Finite Group Databasebeta

← #37532939

Subgroups — #37532939

Order 23168.

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

normal subgroups only

This group has 200 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#26042009C211yesmaximal, characteristic
2#26041561C211yesmaximal, characteristic
3#26041486C211yesmaximal, characteristic
4#26041028C211yesmaximal, characteristic
5#26041011C211yesmaximal, characteristic
6#26041011C211yesmaximal, characteristic
7#487×C181C211yesmaximal, characteristic
8C2×#15668439—21no—
9#19153815—21no—
10#19153815—21no—
11#19153814—22no—
12C4×Dic362C2211yescharacteristic
13C4×Dic362C2211yescharacteristic
14#19153781—21no—
15#19153781—21no—
16#19153747—21no—
17C4⋊#13089678C2211yescharacteristic
18C4⋊#13089678C2211yescharacteristic
19#19153740—21no—
20#19153739—21no—
21C4⋊Q8×C181C2211yescharacteristic
22C4⋊Q8×C181C2211yescharacteristic
23#103×C181—22no—
24C4×C8×C181C2211yescharacteristic
25C2×Dic362—22no—
26C2×Dic362D411yescharacteristic
27C2×Dic362D411yescharacteristic
28#15668439—42no—
29C2×#13089678—21no—
30C2×#13089678—21no—
31C4⋊Dic181D411yescharacteristic
32C4⋊Dic181D411yescharacteristic
33#15668428—22no—
34#15668428—22no—
35#15668428—21no—
36#15668428—21no—
37C4×Dic181—22no—
38C4×Dic181—21no—
39C4×Dic181—21no—
40C2×Q8×C181—21no—
41C2×Q8×C181D412yes—
42C2×C8×C181—21no—
43C4⋊C4×C181—21no—
44C4⋊C4×C181—21no—
45C4⋊C4×C181—21no—
46C4⋊C4×C181—21no—
47C42×C181C2311yescharacteristic
48Dic362—21no—
49Dic362—21no—
50Dic362—82no—
51Dic362SD1612yes—
52Dic362Q1612yescomplemented
53C2×Dic181—21no—
54C2×Dic181—21no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57#13089678—41no—
58#13089678—41no—
59Q8×C181—42no—
60Q8×C181—41no—
61Q8×C181—41no—
62C2×C4×C181—22no—
63C2×C4×C181—41no—
64C2×C4×C181C2×D411yescharacteristic
65C2×C4×C181C2×D411yescharacteristic
66C2×C4×C181C2×D411yescharacteristic
67C8×C181—41no—
68C22×C181#12011yescharacteristic
69C4×C181—21no—
70C4×C181—42no—
71C4×C181—81no—
72C4×C181C2×SD1611yescharacteristic
73C4×C181C2×Q1611yescharacteristic
74C4×C181#13711yescharacteristic
75C4×C181#13711yescharacteristic
76Dic181—22no—
77Dic181—22no—
78Dic181—41no—
79Dic181—41no—
80C2×C181#44811yescharacteristic
81C2×C181#45111yescharacteristic
82C2×C181#45511yescharacteristic
83C181#164511yescharacteristic, complemented, Sylow
84#1645—1811nomaximal, Sylow
85Q82—1811no—
86#487D18111yescharacteristic
87#475—1811no—
88#462—1811no—
89#333—1811no—
90Q8⋊C8—1811no—
91Q8⋊C8—1811no—
92C2×Q16—3621no—
93C4⋊Q8—3621no—
94C4⋊Q8—3621no—
95C4⋊Q8—3622no—
96C4⋊Q8C2×D18111yescharacteristic
97C4⋊Q8C2×D18111yescharacteristic
98C4×Q8—3621no—
99C4×Q8—3621no—
100C4×Q8—1811no—
101C4×Q8—1811no—
102#106—3621no—
103C4⋊C8—1811no—
104C4⋊C8—1811no—
105#103—22no—
106#103—3621no—
107#103—3621no—
108C4×C8C2×D18111yescharacteristic
109C2×Q8—21no—
110C2×Q8—3622no—
111C2×Q8—1811no—
112C2×Q8—1811no—
113C2×Q8C22⋊D18112yes—
114Q16—7242no—
115C2×C8—21no—
116C2×C8—3621no—
117C2×C8—3621no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—3622no—
123C4⋊C4—3622no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—1811no—
127C4⋊C4—1811no—
128C42—3622no—
129C42—3621no—
130C42—3621no—
131C42C22×D18111yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—3621no—
136Q8—3621no—
137Q8—14482no—
138Q8—1812no—
139Q8—1812no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—3621no—
143C2×C4—3621no—
144C2×C4—3621no—
145C2×C4—3621no—
146C2×C4D4×D18111yescharacteristic
147C2×C4D4×D18111yescharacteristic
148C2×C4C2×C22⋊D18111yescharacteristic
149C8—41no—
150C8—7241no—
151C8—7241no—
152C22#1915378411yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—3622no—
157C4—3622no—
158C4—7241no—
159C4—7241no—
160C4SD16×D18111yescharacteristic
161C4Q16×D18111yescharacteristic
162C4#1915384511yescharacteristic
163C4#1915384811yescharacteristic
164C2#2604141611yescharacteristic
165C2#2604143311yescharacteristic
166C2#2604145611yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
Fitting#487×C181C2
socle, prime radicalC22×C181#120
hypercenter#487D181
hypocenterC181#1645
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
52. Dic362Q16semidirect
83. C181#1645semidirect

Maximal subgroups

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

subgroupindex
#260420092
#260415612
#260414862
#260410282
#260410112
#487×C1812
#1645181