Finite Group Databasebeta

← #37535072

Subgroups — #37535072

Order 23168.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#26041910C211yesmaximal, characteristic
2#26041321C212yesmaximal
3#26041144C211yesmaximal, characteristic
4#26041040C212yesmaximal
5#343×C181C211yesmaximal, characteristic
6#19153815—22no—
7#19153807—22no—
8#19153795—22no—
9#19153775C2212yes—
10C2×C4⋊Dic181C2211yescharacteristic
11C2×C4×Dic181C2211yescharacteristic
12#19153750—22no—
13#19153748—22no—
14#19153723—22no—
15C2×M16×C181C2212yes—
16C2×C4⋊C4×C181C2211yescharacteristic
17C2×Dic362—22no—
18C22×Dic181—21no—
19C22×Dic181—21no—
20C4⋊Dic181—22no—
21C4⋊Dic181—22no—
22C4⋊Dic181D412yes—
23C4⋊Dic181D412yes—
24#15668428—24no—
25C22⋊Dic181—22no—
26C4×Dic181—22no—
27C4×Dic181—21no—
28C4×Dic181Q812yescomplemented
29C22×C4×C181D412yes—
30C22×C4×C181C2311yescharacteristic
31M16×C181—22no—
32M16×C181Q814yescomplemented
33C2×C8×C181—22no—
34C4⋊C4×C181—22no—
35Dic362—82no—
36C2×Dic181—22no—
37C2×Dic181—22no—
38C2×Dic181—22no—
39C2×Dic181—41no—
40C2×Dic181—41no—
41C2×Dic181—42no—
42C2×Dic181—41no—
43C23×C181C2×D411yescharacteristic
44C2×C4×C181—22no—
45C2×C4×C181—42no—
46C2×C4×C181C2×D412yes—
47C2×C4×C181C2×Q811yescharacteristic
48C2×C4×C181C2×Q812yes—
49C2×C4×C181#4111yescharacteristic
50C8×C181—24no—
51C22×C181—21no—
52C22×C181—21no—
53C22×C181#12011yescharacteristic
54C22×C181C22⋊Q811yescharacteristic
55C22×C181C4⋊Q811yescharacteristic
56C4×C181—42no—
57C4×C181C22⋊Q812yes—
58C4×C181C4⋊Q812yes—
59Dic181—42no—
60Dic181—42no—
61Dic181—42no—
62Dic181—81no—
63C2×C181—21no—
64C2×C181—21no—
65C2×C181#39511yescharacteristic
66C2×C181#45411yescharacteristic
67C2×C181#45511yescharacteristic
68C181#206111yescharacteristic, complemented, Sylow
69#2061—1811nomaximal, Sylow
70#544—1811no—
71#428—1812no—
72#382—1811no—
73#343D18111yescharacteristic
74#339—1812no—
75C2×M16C2×D18112yes—
76C4⋊Q8—3622no—
77#125—3622no—
78C22⋊Q8—3622no—
79#117—1812no—
80C2×C4⋊C4—1811no—
81C2×C4⋊C4C2×D18111yescharacteristic
82C2×C42—1811no—
83#107—3622no—
84#106—3622no—
85#95—3622no—
86C2×Q8—3622no—
87C22×C4—3621no—
88C22×C4—3621no—
89C22×C4D72412yes—
90C22×C4C22×D18111yescharacteristic
91M16—22no—
92M16Dic36214yescomplemented
93C2×C8—22no—
94C4⋊C4—22no—
95C4⋊C4—3622no—
96C4⋊C4—3624no—
97C4⋊C4—3622no—
98C4⋊C4—1812no—
99C4⋊C4—1812no—
100C22⋊C4—3622no—
101C42—3622no—
102C42—3621no—
103C42—1812no—
104C23C2×D72411yescharacteristic
105Q8—14482no—
106C2×C4—22no—
107C2×C4—42no—
108C2×C4—3622no—
109C2×C4—3622no—
110C2×C4—3622no—
111C2×C4—7242no—
112C2×C4—7241no—
113C2×C4—7241no—
114C2×C4—7241no—
115C2×C4D4×D18112yes—
116C2×C4Q8×D18111yescharacteristic
117C2×C4C2×Dic36212yes—
118C2×C4#1566844811yescharacteristic
119C8—24no—
120C22—21no—
121C22—21no—
122C22#1915378611yescharacteristic
123C22#1915379611yescharacteristic
124C22#1915381611yescharacteristic
125C4—42no—
126C4—14481no—
127C4—7242no—
128C4—7242no—
129C4—7242no—
130C4#1915379312yes—
131C4#1915381512yes—
132C2—21no—
133C2—21no—
134C2#2604120011yescharacteristic
135C2#2604145411yescharacteristic
136C2#2604145911yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#343×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#343D181
hypocenterC181#2061
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
28. C4×Dic181Q8semidirect
32. M16×C181Q8semidirect
68. C181#2061semidirect
92. M16Dic362semidirect

Maximal subgroups

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

subgroupindex
#260419102
#260413212
#260411442
#260410402
#343×C1812
#2061181