Finite Group Databasebeta

← #37549230

Subgroups — #37549230

Order 23168.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#26042296C211yesmaximal, characteristic
2#26042282C211yesmaximal, characteristic
3#26042138C214yesmaximal, complemented
4C2×#19153815C211yesmaximal, characteristic
5C2×#15668458—21no—
6#19153883C2212yes—
7#19153883C2212yes—
8C4⋊#13089685—21no—
9C22⋊#13089685—21no—
10C4×#13089685—21no—
11C22×Dic362—21no—
12#19153815—21no—
13#19153815—21no—
14#19153815C412yes—
15#19153815C2212yes—
16C2×C4⋊Dic181C411yescharacteristic
17C2×#15668428—21no—
18C2×C4×Dic181C2211yescharacteristic
19C2×C4⋊C4×C181C411yescharacteristic
20#15668458—42no—
21C2×#13089685—22no—
22C2×#13089685—22no—
23C2×Dic362—22no—
24C2×Dic362—22no—
25C2×Dic362—42no—
26C2×Dic362—42no—
27C22×Dic181—21no—
28C22×Dic181D411yescharacteristic
29C22×Dic181D411yescharacteristic
30C4⋊Dic181—21no—
31C4⋊Dic181C2×C412yes—
32#15668428—22no—
33#15668428—22no—
34C4×Dic181C2×C411yescharacteristic
35C4×Dic181D411yescharacteristic
36C4×Dic181D411yescharacteristic
37C4×Dic181C2311yescharacteristic
38C22×C4×C181—21no—
39C22×C4×C181C2×C411yescharacteristic
40C4⋊C4×C181—21no—
41C4⋊C4×C181C2×C412yes—
42#13089685—42no—
43#13089685—42no—
44Dic362—44no—
45Dic362—42no—
46Dic362—42no—
47C2×Dic181—22no—
48C2×Dic181—22no—
49C2×Dic181—42no—
50C2×Dic181C22⋊C411yescharacteristic
51C2×Dic181C22⋊C411yescharacteristic
52C2×Dic181D812yes—
53C2×Dic181SD1612yes—
54C2×Dic181C2×D411yescharacteristic
55C2×Dic181C2×D411yescharacteristic
56C23×C181C22⋊C411yescharacteristic
57C2×C4×C181—22no—
58C2×C4×C181—22no—
59C2×C4×C181—42no—
60C2×C4×C181C22⋊C411yescharacteristic
61C2×C4×C181C22×C411yescharacteristic
62C22×C181—21no—
63C22×C181—21no—
64C22×C181#10212yes—
65C22×C181C2×C22⋊C411yescharacteristic
66C4×C181—21no—
67C4×C181—42no—
68C4×C181#10112yes—
69Dic181—21no—
70Dic181—42no—
71Dic181#10212yes—
72Dic181C2×D811yescharacteristic
73Dic181C2×SD1611yescharacteristic
74Dic181#13712yes—
75C2×C181—22no—
76C2×C181C2×#10111yescharacteristic
77C2×C181C2×#10211yescharacteristic
78C2×C181#41911yescharacteristic
79C181#154611yescharacteristic, complemented, Sylow
80#1546—1811nomaximal, Sylow
81C2×C4⋊Q8—1811no—
82#431—1811no—
83#423—1811no—
84#332—1814no—
85C22×Q8—3621no—
86C2×M16—3621no—
87C4⋊Q8—3621no—
88C4⋊Q8—3621no—
89C4⋊Q8—1812no—
90C4⋊Q8—1812no—
91C2×C4⋊C4—3621no—
92C2×C4⋊C4—1811no—
93C2×C4⋊C4#1062438211yescharacteristic
94C2×C42—1811no—
95C4⋊C8—3621no—
96C4⋊C8—1812no—
97C4⋊C8—1812no—
98C22⋊C8—3621no—
99C4×C8—3621no—
100C2×Q8—3622no—
101C2×Q8—3622no—
102C2×Q8—7242no—
103C2×Q8—7242no—
104C22×C4—21no—
105C22×C4—3621no—
106C22×C4—1811no—
107C22×C4—1811no—
108C22×C4C2×#1062438211yescharacteristic
109M16—7242no—
110C2×C8—3622no—
111C2×C8—3622no—
112C4⋊C4—21no—
113C4⋊C4—3622no—
114C4⋊C4—3622no—
115C4⋊C4—3621no—
116C4⋊C4—1812no—
117C4⋊C4C2×#1062438212yes—
118C42—1811no—
119C42—1811no—
120C42—1811no—
121C42—1811no—
122C23C22⋊#1062438211yescharacteristic
123Q8—7242no—
124Q8—7244no—
125Q8—7242no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—3622no—
130C2×C4—3622no—
131C2×C4—1811no—
132C2×C4—1812no—
133C2×C4—1812no—
134C2×C4—1811no—
135C2×C4—1811no—
136C2×C4—1811no—
137C2×C4—7242no—
138C2×C4C22⋊#1062438211yescharacteristic
139C2×C4C22×#1062438211yescharacteristic
140C8—7242no—
141C8—7242no—
142C22—21no—
143C22—21no—
144C22#1915387812yes—
145C22C2×C22⋊#1062438211yescharacteristic
146C4—21no—
147C4—42no—
148C4—3621no—
149C4—1811no—
150C4—1812no—
151C4—1811no—
152C4—1812no—
153C4—7242no—
154C4#1915387712yes—
155C2—22no—
156C2C2×#1915387711yescharacteristic
157C2C2×#1915387811yescharacteristic
158C2#2604227211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×C181C22⋊C4
cosocleC4×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1546
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #26042138C2semidirect
79. C181#1546semidirect

Maximal subgroups

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

subgroupindex
#260422962
#260422822
#260421382
C2×#191538152
#1546181