109C42GO+(4,𝔽2)11yescharacteristic
110C16—182no—
111C22×C3—21no—
112C22×C3—21no—
113C22×C3—242no—
114C22×C3—244no—
115C2×D3—82no—
116C2×D3—84no—
117C3×C4—24no—
118C3×C4—21no—
119C3×C4—21no—
120C3×C4—21no—
121C3×C4—21no—
122C3×C4—42no—
123C3×C4—242no—
124Dic3—82no—
125C32#224411yescharacteristic, complemented, Sylow
126C23—122no—
127D4—122no—
128D4—122no—
129D4—244no—
130C2×C4—122no—
131C2×C4#377412yes—
132C2×C4C2×GO+(4,𝔽2)11yescharacteristic
133C8—92no—
134C8—92no—
135C2×C3—22no—
136C2×C3—22no—
137C2×C3—21no—
138C2×C3—21no—
139C2×C3—482no—
140D3—162no—
141C22—244no—
142C22—242no—
143C22C2×#377411yescharacteristic
144C4—22no—
145C4—242no—
146C4#6422111yescharacteristic
147C4#6422711yescharacteristic
148C3—21no—
149C3—21no—
150C2—482no—
151C2#1059333412yes—
152C2#1059334811yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radical#10590352C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2244
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590314C2semidirect
3. #10590148C2semidirect
4. #10590061C2semidirect
125. C32#2244semidirect

Maximal subgroups

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

subgroupindex
#105903522
#105903142
#105901482
#105900612
#22449