Finite Group Databasebeta

← #37532938

Subgroups — #37532938

Order 23168.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#26041986C211yesmaximal, characteristic
2#26041630C211yesmaximal, characteristic, complemented
3#26041559C211yesmaximal, characteristic
4#26041490C211yesmaximal, characteristic, complemented
5#26041027C211yesmaximal, characteristic, complemented
6#26041011C211yesmaximal, characteristic, complemented
7D4⋊C8×C181C211yesmaximal, characteristic
8C2×Dic724—21no—
9#19153816C2211yescharacteristic
10#19153816C2211yescharacteristic
11#19153807—21no—
12#19153795—21no—
13#19153793—22no—
14C4×Dic362C2211yescharacteristic
15D4×Dic181—21no—
16C2×C4⋊Dic181—21no—
17#19153749—21no—
18C4⋊#13089678C2211yescharacteristic
19#19153741—22no—
20#19153741—21no—
21#19153737—21no—
22C4×D4×C181C2211yescharacteristic
23C4⋊C8×C181C2211yescharacteristic
24C4×C8×C181C2211yescharacteristic
25C2×Dic362—21no—
26C2×Dic362D411yescharacteristic
27C2×Dic362D412yes—
28C22×Dic181—22no—
29Dic724—42no—
30C2×#13089678—21no—
31C4⋊Dic181—22no—
32C4⋊Dic181—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181D411yescharacteristic
37#15668428—22no—
38#15668428—21no—
39C22⋊Dic181—22no—
40C4×Dic181—21no—
41C2×D4×C181D411yescharacteristic
42C22×C4×C181—21no—
43C2×C8×C181—21no—
44C2×C8×C181—21no—
45C4⋊C4×C181D411yescharacteristic
46C22⋊C4×C181—21no—
47C42×C181C2311yescharacteristic
48Dic362—21no—
49Dic362—21no—
50Dic362—42no—
51Dic362—41no—
52Dic362—41no—
53C2×Dic181—21no—
54C2×Dic181—21no—
55C2×Dic181—22no—
56C2×Dic181—41no—
57C2×Dic181—82no—
58#13089678—41no—
59C23×C181—21no—
60D4×C181—21no—
61D4×C181Q1612yescomplemented
62C2×C4×C181—21no—
63C2×C4×C181—41no—
64C2×C4×C181—41no—
65C2×C4×C181C2×D411yescharacteristic
66C2×C4×C181C2×D411yescharacteristic
67C2×C4×C181C2×D411yescharacteristic
68C8×C181—41no—
69C8×C181—41no—
70C22×C181—22no—
71C22×C181—41no—
72C22×C181—41no—
73C22×C181#12011yescharacteristic
74C4×C181—21no—
75C4×C181—41no—
76C4×C181C2×Q1611yescharacteristic
77C4×C181#13511yescharacteristic
78C4×C181AGL(1,ℤ/8)11yescharacteristic
79C4×C181#13711yescharacteristic
80Dic181—41no—
81Dic181—41no—
82Dic181—42no—
83Dic181—81no—
84C2×C181—42no—
85C2×C181#44911yescharacteristic
86C2×C181#45111yescharacteristic
87C2×C181#45511yescharacteristic
88C181#164411yescharacteristic, complemented, Sylow
89#1644—1811nomaximal, Sylow
90#554—1811no—
91#487—1811no—
92#474—1811no—
93#462—1811no—
94#333—1811no—
95Q8⋊C8—1811no—
96D4⋊C8D18111yescharacteristic
97C2×Q16—3621no—
98C4⋊Q8—1811no—
99C4⋊Q8—1811no—
100#125—3621no—
101C22⋊Q8—3622no—
102C22⋊Q8—3621no—
103C4×Q8—1811no—
104C4×D4—3621no—
105C4×D4C2×D18111yescharacteristic
106C2×C4⋊C4—3621no—
107#107—3621no—
108C4⋊C8—1811no—
109C4⋊C8C2×D18111yescharacteristic
110#103—3622no—
111#103—3621no—
112#102—3621no—
113C4×C8C2×D18111yescharacteristic
114C2×Q8—3621no—
115C2×Q8—1811no—
116C2×Q8—1812no—
117C2×D4D72411yescharacteristic
118C22×C4—21no—
119C22×C4—3622no—
120Q16—7242no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—3621no—
124C4⋊C4—3622no—
125C4⋊C4—3622no—
126C4⋊C4—3621no—
127C4⋊C4—3621no—
128C4⋊C4—3621no—
129C4⋊C4—3621no—
130C4⋊C4—3621no—
131C4⋊C4—1811no—
132C4⋊C4D72411yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—3622no—
135C42—3621no—
136C42C22×D18111yescharacteristic
137C23—21no—
138Q8—3621no—
139Q8—3621no—
140Q8—7242no—
141Q8—7241no—
142Q8—7241no—
143D4—21no—
144D4Dic72412yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—3621no—
149C2×C4—3621no—
150C2×C4—3622no—
151C2×C4—14482no—
152C2×C4—7241no—
153C2×C4D4×D18111yescharacteristic
154C2×C4D4×D18111yescharacteristic
155C2×C4C2×D72411yescharacteristic
156C8—41no—
157C8—41no—
158C8—7241no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1915378611yescharacteristic
163C4—21no—
164C4—41no—
165C4—14481no—
166C4—7241no—
167C4—7241no—
168C4—7242no—
169C4C2×Dic72411yescharacteristic
170C4#1915383711yescharacteristic
171C4#1915384011yescharacteristic
172C4#1915384911yescharacteristic
173C2—42no—
174C2#2604142511yescharacteristic
175C2#2604143711yescharacteristic
176C2#2604145811yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
FittingD4⋊C8×C181C2
socleC22×C181#120
prime radicalC2×D4×C181D4
hypercenterD4⋊C8D181
hypocenterC181#1644
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #26041630C2semidirect
4. #26041490C2semidirect
5. #26041027C2semidirect
6. #26041011C2semidirect
61. D4×C181Q16semidirect
88. C181#1644semidirect
144. D4Dic724semidirect

Maximal subgroups

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

subgroupindex
#260419862
#260416302
#260415592
#260414902
#260410272
#260410112
D4⋊C8×C1812
#1644181